packages feed

cpsa 2.2.4 → 2.2.5

raw patch · 86 files changed

+17664/−403 lines, 86 files

Files

ChangeLog view
@@ -1,3 +1,30 @@+2011-08-16  John D. Ramsdell  <ramsdell@mitre.org>++	* cpsa.cabal (Version):  Tagged as version 2.2.5.++2011-08-15  John D. Ramsdell  <ramsdell@mitre.org>++	* src/cpsa.pl: Changed the internal form so that compound terms+	are represented as function symbols applied to terms, not as+	S-expressions.++2011-08-12  John D. Ramsdell  <ramsdell@mitre.org>++	* doc/*: Updated documentation to reflect support for hashing.++2011-08-11  Paul Rowe  <prowe@mitre.org>++	* src/CPSA/Basic/Algebra.hs: Added support for hashing.++2011-07-26  John D. Ramsdell  <ramsdell@mitre.org>++	* src/CPSA/Lib/Strand.hs (ksubst): Made the flag validate the+	first argument.++	* src/CPSA/Lib/Strand.hs (compress): Added a flag validate.  When+	false, compression does not check for intrastrand orderings that+	create cycles.  Used in thinning.+ 2011-05-18  John D. Ramsdell  <ramsdell@mitre.org>  	* cpsa.cabal (Version):  Tagged as version 2.2.4.
NEWS view
@@ -1,5 +1,13 @@ CPSA NEWS -- history of user-visible changes. +* Changes in version 2.2.5++** Support for hashing added+   Both the Basic and Diffie-Hellman term algebras have a new function+   symbol hash that provides support for hashing.  The term (hash X)+   is treated as a kind of encryption in which the term X is the+   encryption key.+ * Changes in version 2.2.4  ** GHC link time option added
cpsa.cabal view
@@ -1,5 +1,5 @@ Name:			cpsa-Version:		2.2.4+Version:		2.2.5 Maintainer:		ramsdell@mitre.org Cabal-Version:		>= 1.6 License:		BSD3@@ -44,7 +44,8 @@ Build-Type:		Simple Data-Files:    index.html cpsauser.html cpsa.mk Make.hs cpsaprimer.pdf-   cpsaoverview.pdf ffgg.scm ns.scm or.scm woolam.scm yahalom.scm+   cpsaoverview.pdf cpsaspec.pdf cpsadesign.pdf ffgg.scm ns.scm or.scm+   woolam.scm yahalom.scm Data-Dir:	    	doc Extra-Source-Files:   Makefile ChangeLog README NEWS ghci cpsatst setup.bat doc/README@@ -95,7 +96,11 @@   tst/tor.tst tst/dh_cert.scm tst/dh_cert.tst   tst/epmo_acctnum-key-hash.scm tst/epmo_acctnum-key-hash.tst   tst/epmo-key-hash.scm tst/epmo-key-hash.tst tst/wang.lisp-  tst/pkinit.scm tst/pkinit.tst+  tst/pkinit.scm tst/pkinit.tst tst/print.scm tst/print.tst+  tst/epmo-hash.scm tst/epmo-hash.tst tst/hashtest-key-hash.scm+  tst/hashtest-key-hash.tst tst/hashtest.scm tst/hashtest.tst+  tst/wang-key-hash.scm tst/wang-key-hash.tst tst/wang-hash.scm+  tst/wang-hash.tst  -- Algebra implementations must import CPSA.Lib.CPSA. -- Tools may additionally import CPSA.Lib.Entry.
doc/README view
@@ -14,11 +14,10 @@ * cpsatheory.pdf: CPSA Theory, the beginnings of a connectness proof   of the CPSA algorithm -To build the documentation, the file supp-pdf.tex must be installed.-It is part of the TexLive texmf ConTeXt package.  On Linux, the name-of the package is context or texlive-context.  The design document and-the specification document require the xy-pic package, which is-included in texlive-pictures.+To build the documentation, you need Metapost and XY-pic.  On Linux,+Metapost is supplied via the package texlive-metapost, and XY-pic is+supplied in package texlive-pictures.  On some older versions of+Linux, you may also have to install texlive-context.  If you want to build the documentation from the sources, and you don't have and want to install the cmarrows package for Metapost, comment
doc/bcasyntax.tex view
@@ -45,7 +45,7 @@ \\ &$\mid$&$(\sym{pubk}\mbox{ id}\mbox{ string}) \mid(\sym{privk}\mbox{ id}\mbox{ string})$ \\ &$\mid$&$(\sym{ltk}\mbox{ id id})\mid\mbox{string}\mid(\sym{cat}\mbox{ term+})$-\\ &$\mid$&$(\sym{enc}\mbox{ term+ term})$+\\ &$\mid$&$(\sym{enc}\mbox{ term+ term})\mid(\sym{hash}\mbox{ term+})$ \\ role-alist&$\leftarrow$&$ (\sym{non-orig}\mbox{ ht-term}\ast)\mbox{ role-alist}$ \\ &$\mid$&$(\sym{uniq-orig}\mbox{ term}\ast)\mbox{ role-alist}\mid\ldots$
doc/cpsa.bib view
@@ -225,11 +225,11 @@   OPTannote = 	 {} } -@unpublished{algimpl,+@unpublished{algimpl11,   author = {Moses Liskov and John D. Ramsdell},   title = {Implementing Strand Space Algebras},-  note = {Unpublished manuscript, submitted to {ESORICS} 2011},-  year = 2010+  note = {\url{http://www.ccs.neu.edu/home/ramsdell/papers/algimpl.pdf}},+  year = 2011 }  @incollection{ComonLundhMillen10,@@ -270,7 +270,9 @@    publisher = {Springer Berlin / Heidelberg},    issn = {1615-5262},    keyword = {Computer Science},-   pages = {1--19},+   pages = {63-81},+   volume = {10},+   issue = {2},    url = {http://dx.doi.org/10.1007/s10207-011-0124-7},    note = {10.1007/s10207-011-0124-7},    year = {2011}
doc/cpsadesign.pdf view

binary file changed (213513 → 214157 bytes)

doc/cpsadesign.tex view
@@ -124,6 +124,8 @@ \begin{tabular}{@{}ll} $\enc{\cdot}{(\cdot)}\colon\dom{mesg}\times\dom{mesg}\rightarrow\dom{mesg}$ &Encryption\\+$\#\colon\dom{mesg}\rightarrow\dom{mesg}$+&Hashing\\ $(\cdot,\cdot)\colon\dom{mesg}\times\dom{mesg}\rightarrow\dom{mesg}$ &Pairing\\ ``\ldots''$\colon\dom{mesg}$& Tag constants\\@@ -165,6 +167,8 @@ \sembrack{\texttt{"}\ldots\texttt{"}}&{}={}&\mbox{``\ldots''}\\ \sembrack{\texttt{(enc~}t_0~\ldots~t_{n-1}~t_n\texttt{)}}&{}={}& \enc{\sembrack{\texttt{(cat~}t_0~\ldots~t_{n-1}\texttt{)}}}{\sembrack{t_n}}\\+\sembrack{\texttt{(hash~}t_0~\ldots~t_{n-1}\texttt{)}}&{}={}&+\hash{\sembrack{\texttt{(cat~}t_0~\ldots~t_{n-1}\texttt{)}}}\\ \sembrack{\texttt{(cat~}t\texttt{)}}&{}={}&\sembrack{t}\\ \sembrack{\texttt{(cat~}t_0~t_1~\ldots\texttt{)}}&{}={}& (\sembrack{t_0},\sembrack{\texttt{(cat~}t_1~\ldots\texttt{)}})@@ -296,20 +300,23 @@ \emph{decryption key} function returns the key used to decrypt a term if it is an encryption, otherwise it returns an error indicator.  The \emph{encryptions} function returns the set of encryption terms-carried by a term, each one paired with its encryption key.  The-penetrator derivable function from the section in the specification of-the same name is in the interface.  Given a derivable predicate that-has been specialized with a given set of supported terms and a set of-atoms to avoid, a target term, and a source term, the-\emph{protectors} function returns an error indicator if the target is-carried by the source outside of an encryption, where the derivable-predicate is used to determine if a decryption key can be used to-expose the target.  Otherwise, it returns a set of encryptions in the-source that carry the target and have underivable decryption keys.  If-two encryptions protect the target, only the outside one is returned.-The inside encryption is the one that is carried by the outside-encryption.  Pseudo code for the decryption key and the protectors-functions is in the specification.+carried by a term, each one paired with its encryption key.  {\cpsa}+treats a hashed term as if it were an encryption in which the term+that is hashed is the encryption key, so hashes with their content is+also returned by this function.  The penetrator derivable function+from the section in the specification of the same name is in the+interface.  Given a derivable predicate that has been specialized with+a given set of supported terms and a set of atoms to avoid, a target+term, and a source term, the \emph{protectors} function returns an+error indicator if the target is carried by the source outside of an+encryption, where the derivable predicate is used to determine if a+decryption key can be used to expose the target.  Otherwise, it+returns a set of encryptions in the source that carry the target and+have underivable decryption keys.  If two encryptions protect the+target, only the outside one is returned.  The inside encryption is+the one that is carried by the outside encryption.  Pseudo code for+the decryption key and the protectors functions is in the+specification.  \chapter{Protocols and Preskeletons}\label{cha:prots and preskels} @@ -1043,7 +1050,8 @@ \cn{ltk}\colon\dom{name}\times\dom{name}\rightarrow\dom{skey}$\\ $\cn{enc}\colon\dom{mesg} \times\dom{mesg}\rightarrow\dom{mesg}\quad-\cn{cat}\colon\dom{mesg}+\cn{hash}\colon\dom{mesg}\rightarrow\dom{mesg}$\\+$\cn{cat}\colon\dom{mesg} \times\dom{mesg}\rightarrow\dom{mesg}\quad C_i\colon\dom{mesg}$\\[1ex] Axiom: $\cn{invk}(\cn{invk}(x))\approx x$ for $x\colon\dom{akey}$\\ \caption{Basic Crypto Order-Sorted Signature}\label{tab:order-sorted}@@ -1052,10 +1060,11 @@  Terms are constructed from a set $I$ of identifiers\index{identifiers} and a set of functions symbols.  The symbols of arity one are-\cn{text}, \cn{data}, \cn{name}, \cn{skey}, \cn{akey}, \cn{pubk}, and-\cn{invk}.  The symbols of arity two are \cn{ltk}, \cn{cat}, and-\cn{enc}.  The signature is given in Table~\ref{tab:many-sorted}.-Grammar rules define the terms used by this algebra.+\cn{text}, \cn{data}, \cn{name}, \cn{skey}, \cn{akey}, \cn{pubk},+\cn{invk}, and \cn{hash}.  The symbols of arity two are \cn{ltk},+\cn{cat}, and \cn{enc}.  The signature is given in+Table~\ref{tab:many-sorted}.  Grammar rules define the terms used by+this algebra.  \begin{table} \begin{center}@@ -1066,7 +1075,9 @@ \cn{ltk}\colon\dom{name}\times\dom{name}\rightarrow\dom{skey}$\\ $\cn{enc}\colon\dom{mesg} \times\dom{mesg}\rightarrow\dom{mesg}\quad-\cn{cat}\colon\dom{mesg}+\cn{hash}\colon\dom{mesg}+\rightarrow\dom{mesg}$\\+$\cn{cat}\colon\dom{mesg} \times\dom{mesg}\rightarrow\dom{mesg}\quad C_i\colon\dom{mesg}$\\ $\cn{name}\colon\dom{name}\rightarrow\dom{mesg}\quad \cn{text}\colon\dom{text}\rightarrow\dom{mesg}\quad@@ -1103,10 +1114,10 @@  The set of terms $T$ is defined as follows. $$ T \leftarrow I \mid B \mid Q \mid \cn{cat}(T, T) \mid \cn{enc}(T,-T)$$ where $Q$ is the set of tags, represented by quoted string-literals.  The second argument in \cn{enc} is a term for a key.  A-term of the form $x$ is called an indeterminate, and the identifier-occurrence has sort~\dom{mesg}.+T) \mid \cn{hash}(T)$$ where $Q$ is the set of tags, represented by+quoted string literals.  The second argument in \cn{enc} is a term for+a key.  A term of the form $x$ is called an indeterminate, and the+identifier occurrence has sort~\dom{mesg}.  The terms of interest are \index{well-formed term}well-formed.  A term is \emph{well-formed} if every occurrence of each identifier has the@@ -1232,6 +1243,8 @@ \begin{tabular}{@{}ll} $\enc{\cdot}{(\cdot)}\colon\dom{mesg}\times\dom{mesg}\rightarrow\dom{mesg}$ &Encryption\\+$\#\colon\dom{mesg}\rightarrow\dom{mesg}$+&Hashing\\ $(\cdot,\cdot)\colon\dom{mesg}\times\dom{mesg}\rightarrow\dom{mesg}$ &Pairing\\ ``\ldots''$\colon\dom{mesg}$& Tag constants\\
doc/cpsaoverview.pdf view

binary file changed (78170 → 78230 bytes)

doc/cpsaoverview.tex view
@@ -38,11 +38,12 @@ construct~\texttt{k}.  Non-atomic terms are constructed by applications of encryption-(\texttt{enc}) and pairing (\texttt{cat}), where $n$-ary concatenation-is parsed right-associatively.  The second argument of an encryption-is the key. Encryption may also be written in an $n$-ary form where-the last argument is the key and the arguments preceding it are-implicitly concatenated.+(\texttt{enc}), hashing (\texttt{hash}), and pairing (\texttt{cat}),+where $n$-ary concatenation is parsed right-associatively.  The second+argument of an encryption is the key. Encryption may also be written+in an $n$-ary form where the last argument is the key and the+arguments preceding it are implicitly concatenated.  Hashing also may+written in an $n$-ary form and its arguments are implicitly concatenated.  A term carries one of its subterms if the possession of the right set of keys allows the extraction of the subterm.  The carries relation is
doc/cpsaprimer.pdf view

binary file changed (199120 → 199577 bytes)

doc/cpsaprimer.tex view
@@ -193,22 +193,27 @@ \texttt{(invk~k)} will be written as $K^{-1}$, and \texttt{(pubk~n)} as $K_{N}$. -The terms in this algebra are freely generated from the atoms,-tags, encryption, and concatenation.  A tag is a quoted constant.+The terms in this algebra are freely generated from the atoms, tags,+concatenation, encryption, and hashing.  A tag is a quoted constant.+The concatenation of terms~$t$ and~$t'$ is~$t,t'$ in traditional infix+notation and \texttt{(cat $t$ $t'$)} in S-expression syntax.  The+comma operator is right associative and \texttt{(cat $a$ $b$ $c$ $d$)}+is equivalent to \texttt{(cat $a$ (cat $b$ (cat $c$ $d$)))}. Given~$t$, the term to be protected, and key term~$k$, the encryption of~$t$ using~$k$ is~$\enc{t}{k}$ in traditional notation and \texttt{(enc $t$ $k$)} in S-expression syntax.  The term represents asymmetric encryption when the key is of sort \dom{akey}, otherwise it-represents symmetric encryption.  The concatenation of terms~$t$-and~$t'$ is~$t,t'$ in traditional infix notation and \texttt{(cat $t$-  $t'$)} in S-expression syntax.  The comma operator is right-associative and \texttt{(cat $a$ $b$ $c$ $d$)} is equivalent to-\texttt{(cat $a$ (cat $b$ (cat $c$ $d$)))}.  Finally, \texttt{(enc $a$-  $b$ $c$ $d$ $k$)} is equivalent to \texttt{(enc (cat $a$ $b$ $c$-  $d$) $k$)}.  Figure~\ref{fig:ns responder} on Page~\pageref{fig:ns-  responder} contains examples of \textsc{bca} message terms.  Also-see \textsc{term} in Table~\ref{tab:syntax}, Appendix~\ref{sec:syntax-  reference}.+represents symmetric encryption.  Additionally, \texttt{(enc $a$ $b$+  $c$ $d$ $k$)} is equivalent to \texttt{(enc (cat $a$ $b$ $c$ $d$)+  $k$)}.  Given~$t$, the term to be hashed, its hash is $\hash{t}$ in+traditional notation and \texttt{(hash $t$)} in S-expression syntax.+{\cpsa} treats a hashed term as if it were an encryption in which the+term that is hashed is the encryption key.  As with encryption,+\texttt{(hash $a$ $b$ $c$ $d$)} is equivalent to \texttt{hash (cat $a$+  $b$ $c$ $d$))}.  Figure~\ref{fig:ns responder} on+Page~\pageref{fig:ns responder} contains examples of \textsc{bca}+message terms.  Also see \textsc{term} in Table~\ref{tab:syntax},+Appendix~\ref{sec:syntax reference}.  A message term \emph{carries}\index{carries} a subterm of the message if the possession of the right set of keys allows the extraction of@@ -1123,19 +1128,6 @@ originating data is carried in fields with predictable values, the convention is to use the sort \dom{data} for uniquely originating data, and sort \dom{text} for the other fields.--Protocols that make use of \index{hashing}hashing can be handled by-encrypting the tag \texttt{"hash"} using the value to be hashed as the-key.  If the hash value is a variable of sort \dom{mesg}, a tag must-be added to the key so as to force {\cpsa} to use symmetric-encryption.  The following {\cpsa} macro captures the usage pattern.--\begin{quote}-\begin{verbatim}-(defmacro (hash x)-  (enc "hash" (cat "hash" x)))-\end{verbatim}-\end{quote}  When looking at the output, try extracting the shapes first.  If the shapes only version of the output does not answer your questions, try
doc/cpsaspec.pdf view

binary file changed (326000 → 337453 bytes)

doc/cpsaspec.tex view
@@ -50,6 +50,7 @@ \newcommand{\role}{\mathsf{r}} \newcommand{\skel}{\mathsf{k}} \newcommand{\rl}{\fn{rl}}+\newcommand{\inst}{\mathsf{i}} \newcommand{\nodes}{\fn{nodes}} \newcommand{\lsn}{\fn{lsn}} \newcommand{\init}{\fn{init}}@@ -187,6 +188,8 @@ \begin{tabular}{@{}ll} $\enc{\bullet}{(\cdot)}\colon\dom{mesg}\times\dom{mesg}\rightarrow\dom{mesg} $&Encryption\\+$\hash{(\cdot)}\colon\dom{mesg}\rightarrow\dom{mesg}+$&Hashing\\ $(\bullet,\bullet)\colon\dom{mesg}\times\dom{mesg}\rightarrow\dom{mesg}$ &Pairing\\ ``\ldots''$\colon{}\dom{mesg}$& Tag constants\\@@ -240,7 +243,8 @@ {}\cup\{\{(t_0,t_1)\mid t_0\in T_0, t_1\in T_1\}\mid  T_0\in\alga^n,T_1\in\alga^n\}\\ {}\cup\{\{\enc{t_0}{t_1}\mid t_0\in T_0, t_1\in T_1\}\mid- T_0\in\alga^n,T_1\in\alga^n\}+ T_0\in\alga^n,T_1\in\alga^n\}\\+{}\cup\{\{\hash{t}\mid t\in T\}\mid T\in\alga^n\} \end{array}\\ \alga = \alga_{\dom{mesg}}&\bigcup_{n\in\nat}\alga^n \end{array}$$@@ -280,12 +284,15 @@ t&\mbox{otherwise.} \end{array}\right.$$ -An important property possessed by the algebra is that for all $T\in\alga$,-if there are any encryptions in $T$ then all members of $T$ are encryptions.-As a result, a message can be identified as representing an encryption-and if it is, decomposed into its plaintext and its decryption key.-This property is a consequence of the fact that equations relate-atoms, not arbitrary messages.  A similar property holds for pairs.+An important property possessed by the algebra is that for all+$T\in\alga$, if there are any encryptions in $T$ then all members of+$T$ are encryptions.  As a result, a message can be identified as+representing an encryption and if it is, decomposed into its plaintext+and its decryption key.  This property is a consequence of the fact+that equations relate atoms, not arbitrary messages.  A similar+property holds for pairs and hashes.  A hash\index{hash} is treated as+a kind of encryption in which the term that is hashed is the+encryption key.  We write $\alga_X$ when it is important to identify the variable set~$X$ that generates the algebra.  Given two variable sets~$X$@@ -470,7 +477,9 @@ \seq{\inbnd(x, y),\outbnd x,\outbnd y}\\ \mbox{Encrypt}(x,y\colon\top)& \seq{\inbnd x,\inbnd y,\outbnd\enc{x}{y}}&-\seq{\inbnd\enc{x}{y},\inbnd \fn{inv}(y),\outbnd x}+\seq{\inbnd\enc{x}{y},\inbnd \fn{inv}(y),\outbnd x}\\+\mbox{Hash}(x\colon\top)&+\seq{\inbnd x,\outbnd\hash{x}} \end{array}$$ \caption{Basic Crypto Algebra Penetrator Role Traces}\label{fig:pen} \end{figure}@@ -590,12 +599,12 @@ strands, and adjusting the communication ordering $\to$ appropriately.  The set of bundles denoted by preskeleton~$k$, $\sembrack{k}$, is:-$$\sembrack{k_0} = \{\Upsilon\mid-\mbox{$k_0\homomorphism{\phi,\sigma}k_1$ and $k_1$ realizes modulo+$$\sembrack{k} = \{\Upsilon\mid+\mbox{$k\homomorphism{\phi,\sigma}k'$ and $k'$ realizes modulo   listeners $\Upsilon$}\}$$ A {\cpsa} algorithm is \emph{complete} if-when given a preskeleton~$k_0$, either the algorithm diverges, or else it+when given a preskeleton~$k$, either the algorithm diverges, or else it terminates and produces a finite set of realized skeletons~$K$, such-that $\sembrack{k_0}=\bigcup_{k_1\in K}\sembrack{k_1}$.+that $\sembrack{k}=\bigcup_{k'\in K}\sembrack{k'}$. \label{def:preskeleton denotation}  \section{Blanchet's Simple Example Protocol}\label{sec:blanchet's@@ -640,7 +649,7 @@ &\{\init(a_0,b_0,s_0,d_0),\resp(a_1,b_1,s_1,d_1)\}, &\mbox{Protocol}\\ &\seq{\seq{\outbnd\enc{\enc{s}{a^{-1}}}{b},\inbnd\enc{d}{s}}},-&\mbox{Strands}\\+&\mbox{Traces}\\ &\emptyset, &\mbox{Node orderings}\\ &\{a^{-1},b^{-1}\},@@ -667,7 +676,7 @@ \seq{\outbnd\enc{\enc{s}{a^{-1}}}{b},\inbnd\enc{d}{s}},\\ \seq{\inbnd\enc{\enc{s}{a^{-1}}}{b},\outbnd\enc{d}{s}}\rangle, \end{array}-&\mbox{Strands}\\+&\mbox{Traces}\\ &\{(1,1)\prec(2,1),(2,2)\prec(1,2)\}, &\mbox{Node orderings}\\ &\{a^{-1},b^{-1}\},@@ -706,7 +715,7 @@ &\{\init(a_0,b_0,s_0,d_0),\resp(a_1,b_1,s_1,d_1)\}, &\mbox{Protocol}\\ &\seq{\seq{\inbnd\enc{\enc{s}{a^{-1}}}{b},\outbnd\enc{d}{s}}},-&\mbox{Strands}\\+&\mbox{Traces}\\ &\emptyset, &\mbox{Node orderings}\\ &\{a^{-1},b^{-1}\},@@ -730,7 +739,7 @@ \seq{\outbnd\enc{\enc{s}{a^{-1}}}{b'}}\rangle, \end{array} &\begin{array}[t]{@{}l}-\mbox{Strands}\\+\mbox{Traces}\\ \mbox{\emph{Note key is $b'$ not $b$!}} \end{array}\\ &\{(2,1)\prec(1,1)\},@@ -755,7 +764,7 @@ &\seq{ \seq{\inbnd\enc{\enc{s}{a^{-1}}}{b},\outbnd\enc{d}{s}}, \seq{\inbnd d,\outbnd d}},-&\mbox{Strands}\\+&\mbox{Traces}\\ &\{(1,2)\prec(2,1), &\mbox{Node orderings}\\ &\{a^{-1},b^{-1}\},@@ -797,7 +806,7 @@ &\{\init(a_0,b_0,m_0),\resp(a_1,b_1,m_1),\lsn(x)\}, &\mbox{Protocol}\\ &\seq{\seq{\outbnd\enc{\enc{m}{b},a}{b}},\seq{\inbnd m}},-&\mbox{Strands}\\+&\mbox{Traces}\\ &\emptyset, &\mbox{Node orderings}\\ &\{a^{-1},b^{-1}\},@@ -888,6 +897,27 @@ \caption{A Bundle Realized by the Example Skeleton}\label{fig:bundle} \end{figure} +\section{External Syntax and Instances}\label{sec:instances}++The external syntax used by {\cpsa} is a little different than what+has been described here.  In the external syntax, the trace and the+role associated with a strand is specified by an+\index{instance}\emph{instance}.  An instance is of the form+$\inst(r,h,\sigma)$, where~$r$ is a role, $h$ specifies the length of+a trace instantiated from the role, and~$\sigma$ specifies how to+instantiate the variables in the role to obtain the trace.  Thus when+$r=\role_Y(C,N,U)$, the trace associated with $\inst(r,h,\sigma)$ is+$\sigma\circ\prefix{C}{h}$.  An instance is well-formed if $1\leq+h\leq|C|$, and $\sdom(\sigma)$ is the set of variables that occur+in~$\prefix{C}{h}$.++In the external syntax, the role map and sequence of traces are+replaced by a sequence of instances.  So for preskeleton+$\skel_X(\rl,P,\Theta_X,\prec,N,U)$ the external syntax is+$\skel_X(P,I,\prec,N,U)$, where for each $s\in\sdom(\Theta_x)$,+$I(s)=\inst(r,h,\sigma)$, $r=\rl(s)$, and the trace of+$\inst(r,h,\sigma)$ is $\Theta_X(s)$.+ \chapter{Algorithms as Reduction Systems}\label{chp:algorithms}  Algorithms in this paper are specified as abstract reduction@@ -1101,11 +1131,14 @@ $k_0\reduction{\ops{S}_\sigma}k\reduction{\ops{C}_{s,s'}}k_1$, $k_0\homomorphism{\phi,\sigma}k_1$, and $k_1\homomorphism{\phi',\sigma'}k_0$, where-$\comp{\phi}{\phi'}=\idphi$ and $\comp{\sigma}{\sigma'}=\idsigma$.-In particular $\phi=\phi_{s,s'}$ and $\phi'=\phi'_s$-with~$\phi_{s,s'}$ and~$\phi'_s$ as in Definition~\ref{def:compression-  operator}.  The bidirectional homomorphism requirement leads to the-following definition.+$\comp{\phi}{\phi'}=\idphi$ and+$\comp{\sigma}{\sigma'}=\idsigma$.\footnote{In category theory,+  $(\phi',\sigma')$ is a section of $(\phi,\sigma)$, and+  $(\phi,\sigma)$ is a retraction of $(\phi',\sigma')$.}  In+particular $\phi=\phi_{s,s'}$ and $\phi'=\phi'_s$ with~$\phi_{s,s'}$+and~$\phi'_s$ as in Definition~\ref{def:compression operator}.  The+bidirectional homomorphism requirement leads to the following+definition.  \begin{defn}[Pruning]\label{def:pruning} Suppose skeleton~$k_0$ has a redundant strand~$s$.  Then there exists@@ -1145,6 +1178,18 @@ point-of-view skeleton, but the notation in the chapter on generalization shows how it might be done. +\begin{defn}[Thinning]+Two strands $s$ and $s'$ in a skeleton $k$ are \emph{effectively+  equivalent} if $k$ with $s$ removed and $k$ with $s'$ removed are+isomorphic.  We can define a different form of pruning based on this+idea.  Skeleton $k_0$ reduces to skeleton $k_1$ by pruning, written+$k_0\reduction{\ops{P}_s}k_1$, if and only if there exists a strand+$s'$ that is effectively equivalent to $s$ in $k_0$ and $k_1$ is+isomorphic to both $k_0$ with $s$ removed and $k_0$ with $s'$ removed.+\end{defn}++Thinning is not used yet.+ \section{Reduction Systems}  Notice that a setwise hulling reduction may produce the empty set, but@@ -1194,7 +1239,8 @@ \fn{enc}(t_0,t_1)=\seq{\inbnd t_0,\inbnd t_1, \outbnd\enc{t_0}{t_1}}\\ \fn{dec}(t_0,t_1)=\seq{\inbnd\enc{t_0}{t_1},-\inbnd t_2,\outbnd t_0},\mbox{ where $t_2=\fn{inv}(t_1)$}+\inbnd t_2,\outbnd t_0},\mbox{ where $t_2=\fn{inv}(t_1)$}\\+\fn{hash}(t)=\seq{\inbnd t,\outbnd\hash t} \end{array}$$ \caption{Penetrator Traces}\label{fig:pen traces} \end{figure}@@ -1234,13 +1280,16 @@ [\mbox{by $\fn{dec}(t_0,t_1)$}] \end{equation} -There are two constructive steps.+There are three constructive steps. $$\infer{\der{t_0}{T_p}{T_a}\qquad\der{t_1}{T_p}{T_a}}% {\der{(t_0,t_1)}{T_p}{T_a}}\quad [\mbox{by $\fn{cat}(t_0,t_1)$}]$$ $$\infer{\der{t_0}{T_p}{T_a}\qquad\der{t_1}{T_p}{T_a}}% {\der{\enc{t_0}{t_1}}{T_p}{T_a}}\quad [\mbox{by $\fn{enc}(t_0,t_1)$}]$$+$$\infer{\der{t}{T_p}{T_a}}%+{\der{\hash{t}}{T_p}{T_a}}\quad+[\mbox{by $\fn{hash}(t)$}]$$  There are three rules for indivisible messages. $$\der{C_i}{T_p}{T_a}\quad@@ -1444,7 +1493,7 @@ Figure~\ref{fig:cows} displays the iterative procedure that breaks the cyclic dependencies.  Each step of the iteration improves an approximation of a solution to the problem.  The correctness of this-function is shown in~\cite{algimpl}, although for a version of the+function is shown in~\cite{algimpl11}, although for a version of the algorithm with the alternate definition for the function~$\fn{fold}$ in Figure~\ref{fig:fold}. @@ -1502,8 +1551,8 @@ $t=\msg_k(n)$ if \begin{enumerate} \item $p$ is a carried position in~$t$,-\item either $t\termat p\in U_k$ or $t\termat p=\enc{t_0}{t_1}$-  and~$t_1$ is not derivable before~$n$ in~$k$,+\item either $t\termat p\in U_k$, $t\termat p=\hash t_1$, or $t\termat+  p=\enc{t_0}{t_1}$ and~$t_1$ is not derivable before~$n$ in~$k$, \item $\fn{esc}(k,n,t\termat p)$ is defined, and \item $\fn{anc}(t,p)\cap \fn{esc}(k,n,t\termat p)=\emptyset$. \end{enumerate}@@ -1512,8 +1561,10 @@ The message at a critical position is called an \emph{authentication   test}.  It is a \index{nonce test}\emph{nonce test} if the message is an atom, otherwise it is a \index{encryption test}\emph{encryption-  test}.  Observe that every critical message at a node in a skeleton-is not derivable at the node.+  test}.  (A hash\index{hash} is treated as a kind of encryption in+which the term that is hashed is the encryption key.)  Observe that+every critical message at a node in a skeleton is not derivable at the+node.  \begin{conj} A reception node is unrealized iff it has a critical position.@@ -1538,7 +1589,7 @@ \item for some~$t_p\in\outpred(k_1,n_1)$, $t_1$ is not carried   only within~$T_1$ in~$t_p$, or \item-  $\fn{targ}(t_1,T_1)\setminus\sigma(\fn{targ}(t_0,T_0))\neq\emptyset$+  $\fn{targ}(t_1,\fn{esc}(k_1,n_1,t_1))\setminus\sigma(\fn{targ}(t_0,T_0))\neq\emptyset$   and there are variables in $k$'s protocol that are not atoms, or \item the decryption key of a member of~$T_1$ is derivable   before~$n_1$ in~$k_1$, or@@ -1919,11 +1970,12 @@ message is the same as the expected message, and abort the run if not.  Here is an example of when the second behavior is desired.  In-{\cpsa}, encryption can be used to represent hashing.  The hash of~$t$,-$\#t$, expands to $\enc{\mbox{``hash''},t}{h}$, where~$h$ is an-asymmetric key known to all, but no one knows~$h^{-1}$.  The tag-``hash'' is added to the encryption so as to ensure a hash is never-confused with other uses of encryption.+{\cpsa}, before hashing was part of the algebra, an encryption was+used to represent hashing.  The hash of~$t$, $\#t$, expanded to+$\enc{\mbox{``hash''},t}{h}$, where~$h$ was an asymmetric key known to+all, but no one knew~$h^{-1}$.  The tag ``hash'' was added to the+encryption so as to ensure a hash was never confused with other uses of+encryption.  A role does not specify a valid program if the only possible way of interpreting the event~$\inbnd\#t$ is by using~$h^{-1}$ to decrypt@@ -2040,12 +2092,12 @@ is a formula in the language of order-sorted first-order logic called a \index{shape analysis sentence}\emph{shape analysis sentence,} often shortened to a shape sentence.  The sentence has a special form,-$\all{X}\Psi\rightarrow\bigvee_i\some{Y_i}\Delta_i\wedge\Phi_i$,+$\all{X}(\Psi\supset\bigvee_i\some{Y_i}(\Delta_i\wedge\Phi_i$)), where~$\Psi$ and~$\Phi_i$ are conjunctions of atomic formulas and~$X$ and~$Y_i$ are variable sets.  This fragment of first-order logic is called coherent logic.  Formula~$\Psi$ describes the point-of-view-skeleton~$k$.  For each homomorphism to a shape,-$k\homomorphism{\delta_i}k_i$, formula~$\Delta_i$ describes the+skeleton~$k_0$.  For each homomorphism to a shape,+$k_0\homomorphism{\delta_i}k_i$, formula~$\Delta_i$ describes the structure preserving maps~$\delta_i$, and the shape~$k_i$ is described by~$\Phi_i$. @@ -2077,19 +2129,17 @@ zero and, of course, equality is binary.  We define~$\form(k)=(Y,\Phi)$, where~$\Phi$ is $k$'s skeleton formula,-and~$Y$ is the formula's variable set.  Let-$k=\skel_X(\rl,P,\Theta,\prec,N,U)$.  The variable set~$Y$ is~$X$-augmented with a variable~$z_s\colon\dom{nat}$ for each strand-$s\in\sdom(\Theta)$.  The formula~$\Phi$ is a conjunction of atomic+and~$Y$ is the formula's variable set.  Using the external syntax+presented in Section~\ref{sec:instances}, let+$k=\skel_X(P,I,\prec,N,U)$.  The variable set~$Y$ is~$X$ augmented+with a variable~$z_s\colon\dom{nat}$ for each strand+$s\in\sdom(I)$.  The formula~$\Phi$ is a conjunction of atomic formulas composed as follows.  \begin{itemize}-\item For each $s\in\sdom(\Theta)$, let $r=\rl(s)=\role_Y(C,N,U)$,-  $\comp{\sigma}{C|_h}=\Theta(s)$, and $h=|\Theta(s)|$.  For each-  variable $x\in\sdom(\sigma)$ and term $t=\sigma(x)$, assert-  $P[r,h,x](z_s,t)$.  Note $\sigma\colon\alga_Y\to\alga_X$ is the-  homomorphism described near the end of Chapter~\ref{chp:strand-    spaces and bundles}.+\item For each $s\in\sdom(I)$, let $I(s)=\inst(r,h,\sigma)$.  For+  each variable $x\in\sdom(\sigma)$ and term $t=\sigma(x)$, assert+  $P[r,h,x](z_s,t)$. \item For each $(s,i)\prec(s',i')$, assert   $\cn{prec}(z_s,i,z_{s'},i')$. \item For each $t\in N$, assert $\cn{non}(t)$.@@ -2104,20 +2154,20 @@ the~$\prec$ relation.  The missing relations must be asserted as axioms for proper handling of a shape sentence. -Given a set of homomorphisms $k\homomorphism{\delta_i}k_i$, its shape+Given a set of homomorphisms $k_0\homomorphism{\delta_i}k_i$, its shape sentence is \begin{equation}-\sent(k\homomorphism{\delta_i}k_i)=\all{X}\Psi\rightarrow-\bigvee_i\some{Y_i}\Delta_i\wedge\Phi_i,\label{eq:shape sentence}+\sent(k_0\homomorphism{\delta_i}k_i)=\all{X}(\Psi\supset+\bigvee_i\some{Y_i}(\Delta_i\wedge\Phi_i)),\label{eq:shape sentence} \end{equation}-where $\form(k)=(X,\Psi)$.  The same procedure produces~$Y_i$+where $\form(k_0)=(X,\Psi)$.  The same procedure produces~$Y_i$ and~$\Phi_i$ for shape~$k_i$ with one proviso---the variables in $Y_i$ that also occur in~$X$ must be renamed to avoid trouble while encoding the structure preserving maps~$\delta_i$.  \begin{figure} $$\begin{array}{l}-\all{a_0,b_0\colon A, s_0\colon S, d_0\colon D, z_0\colon N}\\+\all{a_0,b_0\colon A, s_0\colon S, d_0\colon D, z_0\colon N}(\\ \quad\init_{2,a}(z_0,a_0)\wedge \init_{2,b}(z_0,b_0)\wedge \init_{2,s}(z_0,s_0)\wedge@@ -2125,9 +2175,9 @@ \quad\cn{non}(a_0^{-1})\wedge \cn{non}(b_0^{-1})\wedge \cn{uniq}(s_0)\wedge\cn{orig}(s_0,z_0,1)\\-\quad\rightarrow\\+\quad\supset\\ \quad\some{a_1,b_1\colon A, s_1\colon S, d_1\colon D, z_1,z_2\colon-  N}\\+  N}(\\ \qquad z_0=z_1\wedge a_0=a_1\wedge b_0=b_1\wedge s_0=s_1\wedge d_0=d_1\wedge{}\\ \qquad\init_{2,a}(z_1,a_1)\wedge \init_{2,b}(z_1,b_1)\wedge@@ -2141,7 +2191,7 @@ \cn{prec}(z_2,2,z_1,2)\wedge{}\\ \qquad\cn{non}(a_1^{-1})\wedge \cn{non}(b_1^{-1})\wedge-\cn{uniq}(s_1)\wedge\cn{orig}(s_1,z_1,1)+\cn{uniq}(s_1)\wedge\cn{orig}(s_1,z_1,1))) \end{array}$$ \caption{A Shape Analysis Sentence for Blanchet's   Protocol}\label{fig:blanchet's shape analysis sentence}@@ -2153,7 +2203,7 @@ of~$\sigma_i$ and the term it maps to.  Map~$\phi_i$ is coded as equalities between strand variables in~$\Psi$ and strand variables in~$\Phi_i$.  Let~$Z$ be the sequence of strand variables freshly-generated for~$k$, and~$Z_i$ be the ones generated for~$k_i$.  The+generated for~$k_0$, and~$Z_i$ be the ones generated for~$k_i$.  The strand mapping part of~$\Delta_i$ is $\bigwedge_{j\in\sdom(\Theta)}Z(j)=Z_i(\phi_i(j))$. @@ -2166,21 +2216,21 @@  \section{Semantics of Shape Formulas} -Once again, let $k=\skel_X(\rl,P,\Theta,\prec,N,U)$.  The universe of-discourse is $\alg{D}=\nat\cup\alga_X$.  When formula~$\Psi$ is-satisfied in skeleton~$k$ with variable assignment $\alpha\colon Y\to-\alg{D}$, we write $k,\alpha\models\Psi$.  When sentence~$\Sigma$ is-satisfied in skeleton~$k$, we write $k\models\Sigma$.+Let $k=\skel_X(\rl,P,\Theta,\prec,N,U)$.  The universe of discourse is+$\alg{D}=\nat\cup\alga_X$.  When formula~$\Psi$ is satisfied in+skeleton~$k$ with variable assignment $\alpha\colon Y\to \alg{D}$, we+write $k,\alpha\models\Psi$.  When sentence~$\Sigma$ is satisfied in+skeleton~$k$, we write $k\models\Sigma$.  For each protocol specific predicate $P[r,h,x]$, $k,\alpha\models P[r,h,x](y,z)$ iff $\alpha(y)\in\nat$, $\alpha(z)\in\alga$, and with-$\alpha(y)=s$,+$\alpha(y)=s$ and $r=\role(C,N,U)$,  \begin{enumerate} \item $s\in\sdom(\Theta)$, \item $h\in\sdom(\Theta(s))$, and-\item $\alpha(z)=\sigma(x)$, where $\rl(s)=\role(C,N,U)$,-$\comp{\sigma}{C|_\ell}=\Theta(s)$, and $\ell=|\Theta(s)|$.+\item $\prefix{\Theta(s)}{h}=\sigma\circ\{x\mapsto\alpha(z)\}\circ\prefix{C}{h}$+  for some~$\sigma$. \end{enumerate}  In an interpretation, $\rl(s)$ need not be~$r$.  The events that make@@ -2204,10 +2254,10 @@ \end{itemize}  \begin{thm}\label{thm:skeleton models}-Let $\form(k)=(X,\Psi)$ and $\Phi=\some{X}\Psi$.  Formula~$\Phi$ is-satisfied in~$k'$ iff there is a homomorphism from~$k$ to-$k'$, i.e.\ $k'\models\Phi$ iff-$\some{\delta}k\homomorphism{\delta}k'$.+Let $\form(k_0)=(X,\Psi)$ and $\Phi=\some{X}\Psi$.  Formula~$\Phi$ is+satisfied in~$k$ iff there is a homomorphism from~$k_0$ to+$k$, i.e.\ $k\models\Phi$ iff+$\some{\delta}k_0\homomorphism{\delta}k$. \end{thm}  This theorem corrects the first of the two main results@@ -2215,16 +2265,16 @@  \begin{proof} For the forward direction, assume~$\alpha$ is a variable assignment-for the variables in~$X$ such that $k',\alpha\models\Psi$, and let~$Z$+for the variables in~$X$ such that $k,\alpha\models\Psi$, and let~$Z$ be the sequence of strand variables constructed while-generating~$\Psi$ from~$k$.  Then the pair of maps-$\delta=(\comp{\alpha}{Z},\alpha)$ demonstrate a homomorphism from~$k$-to~$k'$, i.e.\ each item in the definition of a preskeleton+generating~$\Psi$ from~$k_0$.  Then the pair of maps+$\delta=(\comp{\alpha}{Z},\alpha)$ demonstrate a homomorphism from~$k_0$+to~$k$, i.e.\ each item in the definition of a preskeleton homomorphism on Page~\pageref{def:preskeleton homomorphism} is satisfied.  For the reverse direction, assume maps $\delta=(\phi,\sigma)$ are such-that $k\homomorphism{\delta}k'$.  Then the desired variable assigment is+that $k_0\homomorphism{\delta}k$.  Then the desired variable assigment is $$\alpha(x)=\left\{ \begin{array}{ll} \phi(Z^{-1}(x))&x\in\sran(Z)\\@@ -2236,10 +2286,10 @@ defined on Page~\pageref{def:preskeleton denotation}.  \begin{thm}\label{thm:sentence implies}-Let $k\homomorphism{\delta_i}k_i$ be a complete set of homomorphisms-for shapes $k_i\in K$, and assume $\sembrack{k}=\bigcup_{k'\in-  K}\sembrack{k'}$.  Then the shape analysis-sentence~$\Sigma=\sent(k\homomorphism{\delta_i}k_i)$ is satisfied in+Let $k_0\homomorphism{\delta_i}k_i$ be a complete set of homomorphisms+for shapes $k_i\in K$, and assume $\sembrack{k_0}=\bigcup_{k\in+  K}\sembrack{k}$.  Then the shape analysis+sentence~$\Sigma=\sent(k_0\homomorphism{\delta_i}k_i)$ is satisfied in all realized skeletons~$k$, i.e.\ $k\models\Sigma$. \end{thm} @@ -2248,7 +2298,7 @@ skeleton in the image of~$k$ that is not in the image of one of the shapes.  Therefore, by Theorem~\ref{thm:skeleton models}, the negation of the hypothesis of the implication is satisfied in all realized-skeletons that are not in the image of~$k$, and the disjunction is+skeletons that are not in the image of~$k_0$, and the disjunction is satisfied in the remaining realized skeletons. \end{proof}
doc/cpsatheory.pdf view

binary file changed (292086 → 292074 bytes)

doc/cpsauser.html view
@@ -5,7 +5,7 @@ <head>   <meta http-equiv="content-type"   content="application/xhtml+xml; charset=UTF-8" />-  <title>CPSA 2.0 User Guide</title>+  <title>CPSA 2.2 User Guide</title>   <meta name="generator" content="Amaya 9.54, see http://www.w3.org/Amaya/" />   <style type="text/css">     h1 { text-align: center }@@ -14,7 +14,7 @@ </head>  <body>-<h1>CPSA 2.0 User Guide</h1>+<h1>CPSA 2.2 User Guide</h1>  <p>The Cryptographic Protocol Shapes Analyzer (CPSA) attempts to enumerate all essentially different executions possible for a cryptographic protocol. We call@@ -157,7 +157,7 @@  <blockquote>   <pre>SORT ::= text | data | name | skey | akey | mesg-TERM ::= ID | STRING | (cat TERM+) | (enc TERM+ TERM)+TERM ::= ID | STRING | (cat TERM+) | (enc TERM+ TERM) | (hash TERM+)       |  (pubk ID) | (privk ID) | (invk ID) | (ltk ID ID)       |  (pubk STRING ID) | (privk STRING ID)</pre> </blockquote>
doc/macros.tex view
@@ -1,5 +1,5 @@ \newcommand{\cpsa}{\textsc{cpsa}}-\newcommand{\version}{2.2.4}+\newcommand{\version}{2.2.5} \newcommand{\cpsacopying}{\begingroup   \renewcommand{\thefootnote}{}\footnotetext{{\copyright} 2010 The     MITRE Corporation.  Permission to copy without fee all or part of@@ -15,6 +15,7 @@ \newcommand{\fn}[1]{\ensuremath{\operatorname{\mathit{#1}}}} \newcommand{\seq}[1]{\ensuremath{\langle#1\rangle}} \newcommand{\enc}[2]{\ensuremath{\{\!|#1|\!\}_{#2}}}+\newcommand{\hash}[1]{\ensuremath{\##1}} \newcommand{\comp}[2]{{\mathord{#1}}\circ{\mathord{#2}}} \newcommand{\sembrack}[1]{[\![#1]\!]} \newcommand{\semfn}[1]{\mathcal{#1}}@@ -25,8 +26,8 @@ \newcommand{\inbnd}{\mathord -} \newcommand{\outbnd}{\mathord +} \newcommand{\nat}{\mathbb{N}}-\newcommand{\all}[1]{\forall#1\mathpunct{.}}-\newcommand{\some}[1]{\exists#1\mathpunct{.}}+\newcommand{\all}[1]{\mathop{\forall#1}}+\newcommand{\some}[1]{\mathop{\exists#1}} \newcommand{\baseterms}{\mathbb{B}} \newcommand{\cons}{\mathbin{::}} \newcommand{\ith}{\imath^\mathrm{th}}
src/CPSA/Basic/Algebra.hs view
@@ -64,6 +64,7 @@ -- Operations: --   cat : mesg X mesg -> mesg               Pairing --   enc : mesg X mesg -> mesg               Encryption+--   hash : mesg X mesg -> mesg              Hashing --   string : mesg                           Tag constants --   ltk : name X name -> skey               Long term shared key --   pubk : name -> akey                     Public key of principal@@ -82,6 +83,7 @@ -- Operations: --   cat : mesg X mesg -> mesg               Pairing --   enc : mesg X mesg -> mesg               Encryption+--   hash : mesg -> mesg                     Hashing --   string : mesg                           Tag constants --   ltk : name X name -> skey               Long term shared key --   pubk : name -> akey                     Public key of principal@@ -107,6 +109,7 @@     | Pubk                      -- Public asymmetric key of a principal     | Cat                       -- Term concatenation (Pairing really)     | Enc                       -- Encryption+    | Hash                      -- Hashing       deriving (Show, Eq, Ord, Enum, Bounded)  -- A Basic Crypto Algebra Term@@ -175,7 +178,7 @@ -- The non-terminal symbols are B, K, and T.  Symbol B is for base -- sorted terms, and K is for asymmetric keys. -----     T ::= I | C | B | cat(T, T) | enc(T, T)+--     T ::= I | C | B | cat(T, T) | enc(T, T) | hash(T) -- --     B ::= text(I) | data(I) | name(I) | skey(I) --        |  skey(I) | skey(ltk(I, I)) | akey(K)@@ -212,6 +215,8 @@     doubleTermWellFormed xts t0 t1  -- Concatenation termWellFormed xts (F Enc [t0, t1]) =     doubleTermWellFormed xts t0 t1  -- Encryption+termWellFormed xts (F Hash [t])     =+    termWellFormed xts t            -- Hashing termWellFormed _ _ = Nothing  -- Extend when sorts agree@@ -262,6 +267,8 @@     foldVars f (foldVars f acc t0) t1 foldVars f acc (F Enc [t0, t1]) = -- Encryption     foldVars f (foldVars f acc t0) t1+foldVars f acc (F Hash [t])     = -- Hashing+    foldVars f acc t foldVars _ _ t = error $ "Algebra.foldVars: Bad term " ++ show t  -- Fold f through a term applying it to each term that is carried by the term.@@ -296,6 +303,8 @@           ba t0 && ba t1       ba t@(F Enc [t0, t1]) =           S.member t knowns || ba t0 && ba t1+      ba t@(F Hash [t1]) =+          S.member t knowns || ba t1       ba t = isAtom t && not (S.member t unguessable)  -- Compute the decomposition given some known terms and some unguessable@@ -315,6 +324,8 @@           | buildable knowns unguessable (inv t1) = -- Add plaintext               loop unguessable (decat t0 knowns) old todo           | otherwise = loop unguessable knowns old todo+      loop unguessable knowns old ((F Hash [_]) : todo) =+          loop unguessable knowns old todo -- Hash can't be decomposed       loop unguessable knowns old (t : todo) =           loop (S.delete t unguessable) (S.delete t knowns) old todo       -- Decat@@ -329,7 +340,8 @@ inv t = t  -- Extracts every encryption that is carried by a term along with its--- encryption key.+-- encryption key.  Note that a hash is treated as a kind of+-- encryption in which the term that is hashed is the encryption key. encryptions :: Term -> [(Term, Term)] encryptions t =     reverse $ loop t []@@ -338,6 +350,8 @@           loop t' (loop t acc)       loop t@(F Enc [t', t'']) acc =           loop t' (adjoin (t, t'') acc)+      loop t@(F Hash [t']) acc =+          adjoin (t, t') acc       loop _ acc = acc       adjoin x xs           | x `elem` xs = xs@@ -388,6 +402,8 @@     comb (outFlow t1) (outFlow t0) a outFlow (F Enc [t0, t1]) a =     comb (outFlow t1) (outFlow t0) a+outFlow (F Hash [t]) a =+    outFlow t a outFlow t (initial, available) = -- Don't look inside atoms     S.singleton (S.insert t initial, S.insert t available) @@ -399,11 +415,13 @@          (comb (inFlow t1) (inFlow t0) a)          (comb (inFlow t0) (inFlow t1) a) inFlow t@(F Enc [t0, t1]) (initial, available) =-    S.union                     -- Encryption can be built-         (outFlow t (initial, available)) -- or decrypted-         (comb (inFlow t0) (outFlow (inv t1)) a)+    S.union+         (outFlow t (initial, available)) -- Encryption can be built+         (comb (inFlow t0) (outFlow (inv t1)) a) -- or decrypted     where                       -- Derive decryption key first       a = (initial, S.insert t available)+inFlow (F Hash [t0]) (initial, available) =+    outFlow t0 (initial, available) inFlow t (initial, available) =     S.singleton (initial, S.insert t available) @@ -467,9 +485,9 @@       f paths path source           | target == source = Place (reverse path) : paths       f paths path (F Cat [t, t']) =-	  f (f paths  (0 : path) t) (1 : path) t'+          f (f paths  (0 : path) t) (1 : path) t'       f paths path (F Enc [t, _]) =-	  f paths (0 : path) t+          f paths (0 : path) t       f paths _ _ = paths  -- Return the ancestors of the term at the given place.@@ -877,6 +895,7 @@     ,("ltk", loadLtk)     ,("cat", loadCat)     ,("enc", loadEnc)+    ,("hash", loadHash)     ]  -- Atom constructors: pubk privk invk ltk@@ -943,6 +962,13 @@       loop z x [] = (reverse z, x)       loop z x (y : ys) = loop (x : z) y ys +loadHash :: Monad m => LoadFunction m+loadHash _ vars (l : ls) =+   do+     ts <- mapM (loadTerm vars) (l : ls)+     return $ F Hash [foldr1 (\a b -> F Cat [a, b]) ts]+loadHash pos _ _ = fail (shows pos "Malformed hash")+ -- Term specific displaying functions  newtype Context = Context [(Id, String)] deriving Show@@ -1002,6 +1028,8 @@     L () (S () "cat" : displayTerm ctx t0 : displayList ctx t1) displayTerm ctx (F Enc [t0, t1]) =     L () (S () "enc" : displayEnc ctx t0 t1)+displayTerm ctx (F Hash [t]) =+    L () (S () "hash" : displayList ctx t) displayTerm _ t = error ("Algebra.displayTerm: Bad term " ++ show t)  displayList :: Context -> Term -> [SExpr ()]
src/CPSA/Lib/Displayer.hs view
@@ -71,7 +71,7 @@ displayPreskel k rest =     L () (S () "defskeleton" :           S () (pname (protocol k)) :-          L () (S () "vars" : displayVars ctx (L.sort vars)) :+          L () (S () "vars" : displayVars ctx vars) :           foldr f (displayRest k ctx rest) (insts k))     where       ctx = varsContext vars
src/CPSA/Lib/Strand.hs view
@@ -72,6 +72,9 @@ useCheckVars :: Bool useCheckVars = False +useThinning :: Bool+useThinning = False -- True+ usePruningDuringCollapsing :: Bool usePruningDuringCollapsing = False -- True @@ -836,9 +839,9 @@ -- at which each maybe uniquely originating term originates are filter -- out. -ksubst :: Algebra t p g s e c => PRS t p g s e c ->-          Bool -> (g, s) -> [PRS t p g s e c]-ksubst (k0, k, n, phi, hsubst) validate (gen, subst) =+ksubst :: Algebra t p g s e c => Bool -> PRS t p g s e c ->+          (g, s) -> [PRS t p g s e c]+ksubst validate (k0, k, n, phi, hsubst) (gen, subst) =     do       (gen', insts') <- foldMapM (substInst subst) gen (insts k)       let non' = map (substitute subst) (knon k)@@ -886,12 +889,13 @@     Cause dir n (substitute subst t) (S.map (substitute subst) escape)  -- A compression (s is to be eliminated)-compress :: Algebra t p g s e c => PRS t p g s e c ->+compress :: Algebra t p g s e c => Bool -> PRS t p g s e c ->             Sid -> Sid -> [PRS t p g s e c]-compress (k0, k, n, phi, hsubst) s s' =+compress validate (k0, k, n, phi, hsubst) s s' =     do       let perm = updatePerm s s' (strandids k)-      orderings' <- normalizeOrderings (permuteOrderings perm (orderings k))+      orderings' <- normalizeOrderings validate+                    (permuteOrderings perm (orderings k))       let k' =               newPreskel               (gen k)@@ -918,9 +922,9 @@           if j > old then j - 1 else j  -- Eliminates implied intrastrand orderings and fails if it finds a--- reverse intrastrand ordering.-normalizeOrderings :: [Pair] -> [[Pair]]-normalizeOrderings orderings =+-- reverse intrastrand ordering when flag is true.+normalizeOrderings :: Bool -> [Pair] -> [[Pair]]+normalizeOrderings True orderings =     loop [] orderings     where       loop acc [] = [acc]@@ -928,6 +932,8 @@           | s0 /= s1 = loop (p : acc) ps           | p0 < p1 = loop acc ps           | otherwise = []+normalizeOrderings False orderings =+    [filter (\ ((s0, _), (s1, _)) -> s0 /= s1) orderings]  updateProb :: [Sid] -> [Sid] -> [Sid] updateProb mapping prob =@@ -957,8 +963,8 @@ hullByCompressing prune prs s s' =     do       (s'', s''', subst) <- unifyStrands (skel prs) s s'-      prs <- ksubst prs False subst-      prs' <- compress prs s'' s'''+      prs <- ksubst False prs subst+      prs' <- compress True prs s'' s'''       hull prune prs'  -- See if two strands unify.  They can be of differing heights.  The@@ -997,7 +1003,7 @@ hullByDeOrigination  prune prs u (s, p) (s', p') =     do       subst <- deOrig (skel prs) u (s, p) ++ deOrig (skel prs) u (s', p')-      prs <- ksubst prs False subst+      prs <- ksubst False prs subst       hull prune prs  deOrig :: Algebra t p g s e c => Preskel t p g s e c -> t -> Node -> [(g, s)]@@ -1043,7 +1049,9 @@  maybePrune :: Algebra t p g s e c => Bool -> PRS t p g s e c ->               [PRS t p g s e c]-maybePrune True prs = prune prs+maybePrune True prs+  | useThinning = thin prs+  | otherwise = prune prs maybePrune False prs = reduce prs  origNode :: Algebra t p g s e c => Preskel t p g s e c ->@@ -1138,8 +1146,8 @@       case not usePruningUnboundCheck || unboundCheck k s s' env' of         True -> return ()         False -> fail ""-      prs <- ksubst prs True (gen', substitution env')-      compress prs s s'+      prs <- ksubst True prs (gen', substitution env')+      compress True prs s s'  matchTraces :: Algebra t p g s e c => Trace t p g s e c ->                Trace t p g s e c -> (g, e) -> [(g, e)]@@ -1205,6 +1213,58 @@           | otherwise =               loop (addIvars xs i) is (s'' + 1) +-- Thinning++thin :: Algebra t p g s e c => PRS t p g s e c -> [PRS t p g s e c]+thin prs =+    thinStrands prs $ reverse ss+    where                       -- Remove strands in image of POV+      ss = filter (\s -> notElem s (prob $ skel prs)) (strandids $ skel prs)+++thinStrands :: Algebra t p g s e c => PRS t p g s e c ->+               [Sid] -> [PRS t p g s e c]+thinStrands prs [] =+  reduce prs+thinStrands prs (s:ss) =+  thinStrandPairs prs s ss ss++thinStrandPairs :: Algebra t p g s e c => PRS t p g s e c ->+                   Sid -> [Sid] -> [Sid] -> [PRS t p g s e c]+thinStrandPairs prs _ ss [] =+  thinStrands prs ss+thinStrandPairs prs s ss (s':ss') =+  case thinStrand prs s s' of+    [] -> thinStrandPairs prs s ss ss' -- Try next pair+    prss ->                           -- Success+      do+        prs <- prss+        thin prs++thinStrand :: Algebra t p g s e c => PRS t p g s e c ->+              Sid -> Sid -> [PRS t p g s e c]+thinStrand prs s s' =+  do+    let k = skel prs+    let i = strandInst k s+    let i' = strandInst k s'+    case height i /= height i' of+      True -> fail ""+      False -> return ()+    env <- matchTraces (trace i) (trace i') (gen k, emptyEnv)+    (gen', env') <- idempotentEnvFor env+                    (concatMap (tterms . trace) $ deleteNth s $ insts k)+    case matchRenaming (gen', env') of+      True -> return ()+      False -> fail ""+    case origCheck k env' of+      True -> return ()+      False -> fail ""+    [ prs' | prs <- ksubst False prs (gen', substitution env'),+             prs' <- compress False prs s s',+             prs'' <- compress False prs s' s,+             gist (skel prs') == gist (skel prs'')]+ -- Transitive Reduction  -- An edge is essential if its removal eliminates all paths from its@@ -1274,8 +1334,8 @@             Cause t p g s e c -> (g, s) -> [Ans t p g s e c] contract k n cause subst =     do-      prs <- ksubst (k, k { operation = Contracted emptySubst cause },-                     n, strandids k, emptySubst) False subst+      prs <- ksubst False (k, k { operation = Contracted emptySubst cause },+                           n, strandids k, emptySubst) subst       prs' <- hull usePruningWhileSolving prs       homomorphismFilter prs' @@ -1324,8 +1384,8 @@ substAndAugment k n cause role subst inst =     do       let operation' = AddedStrand (rname role) (height inst) cause-      prs <- ksubst (k, k { operation = operation' }, n,-                     strandids k, emptySubst) False subst+      prs <- ksubst False (k, k { operation = operation' }, n,+                           strandids k, emptySubst) subst       aug prs inst  -- Apply the augmentation operator by adding an instance and one@@ -1375,8 +1435,8 @@     do       (s, s', subst) <- unifyStrands k s s'       let op = addedToDisplaced (operation k) s s'-      prs <- ksubst (k0, k { operation = op}, n, phi, hsubst) False subst-      prs <- compress prs s s'+      prs <- ksubst False (k0, k { operation = op}, n, phi, hsubst) subst+      prs <- compress True prs s s'       hull usePruningWhileSolving prs  addedToDisplaced :: Algebra t p g s e c => Operation t p g s e c ->@@ -1783,8 +1843,8 @@ collapseStrands k s s' =     do       (s, s', subst) <- unifyStrands k s s'-      prs <- ksubst (k, k { operation = Collapsed s s' },-                     (0, 0), strandids k, emptySubst) False subst-      prs <- compress prs s s'+      prs <- ksubst False (k, k { operation = Collapsed s s' },+                           (0, 0), strandids k, emptySubst) subst+      prs <- compress True prs s s'       prs <- hull usePruningDuringCollapsing prs       return $ skel prs
src/CPSA/SimpleDiffieHellman/Algebra.hs view
@@ -72,6 +72,7 @@ -- Operations: --   cat : mesg X mesg -> mesg               Pairing --   enc : mesg X mesg -> mesg               Encryption+--   hash : mesg X mesg -> mesg              Hashing --   string : mesg                           Tag constants --   ltk : name X name -> skey               Long term shared key --   pubk : name -> akey                     Public key of principal@@ -92,6 +93,7 @@ -- Operations: --   cat : mesg X mesg -> mesg               Pairing --   enc : mesg X mesg -> mesg               Encryption+--   hash : mesg -> mesg                     Hashing --   string : mesg                           Tag constants --   ltk : name X name -> skey               Long term shared key --   pubk : name -> akey                     Public key of principal@@ -127,6 +129,7 @@     | Exp                       -- Exponentiation function symbol     | Cat                       -- Term concatenation (Pairing really)     | Enc                       -- Encryption+    | Hash                      -- Hashing       deriving (Show, Eq, Ord, Enum, Bounded)  -- A Basic Crypto Algebra Term@@ -242,7 +245,7 @@ -- sorted terms, K is for asymmetric keys, E is for the base of an -- exponent. -----     T ::= I | C | B | cat(T, T) | enc(T, T)+--     T ::= I | C | B | cat(T, T) | enc(T, T) | hash(T) -- --     B ::= text(I) | data(I) | name(I) | skey(I) --        |  skey(I) | skey(ltk(I, I)) | akey(K) | base(E) | expn(I)@@ -292,6 +295,8 @@     doubleTermWellFormed xts t0 t1  -- Concatenation termWellFormed xts (F Enc [t0, t1]) =     doubleTermWellFormed xts t0 t1  -- Encryption+termWellFormed xts (F Hash [t])     =+    termWellFormed xts t            -- Hashing termWellFormed _ _ = Nothing  -- Extend when sorts agree@@ -348,6 +353,8 @@     foldVars f (foldVars f acc t0) t1 foldVars f acc (F Enc [t0, t1]) = -- Encryption     foldVars f (foldVars f acc t0) t1+foldVars f acc (F Hash [t])     = -- Hashing+    foldVars f acc t foldVars _ _ t = error $ "Algebra.foldVars: Bad term " ++ show t  -- Fold f through a term applying it to each term that is held by the@@ -403,6 +410,8 @@       ba (C _) = True           -- So is a tag       ba (F Cat [t0, t1]) =           ba t0 && ba t1+      ba t@(F Hash [t1]) =+          S.member t knowns || ba t1       ba t@(F Enc [t0, t1]) =           S.member t knowns || ba t0 && ba t1       ba t@(F Base [t0]) =@@ -434,6 +443,8 @@           | buildable knowns unguessable (inv t1) = -- Add plaintext               loop unguessable (decat t0 knowns) old todo           | otherwise = loop unguessable knowns old todo+      loop unguessable knowns old ((F Hash [_]) : todo) =+          loop unguessable knowns old todo -- Hash can't be decomposed       loop unguessable knowns old ((F Base [F Exp [_, _]]) : todo) =           loop unguessable knowns old todo       loop unguessable knowns old (t : todo) =@@ -450,7 +461,9 @@ inv t = t  -- Extracts every encryption that is carried by a term along with its--- encryption key.  (This needs more work.)+-- encryption key.  Note that a hash is treated as a kind of+-- encryption in which the term that is hashed is the encryption key.+-- (This needs more work.) encryptions :: Term -> [(Term, Term)] encryptions t =     reverse $ loop t []@@ -459,6 +472,8 @@           loop t' (loop t acc)       loop t@(F Enc [t', t'']) acc =           loop t' (adjoin (t, t'') acc)+      loop t@(F Hash [t']) acc =+          adjoin (t, t') acc       loop t@(F Base [F Exp [F Exp [t', t''], t''']]) acc =           adjoin (e, F Expn [t'']) (adjoin (t, F Expn [t''']) acc)           where@@ -522,6 +537,8 @@     comb (outFlow t1) (outFlow t0) a outFlow (F Enc [t0, t1]) a =     comb (outFlow t1) (outFlow t0) a+outFlow (F Hash [t]) a =+    outFlow t a outFlow (F Base [F Exp [t0, t1]]) a =     comb (outFlow (F Base [t0])) (outFlow (F Expn [t1])) a outFlow t (initial, available) = -- Don't look inside atoms@@ -536,13 +553,15 @@          (comb (inFlow t1) (inFlow t0) a)          (comb (inFlow t0) (inFlow t1) a) inFlow t@(F Enc [t0, t1]) (initial, available) =-    S.union                     -- Encryption can be built-         (outFlow t (initial, available)) -- or decrypted-         (comb (inFlow t0) (outFlow (inv t1)) a)+    S.union+         (outFlow t (initial, available)) -- Encryption can be built+         (comb (inFlow t0) (outFlow (inv t1)) a) -- or decrypted     where                       -- Derive decryption key first       a = (initial, S.insert t available) inFlow t@(F Base [F Exp [_, _]]) a =     outFlow t a                 -- Can be built+inFlow (F Hash [t0]) (initial, available) =+    outFlow t0 (initial, available) inFlow t (initial, available) =     S.singleton (initial, S.insert t available) @@ -609,9 +628,9 @@       f paths path source           | target == source = Place (reverse path) : paths       f paths path (F Cat [t, t']) =-	  f (f paths  (0 : path) t) (1 : path) t'+          f (f paths  (0 : path) t) (1 : path) t'       f paths path (F Enc [t, _]) =-	  f paths (0 : path) t+          f paths (0 : path) t       f paths path (F Base [t]) =           exp paths (0 : path) t           where@@ -1056,6 +1075,7 @@     ,("exp", loadExp)     ,("cat", loadCat)     ,("enc", loadEnc)+    ,("hash", loadHash)     ]  -- Atom constructors: pubk privk invk ltk@@ -1153,6 +1173,13 @@       loop z x [] = (reverse z, x)       loop z x (y : ys) = loop (x : z) y ys +loadHash :: Monad m => LoadFunction m+loadHash _ vars (l : ls) =+   do+     ts <- mapM (loadTerm vars) (l : ls)+     return $ F Hash [foldr1 (\a b -> F Cat [a, b]) ts]+loadHash pos _ _ = fail (shows pos "Malformed hash")+ -- Term specific displaying functions  newtype Context = Context [(Id, String)] deriving Show@@ -1227,6 +1254,8 @@     L () (S () "cat" : displayTerm ctx t0 : displayList ctx t1) displayTerm ctx (F Enc [t0, t1]) =     L () (S () "enc" : displayEnc ctx t0 t1)+displayTerm ctx (F Hash [t]) =+    L () (S () "hash" : displayList ctx t) displayTerm _ t = error ("Algebra.displayTerm: Bad term " ++ show t)  displayList :: Context -> Term -> [SExpr ()]
src/cpsa.pl view
@@ -84,6 +84,12 @@ 	sexpr:sexpr_to_pretty(Sexpr, Pretty), 	sexprs_to_cpsa_pretty(Sexprs, Pretties). +%% Programmer's hint--test translations with the query:+%%   cpsa:cpsa('../tst/blanchet.scm',A),+%%   cpsa:cpsas_to_sexprs(A, B),+%%   current_output(Out),+%%   cpsa:cpsa_sexprs_pp(Out, B).+ %% Translate between S-expressions and an internal form.  %% Currently, you have to read the code or look at output to@@ -111,8 +117,10 @@ 	sexpr_to_strands(Rest, Strands, Alist), 	lookup(precedes, Alist, Values), 	edges(Values, Precedes),-	lookup('non-orig', Alist, Nons),-	lookup('uniq-orig', Alist, Uniqs).+	lookup('non-orig', Alist, Snons),+	sexprs_to_terms(Snons, Nons),+	lookup('uniq-orig', Alist, Suniqs),+	sexprs_to_terms(Suniqs, Uniqs).  sexpr_to_roles([[defrole|Sexpr]|Rest], [Role|Roles]) :- 	!,@@ -120,12 +128,55 @@ 	sexpr_to_roles(Rest, Roles). sexpr_to_roles(_, []). -sexpr_to_role([Name, [vars|Vars], [trace|Trace]|Alist],+sexpr_to_role([Name, [vars|Vars], [trace|Strace]|Alist], 	r(Name, Decls, Trace, Nons, Uniqs)) :- 	decls(Vars, Decls),-	lookup('non-orig', Alist, Nons),-	lookup('uniq-orig', Alist, Uniqs).+	sexprs_to_trace(Strace, Trace),+	lookup('non-orig', Alist, Snons),+	sexprs_to_terms(Snons, Nons),+	lookup('uniq-orig', Alist, Suniqs),+	sexprs_to_terms(Suniqs, Uniqs). +sexprs_to_trace([], []).+sexprs_to_trace([[send, Sexpr]|Strace], [send(Term)|Trace]) :-+	sexpr_to_term(Sexpr, Term),+	sexprs_to_trace(Strace, Trace).+sexprs_to_trace([[recv, Sexpr]|Strace], [recv(Term)|Trace]) :-+	sexpr_to_term(Sexpr, Term),+	sexprs_to_trace(Strace, Trace).++sexprs_to_terms([], []).+sexprs_to_terms([Sterm|Sterms], [Term|Terms]) :-+	sexpr_to_term(Sterm, Term),+	sexprs_to_terms(Sterms, Terms).++sexpr_to_term(Term, Term) :-+	atom(Term).+sexpr_to_term(Term, Term) :-+	string(Term).+sexpr_to_term([cat, Sterm], Term) :-+	sexpr_to_term(Sterm, Term).+sexpr_to_term([cat, Sterm1, Sterm2|Sterms], cat(Term1, Term)) :-+	sexpr_to_term(Sterm1, Term1),+	sexpr_to_term([cat, Sterm2|Sterms], Term).+sexpr_to_term([hash|Sterms], hash(Term)) :-+	sexpr_to_term([cat|Sterms], Term).+sexpr_to_term([enc|Sterms], enc(Term, Key)) :-+	split(Sterms, Cats, Sexpr),+	sexpr_to_term(Sexpr, Key),+	sexpr_to_term([cat|Cats], Term).+sexpr_to_term([Fun|Sterms], Term) :-+	atom(Fun),+	Fun \= cat,+	Fun \= hash,+	Fun \= enc,+	sexprs_to_terms(Sterms, Terms),+	Term =.. [Fun|Terms].++split([X, Y], [X], Y).+split([X, Y|Z], [X|U], V) :-+	split([Y|Z], U, V).+ sexpr_to_strands([[defstrand|Sexpr]|Rest], [Strand|Strands], Alist) :- 	!, 	sexpr_to_strand([defstrand|Sexpr], Strand),@@ -139,8 +190,9 @@ sexpr_to_strand([defstrand, Role, Height|Sexprs], s(Role, Height, Map)) :- 	atom(Role), 	integer(Height),-	maplets(Sexprs, Map).-sexpr_to_strand([deflistener, Term], l(Term)).+	sexprs_to_map(Sexprs, Map).+sexpr_to_strand([deflistener, Sexpr], l(Term)) :-+	sexpr_to_term(Sexpr, Term).  decls([], []). decls([Sexpr|Sexprs], [Decl|Decls]) :-@@ -157,9 +209,10 @@ 	atom(Var), 	decl_vars(Decl, Type, Vars). -maplets([], []).-maplets([[Key, Value]|Sexprs], [[Key|Value]|Map]) :--	maplets(Sexprs, Map).+sexprs_to_map([], []).+sexprs_to_map([[Key, Svalue]|Sexprs], [[Key|Value]|Map]) :-+	sexpr_to_term(Svalue, Value),+	sexprs_to_map(Sexprs, Map).  lookup(_, [], []). lookup(Key, [[Key|Value]|Alist], Values) :-@@ -208,24 +261,77 @@  strands_to_sexprs([], Alist, Alist). strands_to_sexprs([Strand|Strands], Alist, [Sexpr|Sexprs]) :--	sexpr_to_strand(Sexpr, Strand),+	strand_to_sexpr(Strand, Sexpr), 	strands_to_sexprs(Strands, Alist, Sexprs). +strand_to_sexpr(s(Role, Height, Map), [defstrand, Role, Height|Sexprs]) :-+	map_to_sexprs(Map, Sexprs).+strand_to_sexpr(l(Term), [deflistener, Sexpr]) :-+	term_to_sexpr(Term, Sexpr).++map_to_sexprs([], []).+map_to_sexprs([[Key|Value]|Map], [[Key, Svalue]|Sexprs]) :-+	term_to_sexpr(Value, Svalue),+	map_to_sexprs(Map, Sexprs).+ roles_to_sexprs([], []). roles_to_sexprs([Role|Roles], [Sexpr|Sexprs]) :- 	role_to_sexpr(Role, Sexpr), 	roles_to_sexprs(Roles, Sexprs).  role_to_sexpr(r(Name, Decls, Trace, Nons, Uniqs),-	[defrole, Name, [vars|Vars], [trace|Trace]|Alist]) :-+	[defrole, Name, [vars|Vars], [trace|Strace]|Alist]) :- 	decls(Vars, Decls),+	traces_to_sexprs(Trace, Strace), 	origs(Nons, Uniqs, Alist). +traces_to_sexprs([], []).+traces_to_sexprs([send(Term)|Trace], [[send, Sterm]|Straces]) :-+	term_to_sexpr(Term, Sterm),+	traces_to_sexprs(Trace, Straces).+traces_to_sexprs([recv(Term)|Trace], [[recv, Sterm]|Straces]) :-+	term_to_sexpr(Term, Sterm),+	traces_to_sexprs(Trace, Straces).+ origs([], Uniqs, Alist) :- 	!, 	uniq_origs(Uniqs, Alist).-origs(Nons, Uniqs, [['non-orig'|Nons]|Alist]) :-+origs(Nons, Uniqs, [['non-orig'|Snons]|Alist]) :-+	terms_to_sexprs(Nons, Snons), 	uniq_origs(Uniqs, Alist).  uniq_origs([], []) :- !.-uniq_origs(Uniqs, [['uniq-orig'|Uniqs]]).+uniq_origs(Uniqs, [['uniq-orig'|Suniqs]]) :-+	terms_to_sexprs(Uniqs, Suniqs).++terms_to_sexprs([], []).+terms_to_sexprs([Term|Terms], [Sexpr|Sexprs]) :-+	term_to_sexpr(Term, Sexpr),+	terms_to_sexprs(Terms, Sexprs).++term_to_sexpr(Term, Term) :-+	atom(Term).+term_to_sexpr(Term, Term) :-+	string(Term).+term_to_sexpr(cat(Term1, Term2), [cat, Sterm1|Sterms]) :-+	term_to_sexpr(Term1, Sterm1),+	term_to_sexprs(Term2, Sterms).+term_to_sexpr(hash(Term), [hash|Sterms]) :-+	term_to_sexprs(Term, Sterms).+term_to_sexpr(enc(Term, Key), [enc|All]) :-+	term_to_sexpr(Key, Sexpr),+	term_to_sexprs(Term, Sterms),+	split(All, Sterms, Sexpr).+term_to_sexpr(Term, [Fun|Sterms]) :-+	Term =.. [Fun|Args],+	Fun \= cat,+	Fun \= hash,+	Fun \= enc,+	terms_to_sexprs(Args, Sterms).++term_to_sexprs(cat(Term1, Term2), [Sterm1|Sterms]) :-+	!,+	term_to_sexpr(Term1, Sterm1),+	term_to_sexprs(Term2, Sterms).+term_to_sexprs(Term, [Sterm]) :-+	term_to_sexpr(Term, Sterm).
tst/blanchet.scm view
@@ -3,52 +3,86 @@  (defprotocol blanchet basic   (defrole init-    (vars (a b name) (s skey) (d text))+    (vars (a b name) (s skey) (d data))     (trace      (send (enc (enc s (privk a)) (pubk b)))      (recv (enc d s))))   (defrole resp-    (vars (a b name) (s skey) (d text))+    (vars (a b name) (s skey) (d data))     (trace      (recv (enc (enc s (privk a)) (pubk b)))-     (send (enc d s)))))+     (send (enc d s))))+  (comment "Blanchet's protocol using named asymmetric keys"))  (defskeleton blanchet-  (vars (a b name) (s skey) (d text))+  (vars (a b name) (s skey) (d data))   (defstrand init 2 (a a) (b b) (s s) (d d))-  (non-orig (privk a) (privk b))-  (uniq-orig s))+  (non-orig (privk b))+  (uniq-orig s)+  (comment "Analyze from the initiator's perspective"))  (defskeleton blanchet-  (vars (a b name) (s skey) (d text))+  (vars (a b name) (s skey) (d data))   (defstrand init 2 (a a) (b b) (s s) (d d))   (deflistener d)-  (non-orig (privk a) (privk b))-  (uniq-orig s d))+  (non-orig (privk b))+  (uniq-orig s d)+  (comment "From the initiator's perspective, is the secret leaked?"))  (defskeleton blanchet-  (vars (a b name) (s skey) (d text))+  (vars (a b name) (s skey) (d data))   (defstrand resp 2 (a a) (b b) (s s) (d d))   (non-orig (privk a) (privk b))-  (uniq-orig s))+  (uniq-orig s)+  (comment "Analyze from the responder's perspective"))  (defskeleton blanchet-  (vars (a b name) (s skey) (d text))+  (vars (a b name) (s skey) (d data))   (defstrand resp 2 (a a) (b b) (s s) (d d))   (deflistener d)   (non-orig (privk a) (privk b))-  (uniq-orig s d))+  (uniq-orig s d)+  (comment "From the responders's perspective, is the secret leaked?")) -(defskeleton blanchet-  (vars (a b name) (s skey) (d text))-  (defstrand resp 2 (a a) (b b) (s s) (d d))-  (deflistener d)-  (non-orig (privk a))-  (uniq-orig s d))+(defprotocol blanchet-akey basic+  (defrole init+    (vars (a b akey) (s skey) (d data))+    (trace+     (send (enc (enc s (invk a)) b))+     (recv (enc d s))))+  (defrole resp+    (vars (a b akey) (s skey) (d data))+    (trace+     (recv (enc (enc s (invk a)) b))+     (send (enc d s))))+  (comment "Blanchet's protocol using unnamed asymmetric keys")) -(defskeleton blanchet-  (vars (a b name) (s skey) (d text))+(defskeleton blanchet-akey+  (vars (a b akey) (s skey) (d data))   (defstrand init 2 (a a) (b b) (s s) (d d))+  (non-orig (invk b))+  (uniq-orig s)+  (comment "Analyze from the initiator's perspective"))++(defskeleton blanchet-akey+  (vars (a b akey) (s skey) (d data))+  (defstrand init 2 (a a) (b b) (s s) (d d))   (deflistener d)-  (non-orig (privk b))-  (uniq-orig s d))+  (non-orig (invk b))+  (uniq-orig s d)+  (comment "From the initiator's perspective, is the secret leaked?"))++(defskeleton blanchet-akey+  (vars (a b akey) (s skey) (d data))+  (defstrand resp 2 (a a) (b b) (s s) (d d))+  (non-orig (invk a) (invk b))+  (uniq-orig s)+  (comment "Analyze from the responder's perspective"))++(defskeleton blanchet-akey+  (vars (a b akey) (s skey) (d data))+  (defstrand resp 2 (a a) (b b) (s s) (d d))+  (deflistener d)+  (non-orig (invk a) (invk b))+  (uniq-orig s d)+  (comment "From the responders's perspective, is the secret leaked?"))
tst/blanchet.tst view
@@ -1,22 +1,24 @@ (herald "Blanchet's Simple Example Protocol"   (comment "There is a flaw in this protocol by design")) -(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol blanchet basic   (defrole init-    (vars (a b name) (s skey) (d text))+    (vars (a b name) (s skey) (d data))     (trace (send (enc (enc s (privk a)) (pubk b))) (recv (enc d s))))   (defrole resp-    (vars (a b name) (s skey) (d text))-    (trace (recv (enc (enc s (privk a)) (pubk b))) (send (enc d s)))))+    (vars (a b name) (s skey) (d data))+    (trace (recv (enc (enc s (privk a)) (pubk b))) (send (enc d s))))+  (comment "Blanchet's protocol using named asymmetric keys"))  (defskeleton blanchet-  (vars (d text) (a b name) (s skey))+  (vars (d data) (a b name) (s skey))   (defstrand init 2 (d d) (a a) (b b) (s s))-  (non-orig (privk a) (privk b))+  (non-orig (privk b))   (uniq-orig s)+  (comment "Analyze from the initiator's perspective")   (traces ((send (enc (enc s (privk a)) (pubk b))) (recv (enc d s))))   (label 0)   (unrealized (0 1))@@ -24,11 +26,11 @@   (comment "2 in cohort - 2 not yet seen"))  (defskeleton blanchet-  (vars (d text) (a b a-0 b-0 name) (s skey))+  (vars (d data) (a b a-0 b-0 name) (s skey))   (defstrand init 2 (d d) (a a) (b b) (s s))   (defstrand resp 2 (d d) (a a-0) (b b-0) (s s))   (precedes ((0 0) (1 0)) ((1 1) (0 1)))-  (non-orig (privk a) (privk b))+  (non-orig (privk b))   (uniq-orig s)   (operation encryption-test (added-strand resp 2) (enc d s) (0 1))   (traces ((send (enc (enc s (privk a)) (pubk b))) (recv (enc d s)))@@ -39,11 +41,11 @@   (comment "1 in cohort - 1 not yet seen"))  (defskeleton blanchet-  (vars (d text) (a b name) (s skey))+  (vars (d data) (a b name) (s skey))   (defstrand init 2 (d d) (a a) (b b) (s s))   (deflistener s)   (precedes ((0 0) (1 0)) ((1 1) (0 1)))-  (non-orig (privk a) (privk b))+  (non-orig (privk b))   (uniq-orig s)   (operation encryption-test (added-listener s) (enc d s) (0 1))   (traces ((send (enc (enc s (privk a)) (pubk b))) (recv (enc d s)))@@ -54,11 +56,11 @@   (comment "empty cohort"))  (defskeleton blanchet-  (vars (d text) (a b name) (s skey))+  (vars (d data) (a b name) (s skey))   (defstrand init 2 (d d) (a a) (b b) (s s))   (defstrand resp 2 (d d) (a a) (b b) (s s))   (precedes ((0 0) (1 0)) ((1 1) (0 1)))-  (non-orig (privk a) (privk b))+  (non-orig (privk b))   (uniq-orig s)   (operation nonce-test (contracted (a-0 a) (b-0 b)) s (1 0)     (enc (enc s (privk a)) (pubk b)))@@ -75,18 +77,20 @@  (defprotocol blanchet basic   (defrole init-    (vars (a b name) (s skey) (d text))+    (vars (a b name) (s skey) (d data))     (trace (send (enc (enc s (privk a)) (pubk b))) (recv (enc d s))))   (defrole resp-    (vars (a b name) (s skey) (d text))-    (trace (recv (enc (enc s (privk a)) (pubk b))) (send (enc d s)))))+    (vars (a b name) (s skey) (d data))+    (trace (recv (enc (enc s (privk a)) (pubk b))) (send (enc d s))))+  (comment "Blanchet's protocol using named asymmetric keys"))  (defskeleton blanchet-  (vars (d text) (a b name) (s skey))+  (vars (d data) (a b name) (s skey))   (defstrand init 2 (d d) (a a) (b b) (s s))   (deflistener d)-  (non-orig (privk a) (privk b))+  (non-orig (privk b))   (uniq-orig d s)+  (comment "From the initiator's perspective, is the secret leaked?")   (traces ((send (enc (enc s (privk a)) (pubk b))) (recv (enc d s)))     ((recv d) (send d)))   (label 4)@@ -95,12 +99,12 @@   (comment "2 in cohort - 2 not yet seen"))  (defskeleton blanchet-  (vars (d text) (a b a-0 b-0 name) (s skey))+  (vars (d data) (a b a-0 b-0 name) (s skey))   (defstrand init 2 (d d) (a a) (b b) (s s))   (deflistener d)   (defstrand resp 2 (d d) (a a-0) (b b-0) (s s))   (precedes ((0 0) (2 0)) ((2 1) (0 1)) ((2 1) (1 0)))-  (non-orig (privk a) (privk b))+  (non-orig (privk b))   (uniq-orig d s)   (operation encryption-test (added-strand resp 2) (enc d s) (0 1))   (traces ((send (enc (enc s (privk a)) (pubk b))) (recv (enc d s)))@@ -112,12 +116,12 @@   (comment "1 in cohort - 1 not yet seen"))  (defskeleton blanchet-  (vars (d text) (a b name) (s skey))+  (vars (d data) (a b name) (s skey))   (defstrand init 2 (d d) (a a) (b b) (s s))   (deflistener d)   (deflistener s)   (precedes ((0 0) (2 0)) ((2 1) (0 1)))-  (non-orig (privk a) (privk b))+  (non-orig (privk b))   (uniq-orig d s)   (operation encryption-test (added-listener s) (enc d s) (0 1))   (traces ((send (enc (enc s (privk a)) (pubk b))) (recv (enc d s)))@@ -128,12 +132,12 @@   (comment "empty cohort"))  (defskeleton blanchet-  (vars (d text) (a b name) (s skey))+  (vars (d data) (a b name) (s skey))   (defstrand init 2 (d d) (a a) (b b) (s s))   (deflistener d)   (defstrand resp 2 (d d) (a a) (b b) (s s))   (precedes ((0 0) (2 0)) ((2 1) (0 1)) ((2 1) (1 0)))-  (non-orig (privk a) (privk b))+  (non-orig (privk b))   (uniq-orig d s)   (operation nonce-test (contracted (a-0 a) (b-0 b)) s (2 0)     (enc (enc s (privk a)) (pubk b)))@@ -146,14 +150,14 @@   (comment "1 in cohort - 1 not yet seen"))  (defskeleton blanchet-  (vars (d text) (a b name) (s skey))+  (vars (d data) (a b name) (s skey))   (defstrand init 2 (d d) (a a) (b b) (s s))   (deflistener d)   (defstrand resp 2 (d d) (a a) (b b) (s s))   (deflistener s)   (precedes ((0 0) (2 0)) ((0 0) (3 0)) ((2 1) (0 1)) ((2 1) (1 0))     ((3 1) (1 0)))-  (non-orig (privk a) (privk b))+  (non-orig (privk b))   (uniq-orig d s)   (operation nonce-test (added-listener s) d (1 0) (enc d s))   (traces ((send (enc (enc s (privk a)) (pubk b))) (recv (enc d s)))@@ -169,17 +173,19 @@  (defprotocol blanchet basic   (defrole init-    (vars (a b name) (s skey) (d text))+    (vars (a b name) (s skey) (d data))     (trace (send (enc (enc s (privk a)) (pubk b))) (recv (enc d s))))   (defrole resp-    (vars (a b name) (s skey) (d text))-    (trace (recv (enc (enc s (privk a)) (pubk b))) (send (enc d s)))))+    (vars (a b name) (s skey) (d data))+    (trace (recv (enc (enc s (privk a)) (pubk b))) (send (enc d s))))+  (comment "Blanchet's protocol using named asymmetric keys"))  (defskeleton blanchet-  (vars (d text) (a b name) (s skey))+  (vars (d data) (a b name) (s skey))   (defstrand resp 2 (d d) (a a) (b b) (s s))   (non-orig (privk a) (privk b))   (uniq-orig s)+  (comment "Analyze from the responder's perspective")   (traces ((recv (enc (enc s (privk a)) (pubk b))) (send (enc d s))))   (label 9)   (unrealized (0 0))@@ -187,7 +193,7 @@   (comment "1 in cohort - 1 not yet seen"))  (defskeleton blanchet-  (vars (d text) (a b b-0 name) (s skey))+  (vars (d data) (a b b-0 name) (s skey))   (defstrand resp 2 (d d) (a a) (b b) (s s))   (defstrand init 1 (a a) (b b-0) (s s))   (precedes ((1 0) (0 0)))@@ -208,18 +214,20 @@  (defprotocol blanchet basic   (defrole init-    (vars (a b name) (s skey) (d text))+    (vars (a b name) (s skey) (d data))     (trace (send (enc (enc s (privk a)) (pubk b))) (recv (enc d s))))   (defrole resp-    (vars (a b name) (s skey) (d text))-    (trace (recv (enc (enc s (privk a)) (pubk b))) (send (enc d s)))))+    (vars (a b name) (s skey) (d data))+    (trace (recv (enc (enc s (privk a)) (pubk b))) (send (enc d s))))+  (comment "Blanchet's protocol using named asymmetric keys"))  (defskeleton blanchet-  (vars (d text) (a b name) (s skey))+  (vars (d data) (a b name) (s skey))   (defstrand resp 2 (d d) (a a) (b b) (s s))   (deflistener d)   (non-orig (privk a) (privk b))   (uniq-orig d s)+  (comment "From the responders's perspective, is the secret leaked?")   (traces ((recv (enc (enc s (privk a)) (pubk b))) (send (enc d s)))     ((recv d) (send d)))   (label 11)@@ -228,7 +236,7 @@   (comment "Not a skeleton"))  (defskeleton blanchet-  (vars (d text) (a b name) (s skey))+  (vars (d data) (a b name) (s skey))   (defstrand resp 2 (d d) (a a) (b b) (s s))   (deflistener d)   (precedes ((0 1) (1 0)))@@ -243,7 +251,7 @@   (comment "1 in cohort - 1 not yet seen"))  (defskeleton blanchet-  (vars (d text) (a b b-0 name) (s skey))+  (vars (d data) (a b b-0 name) (s skey))   (defstrand resp 2 (d d) (a a) (b b) (s s))   (deflistener d)   (defstrand init 1 (a a) (b b-0) (s s))@@ -263,153 +271,269 @@  (comment "Nothing left to do") -(defprotocol blanchet basic+(defprotocol blanchet-akey basic   (defrole init-    (vars (a b name) (s skey) (d text))-    (trace (send (enc (enc s (privk a)) (pubk b))) (recv (enc d s))))+    (vars (a b akey) (s skey) (d data))+    (trace (send (enc (enc s (invk a)) b)) (recv (enc d s))))   (defrole resp-    (vars (a b name) (s skey) (d text))-    (trace (recv (enc (enc s (privk a)) (pubk b))) (send (enc d s)))))+    (vars (a b akey) (s skey) (d data))+    (trace (recv (enc (enc s (invk a)) b)) (send (enc d s))))+  (comment "Blanchet's protocol using unnamed asymmetric keys")) -(defskeleton blanchet-  (vars (d text) (a b name) (s skey))-  (defstrand resp 2 (d d) (a a) (b b) (s s))-  (deflistener d)-  (non-orig (privk a))-  (uniq-orig d s)-  (traces ((recv (enc (enc s (privk a)) (pubk b))) (send (enc d s)))-    ((recv d) (send d)))+(defskeleton blanchet-akey+  (vars (d data) (s skey) (a b akey))+  (defstrand init 2 (d d) (s s) (a a) (b b))+  (non-orig (invk b))+  (uniq-orig s)+  (comment "Analyze from the initiator's perspective")+  (traces ((send (enc (enc s (invk a)) b)) (recv (enc d s))))   (label 14)-  (unrealized (0 0) (1 0))-  (preskeleton)-  (comment "Not a skeleton"))+  (unrealized (0 1))+  (origs (s (0 0)))+  (comment "2 in cohort - 2 not yet seen")) -(defskeleton blanchet-  (vars (d text) (a b name) (s skey))-  (defstrand resp 2 (d d) (a a) (b b) (s s))-  (deflistener d)-  (precedes ((0 1) (1 0)))-  (non-orig (privk a))-  (uniq-orig d s)-  (traces ((recv (enc (enc s (privk a)) (pubk b))) (send (enc d s)))-    ((recv d) (send d)))+(defskeleton blanchet-akey+  (vars (d data) (s skey) (a b a-0 b-0 akey))+  (defstrand init 2 (d d) (s s) (a a) (b b))+  (defstrand resp 2 (d d) (s s) (a a-0) (b b-0))+  (precedes ((0 0) (1 0)) ((1 1) (0 1)))+  (non-orig (invk b))+  (uniq-orig s)+  (operation encryption-test (added-strand resp 2) (enc d s) (0 1))+  (traces ((send (enc (enc s (invk a)) b)) (recv (enc d s)))+    ((recv (enc (enc s (invk a-0)) b-0)) (send (enc d s))))   (label 15)   (parent 14)-  (unrealized (0 0))-  (origs (d (0 1)))+  (unrealized (1 0))   (comment "1 in cohort - 1 not yet seen")) -(defskeleton blanchet-  (vars (d text) (a b b-0 name) (s skey))-  (defstrand resp 2 (d d) (a a) (b b) (s s))-  (deflistener d)-  (defstrand init 1 (a a) (b b-0) (s s))-  (precedes ((0 1) (1 0)) ((2 0) (0 0)))-  (non-orig (privk a))-  (uniq-orig d s)-  (operation encryption-test (added-strand init 1) (enc s (privk a))-    (0 0))-  (traces ((recv (enc (enc s (privk a)) (pubk b))) (send (enc d s)))-    ((recv d) (send d)) ((send (enc (enc s (privk a)) (pubk b-0)))))+(defskeleton blanchet-akey+  (vars (d data) (s skey) (a b akey))+  (defstrand init 2 (d d) (s s) (a a) (b b))+  (deflistener s)+  (precedes ((0 0) (1 0)) ((1 1) (0 1)))+  (non-orig (invk b))+  (uniq-orig s)+  (operation encryption-test (added-listener s) (enc d s) (0 1))+  (traces ((send (enc (enc s (invk a)) b)) (recv (enc d s)))+    ((recv s) (send s)))   (label 16)+  (parent 14)+  (unrealized (1 0))+  (comment "empty cohort"))++(defskeleton blanchet-akey+  (vars (d data) (s skey) (a b akey))+  (defstrand init 2 (d d) (s s) (a a) (b b))+  (defstrand resp 2 (d d) (s s) (a a) (b b))+  (precedes ((0 0) (1 0)) ((1 1) (0 1)))+  (non-orig (invk b))+  (uniq-orig s)+  (operation nonce-test (contracted (a-0 a) (b-0 b)) s (1 0)+    (enc (enc s (invk a)) b))+  (traces ((send (enc (enc s (invk a)) b)) (recv (enc d s)))+    ((recv (enc (enc s (invk a)) b)) (send (enc d s))))+  (label 17)   (parent 15)   (unrealized)   (shape)-  (maps ((0 1) ((a a) (b b) (s s) (d d))))-  (origs (s (2 0)) (d (0 1))))+  (maps ((0) ((a a) (b b) (s s) (d d))))+  (origs (s (0 0))))  (comment "Nothing left to do") -(defprotocol blanchet basic+(defprotocol blanchet-akey basic   (defrole init-    (vars (a b name) (s skey) (d text))-    (trace (send (enc (enc s (privk a)) (pubk b))) (recv (enc d s))))+    (vars (a b akey) (s skey) (d data))+    (trace (send (enc (enc s (invk a)) b)) (recv (enc d s))))   (defrole resp-    (vars (a b name) (s skey) (d text))-    (trace (recv (enc (enc s (privk a)) (pubk b))) (send (enc d s)))))+    (vars (a b akey) (s skey) (d data))+    (trace (recv (enc (enc s (invk a)) b)) (send (enc d s))))+  (comment "Blanchet's protocol using unnamed asymmetric keys")) -(defskeleton blanchet-  (vars (d text) (a b name) (s skey))-  (defstrand init 2 (d d) (a a) (b b) (s s))+(defskeleton blanchet-akey+  (vars (d data) (s skey) (a b akey))+  (defstrand init 2 (d d) (s s) (a a) (b b))   (deflistener d)-  (non-orig (privk b))+  (non-orig (invk b))   (uniq-orig d s)-  (traces ((send (enc (enc s (privk a)) (pubk b))) (recv (enc d s)))+  (comment "From the initiator's perspective, is the secret leaked?")+  (traces ((send (enc (enc s (invk a)) b)) (recv (enc d s)))     ((recv d) (send d)))-  (label 17)+  (label 18)   (unrealized (0 1))   (origs (s (0 0)))   (comment "2 in cohort - 2 not yet seen")) -(defskeleton blanchet-  (vars (d text) (a b a-0 b-0 name) (s skey))-  (defstrand init 2 (d d) (a a) (b b) (s s))+(defskeleton blanchet-akey+  (vars (d data) (s skey) (a b a-0 b-0 akey))+  (defstrand init 2 (d d) (s s) (a a) (b b))   (deflistener d)-  (defstrand resp 2 (d d) (a a-0) (b b-0) (s s))+  (defstrand resp 2 (d d) (s s) (a a-0) (b b-0))   (precedes ((0 0) (2 0)) ((2 1) (0 1)) ((2 1) (1 0)))-  (non-orig (privk b))+  (non-orig (invk b))   (uniq-orig d s)   (operation encryption-test (added-strand resp 2) (enc d s) (0 1))-  (traces ((send (enc (enc s (privk a)) (pubk b))) (recv (enc d s)))+  (traces ((send (enc (enc s (invk a)) b)) (recv (enc d s)))     ((recv d) (send d))-    ((recv (enc (enc s (privk a-0)) (pubk b-0))) (send (enc d s))))-  (label 18)-  (parent 17)+    ((recv (enc (enc s (invk a-0)) b-0)) (send (enc d s))))+  (label 19)+  (parent 18)   (unrealized (1 0) (2 0))   (comment "1 in cohort - 1 not yet seen")) -(defskeleton blanchet-  (vars (d text) (a b name) (s skey))-  (defstrand init 2 (d d) (a a) (b b) (s s))+(defskeleton blanchet-akey+  (vars (d data) (s skey) (a b akey))+  (defstrand init 2 (d d) (s s) (a a) (b b))   (deflistener d)   (deflistener s)   (precedes ((0 0) (2 0)) ((2 1) (0 1)))-  (non-orig (privk b))+  (non-orig (invk b))   (uniq-orig d s)   (operation encryption-test (added-listener s) (enc d s) (0 1))-  (traces ((send (enc (enc s (privk a)) (pubk b))) (recv (enc d s)))+  (traces ((send (enc (enc s (invk a)) b)) (recv (enc d s)))     ((recv d) (send d)) ((recv s) (send s)))-  (label 19)-  (parent 17)+  (label 20)+  (parent 18)   (unrealized (2 0))   (comment "empty cohort")) -(defskeleton blanchet-  (vars (d text) (a b name) (s skey))-  (defstrand init 2 (d d) (a a) (b b) (s s))+(defskeleton blanchet-akey+  (vars (d data) (s skey) (a b akey))+  (defstrand init 2 (d d) (s s) (a a) (b b))   (deflistener d)-  (defstrand resp 2 (d d) (a a) (b b) (s s))+  (defstrand resp 2 (d d) (s s) (a a) (b b))   (precedes ((0 0) (2 0)) ((2 1) (0 1)) ((2 1) (1 0)))-  (non-orig (privk b))+  (non-orig (invk b))   (uniq-orig d s)   (operation nonce-test (contracted (a-0 a) (b-0 b)) s (2 0)-    (enc (enc s (privk a)) (pubk b)))-  (traces ((send (enc (enc s (privk a)) (pubk b))) (recv (enc d s)))+    (enc (enc s (invk a)) b))+  (traces ((send (enc (enc s (invk a)) b)) (recv (enc d s)))     ((recv d) (send d))-    ((recv (enc (enc s (privk a)) (pubk b))) (send (enc d s))))-  (label 20)-  (parent 18)+    ((recv (enc (enc s (invk a)) b)) (send (enc d s))))+  (label 21)+  (parent 19)   (unrealized (1 0))   (comment "1 in cohort - 1 not yet seen")) -(defskeleton blanchet-  (vars (d text) (a b name) (s skey))-  (defstrand init 2 (d d) (a a) (b b) (s s))+(defskeleton blanchet-akey+  (vars (d data) (s skey) (a b akey))+  (defstrand init 2 (d d) (s s) (a a) (b b))   (deflistener d)-  (defstrand resp 2 (d d) (a a) (b b) (s s))+  (defstrand resp 2 (d d) (s s) (a a) (b b))   (deflistener s)   (precedes ((0 0) (2 0)) ((0 0) (3 0)) ((2 1) (0 1)) ((2 1) (1 0))     ((3 1) (1 0)))-  (non-orig (privk b))+  (non-orig (invk b))   (uniq-orig d s)   (operation nonce-test (added-listener s) d (1 0) (enc d s))-  (traces ((send (enc (enc s (privk a)) (pubk b))) (recv (enc d s)))+  (traces ((send (enc (enc s (invk a)) b)) (recv (enc d s)))     ((recv d) (send d))-    ((recv (enc (enc s (privk a)) (pubk b))) (send (enc d s)))+    ((recv (enc (enc s (invk a)) b)) (send (enc d s)))     ((recv s) (send s)))-  (label 21)-  (parent 20)+  (label 22)+  (parent 21)   (unrealized (3 0))   (comment "empty cohort"))++(comment "Nothing left to do")++(defprotocol blanchet-akey basic+  (defrole init+    (vars (a b akey) (s skey) (d data))+    (trace (send (enc (enc s (invk a)) b)) (recv (enc d s))))+  (defrole resp+    (vars (a b akey) (s skey) (d data))+    (trace (recv (enc (enc s (invk a)) b)) (send (enc d s))))+  (comment "Blanchet's protocol using unnamed asymmetric keys"))++(defskeleton blanchet-akey+  (vars (d data) (s skey) (a b akey))+  (defstrand resp 2 (d d) (s s) (a a) (b b))+  (non-orig (invk a) (invk b))+  (uniq-orig s)+  (comment "Analyze from the responder's perspective")+  (traces ((recv (enc (enc s (invk a)) b)) (send (enc d s))))+  (label 23)+  (unrealized (0 0))+  (origs)+  (comment "1 in cohort - 1 not yet seen"))++(defskeleton blanchet-akey+  (vars (d data) (s skey) (a b b-0 akey))+  (defstrand resp 2 (d d) (s s) (a a) (b b))+  (defstrand init 1 (s s) (a a) (b b-0))+  (precedes ((1 0) (0 0)))+  (non-orig (invk a) (invk b))+  (uniq-orig s)+  (operation encryption-test (added-strand init 1) (enc s (invk a))+    (0 0))+  (traces ((recv (enc (enc s (invk a)) b)) (send (enc d s)))+    ((send (enc (enc s (invk a)) b-0))))+  (label 24)+  (parent 23)+  (unrealized)+  (shape)+  (maps ((0) ((a a) (b b) (s s) (d d))))+  (origs (s (1 0))))++(comment "Nothing left to do")++(defprotocol blanchet-akey basic+  (defrole init+    (vars (a b akey) (s skey) (d data))+    (trace (send (enc (enc s (invk a)) b)) (recv (enc d s))))+  (defrole resp+    (vars (a b akey) (s skey) (d data))+    (trace (recv (enc (enc s (invk a)) b)) (send (enc d s))))+  (comment "Blanchet's protocol using unnamed asymmetric keys"))++(defskeleton blanchet-akey+  (vars (d data) (s skey) (a b akey))+  (defstrand resp 2 (d d) (s s) (a a) (b b))+  (deflistener d)+  (non-orig (invk a) (invk b))+  (uniq-orig d s)+  (comment "From the responders's perspective, is the secret leaked?")+  (traces ((recv (enc (enc s (invk a)) b)) (send (enc d s)))+    ((recv d) (send d)))+  (label 25)+  (unrealized (0 0) (1 0))+  (preskeleton)+  (comment "Not a skeleton"))++(defskeleton blanchet-akey+  (vars (d data) (s skey) (a b akey))+  (defstrand resp 2 (d d) (s s) (a a) (b b))+  (deflistener d)+  (precedes ((0 1) (1 0)))+  (non-orig (invk a) (invk b))+  (uniq-orig d s)+  (traces ((recv (enc (enc s (invk a)) b)) (send (enc d s)))+    ((recv d) (send d)))+  (label 26)+  (parent 25)+  (unrealized (0 0))+  (origs (d (0 1)))+  (comment "1 in cohort - 1 not yet seen"))++(defskeleton blanchet-akey+  (vars (d data) (s skey) (a b b-0 akey))+  (defstrand resp 2 (d d) (s s) (a a) (b b))+  (deflistener d)+  (defstrand init 1 (s s) (a a) (b b-0))+  (precedes ((0 1) (1 0)) ((2 0) (0 0)))+  (non-orig (invk a) (invk b))+  (uniq-orig d s)+  (operation encryption-test (added-strand init 1) (enc s (invk a))+    (0 0))+  (traces ((recv (enc (enc s (invk a)) b)) (send (enc d s)))+    ((recv d) (send d)) ((send (enc (enc s (invk a)) b-0))))+  (label 27)+  (parent 26)+  (unrealized)+  (shape)+  (maps ((0 1) ((a a) (b b) (s s) (d d))))+  (origs (s (2 0)) (d (0 1))))  (comment "Nothing left to do")
tst/completeness-test.tst view
@@ -1,4 +1,4 @@-(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol completeness-test basic
tst/crushing.tst view
@@ -1,4 +1,4 @@-(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol crushing basic
tst/dass_simple.tst view
@@ -1,6 +1,6 @@ (herald "Distributed Authentication Security Service Protocol Variants") -(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol dass-simple basic
tst/denning-sacco.tst view
@@ -1,6 +1,6 @@ (herald "Denning-Sacco Protocol") -(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol denning-sacco basic
tst/deorig_contract.tst view
@@ -1,4 +1,4 @@-(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol deorig-contract basic
tst/deorig_simple.tst view
@@ -1,4 +1,4 @@-(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol deorig-simple basic
tst/dh_cert.tst view
@@ -1,6 +1,6 @@ (herald "Diffie-Hellman with Certificate" (algebra diffie-hellman)) -(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol dh-cert diffie-hellman
tst/dhke.tst view
@@ -1,6 +1,6 @@ (herald "Diffie-Hellman Key Exchange" (algebra diffie-hellman)) -(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol dhke diffie-hellman
tst/dy.tst view
@@ -1,6 +1,6 @@ (herald "Example 1.3 from 1983 Dolev-Yao Paper") -(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol dy basic
tst/encsig.tst view
@@ -1,7 +1,7 @@ (herald "Encrypted Signed Message Example"   (comment "Shows examples of key usage of asymmetric keys")) -(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol mult-keys-enc-sig basic
+ tst/epmo-hash.scm view
@@ -0,0 +1,77 @@+(herald "Electronic Purchase with Money Order Protocol with Key Hashing"+  (comment "Annotated with trust management formulas"))++(defprotocol epmo basic+  (defrole bank+    (vars (b c m name) (nc nm nb data) (price text))+    (trace+     (recv (enc c nc nm price (pubk b)))+     (send (cat (enc (hash c nc nb nm price) (privk b))+		(enc nc nb (pubk c))))+     (recv (enc (hash b nb nm) (privk m))))+    (uniq-orig nb)+    (annotations b+      (1+        (implies+          (and (forall ((pm name)) (says c (transfer b price pm nm)))+            (forall ((pm name)) (says pm (transfer b price pm nm))))+          (forall ((pm name)) (transfer b price pm nm))))+      (2+        (and (says c (transfer b price m nm))+          (says m (transfer b price m nm))))))+  (defrole customer+    (vars (b c m name) (nb nc nm data) (goods price text))+    (trace+     (send (enc c nc goods price (pubk m)))+     (recv (enc nc nm m goods price (pubk c)))+     (send (enc c nc nm price (pubk b)))+     (recv (cat (enc (hash c nc nb nm price) (privk b))+		(enc nc nb (pubk c))))+     (send (cat (enc (hash c nc nb nm price) (privk b)) nb)))+    (uniq-orig nc)+    (annotations c+      (1+        (says m+          (forall ((pb name))+            (implies (transfer pb price m nm) (ship m goods c)))))+      (3+        (says b+          (implies+            (and (forall ((pm name)) (says c (transfer b price pm nm)))+              (forall ((pm name)) (says m (transfer b price pm nm))))+            (transfer b price m nm))))+      (4 (transfer b price m nm))))+  (defrole merchant+    (vars (b c m name) (nb nc nm data) (goods price text))+    (trace+     (recv (enc c nc goods price (pubk m)))+     (send (enc nc nm m goods price (pubk c)))+     (recv (cat (enc (hash c nc nb nm price) (privk b)) nb))+     (send (enc (hash b nb nm) (privk m))))+    (uniq-orig nm)+    (annotations m+      (1+        (forall ((pb name))+          (implies (transfer pb price m nm) (ship m goods c))))+      (2+        (and+          (says b+            (implies+              (and+                (forall ((pm name)) (says c (transfer b price pm nm)))+                (forall ((pm name)) (says m (transfer b price pm nm))))+              (transfer b price m nm)))+          (says c (transfer b price m nm))))+      (3 (and (transfer b price m nm) (ship m goods c))))))++(defskeleton epmo (vars (b c m name))+  (defstrand customer 5 (b b) (c c) (m m))+  (non-orig (privk b) (privk c) (privk m)))++(defskeleton epmo (vars (b c m name) (goods name))+  (defstrand bank 3 (b b) (c c) (m m))+  (non-orig (privk b) (privk c) (privk m)))++(defskeleton epmo (vars (b c m name))+  (defstrand merchant 4 (b b) (c c) (m m))+  (non-orig (privk b) (privk c) (privk m)))
+ tst/epmo-hash.tst view
@@ -0,0 +1,691 @@+(herald "Electronic Purchase with Money Order Protocol with Key Hashing"+  (comment "Annotated with trust management formulas"))++(comment "CPSA 2.2.5")+(comment "All input read")++(defprotocol epmo basic+  (defrole bank+    (vars (b c m name) (nc nm nb data) (price text))+    (trace (recv (enc c nc nm price (pubk b)))+      (send+        (cat (enc (hash c nc nb nm price) (privk b))+          (enc nc nb (pubk c)))) (recv (enc (hash b nb nm) (privk m))))+    (uniq-orig nb)+    (annotations b+      (1+        (implies+          (and (forall ((pm name)) (says c (transfer b price pm nm)))+            (forall ((pm name)) (says pm (transfer b price pm nm))))+          (forall ((pm name)) (transfer b price pm nm))))+      (2+        (and (says c (transfer b price m nm))+          (says m (transfer b price m nm))))))+  (defrole customer+    (vars (b c m name) (nb nc nm data) (goods price text))+    (trace (send (enc c nc goods price (pubk m)))+      (recv (enc nc nm m goods price (pubk c)))+      (send (enc c nc nm price (pubk b)))+      (recv+        (cat (enc (hash c nc nb nm price) (privk b))+          (enc nc nb (pubk c))))+      (send (cat (enc (hash c nc nb nm price) (privk b)) nb)))+    (uniq-orig nc)+    (annotations c+      (1+        (says m+          (forall ((pb name))+            (implies (transfer pb price m nm) (ship m goods c)))))+      (3+        (says b+          (implies+            (and (forall ((pm name)) (says c (transfer b price pm nm)))+              (forall ((pm name)) (says m (transfer b price pm nm))))+            (transfer b price m nm)))) (4 (transfer b price m nm))))+  (defrole merchant+    (vars (b c m name) (nb nc nm data) (goods price text))+    (trace (recv (enc c nc goods price (pubk m)))+      (send (enc nc nm m goods price (pubk c)))+      (recv (cat (enc (hash c nc nb nm price) (privk b)) nb))+      (send (enc (hash b nb nm) (privk m))))+    (uniq-orig nm)+    (annotations m+      (1+        (forall ((pb name))+          (implies (transfer pb price m nm) (ship m goods c))))+      (2+        (and+          (says b+            (implies+              (and+                (forall ((pm name)) (says c (transfer b price pm nm)))+                (forall ((pm name)) (says m (transfer b price pm nm))))+              (transfer b price m nm)))+          (says c (transfer b price m nm))))+      (3 (and (transfer b price m nm) (ship m goods c))))))++(defskeleton epmo+  (vars (goods price text) (nb nc nm data) (b c m name))+  (defstrand customer 5 (goods goods) (price price) (nb nb) (nc nc)+    (nm nm) (b b) (c c) (m m))+  (non-orig (privk b) (privk c) (privk m))+  (uniq-orig nc)+  (traces+    ((send (enc c nc goods price (pubk m)))+      (recv (enc nc nm m goods price (pubk c)))+      (send (enc c nc nm price (pubk b)))+      (recv+        (cat (enc (hash c nc nb nm price) (privk b))+          (enc nc nb (pubk c))))+      (send (cat (enc (hash c nc nb nm price) (privk b)) nb))))+  (label 0)+  (unrealized (0 1) (0 3))+  (origs (nc (0 0)))+  (comment "1 in cohort - 1 not yet seen"))++(defskeleton epmo+  (vars (goods price text) (nb nc nm nm-0 data) (b c m name))+  (defstrand customer 5 (goods goods) (price price) (nb nb) (nc nc)+    (nm nm) (b b) (c c) (m m))+  (defstrand merchant 2 (goods goods) (price price) (nc nc) (nm nm-0)+    (c c) (m m))+  (precedes ((0 0) (1 0)) ((1 1) (0 1)))+  (non-orig (privk b) (privk c) (privk m))+  (uniq-orig nc nm-0)+  (operation nonce-test (added-strand merchant 2) nc (0 1)+    (enc c nc goods price (pubk m)))+  (traces+    ((send (enc c nc goods price (pubk m)))+      (recv (enc nc nm m goods price (pubk c)))+      (send (enc c nc nm price (pubk b)))+      (recv+        (cat (enc (hash c nc nb nm price) (privk b))+          (enc nc nb (pubk c))))+      (send (cat (enc (hash c nc nb nm price) (privk b)) nb)))+    ((recv (enc c nc goods price (pubk m)))+      (send (enc nc nm-0 m goods price (pubk c)))))+  (label 1)+  (parent 0)+  (unrealized (0 1) (0 3))+  (comment "1 in cohort - 1 not yet seen"))++(defskeleton epmo+  (vars (goods price text) (nb nc nm data) (b c m name))+  (defstrand customer 5 (goods goods) (price price) (nb nb) (nc nc)+    (nm nm) (b b) (c c) (m m))+  (defstrand merchant 2 (goods goods) (price price) (nc nc) (nm nm)+    (c c) (m m))+  (precedes ((0 0) (1 0)) ((1 1) (0 1)))+  (non-orig (privk b) (privk c) (privk m))+  (uniq-orig nc nm)+  (operation nonce-test (contracted (nm-0 nm)) nc (0 1)+    (enc nc nm m goods price (pubk c)) (enc c nc goods price (pubk m)))+  (traces+    ((send (enc c nc goods price (pubk m)))+      (recv (enc nc nm m goods price (pubk c)))+      (send (enc c nc nm price (pubk b)))+      (recv+        (cat (enc (hash c nc nb nm price) (privk b))+          (enc nc nb (pubk c))))+      (send (cat (enc (hash c nc nb nm price) (privk b)) nb)))+    ((recv (enc c nc goods price (pubk m)))+      (send (enc nc nm m goods price (pubk c)))))+  (label 2)+  (parent 1)+  (unrealized (0 3))+  (comment "1 in cohort - 1 not yet seen"))++(defskeleton epmo+  (vars (goods price text) (nb nc nm data) (b c m name))+  (defstrand customer 5 (goods goods) (price price) (nb nb) (nc nc)+    (nm nm) (b b) (c c) (m m))+  (defstrand merchant 2 (goods goods) (price price) (nc nc) (nm nm)+    (c c) (m m))+  (defstrand bank 2 (price price) (nc nc) (nm nm) (nb nb) (b b) (c c))+  (precedes ((0 0) (1 0)) ((1 1) (0 1)) ((1 1) (2 0)) ((2 1) (0 3)))+  (non-orig (privk b) (privk c) (privk m))+  (uniq-orig nb nc nm)+  (operation encryption-test (added-strand bank 2)+    (enc (hash c nc nb nm price) (privk b)) (0 3))+  (traces+    ((send (enc c nc goods price (pubk m)))+      (recv (enc nc nm m goods price (pubk c)))+      (send (enc c nc nm price (pubk b)))+      (recv+        (cat (enc (hash c nc nb nm price) (privk b))+          (enc nc nb (pubk c))))+      (send (cat (enc (hash c nc nb nm price) (privk b)) nb)))+    ((recv (enc c nc goods price (pubk m)))+      (send (enc nc nm m goods price (pubk c))))+    ((recv (enc c nc nm price (pubk b)))+      (send+        (cat (enc (hash c nc nb nm price) (privk b))+          (enc nc nb (pubk c))))))+  (label 3)+  (parent 2)+  (seen 4)+  (unrealized (2 0))+  (comment "2 in cohort - 1 not yet seen"))++(defskeleton epmo+  (vars (goods price text) (nb nc nm data) (b c m name))+  (defstrand customer 5 (goods goods) (price price) (nb nb) (nc nc)+    (nm nm) (b b) (c c) (m m))+  (defstrand merchant 2 (goods goods) (price price) (nc nc) (nm nm)+    (c c) (m m))+  (defstrand bank 2 (price price) (nc nc) (nm nm) (nb nb) (b b) (c c))+  (precedes ((0 0) (1 0)) ((0 2) (2 0)) ((1 1) (0 1)) ((2 1) (0 3)))+  (non-orig (privk b) (privk c) (privk m))+  (uniq-orig nb nc nm)+  (operation nonce-test (added-strand customer 3) nc (2 0)+    (enc nc nm m goods price (pubk c)) (enc c nc goods price (pubk m)))+  (traces+    ((send (enc c nc goods price (pubk m)))+      (recv (enc nc nm m goods price (pubk c)))+      (send (enc c nc nm price (pubk b)))+      (recv+        (cat (enc (hash c nc nb nm price) (privk b))+          (enc nc nb (pubk c))))+      (send (cat (enc (hash c nc nb nm price) (privk b)) nb)))+    ((recv (enc c nc goods price (pubk m)))+      (send (enc nc nm m goods price (pubk c))))+    ((recv (enc c nc nm price (pubk b)))+      (send+        (cat (enc (hash c nc nb nm price) (privk b))+          (enc nc nb (pubk c))))))+  (label 4)+  (parent 3)+  (unrealized)+  (shape)+  (maps+    ((0)+      ((b b) (c c) (m m) (nb nb) (nc nc) (nm nm) (goods goods)+        (price price))))+  (origs (nc (0 0)) (nb (2 1)) (nm (1 1))))++(comment "Nothing left to do")++(defprotocol epmo basic+  (defrole bank+    (vars (b c m name) (nc nm nb data) (price text))+    (trace (recv (enc c nc nm price (pubk b)))+      (send+        (cat (enc (hash c nc nb nm price) (privk b))+          (enc nc nb (pubk c)))) (recv (enc (hash b nb nm) (privk m))))+    (uniq-orig nb)+    (annotations b+      (1+        (implies+          (and (forall ((pm name)) (says c (transfer b price pm nm)))+            (forall ((pm name)) (says pm (transfer b price pm nm))))+          (forall ((pm name)) (transfer b price pm nm))))+      (2+        (and (says c (transfer b price m nm))+          (says m (transfer b price m nm))))))+  (defrole customer+    (vars (b c m name) (nb nc nm data) (goods price text))+    (trace (send (enc c nc goods price (pubk m)))+      (recv (enc nc nm m goods price (pubk c)))+      (send (enc c nc nm price (pubk b)))+      (recv+        (cat (enc (hash c nc nb nm price) (privk b))+          (enc nc nb (pubk c))))+      (send (cat (enc (hash c nc nb nm price) (privk b)) nb)))+    (uniq-orig nc)+    (annotations c+      (1+        (says m+          (forall ((pb name))+            (implies (transfer pb price m nm) (ship m goods c)))))+      (3+        (says b+          (implies+            (and (forall ((pm name)) (says c (transfer b price pm nm)))+              (forall ((pm name)) (says m (transfer b price pm nm))))+            (transfer b price m nm)))) (4 (transfer b price m nm))))+  (defrole merchant+    (vars (b c m name) (nb nc nm data) (goods price text))+    (trace (recv (enc c nc goods price (pubk m)))+      (send (enc nc nm m goods price (pubk c)))+      (recv (cat (enc (hash c nc nb nm price) (privk b)) nb))+      (send (enc (hash b nb nm) (privk m))))+    (uniq-orig nm)+    (annotations m+      (1+        (forall ((pb name))+          (implies (transfer pb price m nm) (ship m goods c))))+      (2+        (and+          (says b+            (implies+              (and+                (forall ((pm name)) (says c (transfer b price pm nm)))+                (forall ((pm name)) (says m (transfer b price pm nm))))+              (transfer b price m nm)))+          (says c (transfer b price m nm))))+      (3 (and (transfer b price m nm) (ship m goods c))))))++(defskeleton epmo+  (vars (price text) (nc nm nb data) (b c m name))+  (defstrand bank 3 (price price) (nc nc) (nm nm) (nb nb) (b b) (c c)+    (m m))+  (non-orig (privk b) (privk c) (privk m))+  (uniq-orig nb)+  (traces+    ((recv (enc c nc nm price (pubk b)))+      (send+        (cat (enc (hash c nc nb nm price) (privk b))+          (enc nc nb (pubk c)))) (recv (enc (hash b nb nm) (privk m)))))+  (label 5)+  (unrealized (0 2))+  (origs (nb (0 1)))+  (comment "1 in cohort - 1 not yet seen"))++(defskeleton epmo+  (vars (price goods price-0 text) (nc nm nb nc-0 data)+    (b c m c-0 name))+  (defstrand bank 3 (price price) (nc nc) (nm nm) (nb nb) (b b) (c c)+    (m m))+  (defstrand merchant 4 (goods goods) (price price-0) (nb nb) (nc nc-0)+    (nm nm) (b b) (c c-0) (m m))+  (precedes ((0 1) (1 2)) ((1 1) (0 0)) ((1 3) (0 2)))+  (non-orig (privk b) (privk c) (privk m))+  (uniq-orig nm nb)+  (operation encryption-test (added-strand merchant 4)+    (enc (hash b nb nm) (privk m)) (0 2))+  (traces+    ((recv (enc c nc nm price (pubk b)))+      (send+        (cat (enc (hash c nc nb nm price) (privk b))+          (enc nc nb (pubk c)))) (recv (enc (hash b nb nm) (privk m))))+    ((recv (enc c-0 nc-0 goods price-0 (pubk m)))+      (send (enc nc-0 nm m goods price-0 (pubk c-0)))+      (recv (cat (enc (hash c-0 nc-0 nb nm price-0) (privk b)) nb))+      (send (enc (hash b nb nm) (privk m)))))+  (label 6)+  (parent 5)+  (seen 7)+  (unrealized (1 2))+  (comment "2 in cohort - 1 not yet seen"))++(defskeleton epmo+  (vars (price goods text) (nc nm nb data) (b c m name))+  (defstrand bank 3 (price price) (nc nc) (nm nm) (nb nb) (b b) (c c)+    (m m))+  (defstrand merchant 4 (goods goods) (price price) (nb nb) (nc nc)+    (nm nm) (b b) (c c) (m m))+  (precedes ((0 1) (1 2)) ((1 1) (0 0)) ((1 3) (0 2)))+  (non-orig (privk b) (privk c) (privk m))+  (uniq-orig nm nb)+  (operation encryption-test (added-strand bank 2)+    (enc (hash c nc nb nm price) (privk b)) (1 2))+  (traces+    ((recv (enc c nc nm price (pubk b)))+      (send+        (cat (enc (hash c nc nb nm price) (privk b))+          (enc nc nb (pubk c)))) (recv (enc (hash b nb nm) (privk m))))+    ((recv (enc c nc goods price (pubk m)))+      (send (enc nc nm m goods price (pubk c)))+      (recv (cat (enc (hash c nc nb nm price) (privk b)) nb))+      (send (enc (hash b nb nm) (privk m)))))+  (label 7)+  (parent 6)+  (unrealized (0 0) (1 2))+  (comment "1 in cohort - 1 not yet seen"))++(defskeleton epmo+  (vars (price goods goods-0 price-0 text) (nc nm nb nm-0 data)+    (b c m b-0 m-0 name))+  (defstrand bank 3 (price price) (nc nc) (nm nm) (nb nb) (b b) (c c)+    (m m))+  (defstrand merchant 4 (goods goods) (price price) (nb nb) (nc nc)+    (nm nm) (b b) (c c) (m m))+  (defstrand customer 5 (goods goods-0) (price price-0) (nb nb) (nc nc)+    (nm nm-0) (b b-0) (c c) (m m-0))+  (precedes ((0 1) (2 3)) ((1 1) (0 0)) ((1 3) (0 2)) ((2 0) (1 0))+    ((2 4) (1 2)))+  (non-orig (privk b) (privk c) (privk m))+  (uniq-orig nc nm nb)+  (operation nonce-test (added-strand customer 5) nb (1 2)+    (enc nc nb (pubk c)))+  (traces+    ((recv (enc c nc nm price (pubk b)))+      (send+        (cat (enc (hash c nc nb nm price) (privk b))+          (enc nc nb (pubk c)))) (recv (enc (hash b nb nm) (privk m))))+    ((recv (enc c nc goods price (pubk m)))+      (send (enc nc nm m goods price (pubk c)))+      (recv (cat (enc (hash c nc nb nm price) (privk b)) nb))+      (send (enc (hash b nb nm) (privk m))))+    ((send (enc c nc goods-0 price-0 (pubk m-0)))+      (recv (enc nc nm-0 m-0 goods-0 price-0 (pubk c)))+      (send (enc c nc nm-0 price-0 (pubk b-0)))+      (recv+        (cat (enc (hash c nc nb nm-0 price-0) (privk b-0))+          (enc nc nb (pubk c))))+      (send (cat (enc (hash c nc nb nm-0 price-0) (privk b-0)) nb))))+  (label 8)+  (parent 7)+  (seen 9)+  (unrealized (0 0) (2 3))+  (comment "3 in cohort - 2 not yet seen"))++(defskeleton epmo+  (vars (price goods goods-0 text) (nc nm nb data) (b c m b-0 m-0 name))+  (defstrand bank 3 (price price) (nc nc) (nm nm) (nb nb) (b b) (c c)+    (m m))+  (defstrand merchant 4 (goods goods) (price price) (nb nb) (nc nc)+    (nm nm) (b b) (c c) (m m))+  (defstrand customer 5 (goods goods-0) (price price) (nb nb) (nc nc)+    (nm nm) (b b-0) (c c) (m m-0))+  (precedes ((0 1) (2 3)) ((1 1) (0 0)) ((1 1) (2 1)) ((1 3) (0 2))+    ((2 0) (1 0)) ((2 4) (1 2)))+  (non-orig (privk b) (privk c) (privk m))+  (uniq-orig nc nm nb)+  (operation encryption-test (added-strand bank 2)+    (hash c nc nb nm price) (2 3))+  (traces+    ((recv (enc c nc nm price (pubk b)))+      (send+        (cat (enc (hash c nc nb nm price) (privk b))+          (enc nc nb (pubk c)))) (recv (enc (hash b nb nm) (privk m))))+    ((recv (enc c nc goods price (pubk m)))+      (send (enc nc nm m goods price (pubk c)))+      (recv (cat (enc (hash c nc nb nm price) (privk b)) nb))+      (send (enc (hash b nb nm) (privk m))))+    ((send (enc c nc goods-0 price (pubk m-0)))+      (recv (enc nc nm m-0 goods-0 price (pubk c)))+      (send (enc c nc nm price (pubk b-0)))+      (recv+        (cat (enc (hash c nc nb nm price) (privk b-0))+          (enc nc nb (pubk c))))+      (send (cat (enc (hash c nc nb nm price) (privk b-0)) nb))))+  (label 9)+  (parent 8)+  (unrealized (0 0) (2 1))+  (comment "1 in cohort - 1 not yet seen"))++(defskeleton epmo+  (vars (price goods goods-0 price-0 text) (nc nm nb nm-0 data)+    (b c m b-0 m-0 name))+  (defstrand bank 3 (price price) (nc nc) (nm nm) (nb nb) (b b) (c c)+    (m m))+  (defstrand merchant 4 (goods goods) (price price) (nb nb) (nc nc)+    (nm nm) (b b) (c c) (m m))+  (defstrand customer 5 (goods goods-0) (price price-0) (nb nb) (nc nc)+    (nm nm-0) (b b-0) (c c) (m m-0))+  (deflistener (cat c nc nb nm-0 price-0))+  (precedes ((0 1) (3 0)) ((1 1) (0 0)) ((1 3) (0 2)) ((2 0) (1 0))+    ((2 4) (1 2)) ((3 1) (2 3)))+  (non-orig (privk b) (privk c) (privk m))+  (uniq-orig nc nm nb)+  (operation encryption-test (added-listener (cat c nc nb nm-0 price-0))+    (hash c nc nb nm-0 price-0) (2 3))+  (traces+    ((recv (enc c nc nm price (pubk b)))+      (send+        (cat (enc (hash c nc nb nm price) (privk b))+          (enc nc nb (pubk c)))) (recv (enc (hash b nb nm) (privk m))))+    ((recv (enc c nc goods price (pubk m)))+      (send (enc nc nm m goods price (pubk c)))+      (recv (cat (enc (hash c nc nb nm price) (privk b)) nb))+      (send (enc (hash b nb nm) (privk m))))+    ((send (enc c nc goods-0 price-0 (pubk m-0)))+      (recv (enc nc nm-0 m-0 goods-0 price-0 (pubk c)))+      (send (enc c nc nm-0 price-0 (pubk b-0)))+      (recv+        (cat (enc (hash c nc nb nm-0 price-0) (privk b-0))+          (enc nc nb (pubk c))))+      (send (cat (enc (hash c nc nb nm-0 price-0) (privk b-0)) nb)))+    ((recv (cat c nc nb nm-0 price-0))+      (send (cat c nc nb nm-0 price-0))))+  (label 10)+  (parent 8)+  (unrealized (0 0) (3 0))+  (comment "empty cohort"))++(defskeleton epmo+  (vars (price goods text) (nc nm nb data) (b c m b-0 name))+  (defstrand bank 3 (price price) (nc nc) (nm nm) (nb nb) (b b) (c c)+    (m m))+  (defstrand merchant 4 (goods goods) (price price) (nb nb) (nc nc)+    (nm nm) (b b) (c c) (m m))+  (defstrand customer 5 (goods goods) (price price) (nb nb) (nc nc)+    (nm nm) (b b-0) (c c) (m m))+  (precedes ((0 1) (2 3)) ((1 1) (0 0)) ((1 1) (2 1)) ((1 3) (0 2))+    ((2 0) (1 0)) ((2 4) (1 2)))+  (non-orig (privk b) (privk c) (privk m))+  (uniq-orig nc nm nb)+  (operation nonce-test (contracted (m-0 m) (goods-0 goods)) nm (2 1)+    (enc nc nm m goods price (pubk c)))+  (traces+    ((recv (enc c nc nm price (pubk b)))+      (send+        (cat (enc (hash c nc nb nm price) (privk b))+          (enc nc nb (pubk c)))) (recv (enc (hash b nb nm) (privk m))))+    ((recv (enc c nc goods price (pubk m)))+      (send (enc nc nm m goods price (pubk c)))+      (recv (cat (enc (hash c nc nb nm price) (privk b)) nb))+      (send (enc (hash b nb nm) (privk m))))+    ((send (enc c nc goods price (pubk m)))+      (recv (enc nc nm m goods price (pubk c)))+      (send (enc c nc nm price (pubk b-0)))+      (recv+        (cat (enc (hash c nc nb nm price) (privk b-0))+          (enc nc nb (pubk c))))+      (send (cat (enc (hash c nc nb nm price) (privk b-0)) nb))))+  (label 11)+  (parent 9)+  (seen 12)+  (unrealized (0 0))+  (comment "2 in cohort - 1 not yet seen"))++(defskeleton epmo+  (vars (price goods text) (nc nm nb data) (b c m b-0 name))+  (defstrand bank 3 (price price) (nc nc) (nm nm) (nb nb) (b b) (c c)+    (m m))+  (defstrand merchant 4 (goods goods) (price price) (nb nb) (nc nc)+    (nm nm) (b b) (c c) (m m))+  (defstrand customer 5 (goods goods) (price price) (nb nb) (nc nc)+    (nm nm) (b b-0) (c c) (m m))+  (precedes ((0 1) (2 3)) ((1 1) (2 1)) ((1 3) (0 2)) ((2 0) (1 0))+    ((2 2) (0 0)) ((2 4) (1 2)))+  (non-orig (privk b) (privk c) (privk m))+  (uniq-orig nc nm nb)+  (operation nonce-test (added-strand customer 3) nm (0 0)+    (enc nc nm m goods price (pubk c)))+  (traces+    ((recv (enc c nc nm price (pubk b)))+      (send+        (cat (enc (hash c nc nb nm price) (privk b))+          (enc nc nb (pubk c)))) (recv (enc (hash b nb nm) (privk m))))+    ((recv (enc c nc goods price (pubk m)))+      (send (enc nc nm m goods price (pubk c)))+      (recv (cat (enc (hash c nc nb nm price) (privk b)) nb))+      (send (enc (hash b nb nm) (privk m))))+    ((send (enc c nc goods price (pubk m)))+      (recv (enc nc nm m goods price (pubk c)))+      (send (enc c nc nm price (pubk b-0)))+      (recv+        (cat (enc (hash c nc nb nm price) (privk b-0))+          (enc nc nb (pubk c))))+      (send (cat (enc (hash c nc nb nm price) (privk b-0)) nb))))+  (label 12)+  (parent 11)+  (unrealized)+  (shape)+  (maps ((0) ((b b) (c c) (m m) (nc nc) (nm nm) (nb nb) (price price))))+  (origs (nc (2 0)) (nb (0 1)) (nm (1 1))))++(comment "Nothing left to do")++(defprotocol epmo basic+  (defrole bank+    (vars (b c m name) (nc nm nb data) (price text))+    (trace (recv (enc c nc nm price (pubk b)))+      (send+        (cat (enc (hash c nc nb nm price) (privk b))+          (enc nc nb (pubk c)))) (recv (enc (hash b nb nm) (privk m))))+    (uniq-orig nb)+    (annotations b+      (1+        (implies+          (and (forall ((pm name)) (says c (transfer b price pm nm)))+            (forall ((pm name)) (says pm (transfer b price pm nm))))+          (forall ((pm name)) (transfer b price pm nm))))+      (2+        (and (says c (transfer b price m nm))+          (says m (transfer b price m nm))))))+  (defrole customer+    (vars (b c m name) (nb nc nm data) (goods price text))+    (trace (send (enc c nc goods price (pubk m)))+      (recv (enc nc nm m goods price (pubk c)))+      (send (enc c nc nm price (pubk b)))+      (recv+        (cat (enc (hash c nc nb nm price) (privk b))+          (enc nc nb (pubk c))))+      (send (cat (enc (hash c nc nb nm price) (privk b)) nb)))+    (uniq-orig nc)+    (annotations c+      (1+        (says m+          (forall ((pb name))+            (implies (transfer pb price m nm) (ship m goods c)))))+      (3+        (says b+          (implies+            (and (forall ((pm name)) (says c (transfer b price pm nm)))+              (forall ((pm name)) (says m (transfer b price pm nm))))+            (transfer b price m nm)))) (4 (transfer b price m nm))))+  (defrole merchant+    (vars (b c m name) (nb nc nm data) (goods price text))+    (trace (recv (enc c nc goods price (pubk m)))+      (send (enc nc nm m goods price (pubk c)))+      (recv (cat (enc (hash c nc nb nm price) (privk b)) nb))+      (send (enc (hash b nb nm) (privk m))))+    (uniq-orig nm)+    (annotations m+      (1+        (forall ((pb name))+          (implies (transfer pb price m nm) (ship m goods c))))+      (2+        (and+          (says b+            (implies+              (and+                (forall ((pm name)) (says c (transfer b price pm nm)))+                (forall ((pm name)) (says m (transfer b price pm nm))))+              (transfer b price m nm)))+          (says c (transfer b price m nm))))+      (3 (and (transfer b price m nm) (ship m goods c))))))++(defskeleton epmo+  (vars (goods price text) (nb nc nm data) (b c m name))+  (defstrand merchant 4 (goods goods) (price price) (nb nb) (nc nc)+    (nm nm) (b b) (c c) (m m))+  (non-orig (privk b) (privk c) (privk m))+  (uniq-orig nm)+  (traces+    ((recv (enc c nc goods price (pubk m)))+      (send (enc nc nm m goods price (pubk c)))+      (recv (cat (enc (hash c nc nb nm price) (privk b)) nb))+      (send (enc (hash b nb nm) (privk m)))))+  (label 13)+  (unrealized (0 2))+  (origs (nm (0 1)))+  (comment "1 in cohort - 1 not yet seen"))++(defskeleton epmo+  (vars (goods price text) (nb nc nm data) (b c m name))+  (defstrand merchant 4 (goods goods) (price price) (nb nb) (nc nc)+    (nm nm) (b b) (c c) (m m))+  (defstrand bank 2 (price price) (nc nc) (nm nm) (nb nb) (b b) (c c))+  (precedes ((0 1) (1 0)) ((1 1) (0 2)))+  (non-orig (privk b) (privk c) (privk m))+  (uniq-orig nb nm)+  (operation encryption-test (added-strand bank 2)+    (enc (hash c nc nb nm price) (privk b)) (0 2))+  (traces+    ((recv (enc c nc goods price (pubk m)))+      (send (enc nc nm m goods price (pubk c)))+      (recv (cat (enc (hash c nc nb nm price) (privk b)) nb))+      (send (enc (hash b nb nm) (privk m))))+    ((recv (enc c nc nm price (pubk b)))+      (send+        (cat (enc (hash c nc nb nm price) (privk b))+          (enc nc nb (pubk c))))))+  (label 14)+  (parent 13)+  (unrealized (0 2) (1 0))+  (comment "1 in cohort - 1 not yet seen"))++(defskeleton epmo+  (vars (goods price text) (nb nc nm data) (b c m b-0 name))+  (defstrand merchant 4 (goods goods) (price price) (nb nb) (nc nc)+    (nm nm) (b b) (c c) (m m))+  (defstrand bank 2 (price price) (nc nc) (nm nm) (nb nb) (b b) (c c))+  (defstrand customer 3 (goods goods) (price price) (nc nc) (nm nm)+    (b b-0) (c c) (m m))+  (precedes ((0 1) (2 1)) ((1 1) (0 2)) ((2 0) (0 0)) ((2 2) (1 0)))+  (non-orig (privk b) (privk c) (privk m))+  (uniq-orig nb nc nm)+  (operation nonce-test (added-strand customer 3) nm (1 0)+    (enc nc nm m goods price (pubk c)))+  (traces+    ((recv (enc c nc goods price (pubk m)))+      (send (enc nc nm m goods price (pubk c)))+      (recv (cat (enc (hash c nc nb nm price) (privk b)) nb))+      (send (enc (hash b nb nm) (privk m))))+    ((recv (enc c nc nm price (pubk b)))+      (send+        (cat (enc (hash c nc nb nm price) (privk b))+          (enc nc nb (pubk c)))))+    ((send (enc c nc goods price (pubk m)))+      (recv (enc nc nm m goods price (pubk c)))+      (send (enc c nc nm price (pubk b-0)))))+  (label 15)+  (parent 14)+  (seen 16)+  (unrealized (0 2))+  (comment "2 in cohort - 1 not yet seen"))++(defskeleton epmo+  (vars (goods price text) (nb nc nm data) (b c b-0 m name))+  (defstrand merchant 4 (goods goods) (price price) (nb nb) (nc nc)+    (nm nm) (b b) (c c) (m m))+  (defstrand bank 2 (price price) (nc nc) (nm nm) (nb nb) (b b) (c c))+  (defstrand customer 5 (goods goods) (price price) (nb nb) (nc nc)+    (nm nm) (b b-0) (c c) (m m))+  (precedes ((0 1) (2 1)) ((1 1) (2 3)) ((2 0) (0 0)) ((2 2) (1 0))+    ((2 4) (0 2)))+  (non-orig (privk b) (privk c) (privk m))+  (uniq-orig nb nc nm)+  (operation nonce-test (added-strand customer 5) nb (0 2)+    (enc nc nb (pubk c)))+  (traces+    ((recv (enc c nc goods price (pubk m)))+      (send (enc nc nm m goods price (pubk c)))+      (recv (cat (enc (hash c nc nb nm price) (privk b)) nb))+      (send (enc (hash b nb nm) (privk m))))+    ((recv (enc c nc nm price (pubk b)))+      (send+        (cat (enc (hash c nc nb nm price) (privk b))+          (enc nc nb (pubk c)))))+    ((send (enc c nc goods price (pubk m)))+      (recv (enc nc nm m goods price (pubk c)))+      (send (enc c nc nm price (pubk b-0)))+      (recv+        (cat (enc (hash c nc nb nm price) (privk b-0))+          (enc nc nb (pubk c))))+      (send (cat (enc (hash c nc nb nm price) (privk b-0)) nb))))+  (label 16)+  (parent 15)+  (unrealized)+  (shape)+  (maps+    ((0)+      ((b b) (c c) (m m) (nb nb) (nc nc) (nm nm) (goods goods)+        (price price))))+  (origs (nc (2 0)) (nb (1 1)) (nm (0 1))))++(comment "Nothing left to do")
tst/epmo-key-hash.tst view
@@ -1,7 +1,7 @@ (herald "Electronic Purchase with Money Order Protocol with Key Hashing"   (comment "Annotated with trust management formulas")) -(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol epmo basic
tst/epmo.tst view
@@ -1,7 +1,7 @@ (herald "Electronic Purchase with Money Order Protocol"   (comment "Annotated with trust management formulas")) -(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol epmo basic
tst/epmo_acctnum-key-hash.tst view
@@ -3,7 +3,7 @@   (displacement)   (comment "This version includes account numbers in exchanges")) -(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read") (comment "Displacement disabled")
tst/epmo_acctnum.tst view
@@ -2,7 +2,7 @@   (displacement)   (comment "This version includes account numbers in exchanges")) -(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read") (comment "Displacement disabled")
tst/ffgg.tst view
@@ -1,7 +1,7 @@ (herald "The ffgg Protocol"   (comment "From A Necessarily Parallel Attack by Jon K. Millen")) -(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol ffgg basic
tst/fragile_pruning.tst view
@@ -1,4 +1,4 @@-(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol fragile_pruning basic
+ tst/hashtest-key-hash.scm view
@@ -0,0 +1,25 @@+;;; Hashtest.scm is designed to test if the+;;; hash is working properly.+(herald "Hashtest")++(defprotocol hashtest basic+  (defrole init (vars (n data) (k akey))+     (trace+       (send (enc n k))+       (recv (enc "h" n))+     )+     (uniq-orig n)+     (non-orig (invk k))+   )+   (defrole resp (vars (k akey) (n data))+     (trace+       (recv (enc n k))+       (send (enc "h" n))+     )+   )+)++(defskeleton hashtest+   (vars)+   (defstrand init 2)+)
+ tst/hashtest-key-hash.tst view
@@ -0,0 +1,73 @@+(herald "Hashtest")++(comment "CPSA 2.2.5")+(comment "All input read")++(defprotocol hashtest basic+  (defrole init+    (vars (n data) (k akey))+    (trace (send (enc n k)) (recv (enc "h" n)))+    (non-orig (invk k))+    (uniq-orig n))+  (defrole resp+    (vars (k akey) (n data))+    (trace (recv (enc n k)) (send (enc "h" n)))))++(defskeleton hashtest+  (vars (n data) (k akey))+  (defstrand init 2 (n n) (k k))+  (non-orig (invk k))+  (uniq-orig n)+  (traces ((send (enc n k)) (recv (enc "h" n))))+  (label 0)+  (unrealized (0 1))+  (origs (n (0 0)))+  (comment "2 in cohort - 2 not yet seen"))++(defskeleton hashtest+  (vars (n data) (k k-0 akey))+  (defstrand init 2 (n n) (k k))+  (defstrand resp 2 (n n) (k k-0))+  (precedes ((0 0) (1 0)) ((1 1) (0 1)))+  (non-orig (invk k))+  (uniq-orig n)+  (operation encryption-test (added-strand resp 2) (enc "h" n) (0 1))+  (traces ((send (enc n k)) (recv (enc "h" n)))+    ((recv (enc n k-0)) (send (enc "h" n))))+  (label 1)+  (parent 0)+  (unrealized (1 0))+  (comment "1 in cohort - 1 not yet seen"))++(defskeleton hashtest+  (vars (n data) (k akey))+  (defstrand init 2 (n n) (k k))+  (deflistener n)+  (precedes ((0 0) (1 0)) ((1 1) (0 1)))+  (non-orig (invk k))+  (uniq-orig n)+  (operation encryption-test (added-listener n) (enc "h" n) (0 1))+  (traces ((send (enc n k)) (recv (enc "h" n))) ((recv n) (send n)))+  (label 2)+  (parent 0)+  (unrealized (1 0))+  (comment "empty cohort"))++(defskeleton hashtest+  (vars (n data) (k akey))+  (defstrand init 2 (n n) (k k))+  (defstrand resp 2 (n n) (k k))+  (precedes ((0 0) (1 0)) ((1 1) (0 1)))+  (non-orig (invk k))+  (uniq-orig n)+  (operation nonce-test (contracted (k-0 k)) n (1 0) (enc n k))+  (traces ((send (enc n k)) (recv (enc "h" n)))+    ((recv (enc n k)) (send (enc "h" n))))+  (label 3)+  (parent 1)+  (unrealized)+  (shape)+  (maps ((0) ((n n) (k k))))+  (origs (n (0 0))))++(comment "Nothing left to do")
+ tst/hashtest.scm view
@@ -0,0 +1,25 @@+;;; Hashtest.scm is designed to test if the+;;; hash is working properly.+(herald "Hashtest")++(defprotocol hashtest basic+  (defrole init (vars (n data) (k akey))+     (trace+       (send (enc n k))+       (recv (hash n))+     )+     (uniq-orig n)+     (non-orig (invk k))+   )+   (defrole resp (vars (k akey) (n data))+     (trace+       (recv (enc n k))+       (send (hash n))+     )+   )+)++(defskeleton hashtest+   (vars)+   (defstrand init 2)+)
+ tst/hashtest.tst view
@@ -0,0 +1,73 @@+(herald "Hashtest")++(comment "CPSA 2.2.5")+(comment "All input read")++(defprotocol hashtest basic+  (defrole init+    (vars (n data) (k akey))+    (trace (send (enc n k)) (recv (hash n)))+    (non-orig (invk k))+    (uniq-orig n))+  (defrole resp+    (vars (k akey) (n data))+    (trace (recv (enc n k)) (send (hash n)))))++(defskeleton hashtest+  (vars (n data) (k akey))+  (defstrand init 2 (n n) (k k))+  (non-orig (invk k))+  (uniq-orig n)+  (traces ((send (enc n k)) (recv (hash n))))+  (label 0)+  (unrealized (0 1))+  (origs (n (0 0)))+  (comment "2 in cohort - 2 not yet seen"))++(defskeleton hashtest+  (vars (n data) (k k-0 akey))+  (defstrand init 2 (n n) (k k))+  (defstrand resp 2 (n n) (k k-0))+  (precedes ((0 0) (1 0)) ((1 1) (0 1)))+  (non-orig (invk k))+  (uniq-orig n)+  (operation encryption-test (added-strand resp 2) (hash n) (0 1))+  (traces ((send (enc n k)) (recv (hash n)))+    ((recv (enc n k-0)) (send (hash n))))+  (label 1)+  (parent 0)+  (unrealized (1 0))+  (comment "1 in cohort - 1 not yet seen"))++(defskeleton hashtest+  (vars (n data) (k akey))+  (defstrand init 2 (n n) (k k))+  (deflistener n)+  (precedes ((0 0) (1 0)) ((1 1) (0 1)))+  (non-orig (invk k))+  (uniq-orig n)+  (operation encryption-test (added-listener n) (hash n) (0 1))+  (traces ((send (enc n k)) (recv (hash n))) ((recv n) (send n)))+  (label 2)+  (parent 0)+  (unrealized (1 0))+  (comment "empty cohort"))++(defskeleton hashtest+  (vars (n data) (k akey))+  (defstrand init 2 (n n) (k k))+  (defstrand resp 2 (n n) (k k))+  (precedes ((0 0) (1 0)) ((1 1) (0 1)))+  (non-orig (invk k))+  (uniq-orig n)+  (operation nonce-test (contracted (k-0 k)) n (1 0) (enc n k))+  (traces ((send (enc n k)) (recv (hash n)))+    ((recv (enc n k)) (send (hash n))))+  (label 3)+  (parent 1)+  (unrealized)+  (shape)+  (maps ((0) ((n n) (k k))))+  (origs (n (0 0))))++(comment "Nothing left to do")
tst/isoreject.tst view
@@ -1,4 +1,4 @@-(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol isoreject basic
tst/kelly1.tst view
@@ -1,4 +1,4 @@-(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol kelly1 basic
tst/kerberos.tst view
@@ -1,4 +1,4 @@-(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol kerberos basic
tst/missing_contraction.tst view
@@ -1,4 +1,4 @@-(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol missing-contraction basic
tst/neuman-stubblebine-reauth.tst view
@@ -1,4 +1,4 @@-(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol neuman-stubblebine-reauth basic
tst/neuman-stubblebine.tst view
@@ -1,4 +1,4 @@-(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol neuman-stubblebine basic
tst/no_contraction.tst view
@@ -1,4 +1,4 @@-(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol no-contraction basic
tst/non_transforming.tst view
@@ -1,4 +1,4 @@-(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol non_transforming basic
tst/nonaug-prune.tst view
@@ -1,4 +1,4 @@-(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol nonaug-prune basic
tst/ns.tst view
@@ -1,6 +1,6 @@ (herald "Needham-Schroeder Public-Key Protocol Variants") -(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol ns basic
tst/nsl3.tst view
@@ -1,6 +1,6 @@ (herald "Three Party Needham-Schroeder-Lowe Protocol") -(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol nsl3 basic
tst/nsl4cm1.tst view
@@ -1,6 +1,6 @@ (herald "Four Party Needham-Schroeder-Lowe Protocol") -(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol nsl4cm basic
tst/nslsk.tst view
@@ -1,6 +1,6 @@ (herald "Needham-Schroeder-Lowe Protocol with symmetric encryption") -(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol nslsk basic
tst/or.tst view
@@ -1,7 +1,7 @@ (herald "Otway-Rees Protocol"   (comment "Standard version using variables of sort mesg")) -(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol or basic
tst/pca.tst view
@@ -1,7 +1,7 @@ (herald "Privacy Certificate Authority"   (comment "Generation of an Attestation Identity Certificate")) -(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol pca basic
tst/pkinit.tst view
@@ -1,6 +1,6 @@ (herald "Kerberos PK init") -(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol pkinit basic
+ tst/print.scm view
@@ -0,0 +1,13 @@+(herald "Print Test"+  (comment "See if read forms look like printed ones"))++(defprotocol print-test basic+  (defrole role+    (vars (a b akey) (f g skey) (x y data))+    (trace (recv (cat a b f g x y)))+    (comment "Check the order in which variables are printed")))++(defskeleton print-test+  (vars (a b akey) (f g skey) (x y data))+  (defstrand role 1 (a a) (b b) (f f) (g g) (x x) (y y))+  (comment "Check the order in which variables are printed"))
+ tst/print.tst view
@@ -0,0 +1,24 @@+(herald "Print Test"+  (comment "See if read forms look like printed ones"))++(comment "CPSA 2.2.5")+(comment "All input read")++(defprotocol print-test basic+  (defrole role+    (vars (a b akey) (f g skey) (x y data))+    (trace (recv (cat a b f g x y)))+    (comment "Check the order in which variables are printed")))++(defskeleton print-test+  (vars (x y data) (f g skey) (a b akey))+  (defstrand role 1 (x x) (y y) (f f) (g g) (a a) (b b))+  (comment "Check the order in which variables are printed")+  (traces ((recv (cat a b f g x y))))+  (label 0)+  (unrealized)+  (shape)+  (maps ((0) ((a a) (b b) (f f) (g g) (x x) (y y))))+  (origs))++(comment "Nothing left to do")
tst/pruning1.tst view
@@ -1,4 +1,4 @@-(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol prune basic
tst/sigenc.tst view
@@ -1,7 +1,7 @@ (herald "Signed Encrypted Message Example"   (comment "Shows examples of key usage of asymmetric keys")) -(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol mult-keys-sig-enc basic
tst/sorted_epmo_acctnum.tst view
@@ -4,7 +4,7 @@     "This version uses sorts to avoid confusion"     "between a nonce and other data")) -(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read") (comment "Displacement disabled")
tst/targetterms2.tst view
@@ -1,4 +1,4 @@-(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol targetterms2 basic
tst/targetterms6.tst view
@@ -1,4 +1,4 @@-(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol targetterms6 basic
tst/targetterms8.tst view
@@ -1,4 +1,4 @@-(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol targetterms8 basic
tst/tor.scm view
@@ -9,14 +9,14 @@ (defprotocol tor diffie-hellman   (defrole init     (vars (x y expn) (b name) (n text) (kh akey))-    (trace +    (trace      (send (enc (exp (gen) x) (pubk b)))      (recv (cat (exp (gen) y) (hash (cat (exp (exp (gen) x) y)))))      (send (enc n (exp (exp (gen) y) x))))     (uniq-orig x n))   (defrole resp     (vars (x y expn) (b name) (n text) (kh akey))-    (trace +    (trace      (recv (enc (exp (gen) x) (pubk b)))      (send (cat (exp (gen) y) (hash (cat (exp (exp (gen) x) y)))))      (recv (enc n (exp (exp (gen) x) y))))
tst/tor.tst view
@@ -1,7 +1,7 @@ (herald "Tor Circuit-Level Handshake Protocol" (algebra diffie-hellman)   (comment "Achieves unilateral authentication")) -(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol tor diffie-hellman
tst/uncarried_keys.tst view
@@ -1,4 +1,4 @@-(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol uncarried-keys basic
tst/uo.tst view
@@ -1,4 +1,4 @@-(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol uniq-orig basic
+ tst/wang-hash.scm view
@@ -0,0 +1,434 @@+(herald "Wang's Fair Exchange Protocol" (bound 10))++;; CPSA input file to represent+;; Wang's Fair Exchange Protocol++;; This macro implements the CPSA+;; convention of regarding a hash as+;; an asymmetric encryption.  The+;; decryption key inverse to (pubk+;; hash) is assumed non-originating+;; in roles using hashing.++;; (defmacro (hash x)+;;  (enc "h" (cat "h" x)))++;; Wang's encrypted format for the+;; message payload.  Observe that m,+;; k get their values from the+;; like-named messages in the context+;; where the macro is expanded.++(defmacro (em)+  (enc m k))++;; The session label L as a fn of+;; the values that *should be* the+;; hashes of the encrypted message EM+;; and the session key K.++(defmacro (l-prime y x)+  (cat a b t y x))++;; The recipient can check that a+;; session label has an l-prime where+;; y is the hash of another parameter.+;; Hence recipient roles use l-star.++(defmacro (l-star e1 x)+  (l-prime (hash e1) x))++;; The Evidence of Origin is checked+;; to be this fn of other parameters+;; available to the recipient.++(defmacro (eoo-star x e1 e2)+  (enc (cat "eootag"+	    (hash (l-star e1 x)) e2)+       (privk "sign" a)))++;; The Evidence of Receipt is computed+;; as this fn of other parameters+;; available to the recipient.++(defmacro (eor-star x e1 e2)+  (enc (cat "eortag"+	    (hash (l-star e1 x)) e2)+       (privk "sign" b)))++;; The Recovery Request as computed by+;; the recipient.++(defmacro (rr-star x e1 e2)+  (cat (l-star e1 x) e2+       (eoo-star x e1 e2)+       (eor-star x e1 e2)+       (enc (cat "rcrq" (l-star e1 x) e2)+            (privk "sign" b))))++;; The Abort Token is checked+;; to be this fn of other parameters+;; available to the recipient.++(defmacro (at-star e1 x)+  (enc (enc "abrq" (l-star e1 x)+            (privk "sign" a))+       (privk "sign" t)))++;; How the initiator computes the+;; encrypted key package:++(defmacro (ek l)+  (enc (cat "keytag" (hash l) k r)+       (pubk "encr" t)))++;; The Initiator's computed+;; version of L.++(defmacro (l)+  (l-prime (hash (enc m k)) (hash k)))++;; The TTP can check that the session+;; label L is this fn of other+;; parameters available to the TTP.++(defmacro (l-prime-prime y)+  (cat a b t y (hash k)))++;; The TTP can check that the EOO+;; is this fn of other parameters+;; available to the TTP.++(defmacro (eoo-prime-prime y)+  (enc (cat "eootag"+            (hash (l-prime-prime y))+	    (ek (l-prime-prime y)))+       (privk "sign" a)))++;; The TTP can check that the EOR+;; is this fn of other parameters+;; available to the TTP.++(defmacro (eor-prime-prime y)+  (enc (cat "eortag"+	    (hash (l-prime-prime y))+	    (ek (l-prime-prime y)))+       (privk "sign" b)))++;; The TTP can check that the RR+;; is this fn of other parameters+;; available to the TTP.++(defmacro (rr-prime-prime y)+  (cat (l-prime-prime y)+       (ek (l-prime-prime y))+       (eoo-prime-prime y)+       (eor-prime-prime y)+       (enc "rcrq" (l-prime-prime y)+	    (ek (l-prime-prime y))+            (privk "sign" b))))++;; The TTP can check that the Confirmation+;; Request is this fn of other parameters+;; available to the TTP.++(defmacro (cf-prime-prime y)+  (cat (l-prime-prime y) (ek (l-prime-prime y))+       (eoo-prime-prime y) (eor-prime-prime y)+       (enc "cfrq" (l-prime-prime y)+	    (ek (l-prime-prime y))+            (privk "sign" b))))++;; Defn of Wang's Fair Exchange Protocol.+;; Closely follows the presentation in the+;; figures in Section 3.  In the TTP roles,+;; we have put a dummy send or receive in place+;; of the state synchronization event to keep+;; the indices matching the spec.++(defprotocol wang basic++  ;; Successful initiator run with no TTP involvement++  (defrole init1+    (vars (a b t hash_id name) (m data) (r text) (k skey))+    (trace+     (send (cat (l) (enc m k) (ek (l))+                (eoo-star (hash k) (enc m k) (ek (l)))))+     (recv (eor-star (hash k) (enc m k) (ek (l))))+     (send (cat k r)))+    (non-orig (privk hash_id)))++  ;; Aborted initiator run++  (defrole init2+    (vars (a b t hash_id name) (m data) (r text) (k skey))+    (trace+     (send (cat (l) (enc m k) (ek (l))+                (eoo-star (hash k) (enc m k) (ek (l)))))+     (send (enc "abrq" (l) (privk "sign" a)))+     (recv (enc "abcf"+                (enc "abrq" (l) (privk "sign" a))+                (privk "sign" t))))+    (non-orig (privk hash_id)))++  ;; Initiator run with abort request and forced recovery++  (defrole init3+    (vars (a b t hash_id name) (m data) (r text) (k skey))+    (trace+     (send (cat (l) (enc m k) (ek (l))+                (eoo-star (hash k) (enc m k) (ek (l)))))+     (send (enc "abrq" (l) (privk "sign" a)))+     (recv (eor-star (hash k) (enc m k) (ek (l)))))+    (non-orig (privk hash_id)))++  ;; Aborted initiator run, but with EOR received++  (defrole init4+    (vars (a b t hash_id name) (m data) (r text) (k skey))+    (trace+     (send (cat (l) (enc m k) (ek (l))+                (eoo-star (hash k) (enc m k) (ek (l)))))+     (recv (eor-star (hash k) (enc m k) (ek (l))))+     (send (enc "abrq" (l) (privk "sign" a)))+     (recv (enc "abcf"+                (enc "abrq" (l) (privk "sign" a))+                (privk "sign" t))))+    (non-orig (privk hash_id)))++  ;; Initiator run with abort requested after EOR received,+  ;; but recovery forced++  (defrole init5+    (vars (a b t hash_id name) (m data) (r text) (k skey))+    (trace+     (send (cat (l) (enc m k) (ek (l))+                (eoo-star (hash k) (enc m k) (ek (l)))))+     (recv (eor-star (hash k) (enc m k) (ek (l))))+     (send (enc "abrq" (l) (privk "sign" a)))+     (recv (eor-star (hash k) (enc m k) (ek (l)))))+    (non-orig (privk hash_id)))++  ;; Successful responder run with no TTP involvement++  (defrole resp1+    (vars (a b t hash_id name) (m data) (r text) (k skey))+    (trace+     (recv (cat (l) (enc m k) (ek (l))+                (eoo-star (hash k) (enc m k) (ek (l)))))+     (send (eor-star (hash k) (enc m k) (ek (l))))+     (recv (cat k r)))+    (non-orig (privk hash_id)))++  ;;Responder run with recovery via TTP++  (defrole resp2+    (vars (a b t hash_id name) (m data) (r text) (k skey))+    (trace+     (recv (cat (l) (enc m k) (ek (l))+                (eoo-star (hash k) (enc m k) (ek (l)))))+     (send (cat (l) (ek (l)) (eoo-star (hash k) (enc m k) (ek (l)))+                (eor-star (hash k) (enc m k) (ek (l)))))+     (send (cat (l) (ek (l)) (eoo-star (hash k) (enc m k) (ek (l)))+                (eor-star (hash k) (enc m k) (ek (l)))+                (enc "rcrq" (l) (ek (l)) (privk "sign" b))))+     (recv (cat k r)))+    (non-orig (privk hash_id)))++  ;; Responder run with recovery request and forced abort++  (defrole resp3+    (vars (a b t hash_id name) (e1 e2 x mesg))+    (trace+     (recv (cat (l-star e1 x) e1 e2 (eoo-star x e1 e2)))+     (send (cat (l-star e1 x) e2 (eoo-star x e1 e2) (eor-star x e1 e2)))+     (send (cat (l-star e1 x) e2 (eoo-star x e1 e2) (eor-star x e1 e2)+                (enc "rcrq" (l-star e1 x) e2 (privk "sign" b))))+     (recv (enc "abcf"+                (enc "abrq" (l-star e1 x) (privk "sign" a))+                (privk "sign" t))))+    (non-orig (privk hash_id)))++  ;; TTP handles an abort++  (defrole ttp-ab1+    (vars (a b t hash_id name) (y x mesg))+    (trace+     (recv (enc "abrq" (l-prime y x) (privk "sign" a)))+     (send (cat "sync-abrq"+                (enc "abrq" (l-prime y x) (privk "sign" a))))+     (send (enc "abcf"+                (enc "abrq" (l-prime y x) (privk "sign" a))+                (privk "sign" t))))+    (non-orig (privk hash_id)))++  ;; TTP forces recovery in response to an abort request++  (defrole ttp-ab2+    (vars (a b t hash_id name) (y x e mesg))+    (trace+     (recv (enc "abrq" (l-prime y x) (privk "sign" a)))+     (recv (cat "sync-abrq"+                (enc "eortag" (hash (l-prime y x)) e+                     (privk "sign" b))))+     (send (enc "eortag" (hash (l-prime y x)) e+                (privk "sign" b))))+    (non-orig (privk hash_id)))++  ;; TTP handles a recovery++  (defrole ttp-rc1+    (vars (a b t hash_id name) (r text) (k skey) (y mesg))+    (trace+     (recv (rr-prime-prime y))+     (send (cat "sync-rc-req"+                (rr-prime-prime y)))+     (send (cat k r)))+    (non-orig (privk hash_id)))++  ;; TTP forces abort in response to a recovery request++  (defrole ttp-rc2+    (vars (a b t hash_id name) (r text) (k skey) (y mesg))+    (trace+     (recv (rr-prime-prime y))+     (recv (cat "sync-rc-req"+		(enc "abrq" (l-prime-prime y) (privk "sign" a))))+     (send (enc "abcf"+                (enc "abrq" (l-prime-prime y) (privk "sign" a))+                (privk "sign" t))))+    (non-orig (privk hash_id)))++  ;; TTP handles a confirm request++  (defrole ttp-cf1+    (vars (a b t hash_id name) (r text) (k skey) (y mesg))+    (trace+     (recv (cf-prime-prime y))+     (send (cat "sync-cf-req"+                (cf-prime-prime y)))+     (send (enc (cf-prime-prime y) (privk "sign" t))))+    (non-orig (privk hash_id)))++  ;; TTP replies with abort token given confirm request++  (defrole ttp-cf2+    (vars (a b t hash_id name) (r text) (k skey) (y mesg))+    (trace+     (recv (cf-prime-prime y))+     (recv (cat "sync-cf-req"+                (enc "abrq"(l-prime-prime y) (privk "sign" a))))+     (send (enc "abcf"+                (enc "abrq"(l-prime-prime y) (privk "sign" a))+                (privk "sign" t))))+    (non-orig (privk hash_id))))++;; End of Wang's protocol defn.++;; Two experiments to prove Lemma 4.1++(defskeleton wang+  (vars (a b t hash_id name) (m data) (r text) (k skey))+  (defstrand init1 1 (b b) (t t) (m m) (r r) (k k))+  (deflistener m)+  (non-orig+   (privk "encr" t))+  (uniq-orig m k)+  (comment "Experiment 1 to prove Lemma 4.1."))++(defskeleton wang+  (vars (a b t hash_id name) (m data) (r text) (k skey))+  (defstrand init1 1 (b b) (t t) (m m) (r r) (k k))+  (deflistener k)+  (non-orig+   (privk "encr" t))+  (uniq-orig m k)+  (comment "Experiment 2 to prove Lemma 4.1."))++;; We now have three experiments+;; to prove Lemma 4.2, clause 1.++(defskeleton wang+  (vars (a b t hash_id name) (m data) (r text) (k skey))+  (defstrand init1 3 (b b) (t t) (m m) (r r) (k k))+  (non-orig+   (privk "sign" b))+  (comment "First of three experiments to prove Lemma 4.2, clause 1."))++(defskeleton wang+  (vars (a b t hash_id name) (m data) (r text) (k skey))+  (defstrand init3 3 (b b) (t t) (m m) (r r) (k k))+  (non-orig+   (privk "sign" b))+  (comment "Second of three experiments to prove Lemma 4.2, clause 1."))++(defskeleton wang+  (vars (a b t hash_id name) (m data) (r text) (k skey))+  (defstrand init5 4 (b b) (t t) (m m) (r r) (k k))+  (non-orig+   (privk "sign" b))+  (comment "Third of three experiments to prove Lemma 4.2, clause 1."))++;; Two experiments to prove 4.2, Clause 2.++(defskeleton wang+  (vars (a b t hash_id name) (m data) (r text) (k skey))+  (defstrand resp1 3 (a a) (t t) (m m) (r r) (k k))+  (non-orig+   (privk "sign" a))+  (comment+   "First of two experiments to prove Lemma 4.2, clause 2."))++(defskeleton wang+  (vars (a b t hash_id name) (m data) (r text) (k skey))+  (defstrand resp2 4 (a a) (t t) (m m) (r r) (k k))+  (non-orig+   (privk "sign" a))+  (comment+   "Second of two experiments to prove Lemma 4.2, clause 2."))++;; Experiment to prove Lemma 4.2, clause 3.++(defskeleton wang+  (vars (a b t hash_id name) (e1 e2 x mesg))+  (defstrand resp3 4 (a a) (t t))+  (non-orig+   (privk "sign" a))+  (comment+   "Experiments to prove Lemma 4.2, clause 3."))++;; One experiment to prove Lemma 4.3, Clause 1.++(defskeleton wang+  (vars (a b t hash_id name) (y x mesg))+  (deflistener+    (enc "abcf" (enc "abrq" (l-prime y x) (privk "sign" a))+	 (privk "sign" t)))+  (non-orig+   (privk "sign" t))+  (comment+   "Experiments to prove Lemma 4.3, clause 1."))++;; Three experiments to prove Lemma 4.3, Clause 2.++(defskeleton wang+  (vars (y x mesg) (a b t name))+  (defstrand ttp-ab1 3 (y y) (x x) (a a) (b b) (t t))+  (non-orig (privk "sign" a)  (privk "encr" t))+  (comment+   "Experiment 1 to prove Lemma 4.3, clause 2."))++(defskeleton wang+  (vars (a b t hash_id name) (r text) (k skey) (y mesg))+  (defstrand ttp-rc2 3 (a a) (b b) (t t))+  (non-orig (privk "sign" a)  (privk "encr" t))+  (comment+   "Experiment 2 to prove Lemma 4.3, clause 2."))++(defskeleton wang+  (vars (a b t hash_id name) (r text) (k skey) (y mesg))+  (defstrand ttp-cf2 3 (a a) (b b) (t t))+  (non-orig (privk "sign" a)  (privk "encr" t))+  (comment+   "Experiment 3 to prove Lemma 4.3, clause 2."))
+ tst/wang-hash.tst view
@@ -0,0 +1,5380 @@+(herald "Wang's Fair Exchange Protocol" (bound 10))++(comment "CPSA 2.2.5")+(comment "All input read")+(comment "Strand count bounded at 10")++(defprotocol wang basic+  (defrole init1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b))) (send (cat k r))))+  (defrole init2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a))+          (privk "sign" t)))))+  (defrole init3+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))))+  (defrole init4+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a))+          (privk "sign" t)))))+  (defrole init5+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))))+  (defrole resp1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b))) (recv (cat k r))))+  (defrole resp2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (cat (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b)))) (recv (cat k r))))+  (defrole resp3+    (vars (a b t name) (e1 e2 x mesg))+    (trace+      (recv+        (cat (cat a b t (hash e1) x) e1 e2+          (enc "eootag" (hash a b t (hash e1) x) e2 (privk "sign" a))))+      (send+        (cat (cat a b t (hash e1) x) e2+          (enc "eootag" (hash a b t (hash e1) x) e2 (privk "sign" a))+          (enc "eortag" (hash a b t (hash e1) x) e2 (privk "sign" b))))+      (send+        (cat (cat a b t (hash e1) x) e2+          (enc "eootag" (hash a b t (hash e1) x) e2 (privk "sign" a))+          (enc "eortag" (hash a b t (hash e1) x) e2 (privk "sign" b))+          (enc "rcrq" (cat a b t (hash e1) x) e2 (privk "sign" b))))+      (recv+        (enc "abcf" (enc "abrq" a b t (hash e1) x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab1+    (vars (a b t name) (y x mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (send (cat "sync-abrq" (enc "abrq" a b t y x (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab2+    (vars (a b t name) (y x e mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (recv+        (cat "sync-abrq"+          (enc "eortag" (hash a b t y x) e (privk "sign" b))))+      (send (enc "eortag" (hash a b t y x) e (privk "sign" b)))))+  (defrole ttp-rc1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat "sync-rc-req" (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b)))) (send (cat k r))))+  (defrole ttp-rc2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (recv+        (cat "sync-rc-req"+          (enc "abrq" a b t y (hash k) (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y (hash k) (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-cf1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat "sync-cf-req" (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (enc (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b)) (privk "sign" t)))))+  (defrole ttp-cf2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (recv+        (cat "sync-cf-req"+          (enc "abrq" a b t y (hash k) (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y (hash k) (privk "sign" a))+          (privk "sign" t))))))++(defskeleton wang+  (vars (r text) (m data) (b t a name) (k skey))+  (defstrand init1 1 (r r) (m m) (a a) (b b) (t t) (k k))+  (deflistener m)+  (non-orig (privk "encr" t))+  (uniq-orig m k)+  (comment "Experiment 1 to prove Lemma 4.1.")+  (traces+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))) ((recv m) (send m)))+  (label 0)+  (unrealized (1 0))+  (preskeleton)+  (comment "Not a skeleton"))++(defskeleton wang+  (vars (r text) (m data) (b t a name) (k skey))+  (defstrand init1 1 (r r) (m m) (a a) (b b) (t t) (k k))+  (deflistener m)+  (precedes ((0 0) (1 0)))+  (non-orig (privk "encr" t))+  (uniq-orig m k)+  (traces+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))) ((recv m) (send m)))+  (label 1)+  (parent 0)+  (unrealized (1 0))+  (origs (m (0 0)) (k (0 0)))+  (comment "1 in cohort - 1 not yet seen"))++(defskeleton wang+  (vars (r text) (m data) (b t a name) (k skey))+  (defstrand init1 1 (r r) (m m) (a a) (b b) (t t) (k k))+  (deflistener m)+  (deflistener k)+  (precedes ((0 0) (2 0)) ((2 1) (1 0)))+  (non-orig (privk "encr" t))+  (uniq-orig m k)+  (operation nonce-test (added-listener k) m (1 0) (enc m k))+  (traces+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))) ((recv m) (send m))+    ((recv k) (send k)))+  (label 2)+  (parent 1)+  (seen 3)+  (unrealized (2 0))+  (comment "3 in cohort - 2 not yet seen"))++(defskeleton wang+  (vars (r text) (m data) (b t a name) (k skey))+  (deflistener m)+  (deflistener k)+  (defstrand init1 3 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 1) (0 0)) ((2 2) (1 0)))+  (non-orig (privk "encr" t))+  (uniq-orig m k)+  (operation nonce-test (added-strand init1 3) k (2 0)+    (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+      (pubk "encr" t)))+  (traces ((recv m) (send m)) ((recv k) (send k))+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b))) (send (cat k r))))+  (label 3)+  (parent 2)+  (unrealized)+  (comment "1 in cohort - 1 not yet seen"))++(defskeleton wang+  (vars (r text) (m data) (b t a name) (k skey))+  (defstrand init1 1 (r r) (m m) (a a) (b b) (t t) (k k))+  (deflistener m)+  (deflistener k)+  (defstrand ttp-rc1 3 (y (hash (enc m k))) (r r) (a a) (b b) (t t)+    (k k))+  (precedes ((0 0) (3 0)) ((2 1) (1 0)) ((3 2) (2 0)))+  (non-orig (privk "encr" t))+  (uniq-orig m k)+  (operation nonce-test (added-strand ttp-rc1 3) k (2 0)+    (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+      (pubk "encr" t)))+  (traces+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))) ((recv m) (send m))+    ((recv k) (send k))+    ((recv+       (cat (cat a b t (hash (enc m k)) (hash k))+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))+         (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" b))+         (enc "rcrq" (cat a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat "sync-rc-req" (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b)))) (send (cat k r))))+  (label 4)+  (parent 2)+  (unrealized)+  (comment "1 in cohort - 1 not yet seen"))++(defskeleton wang+  (vars (r text) (m data) (b t a name) (k skey))+  (deflistener m)+  (defstrand init1 3 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 2) (0 0)))+  (non-orig (privk "encr" t))+  (uniq-orig m k)+  (operation generalization deleted (1 0))+  (traces ((recv m) (send m))+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b))) (send (cat k r))))+  (label 5)+  (parent 3)+  (unrealized)+  (shape)+  (maps ((1 0) ((b b) (t t) (m m) (r r) (k k) (a a))))+  (origs (m (1 0)) (k (1 0))))++(defskeleton wang+  (vars (r text) (m data) (b t a name) (k skey))+  (defstrand init1 1 (r r) (m m) (a a) (b b) (t t) (k k))+  (deflistener m)+  (defstrand ttp-rc1 3 (y (hash (enc m k))) (r r) (a a) (b b) (t t)+    (k k))+  (precedes ((0 0) (2 0)) ((2 2) (1 0)))+  (non-orig (privk "encr" t))+  (uniq-orig m k)+  (operation generalization deleted (2 0))+  (traces+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))) ((recv m) (send m))+    ((recv+       (cat (cat a b t (hash (enc m k)) (hash k))+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))+         (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" b))+         (enc "rcrq" (cat a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat "sync-rc-req" (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b)))) (send (cat k r))))+  (label 6)+  (parent 4)+  (unrealized)+  (shape)+  (maps ((0 1) ((b b) (t t) (m m) (r r) (k k) (a a))))+  (origs (m (0 0)) (k (0 0))))++(comment "Nothing left to do")++(defprotocol wang basic+  (defrole init1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b))) (send (cat k r))))+  (defrole init2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a))+          (privk "sign" t)))))+  (defrole init3+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))))+  (defrole init4+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a))+          (privk "sign" t)))))+  (defrole init5+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))))+  (defrole resp1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b))) (recv (cat k r))))+  (defrole resp2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (cat (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b)))) (recv (cat k r))))+  (defrole resp3+    (vars (a b t name) (e1 e2 x mesg))+    (trace+      (recv+        (cat (cat a b t (hash e1) x) e1 e2+          (enc "eootag" (hash a b t (hash e1) x) e2 (privk "sign" a))))+      (send+        (cat (cat a b t (hash e1) x) e2+          (enc "eootag" (hash a b t (hash e1) x) e2 (privk "sign" a))+          (enc "eortag" (hash a b t (hash e1) x) e2 (privk "sign" b))))+      (send+        (cat (cat a b t (hash e1) x) e2+          (enc "eootag" (hash a b t (hash e1) x) e2 (privk "sign" a))+          (enc "eortag" (hash a b t (hash e1) x) e2 (privk "sign" b))+          (enc "rcrq" (cat a b t (hash e1) x) e2 (privk "sign" b))))+      (recv+        (enc "abcf" (enc "abrq" a b t (hash e1) x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab1+    (vars (a b t name) (y x mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (send (cat "sync-abrq" (enc "abrq" a b t y x (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab2+    (vars (a b t name) (y x e mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (recv+        (cat "sync-abrq"+          (enc "eortag" (hash a b t y x) e (privk "sign" b))))+      (send (enc "eortag" (hash a b t y x) e (privk "sign" b)))))+  (defrole ttp-rc1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat "sync-rc-req" (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b)))) (send (cat k r))))+  (defrole ttp-rc2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (recv+        (cat "sync-rc-req"+          (enc "abrq" a b t y (hash k) (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y (hash k) (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-cf1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat "sync-cf-req" (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (enc (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b)) (privk "sign" t)))))+  (defrole ttp-cf2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (recv+        (cat "sync-cf-req"+          (enc "abrq" a b t y (hash k) (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y (hash k) (privk "sign" a))+          (privk "sign" t))))))++(defskeleton wang+  (vars (r text) (m data) (b t a name) (k skey))+  (defstrand init1 1 (r r) (m m) (a a) (b b) (t t) (k k))+  (deflistener k)+  (non-orig (privk "encr" t))+  (uniq-orig m k)+  (comment "Experiment 2 to prove Lemma 4.1.")+  (traces+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))) ((recv k) (send k)))+  (label 7)+  (unrealized (1 0))+  (preskeleton)+  (comment "Not a skeleton"))++(defskeleton wang+  (vars (r text) (m data) (b t a name) (k skey))+  (defstrand init1 1 (r r) (m m) (a a) (b b) (t t) (k k))+  (deflistener k)+  (precedes ((0 0) (1 0)))+  (non-orig (privk "encr" t))+  (uniq-orig m k)+  (traces+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))) ((recv k) (send k)))+  (label 8)+  (parent 7)+  (seen 9)+  (unrealized (1 0))+  (origs (m (0 0)) (k (0 0)))+  (comment "3 in cohort - 2 not yet seen"))++(defskeleton wang+  (vars (r text) (m data) (b t a name) (k skey))+  (deflistener k)+  (defstrand init1 3 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 2) (0 0)))+  (non-orig (privk "encr" t))+  (uniq-orig m k)+  (operation nonce-test (added-strand init1 3) k (1 0)+    (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+      (pubk "encr" t)))+  (traces ((recv k) (send k))+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b))) (send (cat k r))))+  (label 9)+  (parent 8)+  (unrealized)+  (shape)+  (maps ((1 0) ((b b) (t t) (m m) (r r) (k k) (a a))))+  (origs (m (1 0)) (k (1 0))))++(defskeleton wang+  (vars (r text) (m data) (b t a name) (k skey))+  (defstrand init1 1 (r r) (m m) (a a) (b b) (t t) (k k))+  (deflistener k)+  (defstrand ttp-rc1 3 (y (hash (enc m k))) (r r) (a a) (b b) (t t)+    (k k))+  (precedes ((0 0) (2 0)) ((2 2) (1 0)))+  (non-orig (privk "encr" t))+  (uniq-orig m k)+  (operation nonce-test (added-strand ttp-rc1 3) k (1 0)+    (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+      (pubk "encr" t)))+  (traces+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))) ((recv k) (send k))+    ((recv+       (cat (cat a b t (hash (enc m k)) (hash k))+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))+         (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" b))+         (enc "rcrq" (cat a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat "sync-rc-req" (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b)))) (send (cat k r))))+  (label 10)+  (parent 8)+  (unrealized)+  (shape)+  (maps ((0 1) ((b b) (t t) (m m) (r r) (k k) (a a))))+  (origs (m (0 0)) (k (0 0))))++(comment "Nothing left to do")++(defprotocol wang basic+  (defrole init1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b))) (send (cat k r))))+  (defrole init2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a))+          (privk "sign" t)))))+  (defrole init3+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))))+  (defrole init4+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a))+          (privk "sign" t)))))+  (defrole init5+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))))+  (defrole resp1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b))) (recv (cat k r))))+  (defrole resp2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (cat (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b)))) (recv (cat k r))))+  (defrole resp3+    (vars (a b t name) (e1 e2 x mesg))+    (trace+      (recv+        (cat (cat a b t (hash e1) x) e1 e2+          (enc "eootag" (hash a b t (hash e1) x) e2 (privk "sign" a))))+      (send+        (cat (cat a b t (hash e1) x) e2+          (enc "eootag" (hash a b t (hash e1) x) e2 (privk "sign" a))+          (enc "eortag" (hash a b t (hash e1) x) e2 (privk "sign" b))))+      (send+        (cat (cat a b t (hash e1) x) e2+          (enc "eootag" (hash a b t (hash e1) x) e2 (privk "sign" a))+          (enc "eortag" (hash a b t (hash e1) x) e2 (privk "sign" b))+          (enc "rcrq" (cat a b t (hash e1) x) e2 (privk "sign" b))))+      (recv+        (enc "abcf" (enc "abrq" a b t (hash e1) x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab1+    (vars (a b t name) (y x mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (send (cat "sync-abrq" (enc "abrq" a b t y x (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab2+    (vars (a b t name) (y x e mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (recv+        (cat "sync-abrq"+          (enc "eortag" (hash a b t y x) e (privk "sign" b))))+      (send (enc "eortag" (hash a b t y x) e (privk "sign" b)))))+  (defrole ttp-rc1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat "sync-rc-req" (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b)))) (send (cat k r))))+  (defrole ttp-rc2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (recv+        (cat "sync-rc-req"+          (enc "abrq" a b t y (hash k) (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y (hash k) (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-cf1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat "sync-cf-req" (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (enc (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b)) (privk "sign" t)))))+  (defrole ttp-cf2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (recv+        (cat "sync-cf-req"+          (enc "abrq" a b t y (hash k) (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y (hash k) (privk "sign" a))+          (privk "sign" t))))))++(defskeleton wang+  (vars (r text) (m data) (b t a name) (k skey))+  (defstrand init1 3 (r r) (m m) (a a) (b b) (t t) (k k))+  (non-orig (privk "sign" b))+  (comment "First of three experiments to prove Lemma 4.2, clause 1.")+  (traces+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b))) (send (cat k r))))+  (label 11)+  (seen 13)+  (unrealized (0 1))+  (origs)+  (comment "3 in cohort - 2 not yet seen"))++(defskeleton wang+  (vars (r text) (m data) (b t a name) (k skey))+  (defstrand init1 3 (r r) (m m) (a a) (b b) (t t) (k k))+  (defstrand resp1 2 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 1) (0 1)))+  (non-orig (privk "sign" b))+  (operation encryption-test (added-strand resp1 2)+    (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+      (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+        (pubk "encr" t)) (privk "sign" b)) (0 1))+  (traces+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b))) (send (cat k r)))+    ((recv+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))))+  (label 12)+  (parent 11)+  (unrealized)+  (shape)+  (maps ((0) ((b b) (t t) (m m) (r r) (k k) (a a))))+  (origs))++(defskeleton wang+  (vars (r text) (m data) (b t a name) (k skey))+  (defstrand init1 3 (r r) (m m) (a a) (b b) (t t) (k k))+  (defstrand resp2 2 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 1) (0 1)))+  (non-orig (privk "sign" b))+  (operation encryption-test (added-strand resp2 2)+    (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+      (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+        (pubk "encr" t)) (privk "sign" b)) (0 1))+  (traces+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b))) (send (cat k r)))+    ((recv+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))+      (send+        (cat (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))))))+  (label 13)+  (parent 11)+  (unrealized)+  (shape)+  (maps ((0) ((b b) (t t) (m m) (r r) (k k) (a a))))+  (origs))++(comment "Nothing left to do")++(defprotocol wang basic+  (defrole init1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b))) (send (cat k r))))+  (defrole init2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a))+          (privk "sign" t)))))+  (defrole init3+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))))+  (defrole init4+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a))+          (privk "sign" t)))))+  (defrole init5+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))))+  (defrole resp1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b))) (recv (cat k r))))+  (defrole resp2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (cat (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b)))) (recv (cat k r))))+  (defrole resp3+    (vars (a b t name) (e1 e2 x mesg))+    (trace+      (recv+        (cat (cat a b t (hash e1) x) e1 e2+          (enc "eootag" (hash a b t (hash e1) x) e2 (privk "sign" a))))+      (send+        (cat (cat a b t (hash e1) x) e2+          (enc "eootag" (hash a b t (hash e1) x) e2 (privk "sign" a))+          (enc "eortag" (hash a b t (hash e1) x) e2 (privk "sign" b))))+      (send+        (cat (cat a b t (hash e1) x) e2+          (enc "eootag" (hash a b t (hash e1) x) e2 (privk "sign" a))+          (enc "eortag" (hash a b t (hash e1) x) e2 (privk "sign" b))+          (enc "rcrq" (cat a b t (hash e1) x) e2 (privk "sign" b))))+      (recv+        (enc "abcf" (enc "abrq" a b t (hash e1) x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab1+    (vars (a b t name) (y x mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (send (cat "sync-abrq" (enc "abrq" a b t y x (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab2+    (vars (a b t name) (y x e mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (recv+        (cat "sync-abrq"+          (enc "eortag" (hash a b t y x) e (privk "sign" b))))+      (send (enc "eortag" (hash a b t y x) e (privk "sign" b)))))+  (defrole ttp-rc1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat "sync-rc-req" (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b)))) (send (cat k r))))+  (defrole ttp-rc2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (recv+        (cat "sync-rc-req"+          (enc "abrq" a b t y (hash k) (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y (hash k) (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-cf1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat "sync-cf-req" (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (enc (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b)) (privk "sign" t)))))+  (defrole ttp-cf2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (recv+        (cat "sync-cf-req"+          (enc "abrq" a b t y (hash k) (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y (hash k) (privk "sign" a))+          (privk "sign" t))))))++(defskeleton wang+  (vars (r text) (m data) (b t a name) (k skey))+  (defstrand init3 3 (r r) (m m) (a a) (b b) (t t) (k k))+  (non-orig (privk "sign" b))+  (comment "Second of three experiments to prove Lemma 4.2, clause 1.")+  (traces+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))))+  (label 14)+  (seen 16)+  (unrealized (0 2))+  (origs)+  (comment "3 in cohort - 2 not yet seen"))++(defskeleton wang+  (vars (r text) (m data) (b t a name) (k skey))+  (defstrand init3 3 (r r) (m m) (a a) (b b) (t t) (k k))+  (defstrand resp1 2 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 1) (0 2)))+  (non-orig (privk "sign" b))+  (operation encryption-test (added-strand resp1 2)+    (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+      (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+        (pubk "encr" t)) (privk "sign" b)) (0 2))+  (traces+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b))))+    ((recv+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))))+  (label 15)+  (parent 14)+  (unrealized)+  (shape)+  (maps ((0) ((b b) (t t) (m m) (r r) (k k) (a a))))+  (origs))++(defskeleton wang+  (vars (r text) (m data) (b t a name) (k skey))+  (defstrand init3 3 (r r) (m m) (a a) (b b) (t t) (k k))+  (defstrand resp2 2 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 1) (0 2)))+  (non-orig (privk "sign" b))+  (operation encryption-test (added-strand resp2 2)+    (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+      (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+        (pubk "encr" t)) (privk "sign" b)) (0 2))+  (traces+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b))))+    ((recv+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))+      (send+        (cat (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))))))+  (label 16)+  (parent 14)+  (unrealized)+  (shape)+  (maps ((0) ((b b) (t t) (m m) (r r) (k k) (a a))))+  (origs))++(comment "Nothing left to do")++(defprotocol wang basic+  (defrole init1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b))) (send (cat k r))))+  (defrole init2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a))+          (privk "sign" t)))))+  (defrole init3+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))))+  (defrole init4+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a))+          (privk "sign" t)))))+  (defrole init5+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))))+  (defrole resp1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b))) (recv (cat k r))))+  (defrole resp2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (cat (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b)))) (recv (cat k r))))+  (defrole resp3+    (vars (a b t name) (e1 e2 x mesg))+    (trace+      (recv+        (cat (cat a b t (hash e1) x) e1 e2+          (enc "eootag" (hash a b t (hash e1) x) e2 (privk "sign" a))))+      (send+        (cat (cat a b t (hash e1) x) e2+          (enc "eootag" (hash a b t (hash e1) x) e2 (privk "sign" a))+          (enc "eortag" (hash a b t (hash e1) x) e2 (privk "sign" b))))+      (send+        (cat (cat a b t (hash e1) x) e2+          (enc "eootag" (hash a b t (hash e1) x) e2 (privk "sign" a))+          (enc "eortag" (hash a b t (hash e1) x) e2 (privk "sign" b))+          (enc "rcrq" (cat a b t (hash e1) x) e2 (privk "sign" b))))+      (recv+        (enc "abcf" (enc "abrq" a b t (hash e1) x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab1+    (vars (a b t name) (y x mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (send (cat "sync-abrq" (enc "abrq" a b t y x (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab2+    (vars (a b t name) (y x e mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (recv+        (cat "sync-abrq"+          (enc "eortag" (hash a b t y x) e (privk "sign" b))))+      (send (enc "eortag" (hash a b t y x) e (privk "sign" b)))))+  (defrole ttp-rc1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat "sync-rc-req" (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b)))) (send (cat k r))))+  (defrole ttp-rc2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (recv+        (cat "sync-rc-req"+          (enc "abrq" a b t y (hash k) (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y (hash k) (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-cf1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat "sync-cf-req" (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (enc (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b)) (privk "sign" t)))))+  (defrole ttp-cf2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (recv+        (cat "sync-cf-req"+          (enc "abrq" a b t y (hash k) (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y (hash k) (privk "sign" a))+          (privk "sign" t))))))++(defskeleton wang+  (vars (r text) (m data) (b t a name) (k skey))+  (defstrand init5 4 (r r) (m m) (a a) (b b) (t t) (k k))+  (non-orig (privk "sign" b))+  (comment "Third of three experiments to prove Lemma 4.2, clause 1.")+  (traces+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))))+  (label 17)+  (seen 19)+  (unrealized (0 1) (0 3))+  (origs)+  (comment "3 in cohort - 2 not yet seen"))++(defskeleton wang+  (vars (r text) (m data) (b t a name) (k skey))+  (defstrand init5 4 (r r) (m m) (a a) (b b) (t t) (k k))+  (defstrand resp1 2 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 1) (0 1)))+  (non-orig (privk "sign" b))+  (operation encryption-test (added-strand resp1 2)+    (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+      (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+        (pubk "encr" t)) (privk "sign" b)) (0 1))+  (traces+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b))))+    ((recv+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))))+  (label 18)+  (parent 17)+  (unrealized)+  (shape)+  (maps ((0) ((b b) (t t) (m m) (r r) (k k) (a a))))+  (origs))++(defskeleton wang+  (vars (r text) (m data) (b t a name) (k skey))+  (defstrand init5 4 (r r) (m m) (a a) (b b) (t t) (k k))+  (defstrand resp2 2 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 1) (0 1)))+  (non-orig (privk "sign" b))+  (operation encryption-test (added-strand resp2 2)+    (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+      (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+        (pubk "encr" t)) (privk "sign" b)) (0 1))+  (traces+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b))))+    ((recv+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))+      (send+        (cat (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))))))+  (label 19)+  (parent 17)+  (unrealized)+  (shape)+  (maps ((0) ((b b) (t t) (m m) (r r) (k k) (a a))))+  (origs))++(comment "Nothing left to do")++(defprotocol wang basic+  (defrole init1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b))) (send (cat k r))))+  (defrole init2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a))+          (privk "sign" t)))))+  (defrole init3+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))))+  (defrole init4+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a))+          (privk "sign" t)))))+  (defrole init5+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))))+  (defrole resp1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b))) (recv (cat k r))))+  (defrole resp2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (cat (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b)))) (recv (cat k r))))+  (defrole resp3+    (vars (a b t name) (e1 e2 x mesg))+    (trace+      (recv+        (cat (cat a b t (hash e1) x) e1 e2+          (enc "eootag" (hash a b t (hash e1) x) e2 (privk "sign" a))))+      (send+        (cat (cat a b t (hash e1) x) e2+          (enc "eootag" (hash a b t (hash e1) x) e2 (privk "sign" a))+          (enc "eortag" (hash a b t (hash e1) x) e2 (privk "sign" b))))+      (send+        (cat (cat a b t (hash e1) x) e2+          (enc "eootag" (hash a b t (hash e1) x) e2 (privk "sign" a))+          (enc "eortag" (hash a b t (hash e1) x) e2 (privk "sign" b))+          (enc "rcrq" (cat a b t (hash e1) x) e2 (privk "sign" b))))+      (recv+        (enc "abcf" (enc "abrq" a b t (hash e1) x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab1+    (vars (a b t name) (y x mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (send (cat "sync-abrq" (enc "abrq" a b t y x (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab2+    (vars (a b t name) (y x e mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (recv+        (cat "sync-abrq"+          (enc "eortag" (hash a b t y x) e (privk "sign" b))))+      (send (enc "eortag" (hash a b t y x) e (privk "sign" b)))))+  (defrole ttp-rc1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat "sync-rc-req" (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b)))) (send (cat k r))))+  (defrole ttp-rc2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (recv+        (cat "sync-rc-req"+          (enc "abrq" a b t y (hash k) (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y (hash k) (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-cf1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat "sync-cf-req" (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (enc (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b)) (privk "sign" t)))))+  (defrole ttp-cf2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (recv+        (cat "sync-cf-req"+          (enc "abrq" a b t y (hash k) (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y (hash k) (privk "sign" a))+          (privk "sign" t))))))++(defskeleton wang+  (vars (r text) (m data) (a t b name) (k skey))+  (defstrand resp1 3 (r r) (m m) (a a) (b b) (t t) (k k))+  (non-orig (privk "sign" a))+  (comment "First of two experiments to prove Lemma 4.2, clause 2.")+  (traces+    ((recv+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b))) (recv (cat k r))))+  (label 20)+  (seen 21)+  (unrealized (0 0))+  (origs)+  (comment "5 in cohort - 1 not yet seen"))++(defskeleton wang+  (vars (r text) (m data) (a t b name) (k skey))+  (defstrand resp1 3 (r r) (m m) (a a) (b b) (t t) (k k))+  (defstrand init1 1 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 0) (0 0)))+  (non-orig (privk "sign" a))+  (operation encryption-test (added-strand init1 1)+    (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+      (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+        (pubk "encr" t)) (privk "sign" a)) (0 0))+  (traces+    ((recv+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b))) (recv (cat k r)))+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))))+  (label 21)+  (parent 20)+  (unrealized)+  (shape)+  (maps ((0) ((a a) (t t) (m m) (r r) (k k) (b b))))+  (origs))++(comment "Nothing left to do")++(defprotocol wang basic+  (defrole init1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b))) (send (cat k r))))+  (defrole init2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a))+          (privk "sign" t)))))+  (defrole init3+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))))+  (defrole init4+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a))+          (privk "sign" t)))))+  (defrole init5+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))))+  (defrole resp1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b))) (recv (cat k r))))+  (defrole resp2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (cat (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b)))) (recv (cat k r))))+  (defrole resp3+    (vars (a b t name) (e1 e2 x mesg))+    (trace+      (recv+        (cat (cat a b t (hash e1) x) e1 e2+          (enc "eootag" (hash a b t (hash e1) x) e2 (privk "sign" a))))+      (send+        (cat (cat a b t (hash e1) x) e2+          (enc "eootag" (hash a b t (hash e1) x) e2 (privk "sign" a))+          (enc "eortag" (hash a b t (hash e1) x) e2 (privk "sign" b))))+      (send+        (cat (cat a b t (hash e1) x) e2+          (enc "eootag" (hash a b t (hash e1) x) e2 (privk "sign" a))+          (enc "eortag" (hash a b t (hash e1) x) e2 (privk "sign" b))+          (enc "rcrq" (cat a b t (hash e1) x) e2 (privk "sign" b))))+      (recv+        (enc "abcf" (enc "abrq" a b t (hash e1) x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab1+    (vars (a b t name) (y x mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (send (cat "sync-abrq" (enc "abrq" a b t y x (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab2+    (vars (a b t name) (y x e mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (recv+        (cat "sync-abrq"+          (enc "eortag" (hash a b t y x) e (privk "sign" b))))+      (send (enc "eortag" (hash a b t y x) e (privk "sign" b)))))+  (defrole ttp-rc1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat "sync-rc-req" (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b)))) (send (cat k r))))+  (defrole ttp-rc2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (recv+        (cat "sync-rc-req"+          (enc "abrq" a b t y (hash k) (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y (hash k) (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-cf1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat "sync-cf-req" (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (enc (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b)) (privk "sign" t)))))+  (defrole ttp-cf2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (recv+        (cat "sync-cf-req"+          (enc "abrq" a b t y (hash k) (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y (hash k) (privk "sign" a))+          (privk "sign" t))))))++(defskeleton wang+  (vars (r text) (m data) (a t b name) (k skey))+  (defstrand resp2 4 (r r) (m m) (a a) (b b) (t t) (k k))+  (non-orig (privk "sign" a))+  (comment "Second of two experiments to prove Lemma 4.2, clause 2.")+  (traces+    ((recv+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))+      (send+        (cat (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b)))) (recv (cat k r))))+  (label 22)+  (seen 23)+  (unrealized (0 0))+  (origs)+  (comment "5 in cohort - 1 not yet seen"))++(defskeleton wang+  (vars (r text) (m data) (a t b name) (k skey))+  (defstrand resp2 4 (r r) (m m) (a a) (b b) (t t) (k k))+  (defstrand init1 1 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 0) (0 0)))+  (non-orig (privk "sign" a))+  (operation encryption-test (added-strand init1 1)+    (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+      (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+        (pubk "encr" t)) (privk "sign" a)) (0 0))+  (traces+    ((recv+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))+      (send+        (cat (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b)))) (recv (cat k r)))+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))))+  (label 23)+  (parent 22)+  (unrealized)+  (shape)+  (maps ((0) ((a a) (t t) (m m) (r r) (k k) (b b))))+  (origs))++(comment "Nothing left to do")++(defprotocol wang basic+  (defrole init1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b))) (send (cat k r))))+  (defrole init2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a))+          (privk "sign" t)))))+  (defrole init3+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))))+  (defrole init4+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a))+          (privk "sign" t)))))+  (defrole init5+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))))+  (defrole resp1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b))) (recv (cat k r))))+  (defrole resp2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (cat (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b)))) (recv (cat k r))))+  (defrole resp3+    (vars (a b t name) (e1 e2 x mesg))+    (trace+      (recv+        (cat (cat a b t (hash e1) x) e1 e2+          (enc "eootag" (hash a b t (hash e1) x) e2 (privk "sign" a))))+      (send+        (cat (cat a b t (hash e1) x) e2+          (enc "eootag" (hash a b t (hash e1) x) e2 (privk "sign" a))+          (enc "eortag" (hash a b t (hash e1) x) e2 (privk "sign" b))))+      (send+        (cat (cat a b t (hash e1) x) e2+          (enc "eootag" (hash a b t (hash e1) x) e2 (privk "sign" a))+          (enc "eortag" (hash a b t (hash e1) x) e2 (privk "sign" b))+          (enc "rcrq" (cat a b t (hash e1) x) e2 (privk "sign" b))))+      (recv+        (enc "abcf" (enc "abrq" a b t (hash e1) x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab1+    (vars (a b t name) (y x mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (send (cat "sync-abrq" (enc "abrq" a b t y x (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab2+    (vars (a b t name) (y x e mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (recv+        (cat "sync-abrq"+          (enc "eortag" (hash a b t y x) e (privk "sign" b))))+      (send (enc "eortag" (hash a b t y x) e (privk "sign" b)))))+  (defrole ttp-rc1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat "sync-rc-req" (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b)))) (send (cat k r))))+  (defrole ttp-rc2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (recv+        (cat "sync-rc-req"+          (enc "abrq" a b t y (hash k) (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y (hash k) (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-cf1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat "sync-cf-req" (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (enc (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b)) (privk "sign" t)))))+  (defrole ttp-cf2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (recv+        (cat "sync-cf-req"+          (enc "abrq" a b t y (hash k) (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y (hash k) (privk "sign" a))+          (privk "sign" t))))))++(defskeleton wang+  (vars (e1 e2 x mesg) (a t b name))+  (defstrand resp3 4 (e1 e1) (e2 e2) (x x) (a a) (b b) (t t))+  (non-orig (privk "sign" a))+  (comment "Experiments to prove Lemma 4.2, clause 3.")+  (traces+    ((recv+       (cat (cat a b t (hash e1) x) e1 e2+         (enc "eootag" (hash a b t (hash e1) x) e2 (privk "sign" a))))+      (send+        (cat (cat a b t (hash e1) x) e2+          (enc "eootag" (hash a b t (hash e1) x) e2 (privk "sign" a))+          (enc "eortag" (hash a b t (hash e1) x) e2 (privk "sign" b))))+      (send+        (cat (cat a b t (hash e1) x) e2+          (enc "eootag" (hash a b t (hash e1) x) e2 (privk "sign" a))+          (enc "eortag" (hash a b t (hash e1) x) e2 (privk "sign" b))+          (enc "rcrq" (cat a b t (hash e1) x) e2 (privk "sign" b))))+      (recv+        (enc "abcf" (enc "abrq" a b t (hash e1) x (privk "sign" a))+          (privk "sign" t)))))+  (label 24)+  (seen 25)+  (unrealized (0 0) (0 3))+  (origs)+  (comment "5 in cohort - 1 not yet seen"))++(defskeleton wang+  (vars (r text) (m data) (a t b name) (k skey))+  (defstrand resp3 4 (e1 (enc m k))+    (e2+      (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+        (pubk "encr" t))) (x (hash k)) (a a) (b b) (t t))+  (defstrand init1 1 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 0) (0 0)))+  (non-orig (privk "sign" a))+  (operation encryption-test (added-strand init1 1)+    (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+      (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+        (pubk "encr" t)) (privk "sign" a)) (0 0))+  (traces+    ((recv+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))+      (send+        (cat (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a))+          (privk "sign" t))))+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))))+  (label 25)+  (parent 24)+  (seen 26 27 28 29)+  (unrealized (0 3))+  (comment "8 in cohort - 4 not yet seen"))++(defskeleton wang+  (vars (r r-0 text) (m data) (a t b name) (k skey))+  (defstrand resp3 4 (e1 (enc m k))+    (e2+      (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+        (pubk "encr" t))) (x (hash k)) (a a) (b b) (t t))+  (defstrand init1 1 (r r) (m m) (a a) (b b) (t t) (k k))+  (defstrand init2 2 (r r-0) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 0) (0 0)) ((2 1) (0 3)))+  (non-orig (privk "sign" a))+  (operation encryption-test (added-strand init2 2)+    (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)) (0 3))+  (traces+    ((recv+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))+      (send+        (cat (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a))+          (privk "sign" t))))+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a)))))+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r-0+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r-0+             (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))))+  (label 26)+  (parent 25)+  (seen 27)+  (unrealized)+  (shape)+  (maps+    ((0)+      ((a a) (t t) (b b) (e1 (enc m k))+        (e2+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))) (x (hash k)))))+  (origs)+  (comment "1 in cohort - 0 not yet seen"))++(defskeleton wang+  (vars (r text) (m data) (a t b name) (k skey))+  (defstrand resp3 4 (e1 (enc m k))+    (e2+      (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+        (pubk "encr" t))) (x (hash k)) (a a) (b b) (t t))+  (defstrand init2 2 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 0) (0 0)) ((1 1) (0 3)))+  (non-orig (privk "sign" a))+  (operation encryption-test (displaced 1 2 init2 2)+    (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)) (0 3))+  (traces+    ((recv+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))+      (send+        (cat (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a))+          (privk "sign" t))))+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))))+  (label 27)+  (parent 25)+  (unrealized)+  (shape)+  (maps+    ((0)+      ((a a) (t t) (b b) (e1 (enc m k))+        (e2+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))) (x (hash k)))))+  (origs))++(defskeleton wang+  (vars (r r-0 text) (m data) (a t b name) (k skey))+  (defstrand resp3 4 (e1 (enc m k))+    (e2+      (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+        (pubk "encr" t))) (x (hash k)) (a a) (b b) (t t))+  (defstrand init1 1 (r r) (m m) (a a) (b b) (t t) (k k))+  (defstrand init4 3 (r r-0) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 0) (0 0)) ((2 2) (0 3)))+  (non-orig (privk "sign" a))+  (operation encryption-test (added-strand init4 3)+    (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)) (0 3))+  (traces+    ((recv+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))+      (send+        (cat (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a))+          (privk "sign" t))))+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a)))))+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r-0+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r-0+             (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r-0+            (pubk "encr" t)) (privk "sign" b)))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))))+  (label 28)+  (parent 25)+  (seen 29)+  (unrealized)+  (shape)+  (maps+    ((0)+      ((a a) (t t) (b b) (e1 (enc m k))+        (e2+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))) (x (hash k)))))+  (origs)+  (comment "1 in cohort - 0 not yet seen"))++(defskeleton wang+  (vars (r text) (m data) (a t b name) (k skey))+  (defstrand resp3 4 (e1 (enc m k))+    (e2+      (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+        (pubk "encr" t))) (x (hash k)) (a a) (b b) (t t))+  (defstrand init4 3 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 0) (0 0)) ((1 2) (0 3)))+  (non-orig (privk "sign" a))+  (operation encryption-test (displaced 1 2 init4 3)+    (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)) (0 3))+  (traces+    ((recv+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))+      (send+        (cat (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a))+          (privk "sign" t))))+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))))+  (label 29)+  (parent 25)+  (unrealized)+  (shape)+  (maps+    ((0)+      ((a a) (t t) (b b) (e1 (enc m k))+        (e2+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))) (x (hash k)))))+  (origs))++(comment "Nothing left to do")++(defprotocol wang basic+  (defrole init1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b))) (send (cat k r))))+  (defrole init2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a))+          (privk "sign" t)))))+  (defrole init3+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))))+  (defrole init4+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a))+          (privk "sign" t)))))+  (defrole init5+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))))+  (defrole resp1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b))) (recv (cat k r))))+  (defrole resp2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (cat (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b)))) (recv (cat k r))))+  (defrole resp3+    (vars (a b t name) (e1 e2 x mesg))+    (trace+      (recv+        (cat (cat a b t (hash e1) x) e1 e2+          (enc "eootag" (hash a b t (hash e1) x) e2 (privk "sign" a))))+      (send+        (cat (cat a b t (hash e1) x) e2+          (enc "eootag" (hash a b t (hash e1) x) e2 (privk "sign" a))+          (enc "eortag" (hash a b t (hash e1) x) e2 (privk "sign" b))))+      (send+        (cat (cat a b t (hash e1) x) e2+          (enc "eootag" (hash a b t (hash e1) x) e2 (privk "sign" a))+          (enc "eortag" (hash a b t (hash e1) x) e2 (privk "sign" b))+          (enc "rcrq" (cat a b t (hash e1) x) e2 (privk "sign" b))))+      (recv+        (enc "abcf" (enc "abrq" a b t (hash e1) x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab1+    (vars (a b t name) (y x mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (send (cat "sync-abrq" (enc "abrq" a b t y x (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab2+    (vars (a b t name) (y x e mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (recv+        (cat "sync-abrq"+          (enc "eortag" (hash a b t y x) e (privk "sign" b))))+      (send (enc "eortag" (hash a b t y x) e (privk "sign" b)))))+  (defrole ttp-rc1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat "sync-rc-req" (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b)))) (send (cat k r))))+  (defrole ttp-rc2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (recv+        (cat "sync-rc-req"+          (enc "abrq" a b t y (hash k) (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y (hash k) (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-cf1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat "sync-cf-req" (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (enc (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b)) (privk "sign" t)))))+  (defrole ttp-cf2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (recv+        (cat "sync-cf-req"+          (enc "abrq" a b t y (hash k) (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y (hash k) (privk "sign" a))+          (privk "sign" t))))))++(defskeleton wang+  (vars (y x mesg) (a b t name))+  (deflistener+    (enc "abcf" (enc "abrq" a b t y x (privk "sign" a))+      (privk "sign" t)))+  (non-orig (privk "sign" t))+  (comment "Experiments to prove Lemma 4.3, clause 1.")+  (traces+    ((recv+       (enc "abcf" (enc "abrq" a b t y x (privk "sign" a))+         (privk "sign" t)))+      (send+        (enc "abcf" (enc "abrq" a b t y x (privk "sign" a))+          (privk "sign" t)))))+  (label 30)+  (unrealized (0 0))+  (origs)+  (comment "3 in cohort - 3 not yet seen"))++(defskeleton wang+  (vars (y x mesg) (a b t name))+  (deflistener+    (enc "abcf" (enc "abrq" a b t y x (privk "sign" a))+      (privk "sign" t)))+  (defstrand ttp-ab1 3 (y y) (x x) (a a) (b b) (t t))+  (precedes ((1 2) (0 0)))+  (non-orig (privk "sign" t))+  (operation encryption-test (added-strand ttp-ab1 3)+    (enc "abcf" (enc "abrq" a b t y x (privk "sign" a))+      (privk "sign" t)) (0 0))+  (traces+    ((recv+       (enc "abcf" (enc "abrq" a b t y x (privk "sign" a))+         (privk "sign" t)))+      (send+        (enc "abcf" (enc "abrq" a b t y x (privk "sign" a))+          (privk "sign" t))))+    ((recv (enc "abrq" a b t y x (privk "sign" a)))+      (send (cat "sync-abrq" (enc "abrq" a b t y x (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y x (privk "sign" a))+          (privk "sign" t)))))+  (label 31)+  (parent 30)+  (unrealized)+  (shape)+  (maps ((0) ((a a) (b b) (t t) (y y) (x x))))+  (origs))++(defskeleton wang+  (vars (y mesg) (r text) (a b t name) (k skey))+  (deflistener+    (enc "abcf" (enc "abrq" a b t y (hash k) (privk "sign" a))+      (privk "sign" t)))+  (defstrand ttp-rc2 3 (y y) (r r) (a a) (b b) (t t) (k k))+  (precedes ((1 2) (0 0)))+  (non-orig (privk "sign" t))+  (operation encryption-test (added-strand ttp-rc2 3)+    (enc "abcf" (enc "abrq" a b t y (hash k) (privk "sign" a))+      (privk "sign" t)) (0 0))+  (traces+    ((recv+       (enc "abcf" (enc "abrq" a b t y (hash k) (privk "sign" a))+         (privk "sign" t)))+      (send+        (enc "abcf" (enc "abrq" a b t y (hash k) (privk "sign" a))+          (privk "sign" t))))+    ((recv+       (cat (cat a b t y (hash k))+         (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+         (enc "eootag" (hash a b t y (hash k))+           (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+           (privk "sign" a))+         (enc "eortag" (hash a b t y (hash k))+           (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+           (privk "sign" b))+         (enc "rcrq" (cat a b t y (hash k))+           (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+           (privk "sign" b))))+      (recv+        (cat "sync-rc-req"+          (enc "abrq" a b t y (hash k) (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y (hash k) (privk "sign" a))+          (privk "sign" t)))))+  (label 32)+  (parent 30)+  (unrealized)+  (shape)+  (maps ((0) ((a a) (b b) (t t) (y y) (x (hash k)))))+  (origs))++(defskeleton wang+  (vars (y mesg) (r text) (a b t name) (k skey))+  (deflistener+    (enc "abcf" (enc "abrq" a b t y (hash k) (privk "sign" a))+      (privk "sign" t)))+  (defstrand ttp-cf2 3 (y y) (r r) (a a) (b b) (t t) (k k))+  (precedes ((1 2) (0 0)))+  (non-orig (privk "sign" t))+  (operation encryption-test (added-strand ttp-cf2 3)+    (enc "abcf" (enc "abrq" a b t y (hash k) (privk "sign" a))+      (privk "sign" t)) (0 0))+  (traces+    ((recv+       (enc "abcf" (enc "abrq" a b t y (hash k) (privk "sign" a))+         (privk "sign" t)))+      (send+        (enc "abcf" (enc "abrq" a b t y (hash k) (privk "sign" a))+          (privk "sign" t))))+    ((recv+       (cat (cat a b t y (hash k))+         (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+         (enc "eootag" (hash a b t y (hash k))+           (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+           (privk "sign" a))+         (enc "eortag" (hash a b t y (hash k))+           (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+           (privk "sign" b))+         (enc "cfrq" (cat a b t y (hash k))+           (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+           (privk "sign" b))))+      (recv+        (cat "sync-cf-req"+          (enc "abrq" a b t y (hash k) (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y (hash k) (privk "sign" a))+          (privk "sign" t)))))+  (label 33)+  (parent 30)+  (unrealized)+  (shape)+  (maps ((0) ((a a) (b b) (t t) (y y) (x (hash k)))))+  (origs))++(comment "Nothing left to do")++(defprotocol wang basic+  (defrole init1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b))) (send (cat k r))))+  (defrole init2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a))+          (privk "sign" t)))))+  (defrole init3+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))))+  (defrole init4+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a))+          (privk "sign" t)))))+  (defrole init5+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))))+  (defrole resp1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b))) (recv (cat k r))))+  (defrole resp2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (cat (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b)))) (recv (cat k r))))+  (defrole resp3+    (vars (a b t name) (e1 e2 x mesg))+    (trace+      (recv+        (cat (cat a b t (hash e1) x) e1 e2+          (enc "eootag" (hash a b t (hash e1) x) e2 (privk "sign" a))))+      (send+        (cat (cat a b t (hash e1) x) e2+          (enc "eootag" (hash a b t (hash e1) x) e2 (privk "sign" a))+          (enc "eortag" (hash a b t (hash e1) x) e2 (privk "sign" b))))+      (send+        (cat (cat a b t (hash e1) x) e2+          (enc "eootag" (hash a b t (hash e1) x) e2 (privk "sign" a))+          (enc "eortag" (hash a b t (hash e1) x) e2 (privk "sign" b))+          (enc "rcrq" (cat a b t (hash e1) x) e2 (privk "sign" b))))+      (recv+        (enc "abcf" (enc "abrq" a b t (hash e1) x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab1+    (vars (a b t name) (y x mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (send (cat "sync-abrq" (enc "abrq" a b t y x (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab2+    (vars (a b t name) (y x e mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (recv+        (cat "sync-abrq"+          (enc "eortag" (hash a b t y x) e (privk "sign" b))))+      (send (enc "eortag" (hash a b t y x) e (privk "sign" b)))))+  (defrole ttp-rc1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat "sync-rc-req" (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b)))) (send (cat k r))))+  (defrole ttp-rc2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (recv+        (cat "sync-rc-req"+          (enc "abrq" a b t y (hash k) (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y (hash k) (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-cf1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat "sync-cf-req" (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (enc (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b)) (privk "sign" t)))))+  (defrole ttp-cf2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (recv+        (cat "sync-cf-req"+          (enc "abrq" a b t y (hash k) (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y (hash k) (privk "sign" a))+          (privk "sign" t))))))++(defskeleton wang+  (vars (y x mesg) (a b t name))+  (defstrand ttp-ab1 3 (y y) (x x) (a a) (b b) (t t))+  (non-orig (privk "encr" t) (privk "sign" a))+  (comment "Experiment 1 to prove Lemma 4.3, clause 2.")+  (traces+    ((recv (enc "abrq" a b t y x (privk "sign" a)))+      (send (cat "sync-abrq" (enc "abrq" a b t y x (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y x (privk "sign" a))+          (privk "sign" t)))))+  (label 34)+  (seen 35 36)+  (unrealized (0 0))+  (origs)+  (comment "4 in cohort - 2 not yet seen"))++(defskeleton wang+  (vars (r text) (m data) (a b t name) (k skey))+  (defstrand ttp-ab1 3 (y (hash (enc m k))) (x (hash k)) (a a) (b b)+    (t t))+  (defstrand init2 2 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 1) (0 0)))+  (non-orig (privk "encr" t) (privk "sign" a))+  (operation encryption-test (added-strand init2 2)+    (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)) (0 0))+  (traces+    ((recv+       (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (send+        (cat "sync-abrq"+          (enc "abrq" a b t (hash (enc m k)) (hash k)+            (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a))+          (privk "sign" t))))+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))))+  (label 35)+  (parent 34)+  (unrealized)+  (shape)+  (maps ((0) ((y (hash (enc m k))) (x (hash k)) (a a) (b b) (t t))))+  (origs))++(defskeleton wang+  (vars (r text) (m data) (a b t name) (k skey))+  (defstrand ttp-ab1 3 (y (hash (enc m k))) (x (hash k)) (a a) (b b)+    (t t))+  (defstrand init4 3 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 2) (0 0)))+  (non-orig (privk "encr" t) (privk "sign" a))+  (operation encryption-test (added-strand init4 3)+    (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)) (0 0))+  (traces+    ((recv+       (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (send+        (cat "sync-abrq"+          (enc "abrq" a b t (hash (enc m k)) (hash k)+            (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a))+          (privk "sign" t))))+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))))+  (label 36)+  (parent 34)+  (unrealized)+  (shape)+  (maps ((0) ((y (hash (enc m k))) (x (hash k)) (a a) (b b) (t t))))+  (origs))++(comment "Nothing left to do")++(defprotocol wang basic+  (defrole init1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b))) (send (cat k r))))+  (defrole init2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a))+          (privk "sign" t)))))+  (defrole init3+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))))+  (defrole init4+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a))+          (privk "sign" t)))))+  (defrole init5+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))))+  (defrole resp1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b))) (recv (cat k r))))+  (defrole resp2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (cat (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b)))) (recv (cat k r))))+  (defrole resp3+    (vars (a b t name) (e1 e2 x mesg))+    (trace+      (recv+        (cat (cat a b t (hash e1) x) e1 e2+          (enc "eootag" (hash a b t (hash e1) x) e2 (privk "sign" a))))+      (send+        (cat (cat a b t (hash e1) x) e2+          (enc "eootag" (hash a b t (hash e1) x) e2 (privk "sign" a))+          (enc "eortag" (hash a b t (hash e1) x) e2 (privk "sign" b))))+      (send+        (cat (cat a b t (hash e1) x) e2+          (enc "eootag" (hash a b t (hash e1) x) e2 (privk "sign" a))+          (enc "eortag" (hash a b t (hash e1) x) e2 (privk "sign" b))+          (enc "rcrq" (cat a b t (hash e1) x) e2 (privk "sign" b))))+      (recv+        (enc "abcf" (enc "abrq" a b t (hash e1) x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab1+    (vars (a b t name) (y x mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (send (cat "sync-abrq" (enc "abrq" a b t y x (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab2+    (vars (a b t name) (y x e mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (recv+        (cat "sync-abrq"+          (enc "eortag" (hash a b t y x) e (privk "sign" b))))+      (send (enc "eortag" (hash a b t y x) e (privk "sign" b)))))+  (defrole ttp-rc1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat "sync-rc-req" (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b)))) (send (cat k r))))+  (defrole ttp-rc2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (recv+        (cat "sync-rc-req"+          (enc "abrq" a b t y (hash k) (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y (hash k) (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-cf1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat "sync-cf-req" (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (enc (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b)) (privk "sign" t)))))+  (defrole ttp-cf2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (recv+        (cat "sync-cf-req"+          (enc "abrq" a b t y (hash k) (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y (hash k) (privk "sign" a))+          (privk "sign" t))))))++(defskeleton wang+  (vars (y mesg) (r text) (a b t name) (k skey))+  (defstrand ttp-rc2 3 (y y) (r r) (a a) (b b) (t t) (k k))+  (non-orig (privk "encr" t) (privk "sign" a))+  (comment "Experiment 2 to prove Lemma 4.3, clause 2.")+  (traces+    ((recv+       (cat (cat a b t y (hash k))+         (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+         (enc "eootag" (hash a b t y (hash k))+           (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+           (privk "sign" a))+         (enc "eortag" (hash a b t y (hash k))+           (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+           (privk "sign" b))+         (enc "rcrq" (cat a b t y (hash k))+           (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+           (privk "sign" b))))+      (recv+        (cat "sync-rc-req"+          (enc "abrq" a b t y (hash k) (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y (hash k) (privk "sign" a))+          (privk "sign" t)))))+  (label 37)+  (seen 38)+  (unrealized (0 0) (0 1))+  (origs)+  (comment "5 in cohort - 1 not yet seen"))++(defskeleton wang+  (vars (r text) (m data) (a b t name) (k skey))+  (defstrand ttp-rc2 3 (y (hash (enc m k))) (r r) (a a) (b b) (t t)+    (k k))+  (defstrand init1 1 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 0) (0 0)))+  (non-orig (privk "encr" t) (privk "sign" a))+  (operation encryption-test (added-strand init1 1)+    (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+      (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+        (pubk "encr" t)) (privk "sign" a)) (0 0))+  (traces+    ((recv+       (cat (cat a b t (hash (enc m k)) (hash k))+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))+         (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" b))+         (enc "rcrq" (cat a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" b))))+      (recv+        (cat "sync-rc-req"+          (enc "abrq" a b t (hash (enc m k)) (hash k)+            (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a))+          (privk "sign" t))))+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))))+  (label 38)+  (parent 37)+  (seen 39 40 41 42)+  (unrealized (0 1))+  (comment "8 in cohort - 4 not yet seen"))++(defskeleton wang+  (vars (r r-0 text) (m data) (a b t name) (k skey))+  (defstrand ttp-rc2 3 (y (hash (enc m k))) (r r) (a a) (b b) (t t)+    (k k))+  (defstrand init1 1 (r r) (m m) (a a) (b b) (t t) (k k))+  (defstrand init2 2 (r r-0) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 0) (0 0)) ((2 1) (0 1)))+  (non-orig (privk "encr" t) (privk "sign" a))+  (operation encryption-test (added-strand init2 2)+    (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)) (0 1))+  (traces+    ((recv+       (cat (cat a b t (hash (enc m k)) (hash k))+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))+         (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" b))+         (enc "rcrq" (cat a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" b))))+      (recv+        (cat "sync-rc-req"+          (enc "abrq" a b t (hash (enc m k)) (hash k)+            (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a))+          (privk "sign" t))))+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a)))))+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r-0+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r-0+             (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))))+  (label 39)+  (parent 38)+  (seen 40)+  (unrealized)+  (shape)+  (maps ((0) ((a a) (b b) (t t) (r r) (k k) (y (hash (enc m k))))))+  (origs)+  (comment "1 in cohort - 0 not yet seen"))++(defskeleton wang+  (vars (r text) (m data) (a b t name) (k skey))+  (defstrand ttp-rc2 3 (y (hash (enc m k))) (r r) (a a) (b b) (t t)+    (k k))+  (defstrand init2 2 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 0) (0 0)) ((1 1) (0 1)))+  (non-orig (privk "encr" t) (privk "sign" a))+  (operation encryption-test (displaced 1 2 init2 2)+    (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)) (0 1))+  (traces+    ((recv+       (cat (cat a b t (hash (enc m k)) (hash k))+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))+         (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" b))+         (enc "rcrq" (cat a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" b))))+      (recv+        (cat "sync-rc-req"+          (enc "abrq" a b t (hash (enc m k)) (hash k)+            (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a))+          (privk "sign" t))))+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))))+  (label 40)+  (parent 38)+  (unrealized)+  (shape)+  (maps ((0) ((a a) (b b) (t t) (r r) (k k) (y (hash (enc m k))))))+  (origs))++(defskeleton wang+  (vars (r r-0 text) (m data) (a b t name) (k skey))+  (defstrand ttp-rc2 3 (y (hash (enc m k))) (r r) (a a) (b b) (t t)+    (k k))+  (defstrand init1 1 (r r) (m m) (a a) (b b) (t t) (k k))+  (defstrand init4 3 (r r-0) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 0) (0 0)) ((2 2) (0 1)))+  (non-orig (privk "encr" t) (privk "sign" a))+  (operation encryption-test (added-strand init4 3)+    (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)) (0 1))+  (traces+    ((recv+       (cat (cat a b t (hash (enc m k)) (hash k))+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))+         (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" b))+         (enc "rcrq" (cat a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" b))))+      (recv+        (cat "sync-rc-req"+          (enc "abrq" a b t (hash (enc m k)) (hash k)+            (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a))+          (privk "sign" t))))+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a)))))+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r-0+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r-0+             (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r-0+            (pubk "encr" t)) (privk "sign" b)))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))))+  (label 41)+  (parent 38)+  (seen 42)+  (unrealized)+  (shape)+  (maps ((0) ((a a) (b b) (t t) (r r) (k k) (y (hash (enc m k))))))+  (origs)+  (comment "1 in cohort - 0 not yet seen"))++(defskeleton wang+  (vars (r text) (m data) (a b t name) (k skey))+  (defstrand ttp-rc2 3 (y (hash (enc m k))) (r r) (a a) (b b) (t t)+    (k k))+  (defstrand init4 3 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 0) (0 0)) ((1 2) (0 1)))+  (non-orig (privk "encr" t) (privk "sign" a))+  (operation encryption-test (displaced 1 2 init4 3)+    (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)) (0 1))+  (traces+    ((recv+       (cat (cat a b t (hash (enc m k)) (hash k))+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))+         (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" b))+         (enc "rcrq" (cat a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" b))))+      (recv+        (cat "sync-rc-req"+          (enc "abrq" a b t (hash (enc m k)) (hash k)+            (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a))+          (privk "sign" t))))+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))))+  (label 42)+  (parent 38)+  (unrealized)+  (shape)+  (maps ((0) ((a a) (b b) (t t) (r r) (k k) (y (hash (enc m k))))))+  (origs))++(comment "Nothing left to do")++(defprotocol wang basic+  (defrole init1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b))) (send (cat k r))))+  (defrole init2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a))+          (privk "sign" t)))))+  (defrole init3+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))))+  (defrole init4+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a))+          (privk "sign" t)))))+  (defrole init5+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))))+  (defrole resp1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b))) (recv (cat k r))))+  (defrole resp2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))))+      (send+        (cat (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat (cat a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t))+          (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t (hash (enc m k)) (hash k))+            (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+              (pubk "encr" t)) (privk "sign" b)))) (recv (cat k r))))+  (defrole resp3+    (vars (a b t name) (e1 e2 x mesg))+    (trace+      (recv+        (cat (cat a b t (hash e1) x) e1 e2+          (enc "eootag" (hash a b t (hash e1) x) e2 (privk "sign" a))))+      (send+        (cat (cat a b t (hash e1) x) e2+          (enc "eootag" (hash a b t (hash e1) x) e2 (privk "sign" a))+          (enc "eortag" (hash a b t (hash e1) x) e2 (privk "sign" b))))+      (send+        (cat (cat a b t (hash e1) x) e2+          (enc "eootag" (hash a b t (hash e1) x) e2 (privk "sign" a))+          (enc "eortag" (hash a b t (hash e1) x) e2 (privk "sign" b))+          (enc "rcrq" (cat a b t (hash e1) x) e2 (privk "sign" b))))+      (recv+        (enc "abcf" (enc "abrq" a b t (hash e1) x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab1+    (vars (a b t name) (y x mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (send (cat "sync-abrq" (enc "abrq" a b t y x (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab2+    (vars (a b t name) (y x e mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (recv+        (cat "sync-abrq"+          (enc "eortag" (hash a b t y x) e (privk "sign" b))))+      (send (enc "eortag" (hash a b t y x) e (privk "sign" b)))))+  (defrole ttp-rc1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat "sync-rc-req" (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b)))) (send (cat k r))))+  (defrole ttp-rc2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (recv+        (cat "sync-rc-req"+          (enc "abrq" a b t y (hash k) (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y (hash k) (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-cf1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat "sync-cf-req" (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (enc (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b)) (privk "sign" t)))))+  (defrole ttp-cf2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (hash k))+          (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+          (enc "eootag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag" (hash a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "cfrq" (cat a b t y (hash k))+            (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+            (privk "sign" b))))+      (recv+        (cat "sync-cf-req"+          (enc "abrq" a b t y (hash k) (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y (hash k) (privk "sign" a))+          (privk "sign" t))))))++(defskeleton wang+  (vars (y mesg) (r text) (a b t name) (k skey))+  (defstrand ttp-cf2 3 (y y) (r r) (a a) (b b) (t t) (k k))+  (non-orig (privk "encr" t) (privk "sign" a))+  (comment "Experiment 3 to prove Lemma 4.3, clause 2.")+  (traces+    ((recv+       (cat (cat a b t y (hash k))+         (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+         (enc "eootag" (hash a b t y (hash k))+           (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+           (privk "sign" a))+         (enc "eortag" (hash a b t y (hash k))+           (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+           (privk "sign" b))+         (enc "cfrq" (cat a b t y (hash k))+           (enc "keytag" (hash a b t y (hash k)) k r (pubk "encr" t))+           (privk "sign" b))))+      (recv+        (cat "sync-cf-req"+          (enc "abrq" a b t y (hash k) (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y (hash k) (privk "sign" a))+          (privk "sign" t)))))+  (label 43)+  (seen 44)+  (unrealized (0 0) (0 1))+  (origs)+  (comment "5 in cohort - 1 not yet seen"))++(defskeleton wang+  (vars (r text) (m data) (a b t name) (k skey))+  (defstrand ttp-cf2 3 (y (hash (enc m k))) (r r) (a a) (b b) (t t)+    (k k))+  (defstrand init1 1 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 0) (0 0)))+  (non-orig (privk "encr" t) (privk "sign" a))+  (operation encryption-test (added-strand init1 1)+    (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+      (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+        (pubk "encr" t)) (privk "sign" a)) (0 0))+  (traces+    ((recv+       (cat (cat a b t (hash (enc m k)) (hash k))+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))+         (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" b))+         (enc "cfrq" (cat a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" b))))+      (recv+        (cat "sync-cf-req"+          (enc "abrq" a b t (hash (enc m k)) (hash k)+            (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a))+          (privk "sign" t))))+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))))+  (label 44)+  (parent 43)+  (seen 45 46 47 48)+  (unrealized (0 1))+  (comment "8 in cohort - 4 not yet seen"))++(defskeleton wang+  (vars (r r-0 text) (m data) (a b t name) (k skey))+  (defstrand ttp-cf2 3 (y (hash (enc m k))) (r r) (a a) (b b) (t t)+    (k k))+  (defstrand init1 1 (r r) (m m) (a a) (b b) (t t) (k k))+  (defstrand init2 2 (r r-0) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 0) (0 0)) ((2 1) (0 1)))+  (non-orig (privk "encr" t) (privk "sign" a))+  (operation encryption-test (added-strand init2 2)+    (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)) (0 1))+  (traces+    ((recv+       (cat (cat a b t (hash (enc m k)) (hash k))+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))+         (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" b))+         (enc "cfrq" (cat a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" b))))+      (recv+        (cat "sync-cf-req"+          (enc "abrq" a b t (hash (enc m k)) (hash k)+            (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a))+          (privk "sign" t))))+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a)))))+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r-0+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r-0+             (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))))+  (label 45)+  (parent 44)+  (seen 46)+  (unrealized)+  (shape)+  (maps ((0) ((a a) (b b) (t t) (r r) (k k) (y (hash (enc m k))))))+  (origs)+  (comment "1 in cohort - 0 not yet seen"))++(defskeleton wang+  (vars (r text) (m data) (a b t name) (k skey))+  (defstrand ttp-cf2 3 (y (hash (enc m k))) (r r) (a a) (b b) (t t)+    (k k))+  (defstrand init2 2 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 0) (0 0)) ((1 1) (0 1)))+  (non-orig (privk "encr" t) (privk "sign" a))+  (operation encryption-test (displaced 1 2 init2 2)+    (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)) (0 1))+  (traces+    ((recv+       (cat (cat a b t (hash (enc m k)) (hash k))+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))+         (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" b))+         (enc "cfrq" (cat a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" b))))+      (recv+        (cat "sync-cf-req"+          (enc "abrq" a b t (hash (enc m k)) (hash k)+            (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a))+          (privk "sign" t))))+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))))+  (label 46)+  (parent 44)+  (unrealized)+  (shape)+  (maps ((0) ((a a) (b b) (t t) (r r) (k k) (y (hash (enc m k))))))+  (origs))++(defskeleton wang+  (vars (r r-0 text) (m data) (a b t name) (k skey))+  (defstrand ttp-cf2 3 (y (hash (enc m k))) (r r) (a a) (b b) (t t)+    (k k))+  (defstrand init1 1 (r r) (m m) (a a) (b b) (t t) (k k))+  (defstrand init4 3 (r r-0) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 0) (0 0)) ((2 2) (0 1)))+  (non-orig (privk "encr" t) (privk "sign" a))+  (operation encryption-test (added-strand init4 3)+    (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)) (0 1))+  (traces+    ((recv+       (cat (cat a b t (hash (enc m k)) (hash k))+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))+         (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" b))+         (enc "cfrq" (cat a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" b))))+      (recv+        (cat "sync-cf-req"+          (enc "abrq" a b t (hash (enc m k)) (hash k)+            (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a))+          (privk "sign" t))))+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a)))))+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r-0+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r-0+             (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r-0+            (pubk "encr" t)) (privk "sign" b)))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))))+  (label 47)+  (parent 44)+  (seen 48)+  (unrealized)+  (shape)+  (maps ((0) ((a a) (b b) (t t) (r r) (k k) (y (hash (enc m k))))))+  (origs)+  (comment "1 in cohort - 0 not yet seen"))++(defskeleton wang+  (vars (r text) (m data) (a b t name) (k skey))+  (defstrand ttp-cf2 3 (y (hash (enc m k))) (r r) (a a) (b b) (t t)+    (k k))+  (defstrand init4 3 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 0) (0 0)) ((1 2) (0 1)))+  (non-orig (privk "encr" t) (privk "sign" a))+  (operation encryption-test (displaced 1 2 init4 3)+    (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)) (0 1))+  (traces+    ((recv+       (cat (cat a b t (hash (enc m k)) (hash k))+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))+         (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" b))+         (enc "cfrq" (cat a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" b))))+      (recv+        (cat "sync-cf-req"+          (enc "abrq" a b t (hash (enc m k)) (hash k)+            (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a))+          (privk "sign" t))))+    ((send+       (cat (cat a b t (hash (enc m k)) (hash k)) (enc m k)+         (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+           (pubk "encr" t))+         (enc "eootag" (hash a b t (hash (enc m k)) (hash k))+           (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+             (pubk "encr" t)) (privk "sign" a))))+      (recv+        (enc "eortag" (hash a b t (hash (enc m k)) (hash k))+          (enc "keytag" (hash a b t (hash (enc m k)) (hash k)) k r+            (pubk "encr" t)) (privk "sign" b)))+      (send+        (enc "abrq" a b t (hash (enc m k)) (hash k) (privk "sign" a)))))+  (label 48)+  (parent 44)+  (unrealized)+  (shape)+  (maps ((0) ((a a) (b b) (t t) (r r) (k k) (y (hash (enc m k))))))+  (origs))++(comment "Nothing left to do")
+ tst/wang-key-hash.scm view
@@ -0,0 +1,434 @@+(herald "Wang's Fair Exchange Protocol" (bound 10))++;; CPSA input file to represent+;; Wang's Fair Exchange Protocol++;; This macro implements the CPSA+;; convention of regarding a hash as+;; an asymmetric encryption.  The+;; decryption key inverse to (pubk+;; hash) is assumed non-originating+;; in roles using hashing.++(defmacro (hash x)+  (enc "h" (cat "h" x)))++;; Wang's encrypted format for the+;; message payload.  Observe that m,+;; k get their values from the+;; like-named messages in the context+;; where the macro is expanded.++(defmacro (em)+  (enc m k))++;; The session label L as a fn of+;; the values that *should be* the+;; hashes of the encrypted message EM+;; and the session key K.++(defmacro (l-prime y x)+  (cat a b t y x))++;; The recipient can check that a+;; session label has an l-prime where+;; y is the hash of another parameter.+;; Hence recipient roles use l-star.++(defmacro (l-star e1 x)+  (l-prime (hash e1) x))++;; The Evidence of Origin is checked+;; to be this fn of other parameters+;; available to the recipient.++(defmacro (eoo-star x e1 e2)+  (enc (cat "eootag"+	    (hash (l-star e1 x)) e2)+       (privk "sign" a)))++;; The Evidence of Receipt is computed+;; as this fn of other parameters+;; available to the recipient.++(defmacro (eor-star x e1 e2)+  (enc (cat "eortag"+	    (hash (l-star e1 x)) e2)+       (privk "sign" b)))++;; The Recovery Request as computed by+;; the recipient.++(defmacro (rr-star x e1 e2)+  (cat (l-star e1 x) e2+       (eoo-star x e1 e2)+       (eor-star x e1 e2)+       (enc (cat "rcrq" (l-star e1 x) e2)+            (privk "sign" b))))++;; The Abort Token is checked+;; to be this fn of other parameters+;; available to the recipient.++(defmacro (at-star e1 x)+  (enc (enc "abrq" (l-star e1 x)+            (privk "sign" a))+       (privk "sign" t)))++;; How the initiator computes the+;; encrypted key package:++(defmacro (ek l)+  (enc (cat "keytag" (hash l) k r)+       (pubk "encr" t)))++;; The Initiator's computed+;; version of L.++(defmacro (l)+  (l-prime (hash (enc m k)) (hash k)))++;; The TTP can check that the session+;; label L is this fn of other+;; parameters available to the TTP.++(defmacro (l-prime-prime y)+  (cat a b t y (hash k)))++;; The TTP can check that the EOO+;; is this fn of other parameters+;; available to the TTP.++(defmacro (eoo-prime-prime y)+  (enc (cat "eootag"+            (hash (l-prime-prime y))+	    (ek (l-prime-prime y)))+       (privk "sign" a)))++;; The TTP can check that the EOR+;; is this fn of other parameters+;; available to the TTP.++(defmacro (eor-prime-prime y)+  (enc (cat "eortag"+	    (hash (l-prime-prime y))+	    (ek (l-prime-prime y)))+       (privk "sign" b)))++;; The TTP can check that the RR+;; is this fn of other parameters+;; available to the TTP.++(defmacro (rr-prime-prime y)+  (cat (l-prime-prime y)+       (ek (l-prime-prime y))+       (eoo-prime-prime y)+       (eor-prime-prime y)+       (enc "rcrq" (l-prime-prime y)+	    (ek (l-prime-prime y))+            (privk "sign" b))))++;; The TTP can check that the Confirmation+;; Request is this fn of other parameters+;; available to the TTP.++(defmacro (cf-prime-prime y)+  (cat (l-prime-prime y) (ek (l-prime-prime y))+       (eoo-prime-prime y) (eor-prime-prime y)+       (enc "cfrq" (l-prime-prime y)+	    (ek (l-prime-prime y))+            (privk "sign" b))))++;; Defn of Wang's Fair Exchange Protocol.+;; Closely follows the presentation in the+;; figures in Section 3.  In the TTP roles,+;; we have put a dummy send or receive in place+;; of the state synchronization event to keep+;; the indices matching the spec.++(defprotocol wang basic++  ;; Successful initiator run with no TTP involvement++  (defrole init1+    (vars (a b t hash_id name) (m data) (r text) (k skey))+    (trace+     (send (cat (l) (enc m k) (ek (l))+                (eoo-star (hash k) (enc m k) (ek (l)))))+     (recv (eor-star (hash k) (enc m k) (ek (l))))+     (send (cat k r)))+    (non-orig (privk hash_id)))++  ;; Aborted initiator run++  (defrole init2+    (vars (a b t hash_id name) (m data) (r text) (k skey))+    (trace+     (send (cat (l) (enc m k) (ek (l))+                (eoo-star (hash k) (enc m k) (ek (l)))))+     (send (enc "abrq" (l) (privk "sign" a)))+     (recv (enc "abcf"+                (enc "abrq" (l) (privk "sign" a))+                (privk "sign" t))))+    (non-orig (privk hash_id)))++  ;; Initiator run with abort request and forced recovery++  (defrole init3+    (vars (a b t hash_id name) (m data) (r text) (k skey))+    (trace+     (send (cat (l) (enc m k) (ek (l))+                (eoo-star (hash k) (enc m k) (ek (l)))))+     (send (enc "abrq" (l) (privk "sign" a)))+     (recv (eor-star (hash k) (enc m k) (ek (l)))))+    (non-orig (privk hash_id)))++  ;; Aborted initiator run, but with EOR received++  (defrole init4+    (vars (a b t hash_id name) (m data) (r text) (k skey))+    (trace+     (send (cat (l) (enc m k) (ek (l))+                (eoo-star (hash k) (enc m k) (ek (l)))))+     (recv (eor-star (hash k) (enc m k) (ek (l))))+     (send (enc "abrq" (l) (privk "sign" a)))+     (recv (enc "abcf"+                (enc "abrq" (l) (privk "sign" a))+                (privk "sign" t))))+    (non-orig (privk hash_id)))++  ;; Initiator run with abort requested after EOR received,+  ;; but recovery forced++  (defrole init5+    (vars (a b t hash_id name) (m data) (r text) (k skey))+    (trace+     (send (cat (l) (enc m k) (ek (l))+                (eoo-star (hash k) (enc m k) (ek (l)))))+     (recv (eor-star (hash k) (enc m k) (ek (l))))+     (send (enc "abrq" (l) (privk "sign" a)))+     (recv (eor-star (hash k) (enc m k) (ek (l)))))+    (non-orig (privk hash_id)))++  ;; Successful responder run with no TTP involvement++  (defrole resp1+    (vars (a b t hash_id name) (m data) (r text) (k skey))+    (trace+     (recv (cat (l) (enc m k) (ek (l))+                (eoo-star (hash k) (enc m k) (ek (l)))))+     (send (eor-star (hash k) (enc m k) (ek (l))))+     (recv (cat k r)))+    (non-orig (privk hash_id)))++  ;;Responder run with recovery via TTP++  (defrole resp2+    (vars (a b t hash_id name) (m data) (r text) (k skey))+    (trace+     (recv (cat (l) (enc m k) (ek (l))+                (eoo-star (hash k) (enc m k) (ek (l)))))+     (send (cat (l) (ek (l)) (eoo-star (hash k) (enc m k) (ek (l)))+                (eor-star (hash k) (enc m k) (ek (l)))))+     (send (cat (l) (ek (l)) (eoo-star (hash k) (enc m k) (ek (l)))+                (eor-star (hash k) (enc m k) (ek (l)))+                (enc "rcrq" (l) (ek (l)) (privk "sign" b))))+     (recv (cat k r)))+    (non-orig (privk hash_id)))++  ;; Responder run with recovery request and forced abort++  (defrole resp3+    (vars (a b t hash_id name) (e1 e2 x mesg))+    (trace+     (recv (cat (l-star e1 x) e1 e2 (eoo-star x e1 e2)))+     (send (cat (l-star e1 x) e2 (eoo-star x e1 e2) (eor-star x e1 e2)))+     (send (cat (l-star e1 x) e2 (eoo-star x e1 e2) (eor-star x e1 e2)+                (enc "rcrq" (l-star e1 x) e2 (privk "sign" b))))+     (recv (enc "abcf"+                (enc "abrq" (l-star e1 x) (privk "sign" a))+                (privk "sign" t))))+    (non-orig (privk hash_id)))++  ;; TTP handles an abort++  (defrole ttp-ab1+    (vars (a b t hash_id name) (y x mesg))+    (trace+     (recv (enc "abrq" (l-prime y x) (privk "sign" a)))+     (send (cat "sync-abrq"+                (enc "abrq" (l-prime y x) (privk "sign" a))))+     (send (enc "abcf"+                (enc "abrq" (l-prime y x) (privk "sign" a))+                (privk "sign" t))))+    (non-orig (privk hash_id)))++  ;; TTP forces recovery in response to an abort request++  (defrole ttp-ab2+    (vars (a b t hash_id name) (y x e mesg))+    (trace+     (recv (enc "abrq" (l-prime y x) (privk "sign" a)))+     (recv (cat "sync-abrq"+                (enc "eortag" (hash (l-prime y x)) e+                     (privk "sign" b))))+     (send (enc "eortag" (hash (l-prime y x)) e+                (privk "sign" b))))+    (non-orig (privk hash_id)))++  ;; TTP handles a recovery++  (defrole ttp-rc1+    (vars (a b t hash_id name) (r text) (k skey) (y mesg))+    (trace+     (recv (rr-prime-prime y))+     (send (cat "sync-rc-req"+                (rr-prime-prime y)))+     (send (cat k r)))+    (non-orig (privk hash_id)))++  ;; TTP forces abort in response to a recovery request++  (defrole ttp-rc2+    (vars (a b t hash_id name) (r text) (k skey) (y mesg))+    (trace+     (recv (rr-prime-prime y))+     (recv (cat "sync-rc-req"+		(enc "abrq" (l-prime-prime y) (privk "sign" a))))+     (send (enc "abcf"+                (enc "abrq" (l-prime-prime y) (privk "sign" a))+                (privk "sign" t))))+    (non-orig (privk hash_id)))++  ;; TTP handles a confirm request++  (defrole ttp-cf1+    (vars (a b t hash_id name) (r text) (k skey) (y mesg))+    (trace+     (recv (cf-prime-prime y))+     (send (cat "sync-cf-req"+                (cf-prime-prime y)))+     (send (enc (cf-prime-prime y) (privk "sign" t))))+    (non-orig (privk hash_id)))++  ;; TTP replies with abort token given confirm request++  (defrole ttp-cf2+    (vars (a b t hash_id name) (r text) (k skey) (y mesg))+    (trace+     (recv (cf-prime-prime y))+     (recv (cat "sync-cf-req"+                (enc "abrq"(l-prime-prime y) (privk "sign" a))))+     (send (enc "abcf"+                (enc "abrq"(l-prime-prime y) (privk "sign" a))+                (privk "sign" t))))+    (non-orig (privk hash_id))))++;; End of Wang's protocol defn.++;; Two experiments to prove Lemma 4.1++(defskeleton wang+  (vars (a b t hash_id name) (m data) (r text) (k skey))+  (defstrand init1 1 (b b) (t t) (m m) (r r) (k k))+  (deflistener m)+  (non-orig+   (privk "encr" t))+  (uniq-orig m k)+  (comment "Experiment 1 to prove Lemma 4.1."))++(defskeleton wang+  (vars (a b t hash_id name) (m data) (r text) (k skey))+  (defstrand init1 1 (b b) (t t) (m m) (r r) (k k))+  (deflistener k)+  (non-orig+   (privk "encr" t))+  (uniq-orig m k)+  (comment "Experiment 2 to prove Lemma 4.1."))++;; We now have three experiments+;; to prove Lemma 4.2, clause 1.++(defskeleton wang+  (vars (a b t hash_id name) (m data) (r text) (k skey))+  (defstrand init1 3 (b b) (t t) (m m) (r r) (k k))+  (non-orig+   (privk "sign" b))+  (comment "First of three experiments to prove Lemma 4.2, clause 1."))++(defskeleton wang+  (vars (a b t hash_id name) (m data) (r text) (k skey))+  (defstrand init3 3 (b b) (t t) (m m) (r r) (k k))+  (non-orig+   (privk "sign" b))+  (comment "Second of three experiments to prove Lemma 4.2, clause 1."))++(defskeleton wang+  (vars (a b t hash_id name) (m data) (r text) (k skey))+  (defstrand init5 4 (b b) (t t) (m m) (r r) (k k))+  (non-orig+   (privk "sign" b))+  (comment "Third of three experiments to prove Lemma 4.2, clause 1."))++;; Two experiments to prove 4.2, Clause 2.++(defskeleton wang+  (vars (a b t hash_id name) (m data) (r text) (k skey))+  (defstrand resp1 3 (a a) (t t) (m m) (r r) (k k))+  (non-orig+   (privk "sign" a))+  (comment+   "First of two experiments to prove Lemma 4.2, clause 2."))++(defskeleton wang+  (vars (a b t hash_id name) (m data) (r text) (k skey))+  (defstrand resp2 4 (a a) (t t) (m m) (r r) (k k))+  (non-orig+   (privk "sign" a))+  (comment+   "Second of two experiments to prove Lemma 4.2, clause 2."))++;; Experiment to prove Lemma 4.2, clause 3.++(defskeleton wang+  (vars (a b t hash_id name) (e1 e2 x mesg))+  (defstrand resp3 4 (a a) (t t))+  (non-orig+   (privk "sign" a))+  (comment+   "Experiments to prove Lemma 4.2, clause 3."))++;; One experiment to prove Lemma 4.3, Clause 1.++(defskeleton wang+  (vars (a b t hash_id name) (y x mesg))+  (deflistener+    (enc "abcf" (enc "abrq" (l-prime y x) (privk "sign" a))+	 (privk "sign" t)))+  (non-orig+   (privk "sign" t))+  (comment+   "Experiments to prove Lemma 4.3, clause 1."))++;; Three experiments to prove Lemma 4.3, Clause 2.++(defskeleton wang+  (vars (y x mesg) (a b t name))+  (defstrand ttp-ab1 3 (y y) (x x) (a a) (b b) (t t))+  (non-orig (privk "sign" a)  (privk "encr" t))+  (comment+   "Experiment 1 to prove Lemma 4.3, clause 2."))++(defskeleton wang+  (vars (a b t hash_id name) (r text) (k skey) (y mesg))+  (defstrand ttp-rc2 3 (a a) (b b) (t t))+  (non-orig (privk "sign" a)  (privk "encr" t))+  (comment+   "Experiment 2 to prove Lemma 4.3, clause 2."))++(defskeleton wang+  (vars (a b t hash_id name) (r text) (k skey) (y mesg))+  (defstrand ttp-cf2 3 (a a) (b b) (t t))+  (non-orig (privk "sign" a)  (privk "encr" t))+  (comment+   "Experiment 3 to prove Lemma 4.3, clause 2."))
+ tst/wang-key-hash.tst view
@@ -0,0 +1,9533 @@+(herald "Wang's Fair Exchange Protocol" (bound 10))++(comment "CPSA 2.2.5")+(comment "All input read")+(comment "Strand count bounded at 10")++(defprotocol wang basic+  (defrole init1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b))) (send (cat k r))))+  (defrole init2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a)) (privk "sign" t)))))+  (defrole init3+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))))+  (defrole init4+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a)) (privk "sign" t)))))+  (defrole init5+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))))+  (defrole resp1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b))) (recv (cat k r))))+  (defrole resp2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq"+            (cat a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b)))) (recv (cat k r))))+  (defrole resp3+    (vars (a b t name) (e1 e2 x mesg))+    (trace+      (recv+        (cat (cat a b t (enc "h" (cat "h" e1)) x) e1 e2+          (enc "eootag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" a))))+      (send+        (cat (cat a b t (enc "h" (cat "h" e1)) x) e2+          (enc "eootag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" b))))+      (send+        (cat (cat a b t (enc "h" (cat "h" e1)) x) e2+          (enc "eootag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" b))+          (enc "rcrq" (cat a b t (enc "h" (cat "h" e1)) x) e2+            (privk "sign" b))))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" e1)) x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab1+    (vars (a b t name) (y x mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (send (cat "sync-abrq" (enc "abrq" a b t y x (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab2+    (vars (a b t name) (y x e mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (recv+        (cat "sync-abrq"+          (enc "eortag" (enc "h" (cat "h" a b t y x)) e+            (privk "sign" b))))+      (send+        (enc "eortag" (enc "h" (cat "h" a b t y x)) e+          (privk "sign" b)))))+  (defrole ttp-rc1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat "sync-rc-req" (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b)))) (send (cat k r))))+  (defrole ttp-rc2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (recv+        (cat "sync-rc-req"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-cf1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat "sync-cf-req" (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (enc (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b)) (privk "sign" t)))))+  (defrole ttp-cf2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (recv+        (cat "sync-cf-req"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))+          (privk "sign" t))))))++(defskeleton wang+  (vars (r text) (m data) (b t a name) (k skey))+  (defstrand init1 1 (r r) (m m) (a a) (b b) (t t) (k k))+  (deflistener m)+  (non-orig (privk "encr" t))+  (uniq-orig m k)+  (comment "Experiment 1 to prove Lemma 4.1.")+  (traces+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))) ((recv m) (send m)))+  (label 0)+  (unrealized (1 0))+  (preskeleton)+  (comment "Not a skeleton"))++(defskeleton wang+  (vars (r text) (m data) (b t a name) (k skey))+  (defstrand init1 1 (r r) (m m) (a a) (b b) (t t) (k k))+  (deflistener m)+  (precedes ((0 0) (1 0)))+  (non-orig (privk "encr" t))+  (uniq-orig m k)+  (traces+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))) ((recv m) (send m)))+  (label 1)+  (parent 0)+  (unrealized (1 0))+  (origs (m (0 0)) (k (0 0)))+  (comment "1 in cohort - 1 not yet seen"))++(defskeleton wang+  (vars (r text) (m data) (b t a name) (k skey))+  (defstrand init1 1 (r r) (m m) (a a) (b b) (t t) (k k))+  (deflistener m)+  (deflistener k)+  (precedes ((0 0) (2 0)) ((2 1) (1 0)))+  (non-orig (privk "encr" t))+  (uniq-orig m k)+  (operation nonce-test (added-listener k) m (1 0) (enc m k))+  (traces+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))) ((recv m) (send m)) ((recv k) (send k)))+  (label 2)+  (parent 1)+  (seen 3)+  (unrealized (2 0))+  (comment "3 in cohort - 2 not yet seen"))++(defskeleton wang+  (vars (r text) (m data) (b t a name) (k skey))+  (deflistener m)+  (deflistener k)+  (defstrand init1 3 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 1) (0 0)) ((2 2) (1 0)))+  (non-orig (privk "encr" t))+  (uniq-orig m k)+  (operation nonce-test (added-strand init1 3) k (2 0)+    (enc "keytag"+      (enc "h"+        (cat "h" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)))) k r (pubk "encr" t)))+  (traces ((recv m) (send m)) ((recv k) (send k))+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b))) (send (cat k r))))+  (label 3)+  (parent 2)+  (unrealized)+  (comment "1 in cohort - 1 not yet seen"))++(defskeleton wang+  (vars (r text) (m data) (b t a name) (k skey))+  (defstrand init1 1 (r r) (m m) (a a) (b b) (t t) (k k))+  (deflistener m)+  (deflistener k)+  (defstrand ttp-rc1 3 (y (enc "h" (cat "h" (enc m k)))) (r r) (a a)+    (b b) (t t) (k k))+  (precedes ((0 0) (3 0)) ((2 1) (1 0)) ((3 2) (2 0)))+  (non-orig (privk "encr" t))+  (uniq-orig m k)+  (operation nonce-test (added-strand ttp-rc1 3) k (2 0)+    (enc "keytag"+      (enc "h"+        (cat "h" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)))) k r (pubk "encr" t)))+  (traces+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))) ((recv m) (send m)) ((recv k) (send k))+    ((recv+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))+         (enc "eortag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" b))+         (enc "rcrq"+           (cat a b t (enc "h" (cat "h" (enc m k)))+             (enc "h" (cat "h" k)))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" b))))+      (send+        (cat "sync-rc-req"+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq"+            (cat a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b)))) (send (cat k r))))+  (label 4)+  (parent 2)+  (unrealized)+  (comment "1 in cohort - 1 not yet seen"))++(defskeleton wang+  (vars (r text) (m data) (b t a name) (k skey))+  (deflistener m)+  (defstrand init1 3 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 2) (0 0)))+  (non-orig (privk "encr" t))+  (uniq-orig m k)+  (operation generalization deleted (1 0))+  (traces ((recv m) (send m))+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b))) (send (cat k r))))+  (label 5)+  (parent 3)+  (unrealized)+  (shape)+  (maps ((1 0) ((b b) (t t) (m m) (r r) (k k) (a a))))+  (origs (m (1 0)) (k (1 0))))++(defskeleton wang+  (vars (r text) (m data) (b t a name) (k skey))+  (defstrand init1 1 (r r) (m m) (a a) (b b) (t t) (k k))+  (deflistener m)+  (defstrand ttp-rc1 3 (y (enc "h" (cat "h" (enc m k)))) (r r) (a a)+    (b b) (t t) (k k))+  (precedes ((0 0) (2 0)) ((2 2) (1 0)))+  (non-orig (privk "encr" t))+  (uniq-orig m k)+  (operation generalization deleted (2 0))+  (traces+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))) ((recv m) (send m))+    ((recv+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))+         (enc "eortag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" b))+         (enc "rcrq"+           (cat a b t (enc "h" (cat "h" (enc m k)))+             (enc "h" (cat "h" k)))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" b))))+      (send+        (cat "sync-rc-req"+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq"+            (cat a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b)))) (send (cat k r))))+  (label 6)+  (parent 4)+  (unrealized)+  (shape)+  (maps ((0 1) ((b b) (t t) (m m) (r r) (k k) (a a))))+  (origs (m (0 0)) (k (0 0))))++(comment "Nothing left to do")++(defprotocol wang basic+  (defrole init1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b))) (send (cat k r))))+  (defrole init2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a)) (privk "sign" t)))))+  (defrole init3+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))))+  (defrole init4+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a)) (privk "sign" t)))))+  (defrole init5+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))))+  (defrole resp1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b))) (recv (cat k r))))+  (defrole resp2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq"+            (cat a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b)))) (recv (cat k r))))+  (defrole resp3+    (vars (a b t name) (e1 e2 x mesg))+    (trace+      (recv+        (cat (cat a b t (enc "h" (cat "h" e1)) x) e1 e2+          (enc "eootag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" a))))+      (send+        (cat (cat a b t (enc "h" (cat "h" e1)) x) e2+          (enc "eootag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" b))))+      (send+        (cat (cat a b t (enc "h" (cat "h" e1)) x) e2+          (enc "eootag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" b))+          (enc "rcrq" (cat a b t (enc "h" (cat "h" e1)) x) e2+            (privk "sign" b))))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" e1)) x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab1+    (vars (a b t name) (y x mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (send (cat "sync-abrq" (enc "abrq" a b t y x (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab2+    (vars (a b t name) (y x e mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (recv+        (cat "sync-abrq"+          (enc "eortag" (enc "h" (cat "h" a b t y x)) e+            (privk "sign" b))))+      (send+        (enc "eortag" (enc "h" (cat "h" a b t y x)) e+          (privk "sign" b)))))+  (defrole ttp-rc1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat "sync-rc-req" (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b)))) (send (cat k r))))+  (defrole ttp-rc2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (recv+        (cat "sync-rc-req"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-cf1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat "sync-cf-req" (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (enc (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b)) (privk "sign" t)))))+  (defrole ttp-cf2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (recv+        (cat "sync-cf-req"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))+          (privk "sign" t))))))++(defskeleton wang+  (vars (r text) (m data) (b t a name) (k skey))+  (defstrand init1 1 (r r) (m m) (a a) (b b) (t t) (k k))+  (deflistener k)+  (non-orig (privk "encr" t))+  (uniq-orig m k)+  (comment "Experiment 2 to prove Lemma 4.1.")+  (traces+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))) ((recv k) (send k)))+  (label 7)+  (unrealized (1 0))+  (preskeleton)+  (comment "Not a skeleton"))++(defskeleton wang+  (vars (r text) (m data) (b t a name) (k skey))+  (defstrand init1 1 (r r) (m m) (a a) (b b) (t t) (k k))+  (deflistener k)+  (precedes ((0 0) (1 0)))+  (non-orig (privk "encr" t))+  (uniq-orig m k)+  (traces+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))) ((recv k) (send k)))+  (label 8)+  (parent 7)+  (seen 9)+  (unrealized (1 0))+  (origs (m (0 0)) (k (0 0)))+  (comment "3 in cohort - 2 not yet seen"))++(defskeleton wang+  (vars (r text) (m data) (b t a name) (k skey))+  (deflistener k)+  (defstrand init1 3 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 2) (0 0)))+  (non-orig (privk "encr" t))+  (uniq-orig m k)+  (operation nonce-test (added-strand init1 3) k (1 0)+    (enc "keytag"+      (enc "h"+        (cat "h" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)))) k r (pubk "encr" t)))+  (traces ((recv k) (send k))+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b))) (send (cat k r))))+  (label 9)+  (parent 8)+  (unrealized)+  (shape)+  (maps ((1 0) ((b b) (t t) (m m) (r r) (k k) (a a))))+  (origs (m (1 0)) (k (1 0))))++(defskeleton wang+  (vars (r text) (m data) (b t a name) (k skey))+  (defstrand init1 1 (r r) (m m) (a a) (b b) (t t) (k k))+  (deflistener k)+  (defstrand ttp-rc1 3 (y (enc "h" (cat "h" (enc m k)))) (r r) (a a)+    (b b) (t t) (k k))+  (precedes ((0 0) (2 0)) ((2 2) (1 0)))+  (non-orig (privk "encr" t))+  (uniq-orig m k)+  (operation nonce-test (added-strand ttp-rc1 3) k (1 0)+    (enc "keytag"+      (enc "h"+        (cat "h" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)))) k r (pubk "encr" t)))+  (traces+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))) ((recv k) (send k))+    ((recv+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))+         (enc "eortag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" b))+         (enc "rcrq"+           (cat a b t (enc "h" (cat "h" (enc m k)))+             (enc "h" (cat "h" k)))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" b))))+      (send+        (cat "sync-rc-req"+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq"+            (cat a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b)))) (send (cat k r))))+  (label 10)+  (parent 8)+  (unrealized)+  (shape)+  (maps ((0 1) ((b b) (t t) (m m) (r r) (k k) (a a))))+  (origs (m (0 0)) (k (0 0))))++(comment "Nothing left to do")++(defprotocol wang basic+  (defrole init1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b))) (send (cat k r))))+  (defrole init2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a)) (privk "sign" t)))))+  (defrole init3+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))))+  (defrole init4+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a)) (privk "sign" t)))))+  (defrole init5+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))))+  (defrole resp1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b))) (recv (cat k r))))+  (defrole resp2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq"+            (cat a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b)))) (recv (cat k r))))+  (defrole resp3+    (vars (a b t name) (e1 e2 x mesg))+    (trace+      (recv+        (cat (cat a b t (enc "h" (cat "h" e1)) x) e1 e2+          (enc "eootag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" a))))+      (send+        (cat (cat a b t (enc "h" (cat "h" e1)) x) e2+          (enc "eootag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" b))))+      (send+        (cat (cat a b t (enc "h" (cat "h" e1)) x) e2+          (enc "eootag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" b))+          (enc "rcrq" (cat a b t (enc "h" (cat "h" e1)) x) e2+            (privk "sign" b))))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" e1)) x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab1+    (vars (a b t name) (y x mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (send (cat "sync-abrq" (enc "abrq" a b t y x (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab2+    (vars (a b t name) (y x e mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (recv+        (cat "sync-abrq"+          (enc "eortag" (enc "h" (cat "h" a b t y x)) e+            (privk "sign" b))))+      (send+        (enc "eortag" (enc "h" (cat "h" a b t y x)) e+          (privk "sign" b)))))+  (defrole ttp-rc1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat "sync-rc-req" (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b)))) (send (cat k r))))+  (defrole ttp-rc2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (recv+        (cat "sync-rc-req"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-cf1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat "sync-cf-req" (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (enc (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b)) (privk "sign" t)))))+  (defrole ttp-cf2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (recv+        (cat "sync-cf-req"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))+          (privk "sign" t))))))++(defskeleton wang+  (vars (r text) (m data) (b t a name) (k skey))+  (defstrand init1 3 (r r) (m m) (a a) (b b) (t t) (k k))+  (non-orig (privk "sign" b))+  (comment "First of three experiments to prove Lemma 4.2, clause 1.")+  (traces+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b))) (send (cat k r))))+  (label 11)+  (seen 13)+  (unrealized (0 1))+  (origs)+  (comment "3 in cohort - 2 not yet seen"))++(defskeleton wang+  (vars (r text) (m data) (b t a name) (k skey))+  (defstrand init1 3 (r r) (m m) (a a) (b b) (t t) (k k))+  (defstrand resp1 2 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 1) (0 1)))+  (non-orig (privk "sign" b))+  (operation encryption-test (added-strand resp1 2)+    (enc "eortag"+      (enc "h"+        (cat "h" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k))))+      (enc "keytag"+        (enc "h"+          (cat "h" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))) k r (pubk "encr" t))+      (privk "sign" b)) (0 1))+  (traces+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b))) (send (cat k r)))+    ((recv+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))+      (send+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))))+  (label 12)+  (parent 11)+  (unrealized)+  (shape)+  (maps ((0) ((b b) (t t) (m m) (r r) (k k) (a a))))+  (origs))++(defskeleton wang+  (vars (r text) (m data) (b t a name) (k skey))+  (defstrand init1 3 (r r) (m m) (a a) (b b) (t t) (k k))+  (defstrand resp2 2 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 1) (0 1)))+  (non-orig (privk "sign" b))+  (operation encryption-test (added-strand resp2 2)+    (enc "eortag"+      (enc "h"+        (cat "h" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k))))+      (enc "keytag"+        (enc "h"+          (cat "h" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))) k r (pubk "encr" t))+      (privk "sign" b)) (0 1))+  (traces+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b))) (send (cat k r)))+    ((recv+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))))))+  (label 13)+  (parent 11)+  (unrealized)+  (shape)+  (maps ((0) ((b b) (t t) (m m) (r r) (k k) (a a))))+  (origs))++(comment "Nothing left to do")++(defprotocol wang basic+  (defrole init1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b))) (send (cat k r))))+  (defrole init2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a)) (privk "sign" t)))))+  (defrole init3+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))))+  (defrole init4+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a)) (privk "sign" t)))))+  (defrole init5+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))))+  (defrole resp1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b))) (recv (cat k r))))+  (defrole resp2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq"+            (cat a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b)))) (recv (cat k r))))+  (defrole resp3+    (vars (a b t name) (e1 e2 x mesg))+    (trace+      (recv+        (cat (cat a b t (enc "h" (cat "h" e1)) x) e1 e2+          (enc "eootag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" a))))+      (send+        (cat (cat a b t (enc "h" (cat "h" e1)) x) e2+          (enc "eootag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" b))))+      (send+        (cat (cat a b t (enc "h" (cat "h" e1)) x) e2+          (enc "eootag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" b))+          (enc "rcrq" (cat a b t (enc "h" (cat "h" e1)) x) e2+            (privk "sign" b))))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" e1)) x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab1+    (vars (a b t name) (y x mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (send (cat "sync-abrq" (enc "abrq" a b t y x (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab2+    (vars (a b t name) (y x e mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (recv+        (cat "sync-abrq"+          (enc "eortag" (enc "h" (cat "h" a b t y x)) e+            (privk "sign" b))))+      (send+        (enc "eortag" (enc "h" (cat "h" a b t y x)) e+          (privk "sign" b)))))+  (defrole ttp-rc1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat "sync-rc-req" (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b)))) (send (cat k r))))+  (defrole ttp-rc2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (recv+        (cat "sync-rc-req"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-cf1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat "sync-cf-req" (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (enc (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b)) (privk "sign" t)))))+  (defrole ttp-cf2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (recv+        (cat "sync-cf-req"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))+          (privk "sign" t))))))++(defskeleton wang+  (vars (r text) (m data) (b t a name) (k skey))+  (defstrand init3 3 (r r) (m m) (a a) (b b) (t t) (k k))+  (non-orig (privk "sign" b))+  (comment "Second of three experiments to prove Lemma 4.2, clause 1.")+  (traces+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))))+  (label 14)+  (seen 16)+  (unrealized (0 2))+  (origs)+  (comment "3 in cohort - 2 not yet seen"))++(defskeleton wang+  (vars (r text) (m data) (b t a name) (k skey))+  (defstrand init3 3 (r r) (m m) (a a) (b b) (t t) (k k))+  (defstrand resp1 2 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 1) (0 2)))+  (non-orig (privk "sign" b))+  (operation encryption-test (added-strand resp1 2)+    (enc "eortag"+      (enc "h"+        (cat "h" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k))))+      (enc "keytag"+        (enc "h"+          (cat "h" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))) k r (pubk "encr" t))+      (privk "sign" b)) (0 2))+  (traces+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b))))+    ((recv+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))+      (send+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))))+  (label 15)+  (parent 14)+  (unrealized)+  (shape)+  (maps ((0) ((b b) (t t) (m m) (r r) (k k) (a a))))+  (origs))++(defskeleton wang+  (vars (r text) (m data) (b t a name) (k skey))+  (defstrand init3 3 (r r) (m m) (a a) (b b) (t t) (k k))+  (defstrand resp2 2 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 1) (0 2)))+  (non-orig (privk "sign" b))+  (operation encryption-test (added-strand resp2 2)+    (enc "eortag"+      (enc "h"+        (cat "h" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k))))+      (enc "keytag"+        (enc "h"+          (cat "h" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))) k r (pubk "encr" t))+      (privk "sign" b)) (0 2))+  (traces+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b))))+    ((recv+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))))))+  (label 16)+  (parent 14)+  (unrealized)+  (shape)+  (maps ((0) ((b b) (t t) (m m) (r r) (k k) (a a))))+  (origs))++(comment "Nothing left to do")++(defprotocol wang basic+  (defrole init1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b))) (send (cat k r))))+  (defrole init2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a)) (privk "sign" t)))))+  (defrole init3+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))))+  (defrole init4+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a)) (privk "sign" t)))))+  (defrole init5+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))))+  (defrole resp1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b))) (recv (cat k r))))+  (defrole resp2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq"+            (cat a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b)))) (recv (cat k r))))+  (defrole resp3+    (vars (a b t name) (e1 e2 x mesg))+    (trace+      (recv+        (cat (cat a b t (enc "h" (cat "h" e1)) x) e1 e2+          (enc "eootag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" a))))+      (send+        (cat (cat a b t (enc "h" (cat "h" e1)) x) e2+          (enc "eootag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" b))))+      (send+        (cat (cat a b t (enc "h" (cat "h" e1)) x) e2+          (enc "eootag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" b))+          (enc "rcrq" (cat a b t (enc "h" (cat "h" e1)) x) e2+            (privk "sign" b))))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" e1)) x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab1+    (vars (a b t name) (y x mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (send (cat "sync-abrq" (enc "abrq" a b t y x (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab2+    (vars (a b t name) (y x e mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (recv+        (cat "sync-abrq"+          (enc "eortag" (enc "h" (cat "h" a b t y x)) e+            (privk "sign" b))))+      (send+        (enc "eortag" (enc "h" (cat "h" a b t y x)) e+          (privk "sign" b)))))+  (defrole ttp-rc1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat "sync-rc-req" (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b)))) (send (cat k r))))+  (defrole ttp-rc2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (recv+        (cat "sync-rc-req"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-cf1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat "sync-cf-req" (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (enc (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b)) (privk "sign" t)))))+  (defrole ttp-cf2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (recv+        (cat "sync-cf-req"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))+          (privk "sign" t))))))++(defskeleton wang+  (vars (r text) (m data) (b t a name) (k skey))+  (defstrand init5 4 (r r) (m m) (a a) (b b) (t t) (k k))+  (non-orig (privk "sign" b))+  (comment "Third of three experiments to prove Lemma 4.2, clause 1.")+  (traces+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))))+  (label 17)+  (seen 19)+  (unrealized (0 1) (0 3))+  (origs)+  (comment "3 in cohort - 2 not yet seen"))++(defskeleton wang+  (vars (r text) (m data) (b t a name) (k skey))+  (defstrand init5 4 (r r) (m m) (a a) (b b) (t t) (k k))+  (defstrand resp1 2 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 1) (0 1)))+  (non-orig (privk "sign" b))+  (operation encryption-test (added-strand resp1 2)+    (enc "eortag"+      (enc "h"+        (cat "h" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k))))+      (enc "keytag"+        (enc "h"+          (cat "h" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))) k r (pubk "encr" t))+      (privk "sign" b)) (0 1))+  (traces+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b))))+    ((recv+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))+      (send+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))))+  (label 18)+  (parent 17)+  (unrealized)+  (shape)+  (maps ((0) ((b b) (t t) (m m) (r r) (k k) (a a))))+  (origs))++(defskeleton wang+  (vars (r text) (m data) (b t a name) (k skey))+  (defstrand init5 4 (r r) (m m) (a a) (b b) (t t) (k k))+  (defstrand resp2 2 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 1) (0 1)))+  (non-orig (privk "sign" b))+  (operation encryption-test (added-strand resp2 2)+    (enc "eortag"+      (enc "h"+        (cat "h" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k))))+      (enc "keytag"+        (enc "h"+          (cat "h" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))) k r (pubk "encr" t))+      (privk "sign" b)) (0 1))+  (traces+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b))))+    ((recv+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))))))+  (label 19)+  (parent 17)+  (unrealized)+  (shape)+  (maps ((0) ((b b) (t t) (m m) (r r) (k k) (a a))))+  (origs))++(comment "Nothing left to do")++(defprotocol wang basic+  (defrole init1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b))) (send (cat k r))))+  (defrole init2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a)) (privk "sign" t)))))+  (defrole init3+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))))+  (defrole init4+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a)) (privk "sign" t)))))+  (defrole init5+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))))+  (defrole resp1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b))) (recv (cat k r))))+  (defrole resp2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq"+            (cat a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b)))) (recv (cat k r))))+  (defrole resp3+    (vars (a b t name) (e1 e2 x mesg))+    (trace+      (recv+        (cat (cat a b t (enc "h" (cat "h" e1)) x) e1 e2+          (enc "eootag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" a))))+      (send+        (cat (cat a b t (enc "h" (cat "h" e1)) x) e2+          (enc "eootag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" b))))+      (send+        (cat (cat a b t (enc "h" (cat "h" e1)) x) e2+          (enc "eootag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" b))+          (enc "rcrq" (cat a b t (enc "h" (cat "h" e1)) x) e2+            (privk "sign" b))))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" e1)) x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab1+    (vars (a b t name) (y x mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (send (cat "sync-abrq" (enc "abrq" a b t y x (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab2+    (vars (a b t name) (y x e mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (recv+        (cat "sync-abrq"+          (enc "eortag" (enc "h" (cat "h" a b t y x)) e+            (privk "sign" b))))+      (send+        (enc "eortag" (enc "h" (cat "h" a b t y x)) e+          (privk "sign" b)))))+  (defrole ttp-rc1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat "sync-rc-req" (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b)))) (send (cat k r))))+  (defrole ttp-rc2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (recv+        (cat "sync-rc-req"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-cf1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat "sync-cf-req" (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (enc (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b)) (privk "sign" t)))))+  (defrole ttp-cf2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (recv+        (cat "sync-cf-req"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))+          (privk "sign" t))))))++(defskeleton wang+  (vars (r text) (m data) (a t b name) (k skey))+  (defstrand resp1 3 (r r) (m m) (a a) (b b) (t t) (k k))+  (non-orig (privk "sign" a))+  (comment "First of two experiments to prove Lemma 4.2, clause 2.")+  (traces+    ((recv+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))+      (send+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b))) (recv (cat k r))))+  (label 20)+  (seen 21)+  (unrealized (0 0))+  (origs)+  (comment "5 in cohort - 1 not yet seen"))++(defskeleton wang+  (vars (r text) (m data) (a t b name) (k skey))+  (defstrand resp1 3 (r r) (m m) (a a) (b b) (t t) (k k))+  (defstrand init1 1 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 0) (0 0)))+  (non-orig (privk "sign" a))+  (operation encryption-test (added-strand init1 1)+    (enc "eootag"+      (enc "h"+        (cat "h" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k))))+      (enc "keytag"+        (enc "h"+          (cat "h" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))) k r (pubk "encr" t))+      (privk "sign" a)) (0 0))+  (traces+    ((recv+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))+      (send+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b))) (recv (cat k r)))+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))))+  (label 21)+  (parent 20)+  (unrealized)+  (shape)+  (maps ((0) ((a a) (t t) (m m) (r r) (k k) (b b))))+  (origs))++(comment "Nothing left to do")++(defprotocol wang basic+  (defrole init1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b))) (send (cat k r))))+  (defrole init2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a)) (privk "sign" t)))))+  (defrole init3+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))))+  (defrole init4+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a)) (privk "sign" t)))))+  (defrole init5+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))))+  (defrole resp1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b))) (recv (cat k r))))+  (defrole resp2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq"+            (cat a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b)))) (recv (cat k r))))+  (defrole resp3+    (vars (a b t name) (e1 e2 x mesg))+    (trace+      (recv+        (cat (cat a b t (enc "h" (cat "h" e1)) x) e1 e2+          (enc "eootag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" a))))+      (send+        (cat (cat a b t (enc "h" (cat "h" e1)) x) e2+          (enc "eootag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" b))))+      (send+        (cat (cat a b t (enc "h" (cat "h" e1)) x) e2+          (enc "eootag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" b))+          (enc "rcrq" (cat a b t (enc "h" (cat "h" e1)) x) e2+            (privk "sign" b))))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" e1)) x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab1+    (vars (a b t name) (y x mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (send (cat "sync-abrq" (enc "abrq" a b t y x (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab2+    (vars (a b t name) (y x e mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (recv+        (cat "sync-abrq"+          (enc "eortag" (enc "h" (cat "h" a b t y x)) e+            (privk "sign" b))))+      (send+        (enc "eortag" (enc "h" (cat "h" a b t y x)) e+          (privk "sign" b)))))+  (defrole ttp-rc1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat "sync-rc-req" (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b)))) (send (cat k r))))+  (defrole ttp-rc2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (recv+        (cat "sync-rc-req"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-cf1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat "sync-cf-req" (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (enc (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b)) (privk "sign" t)))))+  (defrole ttp-cf2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (recv+        (cat "sync-cf-req"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))+          (privk "sign" t))))))++(defskeleton wang+  (vars (r text) (m data) (a t b name) (k skey))+  (defstrand resp2 4 (r r) (m m) (a a) (b b) (t t) (k k))+  (non-orig (privk "sign" a))+  (comment "Second of two experiments to prove Lemma 4.2, clause 2.")+  (traces+    ((recv+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq"+            (cat a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b)))) (recv (cat k r))))+  (label 22)+  (seen 23)+  (unrealized (0 0))+  (origs)+  (comment "5 in cohort - 1 not yet seen"))++(defskeleton wang+  (vars (r text) (m data) (a t b name) (k skey))+  (defstrand resp2 4 (r r) (m m) (a a) (b b) (t t) (k k))+  (defstrand init1 1 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 0) (0 0)))+  (non-orig (privk "sign" a))+  (operation encryption-test (added-strand init1 1)+    (enc "eootag"+      (enc "h"+        (cat "h" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k))))+      (enc "keytag"+        (enc "h"+          (cat "h" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))) k r (pubk "encr" t))+      (privk "sign" a)) (0 0))+  (traces+    ((recv+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq"+            (cat a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b)))) (recv (cat k r)))+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))))+  (label 23)+  (parent 22)+  (unrealized)+  (shape)+  (maps ((0) ((a a) (t t) (m m) (r r) (k k) (b b))))+  (origs))++(comment "Nothing left to do")++(defprotocol wang basic+  (defrole init1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b))) (send (cat k r))))+  (defrole init2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a)) (privk "sign" t)))))+  (defrole init3+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))))+  (defrole init4+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a)) (privk "sign" t)))))+  (defrole init5+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))))+  (defrole resp1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b))) (recv (cat k r))))+  (defrole resp2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq"+            (cat a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b)))) (recv (cat k r))))+  (defrole resp3+    (vars (a b t name) (e1 e2 x mesg))+    (trace+      (recv+        (cat (cat a b t (enc "h" (cat "h" e1)) x) e1 e2+          (enc "eootag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" a))))+      (send+        (cat (cat a b t (enc "h" (cat "h" e1)) x) e2+          (enc "eootag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" b))))+      (send+        (cat (cat a b t (enc "h" (cat "h" e1)) x) e2+          (enc "eootag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" b))+          (enc "rcrq" (cat a b t (enc "h" (cat "h" e1)) x) e2+            (privk "sign" b))))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" e1)) x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab1+    (vars (a b t name) (y x mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (send (cat "sync-abrq" (enc "abrq" a b t y x (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab2+    (vars (a b t name) (y x e mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (recv+        (cat "sync-abrq"+          (enc "eortag" (enc "h" (cat "h" a b t y x)) e+            (privk "sign" b))))+      (send+        (enc "eortag" (enc "h" (cat "h" a b t y x)) e+          (privk "sign" b)))))+  (defrole ttp-rc1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat "sync-rc-req" (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b)))) (send (cat k r))))+  (defrole ttp-rc2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (recv+        (cat "sync-rc-req"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-cf1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat "sync-cf-req" (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (enc (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b)) (privk "sign" t)))))+  (defrole ttp-cf2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (recv+        (cat "sync-cf-req"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))+          (privk "sign" t))))))++(defskeleton wang+  (vars (e1 e2 x mesg) (a t b name))+  (defstrand resp3 4 (e1 e1) (e2 e2) (x x) (a a) (b b) (t t))+  (non-orig (privk "sign" a))+  (comment "Experiments to prove Lemma 4.2, clause 3.")+  (traces+    ((recv+       (cat (cat a b t (enc "h" (cat "h" e1)) x) e1 e2+         (enc "eootag"+           (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+           (privk "sign" a))))+      (send+        (cat (cat a b t (enc "h" (cat "h" e1)) x) e2+          (enc "eootag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" b))))+      (send+        (cat (cat a b t (enc "h" (cat "h" e1)) x) e2+          (enc "eootag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" b))+          (enc "rcrq" (cat a b t (enc "h" (cat "h" e1)) x) e2+            (privk "sign" b))))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" e1)) x (privk "sign" a))+          (privk "sign" t)))))+  (label 24)+  (seen 25)+  (unrealized (0 0) (0 3))+  (origs)+  (comment "5 in cohort - 1 not yet seen"))++(defskeleton wang+  (vars (r text) (m data) (a t b name) (k skey))+  (defstrand resp3 4 (e1 (enc m k))+    (e2+      (enc "keytag"+        (enc "h"+          (cat "h" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))) k r (pubk "encr" t)))+    (x (enc "h" (cat "h" k))) (a a) (b b) (t t))+  (defstrand init1 1 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 0) (0 0)))+  (non-orig (privk "sign" a))+  (operation encryption-test (added-strand init1 1)+    (enc "eootag"+      (enc "h"+        (cat "h" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k))))+      (enc "keytag"+        (enc "h"+          (cat "h" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))) k r (pubk "encr" t))+      (privk "sign" a)) (0 0))+  (traces+    ((recv+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq"+            (cat a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a)) (privk "sign" t))))+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))))+  (label 25)+  (parent 24)+  (seen 26 27 28 29)+  (unrealized (0 3))+  (comment "8 in cohort - 4 not yet seen"))++(defskeleton wang+  (vars (r r-0 text) (m data) (a t b name) (k skey))+  (defstrand resp3 4 (e1 (enc m k))+    (e2+      (enc "keytag"+        (enc "h"+          (cat "h" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))) k r (pubk "encr" t)))+    (x (enc "h" (cat "h" k))) (a a) (b b) (t t))+  (defstrand init1 1 (r r) (m m) (a a) (b b) (t t) (k k))+  (defstrand init2 2 (r r-0) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 0) (0 0)) ((2 1) (0 3)))+  (non-orig (privk "sign" a))+  (operation encryption-test (added-strand init2 2)+    (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+      (enc "h" (cat "h" k)) (privk "sign" a)) (0 3))+  (traces+    ((recv+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq"+            (cat a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a)) (privk "sign" t))))+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a)))))+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r-0 (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r-0 (pubk "encr" t))+           (privk "sign" a))))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))))+  (label 26)+  (parent 25)+  (seen 27)+  (unrealized)+  (shape)+  (maps+    ((0)+      ((a a) (t t) (b b) (e1 (enc m k))+        (e2+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t)))+        (x (enc "h" (cat "h" k))))))+  (origs)+  (comment "1 in cohort - 0 not yet seen"))++(defskeleton wang+  (vars (r text) (m data) (a t b name) (k skey))+  (defstrand resp3 4 (e1 (enc m k))+    (e2+      (enc "keytag"+        (enc "h"+          (cat "h" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))) k r (pubk "encr" t)))+    (x (enc "h" (cat "h" k))) (a a) (b b) (t t))+  (defstrand init2 2 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 0) (0 0)) ((1 1) (0 3)))+  (non-orig (privk "sign" a))+  (operation encryption-test (displaced 1 2 init2 2)+    (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+      (enc "h" (cat "h" k)) (privk "sign" a)) (0 3))+  (traces+    ((recv+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq"+            (cat a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a)) (privk "sign" t))))+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))))+  (label 27)+  (parent 25)+  (unrealized)+  (shape)+  (maps+    ((0)+      ((a a) (t t) (b b) (e1 (enc m k))+        (e2+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t)))+        (x (enc "h" (cat "h" k))))))+  (origs))++(defskeleton wang+  (vars (r r-0 text) (m data) (a t b name) (k skey))+  (defstrand resp3 4 (e1 (enc m k))+    (e2+      (enc "keytag"+        (enc "h"+          (cat "h" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))) k r (pubk "encr" t)))+    (x (enc "h" (cat "h" k))) (a a) (b b) (t t))+  (defstrand init1 1 (r r) (m m) (a a) (b b) (t t) (k k))+  (defstrand init4 3 (r r-0) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 0) (0 0)) ((2 2) (0 3)))+  (non-orig (privk "sign" a))+  (operation encryption-test (added-strand init4 3)+    (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+      (enc "h" (cat "h" k)) (privk "sign" a)) (0 3))+  (traces+    ((recv+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq"+            (cat a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a)) (privk "sign" t))))+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a)))))+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r-0 (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r-0 (pubk "encr" t))+           (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r-0 (pubk "encr" t))+          (privk "sign" b)))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))))+  (label 28)+  (parent 25)+  (seen 29)+  (unrealized)+  (shape)+  (maps+    ((0)+      ((a a) (t t) (b b) (e1 (enc m k))+        (e2+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t)))+        (x (enc "h" (cat "h" k))))))+  (origs)+  (comment "1 in cohort - 0 not yet seen"))++(defskeleton wang+  (vars (r text) (m data) (a t b name) (k skey))+  (defstrand resp3 4 (e1 (enc m k))+    (e2+      (enc "keytag"+        (enc "h"+          (cat "h" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))) k r (pubk "encr" t)))+    (x (enc "h" (cat "h" k))) (a a) (b b) (t t))+  (defstrand init4 3 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 0) (0 0)) ((1 2) (0 3)))+  (non-orig (privk "sign" a))+  (operation encryption-test (displaced 1 2 init4 3)+    (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+      (enc "h" (cat "h" k)) (privk "sign" a)) (0 3))+  (traces+    ((recv+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq"+            (cat a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a)) (privk "sign" t))))+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))))+  (label 29)+  (parent 25)+  (unrealized)+  (shape)+  (maps+    ((0)+      ((a a) (t t) (b b) (e1 (enc m k))+        (e2+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t)))+        (x (enc "h" (cat "h" k))))))+  (origs))++(comment "Nothing left to do")++(defprotocol wang basic+  (defrole init1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b))) (send (cat k r))))+  (defrole init2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a)) (privk "sign" t)))))+  (defrole init3+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))))+  (defrole init4+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a)) (privk "sign" t)))))+  (defrole init5+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))))+  (defrole resp1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b))) (recv (cat k r))))+  (defrole resp2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq"+            (cat a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b)))) (recv (cat k r))))+  (defrole resp3+    (vars (a b t name) (e1 e2 x mesg))+    (trace+      (recv+        (cat (cat a b t (enc "h" (cat "h" e1)) x) e1 e2+          (enc "eootag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" a))))+      (send+        (cat (cat a b t (enc "h" (cat "h" e1)) x) e2+          (enc "eootag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" b))))+      (send+        (cat (cat a b t (enc "h" (cat "h" e1)) x) e2+          (enc "eootag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" b))+          (enc "rcrq" (cat a b t (enc "h" (cat "h" e1)) x) e2+            (privk "sign" b))))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" e1)) x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab1+    (vars (a b t name) (y x mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (send (cat "sync-abrq" (enc "abrq" a b t y x (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab2+    (vars (a b t name) (y x e mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (recv+        (cat "sync-abrq"+          (enc "eortag" (enc "h" (cat "h" a b t y x)) e+            (privk "sign" b))))+      (send+        (enc "eortag" (enc "h" (cat "h" a b t y x)) e+          (privk "sign" b)))))+  (defrole ttp-rc1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat "sync-rc-req" (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b)))) (send (cat k r))))+  (defrole ttp-rc2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (recv+        (cat "sync-rc-req"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-cf1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat "sync-cf-req" (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (enc (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b)) (privk "sign" t)))))+  (defrole ttp-cf2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (recv+        (cat "sync-cf-req"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))+          (privk "sign" t))))))++(defskeleton wang+  (vars (y x mesg) (a b t name))+  (deflistener+    (enc "abcf" (enc "abrq" a b t y x (privk "sign" a))+      (privk "sign" t)))+  (non-orig (privk "sign" t))+  (comment "Experiments to prove Lemma 4.3, clause 1.")+  (traces+    ((recv+       (enc "abcf" (enc "abrq" a b t y x (privk "sign" a))+         (privk "sign" t)))+      (send+        (enc "abcf" (enc "abrq" a b t y x (privk "sign" a))+          (privk "sign" t)))))+  (label 30)+  (unrealized (0 0))+  (origs)+  (comment "3 in cohort - 3 not yet seen"))++(defskeleton wang+  (vars (y x mesg) (a b t name))+  (deflistener+    (enc "abcf" (enc "abrq" a b t y x (privk "sign" a))+      (privk "sign" t)))+  (defstrand ttp-ab1 3 (y y) (x x) (a a) (b b) (t t))+  (precedes ((1 2) (0 0)))+  (non-orig (privk "sign" t))+  (operation encryption-test (added-strand ttp-ab1 3)+    (enc "abcf" (enc "abrq" a b t y x (privk "sign" a))+      (privk "sign" t)) (0 0))+  (traces+    ((recv+       (enc "abcf" (enc "abrq" a b t y x (privk "sign" a))+         (privk "sign" t)))+      (send+        (enc "abcf" (enc "abrq" a b t y x (privk "sign" a))+          (privk "sign" t))))+    ((recv (enc "abrq" a b t y x (privk "sign" a)))+      (send (cat "sync-abrq" (enc "abrq" a b t y x (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y x (privk "sign" a))+          (privk "sign" t)))))+  (label 31)+  (parent 30)+  (unrealized)+  (shape)+  (maps ((0) ((a a) (b b) (t t) (y y) (x x))))+  (origs))++(defskeleton wang+  (vars (y mesg) (r text) (a b t name) (k skey))+  (deflistener+    (enc "abcf"+      (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))+      (privk "sign" t)))+  (defstrand ttp-rc2 3 (y y) (r r) (a a) (b b) (t t) (k k))+  (precedes ((1 2) (0 0)))+  (non-orig (privk "sign" t))+  (operation encryption-test (added-strand ttp-rc2 3)+    (enc "abcf"+      (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))+      (privk "sign" t)) (0 0))+  (traces+    ((recv+       (enc "abcf"+         (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))+         (privk "sign" t)))+      (send+        (enc "abcf"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))+          (privk "sign" t))))+    ((recv+       (cat (cat a b t y (enc "h" (cat "h" k)))+         (enc "keytag" (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+           k r (pubk "encr" t))+         (enc "eootag" (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+             (pubk "encr" t)) (privk "sign" a))+         (enc "eortag" (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+             (pubk "encr" t)) (privk "sign" b))+         (enc "rcrq" (cat a b t y (enc "h" (cat "h" k)))+           (enc "keytag"+             (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+             (pubk "encr" t)) (privk "sign" b))))+      (recv+        (cat "sync-rc-req"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))+          (privk "sign" t)))))+  (label 32)+  (parent 30)+  (unrealized)+  (shape)+  (maps ((0) ((a a) (b b) (t t) (y y) (x (enc "h" (cat "h" k))))))+  (origs))++(defskeleton wang+  (vars (y mesg) (r text) (a b t name) (k skey))+  (deflistener+    (enc "abcf"+      (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))+      (privk "sign" t)))+  (defstrand ttp-cf2 3 (y y) (r r) (a a) (b b) (t t) (k k))+  (precedes ((1 2) (0 0)))+  (non-orig (privk "sign" t))+  (operation encryption-test (added-strand ttp-cf2 3)+    (enc "abcf"+      (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))+      (privk "sign" t)) (0 0))+  (traces+    ((recv+       (enc "abcf"+         (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))+         (privk "sign" t)))+      (send+        (enc "abcf"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))+          (privk "sign" t))))+    ((recv+       (cat (cat a b t y (enc "h" (cat "h" k)))+         (enc "keytag" (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+           k r (pubk "encr" t))+         (enc "eootag" (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+             (pubk "encr" t)) (privk "sign" a))+         (enc "eortag" (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+             (pubk "encr" t)) (privk "sign" b))+         (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+           (enc "keytag"+             (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+             (pubk "encr" t)) (privk "sign" b))))+      (recv+        (cat "sync-cf-req"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))+          (privk "sign" t)))))+  (label 33)+  (parent 30)+  (unrealized)+  (shape)+  (maps ((0) ((a a) (b b) (t t) (y y) (x (enc "h" (cat "h" k))))))+  (origs))++(comment "Nothing left to do")++(defprotocol wang basic+  (defrole init1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b))) (send (cat k r))))+  (defrole init2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a)) (privk "sign" t)))))+  (defrole init3+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))))+  (defrole init4+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a)) (privk "sign" t)))))+  (defrole init5+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))))+  (defrole resp1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b))) (recv (cat k r))))+  (defrole resp2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq"+            (cat a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b)))) (recv (cat k r))))+  (defrole resp3+    (vars (a b t name) (e1 e2 x mesg))+    (trace+      (recv+        (cat (cat a b t (enc "h" (cat "h" e1)) x) e1 e2+          (enc "eootag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" a))))+      (send+        (cat (cat a b t (enc "h" (cat "h" e1)) x) e2+          (enc "eootag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" b))))+      (send+        (cat (cat a b t (enc "h" (cat "h" e1)) x) e2+          (enc "eootag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" b))+          (enc "rcrq" (cat a b t (enc "h" (cat "h" e1)) x) e2+            (privk "sign" b))))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" e1)) x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab1+    (vars (a b t name) (y x mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (send (cat "sync-abrq" (enc "abrq" a b t y x (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab2+    (vars (a b t name) (y x e mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (recv+        (cat "sync-abrq"+          (enc "eortag" (enc "h" (cat "h" a b t y x)) e+            (privk "sign" b))))+      (send+        (enc "eortag" (enc "h" (cat "h" a b t y x)) e+          (privk "sign" b)))))+  (defrole ttp-rc1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat "sync-rc-req" (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b)))) (send (cat k r))))+  (defrole ttp-rc2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (recv+        (cat "sync-rc-req"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-cf1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat "sync-cf-req" (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (enc (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b)) (privk "sign" t)))))+  (defrole ttp-cf2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (recv+        (cat "sync-cf-req"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))+          (privk "sign" t))))))++(defskeleton wang+  (vars (y x mesg) (a b t name))+  (defstrand ttp-ab1 3 (y y) (x x) (a a) (b b) (t t))+  (non-orig (privk "encr" t) (privk "sign" a))+  (comment "Experiment 1 to prove Lemma 4.3, clause 2.")+  (traces+    ((recv (enc "abrq" a b t y x (privk "sign" a)))+      (send (cat "sync-abrq" (enc "abrq" a b t y x (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y x (privk "sign" a))+          (privk "sign" t)))))+  (label 34)+  (seen 35 36)+  (unrealized (0 0))+  (origs)+  (comment "4 in cohort - 2 not yet seen"))++(defskeleton wang+  (vars (r text) (m data) (a b t name) (k skey))+  (defstrand ttp-ab1 3 (y (enc "h" (cat "h" (enc m k))))+    (x (enc "h" (cat "h" k))) (a a) (b b) (t t))+  (defstrand init2 2 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 1) (0 0)))+  (non-orig (privk "encr" t) (privk "sign" a))+  (operation encryption-test (added-strand init2 2)+    (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+      (enc "h" (cat "h" k)) (privk "sign" a)) (0 0))+  (traces+    ((recv+       (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+         (enc "h" (cat "h" k)) (privk "sign" a)))+      (send+        (cat "sync-abrq"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a)) (privk "sign" t))))+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))))+  (label 35)+  (parent 34)+  (unrealized)+  (shape)+  (maps+    ((0)+      ((y (enc "h" (cat "h" (enc m k)))) (x (enc "h" (cat "h" k))) (a a)+        (b b) (t t))))+  (origs))++(defskeleton wang+  (vars (r text) (m data) (a b t name) (k skey))+  (defstrand ttp-ab1 3 (y (enc "h" (cat "h" (enc m k))))+    (x (enc "h" (cat "h" k))) (a a) (b b) (t t))+  (defstrand init4 3 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 2) (0 0)))+  (non-orig (privk "encr" t) (privk "sign" a))+  (operation encryption-test (added-strand init4 3)+    (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+      (enc "h" (cat "h" k)) (privk "sign" a)) (0 0))+  (traces+    ((recv+       (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+         (enc "h" (cat "h" k)) (privk "sign" a)))+      (send+        (cat "sync-abrq"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a)) (privk "sign" t))))+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))))+  (label 36)+  (parent 34)+  (unrealized)+  (shape)+  (maps+    ((0)+      ((y (enc "h" (cat "h" (enc m k)))) (x (enc "h" (cat "h" k))) (a a)+        (b b) (t t))))+  (origs))++(comment "Nothing left to do")++(defprotocol wang basic+  (defrole init1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b))) (send (cat k r))))+  (defrole init2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a)) (privk "sign" t)))))+  (defrole init3+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))))+  (defrole init4+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a)) (privk "sign" t)))))+  (defrole init5+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))))+  (defrole resp1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b))) (recv (cat k r))))+  (defrole resp2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq"+            (cat a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b)))) (recv (cat k r))))+  (defrole resp3+    (vars (a b t name) (e1 e2 x mesg))+    (trace+      (recv+        (cat (cat a b t (enc "h" (cat "h" e1)) x) e1 e2+          (enc "eootag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" a))))+      (send+        (cat (cat a b t (enc "h" (cat "h" e1)) x) e2+          (enc "eootag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" b))))+      (send+        (cat (cat a b t (enc "h" (cat "h" e1)) x) e2+          (enc "eootag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" b))+          (enc "rcrq" (cat a b t (enc "h" (cat "h" e1)) x) e2+            (privk "sign" b))))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" e1)) x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab1+    (vars (a b t name) (y x mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (send (cat "sync-abrq" (enc "abrq" a b t y x (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab2+    (vars (a b t name) (y x e mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (recv+        (cat "sync-abrq"+          (enc "eortag" (enc "h" (cat "h" a b t y x)) e+            (privk "sign" b))))+      (send+        (enc "eortag" (enc "h" (cat "h" a b t y x)) e+          (privk "sign" b)))))+  (defrole ttp-rc1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat "sync-rc-req" (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b)))) (send (cat k r))))+  (defrole ttp-rc2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (recv+        (cat "sync-rc-req"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-cf1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat "sync-cf-req" (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (enc (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b)) (privk "sign" t)))))+  (defrole ttp-cf2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (recv+        (cat "sync-cf-req"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))+          (privk "sign" t))))))++(defskeleton wang+  (vars (y mesg) (r text) (a b t name) (k skey))+  (defstrand ttp-rc2 3 (y y) (r r) (a a) (b b) (t t) (k k))+  (non-orig (privk "encr" t) (privk "sign" a))+  (comment "Experiment 2 to prove Lemma 4.3, clause 2.")+  (traces+    ((recv+       (cat (cat a b t y (enc "h" (cat "h" k)))+         (enc "keytag" (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+           k r (pubk "encr" t))+         (enc "eootag" (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+             (pubk "encr" t)) (privk "sign" a))+         (enc "eortag" (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+             (pubk "encr" t)) (privk "sign" b))+         (enc "rcrq" (cat a b t y (enc "h" (cat "h" k)))+           (enc "keytag"+             (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+             (pubk "encr" t)) (privk "sign" b))))+      (recv+        (cat "sync-rc-req"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))+          (privk "sign" t)))))+  (label 37)+  (seen 38)+  (unrealized (0 0) (0 1))+  (origs)+  (comment "5 in cohort - 1 not yet seen"))++(defskeleton wang+  (vars (r text) (m data) (a b t name) (k skey))+  (defstrand ttp-rc2 3 (y (enc "h" (cat "h" (enc m k)))) (r r) (a a)+    (b b) (t t) (k k))+  (defstrand init1 1 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 0) (0 0)))+  (non-orig (privk "encr" t) (privk "sign" a))+  (operation encryption-test (added-strand init1 1)+    (enc "eootag"+      (enc "h"+        (cat "h" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k))))+      (enc "keytag"+        (enc "h"+          (cat "h" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))) k r (pubk "encr" t))+      (privk "sign" a)) (0 0))+  (traces+    ((recv+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))+         (enc "eortag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" b))+         (enc "rcrq"+           (cat a b t (enc "h" (cat "h" (enc m k)))+             (enc "h" (cat "h" k)))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" b))))+      (recv+        (cat "sync-rc-req"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a)) (privk "sign" t))))+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))))+  (label 38)+  (parent 37)+  (seen 39 40 41 42)+  (unrealized (0 1))+  (comment "8 in cohort - 4 not yet seen"))++(defskeleton wang+  (vars (r r-0 text) (m data) (a b t name) (k skey))+  (defstrand ttp-rc2 3 (y (enc "h" (cat "h" (enc m k)))) (r r) (a a)+    (b b) (t t) (k k))+  (defstrand init1 1 (r r) (m m) (a a) (b b) (t t) (k k))+  (defstrand init2 2 (r r-0) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 0) (0 0)) ((2 1) (0 1)))+  (non-orig (privk "encr" t) (privk "sign" a))+  (operation encryption-test (added-strand init2 2)+    (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+      (enc "h" (cat "h" k)) (privk "sign" a)) (0 1))+  (traces+    ((recv+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))+         (enc "eortag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" b))+         (enc "rcrq"+           (cat a b t (enc "h" (cat "h" (enc m k)))+             (enc "h" (cat "h" k)))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" b))))+      (recv+        (cat "sync-rc-req"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a)) (privk "sign" t))))+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a)))))+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r-0 (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r-0 (pubk "encr" t))+           (privk "sign" a))))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))))+  (label 39)+  (parent 38)+  (seen 40)+  (unrealized)+  (shape)+  (maps+    ((0)+      ((a a) (b b) (t t) (r r) (k k)+        (y (enc "h" (cat "h" (enc m k)))))))+  (origs)+  (comment "1 in cohort - 0 not yet seen"))++(defskeleton wang+  (vars (r text) (m data) (a b t name) (k skey))+  (defstrand ttp-rc2 3 (y (enc "h" (cat "h" (enc m k)))) (r r) (a a)+    (b b) (t t) (k k))+  (defstrand init2 2 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 0) (0 0)) ((1 1) (0 1)))+  (non-orig (privk "encr" t) (privk "sign" a))+  (operation encryption-test (displaced 1 2 init2 2)+    (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+      (enc "h" (cat "h" k)) (privk "sign" a)) (0 1))+  (traces+    ((recv+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))+         (enc "eortag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" b))+         (enc "rcrq"+           (cat a b t (enc "h" (cat "h" (enc m k)))+             (enc "h" (cat "h" k)))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" b))))+      (recv+        (cat "sync-rc-req"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a)) (privk "sign" t))))+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))))+  (label 40)+  (parent 38)+  (unrealized)+  (shape)+  (maps+    ((0)+      ((a a) (b b) (t t) (r r) (k k)+        (y (enc "h" (cat "h" (enc m k)))))))+  (origs))++(defskeleton wang+  (vars (r r-0 text) (m data) (a b t name) (k skey))+  (defstrand ttp-rc2 3 (y (enc "h" (cat "h" (enc m k)))) (r r) (a a)+    (b b) (t t) (k k))+  (defstrand init1 1 (r r) (m m) (a a) (b b) (t t) (k k))+  (defstrand init4 3 (r r-0) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 0) (0 0)) ((2 2) (0 1)))+  (non-orig (privk "encr" t) (privk "sign" a))+  (operation encryption-test (added-strand init4 3)+    (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+      (enc "h" (cat "h" k)) (privk "sign" a)) (0 1))+  (traces+    ((recv+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))+         (enc "eortag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" b))+         (enc "rcrq"+           (cat a b t (enc "h" (cat "h" (enc m k)))+             (enc "h" (cat "h" k)))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" b))))+      (recv+        (cat "sync-rc-req"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a)) (privk "sign" t))))+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a)))))+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r-0 (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r-0 (pubk "encr" t))+           (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r-0 (pubk "encr" t))+          (privk "sign" b)))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))))+  (label 41)+  (parent 38)+  (seen 42)+  (unrealized)+  (shape)+  (maps+    ((0)+      ((a a) (b b) (t t) (r r) (k k)+        (y (enc "h" (cat "h" (enc m k)))))))+  (origs)+  (comment "1 in cohort - 0 not yet seen"))++(defskeleton wang+  (vars (r text) (m data) (a b t name) (k skey))+  (defstrand ttp-rc2 3 (y (enc "h" (cat "h" (enc m k)))) (r r) (a a)+    (b b) (t t) (k k))+  (defstrand init4 3 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 0) (0 0)) ((1 2) (0 1)))+  (non-orig (privk "encr" t) (privk "sign" a))+  (operation encryption-test (displaced 1 2 init4 3)+    (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+      (enc "h" (cat "h" k)) (privk "sign" a)) (0 1))+  (traces+    ((recv+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))+         (enc "eortag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" b))+         (enc "rcrq"+           (cat a b t (enc "h" (cat "h" (enc m k)))+             (enc "h" (cat "h" k)))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" b))))+      (recv+        (cat "sync-rc-req"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a)) (privk "sign" t))))+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))))+  (label 42)+  (parent 38)+  (unrealized)+  (shape)+  (maps+    ((0)+      ((a a) (b b) (t t) (r r) (k k)+        (y (enc "h" (cat "h" (enc m k)))))))+  (origs))++(comment "Nothing left to do")++(defprotocol wang basic+  (defrole init1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b))) (send (cat k r))))+  (defrole init2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a)) (privk "sign" t)))))+  (defrole init3+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))))+  (defrole init4+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a)) (privk "sign" t)))))+  (defrole init5+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))))+  (defrole resp1+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b))) (recv (cat k r))))+  (defrole resp2+    (vars (a b t name) (m data) (r text) (k skey))+    (trace+      (recv+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k))) (enc m k)+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))))+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))))+      (send+        (cat+          (cat a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (enc "eootag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" a))+          (enc "eortag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b))+          (enc "rcrq"+            (cat a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h"+                (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                  (enc "h" (cat "h" k)))) k r (pubk "encr" t))+            (privk "sign" b)))) (recv (cat k r))))+  (defrole resp3+    (vars (a b t name) (e1 e2 x mesg))+    (trace+      (recv+        (cat (cat a b t (enc "h" (cat "h" e1)) x) e1 e2+          (enc "eootag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" a))))+      (send+        (cat (cat a b t (enc "h" (cat "h" e1)) x) e2+          (enc "eootag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" b))))+      (send+        (cat (cat a b t (enc "h" (cat "h" e1)) x) e2+          (enc "eootag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t (enc "h" (cat "h" e1)) x)) e2+            (privk "sign" b))+          (enc "rcrq" (cat a b t (enc "h" (cat "h" e1)) x) e2+            (privk "sign" b))))+      (recv+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" e1)) x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab1+    (vars (a b t name) (y x mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (send (cat "sync-abrq" (enc "abrq" a b t y x (privk "sign" a))))+      (send+        (enc "abcf" (enc "abrq" a b t y x (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-ab2+    (vars (a b t name) (y x e mesg))+    (trace (recv (enc "abrq" a b t y x (privk "sign" a)))+      (recv+        (cat "sync-abrq"+          (enc "eortag" (enc "h" (cat "h" a b t y x)) e+            (privk "sign" b))))+      (send+        (enc "eortag" (enc "h" (cat "h" a b t y x)) e+          (privk "sign" b)))))+  (defrole ttp-rc1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat "sync-rc-req" (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b)))) (send (cat k r))))+  (defrole ttp-rc2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "rcrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (recv+        (cat "sync-rc-req"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))+          (privk "sign" t)))))+  (defrole ttp-cf1+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (cat "sync-cf-req" (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (send+        (enc (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b)) (privk "sign" t)))))+  (defrole ttp-cf2+    (vars (a b t name) (r text) (k skey) (y mesg))+    (trace+      (recv+        (cat (cat a b t y (enc "h" (cat "h" k)))+          (enc "keytag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+            (pubk "encr" t))+          (enc "eootag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" a))+          (enc "eortag"+            (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))+          (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+            (enc "keytag"+              (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+              (pubk "encr" t)) (privk "sign" b))))+      (recv+        (cat "sync-cf-req"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))+          (privk "sign" t))))))++(defskeleton wang+  (vars (y mesg) (r text) (a b t name) (k skey))+  (defstrand ttp-cf2 3 (y y) (r r) (a a) (b b) (t t) (k k))+  (non-orig (privk "encr" t) (privk "sign" a))+  (comment "Experiment 3 to prove Lemma 4.3, clause 2.")+  (traces+    ((recv+       (cat (cat a b t y (enc "h" (cat "h" k)))+         (enc "keytag" (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+           k r (pubk "encr" t))+         (enc "eootag" (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+             (pubk "encr" t)) (privk "sign" a))+         (enc "eortag" (enc "h" (cat "h" a b t y (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+             (pubk "encr" t)) (privk "sign" b))+         (enc "cfrq" (cat a b t y (enc "h" (cat "h" k)))+           (enc "keytag"+             (enc "h" (cat "h" a b t y (enc "h" (cat "h" k)))) k r+             (pubk "encr" t)) (privk "sign" b))))+      (recv+        (cat "sync-cf-req"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t y (enc "h" (cat "h" k)) (privk "sign" a))+          (privk "sign" t)))))+  (label 43)+  (seen 44)+  (unrealized (0 0) (0 1))+  (origs)+  (comment "5 in cohort - 1 not yet seen"))++(defskeleton wang+  (vars (r text) (m data) (a b t name) (k skey))+  (defstrand ttp-cf2 3 (y (enc "h" (cat "h" (enc m k)))) (r r) (a a)+    (b b) (t t) (k k))+  (defstrand init1 1 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 0) (0 0)))+  (non-orig (privk "encr" t) (privk "sign" a))+  (operation encryption-test (added-strand init1 1)+    (enc "eootag"+      (enc "h"+        (cat "h" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k))))+      (enc "keytag"+        (enc "h"+          (cat "h" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)))) k r (pubk "encr" t))+      (privk "sign" a)) (0 0))+  (traces+    ((recv+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))+         (enc "eortag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" b))+         (enc "cfrq"+           (cat a b t (enc "h" (cat "h" (enc m k)))+             (enc "h" (cat "h" k)))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" b))))+      (recv+        (cat "sync-cf-req"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a)) (privk "sign" t))))+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))))+  (label 44)+  (parent 43)+  (seen 45 46 47 48)+  (unrealized (0 1))+  (comment "8 in cohort - 4 not yet seen"))++(defskeleton wang+  (vars (r r-0 text) (m data) (a b t name) (k skey))+  (defstrand ttp-cf2 3 (y (enc "h" (cat "h" (enc m k)))) (r r) (a a)+    (b b) (t t) (k k))+  (defstrand init1 1 (r r) (m m) (a a) (b b) (t t) (k k))+  (defstrand init2 2 (r r-0) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 0) (0 0)) ((2 1) (0 1)))+  (non-orig (privk "encr" t) (privk "sign" a))+  (operation encryption-test (added-strand init2 2)+    (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+      (enc "h" (cat "h" k)) (privk "sign" a)) (0 1))+  (traces+    ((recv+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))+         (enc "eortag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" b))+         (enc "cfrq"+           (cat a b t (enc "h" (cat "h" (enc m k)))+             (enc "h" (cat "h" k)))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" b))))+      (recv+        (cat "sync-cf-req"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a)) (privk "sign" t))))+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a)))))+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r-0 (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r-0 (pubk "encr" t))+           (privk "sign" a))))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))))+  (label 45)+  (parent 44)+  (seen 46)+  (unrealized)+  (shape)+  (maps+    ((0)+      ((a a) (b b) (t t) (r r) (k k)+        (y (enc "h" (cat "h" (enc m k)))))))+  (origs)+  (comment "1 in cohort - 0 not yet seen"))++(defskeleton wang+  (vars (r text) (m data) (a b t name) (k skey))+  (defstrand ttp-cf2 3 (y (enc "h" (cat "h" (enc m k)))) (r r) (a a)+    (b b) (t t) (k k))+  (defstrand init2 2 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 0) (0 0)) ((1 1) (0 1)))+  (non-orig (privk "encr" t) (privk "sign" a))+  (operation encryption-test (displaced 1 2 init2 2)+    (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+      (enc "h" (cat "h" k)) (privk "sign" a)) (0 1))+  (traces+    ((recv+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))+         (enc "eortag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" b))+         (enc "cfrq"+           (cat a b t (enc "h" (cat "h" (enc m k)))+             (enc "h" (cat "h" k)))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" b))))+      (recv+        (cat "sync-cf-req"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a)) (privk "sign" t))))+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))))+  (label 46)+  (parent 44)+  (unrealized)+  (shape)+  (maps+    ((0)+      ((a a) (b b) (t t) (r r) (k k)+        (y (enc "h" (cat "h" (enc m k)))))))+  (origs))++(defskeleton wang+  (vars (r r-0 text) (m data) (a b t name) (k skey))+  (defstrand ttp-cf2 3 (y (enc "h" (cat "h" (enc m k)))) (r r) (a a)+    (b b) (t t) (k k))+  (defstrand init1 1 (r r) (m m) (a a) (b b) (t t) (k k))+  (defstrand init4 3 (r r-0) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 0) (0 0)) ((2 2) (0 1)))+  (non-orig (privk "encr" t) (privk "sign" a))+  (operation encryption-test (added-strand init4 3)+    (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+      (enc "h" (cat "h" k)) (privk "sign" a)) (0 1))+  (traces+    ((recv+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))+         (enc "eortag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" b))+         (enc "cfrq"+           (cat a b t (enc "h" (cat "h" (enc m k)))+             (enc "h" (cat "h" k)))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" b))))+      (recv+        (cat "sync-cf-req"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a)) (privk "sign" t))))+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a)))))+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r-0 (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r-0 (pubk "encr" t))+           (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r-0 (pubk "encr" t))+          (privk "sign" b)))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))))+  (label 47)+  (parent 44)+  (seen 48)+  (unrealized)+  (shape)+  (maps+    ((0)+      ((a a) (b b) (t t) (r r) (k k)+        (y (enc "h" (cat "h" (enc m k)))))))+  (origs)+  (comment "1 in cohort - 0 not yet seen"))++(defskeleton wang+  (vars (r text) (m data) (a b t name) (k skey))+  (defstrand ttp-cf2 3 (y (enc "h" (cat "h" (enc m k)))) (r r) (a a)+    (b b) (t t) (k k))+  (defstrand init4 3 (r r) (m m) (a a) (b b) (t t) (k k))+  (precedes ((1 0) (0 0)) ((1 2) (0 1)))+  (non-orig (privk "encr" t) (privk "sign" a))+  (operation encryption-test (displaced 1 2 init4 3)+    (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+      (enc "h" (cat "h" k)) (privk "sign" a)) (0 1))+  (traces+    ((recv+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))+         (enc "eortag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" b))+         (enc "cfrq"+           (cat a b t (enc "h" (cat "h" (enc m k)))+             (enc "h" (cat "h" k)))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" b))))+      (recv+        (cat "sync-cf-req"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a))))+      (send+        (enc "abcf"+          (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+            (enc "h" (cat "h" k)) (privk "sign" a)) (privk "sign" t))))+    ((send+       (cat+         (cat a b t (enc "h" (cat "h" (enc m k))) (enc "h" (cat "h" k)))+         (enc m k)+         (enc "keytag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k)))) k r (pubk "encr" t))+         (enc "eootag"+           (enc "h"+             (cat "h" a b t (enc "h" (cat "h" (enc m k)))+               (enc "h" (cat "h" k))))+           (enc "keytag"+             (enc "h"+               (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                 (enc "h" (cat "h" k)))) k r (pubk "encr" t))+           (privk "sign" a))))+      (recv+        (enc "eortag"+          (enc "h"+            (cat "h" a b t (enc "h" (cat "h" (enc m k)))+              (enc "h" (cat "h" k))))+          (enc "keytag"+            (enc "h"+              (cat "h" a b t (enc "h" (cat "h" (enc m k)))+                (enc "h" (cat "h" k)))) k r (pubk "encr" t))+          (privk "sign" b)))+      (send+        (enc "abrq" a b t (enc "h" (cat "h" (enc m k)))+          (enc "h" (cat "h" k)) (privk "sign" a)))))+  (label 48)+  (parent 44)+  (unrealized)+  (shape)+  (maps+    ((0)+      ((a a) (b b) (t t) (r r) (k k)+        (y (enc "h" (cat "h" (enc m k)))))))+  (origs))++(comment "Nothing left to do")
tst/weird.tst view
@@ -1,4 +1,4 @@-(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol weird basic
tst/wide-mouth-frog.tst view
@@ -1,7 +1,7 @@ (herald "Wide-Mouth Frog Protocol"   (comment "This protocol has an infinite number of shapes")) -(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol wide-mouth-frog basic
tst/wonthull.tst view
@@ -1,4 +1,4 @@-(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol wonthull basic
tst/wonthull2.tst view
@@ -1,4 +1,4 @@-(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol wonthull2 basic
tst/wonthull3.tst view
@@ -1,4 +1,4 @@-(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol wonthull3 basic
tst/woolam.tst view
@@ -1,6 +1,6 @@ (herald "Woo-Lam Protocol") -(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol woolam basic
tst/yahalom-6.3.6.tst view
@@ -4,7 +4,7 @@     "Yahalom Protocol, Section 6.3.6, Page 49")   (url "http://www.eecs.umich.edu/acal/swerve/docs/49-1.pdf")) -(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol yahalom basic
tst/yahalom.tst view
@@ -1,6 +1,6 @@ (herald "Yahalom Protocol Without Forwarding") -(comment "CPSA 2.2.4")+(comment "CPSA 2.2.5") (comment "All input read")  (defprotocol yahalom basic