scyther-proof-0.10.0.0: data/examples/iso9798/isabelle-parallel-proofs/isoiec-9798-4-bdkey_cert_auto.thy
theory "isoiec-9798-4-bdkey_cert_auto"
imports
"ESPLogic"
begin
role isoiec_9798_4_1_bdkey_A
where "isoiec_9798_4_1_bdkey_A =
[ Send ''leak_A'' ( sN ''TNA'' )
, Recv ''text_1'' <| sMV ''Text1'', sMV ''Text2'' |>
, Send ''1'' <| sAV ''A'', sAV ''B'', sN ''TNA'', sMV ''Text2'',
sMV ''Text1'',
PHash <| <| sC ''CCF'', sKbd (AVar ''A'') (AVar ''B'') |>,
sC ''isoiec_9798_4_1_ccf_1'', sN ''TNA'', sAV ''B'', sMV ''Text1''
|>
|>
]"
role isoiec_9798_4_1_bdkey_B
where "isoiec_9798_4_1_bdkey_B =
[ Recv ''1'' <| sMV ''A'', sAV ''B'', sMV ''TNA'', sMV ''Text2'',
sMV ''Text1'',
PHash <| <| sC ''CCF'', sKbd (MVar ''A'') (AVar ''B'') |>,
sC ''isoiec_9798_4_1_ccf_1'', sMV ''TNA'', sAV ''B'', sMV ''Text1''
|>
|>
]"
role isoiec_9798_4_2_bdkey_A
where "isoiec_9798_4_2_bdkey_A =
[ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''Rb'', sMV ''Text1'' |>
, Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'' |>
, Send ''2'' <| sAV ''A'', sMV ''B'', sMV ''Text3'', sMV ''Rb'',
sMV ''Text2'',
PHash <| <| sC ''CCF'', sKbd (AVar ''A'') (MVar ''B'') |>,
sC ''isoiec_9798_4_2_ccf_2'', sMV ''Rb'', sMV ''B'', sMV ''Text2''
|>
|>
]"
role isoiec_9798_4_2_bdkey_B
where "isoiec_9798_4_2_bdkey_B =
[ Recv ''text_1'' ( sMV ''Text1'' )
, Send ''1'' <| sAV ''B'', sAV ''A'', sN ''Rb'', sMV ''Text1'' |>
, Recv ''2'' <| sAV ''A'', sAV ''B'', sMV ''Text3'', sN ''Rb'',
sMV ''Text2'',
PHash <| <| sC ''CCF'', sKbd (AVar ''A'') (AVar ''B'') |>,
sC ''isoiec_9798_4_2_ccf_2'', sN ''Rb'', sAV ''B'', sMV ''Text2''
|>
|>
]"
role isoiec_9798_4_3_bdkey_A
where "isoiec_9798_4_3_bdkey_A =
[ Send ''leak_A'' ( sN ''TNa'' )
, Recv ''text_1'' <| sMV ''Text1'', sMV ''Text2'' |>
, Send ''1'' <| sAV ''A'', sAV ''B'', sN ''TNa'', sMV ''Text2'',
sMV ''Text1'',
PHash <| <| sC ''CCF'', sKbd (AVar ''A'') (AVar ''B'') |>,
sC ''isoiec_9798_4_3_ccf_1'', sN ''TNa'', sAV ''B'', sMV ''Text1''
|>
|>
, Recv ''2'' <| sAV ''B'', sAV ''A'', sMV ''TNb'', sMV ''Text4'',
sMV ''Text3'',
PHash <| <| sC ''CCF'', sKbd (AVar ''A'') (AVar ''B'') |>,
sC ''isoiec_9798_4_3_ccf_2'', sMV ''TNb'', sAV ''A'', sMV ''Text3''
|>
|>
]"
role isoiec_9798_4_3_bdkey_B
where "isoiec_9798_4_3_bdkey_B =
[ Send ''leak_B'' ( sN ''TNb'' )
, Recv ''1'' <| sMV ''A'', sAV ''B'', sMV ''TNa'', sMV ''Text2'',
sMV ''Text1'',
PHash <| <| sC ''CCF'', sKbd (MVar ''A'') (AVar ''B'') |>,
sC ''isoiec_9798_4_3_ccf_1'', sMV ''TNa'', sAV ''B'', sMV ''Text1''
|>
|>
, Recv ''text_2'' <| sMV ''Text3'', sMV ''Text4'' |>
, Send ''2'' <| sAV ''B'', sMV ''A'', sN ''TNb'', sMV ''Text4'',
sMV ''Text3'',
PHash <| <| sC ''CCF'', sKbd (MVar ''A'') (AVar ''B'') |>,
sC ''isoiec_9798_4_3_ccf_2'', sN ''TNb'', sMV ''A'', sMV ''Text3''
|>
|>
]"
role isoiec_9798_4_4_bdkey_A
where "isoiec_9798_4_4_bdkey_A =
[ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''Rb'', sMV ''Text1'' |>
, Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'' |>
, Send ''2'' <| sAV ''A'', sMV ''B'', sN ''Ra'', sMV ''Text3'',
sMV ''Text2'',
PHash <| <| sC ''CCF'', sKbd (AVar ''A'') (MVar ''B'') |>,
sC ''isoiec_9798_4_4_ccf_2'', sN ''Ra'', sMV ''Rb'', sMV ''B'',
sMV ''Text2''
|>
|>
, Recv ''3'' <| sMV ''B'', sAV ''A'', sMV ''Text5'', sMV ''Text4'',
PHash <| <| sC ''CCF'', sKbd (AVar ''A'') (MVar ''B'') |>,
sC ''isoiec_9798_4_4_ccf_3'', sMV ''Rb'', sN ''Ra'', sMV ''Text4''
|>
|>
]"
role isoiec_9798_4_4_bdkey_B
where "isoiec_9798_4_4_bdkey_B =
[ Recv ''text_1'' ( sMV ''Text1'' )
, Send ''1'' <| sAV ''B'', sAV ''A'', sN ''Rb'', sMV ''Text1'' |>
, Recv ''2'' <| sAV ''A'', sAV ''B'', sMV ''Ra'', sMV ''Text3'',
sMV ''Text2'',
PHash <| <| sC ''CCF'', sKbd (AVar ''A'') (AVar ''B'') |>,
sC ''isoiec_9798_4_4_ccf_2'', sMV ''Ra'', sN ''Rb'', sAV ''B'',
sMV ''Text2''
|>
|>
, Recv ''text_3'' <| sMV ''Text4'', sMV ''Text5'' |>
, Send ''3'' <| sAV ''B'', sAV ''A'', sMV ''Text5'', sMV ''Text4'',
PHash <| <| sC ''CCF'', sKbd (AVar ''A'') (AVar ''B'') |>,
sC ''isoiec_9798_4_4_ccf_3'', sN ''Rb'', sMV ''Ra'', sMV ''Text4''
|>
|>
]"
protocol isoiec_9798_4_bdkey
where "isoiec_9798_4_bdkey =
{ isoiec_9798_4_1_bdkey_A, isoiec_9798_4_1_bdkey_B,
isoiec_9798_4_2_bdkey_A, isoiec_9798_4_2_bdkey_B,
isoiec_9798_4_3_bdkey_A, isoiec_9798_4_3_bdkey_B,
isoiec_9798_4_4_bdkey_A, isoiec_9798_4_4_bdkey_B
}"
locale restricted_isoiec_9798_4_bdkey_state = isoiec_9798_4_bdkey_state
type_invariant isoiec_9798_4_bdkey_composed_typing for isoiec_9798_4_bdkey
where "isoiec_9798_4_bdkey_composed_typing = mk_typing
[ ((isoiec_9798_4_1_bdkey_B, ''A''), (KnownT isoiec_9798_4_1_bdkey_B_1))
, ((isoiec_9798_4_3_bdkey_B, ''A''), (KnownT isoiec_9798_4_3_bdkey_B_1))
, ((isoiec_9798_4_2_bdkey_A, ''B''), (KnownT isoiec_9798_4_2_bdkey_A_1))
, ((isoiec_9798_4_4_bdkey_A, ''B''), (KnownT isoiec_9798_4_4_bdkey_A_1))
, ((isoiec_9798_4_4_bdkey_B, ''Ra''), (KnownT isoiec_9798_4_4_bdkey_B_2))
, ((isoiec_9798_4_2_bdkey_A, ''Rb''), (KnownT isoiec_9798_4_2_bdkey_A_1))
, ((isoiec_9798_4_4_bdkey_A, ''Rb''), (KnownT isoiec_9798_4_4_bdkey_A_1))
, ((isoiec_9798_4_1_bdkey_B, ''TNA''),
(KnownT isoiec_9798_4_1_bdkey_B_1))
, ((isoiec_9798_4_3_bdkey_B, ''TNa''),
(KnownT isoiec_9798_4_3_bdkey_B_1))
, ((isoiec_9798_4_3_bdkey_A, ''TNb''),
(KnownT isoiec_9798_4_3_bdkey_A_2))
, ((isoiec_9798_4_1_bdkey_A, ''Text1''),
(KnownT isoiec_9798_4_1_bdkey_A_text_1))
, ((isoiec_9798_4_1_bdkey_B, ''Text1''),
(KnownT isoiec_9798_4_1_bdkey_B_1))
, ((isoiec_9798_4_2_bdkey_A, ''Text1''),
(KnownT isoiec_9798_4_2_bdkey_A_1))
, ((isoiec_9798_4_2_bdkey_B, ''Text1''),
(KnownT isoiec_9798_4_2_bdkey_B_text_1))
, ((isoiec_9798_4_3_bdkey_A, ''Text1''),
(KnownT isoiec_9798_4_3_bdkey_A_text_1))
, ((isoiec_9798_4_3_bdkey_B, ''Text1''),
(KnownT isoiec_9798_4_3_bdkey_B_1))
, ((isoiec_9798_4_4_bdkey_A, ''Text1''),
(KnownT isoiec_9798_4_4_bdkey_A_1))
, ((isoiec_9798_4_4_bdkey_B, ''Text1''),
(KnownT isoiec_9798_4_4_bdkey_B_text_1))
, ((isoiec_9798_4_1_bdkey_A, ''Text2''),
(KnownT isoiec_9798_4_1_bdkey_A_text_1))
, ((isoiec_9798_4_1_bdkey_B, ''Text2''),
(KnownT isoiec_9798_4_1_bdkey_B_1))
, ((isoiec_9798_4_2_bdkey_A, ''Text2''),
(KnownT isoiec_9798_4_2_bdkey_A_text_2))
, ((isoiec_9798_4_2_bdkey_B, ''Text2''),
(KnownT isoiec_9798_4_2_bdkey_B_2))
, ((isoiec_9798_4_3_bdkey_A, ''Text2''),
(KnownT isoiec_9798_4_3_bdkey_A_text_1))
, ((isoiec_9798_4_3_bdkey_B, ''Text2''),
(KnownT isoiec_9798_4_3_bdkey_B_1))
, ((isoiec_9798_4_4_bdkey_A, ''Text2''),
(KnownT isoiec_9798_4_4_bdkey_A_text_2))
, ((isoiec_9798_4_4_bdkey_B, ''Text2''),
(KnownT isoiec_9798_4_4_bdkey_B_2))
, ((isoiec_9798_4_2_bdkey_A, ''Text3''),
(KnownT isoiec_9798_4_2_bdkey_A_text_2))
, ((isoiec_9798_4_2_bdkey_B, ''Text3''),
(KnownT isoiec_9798_4_2_bdkey_B_2))
, ((isoiec_9798_4_3_bdkey_A, ''Text3''),
(KnownT isoiec_9798_4_3_bdkey_A_2))
, ((isoiec_9798_4_3_bdkey_B, ''Text3''),
(KnownT isoiec_9798_4_3_bdkey_B_text_2))
, ((isoiec_9798_4_4_bdkey_A, ''Text3''),
(KnownT isoiec_9798_4_4_bdkey_A_text_2))
, ((isoiec_9798_4_4_bdkey_B, ''Text3''),
(KnownT isoiec_9798_4_4_bdkey_B_2))
, ((isoiec_9798_4_3_bdkey_A, ''Text4''),
(KnownT isoiec_9798_4_3_bdkey_A_2))
, ((isoiec_9798_4_3_bdkey_B, ''Text4''),
(KnownT isoiec_9798_4_3_bdkey_B_text_2))
, ((isoiec_9798_4_4_bdkey_A, ''Text4''),
(KnownT isoiec_9798_4_4_bdkey_A_3))
, ((isoiec_9798_4_4_bdkey_B, ''Text4''),
(KnownT isoiec_9798_4_4_bdkey_B_text_3))
, ((isoiec_9798_4_4_bdkey_A, ''Text5''),
(KnownT isoiec_9798_4_4_bdkey_A_3))
, ((isoiec_9798_4_4_bdkey_B, ''Text5''),
(KnownT isoiec_9798_4_4_bdkey_B_text_3))
]"
sublocale isoiec_9798_4_bdkey_state < isoiec_9798_4_bdkey_composed_typing_state
proof -
have "(t,r,s) : approx isoiec_9798_4_bdkey_composed_typing"
proof(cases rule: reachable_in_approxI_ext
[OF isoiec_9798_4_bdkey_composed_typing.monoTyp, completeness_cases_rule])
case (isoiec_9798_4_1_bdkey_A_text_1_Text1 t r s tid0)
then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s
by unfold_locales auto
note_prefix_closed (state) facts = isoiec_9798_4_1_bdkey_A_text_1_Text1
thus ?case
by (fastforce intro: event_predOrdI split: if_splits)
next
case (isoiec_9798_4_1_bdkey_A_text_1_Text2 t r s tid0)
then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s
by unfold_locales auto
note_prefix_closed (state) facts = isoiec_9798_4_1_bdkey_A_text_1_Text2
thus ?case
by (fastforce intro: event_predOrdI split: if_splits)
next
case (isoiec_9798_4_1_bdkey_B_1_A t r s tid0)
then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s
by unfold_locales auto
note_prefix_closed (state) facts = isoiec_9798_4_1_bdkey_B_1_A
thus ?case
by (fastforce intro: event_predOrdI split: if_splits)
next
case (isoiec_9798_4_1_bdkey_B_1_TNA t r s tid0)
then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s
by unfold_locales auto
note_prefix_closed (state) facts = isoiec_9798_4_1_bdkey_B_1_TNA
thus ?case
by (fastforce intro: event_predOrdI split: if_splits)
next
case (isoiec_9798_4_1_bdkey_B_1_Text1 t r s tid0)
then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s
by unfold_locales auto
note_prefix_closed (state) facts = isoiec_9798_4_1_bdkey_B_1_Text1
thus ?case
by (fastforce intro: event_predOrdI split: if_splits)
next
case (isoiec_9798_4_1_bdkey_B_1_Text2 t r s tid0)
then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s
by unfold_locales auto
note_prefix_closed (state) facts = isoiec_9798_4_1_bdkey_B_1_Text2
thus ?case
by (fastforce intro: event_predOrdI split: if_splits)
next
case (isoiec_9798_4_2_bdkey_A_1_B t r s tid0)
then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s
by unfold_locales auto
note_prefix_closed (state) facts = isoiec_9798_4_2_bdkey_A_1_B
thus ?case
by (fastforce intro: event_predOrdI split: if_splits)
next
case (isoiec_9798_4_2_bdkey_A_1_Rb t r s tid0)
then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s
by unfold_locales auto
note_prefix_closed (state) facts = isoiec_9798_4_2_bdkey_A_1_Rb
thus ?case
by (fastforce intro: event_predOrdI split: if_splits)
next
case (isoiec_9798_4_2_bdkey_A_1_Text1 t r s tid0)
then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s
by unfold_locales auto
note_prefix_closed (state) facts = isoiec_9798_4_2_bdkey_A_1_Text1
thus ?case
by (fastforce intro: event_predOrdI split: if_splits)
next
case (isoiec_9798_4_2_bdkey_A_text_2_Text2 t r s tid0)
then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s
by unfold_locales auto
note_prefix_closed (state) facts = isoiec_9798_4_2_bdkey_A_text_2_Text2
thus ?case
by (fastforce intro: event_predOrdI split: if_splits)
next
case (isoiec_9798_4_2_bdkey_A_text_2_Text3 t r s tid0)
then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s
by unfold_locales auto
note_prefix_closed (state) facts = isoiec_9798_4_2_bdkey_A_text_2_Text3
thus ?case
by (fastforce intro: event_predOrdI split: if_splits)
next
case (isoiec_9798_4_2_bdkey_B_2_Text2 t r s tid0)
then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s
by unfold_locales auto
note_prefix_closed (state) facts = isoiec_9798_4_2_bdkey_B_2_Text2
thus ?case
by (fastforce intro: event_predOrdI split: if_splits)
next
case (isoiec_9798_4_2_bdkey_B_2_Text3 t r s tid0)
then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s
by unfold_locales auto
note_prefix_closed (state) facts = isoiec_9798_4_2_bdkey_B_2_Text3
thus ?case
by (fastforce intro: event_predOrdI split: if_splits)
next
case (isoiec_9798_4_3_bdkey_A_text_1_Text1 t r s tid0)
then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s
by unfold_locales auto
note_prefix_closed (state) facts = isoiec_9798_4_3_bdkey_A_text_1_Text1
thus ?case
by (fastforce intro: event_predOrdI split: if_splits)
next
case (isoiec_9798_4_3_bdkey_A_text_1_Text2 t r s tid0)
then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s
by unfold_locales auto
note_prefix_closed (state) facts = isoiec_9798_4_3_bdkey_A_text_1_Text2
thus ?case
by (fastforce intro: event_predOrdI split: if_splits)
next
case (isoiec_9798_4_3_bdkey_A_2_TNb t r s tid0)
then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s
by unfold_locales auto
note_prefix_closed (state) facts = isoiec_9798_4_3_bdkey_A_2_TNb
thus ?case
by (fastforce intro: event_predOrdI split: if_splits)
next
case (isoiec_9798_4_3_bdkey_A_2_Text3 t r s tid0)
then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s
by unfold_locales auto
note_prefix_closed (state) facts = isoiec_9798_4_3_bdkey_A_2_Text3
thus ?case
by (fastforce intro: event_predOrdI split: if_splits)
next
case (isoiec_9798_4_3_bdkey_A_2_Text4 t r s tid0)
then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s
by unfold_locales auto
note_prefix_closed (state) facts = isoiec_9798_4_3_bdkey_A_2_Text4
thus ?case
by (fastforce intro: event_predOrdI split: if_splits)
next
case (isoiec_9798_4_3_bdkey_B_1_A t r s tid0)
then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s
by unfold_locales auto
note_prefix_closed (state) facts = isoiec_9798_4_3_bdkey_B_1_A
thus ?case
by (fastforce intro: event_predOrdI split: if_splits)
next
case (isoiec_9798_4_3_bdkey_B_1_TNa t r s tid0)
then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s
by unfold_locales auto
note_prefix_closed (state) facts = isoiec_9798_4_3_bdkey_B_1_TNa
thus ?case
by (fastforce intro: event_predOrdI split: if_splits)
next
case (isoiec_9798_4_3_bdkey_B_1_Text1 t r s tid0)
then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s
by unfold_locales auto
note_prefix_closed (state) facts = isoiec_9798_4_3_bdkey_B_1_Text1
thus ?case
by (fastforce intro: event_predOrdI split: if_splits)
next
case (isoiec_9798_4_3_bdkey_B_1_Text2 t r s tid0)
then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s
by unfold_locales auto
note_prefix_closed (state) facts = isoiec_9798_4_3_bdkey_B_1_Text2
thus ?case
by (fastforce intro: event_predOrdI split: if_splits)
next
case (isoiec_9798_4_3_bdkey_B_text_2_Text3 t r s tid0)
then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s
by unfold_locales auto
note_prefix_closed (state) facts = isoiec_9798_4_3_bdkey_B_text_2_Text3
thus ?case
by (fastforce intro: event_predOrdI split: if_splits)
next
case (isoiec_9798_4_3_bdkey_B_text_2_Text4 t r s tid0)
then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s
by unfold_locales auto
note_prefix_closed (state) facts = isoiec_9798_4_3_bdkey_B_text_2_Text4
thus ?case
by (fastforce intro: event_predOrdI split: if_splits)
next
case (isoiec_9798_4_4_bdkey_A_1_B t r s tid0)
then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s
by unfold_locales auto
note_prefix_closed (state) facts = isoiec_9798_4_4_bdkey_A_1_B
thus ?case
by (fastforce intro: event_predOrdI split: if_splits)
next
case (isoiec_9798_4_4_bdkey_A_1_Rb t r s tid0)
then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s
by unfold_locales auto
note_prefix_closed (state) facts = isoiec_9798_4_4_bdkey_A_1_Rb
thus ?case
by (fastforce intro: event_predOrdI split: if_splits)
next
case (isoiec_9798_4_4_bdkey_A_1_Text1 t r s tid0)
then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s
by unfold_locales auto
note_prefix_closed (state) facts = isoiec_9798_4_4_bdkey_A_1_Text1
thus ?case
by (fastforce intro: event_predOrdI split: if_splits)
next
case (isoiec_9798_4_4_bdkey_A_text_2_Text2 t r s tid0)
then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s
by unfold_locales auto
note_prefix_closed (state) facts = isoiec_9798_4_4_bdkey_A_text_2_Text2
thus ?case
by (fastforce intro: event_predOrdI split: if_splits)
next
case (isoiec_9798_4_4_bdkey_A_text_2_Text3 t r s tid0)
then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s
by unfold_locales auto
note_prefix_closed (state) facts = isoiec_9798_4_4_bdkey_A_text_2_Text3
thus ?case
by (fastforce intro: event_predOrdI split: if_splits)
next
case (isoiec_9798_4_4_bdkey_A_3_Text4 t r s tid0)
then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s
by unfold_locales auto
note_prefix_closed (state) facts = isoiec_9798_4_4_bdkey_A_3_Text4
thus ?case
by (fastforce intro: event_predOrdI split: if_splits)
next
case (isoiec_9798_4_4_bdkey_A_3_Text5 t r s tid0)
then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s
by unfold_locales auto
note_prefix_closed (state) facts = isoiec_9798_4_4_bdkey_A_3_Text5
thus ?case
by (fastforce intro: event_predOrdI split: if_splits)
next
case (isoiec_9798_4_4_bdkey_B_2_Ra t r s tid0)
then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s
by unfold_locales auto
note_prefix_closed (state) facts = isoiec_9798_4_4_bdkey_B_2_Ra
thus ?case
by (fastforce intro: event_predOrdI split: if_splits)
next
case (isoiec_9798_4_4_bdkey_B_2_Text2 t r s tid0)
then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s
by unfold_locales auto
note_prefix_closed (state) facts = isoiec_9798_4_4_bdkey_B_2_Text2
thus ?case
by (fastforce intro: event_predOrdI split: if_splits)
next
case (isoiec_9798_4_4_bdkey_B_2_Text3 t r s tid0)
then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s
by unfold_locales auto
note_prefix_closed (state) facts = isoiec_9798_4_4_bdkey_B_2_Text3
thus ?case
by (fastforce intro: event_predOrdI split: if_splits)
next
case (isoiec_9798_4_4_bdkey_B_text_3_Text4 t r s tid0)
then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s
by unfold_locales auto
note_prefix_closed (state) facts = isoiec_9798_4_4_bdkey_B_text_3_Text4
thus ?case
by (fastforce intro: event_predOrdI split: if_splits)
next
case (isoiec_9798_4_4_bdkey_B_text_3_Text5 t r s tid0)
then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s
by unfold_locales auto
note_prefix_closed (state) facts = isoiec_9798_4_4_bdkey_B_text_3_Text5
thus ?case
by (fastforce intro: event_predOrdI split: if_splits)
qed
thus "isoiec_9798_4_bdkey_composed_typing_state t r s" by unfold_locales auto
qed
text{* Prove secrecy of long-term keys. *}
context isoiec_9798_4_bdkey_state begin
(* This rule is unsafe in general, but OK here,
as we are only reasoning about static compromise.
*)
lemma static_longterm_key_reveal[dest!]:
"predOrd t (LKR a) e ==> RLKR a : reveals t"
by (auto intro: compr_predOrdI)
lemma longterm_private_key_secrecy:
assumes facts:
"SK m : knows t"
"RLKR m ~: reveals t"
shows "False"
using facts by (sources "SK m")
lemma longterm_sym_ud_key_secrecy:
assumes facts:
"K m1 m2 : knows t"
"RLKR m1 ~: reveals t"
"RLKR m2 ~: reveals t"
shows "False"
using facts by (sources "K m1 m2")
lemma longterm_sym_bd_key_secrecy:
assumes facts:
"Kbd m1 m2 : knows t"
"RLKR m1 ~: reveals t"
"RLKR m2 ~: reveals t"
"m1 : Agent"
"m2 : Agent"
shows "False"
proof -
from facts
have "KShr (agents {m1, m2}) : knows t"
by (auto simp: Kbd_def)
thus ?thesis using facts
proof (sources "KShr (agents {m1, m2})")
qed (auto simp: agents_def Agent_def)
qed
lemmas ltk_secrecy =
longterm_sym_ud_key_secrecy
longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]
longterm_sym_bd_key_secrecy
longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]
longterm_private_key_secrecy
longterm_private_key_secrecy[OF in_knows_predOrd1]
end
lemma (in restricted_isoiec_9798_4_bdkey_state) isoiec_9798_4_1_bdkey_B_non_injective_agreement:
assumes facts:
"roleMap r tid0 = Some isoiec_9798_4_1_bdkey_B"
"RLKR(s(AV ''B'' tid0)) ~: reveals t"
"RLKR(s(MV ''A'' tid0)) ~: reveals t"
"( tid0, isoiec_9798_4_1_bdkey_B_1 ) : steps t"
shows
"(? tid1.
roleMap r tid1 = Some isoiec_9798_4_1_bdkey_A &
( tid1, isoiec_9798_4_1_bdkey_A_1 ) : steps t &
{| s(AV ''A'' tid1), s(AV ''B'' tid1), LN ''TNA'' tid1,
s(MV ''Text1'' tid1)
|} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''TNA'' tid0),
s(MV ''Text1'' tid0)
|})"
proof -
note_prefix_closed facts = facts
thus ?thesis proof(sources! "
Hash {| {| LC ''CCF'', Kbd ( s(AV ''B'' tid0) ) ( s(MV ''A'' tid0) ) |},
LC ''isoiec_9798_4_1_ccf_1'', s(MV ''TNA'' tid0), s(AV ''B'' tid0),
s(MV ''Text1'' tid0)
|} ")
case fake note_unified facts = this facts
thus ?thesis by (auto dest!: ltk_secrecy)
next
case (isoiec_9798_4_1_bdkey_A_1_hash tid1) note_unified facts = this facts
thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)
qed (safe?, simp_all?, insert facts, (fastforce+)?)
qed
lemma (in restricted_isoiec_9798_4_bdkey_state) isoiec_9798_4_2_bdkey_B_injective_agreement:
"let
prems =
(% tid0.
roleMap r tid0 = Some isoiec_9798_4_2_bdkey_B &
RLKR(s(AV ''A'' tid0)) ~: reveals t &
RLKR(s(AV ''B'' tid0)) ~: reveals t &
( tid0, isoiec_9798_4_2_bdkey_B_2 ) : steps t);
concs =
(% tid0 tid1.
roleMap r tid1 = Some isoiec_9798_4_2_bdkey_A &
( tid1, isoiec_9798_4_2_bdkey_A_2 ) : steps t &
{| s(AV ''A'' tid1), s(MV ''B'' tid1), s(MV ''Rb'' tid1),
s(MV ''Text2'' tid1)
|} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), LN ''Rb'' tid0,
s(MV ''Text2'' tid0)
|})
in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"
(is "let prems = ?prems; concs = ?concs in ?P prems concs")
proof -
{ fix tid0 tid1
assume facts: "?prems tid0"
have " ? tid1. ?concs tid0 tid1"
proof -
note_unified facts = facts
note_prefix_closed facts = facts
thus ?thesis proof(sources! "
Hash {| {| LC ''CCF'', Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) |},
LC ''isoiec_9798_4_2_ccf_2'', LN ''Rb'' tid0, s(AV ''B'' tid0),
s(MV ''Text2'' tid0)
|} ")
case fake note_unified facts = this facts
thus ?thesis by (auto dest!: ltk_secrecy)
next
case (isoiec_9798_4_2_bdkey_A_2_hash tid1) note_unified facts = this facts
thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)
qed (safe?, simp_all?, insert facts, (fastforce+)?)
qed
}
note niagree = this
{ fix i1 i2 j
assume "?concs i1 j & ?concs i2 j"
note_unified facts = this
have "i1 = i2" using facts by simp
}
note conc_inj = this
show ?thesis
by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)
qed
lemma (in restricted_isoiec_9798_4_bdkey_state) isoiec_9798_4_3_bdkey_A_non_injective_agreement:
assumes facts:
"roleMap r tid0 = Some isoiec_9798_4_3_bdkey_A"
"RLKR(s(AV ''A'' tid0)) ~: reveals t"
"RLKR(s(AV ''B'' tid0)) ~: reveals t"
"( tid0, isoiec_9798_4_3_bdkey_A_2 ) : steps t"
shows
"(? tid1.
roleMap r tid1 = Some isoiec_9798_4_3_bdkey_B &
( tid1, isoiec_9798_4_3_bdkey_B_2 ) : steps t &
{| s(MV ''A'' tid1), s(AV ''B'' tid1), LN ''TNb'' tid1,
s(MV ''Text3'' tid1)
|} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''TNb'' tid0),
s(MV ''Text3'' tid0)
|})"
proof -
note_prefix_closed facts = facts
thus ?thesis proof(sources! "
Hash {| {| LC ''CCF'', Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) |},
LC ''isoiec_9798_4_3_ccf_2'', s(MV ''TNb'' tid0), s(AV ''A'' tid0),
s(MV ''Text3'' tid0)
|} ")
case fake note_unified facts = this facts
thus ?thesis by (auto dest!: ltk_secrecy)
next
case (isoiec_9798_4_3_bdkey_B_2_hash tid1) note_unified facts = this facts
thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)
qed (safe?, simp_all?, insert facts, (fastforce+)?)
qed
lemma (in restricted_isoiec_9798_4_bdkey_state) isoiec_9798_4_3_bdkey_B_non_injective_agreement:
assumes facts:
"roleMap r tid0 = Some isoiec_9798_4_3_bdkey_B"
"RLKR(s(AV ''B'' tid0)) ~: reveals t"
"RLKR(s(MV ''A'' tid0)) ~: reveals t"
"( tid0, isoiec_9798_4_3_bdkey_B_1 ) : steps t"
shows
"(? tid1.
roleMap r tid1 = Some isoiec_9798_4_3_bdkey_A &
( tid1, isoiec_9798_4_3_bdkey_A_1 ) : steps t &
{| s(AV ''A'' tid1), s(AV ''B'' tid1), LN ''TNa'' tid1,
s(MV ''Text1'' tid1)
|} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''TNa'' tid0),
s(MV ''Text1'' tid0)
|})"
proof -
note_prefix_closed facts = facts
thus ?thesis proof(sources! "
Hash {| {| LC ''CCF'', Kbd ( s(AV ''B'' tid0) ) ( s(MV ''A'' tid0) ) |},
LC ''isoiec_9798_4_3_ccf_1'', s(MV ''TNa'' tid0), s(AV ''B'' tid0),
s(MV ''Text1'' tid0)
|} ")
case fake note_unified facts = this facts
thus ?thesis by (auto dest!: ltk_secrecy)
next
case (isoiec_9798_4_3_bdkey_A_1_hash tid1) note_unified facts = this facts
thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)
qed (safe?, simp_all?, insert facts, (fastforce+)?)
qed
lemma (in restricted_isoiec_9798_4_bdkey_state) isoiec_9798_4_4_bdkey_A_injective_agreement:
"let
prems =
(% tid0.
roleMap r tid0 = Some isoiec_9798_4_4_bdkey_A &
RLKR(s(AV ''A'' tid0)) ~: reveals t &
RLKR(s(MV ''B'' tid0)) ~: reveals t &
( tid0, isoiec_9798_4_4_bdkey_A_3 ) : steps t);
concs =
(% tid0 tid1.
roleMap r tid1 = Some isoiec_9798_4_4_bdkey_B &
( tid1, isoiec_9798_4_4_bdkey_B_3 ) : steps t &
{| s(AV ''A'' tid1), s(AV ''B'' tid1), s(MV ''Ra'' tid1), LN ''Rb'' tid1,
s(MV ''Text2'' tid1), s(MV ''Text4'' tid1)
|} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), LN ''Ra'' tid0,
s(MV ''Rb'' tid0), s(MV ''Text2'' tid0), s(MV ''Text4'' tid0)
|})
in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"
(is "let prems = ?prems; concs = ?concs in ?P prems concs")
proof -
{ fix tid0 tid1
assume facts: "?prems tid0"
have " ? tid1. ?concs tid0 tid1"
proof -
note_unified facts = facts
note_prefix_closed facts = facts
thus ?thesis proof(sources! "
Hash {| {| LC ''CCF'', Kbd ( s(AV ''A'' tid0) ) ( s(MV ''B'' tid0) ) |},
LC ''isoiec_9798_4_4_ccf_3'', s(MV ''Rb'' tid0), LN ''Ra'' tid0,
s(MV ''Text4'' tid0)
|} ")
case fake note_unified facts = this facts
thus ?thesis by (auto dest!: ltk_secrecy)
next
case (isoiec_9798_4_4_bdkey_B_3_hash tid1) note_unified facts = this facts
hence "Kbd ( s(AV ''A'' tid1) )
( s(AV ''B'' tid1) ) = Kbd ( s(AV ''A'' tid0) ) ( s(MV ''B'' tid0) )"
by simp note facts = this facts
thus ?thesis proof(cases rule: Kbd_cases)
case noswap note_unified facts = this facts
thus ?thesis proof(sources! "
Hash {| {| LC ''CCF'', Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid1) ) |},
LC ''isoiec_9798_4_4_ccf_2'', LN ''Ra'' tid0, LN ''Rb'' tid1,
s(AV ''B'' tid1), s(MV ''Text2'' tid1)
|} ")
case fake note_unified facts = this facts
thus ?thesis by (auto dest!: ltk_secrecy)
next
case (isoiec_9798_4_4_bdkey_A_2_hash tid2) note_unified facts = this facts
thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)
qed (safe?, simp_all?, insert facts, (fastforce+)?)
next
case swapped note_unified facts = this facts
thus ?thesis proof(sources! "
Hash {| {| LC ''CCF'', Kbd ( s(AV ''A'' tid0) ) ( s(AV ''A'' tid1) ) |},
LC ''isoiec_9798_4_4_ccf_2'', LN ''Ra'' tid0, LN ''Rb'' tid1,
s(AV ''A'' tid0), s(MV ''Text2'' tid1)
|} ")
case fake note_unified facts = this facts
thus ?thesis by (auto dest!: ltk_secrecy)
next
case (isoiec_9798_4_4_bdkey_A_2_hash tid2) note_unified facts = this facts
thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)
qed (safe?, simp_all?, insert facts, (fastforce+)?)
qed (fastforce+)?
qed (safe?, simp_all?, insert facts, (fastforce+)?)
qed
}
note niagree = this
{ fix i1 i2 j
assume "?concs i1 j & ?concs i2 j"
note_unified facts = this
have "i1 = i2" using facts by simp
}
note conc_inj = this
show ?thesis
by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)
qed
lemma (in restricted_isoiec_9798_4_bdkey_state) isoiec_9798_4_4_bdkey_B_injective_agreement:
"let
prems =
(% tid0.
roleMap r tid0 = Some isoiec_9798_4_4_bdkey_B &
RLKR(s(AV ''A'' tid0)) ~: reveals t &
RLKR(s(AV ''B'' tid0)) ~: reveals t &
( tid0, isoiec_9798_4_4_bdkey_B_2 ) : steps t);
concs =
(% tid0 tid1.
roleMap r tid1 = Some isoiec_9798_4_4_bdkey_A &
( tid1, isoiec_9798_4_4_bdkey_A_2 ) : steps t &
{| s(AV ''A'' tid1), s(MV ''B'' tid1), LN ''Ra'' tid1, s(MV ''Rb'' tid1),
s(MV ''Text2'' tid1)
|} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''Ra'' tid0),
LN ''Rb'' tid0, s(MV ''Text2'' tid0)
|})
in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"
(is "let prems = ?prems; concs = ?concs in ?P prems concs")
proof -
{ fix tid0 tid1
assume facts: "?prems tid0"
have " ? tid1. ?concs tid0 tid1"
proof -
note_unified facts = facts
note_prefix_closed facts = facts
thus ?thesis proof(sources! "
Hash {| {| LC ''CCF'', Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) |},
LC ''isoiec_9798_4_4_ccf_2'', s(MV ''Ra'' tid0), LN ''Rb'' tid0,
s(AV ''B'' tid0), s(MV ''Text2'' tid0)
|} ")
case fake note_unified facts = this facts
thus ?thesis by (auto dest!: ltk_secrecy)
next
case (isoiec_9798_4_4_bdkey_A_2_hash tid1) note_unified facts = this facts
thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)
qed (safe?, simp_all?, insert facts, (fastforce+)?)
qed
}
note niagree = this
{ fix i1 i2 j
assume "?concs i1 j & ?concs i2 j"
note_unified facts = this
have "i1 = i2" using facts by simp
}
note conc_inj = this
show ?thesis
by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)
qed
end