diff --git a/CHANGELOG.md b/CHANGELOG.md new file mode 100644 --- /dev/null +++ b/CHANGELOG.md @@ -0,0 +1,3 @@ +# Version 0.1 + +* Initial version. diff --git a/LICENSE b/LICENSE new file mode 100644 --- /dev/null +++ b/LICENSE @@ -0,0 +1,219 @@ +Copyright 2020, Renzo Carbonara. + +Except where otherwise explicitly mentioned, all of contents of the +"bitcoin-keys" project are licensed under the Apache License, +Version 2.0 (the "License"); you may not use this file except in +compliance with the License. You may obtain a copy of the License at the +end of this file or at http://www.apache.org/licenses/LICENSE-2.0 + +Unless required by applicable law or agreed to in writing, software +distributed under the License is distributed on an "AS IS" BASIS, +WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +See the License for the specific language governing permissions and +limitations under the License. + + +------------------------------------------------------------------------------- + + + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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We also recommend that a + file or class name and description of purpose be included on the + same "printed page" as the copyright notice for easier + identification within third-party archives. + + Copyright [yyyy] [name of copyright owner] + + Licensed under the Apache License, Version 2.0 (the "License"); + you may not use this file except in compliance with the License. + You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + + Unless required by applicable law or agreed to in writing, software + distributed under the License is distributed on an "AS IS" BASIS, + WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + See the License for the specific language governing permissions and + limitations under the License. diff --git a/README.md b/README.md new file mode 100644 --- /dev/null +++ b/README.md @@ -0,0 +1,16 @@ +# bitcoin-keys + +Bitcoin keys. + +This library builds on GHC and GHCJS. + +## Developing in GHCJS + +* `cabal --ghcjs build` will build the Haskell `bitcoin-keys` library with the + JavaScript dependencies already compiled at `js/index.compiled.js`. + +* If the `js/index.js` file changes, run `npx webpack` to regenerate + `js/index.compiled.js` and commit both files to the repository. + +* If the `package.json` file changes, run `npm install -D` to get new JS + dependencies, and then run `npx webpack` as above. diff --git a/bitcoin-keys.cabal b/bitcoin-keys.cabal new file mode 100644 --- /dev/null +++ b/bitcoin-keys.cabal @@ -0,0 +1,51 @@ +cabal-version: 2.4 +name: bitcoin-keys +version: 0.1 +license: Apache-2.0 +license-file: LICENSE +extra-source-files: README.md CHANGELOG.md +author: Renzo Carbonara +maintainer: renĪ»ren.zone +copyright: Copyright (c) Renzo Carbonara 2020 +category: Cryptography +build-type: Simple +synopsis: Bitcoin keys +description: + Bitcoin keys. + . + This library builds in GHC and GHCJS. +homepage: https://gitlab.com/k0001/hs-bitcoin-keys +bug-reports: https://gitlab.com/k0001/hs-bitcoin-keys/issues +tested-with: GHC == 8.8.3, GHC == 8.6.5, GHCJS == 8.6.0 + +common basic + default-language: Haskell2010 + ghc-options: -O2 -Wall -Werror=incomplete-patterns + ghcjs-options: -O3 -Wall -Werror=incomplete-patterns + build-depends: base == 4.*, bytestring + +library + import: basic + hs-source-dirs: lib + exposed-modules: Bitcoin.Keys + If impl(ghcjs) + other-modules: Bitcoin.Keys.GHCJS + build-depends: ghcjs-base + -- This is file is generated. See README.md. + js-sources: js/index.compiled.js + else + other-modules: Bitcoin.Keys.GHC + build-depends: secp256k1-haskell + +test-suite test + import: basic + type: exitcode-stdio-1.0 + hs-source-dirs: test + main-is: Main.hs + build-depends: + base16-bytestring, + hedgehog, + bitcoin-keys, + tasty, + tasty-hedgehog, + tasty-hunit, diff --git a/js/index.compiled.js b/js/index.compiled.js new file mode 100644 --- /dev/null +++ b/js/index.compiled.js @@ -0,0 +1,1 @@ +var h$bitcoin_keys=function(e){var t={};function r(i){if(t[i])return t[i].exports;var f=t[i]={i:i,l:!1,exports:{}};return e[i].call(f.exports,f,f.exports,r),f.l=!0,f.exports}return r.m=e,r.c=t,r.d=function(e,t,i){r.o(e,t)||Object.defineProperty(e,t,{enumerable:!0,get:i})},r.r=function(e){"undefined"!=typeof Symbol&&Symbol.toStringTag&&Object.defineProperty(e,Symbol.toStringTag,{value:"Module"}),Object.defineProperty(e,"__esModule",{value:!0})},r.t=function(e,t){if(1&t&&(e=r(e)),8&t)return e;if(4&t&&"object"==typeof 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0==(8191&t)&&(r+=13,t>>>=13),0==(127&t)&&(r+=7,t>>>=7),0==(15&t)&&(r+=4,t>>>=4),0==(3&t)&&(r+=2,t>>>=2),0==(1&t)&&r++,r},n.prototype.bitLength=function(){var e=this.words[this.length-1],t=this._countBits(e);return 26*(this.length-1)+t},n.prototype.zeroBits=function(){if(this.isZero())return 0;for(var e=0,t=0;te.length?this.clone().ior(e):e.clone().ior(this)},n.prototype.uor=function(e){return this.length>e.length?this.clone().iuor(e):e.clone().iuor(this)},n.prototype.iuand=function(e){var t;t=this.length>e.length?e:this;for(var r=0;re.length?this.clone().iand(e):e.clone().iand(this)},n.prototype.uand=function(e){return this.length>e.length?this.clone().iuand(e):e.clone().iuand(this)},n.prototype.iuxor=function(e){var t,r;this.length>e.length?(t=this,r=e):(t=e,r=this);for(var i=0;ie.length?this.clone().ixor(e):e.clone().ixor(this)},n.prototype.uxor=function(e){return this.length>e.length?this.clone().iuxor(e):e.clone().iuxor(this)},n.prototype.inotn=function(e){i("number"==typeof e&&e>=0);var t=0|Math.ceil(e/26),r=e%26;this._expand(t),r>0&&t--;for(var f=0;f0&&(this.words[f]=~this.words[f]&67108863>>26-r),this.strip()},n.prototype.notn=function(e){return this.clone().inotn(e)},n.prototype.setn=function(e,t){i("number"==typeof e&&e>=0);var r=e/26|0,f=e%26;return this._expand(r+1),this.words[r]=t?this.words[r]|1<e.length?(r=this,i=e):(r=e,i=this);for(var f=0,n=0;n>>26;for(;0!==f&&n>>26;if(this.length=r.length,0!==f)this.words[this.length]=f,this.length++;else if(r!==this)for(;ne.length?this.clone().iadd(e):e.clone().iadd(this)},n.prototype.isub=function(e){if(0!==e.negative){e.negative=0;var t=this.iadd(e);return e.negative=1,t._normSign()}if(0!==this.negative)return this.negative=0,this.iadd(e),this.negative=1,this._normSign();var r,i,f=this.cmp(e);if(0===f)return this.negative=0,this.length=1,this.words[0]=0,this;f>0?(r=this,i=e):(r=e,i=this);for(var n=0,d=0;d>26,this.words[d]=67108863&t;for(;0!==n&&d>26,this.words[d]=67108863&t;if(0===n&&d>>13,b=0|d[1],l=8191&b,p=b>>>13,m=0|d[2],v=8191&m,y=m>>>13,g=0|d[3],w=8191&g,M=g>>>13,S=0|d[4],A=8191&S,_=S>>>13,x=0|d[5],I=8191&x,k=x>>>13,z=0|d[6],q=8191&z,R=z>>>13,P=0|d[7],E=8191&P,N=P>>>13,j=0|d[8],L=8191&j,B=j>>>13,O=0|d[9],T=8191&O,K=O>>>13,C=0|a[0],F=8191&C,Z=C>>>13,U=0|a[1],V=8191&U,J=U>>>13,H=0|a[2],X=8191&H,D=H>>>13,W=0|a[3],Y=8191&W,$=W>>>13,Q=0|a[4],G=8191&Q,ee=Q>>>13,te=0|a[5],re=8191&te,ie=te>>>13,fe=0|a[6],ne=8191&fe,de=fe>>>13,ae=0|a[7],ce=8191&ae,se=ae>>>13,oe=0|a[8],he=8191&oe,ue=oe>>>13,be=0|a[9],le=8191&be,pe=be>>>13;r.negative=e.negative^t.negative,r.length=19;var me=(s+(i=Math.imul(h,F))|0)+((8191&(f=(f=Math.imul(h,Z))+Math.imul(u,F)|0))<<13)|0;s=((n=Math.imul(u,Z))+(f>>>13)|0)+(me>>>26)|0,me&=67108863,i=Math.imul(l,F),f=(f=Math.imul(l,Z))+Math.imul(p,F)|0,n=Math.imul(p,Z);var ve=(s+(i=i+Math.imul(h,V)|0)|0)+((8191&(f=(f=f+Math.imul(h,J)|0)+Math.imul(u,V)|0))<<13)|0;s=((n=n+Math.imul(u,J)|0)+(f>>>13)|0)+(ve>>>26)|0,ve&=67108863,i=Math.imul(v,F),f=(f=Math.imul(v,Z))+Math.imul(y,F)|0,n=Math.imul(y,Z),i=i+Math.imul(l,V)|0,f=(f=f+Math.imul(l,J)|0)+Math.imul(p,V)|0,n=n+Math.imul(p,J)|0;var ye=(s+(i=i+Math.imul(h,X)|0)|0)+((8191&(f=(f=f+Math.imul(h,D)|0)+Math.imul(u,X)|0))<<13)|0;s=((n=n+Math.imul(u,D)|0)+(f>>>13)|0)+(ye>>>26)|0,ye&=67108863,i=Math.imul(w,F),f=(f=Math.imul(w,Z))+Math.imul(M,F)|0,n=Math.imul(M,Z),i=i+Math.imul(v,V)|0,f=(f=f+Math.imul(v,J)|0)+Math.imul(y,V)|0,n=n+Math.imul(y,J)|0,i=i+Math.imul(l,X)|0,f=(f=f+Math.imul(l,D)|0)+Math.imul(p,X)|0,n=n+Math.imul(p,D)|0;var ge=(s+(i=i+Math.imul(h,Y)|0)|0)+((8191&(f=(f=f+Math.imul(h,$)|0)+Math.imul(u,Y)|0))<<13)|0;s=((n=n+Math.imul(u,$)|0)+(f>>>13)|0)+(ge>>>26)|0,ge&=67108863,i=Math.imul(A,F),f=(f=Math.imul(A,Z))+Math.imul(_,F)|0,n=Math.imul(_,Z),i=i+Math.imul(w,V)|0,f=(f=f+Math.imul(w,J)|0)+Math.imul(M,V)|0,n=n+Math.imul(M,J)|0,i=i+Math.imul(v,X)|0,f=(f=f+Math.imul(v,D)|0)+Math.imul(y,X)|0,n=n+Math.imul(y,D)|0,i=i+Math.imul(l,Y)|0,f=(f=f+Math.imul(l,$)|0)+Math.imul(p,Y)|0,n=n+Math.imul(p,$)|0;var we=(s+(i=i+Math.imul(h,G)|0)|0)+((8191&(f=(f=f+Math.imul(h,ee)|0)+Math.imul(u,G)|0))<<13)|0;s=((n=n+Math.imul(u,ee)|0)+(f>>>13)|0)+(we>>>26)|0,we&=67108863,i=Math.imul(I,F),f=(f=Math.imul(I,Z))+Math.imul(k,F)|0,n=Math.imul(k,Z),i=i+Math.imul(A,V)|0,f=(f=f+Math.imul(A,J)|0)+Math.imul(_,V)|0,n=n+Math.imul(_,J)|0,i=i+Math.imul(w,X)|0,f=(f=f+Math.imul(w,D)|0)+Math.imul(M,X)|0,n=n+Math.imul(M,D)|0,i=i+Math.imul(v,Y)|0,f=(f=f+Math.imul(v,$)|0)+Math.imul(y,Y)|0,n=n+Math.imul(y,$)|0,i=i+Math.imul(l,G)|0,f=(f=f+Math.imul(l,ee)|0)+Math.imul(p,G)|0,n=n+Math.imul(p,ee)|0;var Me=(s+(i=i+Math.imul(h,re)|0)|0)+((8191&(f=(f=f+Math.imul(h,ie)|0)+Math.imul(u,re)|0))<<13)|0;s=((n=n+Math.imul(u,ie)|0)+(f>>>13)|0)+(Me>>>26)|0,Me&=67108863,i=Math.imul(q,F),f=(f=Math.imul(q,Z))+Math.imul(R,F)|0,n=Math.imul(R,Z),i=i+Math.imul(I,V)|0,f=(f=f+Math.imul(I,J)|0)+Math.imul(k,V)|0,n=n+Math.imul(k,J)|0,i=i+Math.imul(A,X)|0,f=(f=f+Math.imul(A,D)|0)+Math.imul(_,X)|0,n=n+Math.imul(_,D)|0,i=i+Math.imul(w,Y)|0,f=(f=f+Math.imul(w,$)|0)+Math.imul(M,Y)|0,n=n+Math.imul(M,$)|0,i=i+Math.imul(v,G)|0,f=(f=f+Math.imul(v,ee)|0)+Math.imul(y,G)|0,n=n+Math.imul(y,ee)|0,i=i+Math.imul(l,re)|0,f=(f=f+Math.imul(l,ie)|0)+Math.imul(p,re)|0,n=n+Math.imul(p,ie)|0;var Se=(s+(i=i+Math.imul(h,ne)|0)|0)+((8191&(f=(f=f+Math.imul(h,de)|0)+Math.imul(u,ne)|0))<<13)|0;s=((n=n+Math.imul(u,de)|0)+(f>>>13)|0)+(Se>>>26)|0,Se&=67108863,i=Math.imul(E,F),f=(f=Math.imul(E,Z))+Math.imul(N,F)|0,n=Math.imul(N,Z),i=i+Math.imul(q,V)|0,f=(f=f+Math.imul(q,J)|0)+Math.imul(R,V)|0,n=n+Math.imul(R,J)|0,i=i+Math.imul(I,X)|0,f=(f=f+Math.imul(I,D)|0)+Math.imul(k,X)|0,n=n+Math.imul(k,D)|0,i=i+Math.imul(A,Y)|0,f=(f=f+Math.imul(A,$)|0)+Math.imul(_,Y)|0,n=n+Math.imul(_,$)|0,i=i+Math.imul(w,G)|0,f=(f=f+Math.imul(w,ee)|0)+Math.imul(M,G)|0,n=n+Math.imul(M,ee)|0,i=i+Math.imul(v,re)|0,f=(f=f+Math.imul(v,ie)|0)+Math.imul(y,re)|0,n=n+Math.imul(y,ie)|0,i=i+Math.imul(l,ne)|0,f=(f=f+Math.imul(l,de)|0)+Math.imul(p,ne)|0,n=n+Math.imul(p,de)|0;var Ae=(s+(i=i+Math.imul(h,ce)|0)|0)+((8191&(f=(f=f+Math.imul(h,se)|0)+Math.imul(u,ce)|0))<<13)|0;s=((n=n+Math.imul(u,se)|0)+(f>>>13)|0)+(Ae>>>26)|0,Ae&=67108863,i=Math.imul(L,F),f=(f=Math.imul(L,Z))+Math.imul(B,F)|0,n=Math.imul(B,Z),i=i+Math.imul(E,V)|0,f=(f=f+Math.imul(E,J)|0)+Math.imul(N,V)|0,n=n+Math.imul(N,J)|0,i=i+Math.imul(q,X)|0,f=(f=f+Math.imul(q,D)|0)+Math.imul(R,X)|0,n=n+Math.imul(R,D)|0,i=i+Math.imul(I,Y)|0,f=(f=f+Math.imul(I,$)|0)+Math.imul(k,Y)|0,n=n+Math.imul(k,$)|0,i=i+Math.imul(A,G)|0,f=(f=f+Math.imul(A,ee)|0)+Math.imul(_,G)|0,n=n+Math.imul(_,ee)|0,i=i+Math.imul(w,re)|0,f=(f=f+Math.imul(w,ie)|0)+Math.imul(M,re)|0,n=n+Math.imul(M,ie)|0,i=i+Math.imul(v,ne)|0,f=(f=f+Math.imul(v,de)|0)+Math.imul(y,ne)|0,n=n+Math.imul(y,de)|0,i=i+Math.imul(l,ce)|0,f=(f=f+Math.imul(l,se)|0)+Math.imul(p,ce)|0,n=n+Math.imul(p,se)|0;var _e=(s+(i=i+Math.imul(h,he)|0)|0)+((8191&(f=(f=f+Math.imul(h,ue)|0)+Math.imul(u,he)|0))<<13)|0;s=((n=n+Math.imul(u,ue)|0)+(f>>>13)|0)+(_e>>>26)|0,_e&=67108863,i=Math.imul(T,F),f=(f=Math.imul(T,Z))+Math.imul(K,F)|0,n=Math.imul(K,Z),i=i+Math.imul(L,V)|0,f=(f=f+Math.imul(L,J)|0)+Math.imul(B,V)|0,n=n+Math.imul(B,J)|0,i=i+Math.imul(E,X)|0,f=(f=f+Math.imul(E,D)|0)+Math.imul(N,X)|0,n=n+Math.imul(N,D)|0,i=i+Math.imul(q,Y)|0,f=(f=f+Math.imul(q,$)|0)+Math.imul(R,Y)|0,n=n+Math.imul(R,$)|0,i=i+Math.imul(I,G)|0,f=(f=f+Math.imul(I,ee)|0)+Math.imul(k,G)|0,n=n+Math.imul(k,ee)|0,i=i+Math.imul(A,re)|0,f=(f=f+Math.imul(A,ie)|0)+Math.imul(_,re)|0,n=n+Math.imul(_,ie)|0,i=i+Math.imul(w,ne)|0,f=(f=f+Math.imul(w,de)|0)+Math.imul(M,ne)|0,n=n+Math.imul(M,de)|0,i=i+Math.imul(v,ce)|0,f=(f=f+Math.imul(v,se)|0)+Math.imul(y,ce)|0,n=n+Math.imul(y,se)|0,i=i+Math.imul(l,he)|0,f=(f=f+Math.imul(l,ue)|0)+Math.imul(p,he)|0,n=n+Math.imul(p,ue)|0;var xe=(s+(i=i+Math.imul(h,le)|0)|0)+((8191&(f=(f=f+Math.imul(h,pe)|0)+Math.imul(u,le)|0))<<13)|0;s=((n=n+Math.imul(u,pe)|0)+(f>>>13)|0)+(xe>>>26)|0,xe&=67108863,i=Math.imul(T,V),f=(f=Math.imul(T,J))+Math.imul(K,V)|0,n=Math.imul(K,J),i=i+Math.imul(L,X)|0,f=(f=f+Math.imul(L,D)|0)+Math.imul(B,X)|0,n=n+Math.imul(B,D)|0,i=i+Math.imul(E,Y)|0,f=(f=f+Math.imul(E,$)|0)+Math.imul(N,Y)|0,n=n+Math.imul(N,$)|0,i=i+Math.imul(q,G)|0,f=(f=f+Math.imul(q,ee)|0)+Math.imul(R,G)|0,n=n+Math.imul(R,ee)|0,i=i+Math.imul(I,re)|0,f=(f=f+Math.imul(I,ie)|0)+Math.imul(k,re)|0,n=n+Math.imul(k,ie)|0,i=i+Math.imul(A,ne)|0,f=(f=f+Math.imul(A,de)|0)+Math.imul(_,ne)|0,n=n+Math.imul(_,de)|0,i=i+Math.imul(w,ce)|0,f=(f=f+Math.imul(w,se)|0)+Math.imul(M,ce)|0,n=n+Math.imul(M,se)|0,i=i+Math.imul(v,he)|0,f=(f=f+Math.imul(v,ue)|0)+Math.imul(y,he)|0,n=n+Math.imul(y,ue)|0;var Ie=(s+(i=i+Math.imul(l,le)|0)|0)+((8191&(f=(f=f+Math.imul(l,pe)|0)+Math.imul(p,le)|0))<<13)|0;s=((n=n+Math.imul(p,pe)|0)+(f>>>13)|0)+(Ie>>>26)|0,Ie&=67108863,i=Math.imul(T,X),f=(f=Math.imul(T,D))+Math.imul(K,X)|0,n=Math.imul(K,D),i=i+Math.imul(L,Y)|0,f=(f=f+Math.imul(L,$)|0)+Math.imul(B,Y)|0,n=n+Math.imul(B,$)|0,i=i+Math.imul(E,G)|0,f=(f=f+Math.imul(E,ee)|0)+Math.imul(N,G)|0,n=n+Math.imul(N,ee)|0,i=i+Math.imul(q,re)|0,f=(f=f+Math.imul(q,ie)|0)+Math.imul(R,re)|0,n=n+Math.imul(R,ie)|0,i=i+Math.imul(I,ne)|0,f=(f=f+Math.imul(I,de)|0)+Math.imul(k,ne)|0,n=n+Math.imul(k,de)|0,i=i+Math.imul(A,ce)|0,f=(f=f+Math.imul(A,se)|0)+Math.imul(_,ce)|0,n=n+Math.imul(_,se)|0,i=i+Math.imul(w,he)|0,f=(f=f+Math.imul(w,ue)|0)+Math.imul(M,he)|0,n=n+Math.imul(M,ue)|0;var ke=(s+(i=i+Math.imul(v,le)|0)|0)+((8191&(f=(f=f+Math.imul(v,pe)|0)+Math.imul(y,le)|0))<<13)|0;s=((n=n+Math.imul(y,pe)|0)+(f>>>13)|0)+(ke>>>26)|0,ke&=67108863,i=Math.imul(T,Y),f=(f=Math.imul(T,$))+Math.imul(K,Y)|0,n=Math.imul(K,$),i=i+Math.imul(L,G)|0,f=(f=f+Math.imul(L,ee)|0)+Math.imul(B,G)|0,n=n+Math.imul(B,ee)|0,i=i+Math.imul(E,re)|0,f=(f=f+Math.imul(E,ie)|0)+Math.imul(N,re)|0,n=n+Math.imul(N,ie)|0,i=i+Math.imul(q,ne)|0,f=(f=f+Math.imul(q,de)|0)+Math.imul(R,ne)|0,n=n+Math.imul(R,de)|0,i=i+Math.imul(I,ce)|0,f=(f=f+Math.imul(I,se)|0)+Math.imul(k,ce)|0,n=n+Math.imul(k,se)|0,i=i+Math.imul(A,he)|0,f=(f=f+Math.imul(A,ue)|0)+Math.imul(_,he)|0,n=n+Math.imul(_,ue)|0;var ze=(s+(i=i+Math.imul(w,le)|0)|0)+((8191&(f=(f=f+Math.imul(w,pe)|0)+Math.imul(M,le)|0))<<13)|0;s=((n=n+Math.imul(M,pe)|0)+(f>>>13)|0)+(ze>>>26)|0,ze&=67108863,i=Math.imul(T,G),f=(f=Math.imul(T,ee))+Math.imul(K,G)|0,n=Math.imul(K,ee),i=i+Math.imul(L,re)|0,f=(f=f+Math.imul(L,ie)|0)+Math.imul(B,re)|0,n=n+Math.imul(B,ie)|0,i=i+Math.imul(E,ne)|0,f=(f=f+Math.imul(E,de)|0)+Math.imul(N,ne)|0,n=n+Math.imul(N,de)|0,i=i+Math.imul(q,ce)|0,f=(f=f+Math.imul(q,se)|0)+Math.imul(R,ce)|0,n=n+Math.imul(R,se)|0,i=i+Math.imul(I,he)|0,f=(f=f+Math.imul(I,ue)|0)+Math.imul(k,he)|0,n=n+Math.imul(k,ue)|0;var qe=(s+(i=i+Math.imul(A,le)|0)|0)+((8191&(f=(f=f+Math.imul(A,pe)|0)+Math.imul(_,le)|0))<<13)|0;s=((n=n+Math.imul(_,pe)|0)+(f>>>13)|0)+(qe>>>26)|0,qe&=67108863,i=Math.imul(T,re),f=(f=Math.imul(T,ie))+Math.imul(K,re)|0,n=Math.imul(K,ie),i=i+Math.imul(L,ne)|0,f=(f=f+Math.imul(L,de)|0)+Math.imul(B,ne)|0,n=n+Math.imul(B,de)|0,i=i+Math.imul(E,ce)|0,f=(f=f+Math.imul(E,se)|0)+Math.imul(N,ce)|0,n=n+Math.imul(N,se)|0,i=i+Math.imul(q,he)|0,f=(f=f+Math.imul(q,ue)|0)+Math.imul(R,he)|0,n=n+Math.imul(R,ue)|0;var Re=(s+(i=i+Math.imul(I,le)|0)|0)+((8191&(f=(f=f+Math.imul(I,pe)|0)+Math.imul(k,le)|0))<<13)|0;s=((n=n+Math.imul(k,pe)|0)+(f>>>13)|0)+(Re>>>26)|0,Re&=67108863,i=Math.imul(T,ne),f=(f=Math.imul(T,de))+Math.imul(K,ne)|0,n=Math.imul(K,de),i=i+Math.imul(L,ce)|0,f=(f=f+Math.imul(L,se)|0)+Math.imul(B,ce)|0,n=n+Math.imul(B,se)|0,i=i+Math.imul(E,he)|0,f=(f=f+Math.imul(E,ue)|0)+Math.imul(N,he)|0,n=n+Math.imul(N,ue)|0;var Pe=(s+(i=i+Math.imul(q,le)|0)|0)+((8191&(f=(f=f+Math.imul(q,pe)|0)+Math.imul(R,le)|0))<<13)|0;s=((n=n+Math.imul(R,pe)|0)+(f>>>13)|0)+(Pe>>>26)|0,Pe&=67108863,i=Math.imul(T,ce),f=(f=Math.imul(T,se))+Math.imul(K,ce)|0,n=Math.imul(K,se),i=i+Math.imul(L,he)|0,f=(f=f+Math.imul(L,ue)|0)+Math.imul(B,he)|0,n=n+Math.imul(B,ue)|0;var Ee=(s+(i=i+Math.imul(E,le)|0)|0)+((8191&(f=(f=f+Math.imul(E,pe)|0)+Math.imul(N,le)|0))<<13)|0;s=((n=n+Math.imul(N,pe)|0)+(f>>>13)|0)+(Ee>>>26)|0,Ee&=67108863,i=Math.imul(T,he),f=(f=Math.imul(T,ue))+Math.imul(K,he)|0,n=Math.imul(K,ue);var Ne=(s+(i=i+Math.imul(L,le)|0)|0)+((8191&(f=(f=f+Math.imul(L,pe)|0)+Math.imul(B,le)|0))<<13)|0;s=((n=n+Math.imul(B,pe)|0)+(f>>>13)|0)+(Ne>>>26)|0,Ne&=67108863;var je=(s+(i=Math.imul(T,le))|0)+((8191&(f=(f=Math.imul(T,pe))+Math.imul(K,le)|0))<<13)|0;return s=((n=Math.imul(K,pe))+(f>>>13)|0)+(je>>>26)|0,je&=67108863,c[0]=me,c[1]=ve,c[2]=ye,c[3]=ge,c[4]=we,c[5]=Me,c[6]=Se,c[7]=Ae,c[8]=_e,c[9]=xe,c[10]=Ie,c[11]=ke,c[12]=ze,c[13]=qe,c[14]=Re,c[15]=Pe,c[16]=Ee,c[17]=Ne,c[18]=je,0!==s&&(c[19]=s,r.length++),r};function l(e,t,r){return(new p).mulp(e,t,r)}function p(e,t){this.x=e,this.y=t}Math.imul||(b=u),n.prototype.mulTo=function(e,t){var r=this.length+e.length;return 10===this.length&&10===e.length?b(this,e,t):r<63?u(this,e,t):r<1024?function(e,t,r){r.negative=t.negative^e.negative,r.length=e.length+t.length;for(var i=0,f=0,n=0;n>>26)|0)>>>26,d&=67108863}r.words[n]=a,i=d,d=f}return 0!==i?r.words[n]=i:r.length--,r.strip()}(this,e,t):l(this,e,t)},p.prototype.makeRBT=function(e){for(var t=new Array(e),r=n.prototype._countBits(e)-1,i=0;i>=1;return i},p.prototype.permute=function(e,t,r,i,f,n){for(var d=0;d>>=1)f++;return 1<>>=13,r[2*d+1]=8191&n,n>>>=13;for(d=2*t;d>=26,t+=f/67108864|0,t+=n>>>26,this.words[r]=67108863&n}return 0!==t&&(this.words[r]=t,this.length++),this},n.prototype.muln=function(e){return this.clone().imuln(e)},n.prototype.sqr=function(){return this.mul(this)},n.prototype.isqr=function(){return this.imul(this.clone())},n.prototype.pow=function(e){var t=function(e){for(var t=new Array(e.bitLength()),r=0;r>>f}return t}(e);if(0===t.length)return new n(1);for(var r=this,i=0;i=0);var t,r=e%26,f=(e-r)/26,n=67108863>>>26-r<<26-r;if(0!==r){var d=0;for(t=0;t>>26-r}d&&(this.words[t]=d,this.length++)}if(0!==f){for(t=this.length-1;t>=0;t--)this.words[t+f]=this.words[t];for(t=0;t=0),f=t?(t-t%26)/26:0;var n=e%26,d=Math.min((e-n)/26,this.length),a=67108863^67108863>>>n<d)for(this.length-=d,s=0;s=0&&(0!==o||s>=f);s--){var h=0|this.words[s];this.words[s]=o<<26-n|h>>>n,o=h&a}return c&&0!==o&&(c.words[c.length++]=o),0===this.length&&(this.words[0]=0,this.length=1),this.strip()},n.prototype.ishrn=function(e,t,r){return i(0===this.negative),this.iushrn(e,t,r)},n.prototype.shln=function(e){return this.clone().ishln(e)},n.prototype.ushln=function(e){return this.clone().iushln(e)},n.prototype.shrn=function(e){return this.clone().ishrn(e)},n.prototype.ushrn=function(e){return this.clone().iushrn(e)},n.prototype.testn=function(e){i("number"==typeof e&&e>=0);var t=e%26,r=(e-t)/26,f=1<=0);var t=e%26,r=(e-t)/26;if(i(0===this.negative,"imaskn works only with positive numbers"),this.length<=r)return this;if(0!==t&&r++,this.length=Math.min(r,this.length),0!==t){var f=67108863^67108863>>>t<=67108864;t++)this.words[t]-=67108864,t===this.length-1?this.words[t+1]=1:this.words[t+1]++;return this.length=Math.max(this.length,t+1),this},n.prototype.isubn=function(e){if(i("number"==typeof e),i(e<67108864),e<0)return this.iaddn(-e);if(0!==this.negative)return this.negative=0,this.iaddn(e),this.negative=1,this;if(this.words[0]-=e,1===this.length&&this.words[0]<0)this.words[0]=-this.words[0],this.negative=1;else for(var t=0;t>26)-(c/67108864|0),this.words[f+r]=67108863&n}for(;f>26,this.words[f+r]=67108863&n;if(0===a)return this.strip();for(i(-1===a),a=0,f=0;f>26,this.words[f]=67108863&n;return this.negative=1,this.strip()},n.prototype._wordDiv=function(e,t){var r=(this.length,e.length),i=this.clone(),f=e,d=0|f.words[f.length-1];0!==(r=26-this._countBits(d))&&(f=f.ushln(r),i.iushln(r),d=0|f.words[f.length-1]);var a,c=i.length-f.length;if("mod"!==t){(a=new n(null)).length=c+1,a.words=new Array(a.length);for(var s=0;s=0;h--){var u=67108864*(0|i.words[f.length+h])+(0|i.words[f.length+h-1]);for(u=Math.min(u/d|0,67108863),i._ishlnsubmul(f,u,h);0!==i.negative;)u--,i.negative=0,i._ishlnsubmul(f,1,h),i.isZero()||(i.negative^=1);a&&(a.words[h]=u)}return a&&a.strip(),i.strip(),"div"!==t&&0!==r&&i.iushrn(r),{div:a||null,mod:i}},n.prototype.divmod=function(e,t,r){return i(!e.isZero()),this.isZero()?{div:new n(0),mod:new n(0)}:0!==this.negative&&0===e.negative?(a=this.neg().divmod(e,t),"mod"!==t&&(f=a.div.neg()),"div"!==t&&(d=a.mod.neg(),r&&0!==d.negative&&d.iadd(e)),{div:f,mod:d}):0===this.negative&&0!==e.negative?(a=this.divmod(e.neg(),t),"mod"!==t&&(f=a.div.neg()),{div:f,mod:a.mod}):0!=(this.negative&e.negative)?(a=this.neg().divmod(e.neg(),t),"div"!==t&&(d=a.mod.neg(),r&&0!==d.negative&&d.isub(e)),{div:a.div,mod:d}):e.length>this.length||this.cmp(e)<0?{div:new n(0),mod:this}:1===e.length?"div"===t?{div:this.divn(e.words[0]),mod:null}:"mod"===t?{div:null,mod:new n(this.modn(e.words[0]))}:{div:this.divn(e.words[0]),mod:new n(this.modn(e.words[0]))}:this._wordDiv(e,t);var f,d,a},n.prototype.div=function(e){return this.divmod(e,"div",!1).div},n.prototype.mod=function(e){return this.divmod(e,"mod",!1).mod},n.prototype.umod=function(e){return this.divmod(e,"mod",!0).mod},n.prototype.divRound=function(e){var t=this.divmod(e);if(t.mod.isZero())return t.div;var r=0!==t.div.negative?t.mod.isub(e):t.mod,i=e.ushrn(1),f=e.andln(1),n=r.cmp(i);return n<0||1===f&&0===n?t.div:0!==t.div.negative?t.div.isubn(1):t.div.iaddn(1)},n.prototype.modn=function(e){i(e<=67108863);for(var t=(1<<26)%e,r=0,f=this.length-1;f>=0;f--)r=(t*r+(0|this.words[f]))%e;return r},n.prototype.idivn=function(e){i(e<=67108863);for(var t=0,r=this.length-1;r>=0;r--){var f=(0|this.words[r])+67108864*t;this.words[r]=f/e|0,t=f%e}return this.strip()},n.prototype.divn=function(e){return this.clone().idivn(e)},n.prototype.egcd=function(e){i(0===e.negative),i(!e.isZero());var t=this,r=e.clone();t=0!==t.negative?t.umod(e):t.clone();for(var f=new n(1),d=new n(0),a=new n(0),c=new n(1),s=0;t.isEven()&&r.isEven();)t.iushrn(1),r.iushrn(1),++s;for(var o=r.clone(),h=t.clone();!t.isZero();){for(var u=0,b=1;0==(t.words[0]&b)&&u<26;++u,b<<=1);if(u>0)for(t.iushrn(u);u-- >0;)(f.isOdd()||d.isOdd())&&(f.iadd(o),d.isub(h)),f.iushrn(1),d.iushrn(1);for(var l=0,p=1;0==(r.words[0]&p)&&l<26;++l,p<<=1);if(l>0)for(r.iushrn(l);l-- >0;)(a.isOdd()||c.isOdd())&&(a.iadd(o),c.isub(h)),a.iushrn(1),c.iushrn(1);t.cmp(r)>=0?(t.isub(r),f.isub(a),d.isub(c)):(r.isub(t),a.isub(f),c.isub(d))}return{a:a,b:c,gcd:r.iushln(s)}},n.prototype._invmp=function(e){i(0===e.negative),i(!e.isZero());var t=this,r=e.clone();t=0!==t.negative?t.umod(e):t.clone();for(var f,d=new n(1),a=new n(0),c=r.clone();t.cmpn(1)>0&&r.cmpn(1)>0;){for(var s=0,o=1;0==(t.words[0]&o)&&s<26;++s,o<<=1);if(s>0)for(t.iushrn(s);s-- >0;)d.isOdd()&&d.iadd(c),d.iushrn(1);for(var h=0,u=1;0==(r.words[0]&u)&&h<26;++h,u<<=1);if(h>0)for(r.iushrn(h);h-- >0;)a.isOdd()&&a.iadd(c),a.iushrn(1);t.cmp(r)>=0?(t.isub(r),d.isub(a)):(r.isub(t),a.isub(d))}return(f=0===t.cmpn(1)?d:a).cmpn(0)<0&&f.iadd(e),f},n.prototype.gcd=function(e){if(this.isZero())return e.abs();if(e.isZero())return this.abs();var t=this.clone(),r=e.clone();t.negative=0,r.negative=0;for(var i=0;t.isEven()&&r.isEven();i++)t.iushrn(1),r.iushrn(1);for(;;){for(;t.isEven();)t.iushrn(1);for(;r.isEven();)r.iushrn(1);var f=t.cmp(r);if(f<0){var n=t;t=r,r=n}else if(0===f||0===r.cmpn(1))break;t.isub(r)}return r.iushln(i)},n.prototype.invm=function(e){return this.egcd(e).a.umod(e)},n.prototype.isEven=function(){return 0==(1&this.words[0])},n.prototype.isOdd=function(){return 1==(1&this.words[0])},n.prototype.andln=function(e){return this.words[0]&e},n.prototype.bincn=function(e){i("number"==typeof e);var t=e%26,r=(e-t)/26,f=1<>>26,a&=67108863,this.words[d]=a}return 0!==n&&(this.words[d]=n,this.length++),this},n.prototype.isZero=function(){return 1===this.length&&0===this.words[0]},n.prototype.cmpn=function(e){var t,r=e<0;if(0!==this.negative&&!r)return-1;if(0===this.negative&&r)return 1;if(this.strip(),this.length>1)t=1;else{r&&(e=-e),i(e<=67108863,"Number is too big");var f=0|this.words[0];t=f===e?0:fe.length)return 1;if(this.length=0;r--){var i=0|this.words[r],f=0|e.words[r];if(i!==f){if&&(t=1);break}}return t},n.prototype.gtn=function(e){return 1===this.cmpn(e)},n.prototype.gt=function(e){return 1===this.cmp(e)},n.prototype.gten=function(e){return this.cmpn(e)>=0},n.prototype.gte=function(e){return this.cmp(e)>=0},n.prototype.ltn=function(e){return-1===this.cmpn(e)},n.prototype.lt=function(e){return-1===this.cmp(e)},n.prototype.lten=function(e){return this.cmpn(e)<=0},n.prototype.lte=function(e){return this.cmp(e)<=0},n.prototype.eqn=function(e){return 0===this.cmpn(e)},n.prototype.eq=function(e){return 0===this.cmp(e)},n.red=function(e){return new S(e)},n.prototype.toRed=function(e){return i(!this.red,"Already a number in reduction context"),i(0===this.negative,"red works only with positives"),e.convertTo(this)._forceRed(e)},n.prototype.fromRed=function(){return i(this.red,"fromRed works only with numbers in reduction context"),this.red.convertFrom(this)},n.prototype._forceRed=function(e){return this.red=e,this},n.prototype.forceRed=function(e){return i(!this.red,"Already a number in reduction context"),this._forceRed(e)},n.prototype.redAdd=function(e){return i(this.red,"redAdd works only with red numbers"),this.red.add(this,e)},n.prototype.redIAdd=function(e){return i(this.red,"redIAdd works only with red numbers"),this.red.iadd(this,e)},n.prototype.redSub=function(e){return i(this.red,"redSub works only with red numbers"),this.red.sub(this,e)},n.prototype.redISub=function(e){return i(this.red,"redISub works only with red numbers"),this.red.isub(this,e)},n.prototype.redShl=function(e){return i(this.red,"redShl works only with red numbers"),this.red.shl(this,e)},n.prototype.redMul=function(e){return i(this.red,"redMul works only with red numbers"),this.red._verify2(this,e),this.red.mul(this,e)},n.prototype.redIMul=function(e){return i(this.red,"redMul works only with red numbers"),this.red._verify2(this,e),this.red.imul(this,e)},n.prototype.redSqr=function(){return i(this.red,"redSqr works only with red numbers"),this.red._verify1(this),this.red.sqr(this)},n.prototype.redISqr=function(){return i(this.red,"redISqr works only with red numbers"),this.red._verify1(this),this.red.isqr(this)},n.prototype.redSqrt=function(){return i(this.red,"redSqrt works only with red numbers"),this.red._verify1(this),this.red.sqrt(this)},n.prototype.redInvm=function(){return i(this.red,"redInvm works only with red numbers"),this.red._verify1(this),this.red.invm(this)},n.prototype.redNeg=function(){return i(this.red,"redNeg works only with red numbers"),this.red._verify1(this),this.red.neg(this)},n.prototype.redPow=function(e){return i(this.red&&!e.red,"redPow(normalNum)"),this.red._verify1(this),this.red.pow(this,e)};var m={k256:null,p224:null,p192:null,p25519:null};function v(e,t){this.name=e,this.p=new n(t,16),this.n=this.p.bitLength(),this.k=new n(1).iushln(this.n).isub(this.p),this.tmp=this._tmp()}function y(){v.call(this,"k256","ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff fffffffe fffffc2f")}function g(){v.call(this,"p224","ffffffff ffffffff ffffffff ffffffff 00000000 00000000 00000001")}function w(){v.call(this,"p192","ffffffff ffffffff ffffffff fffffffe ffffffff ffffffff")}function M(){v.call(this,"25519","7fffffffffffffff ffffffffffffffff ffffffffffffffff ffffffffffffffed")}function S(e){if("string"==typeof e){var t=n._prime(e);this.m=t.p,this.prime=t}else i(e.gtn(1),"modulus must be greater than 1"),this.m=e,this.prime=null}function A(e){S.call(this,e),this.shift=this.m.bitLength(),this.shift%26!=0&&(this.shift+=26-this.shift%26),this.r=new n(1).iushln(this.shift),this.r2=this.imod(this.r.sqr()),this.rinv=this.r._invmp(this.m),this.minv=this.rinv.mul(this.r).isubn(1).div(this.m),this.minv=this.minv.umod(this.r),this.minv=this.r.sub(this.minv)}v.prototype._tmp=function(){var e=new n(null);return e.words=new Array(Math.ceil(this.n/13)),e},v.prototype.ireduce=function(e){var t,r=e;do{this.split(r,this.tmp),t=(r=(r=this.imulK(r)).iadd(this.tmp)).bitLength()}while(t>this.n);var i=t0?r.isub(this.p):void 0!==r.strip?r.strip():r._strip(),r},v.prototype.split=function(e,t){e.iushrn(this.n,0,t)},v.prototype.imulK=function(e){return e.imul(this.k)},f(y,v),y.prototype.split=function(e,t){for(var r=Math.min(e.length,9),i=0;i>>22,f=n}f>>>=22,e.words[i-10]=f,0===f&&e.length>10?e.length-=10:e.length-=9},y.prototype.imulK=function(e){e.words[e.length]=0,e.words[e.length+1]=0,e.length+=2;for(var t=0,r=0;r>>=26,e.words[r]=f,t=i}return 0!==t&&(e.words[e.length++]=t),e},n._prime=function(e){if(m[e])return m[e];var t;if("k256"===e)t=new y;else if("p224"===e)t=new g;else if("p192"===e)t=new w;else{if("p25519"!==e)throw new Error("Unknown prime "+e);t=new M}return m[e]=t,t},S.prototype._verify1=function(e){i(0===e.negative,"red works only with positives"),i(e.red,"red works only with red numbers")},S.prototype._verify2=function(e,t){i(0==(e.negative|t.negative),"red works only with positives"),i(e.red&&e.red===t.red,"red works only with red numbers")},S.prototype.imod=function(e){return this.prime?this.prime.ireduce(e)._forceRed(this):e.umod(this.m)._forceRed(this)},S.prototype.neg=function(e){return e.isZero()?e.clone():this.m.sub(e)._forceRed(this)},S.prototype.add=function(e,t){this._verify2(e,t);var r=e.add(t);return r.cmp(this.m)>=0&&r.isub(this.m),r._forceRed(this)},S.prototype.iadd=function(e,t){this._verify2(e,t);var r=e.iadd(t);return r.cmp(this.m)>=0&&r.isub(this.m),r},S.prototype.sub=function(e,t){this._verify2(e,t);var r=e.sub(t);return r.cmpn(0)<0&&r.iadd(this.m),r._forceRed(this)},S.prototype.isub=function(e,t){this._verify2(e,t);var r=e.isub(t);return r.cmpn(0)<0&&r.iadd(this.m),r},S.prototype.shl=function(e,t){return this._verify1(e),this.imod(e.ushln(t))},S.prototype.imul=function(e,t){return this._verify2(e,t),this.imod(e.imul(t))},S.prototype.mul=function(e,t){return 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t===e?t.clone():t},S.prototype.convertFrom=function(e){var t=e.clone();return t.red=null,t},n.mont=function(e){return new A(e)},f(A,S),A.prototype.convertTo=function(e){return this.imod(e.ushln(this.shift))},A.prototype.convertFrom=function(e){var t=this.imod(e.mul(this.rinv));return t.red=null,t},A.prototype.imul=function(e,t){if(e.isZero()||t.isZero())return e.words[0]=0,e.length=1,e;var r=e.imul(t),i=r.maskn(this.shift).mul(this.minv).imaskn(this.shift).mul(this.m),f=r.isub(i).iushrn(this.shift),n=f;return f.cmp(this.m)>=0?n=f.isub(this.m):f.cmpn(0)<0&&(n=f.iadd(this.m)),n._forceRed(this)},A.prototype.mul=function(e,t){if(e.isZero()||t.isZero())return new n(0)._forceRed(this);var r=e.mul(t),i=r.maskn(this.shift).mul(this.minv).imaskn(this.shift).mul(this.m),f=r.isub(i).iushrn(this.shift),d=f;return f.cmp(this.m)>=0?d=f.isub(this.m):f.cmpn(0)<0&&(d=f.iadd(this.m)),d._forceRed(this)},A.prototype.invm=function(e){return this.imod(e._invmp(this.m).mul(this.r2))._forceRed(this)}}(e,this)}).call(this,r(21)(e))},function(e,t){function r(e,t){if(!e)throw new Error(t||"Assertion failed")}e.exports=r,r.equal=function(e,t,r){if(e!=t)throw new Error(r||"Assertion failed: "+e+" != "+t)}},function(e,t,r){e.exports=r(17)(r(18))},function(e,t,r){"use strict";var i=r(1),f=r(3);function n(){this.pending=null,this.pendingTotal=0,this.blockSize=this.constructor.blockSize,this.outSize=this.constructor.outSize,this.hmacStrength=this.constructor.hmacStrength,this.padLength=this.constructor.padLength/8,this.endian="big",this._delta8=this.blockSize/8,this._delta32=this.blockSize/32}t.BlockHash=n,n.prototype.update=function(e,t){if(e=i.toArray(e,t),this.pending?this.pending=this.pending.concat(e):this.pending=e,this.pendingTotal+=e.length,this.pending.length>=this._delta8){var r=(e=this.pending).length%this._delta8;this.pending=e.slice(e.length-r,e.length),0===this.pending.length&&(this.pending=null),e=i.join32(e,0,e.length-r,this.endian);for(var f=0;f>>24&255,i[f++]=e>>>16&255,i[f++]=e>>>8&255,i[f++]=255&e}else for(i[f++]=255&e,i[f++]=e>>>8&255,i[f++]=e>>>16&255,i[f++]=e>>>24&255,i[f++]=0,i[f++]=0,i[f++]=0,i[f++]=0,n=8;n0?this.redN=null:(this._maxwellTrick=!0,this.redN=this.n.toRed(this.red))}function s(e,t){this.curve=e,this.type=t,this.precomputed=null}e.exports=c,c.prototype.point=function(){throw new Error("Not implemented")},c.prototype.validate=function(){throw new Error("Not implemented")},c.prototype._fixedNafMul=function(e,t){a(e.precomputed);var r=e._getDoubles(),i=n(t,1,this._bitLength),f=(1<=c;t--)s=(s<<1)+i[t];d.push(s)}for(var o=this.jpoint(null,null,null),h=this.jpoint(null,null,null),u=f;u>0;u--){for(c=0;c=0;s--){for(t=0;s>=0&&0===d[s];s--)t++;if(s>=0&&t++,c=c.dblp(t),s<0)break;var o=d[s];a(0!==o),c="affine"===e.type?o>0?c.mixedAdd(f[o-1>>1]):c.mixedAdd(f[-o-1>>1].neg()):o>0?c.add(f[o-1>>1]):c.add(f[-o-1>>1].neg())}return"affine"===e.type?c.toP():c},c.prototype._wnafMulAdd=function(e,t,r,i,f){for(var a=this._wnafT1,c=this._wnafT2,s=this._wnafT3,o=0,h=0;h=1;h-=2){var b=h-1,l=h;if(1===a[b]&&1===a[l]){var p=[t[b],null,null,t[l]];0===t[b].y.cmp(t[l].y)?(p[1]=t[b].add(t[l]),p[2]=t[b].toJ().mixedAdd(t[l].neg())):0===t[b].y.cmp(t[l].y.redNeg())?(p[1]=t[b].toJ().mixedAdd(t[l]),p[2]=t[b].add(t[l].neg())):(p[1]=t[b].toJ().mixedAdd(t[l]),p[2]=t[b].toJ().mixedAdd(t[l].neg()));var m=[-3,-1,-5,-7,0,7,5,1,3],v=d(r[b],r[l]);o=Math.max(v[0].length,o),s[b]=new Array(o),s[l]=new Array(o);for(var y=0;y=0;h--){for(var A=0;h>=0;){var _=!0;for(y=0;y=0&&A++,M=M.dblp(A),h<0)break;for(y=0;y0?x=c[y][I-1>>1]:I<0&&(x=c[y][-I-1>>1].neg()),M="affine"===x.type?M.mixedAdd(x):M.add(x))}}for(h=0;h=Math.ceil((e.bitLength()+1)/t.step)},s.prototype._getDoubles=function(e,t){if(this.precomputed&&this.precomputed.doubles)return this.precomputed.doubles;for(var r=[this],i=this,f=0;f>8,d=255&f;n?r.push(n,d):r.push(d)}return r},i.zero2=f,i.toHex=n,i.encode=function(e,t){return"hex"===t?n(e):e}},function(e,t,r){var i;function f(e){this.rand=e}if(e.exports=function(e){return i||(i=new f(null)),i.generate(e)},e.exports.Rand=f,f.prototype.generate=function(e){return this._rand(e)},f.prototype._rand=function(e){if(this.rand.getBytes)return this.rand.getBytes(e);for(var t=new Uint8Array(e),r=0;r>>3},t.g1_256=function(e){return i(e,17)^i(e,19)^e>>>10}},function(e,t,r){"use strict";var i=r(1),f=r(5),n=r(13),d=r(3),a=i.sum32,c=i.sum32_4,s=i.sum32_5,o=n.ch32,h=n.maj32,u=n.s0_256,b=n.s1_256,l=n.g0_256,p=n.g1_256,m=f.BlockHash,v=[1116352408,1899447441,3049323471,3921009573,961987163,1508970993,2453635748,2870763221,3624381080,310598401,607225278,1426881987,1925078388,2162078206,2614888103,3248222580,3835390401,4022224774,264347078,604807628,770255983,1249150122,1555081692,1996064986,2554220882,2821834349,2952996808,3210313671,3336571891,3584528711,113926993,338241895,666307205,773529912,1294757372,1396182291,1695183700,1986661051,2177026350,2456956037,2730485921,2820302411,3259730800,3345764771,3516065817,3600352804,4094571909,275423344,430227734,506948616,659060556,883997877,958139571,1322822218,1537002063,1747873779,1955562222,2024104815,2227730452,2361852424,2428436474,2756734187,3204031479,3329325298];function y(){if(!(this instanceof y))return new y;m.call(this),this.h=[1779033703,3144134277,1013904242,2773480762,1359893119,2600822924,528734635,1541459225],this.k=v,this.W=new Array(64)}i.inherits(y,m),e.exports=y,y.blockSize=512,y.outSize=256,y.hmacStrength=192,y.padLength=64,y.prototype._update=function(e,t){for(var r=this.W,i=0;i<16;i++)r[i]=e[t+i];for(;inew Uint8Array(e)),t){return"function"==typeof e&&(e=e(t)),p("output",e,t),e}function y(e){return Object.prototype.toString.call(e).slice(8,-1)}e.exports=e=>({contextRandomize(t){switch(l(null===t||t instanceof Uint8Array,"Expected seed to be an Uint8Array or null"),null!==t&&p("seed",t,32),e.contextRandomize(t)){case 1:throw new Error(n)}},privateKeyVerify:t=>(p("private key",t,32),0===e.privateKeyVerify(t)),privateKeyNegate(t){switch(p("private key",t,32),e.privateKeyNegate(t)){case 0:return t;case 1:throw new Error(r)}},privateKeyTweakAdd(t,r){switch(p("private key",t,32),p("tweak",r,32),e.privateKeyTweakAdd(t,r)){case 0:return t;case 1:throw new 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null;if(d=d.toRed(f.red),a=a.toRed(f.red),(6===e||7===e)&&a.isOdd()!==(7===e))return null;const c=d.redSqr().redIMul(d);return a.redSqr().redISub(c.redIAdd(f.b)).isZero()?i.keyPair({pub:{x:d,y:a}}):null}(t,e.subarray(1,33),e.subarray(33,65));default:return null}}function a(e,t){const r=t.encode(null,33===e.length);for(let t=0;t0,privateKeyVerify(e){const t=new n(e);return t.cmp(f.n)<0&&!t.isZero()?0:1},privateKeyNegate(e){const t=new n(e),r=f.n.sub(t).umod(f.n).toArrayLike(Uint8Array,"be",32);return e.set(r),0},privateKeyTweakAdd(e,t){const r=new n(t);if(r.cmp(f.n)>=0)return 1;if(r.iadd(new n(e)),r.cmp(f.n)>=0&&r.isub(f.n),r.isZero())return 1;const i=r.toArrayLike(Uint8Array,"be",32);return e.set(i),0},privateKeyTweakMul(e,t){let r=new n(t);if(r.cmp(f.n)>=0||r.isZero())return 1;r.imul(new n(e)),r.cmp(f.n)>=0&&(r=r.umod(f.n));const i=r.toArrayLike(Uint8Array,"be",32);return e.set(i),0},publicKeyVerify:e=>null===d(e)?1:0,publicKeyCreate(e,t){const r=new 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Montgomery curve")},c.prototype.jumlAdd=function(){throw new Error("Not supported on Montgomery curve")},c.prototype.eq=function(e){return 0===this.getX().cmp(e.getX())},c.prototype.normalize=function(){return this.x=this.x.redMul(this.z.redInvm()),this.z=this.curve.one,this},c.prototype.getX=function(){return this.normalize(),this.x.fromRed()}},function(e,t,r){"use strict";var i=r(0),f=r(2),n=r(7),d=r(6),a=i.assert;function c(e){this.twisted=1!=(0|e.a),this.mOneA=this.twisted&&-1==(0|e.a),this.extended=this.mOneA,d.call(this,"edwards",e),this.a=new f(e.a,16).umod(this.red.m),this.a=this.a.toRed(this.red),this.c=new f(e.c,16).toRed(this.red),this.c2=this.c.redSqr(),this.d=new f(e.d,16).toRed(this.red),this.dd=this.d.redAdd(this.d),a(!this.twisted||0===this.c.fromRed().cmpn(1)),this.oneC=1==(0|e.c)}function s(e,t,r,i,n){d.BasePoint.call(this,e,"projective"),null===t&&null===r&&null===i?(this.x=this.curve.zero,this.y=this.curve.one,this.z=this.curve.one,this.t=this.curve.zero,this.zOne=!0):(this.x=new f(t,16),this.y=new f(r,16),this.z=i?new f(i,16):this.curve.one,this.t=n&&new f(n,16),this.x.red||(this.x=this.x.toRed(this.curve.red)),this.y.red||(this.y=this.y.toRed(this.curve.red)),this.z.red||(this.z=this.z.toRed(this.curve.red)),this.t&&!this.t.red&&(this.t=this.t.toRed(this.curve.red)),this.zOne=this.z===this.curve.one,this.curve.extended&&!this.t&&(this.t=this.x.redMul(this.y),this.zOne||(this.t=this.t.redMul(this.z.redInvm()))))}n(c,d),e.exports=c,c.prototype._mulA=function(e){return this.mOneA?e.redNeg():this.a.redMul(e)},c.prototype._mulC=function(e){return this.oneC?e:this.c.redMul(e)},c.prototype.jpoint=function(e,t,r,i){return this.point(e,t,r,i)},c.prototype.pointFromX=function(e,t){(e=new f(e,16)).red||(e=e.toRed(this.red));var r=e.redSqr(),i=this.c2.redSub(this.a.redMul(r)),n=this.one.redSub(this.c2.redMul(this.d).redMul(r)),d=i.redMul(n.redInvm()),a=d.redSqrt();if(0!==a.redSqr().redSub(d).cmp(this.zero))throw new Error("invalid point");var c=a.fromRed().isOdd();return(t&&!c||!t&&c)&&(a=a.redNeg()),this.point(e,a)},c.prototype.pointFromY=function(e,t){(e=new f(e,16)).red||(e=e.toRed(this.red));var r=e.redSqr(),i=r.redSub(this.c2),n=r.redMul(this.d).redMul(this.c2).redSub(this.a),d=i.redMul(n.redInvm());if(0===d.cmp(this.zero)){if(t)throw new Error("invalid point");return this.point(this.zero,e)}var a=d.redSqrt();if(0!==a.redSqr().redSub(d).cmp(this.zero))throw new Error("invalid point");return a.fromRed().isOdd()!==t&&(a=a.redNeg()),this.point(a,e)},c.prototype.validate=function(e){if(e.isInfinity())return!0;e.normalize();var t=e.x.redSqr(),r=e.y.redSqr(),i=t.redMul(this.a).redAdd(r),f=this.c2.redMul(this.one.redAdd(this.d.redMul(t).redMul(r)));return 0===i.cmp(f)},n(s,d.BasePoint),c.prototype.pointFromJSON=function(e){return s.fromJSON(this,e)},c.prototype.point=function(e,t,r,i){return new s(this,e,t,r,i)},s.fromJSON=function(e,t){return new s(e,t[0],t[1],t[2])},s.prototype.inspect=function(){return this.isInfinity()?"":""},s.prototype.isInfinity=function(){return 0===this.x.cmpn(0)&&(0===this.y.cmp(this.z)||this.zOne&&0===this.y.cmp(this.curve.c))},s.prototype._extDbl=function(){var e=this.x.redSqr(),t=this.y.redSqr(),r=this.z.redSqr();r=r.redIAdd(r);var i=this.curve._mulA(e),f=this.x.redAdd(this.y).redSqr().redISub(e).redISub(t),n=i.redAdd(t),d=n.redSub(r),a=i.redSub(t),c=f.redMul(d),s=n.redMul(a),o=f.redMul(a),h=d.redMul(n);return this.curve.point(c,s,h,o)},s.prototype._projDbl=function(){var e,t,r,i=this.x.redAdd(this.y).redSqr(),f=this.x.redSqr(),n=this.y.redSqr();if(this.curve.twisted){var d=(s=this.curve._mulA(f)).redAdd(n);if(this.zOne)e=i.redSub(f).redSub(n).redMul(d.redSub(this.curve.two)),t=d.redMul(s.redSub(n)),r=d.redSqr().redSub(d).redSub(d);else{var a=this.z.redSqr(),c=d.redSub(a).redISub(a);e=i.redSub(f).redISub(n).redMul(c),t=d.redMul(s.redSub(n)),r=d.redMul(c)}}else{var s=f.redAdd(n);a=this.curve._mulC(this.z).redSqr(),c=s.redSub(a).redSub(a);e=this.curve._mulC(i.redISub(s)).redMul(c),t=this.curve._mulC(s).redMul(f.redISub(n)),r=s.redMul(c)}return this.curve.point(e,t,r)},s.prototype.dbl=function(){return this.isInfinity()?this:this.curve.extended?this._extDbl():this._projDbl()},s.prototype._extAdd=function(e){var t=this.y.redSub(this.x).redMul(e.y.redSub(e.x)),r=this.y.redAdd(this.x).redMul(e.y.redAdd(e.x)),i=this.t.redMul(this.curve.dd).redMul(e.t),f=this.z.redMul(e.z.redAdd(e.z)),n=r.redSub(t),d=f.redSub(i),a=f.redAdd(i),c=r.redAdd(t),s=n.redMul(d),o=a.redMul(c),h=n.redMul(c),u=d.redMul(a);return this.curve.point(s,o,u,h)},s.prototype._projAdd=function(e){var t,r,i=this.z.redMul(e.z),f=i.redSqr(),n=this.x.redMul(e.x),d=this.y.redMul(e.y),a=this.curve.d.redMul(n).redMul(d),c=f.redSub(a),s=f.redAdd(a),o=this.x.redAdd(this.y).redMul(e.x.redAdd(e.y)).redISub(n).redISub(d),h=i.redMul(c).redMul(o);return this.curve.twisted?(t=i.redMul(s).redMul(d.redSub(this.curve._mulA(n))),r=c.redMul(s)):(t=i.redMul(s).redMul(d.redSub(n)),r=this.curve._mulC(c).redMul(s)),this.curve.point(h,t,r)},s.prototype.add=function(e){return this.isInfinity()?e:e.isInfinity()?this:this.curve.extended?this._extAdd(e):this._projAdd(e)},s.prototype.mul=function(e){return this._hasDoubles(e)?this.curve._fixedNafMul(this,e):this.curve._wnafMul(this,e)},s.prototype.mulAdd=function(e,t,r){return this.curve._wnafMulAdd(1,[this,t],[e,r],2,!1)},s.prototype.jmulAdd=function(e,t,r){return this.curve._wnafMulAdd(1,[this,t],[e,r],2,!0)},s.prototype.normalize=function(){if(this.zOne)return this;var e=this.z.redInvm();return this.x=this.x.redMul(e),this.y=this.y.redMul(e),this.t&&(this.t=this.t.redMul(e)),this.z=this.curve.one,this.zOne=!0,this},s.prototype.neg=function(){return this.curve.point(this.x.redNeg(),this.y,this.z,this.t&&this.t.redNeg())},s.prototype.getX=function(){return this.normalize(),this.x.fromRed()},s.prototype.getY=function(){return this.normalize(),this.y.fromRed()},s.prototype.eq=function(e){return this===e||0===this.getX().cmp(e.getX())&&0===this.getY().cmp(e.getY())},s.prototype.eqXToP=function(e){var t=e.toRed(this.curve.red).redMul(this.z);if(0===this.x.cmp(t))return!0;for(var r=e.clone(),i=this.curve.redN.redMul(this.z);;){if(r.iadd(this.curve.n),r.cmp(this.curve.p)>=0)return!1;if(t.redIAdd(i),0===this.x.cmp(t))return!0}},s.prototype.toP=s.prototype.normalize,s.prototype.mixedAdd=s.prototype.add},function(e,t,r){"use strict";t.sha1=r(28),t.sha224=r(29),t.sha256=r(14),t.sha384=r(30),t.sha512=r(15)},function(e,t,r){"use strict";var i=r(1),f=r(5),n=r(13),d=i.rotl32,a=i.sum32,c=i.sum32_5,s=n.ft_1,o=f.BlockHash,h=[1518500249,1859775393,2400959708,3395469782];function u(){if(!(this instanceof u))return new u;o.call(this),this.h=[1732584193,4023233417,2562383102,271733878,3285377520],this.W=new Array(80)}i.inherits(u,o),e.exports=u,u.blockSize=512,u.outSize=160,u.hmacStrength=80,u.padLength=64,u.prototype._update=function(e,t){for(var r=this.W,i=0;i<16;i++)r[i]=e[t+i];for(;ithis.blockSize&&(e=(new this.Hash).update(e).digest()),f(e.length<=this.blockSize);for(var t=e.length;t0))return d.iaddn(1),this.keyFromPrivate(d)}},h.prototype._truncateToN=function(e,t){var r=8*e.byteLength()-this.n.bitLength();return r>0&&(e=e.ushrn(r)),!t&&e.cmp(this.n)>=0?e.sub(this.n):e},h.prototype.sign=function(e,t,r,n){"object"==typeof r&&(n=r,r=null),n||(n={}),t=this.keyFromPrivate(t,r),e=this._truncateToN(new i(e,16));for(var d=this.n.byteLength(),a=t.getPrivate().toArray("be",d),c=e.toArray("be",d),s=new f({hash:this.hash,entropy:a,nonce:c,pers:n.pers,persEnc:n.persEnc||"utf8"}),h=this.n.sub(new i(1)),u=0;;u++){var b=n.k?n.k(u):new i(s.generate(this.n.byteLength()));if(!((b=this._truncateToN(b,!0)).cmpn(1)<=0||b.cmp(h)>=0)){var l=this.g.mul(b);if(!l.isInfinity()){var p=l.getX(),m=p.umod(this.n);if(0!==m.cmpn(0)){var v=b.invm(this.n).mul(m.mul(t.getPrivate()).iadd(e));if(0!==(v=v.umod(this.n)).cmpn(0)){var y=(l.getY().isOdd()?1:0)|(0!==p.cmp(m)?2:0);return n.canonical&&v.cmp(this.nh)>0&&(v=this.n.sub(v),y^=1),new o({r:m,s:v,recoveryParam:y})}}}}}},h.prototype.verify=function(e,t,r,f){e=this._truncateToN(new i(e,16)),r=this.keyFromPublic(r,f);var n=(t=new o(t,"hex")).r,d=t.s;if(n.cmpn(1)<0||n.cmp(this.n)>=0)return!1;if(d.cmpn(1)<0||d.cmp(this.n)>=0)return!1;var a,c=d.invm(this.n),s=c.mul(e).umod(this.n),h=c.mul(n).umod(this.n);return this.curve._maxwellTrick?!(a=this.g.jmulAdd(s,r.getPublic(),h)).isInfinity()&&a.eqXToP(n):!(a=this.g.mulAdd(s,r.getPublic(),h)).isInfinity()&&0===a.getX().umod(this.n).cmp(n)},h.prototype.recoverPubKey=function(e,t,r,f){c((3&r)===r,"The recovery param is more than two bits"),t=new o(t,f);var n=this.n,d=new i(e),a=t.r,s=t.s,h=1&r,u=r>>1;if(a.cmp(this.curve.p.umod(this.curve.n))>=0&&u)throw new Error("Unable to find sencond key candinate");a=u?this.curve.pointFromX(a.add(this.curve.n),h):this.curve.pointFromX(a,h);var b=t.r.invm(n),l=n.sub(d).mul(b).umod(n),p=s.mul(b).umod(n);return this.g.mulAdd(l,a,p)},h.prototype.getKeyRecoveryParam=function(e,t,r,i){if(null!==(t=new o(t,i)).recoveryParam)return t.recoveryParam;for(var f=0;f<4;f++){var n;try{n=this.recoverPubKey(e,t,f)}catch(e){continue}if(n.eq(r))return f}throw new Error("Unable to find valid recovery factor")}},function(e,t,r){"use strict";var i=r(9),f=r(10),n=r(3);function d(e){if(!(this instanceof d))return new d(e);this.hash=e.hash,this.predResist=!!e.predResist,this.outLen=this.hash.outSize,this.minEntropy=e.minEntropy||this.hash.hmacStrength,this._reseed=null,this.reseedInterval=null,this.K=null,this.V=null;var t=f.toArray(e.entropy,e.entropyEnc||"hex"),r=f.toArray(e.nonce,e.nonceEnc||"hex"),i=f.toArray(e.pers,e.persEnc||"hex");n(t.length>=this.minEntropy/8,"Not enough entropy. Minimum is: "+this.minEntropy+" bits"),this._init(t,r,i)}e.exports=d,d.prototype._init=function(e,t,r){var i=e.concat(t).concat(r);this.K=new Array(this.outLen/8),this.V=new Array(this.outLen/8);for(var f=0;f=this.minEntropy/8,"Not enough entropy. Minimum is: "+this.minEntropy+" bits"),this._update(e.concat(r||[])),this._reseed=1},d.prototype.generate=function(e,t,r,i){if(this._reseed>this.reseedInterval)throw new Error("Reseed is required");"string"!=typeof t&&(i=r,r=t,t=null),r&&(r=f.toArray(r,i||"hex"),this._update(r));for(var n=[];n.length"}},function(e,t,r){"use strict";var i=r(2),f=r(0),n=f.assert;function d(e,t){if(e instanceof d)return e;this._importDER(e,t)||(n(e.r&&e.s,"Signature without r or s"),this.r=new i(e.r,16),this.s=new i(e.s,16),void 0===e.recoveryParam?this.recoveryParam=null:this.recoveryParam=e.recoveryParam)}function a(){this.place=0}function c(e,t){var r=e[t.place++];if(!(128&r))return r;var i=15&r;if(0===i||i>4)return!1;for(var f=0,n=0,d=t.place;n>>=0;return!(f<=127)&&(t.place=d,f)}function s(e){for(var t=0,r=e.length-1;!e[t]&&!(128&e[t+1])&&t>>3);for(e.push(128|r);--r;)e.push(t>>>(r<<3)&255);e.push(t)}}e.exports=d,d.prototype._importDER=function(e,t){e=f.toArray(e,t);var r=new a;if(48!==e[r.place++])return!1;var n=c(e,r);if(!1===n)return!1;if(n+r.place!==e.length)return!1;if(2!==e[r.place++])return!1;var d=c(e,r);if(!1===d)return!1;var s=e.slice(r.place,d+r.place);if(r.place+=d,2!==e[r.place++])return!1;var o=c(e,r);if(!1===o)return!1;if(e.length!==o+r.place)return!1;var h=e.slice(r.place,o+r.place);if(0===s[0]){if(!(128&s[1]))return!1;s=s.slice(1)}if(0===h[0]){if(!(128&h[1]))return!1;h=h.slice(1)}return this.r=new i(s),this.s=new i(h),this.recoveryParam=null,!0},d.prototype.toDER=function(e){var t=this.r.toArray(),r=this.s.toArray();for(128&t[0]&&(t=[0].concat(t)),128&r[0]&&(r=[0].concat(r)),t=s(t),r=s(r);!(r[0]||128&r[1]);)r=r.slice(1);var i=[2];o(i,t.length),(i=i.concat(t)).push(2),o(i,r.length);var n=i.concat(r),d=[48];return o(d,n.length),d=d.concat(n),f.encode(d,e)}},function(e,t,r){"use strict";var i=r(9),f=r(8),n=r(0),d=n.assert,a=n.parseBytes,c=r(39),s=r(40);function o(e){if(d("ed25519"===e,"only tested with ed25519 so far"),!(this instanceof o))return new o(e);e=f[e].curve;this.curve=e,this.g=e.g,this.g.precompute(e.n.bitLength()+1),this.pointClass=e.point().constructor,this.encodingLength=Math.ceil(e.n.bitLength()/8),this.hash=i.sha512}e.exports=o,o.prototype.sign=function(e,t){e=a(e);var r=this.keyFromSecret(t),i=this.hashInt(r.messagePrefix(),e),f=this.g.mul(i),n=this.encodePoint(f),d=this.hashInt(n,r.pubBytes(),e).mul(r.priv()),c=i.add(d).umod(this.curve.n);return this.makeSignature({R:f,S:c,Rencoded:n})},o.prototype.verify=function(e,t,r){e=a(e),t=this.makeSignature(t);var i=this.keyFromPublic(r),f=this.hashInt(t.Rencoded(),i.pubBytes(),e),n=this.g.mul(t.S());return t.R().add(i.pub().mul(f)).eq(n)},o.prototype.hashInt=function(){for(var e=this.hash(),t=0;t Maybe I.Pub +{-# INLINE parsePub #-} +parsePub b = I.parsePubCompressed b <|> parsePubUncompressed b + +-- | Builds a public key from its uncompressed SEC-encoded bytes. +-- +-- Uncompressed keys are 65 bytes. The leftmost byte is @0x04@. The next 32 +-- bytes are the big-endian encoded @x@ cordinate. The next 32 bytes are the +-- big-endian encoded @y@ coordinate. +-- +-- Returns 'Nothing' if something is not satisfied. +parsePubUncompressed :: B.ByteString -> Maybe I.Pub +{-# INLINE parsePubUncompressed #-} +parsePubUncompressed b = do + guard (B.length b == 65 && B.index b 0 == 0x04) + let w0 = 0x02 + (B.index b 64 .&. 0x01) + I.parsePubCompressed (B.cons w0 (B.take 32 (B.drop 1 b))) + + diff --git a/lib/Bitcoin/Keys/GHC.hs b/lib/Bitcoin/Keys/GHC.hs new file mode 100644 --- /dev/null +++ b/lib/Bitcoin/Keys/GHC.hs @@ -0,0 +1,168 @@ +{-# LANGUAGE DerivingStrategies #-} +{-# LANGUAGE GeneralizedNewtypeDeriving #-} +-- | Implementation to be used when compiled with GHC +module Bitcoin.Keys.GHC + ( Prv + , parsePrv + , prvRaw + , prvToPub + , prvAddTweak + + , Pub + , parsePubCompressed + , pubCompressed + , pubUncompressed + , pubAddTweak + + , Tweak + , parseTweak + ) where + +import Control.Monad +import qualified Crypto.Secp256k1 as K +import qualified Data.ByteString as B +import qualified Data.ByteString.Lazy.Char8 as BL8 +import qualified Data.ByteString.Builder as BB + +-------------------------------------------------------------------------------- + +-- | Private key. +-- +-- Construct with 'parsePrv'. +newtype Prv = Prv K.SecKey + deriving newtype (Eq) + +instance Ord Prv where + compare a b = compare (prvRaw a) (prvRaw b) + {-# INLINE compare #-} + +-- | Big-endian base-16. +instance Show Prv where + showsPrec n p = showParen (n > 10) $ + showString "Prv " . + mappend (BL8.unpack (BB.toLazyByteString (BB.byteStringHex (prvRaw p)))) + +-- | Obtain the 32 raw bytes inside a 'Prv' (big-endian). +-- +-- @ +-- 'Just' == 'parsePrv' . 'prvRaw' +-- @ +prvRaw :: Prv -> B.ByteString +{-# INLINE prvRaw #-} +prvRaw (Prv x) = K.getSecKey x + +-- | Construct a 'Prv' key from its raw 32 bytes (big-endian). +-- +-- Returns 'Nothing' if something is not satisfied. +-- +-- @ +-- 'Just' == 'parsePrv' . 'prvRaw' +-- @ +parsePrv :: B.ByteString -> Maybe Prv +{-# INLINE parsePrv #-} +parsePrv x = do + guard (B.length x == 32) + Prv <$> K.secKey x + +-- | Obtain the 'Pub' key for 'Prv'. +prvToPub :: Prv -> Pub +{-# INLINE prvToPub #-} +prvToPub (Prv x) = Pub (K.derivePubKey x) + +-- | Tweak a 'Prv'ate key by adding 'Tweak' times the generator to it. +-- +-- Returns 'Nothing' if the resulting 'Prv' would be invalid. +-- +-- @ +-- 'pubAddTweak' t . 'prvToPub' == fmap 'prvToPub' . 'prvAddTweak' t +-- @ +prvAddTweak :: Tweak -> Prv -> Maybe Prv +{-# INLINE prvAddTweak #-} +prvAddTweak (Tweak t) (Prv p) = Prv <$> K.tweakAddSecKey p t + +-------------------------------------------------------------------------------- + +-- | Public key. +-- +-- Construct with 'Bitcoin.Keys.parsePub'. +newtype Pub = Pub K.PubKey + deriving newtype (Eq) + +instance Ord Pub where + compare a b = compare (pubCompressed a) (pubCompressed b) + {-# INLINE compare #-} + +-- | SEC compressed base-16. +instance Show Pub where + showsPrec n p = showParen (n > 10) $ + showString "Pub " . + mappend (BL8.unpack (BB.toLazyByteString (BB.byteStringHex (pubCompressed p)))) + +-- | Obtain the 33-bytes contatining the SEC compressed 'Pub'lic key. +-- +-- @ +-- 'Just' == 'Bitcoin.Keys.parsePub' . 'pubCompressed' +-- @ +pubCompressed :: Pub -> B.ByteString +{-# INLINE pubCompressed #-} +pubCompressed (Pub x) = K.exportPubKey True x + +-- | Obtain the 65-bytes contatining the SEC uncompressed 'Pub'lic key. +-- +-- @ +-- 'Just' == 'Bitcoin.Keys.parsePub' . 'pubUncompressed' +-- @ +pubUncompressed :: Pub -> B.ByteString +{-# INLINE pubUncompressed #-} +pubUncompressed (Pub x) = K.exportPubKey False x + +-- | Builds a public key from its compressed SEC-encoded bytes. +-- +-- * Compressed keys are 33 bytes. The leftmost byte is @0x02@ if the @y@ +-- coordinate is even, or @0x03@ if odd. The remaining 32 bytes +-- are the big-endian encoded @x@ coordinate. +-- +-- @ +-- 'Just' == 'Bitcoin.Keys.parsePub' . 'pubCompressed' +-- @ +parsePubCompressed :: B.ByteString -> Maybe Pub +{-# INLINE parsePubCompressed #-} +parsePubCompressed x = do + guard (B.length x == 33) + Pub <$> K.importPubKey x + +-- | Tweak a 'Pub'lic key by adding 'Tweak' times the generator to it. +-- +-- Returns 'Nothing' if the resulting 'Pub' would be invalid. +-- +-- @ +-- 'pubAddTweak' t . 'prvToPub' == fmap 'prvToPub' . 'prvAddTweak' t +-- @ +pubAddTweak :: Tweak -> Pub -> Maybe Pub +{-# INLINE pubAddTweak #-} +pubAddTweak (Tweak t) (Pub p) = Pub <$> K.tweakAddPubKey p t + +-------------------------------------------------------------------------------- + +-- | A 32-byte number used to modify a 'Pub' or 'Prv' using 'prvAddTweak' +-- or 'pubAddTweak'. +newtype Tweak = Tweak K.Tweak + deriving newtype (Eq) + +instance Ord Tweak where + compare (Tweak a) (Tweak b) = compare (K.getTweak a) (K.getTweak b) + +-- | Big-endian base-16. +instance Show Tweak where + showsPrec n (Tweak x) = showParen (n > 10) $ + showString "Tweak " . + mappend (BL8.unpack (BB.toLazyByteString (BB.byteStringHex (K.getTweak x)))) + +-- | Construct a 'Tweak' from its raw 32 bytes (big-endian). +-- +-- Returns 'Nothing' if something is not satisfied. +parseTweak :: B.ByteString -> Maybe Tweak +{-# INLINE parseTweak #-} +parseTweak x = do + guard (B.length x == 32) + Tweak <$> K.tweak x diff --git a/lib/Bitcoin/Keys/GHCJS.hs b/lib/Bitcoin/Keys/GHCJS.hs new file mode 100644 --- /dev/null +++ b/lib/Bitcoin/Keys/GHCJS.hs @@ -0,0 +1,216 @@ +{-# LANGUAGE KindSignatures #-} +{-# LANGUAGE DerivingStrategies #-} +{-# LANGUAGE ForeignFunctionInterface #-} +{-# LANGUAGE GeneralizedNewtypeDeriving #-} +{-# LANGUAGE JavaScriptFFI #-} + +-- | Implementation to be used when compiled with GHCJS +module Bitcoin.Keys.GHCJS + ( Prv + , parsePrv + , prvRaw + , prvToPub + , prvAddTweak + + , Pub + , parsePubCompressed + , pubCompressed + , pubUncompressed + , pubAddTweak + + , Tweak + , parseTweak + ) where + +import Control.Monad +import qualified Data.ByteString as B +import qualified Data.ByteString.Lazy.Char8 as BL8 +import qualified Data.ByteString.Builder as BB +import qualified GHCJS.Buffer as Buf +import GHCJS.Types (JSVal) +import GHCJS.Nullable +import qualified JavaScript.TypedArray.ArrayBuffer as AB +import qualified JavaScript.TypedArray as TA + +-------------------------------------------------------------------------------- + +-- | Private key. +-- +-- Construct with 'parsePrv'. +newtype Prv = Prv B.ByteString + deriving newtype (Eq, Ord) + +-- | Big-endian base-16. +instance Show Prv where + showsPrec n p = showParen (n > 10) $ + showString "Prv " . + mappend (BL8.unpack (BB.toLazyByteString (BB.byteStringHex (prvRaw p)))) + +-- | Obtain the 32 raw bytes inside a 'Prv' (big-endian). +-- +-- @ +-- 'Just' == 'parsePrv' . 'prvRaw' +-- @ +prvRaw :: Prv -> B.ByteString +{-# INLINE prvRaw #-} +prvRaw (Prv x) = x + +-- | Construct a 'Prv' key from its raw 32 bytes (big-endian). +-- +-- Returns 'Nothing' if something is not satisfied. +-- +-- @ +-- 'Just' == 'parsePrv' . 'prvRaw' +-- @ +parsePrv :: B.ByteString -> Maybe Prv +parsePrv b = do + guard (B.length b == 32) + guard (js_prvVerify (bsToU8A b)) + pure (Prv b) + +foreign import javascript unsafe + "h$bitcoin_keys.prvVerify($1)" + js_prvVerify :: TA.Uint8Array -> Bool + +-- | Obtain the 'Pub' key for 'Prv'. +prvToPub :: Prv -> Pub +{-# INLINE prvToPub #-} +prvToPub = Pub . bsFromU8A . js_prvToPub . bsToU8A . prvRaw + +foreign import javascript unsafe "h$bitcoin_keys.prvToPub($1)" + js_prvToPub :: TA.Uint8Array -> TA.Uint8Array + +-- | Tweak a 'Prv'ate key by adding 'Tweak' times the generator to it. +-- +-- Returns 'Nothing' if the resulting 'Prv' would be invalid. +prvAddTweak :: Tweak -> Prv -> Maybe Prv +{-# INLINE prvAddTweak #-} +prvAddTweak (Tweak t) (Prv p) = do + jsv <- nullableToMaybe (js_prvAddTweak (bsToU8A p) (bsToU8A t)) + pure $ Prv (bsFromU8A (js_unsafe_JSVal_to_UInt8Array jsv)) + +foreign import javascript unsafe "h$bitcoin_keys.prvAddTweak($1, $2)" + js_prvAddTweak :: TA.Uint8Array -- ^ Private key. + -> TA.Uint8Array -- ^ Tweak. + -> Nullable JSVal -- ^ Nullable Uint8Array + +-------------------------------------------------------------------------------- + +-- | Public key. +-- +-- Construct with 'Bitcoin.Keys.parsePub'. +newtype Pub = Pub B.ByteString + deriving newtype (Eq, Ord) + +-- | SEC compressed base-16. +instance Show Pub where + showsPrec n p = showParen (n > 10) $ + showString "Pub " . + mappend (BL8.unpack (BB.toLazyByteString (BB.byteStringHex (pubCompressed p)))) + +-- | Obtain the 33-bytes contatining the SEC compressed 'Pub'lic key. +-- +-- @ +-- 'Just' == 'Bitcoin.Keys.parsePub' . 'pubCompressed' +-- @ +pubCompressed :: Pub -> B.ByteString +{-# INLINE pubCompressed #-} +pubCompressed (Pub x) = x + +-- | Obtain the 65-bytes contatining the SEC uncompressed 'Pub'lic key. +-- +-- @ +-- 'Just' == 'Bitcoin.Keys.parsePub' . 'pubUncompressed' +-- @ +pubUncompressed :: Pub -> B.ByteString +{-# INLINE pubUncompressed #-} +pubUncompressed = bsFromU8A . js_pubUncompressed . bsToU8A . pubCompressed + +foreign import javascript unsafe "h$bitcoin_keys.pubUncompressed($1)" + js_pubUncompressed :: TA.Uint8Array -- ^ Compressed public key. + -> TA.Uint8Array -- ^ Uncompressed public key. + + +-- | Builds a public key from its compressed SEC-encoded bytes. +-- +-- * Compressed keys are 33 bytes. The leftmost byte is @0x02@ if the @y@ +-- coordinate is even, or @0x03@ if odd. The remaining 32 bytes +-- are the big-endian encoded @x@ coordinate. +-- +-- @ +-- 'Just' == 'Bitcoin.Keys.parsePub' . 'pubCompressed' +-- @ +parsePubCompressed :: B.ByteString -> Maybe Pub +parsePubCompressed b = do + guard (B.length b == 33) + guard (js_pubVerify (bsToU8A b)) + pure (Pub b) + +foreign import javascript unsafe "h$bitcoin_keys.pubVerify($1)" + js_pubVerify :: TA.Uint8Array -- ^ Compressed public key. + -> Bool -- ^ Whether the key is valid. + +-- | Tweak a 'Pub'lic key by adding 'Tweak' times the generator to it. +-- +-- Returns 'Nothing' if the resulting 'Pub' would be invalid. +pubAddTweak :: Tweak -> Pub -> Maybe Pub +{-# INLINE pubAddTweak #-} +pubAddTweak (Tweak t) (Pub p) = do + jsv <- nullableToMaybe (js_pubAddTweak (bsToU8A p) (bsToU8A t)) + pure $ Pub (bsFromU8A (js_unsafe_JSVal_to_UInt8Array jsv)) + +foreign import javascript unsafe "h$bitcoin_keys.pubAddTweak($1, $2)" + js_pubAddTweak :: TA.Uint8Array -- ^ Public key. + -> TA.Uint8Array -- ^ Tweak. + -> Nullable JSVal -- ^ Nullable Uint8Array + +-------------------------------------------------------------------------------- + +-- | A 32-byte number used to modify a 'Pub' or 'Prv' using 'prvAddTweak' +-- or 'pubAddTweak'. +newtype Tweak = Tweak B.ByteString + deriving newtype (Eq, Ord) + +-- | Big-endian base-16. +instance Show Tweak where + showsPrec n (Tweak b) = showParen (n > 10) $ + showString "Tweak " . + mappend (BL8.unpack (BB.toLazyByteString (BB.byteStringHex b))) + +-- | Construct a 'Tweak' from its raw 32 bytes (big-endian). +-- +-- Returns 'Nothing' if something is not satisfied. +parseTweak :: B.ByteString -> Maybe Tweak +parseTweak b = do + guard (B.length b == 32) + pure $ Tweak b + +-------------------------------------------------------------------------------- + +bsToU8A :: B.ByteString -> TA.Uint8Array +bsToU8A x + | B.length x == 0 = js_emptyUint8Array + | otherwise = let (buf, off, len) = Buf.fromByteString x + in js_newUint8Array (Buf.getArrayBuffer buf) off len + +foreign import javascript unsafe "new Uint8Array($1, $2, $3)" + js_newUint8Array :: AB.ArrayBuffer + -> Int -- ^ Byte offset. + -> Int -- ^ Byte length. + -> TA.Uint8Array + +foreign import javascript unsafe "new Uint8Array(0)" + js_emptyUint8Array :: TA.Uint8Array + +-------------------------------------------------------------------------------- + +bsFromU8A :: TA.Uint8Array -> B.ByteString +bsFromU8A x = Buf.toByteString (TA.byteOffset x) + (Just (TA.byteLength x)) + (Buf.createFromArrayBuffer (TA.buffer x)) + +-------------------------------------------------------------------------------- + +foreign import javascript unsafe "$r = $1;" + js_unsafe_JSVal_to_UInt8Array :: JSVal -> TA.Uint8Array + diff --git a/test/Main.hs b/test/Main.hs new file mode 100644 --- /dev/null +++ b/test/Main.hs @@ -0,0 +1,255 @@ +{-# LANGUAGE DataKinds #-} +{-# LANGUAGE KindSignatures #-} +{-# LANGUAGE OverloadedStrings #-} +{-# LANGUAGE ScopedTypeVariables #-} +{-# OPTIONS_GHC -Wno-type-defaults #-} + +module Main (main) where + +import qualified Data.ByteString as B +import qualified Data.ByteString.Base16 as B16 +import Data.Maybe +import Data.Word +import qualified Test.Tasty as Tasty +import qualified Test.Tasty.Runners as Tasty +import Test.Tasty (TestTree, testGroup) +import Test.Tasty.HUnit (testCase, (@?=), (@=?)) +import Test.Tasty.Hedgehog (testProperty, HedgehogTestLimit(..)) +import Hedgehog (MonadGen, property, forAll, (===)) +import qualified Hedgehog.Gen as Gen +import qualified Hedgehog.Range as Range +import qualified System.IO as IO + +import qualified Bitcoin.Keys as S + +-------------------------------------------------------------------------------- + +main :: IO () +main = do + IO.hSetBuffering IO.stdout IO.LineBuffering + IO.hSetBuffering IO.stderr IO.LineBuffering + Tasty.defaultMainWithIngredients + [ Tasty.consoleTestReporter + , Tasty.listingTests + ] $ Tasty.localOption (HedgehogTestLimit (Just 2000)) + $ tt + +tt :: TestTree +tt = testGroup "bitcoin-keys" + [ testCase "Show Pub" $ do + show pub1c @?= "Pub 024ed59d3f6548c41172ec26b9144f547185cb2a9f28fccb6e3ae53dc4f1827154" + + , testCase "Show Prv" $ do + show prv1 @?= "Prv 76deed24fcdfb479656af6c5c4ab906090c5ee39da1c1ad1f1ad56dfce378a03" + + , testCase "Show Tweak" $ do + show tweak1 @?= "Tweak 0ef561fb5f4e9e2319a5b75ed3be3c895e6ec272c0b5185dc414fb7e47c3a770" + + , testCase "parsePub: uncompressed vs compressed (even y)" $ do + pub1c @=? pub1u + S.pubCompressed pub1c @?= pub1c_raw + S.pubCompressed pub1u @?= pub1c_raw + S.pubUncompressed pub1c @?= pub1u_raw + S.pubUncompressed pub1u @?= pub1u_raw + + , testCase "parsePub: uncompressed vs compressed (odd y)" $ do + pub2c @=? pub2u + S.pubCompressed pub2c @?= pub2c_raw + S.pubCompressed pub2u @?= pub2c_raw + S.pubUncompressed pub2c @?= pub2u_raw + S.pubUncompressed pub2u @?= pub2u_raw + + , testCase "Ord Pub" $ do + compare pub1c pub2c @?= LT + compare pub2c pub1c @?= GT + compare pub1c pub1c @?= EQ + compare pub2c pub2c @?= EQ + + , testCase "Ord Prv" $ do + compare prv1 prv2 @?= LT + compare prv2 prv1 @?= GT + compare prv1 prv1 @?= EQ + compare prv2 prv2 @?= EQ + + , testCase "prvToPub prv1" $ do + S.prvToPub prv1 @?= pub1c + + , testCase "prvToPub prv2" $ do + S.prvToPub prv2 @?= pub2c + + , testProperty "parsePrv . prvRaw" $ property $ do + prv <- forAll genPrv + Just prv === S.parsePrv (S.prvRaw prv) + + , testProperty "parsePub . pubCompressed" $ property $ do + pub <- forAll genPub + Just pub === S.parsePub (S.pubCompressed pub) + + , testProperty "parsePub . pubUncompressed" $ property $ do + pub <- forAll genPub + Just pub === S.parsePub (S.pubUncompressed pub) + + , testProperty "parsePrv: invalid" $ property $ do + raw <- forAll $ Gen.bytes (Range.constant 0 200) + case B.length raw of + 32 -> pure () + _ -> Nothing === S.parsePrv raw + + , testProperty "parsePub: invalid" $ property $ do + raw <- forAll $ Gen.bytes (Range.constant 0 200) + case B.length raw of + 33 | B.head raw `elem` [0x02, 0x03] -> pure () + 65 | B.head raw == 0x04 -> pure () + _ -> Nothing === S.parsePub raw + + , testProperty "parseTweak" $ property $ do + raw <- forAll $ Gen.bytes (Range.constant 0 200) + let yt = S.parsePrv raw + case B.length raw of + 32 -> True === isJust yt + _ -> Nothing === yt + + , testProperty "addPrvTweak vs addPubTweak (prop)" $ property $ do + tweak <- forAll genTweak + prv <- forAll genPrv + let pub = S.prvToPub prv + yprv' = S.prvAddTweak tweak prv + ypub' = S.pubAddTweak tweak pub + ypub' === fmap S.prvToPub yprv' + + , testCase "addPrvTweak vs addPubTweak (prv1)" $ do + let Just pub' = S.prvToPub <$> S.prvAddTweak tweak1 prv1 + Just pub' @?= S.pubAddTweak tweak1 pub1c + + , testCase "addPrvTweak vs addPubTweak (prv2)" $ do + let Just pub' = S.prvToPub <$> S.prvAddTweak tweak1 prv2 + Just pub' @?= S.pubAddTweak tweak1 pub2c + + , testCase "addPrvTweak prv1" $ do + let Just x = S.parsePrv $ fromBase16 + "85d44f205c2e529c7f10ae249869cce9ef34b0ac9ad1332fb5c2525e15fb3173" + S.prvAddTweak tweak1 prv1 @?= Just x + + , testCase "addPrvTweak prv2" $ do + let Just x = S.parsePrv $ fromBase16 + "cb186f2bc6a2ace5580fb1fda1861ea2757435aa1e66a812d7decb7d368eddee" + S.prvAddTweak tweak1 prv2 @?= Just x + + , testCase "addPubTweak pub1" $ do + let Just x = S.parsePub $ fromBase16 + "038089e37ec58d5ace95bc84ee11d6c366d1b464ba703c2f8ec189bc2bce76f1f3" + S.pubAddTweak tweak1 pub1c @?= Just x + + , testCase "addPubTweak pub2" $ do + let Just x = S.parsePub $ fromBase16 + "025c8fd62030ba8ee8ede5bf053613a31a4850c9489eb62bec7cfb3efaa1e07b43" + S.pubAddTweak tweak1 pub2c @?= Just x + ] + +-------------------------------------------------------------------------------- + +genTweak :: MonadGen m => m S.Tweak +genTweak = do + b <- Gen.bytes (Range.singleton 32) + let Just k = S.parseTweak b + pure k + +genPrv :: MonadGen m => m S.Prv +genPrv = do + b <- Gen.bytes (Range.singleton 32) + let Just k = S.parsePrv b + pure k + +genPub :: MonadGen m => m S.Pub +genPub = go 10000 where + go 0 = error "genPub: too many attempts" + go n = do + h <- Gen.element [2, 3 :: Word8] + b <- Gen.bytes (Range.singleton 32) + case S.parsePub (B.cons h b) of + Just k -> pure k + Nothing -> go (n - 1) + +-------------------------------------------------------------------------------- +-- BIP39 mnemonic: abandon abandon arm +-- +-- BIP39 seed: 2f7b8b6eeeb7201d88ed45dcd4706ccd76e5feb61f1961990869581781f8944ae2bebff36156c6965054add29f2cf9ee8b7b488179bfba24773ce2b06ec0ce04 +-- +-- BIP32 Derivation path: m/44'/0'/0'/0/0 +-- +-- Private key WIF: L1CnCq2yTvfzngQTF4Fnh5daYUwAuysrqU5dNwZFcv33Cwu4Gf2F + +prv1 :: S.Prv +prv1 = maybe (error "prv1") id (S.parsePrv prv1_raw) + +prv1_raw :: B.ByteString +prv1_raw = fromBase16 + "76deed24fcdfb479656af6c5c4ab906090c5ee39da1c1ad1f1ad56dfce378a03" + +-- | Compressed version of `pub1u` +pub1c :: S.Pub +pub1c = maybe (error "pub1c") id (S.parsePub pub1c_raw) + +pub1c_raw :: B.ByteString +pub1c_raw = fromBase16 + "024ed59d3f6548c41172ec26b9144f547185cb2a9f28fccb6e3ae53dc4f1827154" + +-- | Uncompressed version of `pub1c` +pub1u :: S.Pub +pub1u = maybe (error "pub1u") id (S.parsePub pub1u_raw) + +pub1u_raw :: B.ByteString +pub1u_raw = fromBase16 + "044ed59d3f6548c41172ec26b9144f547185cb2a9f28fccb6e3ae53dc4f1827154\ + \ba3a12d8b383bfff1dacd6930285f4a51a01ee64e102652d5bc137c49b97815e" + +-------------------------------------------------------------------------------- +-- BIP39 mnemonic: abandon abandon arm +-- +-- BIP39 seed: 2f7b8b6eeeb7201d88ed45dcd4706ccd76e5feb61f1961990869581781f8944ae2bebff36156c6965054add29f2cf9ee8b7b488179bfba24773ce2b06ec0ce04 +-- +-- BIP32 Derivation path: m/84'/0'/0'/0/0 +-- +-- Private key WIF: L3XRaAfqnZLCcUpcCi4g1GqMLTKvr9nbvCYBmrs1TAjx4acpZ2eY + +prv2 :: S.Prv +prv2 = maybe (error "prv2") id (S.parsePrv prv2_raw) + +prv2_raw :: B.ByteString +prv2_raw = fromBase16 + "bc230d3067540ec23e69fa9ecdc7e219170573375db18fb513c9cffeeecb367e" + +-- | Compressed version of `pub2u` +pub2c :: S.Pub +pub2c = maybe (error "pub2c") id (S.parsePub pub2c_raw) + +pub2c_raw :: B.ByteString +pub2c_raw = fromBase16 + "0315bd146d8b45383ad431a8204717dc9f46a7a46c1f44eeaab02d49f4511ccff0" + +-- | Uncompressed version of `pub2c` +pub2u :: S.Pub +pub2u = maybe (error "pub2u") id (S.parsePub pub2u_raw) + +pub2u_raw :: B.ByteString +pub2u_raw = fromBase16 + "0415bd146d8b45383ad431a8204717dc9f46a7a46c1f44eeaab02d49f4511ccff0\ + \7d7817de34c0a281b45691eec966e95d936554b2320462214cd2a17aebcf460f" + +-------------------------------------------------------------------------------- +-- Randomly generated + +tweak1 :: S.Tweak +tweak1 = maybe (error "tweak1") id (S.parseTweak tweak1_raw) + +tweak1_raw :: B.ByteString +tweak1_raw = fromBase16 + "0ef561fb5f4e9e2319a5b75ed3be3c895e6ec272c0b5185dc414fb7e47c3a770" + +-------------------------------------------------------------------------------- + +fromBase16 :: B.ByteString -> B.ByteString +fromBase16 a = case B16.decode a of + (b, "") -> b + _ -> error ("Invalid base16 string: " <> show a) +