897 lines
17 KiB
C++
897 lines
17 KiB
C++
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/***************************************************************************
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*
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Copyright 2013 CertiVox UK Ltd. *
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*
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This file is part of CertiVox MIRACL Crypto SDK. *
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*
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The CertiVox MIRACL Crypto SDK provides developers with an *
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extensive and efficient set of cryptographic functions. *
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For further information about its features and functionalities please *
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refer to http://www.certivox.com *
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*
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* The CertiVox MIRACL Crypto SDK is free software: you can *
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redistribute it and/or modify it under the terms of the *
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GNU Affero General Public License as published by the *
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Free Software Foundation, either version 3 of the License, *
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or (at your option) any later version. *
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*
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* The CertiVox MIRACL Crypto SDK is distributed in the hope *
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that it will be useful, but WITHOUT ANY WARRANTY; without even the *
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implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *
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See the GNU Affero General Public License for more details. *
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*
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* You should have received a copy of the GNU Affero General Public *
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License along with CertiVox MIRACL Crypto SDK. *
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If not, see <http://www.gnu.org/licenses/>. *
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*
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You can be released from the requirements of the license by purchasing *
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a commercial license. Buying such a license is mandatory as soon as you *
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develop commercial activities involving the CertiVox MIRACL Crypto SDK *
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without disclosing the source code of your own applications, or shipping *
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the CertiVox MIRACL Crypto SDK with a closed source product. *
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*
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***************************************************************************/
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/*
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* ssp_pair.cpp
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*
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* Supersingular curve, Tate pairing embedding degree 2, ideal for security level AES-80
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*
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* Provides high level interface to pairing functions
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*
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* GT=pairing(G1,G1)
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*
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* This is calculated on a Pairing Friendly Curve (PFC), which must first be defined.
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*
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* G1 is a point over the base field
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* GT is a finite field point over the 2nd extension, where 2 is the embedding degree.
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*/
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#define MR_PAIRING_SSP
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#include "pairing_1.h"
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// Supersingular curve parameters, A,B and n, where p=2nq-1
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// AES_SECURITY=80 bit curve
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static char param_80[]="B83DFB800C851836F9B95087F2642EF80B01601D46BA7CC14978EB4F6225BA7558E3D487FA3639FFE4C36332";
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// AES_SECURITY=128 bit curve
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static char param_128[]="83093742908D4D529CEF06C72191A05D5E6073FE861E637D7747C3E52FBB92DAA5DDF3EF1C61F5F70B256802481A36CAFE995FE33CD54014B846751364C0D3B8327D9E45366EA08F1B3446AC23C9D4B656886731A8D05618CFA1A3B202A2445ABA0E77C5F4F00CA1239975A05377084F256DEAA07D21C4CF2A4279BC117603ACB7B10228C3AB8F8C1742D674395701BB02071A88683041D9C4231E8EE982B8DA";
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void read_only_error(void)
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{
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cout << "Attempt to write to read-only object" << endl;
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exit(0);
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}
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// Using SHA256 as basic hash algorithm
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//
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// Hash function
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//
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#define HASH_LEN 32
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Big H1(char *string)
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{ // Hash a zero-terminated string to a number < modulus
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Big h,p;
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char s[HASH_LEN];
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int i,j;
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sha256 sh;
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shs256_init(&sh);
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for (i=0;;i++)
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{
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if (string[i]==0) break;
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shs256_process(&sh,string[i]);
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}
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shs256_hash(&sh,s);
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p=get_modulus();
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h=1; j=0; i=1;
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forever
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{
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h*=256;
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if (j==HASH_LEN) {h+=i++; j=0;}
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else h+=s[j++];
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if (h>=p) break;
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}
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h%=p;
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return h;
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}
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void PFC::start_hash(void)
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{
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shs256_init(&SH);
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}
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Big PFC::finish_hash_to_group(void)
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{
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Big hash;
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char s[HASH_LEN];
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shs256_hash(&SH,s);
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hash=from_binary(HASH_LEN,s);
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return hash%(*ord);
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}
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void PFC::add_to_hash(const GT& x)
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{ // compress it and add
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ZZn2 u=x.g;
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Big a;
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int m;
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u.get(a);
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while (a>0)
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{
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m=a%256;
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shs256_process(&SH,m);
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a/=256;
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}
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}
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void PFC::add_to_hash(const G1& x)
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{
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Big a,X,Y;
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int i,m;
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x.g.get(X,Y);
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a=X;
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while (a>0)
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{
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m=a%256;
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shs256_process(&SH,m);
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a/=256;
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}
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a=Y;
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while (a>0)
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{
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m=a%256;
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shs256_process(&SH,m);
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a/=256;
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}
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}
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void PFC::add_to_hash(const Big& x)
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{
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int m;
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Big a=x;
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while (a>0)
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{
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m=a%256;
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shs256_process(&SH,m);
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a/=256;
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}
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}
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Big H2(ZZn2 y)
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{ // Hash and compress an Fp2 to a big number
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sha256 sh;
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Big a,h;
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char s[HASH_LEN];
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int m;
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shs256_init(&sh);
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y.get(a);
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while (a>0)
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{
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m=a%256;
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shs256_process(&sh,m);
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a/=256;
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}
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shs256_hash(&sh,s);
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h=from_binary(HASH_LEN,s);
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return h;
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}
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#ifndef MR_AFFINE_ONLY
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void force(ZZn& x,ZZn& y,ZZn& z,ECn& A)
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{ // A=(x,y,z)
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copy(getbig(x),A.get_point()->X);
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copy(getbig(y),A.get_point()->Y);
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copy(getbig(z),A.get_point()->Z);
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A.get_point()->marker=MR_EPOINT_GENERAL;
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}
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void extract(ECn &A, ZZn& x,ZZn& y,ZZn& z)
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{ // (x,y,z) <- A
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big t;
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x=(A.get_point())->X;
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y=(A.get_point())->Y;
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t=(A.get_point())->Z;
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if (A.get_status()!=MR_EPOINT_GENERAL) z=1;
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else z=t;
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}
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#endif
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void force(ZZn& x,ZZn& y,ECn& A)
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{ // A=(x,y)
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copy(getbig(x),A.get_point()->X);
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copy(getbig(y),A.get_point()->Y);
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A.get_point()->marker=MR_EPOINT_NORMALIZED;
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}
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void extract(ECn& A,ZZn& x,ZZn& y)
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{ // (x,y) <- A
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if (A.iszero())
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{
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x=0; y=0;
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return;
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}
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x=(A.get_point())->X;
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y=(A.get_point())->Y;
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}
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void extractZ(ECn& A,ZZn& z)
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{
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big t;
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t=(A.get_point())->Z;
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if (A.get_status()!=MR_EPOINT_GENERAL) z=1;
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else z=t;
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}
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//
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// Line from A to destination C. Let A=(x,y)
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// Line Y-slope.X-c=0, through A, so intercept c=y-slope.x
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// Line Y-slope.X-y+slope.x = (Y-y)-slope.(X-x) = 0
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// Now evaluate at Q -> return (Qy-y)-slope.(Qx-x)
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//
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ZZn2 line(ECn& A,ECn& C,ECn& B,int type,ZZn& slope,ZZn& ex1,ZZn& ex2,ZZn& Px,ZZn& Py)
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{
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ZZn2 w;
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ZZn x,y,z3;
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extractZ(C,z3);
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if (type==MR_ADD)
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{
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extract(B,x,y);
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w.set(slope*(x+Px)-z3*y,z3*Py);
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}
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if (type==MR_DOUBLE)
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{
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extract(A,x,y);
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w.set(-(slope*ex2)*Px-slope*x+ex1,-(z3*ex2)*Py);
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}
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/*
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extract(A,x,y,z);
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x*=z; t=z; z*=z; z*=t; // 9 ZZn muls
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n*=z; n+=x; n*=slope;
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d*=z; w.set(-y,d);
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extractZ(C,z3);
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w*=z3; w+=n;
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*/
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// w.set(Px*z*z*z*slope+slope*x*z-y*z3,Py*z*z*z*z3);
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return w;
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}
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//
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// Add A=A+B (or A=A+A)
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// Return line function value
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//
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ZZn2 g(ECn& A,ECn& B,ZZn& Px,ZZn& Py)
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{
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int type;
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ZZn lam,extra1,extra2;
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ZZn2 u;
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ECn P=A;
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big ptr,ex1,ex2;
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type=A.add(B,&ptr,&ex1,&ex2);
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if (!type) return (ZZn2)1;
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lam=ptr;
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extra1=ex1;
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extra2=ex2;
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return line(P,A,B,type,lam,extra1,extra2,Px,Py);
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}
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// if multiples of G1 can be precalculated, its a lot faster!
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ZZn2 gp(ZZn* ptable,int &j,ZZn& Px,ZZn& Py)
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{
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ZZn2 w;
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w.set(ptable[j]*Px+ptable[j+1],Py);
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j+=2;
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return w;
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}
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//
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// Spill precomputation on pairing to byte array
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//
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int PFC::spill(G1& w,char *& bytes)
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{
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int i,j,n=2*(bits(*ord-1)-2+ham(*ord));
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int bytes_per_big=(MIRACL/8)*(get_mip()->nib-1);
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int len=n*bytes_per_big;
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Big x;
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if (w.ptable==NULL) return 0;
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bytes=new char[len];
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for (i=j=0;i<n;i++)
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{
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x=w.ptable[i];
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to_binary(x,bytes_per_big,&bytes[j],TRUE);
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j+=bytes_per_big;
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}
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delete [] w.ptable;
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w.ptable=NULL;
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return len;
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}
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//
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// Restore precomputation on pairing to byte array
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//
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void PFC::restore(char * bytes,G1& w)
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{
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int i,j,n=2*(bits(*ord-1)-2+ham(*ord));
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int bytes_per_big=(MIRACL/8)*(get_mip()->nib-1);
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int len=n*bytes_per_big;
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Big x;
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if (w.ptable!=NULL) return;
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w.ptable=new ZZn[n];
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for (i=j=0;i<n;i++)
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{
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x=from_binary(bytes_per_big,&bytes[j]);
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w.ptable[i]=x;
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j+=bytes_per_big;
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}
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for (i=0;i<len;i++) bytes[i]=0;
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delete [] bytes;
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}
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// precompute G1 table for pairing
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int PFC::precomp_for_pairing(G1& w)
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{
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int i,j,nb,len;
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ECn A,Q,B;
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ZZn lam,x,y;
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big ptr;
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Big iters=*ord-1;
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A=w.g;
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normalise(A);
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B=A;
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nb=bits(iters);
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j=0;
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len=2*(nb-2+ham(*ord));
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w.ptable=new ZZn[len];
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get_mip()->coord=MR_AFFINE;
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for (i=nb-2;i>=0;i--)
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{
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Q=A;
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// Evaluate line from A to A+B
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A.add(A,&ptr);
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lam=ptr;
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extract(Q,x,y);
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w.ptable[j++]=lam; w.ptable[j++]=lam*x-y;
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if (bit(iters,i)==1)
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{
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Q=A;
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A.add(B,&ptr);
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lam=ptr;
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extract(Q,x,y);
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w.ptable[j++]=lam; w.ptable[j++]=lam*x-y;
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}
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}
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get_mip()->coord=MR_PROJECTIVE;
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return len;
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}
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GT PFC::multi_miller(int n,G1** QQ,G1** PP)
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{
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GT z;
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ZZn *Px,*Py;
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int i,j,*k,nb;
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ECn *Q,*A;
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ECn P;
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ZZn2 res;
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Big iters=*ord-1;
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Px=new ZZn[n];
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Py=new ZZn[n];
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Q=new ECn[n];
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A=new ECn[n];
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k=new int[n];
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nb=bits(iters);
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res=1;
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for (j=0;j<n;j++)
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{
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k[j]=0;
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P=PP[j]->g; normalise(P); Q[j]=QQ[j]->g; normalise(Q[j]);
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extract(P,Px[j],Py[j]);
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}
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for (j=0;j<n;j++) A[j]=Q[j];
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for (i=nb-2;i>=0;i--)
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{
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res*=res;
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for (j=0;j<n;j++)
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{
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if (QQ[j]->ptable==NULL)
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res*=g(A[j],A[j],Px[j],Py[j]);
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else
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res*=gp(QQ[j]->ptable,k[j],Px[j],Py[j]);
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}
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if (bit(iters,i)==1)
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for (j=0;j<n;j++)
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{
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if (QQ[j]->ptable==NULL)
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res*=g(A[j],Q[j],Px[j],Py[j]);
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else
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res*=gp(QQ[j]->ptable,k[j],Px[j],Py[j]);
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}
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if (res.iszero()) return 0;
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}
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delete [] k;
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delete [] A;
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delete [] Q;
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delete [] Py;
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delete [] Px;
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z.g=res;
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return z;
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}
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//
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// Tate Pairing G1 x G1 -> GT
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//
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// P and Q are points of order q in G1.
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//
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GT PFC::miller_loop(const G1& QQ,const G1& PP)
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{
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GT z;
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int i,j,n,nb,nbw,nzs;
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ECn A,Q;
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ECn P;
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ZZn Px,Py;
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BOOL precomp;
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ZZn2 res;
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Big iters=*ord-1; // can omit last addition
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P=PP.g; Q=QQ.g;
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precomp=FALSE;
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if (QQ.ptable!=NULL) precomp=TRUE;
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normalise(P);
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normalise(Q);
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extract(P,Px,Py);
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//Px=-Px;
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res=1;
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A=Q; // reset A
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nb=bits(iters);
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j=0;
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for (i=nb-2;i>=0;i--)
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{
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res*=res;
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if (precomp) res*=gp(QQ.ptable,j,Px,Py);
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else res*=g(A,A,Px,Py);
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if (bit(iters,i)==1)
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{
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if (precomp) res*=gp(QQ.ptable,j,Px,Py);
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else res*=g(A,Q,Px,Py);
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}
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}
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z.g=res;
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return z;
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}
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GT PFC::final_exp(const GT& z)
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{
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GT y;
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Big p;
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ZZn2 res;
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res=z.g;
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p=get_modulus(); // get p
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res=conj(res)/res;
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res=pow(res,(p+1)/(*ord)); // raise to power of (p^2-1)/q
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y.g=res;
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return y;
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}
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PFC::PFC(int s, csprng *rng)
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{
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int mod_bits,words;
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if (s!=80 && s!=128)
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{
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cout << "No suitable curve available" << endl;
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exit(0);
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}
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if (s==80) mod_bits=512;
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if (s==128) mod_bits=1536;
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if (mod_bits%MIRACL==0)
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words=(mod_bits/MIRACL);
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else
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words=(mod_bits/MIRACL)+1;
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#ifdef MR_SIMPLE_BASE
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miracl *mip=mirsys((MIRACL/4)*words,16);
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#else
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miracl *mip=mirsys(words,0);
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mip->IOBASE=16;
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#endif
|
|
mod=new Big;
|
|
cof=new Big;
|
|
ord=new Big;
|
|
|
|
Big A=-3;
|
|
Big B=0;
|
|
if (s==80)
|
|
{
|
|
*cof=param_80;
|
|
*ord=pow((Big)2,159)+pow((Big)2,17)+1;
|
|
}
|
|
if (s==128)
|
|
{
|
|
*cof=param_128;
|
|
*ord=pow((Big)2,255)+pow((Big)2,41)+1;
|
|
}
|
|
|
|
S=s;
|
|
*mod=2*(*cof)*(*ord)-1;
|
|
ecurve(A,B,*mod,MR_PROJECTIVE);
|
|
|
|
RNG=rng;
|
|
}
|
|
|
|
G1 PFC::mult(const G1& w,const Big& k)
|
|
{
|
|
G1 z;
|
|
if (w.mtable!=NULL)
|
|
{ // we have precomputed values
|
|
Big e=k;
|
|
if (k<0) e=-e;
|
|
|
|
int i,j,t=w.mtbits; //MR_ROUNDUP(2*S,WINDOW_SIZE);
|
|
j=recode(e,t,WINDOW_SIZE,t-1);
|
|
z.g=w.mtable[j];
|
|
for (i=t-2;i>=0;i--)
|
|
{
|
|
j=recode(e,t,WINDOW_SIZE,i);
|
|
z.g+=z.g;
|
|
if (j>0) z.g+=w.mtable[j];
|
|
}
|
|
if (k<0) z.g=-z.g;
|
|
}
|
|
else
|
|
{
|
|
z.g=w.g;
|
|
z.g*=k;
|
|
}
|
|
return z;
|
|
}
|
|
|
|
GT PFC::power(const GT& w,const Big& k)
|
|
{
|
|
GT z;
|
|
Big e=k;
|
|
if (k<0) e=-e;
|
|
if (w.etable!=NULL)
|
|
{ // precomputation is available
|
|
int i,j,t=w.etbits; //MR_ROUNDUP(2*S,WINDOW_SIZE);
|
|
j=recode(e,t,WINDOW_SIZE,t-1);
|
|
z.g=w.etable[j];
|
|
for (i=t-2;i>=0;i--)
|
|
{
|
|
j=recode(e,t,WINDOW_SIZE,i);
|
|
z.g*=z.g;
|
|
if (j>0) z.g*=w.etable[j];
|
|
}
|
|
}
|
|
else
|
|
{
|
|
z.g=powu(w.g,e);
|
|
}
|
|
if (k<0) z.g=conj(z.g);
|
|
return z;
|
|
}
|
|
|
|
// random group member
|
|
|
|
void PFC::random(Big& w)
|
|
{
|
|
if (RNG==NULL) w=rand(*ord);
|
|
else w=strong_rand(RNG,*ord);
|
|
}
|
|
|
|
// random AES key
|
|
|
|
void PFC::rankey(Big& k)
|
|
{
|
|
if (RNG==NULL) k=rand(S,2);
|
|
else k=strong_rand(RNG,S,2);
|
|
}
|
|
|
|
// Can be done deterministicly
|
|
|
|
void PFC::hash_and_map(G1& w,char *ID)
|
|
{
|
|
Big x0=H1(ID);
|
|
if (is_on_curve(x0)) w.g.set(x0);
|
|
else w.g.set(-x0);
|
|
w.g*=(*cof);
|
|
}
|
|
|
|
void PFC::random(G1& w)
|
|
{
|
|
Big x0;
|
|
if (RNG==NULL) x0=rand(get_modulus());
|
|
else x0=strong_rand(RNG,get_modulus());
|
|
|
|
while (!w.g.set(x0,x0)) x0+=1;
|
|
w.g*=(*cof);
|
|
}
|
|
|
|
Big PFC::hash_to_aes_key(const GT& w)
|
|
{
|
|
Big m=pow((Big)2,S);
|
|
return H2(w.g)%m;
|
|
}
|
|
|
|
Big PFC::hash_to_group(char *ID)
|
|
{
|
|
Big m=H1(ID);
|
|
return m%(*ord);
|
|
}
|
|
|
|
GT operator*(const GT& x,const GT& y)
|
|
{
|
|
GT z=x;
|
|
z.g*=y.g;
|
|
return z;
|
|
}
|
|
|
|
GT operator/(const GT& x,const GT& y)
|
|
{
|
|
GT z=x;
|
|
z.g*=conj(y.g); // elements in GT are unitary
|
|
return z;
|
|
}
|
|
|
|
//
|
|
// spill precomputation on GT to byte array
|
|
//
|
|
|
|
int GT::spill(char *& bytes)
|
|
{
|
|
int i,j,n=(1<<WINDOW_SIZE);
|
|
int bytes_per_big=(MIRACL/8)*(get_mip()->nib-1);
|
|
int len=n*2*bytes_per_big+1;
|
|
Big x,y;
|
|
|
|
if (etable==NULL) return 0;
|
|
|
|
bytes=new char[len];
|
|
for (i=j=0;i<n;i++)
|
|
{
|
|
etable[i].get(x,y);
|
|
to_binary(x,bytes_per_big,&bytes[j],TRUE);
|
|
j+=bytes_per_big;
|
|
to_binary(y,bytes_per_big,&bytes[j],TRUE);
|
|
j+=bytes_per_big;
|
|
}
|
|
bytes[j]=etbits;
|
|
delete [] etable;
|
|
etable=NULL;
|
|
return len;
|
|
}
|
|
|
|
//
|
|
// restore precomputation for GT from byte array
|
|
//
|
|
|
|
void GT::restore(char *bytes)
|
|
{
|
|
int i,j,n=(1<<WINDOW_SIZE);
|
|
int bytes_per_big=(MIRACL/8)*(get_mip()->nib-1);
|
|
// int len=n*2*bytes_per_big;
|
|
Big x,y;
|
|
if (etable!=NULL) return;
|
|
|
|
etable=new ZZn2[1<<WINDOW_SIZE];
|
|
for (i=j=0;i<n;i++)
|
|
{
|
|
x=from_binary(bytes_per_big,&bytes[j]);
|
|
j+=bytes_per_big;
|
|
y=from_binary(bytes_per_big,&bytes[j]);
|
|
j+=bytes_per_big;
|
|
etable[i].set(x,y);
|
|
}
|
|
etbits=bytes[j];
|
|
delete [] bytes;
|
|
}
|
|
|
|
//
|
|
// spill precomputation on G1 to byte array
|
|
//
|
|
|
|
int G1::spill(char *& bytes)
|
|
{
|
|
int i,j,n=(1<<WINDOW_SIZE);
|
|
int bytes_per_big=(MIRACL/8)*(get_mip()->nib-1);
|
|
int len=n*2*bytes_per_big+1;
|
|
Big x,y;
|
|
|
|
if (mtable==NULL) return 0;
|
|
|
|
bytes=new char[len];
|
|
for (i=j=0;i<n;i++)
|
|
{
|
|
mtable[i].get(x,y);
|
|
to_binary(x,bytes_per_big,&bytes[j],TRUE);
|
|
j+=bytes_per_big;
|
|
to_binary(y,bytes_per_big,&bytes[j],TRUE);
|
|
j+=bytes_per_big;
|
|
}
|
|
bytes[j]=mtbits;
|
|
delete [] mtable;
|
|
mtable=NULL;
|
|
return len;
|
|
}
|
|
|
|
//
|
|
// restore precomputation for G1 from byte array
|
|
//
|
|
|
|
void G1::restore(char *bytes)
|
|
{
|
|
int i,j,n=(1<<WINDOW_SIZE);
|
|
int bytes_per_big=(MIRACL/8)*(get_mip()->nib-1);
|
|
// int len=n*2*bytes_per_big;
|
|
Big x,y;
|
|
if (mtable!=NULL) return;
|
|
|
|
mtable=new ECn[1<<WINDOW_SIZE];
|
|
for (i=j=0;i<n;i++)
|
|
{
|
|
x=from_binary(bytes_per_big,&bytes[j]);
|
|
j+=bytes_per_big;
|
|
y=from_binary(bytes_per_big,&bytes[j]);
|
|
j+=bytes_per_big;
|
|
mtable[i].set(x,y);
|
|
}
|
|
mtbits=bytes[j];
|
|
delete [] bytes;
|
|
}
|
|
|
|
G1 operator+(const G1& x,const G1& y)
|
|
{
|
|
G1 z=x;
|
|
z.g+=y.g;
|
|
return z;
|
|
}
|
|
|
|
G1 operator-(const G1& x)
|
|
{
|
|
G1 z=x;
|
|
z.g=-z.g;
|
|
return z;
|
|
}
|
|
|
|
BOOL PFC::member(const GT& z)
|
|
{
|
|
ZZn2 r=z.g;
|
|
|
|
if (pow(r,*ord)!=(ZZn2)1) return FALSE;
|
|
|
|
return TRUE;
|
|
}
|
|
|
|
GT PFC::pairing(const G1& x,const G1& y)
|
|
{
|
|
GT z;
|
|
z=miller_loop(x,y);
|
|
z=final_exp(z);
|
|
return z;
|
|
}
|
|
|
|
GT PFC::multi_pairing(int n,G1 **y,G1 **x)
|
|
{
|
|
GT z;
|
|
z=multi_miller(n,y,x);
|
|
z=final_exp(z);
|
|
return z;
|
|
|
|
}
|
|
|
|
int PFC::precomp_for_mult(G1& w,BOOL small)
|
|
{
|
|
ECn v=w.g;
|
|
int i,j,k,bp,is,t;
|
|
if (small) t=MR_ROUNDUP(2*S,WINDOW_SIZE);
|
|
else t=MR_ROUNDUP(bits(*ord),WINDOW_SIZE);
|
|
w.mtable=new ECn[1<<WINDOW_SIZE];
|
|
w.mtable[1]=v;
|
|
w.mtbits=t;
|
|
for (j=0;j<t;j++)
|
|
v+=v;
|
|
k=1;
|
|
for (i=2;i<(1<<WINDOW_SIZE);i++)
|
|
{
|
|
if (i==(1<<k))
|
|
{
|
|
k++;
|
|
normalise(v);
|
|
w.mtable[i]=v;
|
|
for (j=0;j<t;j++)
|
|
v+=v;
|
|
continue;
|
|
}
|
|
bp=1;
|
|
for (j=0;j<k;j++)
|
|
{
|
|
if (i&bp)
|
|
{
|
|
is=1<<j;
|
|
w.mtable[i]+=w.mtable[is];
|
|
}
|
|
bp<<=1;
|
|
}
|
|
normalise(w.mtable[i]);
|
|
}
|
|
return (1<<WINDOW_SIZE);
|
|
}
|
|
|
|
int PFC::precomp_for_power(GT& w,BOOL small)
|
|
{
|
|
ZZn2 v=w.g;
|
|
int i,j,k,bp,is,t;
|
|
if (small) t=MR_ROUNDUP(2*S,WINDOW_SIZE);
|
|
else t=MR_ROUNDUP(bits(*ord),WINDOW_SIZE);
|
|
w.etable=new ZZn2[1<<WINDOW_SIZE];
|
|
w.etable[0]=1;
|
|
w.etable[1]=v;
|
|
w.etbits=t;
|
|
for (j=0;j<t;j++)
|
|
v*=v;
|
|
k=1;
|
|
|
|
for (i=2;i<(1<<WINDOW_SIZE);i++)
|
|
{
|
|
if (i==(1<<k))
|
|
{
|
|
k++;
|
|
w.etable[i]=v;
|
|
for (j=0;j<t;j++)
|
|
v*=v;
|
|
continue;
|
|
}
|
|
bp=1;
|
|
w.etable[i]=1;
|
|
for (j=0;j<k;j++)
|
|
{
|
|
if (i&bp)
|
|
{
|
|
is=1<<j;
|
|
w.etable[i]*=w.etable[is];
|
|
}
|
|
bp<<=1;
|
|
}
|
|
}
|
|
return (1<<WINDOW_SIZE);
|
|
}
|