1790 lines
32 KiB
C++
1790 lines
32 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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*
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* kss_pair.cpp
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*
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* KSS curve, ate pairing embedding degree 18, ideal for security level AES-192
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*
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* Irreducible polynomial is of the form x^18+2
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* Provides high level interface to pairing functions
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*
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* GT=pairing(G2,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, and G2 is a point over an extension field of degree 3
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* GT is a finite field point over the 18-th extension, where 18 is the embedding degree.
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*
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*/
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#define MR_PAIRING_KSS
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#include "pairing_3.h"
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// KSS curve parameters x,A,B
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// irreducible poly is x^18+2
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static char param[]= "15000000007004210";
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static char curveB[]="2";
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// Non-Residue. Irreducible Poly is binomial x^18-NR
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#define NR -2
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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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// Note - this representation depends on p-1=12 mod 18
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void set_frobenius_constant(ZZn &X)
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{ // Note X=NR^[(p-13)/18];
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Big p=get_modulus();
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X=pow((ZZn)NR,(p-13)/18);
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}
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ZZn18 Frobenius(const ZZn18& W,ZZn& X,int n)
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{
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int i;
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ZZn18 V=W;
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for (i=0;i<n;i++)
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V.powq(X);
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return V;
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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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{
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ZZn6 u;
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ZZn18 v=x.g;
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ZZn3 h,l;
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Big a;
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ZZn xx[6];
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int i,j,m;
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v.get(u);
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u.get(l,h);
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l.get(xx[0],xx[1],xx[2]);
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h.get(xx[3],xx[4],xx[5]);
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for (i=0;i<6;i++)
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{
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a=(Big)xx[i];
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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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}
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void PFC::add_to_hash(const G2& x)
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{
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ZZn3 X,Y;
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ECn3 v=x.g;
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Big a;
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ZZn xx[6];
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int i,m;
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v.get(X,Y);
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X.get(xx[0],xx[1],xx[2]);
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Y.get(xx[3],xx[4],xx[5]);
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for (i=0;i<6;i++)
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{
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a=(Big)xx[i];
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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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}
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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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void PFC::add_to_hash(char *x)
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{
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int i=0;
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while (x[i]!=0)
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{
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shs256_process(&SH,x[i]);
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i++;
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}
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}
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Big H2(ZZn18 x)
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{ // Compress and hash an Fp18 to a big number
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sha256 sh;
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ZZn6 u;
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ZZn3 h,l;
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Big a,hash;
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ZZn xx[6];
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char s[HASH_LEN];
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int i,j,m;
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shs256_init(&sh);
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x.get(u); // compress to single ZZn6
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u.get(l,h);
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l.get(xx[0],xx[1],xx[2]);
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h.get(xx[3],xx[4],xx[5]);
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for (i=0;i<6;i++)
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{
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a=(Big)xx[i];
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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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shs256_hash(&sh,s);
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hash=from_binary(HASH_LEN,s);
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return hash;
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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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//
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// This calculates p.A quickly using Frobenius
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// 1. Extract A(x,y) from twisted curve to point on curve over full extension, as X=i^2.x and Y=i^3.y
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// where i=NR^(1/k)
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// 2. Using Frobenius calculate (X^p,Y^p)
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// 3. map back to twisted curve
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// Here we simplify things by doing whole calculation on the twisted curve
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//
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// Note we have to be careful as in detail it depends on w where p=w mod k
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// In this case w=13
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//
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ECn3 psi(ECn3 &A,ZZn &W,int n)
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{
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int i;
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ECn3 R;
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ZZn3 X,Y;
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ZZn FF;
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// Fast multiplication of A by q^n
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A.get(X,Y);
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FF=NR*W*W;
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for (i=0;i<n;i++)
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{ // assumes p=13 mod 18
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X.powq(); X=tx(FF*X);
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Y.powq(); Y*=(ZZn)get_mip()->sru;
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}
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R.set(X,Y);
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return R;
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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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ZZn18 line(ECn3& A,ECn3& C,ZZn3& slope,ZZn& Qx,ZZn& Qy)
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{
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ZZn18 w;
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ZZn6 nn,dd;
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ZZn3 X,Y;
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A.get(X,Y);
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nn.set(Qy,Y-slope*X);
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dd.set(slope*Qx);
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w.set(nn,dd);
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//cout << "1. w= " << w << endl;
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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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ZZn18 g(ECn3& A,ECn3& B,ZZn& Qx,ZZn& Qy)
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{
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ZZn3 lam;
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ZZn18 r;
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ECn3 P=A;
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// Evaluate line from A
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A.add(B,lam);
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if (A.iszero()) return (ZZn18)1;
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r=line(P,A,lam,Qx,Qy);
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return r;
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}
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// if multiples of G2 can be precalculated, its a lot faster!
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ZZn18 gp(ZZn3* ptable,int &j,ZZn& Px,ZZn& Py)
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{
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ZZn18 w;
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ZZn6 nn,dd;
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nn.set(Py,ptable[j+1]);
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dd.set(ptable[j]*Px);
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j+=2;
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w.set(nn,dd);
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//cout << "2. w= " << w << endl;
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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(G2& w,char *& bytes)
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{
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int i,j,len,m;
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int bytes_per_big=(MIRACL/8)*(get_mip()->nib-1);
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Big n;
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Big X=*x;
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ZZn a,b,c;
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if (w.ptable==NULL) return 0;
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n=X/7;
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m=2*(bits(n)+ham(n)+1);
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len=m*3*bytes_per_big;
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bytes=new char[len];
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for (i=j=0;i<m;i++)
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{
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w.ptable[i].get(a,b,c);
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to_binary(a,bytes_per_big,&bytes[j],TRUE);
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j+=bytes_per_big;
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to_binary(b,bytes_per_big,&bytes[j],TRUE);
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j+=bytes_per_big;
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to_binary(c,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,G2& w)
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{
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int i,j,len,m;
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int bytes_per_big=(MIRACL/8)*(get_mip()->nib-1);
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Big n;
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Big X=*x;
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ZZn a,b,c;
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if (w.ptable!=NULL) return;
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n=X/7;
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m=2*(bits(n)+ham(n)+1);
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len=m*3*bytes_per_big;
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w.ptable=new ZZn3[m];
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for (i=j=0;i<m;i++)
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{
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a=from_binary(bytes_per_big,&bytes[j]);
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j+=bytes_per_big;
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b=from_binary(bytes_per_big,&bytes[j]);
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j+=bytes_per_big;
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c=from_binary(bytes_per_big,&bytes[j]);
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j+=bytes_per_big;
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w.ptable[i].set(a,b,c);
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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 G2 table for pairing
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int PFC::precomp_for_pairing(G2& w)
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{
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int i,j,nb,len;
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ECn3 A,m2A,dA,Q,B;
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ZZn3 lam,x1,y1;
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Big n;
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Big X=*x;
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A=w.g;
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B=A;
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n=(X/7);
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nb=bits(n);
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j=0;
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len=2*(nb+ham(n)+1);
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w.ptable=new ZZn3[len];
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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,lam);
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Q.get(x1,y1);
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w.ptable[j++]=lam; w.ptable[j++]=y1-lam*x1;
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if (bit(n,i)==1)
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{
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Q=A;
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A.add(B,lam);
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Q.get(x1,y1);
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w.ptable[j++]=lam; w.ptable[j++]=y1-lam*x1;
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}
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}
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dA=A;
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Q=A;
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A.add(A,lam);
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Q.get(x1,y1);
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w.ptable[j++]=lam; w.ptable[j++]=y1-lam*x1;
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m2A=A;
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Q=A;
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A.add(dA,lam);
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Q.get(x1,y1);
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w.ptable[j++]=lam; w.ptable[j++]=y1-lam*x1;
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A=psi(A,*frob,6);
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Q=A;
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A.add(m2A,lam);
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Q.get(x1,y1);
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w.ptable[j++]=lam; w.ptable[j++]=y1-lam*x1;
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return len;
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}
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GT PFC::multi_miller(int n,G2** 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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ECn3 *Q,*A,*A2;
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ECn P;
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ZZn18 res,rd;
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Big m;
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Big X=*x;
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Px=new ZZn[n];
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Py=new ZZn[n];
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Q=new ECn3[n];
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A=new ECn3[n];
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A2=new ECn3[n];
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k=new int[n];
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m=X/7;
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nb=bits(m);
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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;
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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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{
|
|
res*=res;
|
|
for (j=0;j<n;j++)
|
|
{
|
|
if (QQ[j]->ptable==NULL)
|
|
res*=g(A[j],A[j],Px[j],Py[j]);
|
|
else
|
|
res*=gp(QQ[j]->ptable,k[j],Px[j],Py[j]);
|
|
}
|
|
if (bit(m,i)==1)
|
|
for (j=0;j<n;j++)
|
|
{
|
|
if (QQ[j]->ptable==NULL)
|
|
res*=g(A[j],Q[j],Px[j],Py[j]);
|
|
else
|
|
res*=gp(QQ[j]->ptable,k[j],Px[j],Py[j]);
|
|
}
|
|
if (res.iszero()) return 0;
|
|
}
|
|
|
|
rd=res;
|
|
res*=res;
|
|
|
|
for (j=0;j<n;j++)
|
|
{
|
|
|
|
if (QQ[j]->ptable==NULL)
|
|
{
|
|
Q[j]=A[j];
|
|
res*=g(A[j],A[j],Px[j],Py[j]);
|
|
}
|
|
else res*=gp(QQ[j]->ptable,k[j],Px[j],Py[j]);
|
|
}
|
|
|
|
rd*=res;
|
|
|
|
for (j=0;j<n;j++)
|
|
{
|
|
|
|
if (QQ[j]->ptable==NULL)
|
|
{
|
|
A2[j]=A[j];
|
|
rd*=g(A[j],Q[j],Px[j],Py[j]);
|
|
}
|
|
else rd*=gp(QQ[j]->ptable,k[j],Px[j],Py[j]);
|
|
}
|
|
|
|
res*=Frobenius(rd,*frob,6);
|
|
|
|
for (j=0;j<n;j++)
|
|
{
|
|
if (QQ[j]->ptable==NULL)
|
|
{
|
|
A[j]=psi(A[j],*frob,6);
|
|
res*=g(A[j],A2[j],Px[j],Py[j]);
|
|
}
|
|
else
|
|
res*=gp(QQ[j]->ptable,k[j],Px[j],Py[j]);
|
|
}
|
|
|
|
delete [] k;
|
|
delete [] A2;
|
|
delete [] A;
|
|
delete [] Q;
|
|
delete [] Py;
|
|
delete [] Px;
|
|
|
|
z.g=res;
|
|
return z;
|
|
}
|
|
|
|
//
|
|
// R-ate Pairing G2 x G1 -> GT
|
|
//
|
|
// P is a point of order q in G1. Q(x,y) is a point of order q in G2.
|
|
// Note that Q is a point on the sextic twist of the curve over Fp^3, P(x,y) is a point on the
|
|
// curve over the base field Fp
|
|
//
|
|
|
|
GT PFC::miller_loop(const G2& QQ,const G1& PP)
|
|
{
|
|
GT z;
|
|
Big n;
|
|
int i,j,nb,nbw,nzs;
|
|
ECn3 A,m2A,Q;
|
|
ECn P;
|
|
ZZn Px,Py;
|
|
BOOL precomp;
|
|
ZZn18 r,rd;
|
|
Big X=*x;
|
|
|
|
Q=QQ.g; P=PP.g;
|
|
|
|
precomp=FALSE;
|
|
if (QQ.ptable!=NULL) precomp=TRUE;
|
|
|
|
normalise(P);
|
|
extract(P,Px,Py);
|
|
|
|
A=Q;
|
|
n=(X/7);
|
|
|
|
nb=bits(n);
|
|
r=1; j=0;
|
|
r.mark_as_miller();
|
|
for (i=nb-2;i>=0;i--)
|
|
{
|
|
r*=r;
|
|
if (precomp) r*=gp(QQ.ptable,j,Px,Py);
|
|
else r*=g(A,A,Px,Py);
|
|
if (bit(n,i))
|
|
{
|
|
if (precomp) r*=gp(QQ.ptable,j,Px,Py);
|
|
else r*=g(A,Q,Px,Py);
|
|
}
|
|
}
|
|
|
|
rd=r;
|
|
r*=r;
|
|
|
|
Q=A;
|
|
if (precomp) r*=gp(QQ.ptable,j,Px,Py);
|
|
else r*=g(A,A,Px,Py);
|
|
|
|
rd*=r;
|
|
|
|
m2A=A;
|
|
if (precomp) rd*=gp(QQ.ptable,j,Px,Py);
|
|
else rd*=g(A,Q,Px,Py);
|
|
|
|
r*=Frobenius(rd,*frob,6);
|
|
if (precomp) r*=gp(QQ.ptable,j,Px,Py);
|
|
else
|
|
{
|
|
A=psi(A,*frob,6);
|
|
r*=g(A,m2A,Px,Py);
|
|
}
|
|
|
|
z.g=r;
|
|
return z;
|
|
}
|
|
|
|
// Automatically generated by Luis Dominquez
|
|
|
|
ZZn18 HardExpo(ZZn18 &f3x0, ZZn &X, Big &x){
|
|
//vector=[ 3, 5, 7, 14, 15, 21, 25, 35, 49, 54, 62, 70, 87, 98, 112, 245, 273, 319, 343, 434, 450, 581, 609, 784, 931, 1407, 1911, 4802, 6517 ]
|
|
ZZn18 xA;
|
|
ZZn18 xB;
|
|
ZZn18 t0;
|
|
ZZn18 t1;
|
|
ZZn18 t2;
|
|
ZZn18 t3;
|
|
ZZn18 t4;
|
|
ZZn18 t5;
|
|
ZZn18 t6;
|
|
ZZn18 t7;
|
|
ZZn18 f3x1;
|
|
ZZn18 f3x2;
|
|
ZZn18 f3x3;
|
|
ZZn18 f3x4;
|
|
ZZn18 f3x5;
|
|
ZZn18 f3x6;
|
|
ZZn18 f3x7;
|
|
|
|
f3x1=pow(f3x0,x);
|
|
f3x2=pow(f3x1,x);
|
|
f3x3=pow(f3x2,x);
|
|
f3x4=pow(f3x3,x);
|
|
f3x5=pow(f3x4,x);
|
|
f3x6=pow(f3x5,x);
|
|
f3x7=pow(f3x6,x);
|
|
|
|
xA=Frobenius(inverse(f3x1),X,2);
|
|
xB=Frobenius(inverse(f3x0),X,2);
|
|
t0=xA*xB;
|
|
xB=Frobenius(inverse(f3x2),X,2);
|
|
t1=t0*xB;
|
|
t0=t0*t0;
|
|
xB=Frobenius(inverse(f3x0),X,2);
|
|
t0=t0*xB;
|
|
xB=Frobenius(f3x1,X,1);
|
|
t0=t0*xB;
|
|
xA=Frobenius(inverse(f3x5),X,2)*Frobenius(f3x4,X,4)*Frobenius(f3x2,X,5);
|
|
//xB=Frobenius(f3x1,X,1);
|
|
t5=xA*xB;
|
|
t0=t0*t0;
|
|
t3=t0*t1;
|
|
xA=Frobenius(inverse(f3x4),X,2)*Frobenius(f3x1,X,5);
|
|
xB=Frobenius(f3x2,X,1);
|
|
t1=xA*xB;
|
|
xA=xB;//Frobenius(f3x2,X,1);
|
|
xB=xA; //xB=Frobenius(f3x2,X,1);
|
|
t0=xA*xB;
|
|
xB=Frobenius(f3x2,X,4);
|
|
t0=t0*xB;
|
|
xB=Frobenius(f3x1,X,4);
|
|
t2=t3*xB;
|
|
xB=Frobenius(inverse(f3x1),X,2);
|
|
t4=t3*xB;
|
|
t2=t2*t2;
|
|
xB=Frobenius(inverse(f3x2),X,3);
|
|
t3=t0*xB;
|
|
xB=inverse(f3x2);
|
|
t0=t3*xB;
|
|
t4=t3*t4;
|
|
xB=Frobenius(inverse(f3x3),X,3);
|
|
t0=t0*xB;
|
|
t3=t0*t2;
|
|
xB=Frobenius(inverse(f3x3),X,2)*Frobenius(f3x0,X,5);
|
|
t2=t3*xB;
|
|
t3=t3*t5;
|
|
t5=t3*t2;
|
|
xB=inverse(f3x3);
|
|
t2=t2*xB;
|
|
xA=Frobenius(inverse(f3x6),X,3);
|
|
//xB=inverse(f3x3);
|
|
t3=xA*xB;
|
|
t2=t2*t2;
|
|
t4=t2*t4;
|
|
xB=Frobenius(f3x3,X,1);
|
|
t2=t1*xB;
|
|
xA=xB; //xA=Frobenius(f3x3,X,1);
|
|
xB=Frobenius(inverse(f3x2),X,3);
|
|
t1=xA*xB;
|
|
t6=t2*t4;
|
|
xB=Frobenius(f3x4,X,1);
|
|
t4=t2*xB;
|
|
xB=Frobenius(f3x3,X,4);
|
|
t2=t6*xB;
|
|
xB=Frobenius(inverse(f3x5),X,3)*Frobenius(f3x5,X,4);
|
|
t7=t6*xB;
|
|
t4=t2*t4;
|
|
xB=Frobenius(f3x6,X,1);
|
|
t2=t2*xB;
|
|
t4=t4*t4;
|
|
t4=t4*t5;
|
|
xA=inverse(f3x4);
|
|
xB=Frobenius(inverse(f3x4),X,3);
|
|
t5=xA*xB;
|
|
// xB=Frobenius(inverse(f3x4),X,3);
|
|
t3=t3*xB;
|
|
xA=Frobenius(f3x5,X,1);
|
|
xB=xA; //xB=Frobenius(f3x5,X,1);
|
|
t6=xA*xB;
|
|
t7=t6*t7;
|
|
xB=Frobenius(f3x0,X,3);
|
|
t6=t5*xB;
|
|
t4=t6*t4;
|
|
xB=Frobenius(inverse(f3x7),X,3);
|
|
t6=t6*xB;
|
|
t0=t4*t0;
|
|
xB=Frobenius(f3x6,X,4);
|
|
t4=t4*xB;
|
|
t0=t0*t0;
|
|
xB=inverse(f3x5);
|
|
t0=t0*xB;
|
|
t1=t7*t1;
|
|
t4=t4*t7;
|
|
t1=t1*t1;
|
|
t2=t1*t2;
|
|
t1=t0*t3;
|
|
xB=Frobenius(inverse(f3x3),X,3);
|
|
t0=t1*xB;
|
|
t1=t1*t6;
|
|
t0=t0*t0;
|
|
t0=t0*t5;
|
|
xB=inverse(f3x6);
|
|
t2=t2*xB;
|
|
t2=t2*t2;
|
|
t2=t2*t4;
|
|
t0=t0*t0;
|
|
t0=t0*t3;
|
|
t1=t2*t1;
|
|
t0=t1*t0;
|
|
// xB=inverse(f3x6);
|
|
t1=t1*xB;
|
|
t0=t0*t0;
|
|
t0=t0*t2;
|
|
xB=f3x0*inverse(f3x7);
|
|
t0=t0*xB;
|
|
// xB=f3x0*inverse(f3x7);
|
|
t1=t1*xB;
|
|
t0=t0*t0;
|
|
t0=t0*t1;
|
|
|
|
return t0;
|
|
}
|
|
|
|
GT PFC::final_exp(const GT& z)
|
|
{
|
|
GT y;
|
|
ZZn18 rd,r=z.g;
|
|
rd=r;
|
|
Big X=*x;
|
|
|
|
// final exponentiation
|
|
r.conj();
|
|
r/=rd; // r^(p^9-1)
|
|
r.mark_as_regular(); // no longer "miller"
|
|
rd=r;
|
|
r.powq(*frob); r.powq(*frob); r.powq(*frob); r*=rd; //r^(p^3+1)
|
|
|
|
r.mark_as_unitary();
|
|
r=HardExpo(r,*frob,X);
|
|
|
|
y.g=r;
|
|
return y;
|
|
|
|
}
|
|
|
|
PFC::PFC(int s, csprng *rng)
|
|
{
|
|
int i,j,mod_bits,words;
|
|
if (s!=192)
|
|
{
|
|
cout << "No suitable curve available" << endl;
|
|
exit(0);
|
|
}
|
|
|
|
mod_bits=(8*s)/3;
|
|
|
|
if (mod_bits%MIRACL==0)
|
|
words=(mod_bits/MIRACL);
|
|
else
|
|
words=(mod_bits/MIRACL)+1;
|
|
|
|
#ifdef MR_SIMPLE_BASE
|
|
miracl *mip=mirsys((MIRACL/4)*words,16);
|
|
#else
|
|
miracl *mip=mirsys(words,0);
|
|
mip->IOBASE=16;
|
|
#endif
|
|
|
|
|
|
B=new Big;
|
|
x=new Big;
|
|
mod=new Big;
|
|
ord=new Big;
|
|
cof=new Big;
|
|
npoints=new Big;
|
|
trace=new Big;
|
|
|
|
for (i=0;i<6;i++)
|
|
{
|
|
WB[i]=new Big;
|
|
for (j=0;j<6;j++)
|
|
{
|
|
BB[i][j]=new Big;
|
|
}
|
|
}
|
|
for (i=0;i<2;i++)
|
|
{
|
|
W[i]=new Big;
|
|
for (j=0;j<2;j++)
|
|
{
|
|
SB[i][j]=new Big;
|
|
}
|
|
}
|
|
|
|
S=s;
|
|
|
|
Beta=new ZZn;
|
|
frob=new ZZn;
|
|
|
|
*B=curveB;
|
|
*x=param;
|
|
|
|
Big X=*x;
|
|
|
|
*trace=(pow(X,4) + 16*X + 7)/7;
|
|
*ord=(pow(X,6) + 37*pow(X,3) + 343)/343;
|
|
|
|
*cof=(49*X*X+245*X+343)/3;
|
|
*npoints=*cof*(*ord);
|
|
*mod=*cof*(*ord)+*trace-1;
|
|
ecurve(0,*B,*mod,MR_PROJECTIVE);
|
|
|
|
Big BBeta=(3*pow(X,7)-7*pow(X,6)+46*pow(X,5)+68*pow(X,4)-308*pow(X,3)+189*X*X+145*X-3192)/56;
|
|
BBeta+=X*(pow(X,7)/28);
|
|
BBeta/=3;
|
|
|
|
Big sru=*mod-BBeta; // sixth root of unity = -Beta
|
|
set_zzn3(NR,sru);
|
|
*Beta=BBeta;
|
|
set_frobenius_constant(*frob);
|
|
|
|
// Use standard Gallant-Lambert-Vanstone endomorphism method for G1
|
|
|
|
*W[0]=(X*X*X)/343; // This is first column of inverse of SB (without division by determinant)
|
|
*W[1]=(18*X*X*X+343)/343;
|
|
|
|
*SB[0][0]=(X*X*X)/343;
|
|
*SB[0][1]=-(18*X*X*X+343)/343;
|
|
*SB[1][0]=(19*X*X*X+343)/343;
|
|
*SB[1][1]=(X*X*X)/343;
|
|
|
|
// Use Galbraith & Scott Homomorphism idea for G2 & GT ... (http://eprint.iacr.org/2008/117.pdf)
|
|
|
|
*WB[0]=5*pow(X,3)/49+2; // This is first column of inverse of BB (without division by determinant)
|
|
*WB[1]=-(X*X)/49;
|
|
*WB[2]=pow(X,4)/49+3*X/7;
|
|
*WB[3]=-(17*pow(X,3)/343+1);
|
|
*WB[4]=-(pow(X,5)/343+2*(X*X)/49);
|
|
*WB[5]=5*pow(X,4)/343+2*X/7;
|
|
|
|
*BB[0][0]=1; *BB[0][1]=0; *BB[0][2]=5*X/7; *BB[0][3]=1; *BB[0][4]=0; *BB[0][5]=-X/7;
|
|
*BB[1][0]=-5*X/7; *BB[1][1]=-2; *BB[1][2]=0; *BB[1][3]=X/7; *BB[1][4]=1; *BB[1][5]=0;
|
|
*BB[2][0]=0; *BB[2][1]=2*X/7; *BB[2][2]=1; *BB[2][3]=0; *BB[2][4]=X/7; *BB[2][5]=0;
|
|
*BB[3][0]=1; *BB[3][1]=0; *BB[3][2]=X; *BB[3][3]=2; *BB[3][4]=0; *BB[3][5]=0;
|
|
*BB[4][0]=-X; *BB[4][1]=-3; *BB[4][2]=0; *BB[4][3]=0; *BB[4][4]=1; *BB[4][5]=0;
|
|
*BB[5][0]=0; *BB[5][1]=-X; *BB[5][2]=-3; *BB[5][3]=0; *BB[5][4]=0; *BB[5][5]=1;
|
|
|
|
mip->TWIST=MR_SEXTIC_D; // map Server to point on twisted curve E(Fp3)
|
|
|
|
RNG=rng;
|
|
}
|
|
|
|
PFC::~PFC()
|
|
{
|
|
int i,j;
|
|
delete B;
|
|
delete x;
|
|
delete mod;
|
|
delete ord;
|
|
delete cof;
|
|
delete npoints;
|
|
delete trace;
|
|
|
|
for (i=0;i<6;i++)
|
|
{
|
|
delete WB[i];
|
|
for (j=0;j<6;j++)
|
|
delete BB[i][j];
|
|
}
|
|
for (i=0;i<2;i++)
|
|
{
|
|
delete W[i];
|
|
for (j=0;j<2;j++)
|
|
delete SB[i][j];
|
|
}
|
|
|
|
delete Beta;
|
|
delete frob;
|
|
mirexit();
|
|
}
|
|
|
|
// GLV method
|
|
|
|
void glv(const Big &e,Big &r,Big *W[2],Big *B[2][2],Big u[2])
|
|
{
|
|
int i,j;
|
|
Big v[2],w;
|
|
for (i=0;i<2;i++)
|
|
{
|
|
v[i]=mad(*W[i],e,(Big)0,r,w);
|
|
u[i]=0;
|
|
}
|
|
u[0]=e;
|
|
for (i=0;i<2;i++)
|
|
for (j=0;j<2;j++)
|
|
u[i]-=v[j]*(*B[j][i]);
|
|
return;
|
|
}
|
|
|
|
// Use Galbraith & Scott Homomorphism idea ...
|
|
|
|
void galscott(const Big &e,Big &r,Big *WB[6],Big *B[6][6],Big u[6])
|
|
{
|
|
int i,j;
|
|
Big v[6],w;
|
|
|
|
for (i=0;i<6;i++)
|
|
{
|
|
v[i]=mad(*WB[i],e,(Big)0,r,w);
|
|
u[i]=0;
|
|
}
|
|
|
|
u[0]=e;
|
|
for (i=0;i<6;i++)
|
|
{
|
|
for (j=0;j<6;j++)
|
|
u[i]-=v[j]*(*B[j][i]);
|
|
}
|
|
return;
|
|
}
|
|
|
|
void endomorph(ECn &A,ZZn &Beta)
|
|
{ // apply endomorphism (x,y) = (Beta*x,y) where Beta is cube root of unity
|
|
ZZn x;
|
|
x=(A.get_point())->X;
|
|
x*=Beta;
|
|
copy(getbig(x),(A.get_point())->X);
|
|
}
|
|
|
|
G1 PFC::mult(const G1& w,const Big& k)
|
|
{
|
|
G1 z;
|
|
ECn Q;
|
|
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
|
|
{
|
|
Big u[2];
|
|
Q=w.g;
|
|
glv(k,*ord,W,SB,u);
|
|
endomorph(Q,*Beta);
|
|
Q=mul(u[0],w.g,u[1],Q);
|
|
z.g=Q;
|
|
}
|
|
return z;
|
|
}
|
|
|
|
// GLV + Galbraith-Scott
|
|
|
|
G2 PFC::mult(const G2& w,const Big& k)
|
|
{
|
|
G2 z;
|
|
int i;
|
|
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
|
|
{
|
|
ECn3 Q[6];
|
|
Big u[6];
|
|
BOOL small=TRUE;
|
|
galscott(k,*ord,WB,BB,u);
|
|
|
|
Q[0]=w.g;
|
|
|
|
for (i=1;i<6;i++)
|
|
{
|
|
if (u[i]!=0)
|
|
{
|
|
small=FALSE;
|
|
break;
|
|
}
|
|
}
|
|
|
|
if (small)
|
|
{
|
|
if (u[0]<0)
|
|
{
|
|
u[0]=-u[0];
|
|
Q[0]=-Q[0];
|
|
}
|
|
z.g=Q[0];
|
|
z.g*=u[0];
|
|
return z;
|
|
}
|
|
|
|
for (i=1;i<6;i++)
|
|
Q[i]=psi(Q[i-1],*frob,1);
|
|
|
|
// deal with -ve multipliers
|
|
for (i=0;i<6;i++)
|
|
{
|
|
if (u[i]<0)
|
|
{u[i]=-u[i];Q[i]=-Q[i];}
|
|
}
|
|
|
|
// simple multi-addition
|
|
z.g= mul(6,Q,u);
|
|
}
|
|
return z;
|
|
}
|
|
|
|
// GLV method + Galbraith-Scott idea
|
|
|
|
GT PFC::power(const GT& w,const Big& k)
|
|
{
|
|
GT z;
|
|
int i;
|
|
if (w.etable!=NULL)
|
|
{ // precomputation is available
|
|
Big e=k;
|
|
if (k<0) e=-e;
|
|
|
|
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];
|
|
}
|
|
if (k<0) z.g=inverse(z.g);
|
|
}
|
|
else
|
|
{
|
|
ZZn18 Y[6];
|
|
Big u[6];
|
|
|
|
galscott(k,*ord,WB,BB,u);
|
|
|
|
Y[0]=w.g;
|
|
for (i=1;i<6;i++)
|
|
{Y[i]=Y[i-1]; Y[i].powq(*frob);}
|
|
|
|
// deal with -ve exponents
|
|
for (i=0;i<6;i++)
|
|
{
|
|
if (u[i]<0)
|
|
{u[i]=-u[i];Y[i].conj();}
|
|
}
|
|
|
|
// simple multi-exponentiation
|
|
z.g= pow(6,Y,u);
|
|
}
|
|
return z;
|
|
}
|
|
|
|
// Faster Hashing to G2 - Fuentes-Castaneda, Knapp and Rodriguez-Henriquez
|
|
|
|
ECn3 HashG2(ECn3& Qx0,Big &x,ZZn&F)
|
|
{
|
|
ECn3 Qx0_;
|
|
ECn3 Qx1;
|
|
ECn3 Qx1_;
|
|
ECn3 Qx2;
|
|
ECn3 Qx2_;
|
|
ECn3 Qx3;
|
|
ECn3 t1;
|
|
ECn3 t2;
|
|
ECn3 t3;
|
|
ECn3 t4;
|
|
ECn3 t5;
|
|
ECn3 t6;
|
|
|
|
Qx0_=-Qx0;
|
|
Qx1=x*Qx0;
|
|
Qx1_=-Qx1;
|
|
Qx2=x*Qx1;
|
|
Qx2_=-Qx2;
|
|
Qx3=x*Qx2;
|
|
|
|
t1=Qx0;
|
|
t2=psi(Qx1_,F,2);
|
|
t3=Qx1+psi(Qx1,F,5);
|
|
t4=psi(Qx1,F,3)+psi(Qx2,F,1)+psi(Qx2_,F,2);
|
|
t5=psi(Qx0_,F,4);
|
|
t6=psi(Qx0,F,1)+psi(Qx0,F,3)+psi(Qx2_,F,4)+psi(Qx2,F,5)+psi(Qx3,F,1);
|
|
|
|
t2+=t1; // Olivos addition sequence
|
|
t1+=t1;
|
|
t1+=t3;
|
|
t1+=t2;
|
|
t4+=t2;
|
|
t5+=t1;
|
|
t4+=t1;
|
|
t5+=t4;
|
|
t4+=t6;
|
|
t5+=t5;
|
|
t5+=t4;
|
|
|
|
return t5;
|
|
}
|
|
|
|
// random group element
|
|
|
|
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);
|
|
}
|
|
|
|
void PFC::hash_and_map(G2& w,char *ID)
|
|
{
|
|
int i;
|
|
ZZn3 XX;
|
|
Big X=*x;
|
|
|
|
Big x0=H1(ID);
|
|
forever
|
|
{
|
|
x0+=1;
|
|
XX.set((ZZn)0,(ZZn)x0,(ZZn)0);
|
|
if (!w.g.set(XX)) continue;
|
|
break;
|
|
}
|
|
w.g=HashG2(w.g,X,*frob);
|
|
}
|
|
|
|
void PFC::random(G2 &w)
|
|
{
|
|
int i;
|
|
ZZn3 XX;
|
|
Big X=*x;
|
|
|
|
Big x0;
|
|
if (RNG==NULL) x0=rand(*mod);
|
|
else x0=strong_rand(RNG,*mod);
|
|
|
|
forever
|
|
{
|
|
x0+=1;
|
|
XX.set((ZZn)0,(ZZn)x0,(ZZn)0);
|
|
if (!w.g.set(X)) continue;
|
|
break;
|
|
}
|
|
|
|
w.g=HashG2(w.g,X,*frob);
|
|
}
|
|
|
|
void PFC::hash_and_map(G1& w,char *ID)
|
|
{
|
|
Big x0=H1(ID);
|
|
while (!w.g.set(x0,x0)) x0+=1;
|
|
w.g*=*cof;
|
|
}
|
|
|
|
void PFC::random(G1& w)
|
|
{
|
|
Big x0;
|
|
if (RNG==NULL) x0=rand(*mod);
|
|
else x0=strong_rand(RNG,*mod);
|
|
|
|
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/=y.g;
|
|
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*18*bytes_per_big+1;
|
|
ZZn6 a,b,c;
|
|
ZZn3 f,s;
|
|
ZZn x,y,z;
|
|
|
|
if (etable==NULL) return 0;
|
|
|
|
bytes=new char[len];
|
|
for (i=j=0;i<n;i++)
|
|
{
|
|
etable[i].get(a,b,c);
|
|
a.get(f,s);
|
|
f.get(x,y,z);
|
|
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;
|
|
to_binary(z,bytes_per_big,&bytes[j],TRUE);
|
|
j+=bytes_per_big;
|
|
s.get(x,y,z);
|
|
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;
|
|
to_binary(z,bytes_per_big,&bytes[j],TRUE);
|
|
j+=bytes_per_big;
|
|
b.get(f,s);
|
|
f.get(x,y,z);
|
|
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;
|
|
to_binary(z,bytes_per_big,&bytes[j],TRUE);
|
|
j+=bytes_per_big;
|
|
|
|
s.get(x,y,z);
|
|
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;
|
|
to_binary(z,bytes_per_big,&bytes[j],TRUE);
|
|
j+=bytes_per_big;
|
|
|
|
c.get(f,s);
|
|
f.get(x,y,z);
|
|
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;
|
|
to_binary(z,bytes_per_big,&bytes[j],TRUE);
|
|
j+=bytes_per_big;
|
|
|
|
s.get(x,y,z);
|
|
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;
|
|
to_binary(z,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*18*bytes_per_big;
|
|
ZZn6 a,b,c;
|
|
ZZn3 f,s;
|
|
ZZn x,y,z;
|
|
if (etable!=NULL) return;
|
|
|
|
etable=new ZZn18[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;
|
|
z=from_binary(bytes_per_big,&bytes[j]);
|
|
j+=bytes_per_big;
|
|
f.set(x,y,z);
|
|
x=from_binary(bytes_per_big,&bytes[j]);
|
|
j+=bytes_per_big;
|
|
y=from_binary(bytes_per_big,&bytes[j]);
|
|
j+=bytes_per_big;
|
|
z=from_binary(bytes_per_big,&bytes[j]);
|
|
j+=bytes_per_big;
|
|
s.set(x,y,z);
|
|
a.set(f,s);
|
|
x=from_binary(bytes_per_big,&bytes[j]);
|
|
j+=bytes_per_big;
|
|
y=from_binary(bytes_per_big,&bytes[j]);
|
|
j+=bytes_per_big;
|
|
z=from_binary(bytes_per_big,&bytes[j]);
|
|
j+=bytes_per_big;
|
|
|
|
f.set(x,y,z);
|
|
x=from_binary(bytes_per_big,&bytes[j]);
|
|
j+=bytes_per_big;
|
|
y=from_binary(bytes_per_big,&bytes[j]);
|
|
j+=bytes_per_big;
|
|
z=from_binary(bytes_per_big,&bytes[j]);
|
|
j+=bytes_per_big;
|
|
|
|
s.set(x,y,z);
|
|
b.set(f,s);
|
|
x=from_binary(bytes_per_big,&bytes[j]);
|
|
j+=bytes_per_big;
|
|
y=from_binary(bytes_per_big,&bytes[j]);
|
|
j+=bytes_per_big;
|
|
z=from_binary(bytes_per_big,&bytes[j]);
|
|
j+=bytes_per_big;
|
|
|
|
f.set(x,y,z);
|
|
x=from_binary(bytes_per_big,&bytes[j]);
|
|
j+=bytes_per_big;
|
|
y=from_binary(bytes_per_big,&bytes[j]);
|
|
j+=bytes_per_big;
|
|
z=from_binary(bytes_per_big,&bytes[j]);
|
|
j+=bytes_per_big;
|
|
|
|
s.set(x,y,z);
|
|
c.set(f,s);
|
|
etable[i].set(a,b,c);
|
|
}
|
|
etbits=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;
|
|
}
|
|
|
|
//
|
|
// 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;
|
|
}
|
|
|
|
|
|
G2 operator+(const G2& x,const G2& y)
|
|
{
|
|
G2 z=x;
|
|
y.g.norm();
|
|
z.g+=y.g;
|
|
return z;
|
|
}
|
|
|
|
G2 operator-(const G2& x)
|
|
{
|
|
G2 z=x;
|
|
z.g=-z.g;
|
|
return z;
|
|
}
|
|
|
|
//
|
|
// spill precomputation on G2 to byte array
|
|
//
|
|
|
|
int G2::spill(char *& bytes)
|
|
{
|
|
int i,j,n=(1<<WINDOW_SIZE);
|
|
int bytes_per_big=(MIRACL/8)*(get_mip()->nib-1);
|
|
int len=n*6*bytes_per_big+1;
|
|
ZZn3 x,y;
|
|
ZZn a,b,c;
|
|
|
|
if (mtable==NULL) return 0;
|
|
|
|
bytes=new char[len];
|
|
for (i=j=0;i<n;i++)
|
|
{
|
|
mtable[i].get(x,y);
|
|
x.get(a,b,c);
|
|
to_binary((Big)a,bytes_per_big,&bytes[j],TRUE);
|
|
j+=bytes_per_big;
|
|
to_binary((Big)b,bytes_per_big,&bytes[j],TRUE);
|
|
j+=bytes_per_big;
|
|
to_binary((Big)c,bytes_per_big,&bytes[j],TRUE);
|
|
j+=bytes_per_big;
|
|
y.get(a,b,c);
|
|
to_binary((Big)a,bytes_per_big,&bytes[j],TRUE);
|
|
j+=bytes_per_big;
|
|
to_binary((Big)b,bytes_per_big,&bytes[j],TRUE);
|
|
j+=bytes_per_big;
|
|
to_binary((Big)c,bytes_per_big,&bytes[j],TRUE);
|
|
j+=bytes_per_big;
|
|
}
|
|
bytes[j]=mtbits;
|
|
delete [] mtable;
|
|
mtable=NULL;
|
|
return len;
|
|
}
|
|
|
|
//
|
|
// restore precomputation for G2 from byte array
|
|
//
|
|
|
|
void G2::restore(char *bytes)
|
|
{
|
|
int i,j,n=(1<<WINDOW_SIZE);
|
|
int bytes_per_big=(MIRACL/8)*(get_mip()->nib-1);
|
|
// int len=n*6*bytes_per_big;
|
|
ZZn3 x,y;
|
|
ZZn a,b,c;
|
|
if (mtable!=NULL) return;
|
|
|
|
mtable=new ECn3[1<<WINDOW_SIZE];
|
|
for (i=j=0;i<n;i++)
|
|
{
|
|
a=from_binary(bytes_per_big,&bytes[j]);
|
|
j+=bytes_per_big;
|
|
b=from_binary(bytes_per_big,&bytes[j]);
|
|
j+=bytes_per_big;
|
|
c=from_binary(bytes_per_big,&bytes[j]);
|
|
j+=bytes_per_big;
|
|
x.set(a,b,c);
|
|
a=from_binary(bytes_per_big,&bytes[j]);
|
|
j+=bytes_per_big;
|
|
b=from_binary(bytes_per_big,&bytes[j]);
|
|
j+=bytes_per_big;
|
|
c=from_binary(bytes_per_big,&bytes[j]);
|
|
j+=bytes_per_big;
|
|
y.set(a,b,c);
|
|
mtable[i].set(x,y);
|
|
}
|
|
mtbits=bytes[j];
|
|
delete [] bytes;
|
|
}
|
|
|
|
|
|
// test if a ZZn18 element is of order q
|
|
// can't think of a faster way to do this..
|
|
|
|
BOOL PFC::member(const GT& z)
|
|
{
|
|
ZZn18 r=z.g;
|
|
if (!r.is_unitary()) return FALSE;
|
|
if (r*conj(r)!=(ZZn18)1) return FALSE; // not unitary
|
|
if (pow(r,*ord)!=(ZZn18)1) return FALSE;
|
|
return TRUE;
|
|
}
|
|
|
|
GT PFC::pairing(const G2& x,const G1& y)
|
|
{
|
|
GT z;
|
|
z=miller_loop(x,y);
|
|
z=final_exp(z);
|
|
return z;
|
|
}
|
|
|
|
GT PFC::multi_pairing(int n,G2 **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_mult(G2& w,BOOL small)
|
|
{
|
|
ECn3 v=w.g;
|
|
ZZn3 x,y;
|
|
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 ECn3[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++;
|
|
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;
|
|
}
|
|
}
|
|
return (1<<WINDOW_SIZE);
|
|
}
|
|
|
|
int PFC::precomp_for_power(GT& w,BOOL small)
|
|
{
|
|
ZZn18 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 ZZn18[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);
|
|
}
|
|
|