382 lines
8.3 KiB
C++
382 lines
8.3 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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* MIRACL C++ Implementation file ZZn12a.cpp
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*
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* AUTHOR : M. Scott
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*
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* PURPOSE : Implementation of class ZZn12 (Arithmetic over n^12)
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*
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* WARNING: This class has been cobbled together for a specific use with
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* the MIRACL library. It is not complete, and may not work in other
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* applications
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*
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*/
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#include "zzn12a.h"
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using namespace std;
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// Frobenius X=x^p. Assumes p=1 mod 6
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ZZn12& ZZn12::powq(const ZZn2& X)
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{
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ZZn2 XX=X*X;
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ZZn2 XXX=XX*X;
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BOOL ku=unitary;
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BOOL km=miller;
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a.powq(XXX); b.powq(XXX); c.powq(XXX);
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b*=X;
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c*=XX;
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unitary=ku;
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miller=km;
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return *this;
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}
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void ZZn12::get(ZZn4& x,ZZn4& y,ZZn4& z) const
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{x=a; y=b; z=c;}
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void ZZn12::get(ZZn4& x) const
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{x=a; }
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void ZZn12::get1(ZZn4& x) const
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{x=b; }
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void ZZn12::get2(ZZn4& x) const
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{x=c; }
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ZZn12& ZZn12::operator*=(const ZZn12& x)
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{ // optimized to reduce constructor/destructor calls
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if (&x==this)
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{
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ZZn4 A,B,C,D;
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if (unitary)
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{ // Granger & Scott PKC 2010 - only 3 squarings!
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A=a; a*=a; D=a; a+=a; a+=D; A.conj(); A+=A; a-=A;
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B=c; B*=B; B=tx(B); D=B; B+=B; B+=D;
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C=b; C*=C; D=C; C+=C; C+=D;
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b.conj(); b+=b; c.conj(); c+=c; c=-c;
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b+=B; c+=C;
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// cout << "unitary" << endl;
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}
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else
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{
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if (!miller)
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{ // Chung-Hasan SQR2
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A=a; A*=A;
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B=b*c; B+=B;
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C=c; C*=C;
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D=a*b; D+=D;
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c+=(a+b); c*=c;
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a=A+tx(B);
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b=D+tx(C);
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c-=(A+B+C+D);
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}
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else
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{
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// Chung-Hasan SQR3 - actually calculate 2x^2 !
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// Slightly dangerous - but works as will be raised to p^{k/2}-1
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// which wipes out the 2.
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A=a; A*=A; // a0^2 = S0
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C=c; C*=b; C+=C; // 2a1.a2 = S3
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D=c; D*=D; // a2^2 = S4
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c+=a; // a0+a2
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B=b; B+=c; B*=B; // (a0+a1+a2)^2 =S1
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c-=b; c*=c; // (a0-a1+a2)^2 =S2
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C+=C; A+=A; D+=D;
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a=A+tx(C);
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b=B-c-C+tx(D);
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c+=B-A-D; // is this code telling me something...?
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/* if you want to play safe!
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c+=B; c/=2;
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B-=c; B-=C;
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c-=A; c-=D;
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a=A+tx(C);
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b=B+tx(D);
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*/
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}
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}
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}
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else
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{ // Karatsuba
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ZZn4 Z0,Z1,Z2,Z3,T0,T1;
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BOOL zero_c,zero_b;
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zero_c=(x.c).iszero();
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zero_b=(x.b).iszero();
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Z0=a*x.a; //9
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if (!zero_b) Z2=b*x.b; //+6
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T0=a+b;
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T1=x.a+x.b;
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Z1=T0*T1; //+9
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Z1-=Z0;
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if (!zero_b) Z1-=Z2;
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T0=b+c;
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T1=x.b+x.c;
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Z3=T0*T1; //+6
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if (!zero_b) Z3-=Z2;
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T0=a+c;
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T1=x.a+x.c;
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T0*=T1; //+9=39 for "special case"
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if (!zero_b) Z2+=T0;
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else Z2=T0;
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Z2-=Z0;
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b=Z1;
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if (!zero_c)
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{ // exploit special form of BN curve line function
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T0=c*x.c;
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Z2-=T0;
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Z3-=T0;
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b+=tx(T0);
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}
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a=Z0+tx(Z3);
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c=Z2;
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if (!x.unitary) unitary=FALSE;
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}
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return *this;
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}
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ZZn12& ZZn12::operator/=(const ZZn4& x)
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{
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*this*=inverse(x);
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unitary=FALSE;
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return *this;
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}
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ZZn12& ZZn12::operator/=(const ZZn12& x)
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{
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*this*=inverse(x);
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if (!x.unitary) unitary=FALSE;
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return *this;
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}
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ZZn12 conj(const ZZn12& x)
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{
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ZZn12 u=x;
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u.conj();
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return u;
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}
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ZZn12 inverse(const ZZn12& w)
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{
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ZZn12 y;
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if (w.unitary)
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{
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y=conj(w);
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return y;
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}
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ZZn4 f0;
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y.a=w.a*w.a-tx(w.b*w.c);
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y.b=tx(w.c*w.c)-w.a*w.b;
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y.c=w.b*w.b-w.a*w.c;
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f0=tx(w.b*y.c)+w.a*y.a+tx(w.c*y.b);
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f0=inverse(f0);
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y.c*=f0;
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y.b*=f0;
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y.a*=f0;
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return y;
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}
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ZZn12 operator+(const ZZn12& x,const ZZn12& y)
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{ZZn12 w=x; w.a+=y.a; w.b+=y.b; w.c+=y.c; return w; }
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ZZn12 operator+(const ZZn12& x,const ZZn4& y)
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{ZZn12 w=x; w.a+=y; return w; }
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ZZn12 operator-(const ZZn12& x,const ZZn12& y)
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{ZZn12 w=x; w.a-=y.a; w.b-=y.b; w.c-=y.c; return w; }
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ZZn12 operator-(const ZZn12& x,const ZZn4& y)
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{ZZn12 w=x; w.a-=y; return w; }
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ZZn12 operator-(const ZZn12& x)
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{ZZn12 w; w.a=-x.a; w.b=-x.b; w.c-=x.c; w.unitary=FALSE; return w; }
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ZZn12 operator*(const ZZn12& x,const ZZn12& y)
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{
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ZZn12 w=x;
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if (&x==&y) w*=w;
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else w*=y;
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return w;
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}
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ZZn12 operator*(const ZZn12& x,const ZZn4& y)
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{ZZn12 w=x; w*=y; return w;}
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ZZn12 operator*(const ZZn4& y,const ZZn12& x)
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{ZZn12 w=x; w*=y; return w;}
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ZZn12 operator*(const ZZn12& x,int y)
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{ZZn12 w=x; w*=y; return w;}
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ZZn12 operator*(int y,const ZZn12& x)
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{ZZn12 w=x; w*=y; return w;}
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ZZn12 operator/(const ZZn12& x,const ZZn12& y)
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{ZZn12 w=x; w/=y; return w;}
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ZZn12 operator/(const ZZn12& x,const ZZn4& y)
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{ZZn12 w=x; w/=y; return w;}
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#ifndef MR_NO_RAND
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ZZn12 randn12(void)
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{ZZn12 w; w.a=randn4(); w.b=randn4(); w.c=randn4(); w.unitary=FALSE; return w;}
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#endif
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ZZn12 tx(const ZZn12& w)
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{
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ZZn12 u=w;
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ZZn4 t=u.a;
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u.a=tx(u.c);
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u.c=u.b;
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u.b=t;
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return u;
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}
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// regular ZZn12 powering
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// If k is low Hamming weight this will be just as good..
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ZZn12 pow(const ZZn12& x,const Big& k)
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{
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int i,nb;
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ZZn12 u=x;
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Big e=k;
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BOOL invert_it=FALSE;
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if (e==0) return (ZZn12)one();
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if (e<0)
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{
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e=-e;
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invert_it=TRUE;
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}
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nb=bits(e);
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if (nb>1) for (i=nb-2;i>=0;i--)
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{
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u*=u;
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if (bit(e,i)) u*=x;
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}
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if (invert_it) u=inverse(u);
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return u;
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}
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// standard MIRACL multi-exponentiation
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#ifndef MR_STATIC
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ZZn12 pow(int n,const ZZn12* x,const Big* b)
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{
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int k,j,i,m,nb,ea;
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ZZn12 *G;
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ZZn12 r;
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m=1<<n;
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G=new ZZn12[m];
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// precomputation
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for (i=0,k=1;i<n;i++)
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{
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for (j=0; j < (1<<i) ;j++)
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{
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if (j==0) G[k]=x[i];
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else G[k]=G[j]*x[i];
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k++;
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}
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}
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nb=0;
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for (j=0;j<n;j++)
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if ((k=bits(b[j]))>nb) nb=k;
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r=1;
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for (i=nb-1;i>=0;i--)
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{
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ea=0;
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k=1;
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for (j=0;j<n;j++)
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{
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if (bit(b[j],i)) ea+=k;
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k<<=1;
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}
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r*=r;
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if (ea!=0) r*=G[ea];
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}
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delete [] G;
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return r;
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}
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#endif
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#ifndef MR_NO_STANDARD_IO
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ostream& operator<<(ostream& s,const ZZn12& xx)
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{
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ZZn12 b=xx;
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ZZn4 x,y,z;
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b.get(x,y,z);
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s << "[" << x << "," << y << "," << z << "]";
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return s;
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}
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#endif
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