176 lines
3.5 KiB
C++
176 lines
3.5 KiB
C++
//
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// cl /O2 /GX bls24.cpp zzn4.cpp zzn2.cpp zzn.cpp ecn4.cpp ecn.cpp big.cpp miracl.lib
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// Program to generate BLS k=24 pairing friendly curves.
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//
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#include <iostream>
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#include "ecn4.h"
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#include "ecn.h"
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#include "zzn.h"
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Miracl precision(200,0);
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int main()
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{
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miracl *mip=&precision;
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Big s,x,q,p,t,A,B,cf,X,Y,sru,n,best_s,f,tau[5],TAU;
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Big T,P,F,m1,m2,m3,m4;
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BOOL got_one;
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ECn W;
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ECn4 Q;
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ZZn4 XX,YY,r;
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ZZn2 xi;
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int i,ns,sign,best_ham=1000;
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mip->IOBASE=16;
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s=(char *)"E000000000000000";
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ns=1;
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forever
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{
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s+=1;
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for (sign=1;sign<=2;sign++)
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{
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if (sign==1) x=s;
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else x=-s;
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if (x<0 || ham(x)>7) continue; // filter out difficult or poor solutions
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t=1+x;
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p=1+x+x*x-pow(x,4)+2*pow(x,5)-pow(x,6)+pow(x,8)-2*pow(x,9)+pow(x,10);
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q=1-pow(x,4)+pow(x,8);
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if (p%3!=0) continue;
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p/=3;
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if (p%8==1) continue;
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if (!prime(p)) continue;
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if (!prime(q)) continue;
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modulo(p);
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if (p%8==5) xi.set(0,1);
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if (p%8==3) xi.set(1,1);
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if (p%8==7) xi.set(2,1);
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// make sure its irreducible
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if (pow(xi,(p*p-1)/2)==1) {/*cout << "Failed - not a square" << endl; */ continue;}
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if (pow(xi,(p*p-1)/3)==1) {/*cout << "Failed - not a cube" << endl; */ continue;} // make sure that x^6-c is irreducible
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n=p+1-t;
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cf=n/q;
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tau[0]=2; // count points on twist over extension p^4
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tau[1]=t;
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for (i=1;i<4;i++ ) tau[i+1]=t*tau[i]-p*tau[i-1];
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P=p*p*p*p;
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TAU=tau[4];
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F=(4*P-TAU*TAU)/3;
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F=sqrt(F);
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m2=P+1-(3*F+TAU)/2;
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// cout << "m2%q= " << m2%q << endl;
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B=1; // find curve equation
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forever
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{
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B+=1;
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if (B==2)
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{
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X=-1; Y=1;
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}
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else if (B==3)
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{
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X=1; Y=2;
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}
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else if (B==8)
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{
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X=1; Y=3;
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}
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else if (B==15)
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{
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X=1; Y=4;
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}
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else
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{
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do
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{
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X=rand(p);
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Y=sqrt(X*X*X+B,p);
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} while (Y==0);
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}
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ecurve(0,B,p,MR_AFFINE);
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W.set(X,Y);
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W*=cf;
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if ((q*W).iszero()) break;
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}
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mip->TWIST=MR_SEXTIC_M; // is it an M-type twist...?
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do
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{
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r=randn4();
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} while (!Q.set(r));
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got_one=FALSE;
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Q*=(m2/q);
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if ((q*Q).iszero()) got_one=TRUE;
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// cout << "m1*Q= " << m1*Q << endl;
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// cout << "m1%q= " << m1%q << endl;
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else
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{
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mip->TWIST=MR_SEXTIC_D; // no, so it must be D-type.
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do
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{
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r=randn4();
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} while (!Q.set(r));
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Q*=(m2/q);
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if ((q*Q).iszero()) got_one=TRUE;
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}
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if (!got_one) {cout << "Bad twist" << endl; exit(0);} // Huh?
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if (mip->TWIST==MR_SEXTIC_M) continue; // not interested just now
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cout << "solution " << ns << endl;
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cout << "x= " << x << " ham(x)= " << ham(x) << endl;
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cout << "x%72= " << x%72 << endl;
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cout << "p= " << p << " bits(p)= " << bits(p) << endl;
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cout << "q= " << q << " bits(q)= " << bits(q) << endl;
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cout << "n= " << n << endl;
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cout << "t= " << t << endl;
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cout << "cf= " << cf << endl;
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cout << "W= " << W << endl;
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cout << "q*W= " << q*W << endl;
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mip->IOBASE=10;
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cout << "E(Fp): y^2=x^3+" << B << endl;
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cout << "(p-1)%24= " << (p-1)%24 << endl;
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cout << "p%8= " << p%8 << endl;
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mip->IOBASE=16;
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if (mip->TWIST==MR_SEXTIC_M) cout << "Twist type M" << endl;
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if (mip->TWIST==MR_SEXTIC_D) cout << "Twist type D" << endl;
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Q*=q;
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cout << "check - if right twist should be O - q*Q= " << Q << endl;
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if (ham(x)<best_ham) {best_ham=ham(x);best_s=s;}
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cout << "So far minimum hamming weight of x= " << best_ham << endl;
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cout << "for seed= " << best_s << endl;
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cout << endl;
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ns++;
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}
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}
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return 0;
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}
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