miracl大数库 miracl大数库 miracl大数库

				//
				// cl /O2 /GX blsk12.cpp zzn12.cpp zzn6a.cpp zzn2.cpp zzn.cpp ecn2.cpp ecn.cpp big.cpp ms32.lib
				// Program to generate Barreto-Lynn-Scott k=12 rho=1.5 curves for use by ake12s.cpp
				//
				
				#include 
				#include "big.h"
				#include "ecn.h"
				#include "ecn2.h"
				#include "zzn12.h"
				
				using namespace std;
				
				Miracl precision=100;
				
				//
				// Hash functions
				// 
				
				#define HASH_LEN 32
				
				
				Big H1(char *string)
				{ // Hash a zero-terminated string to a number < modulus
				    Big h,p;
				    char s[HASH_LEN];
				    int i,j; 
				    sha256 sh;
				
				    shs256_init(&sh);
				
				    for (i=0;;i++)
				    {
				        if (string[i]==0) break;
				        shs256_process(&sh,string[i]);
				    }
				    shs256_hash(&sh,s);
				    p=get_modulus();
				    h=1; j=0; i=1;
				    forever
				    {
				        h*=256; 
				        if (j==HASH_LEN)  {h+=i++; j=0;}
				        else         h+=s[j++];
				        if (h>=p) break;
				    }
				    h%=p;
				    return h;
				}
				
				
				int main()
				{
				    int ns,twist;
				    int sign;
				    BOOL ontwist;
				    Big cof,r,m1,m2,n,p,t,x,cube,y,b,eta,w,cf[4];
				    Big PP,TT,FF;
				    miracl*mip=&precision;
				    ECn P;
				    ECn2 Q;
				    ZZn2 x2,y2,xi;
				    ZZn12 X,Y;
				    ZZn6 A,B;
				    
				//    mip->IOBASE=16;
				
				    x=pow((Big)2,62)+pow((Big)2,59);  // x is this size to get right size for t, p and n
				                                        // x is low hamming weight
				    mip->IOBASE=16;
				    sign=1;  // 1= positive, 2=negative for +/- x solutions
				    ns=1;
				    forever
				    {
				        forever
				        {
				     //       sign=3-sign;   // always looking for +ve x solutions.
				            if (sign==1) x+=1;
				          
				            if (sign==1) p=243*pow(x,6)+324*pow(x,5)+135*pow(x,4)+18*pow(x,3)+3*x*x+3*x+1;
				            else         p=243*pow(x,6)-324*pow(x,5)+135*pow(x,4)-18*pow(x,3)+3*x*x-3*x+1;
				
				            if (p%8==1) continue;
				            if (p%9==1) continue;
				            if (p%6!=1) continue;   // check congruence conditions
				            if (p%8==7 && (p%5==1 || p%5==4)) continue;
				   
				            if (!prime(p)) continue;
				            modulo(p);
				
				            if (p%8==5) xi.set(0,1);
				            if (p%8==3) xi.set(1,1);
				            if (p%8==7) xi.set(2,1);
				            if (pow(xi,(p-1)/2)==1) continue;
				            if (pow(xi,(p-1)/3)==1) continue;  // make sure that x^6+c is irreducible
				
				            if (sign==1) t=3*x+2;
							else         t=-3*x+2;
							n=p+1-t;
							if (sign==1) r=81*pow(x,4)+108*pow(x,3)+45*x*x+6*x+1;
							else         r=81*pow(x,4)-108*pow(x,3)+45*x*x-6*x+1;
				
							if (prime(r))  break;
				
				        }     
				        
				        cof=n/r;
				
				        cf[3]=3*x*x;
				        cf[2]=9*x*x*x+3*x*x;
				        cf[1]=36*x*x*x*x+18*x*x*x;
				        cf[0]=81*x*x*x*x*x+81*x*x*x*x+18*x*x*x+1;
				
				// find number of points on sextic twist..
				
				        TT=t*t-2*p;
				        PP=p*p;
				
				        FF=sqrt((4*PP-TT*TT)/3);
				
				        m1=PP+1-(-3*FF+TT)/2;  // 2 possibilities...
				        m2=PP+1-(3*FF+TT)/2;
				
				        if (m2%n==0)
				        {
				            cout 				            exit(0);
				        }
				
				
				        b=0;
				        forever
				        {
				            b+=1;
				            ecurve(0,b,p,MR_AFFINE);
				            while (!P.set(rand(p))) ;
				            if ((n*P).iszero()) break; // wrong curve
				        }
				
				        P*=cof;
				
				        mip->TWIST=TRUE;
				        while (!Q.set(randn2())) ;
				
				        ontwist=FALSE;
				        if ((m1*Q).iszero()) 
				        {
				            Q*=m1/r;
				            ontwist=TRUE;  
				            twist=1;
				        }
				        else if ((m2*Q).iszero())
				        {
				            Q*=(m2/r);
				//            ontwist=TRUE;  // always wrong order!
				            twist=2;
				        }
				        
				        if (!ontwist) continue;
				
				        if (!(r*Q).iszero())
				        {
				            cout 				            exit(0);
				        }
				
				        Q.get(x2,y2);
				        A.set((ZZn2)0,x2,(ZZn2)0);
				        B.set((ZZn2)0,y2,(ZZn2)0);
				        X.set(A); Y.set((ZZn6)0,B);
				
				        if (Y*Y!=X*X*X +(ZZn12)b) continue;
				
				        cout 				        cout 				        cout 				        cout 				        cout 				        if (sign==1) cout 				        else         cout 				        cout 				        cout 				        cout 				        cout 				        cout 				        cout 				        cout 				        cout 				        cout 				        cout 				        cout 				        cout 				        cout 				        cout 				        cout 				        cout 				        cout 				        cout 				        ns++;
				
				        if (ns==50) break;
				    }
				    return 0;
				}