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Update Miller.cpp

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paul-wu
2015-05-16 20:49:07 +08:00
parent 5d7d256b6f
commit fa42268a0b
1 changed files with 63 additions and 55 deletions
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118
Miller.cpp
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@ -448,6 +448,13 @@ POINT * phi(POINT * a, lint p, POINT * result)
FPOINT * evalueline(POINT * a, POINT * b, POINT * in, lint p, CURVE * c, FPOINT * result)
{
if(pequl(a,O)&&pequl(b,O)){
assign(result,ONE);
return result;
}
if(pequl(a,O))pneg(b,p,a);
if(pequl(b,O))pneg(a,p,b);
FPOINT * temp1, *temp2;
temp1 = newfpoint(0,0); temp2 = newfpoint(0,0);
@ -480,34 +487,44 @@ FPOINT * evalueline(POINT * a, POINT * b, POINT * in, lint p, CURVE * c, FPOINT
return result;
}
bool evaluelinedivi(POINT * a, POINT * b, POINT * in, CURVE * c, lint p, FPOINT * result)
char * pointasstring(POINT * p)
{
char * result = (char *)malloc(sizeof(50));
sprintf(result,"[(%lld,%lld),(%lld,%lld)]",p->x->x,p->x->y,p->y->x,p->y->y);
return result;
}
bool evaluelinedivi(POINT * a, POINT * b, POINT * in, CURVE * c, lint p, FPOINT * result)
{
FPOINT * temp = newfpoint(0,0);
POINT * tp = newpoint(0,0,0,0), * tp1 = newpoint(0,0,0,0);
if(pequl(a,O)&&pequl(b,O)){
assign(result,ONE);
return false;
}
if(pequl(a,O))pneg(b,p,a);
if(pequl(b,O))pneg(a,p,b);
add(a,b,c,p,tp);
assign(result,ONE); // result = 1
add(a,b,c,p,tp); // point tp = a + b
fmulti(result,evalueline(a,b,in,p,c,temp),p,result);// result = l(in), where l is the line through a and b
if(equl(result,ZERO)){ // if the result = 0, we can conclude that in is in line l
free(temp); freepoint(tp); freepoint(tp1);
if(equl(tp->x,in->x) || pequl(a,in) || pequl(b,in) || pequl(in,O)){
assign(result,ONE);
return false;
}
evalueline(tp,pneg(tp,p,tp1),in,p,c,temp); // temp = l'(in), where l' is the line through a + b and -(a+b)
if(equl(temp,ZERO)){
free(temp); freepoint(tp); freepoint(tp1);
return false;
if(pequl(tp,O)){
fminus(in->x,a->x,p,result);
}else{
evalueline(a,b,in,p,c,result);
inverse(fminus(in->x, tp->x, p, temp),p,temp);
fmulti(result,temp,p,result);
}
fmulti(inverse(temp,p,temp),result,p,result); // result = result / temp = l(in) / l'(in)
free(temp); freepoint(tp); freepoint(tp1);
return true;
}
bool miller(POINT * a, POINT * b, CURVE * c, lint m, lint p, FPOINT * f)
bool miller(POINT * a, POINT * b, CURVE * c, lint p, lint m, FPOINT * f)
{
FPOINT * temp = newfpoint(0,0);
POINT * t = newpoint(0,0,0,0);
@ -525,7 +542,7 @@ bool miller(POINT * a, POINT * b, CURVE * c, lint m, lint p, FPOINT * f)
i++;
}
for(lint j = i - 1;j >= 1; j--){
for(lint j = i - 2;j >= 0; j--){
fmulti(f,f,p,f); // f = f*f
if(!evaluelinedivi(t,t,b,c,p,temp)){ // temp = l(b) / l'(b) where l is the targent line of t at curve c, and l' is the line through 2t and -2t
free(temp); freepoint(t);
@ -533,12 +550,14 @@ bool miller(POINT * a, POINT * b, CURVE * c, lint m, lint p, FPOINT * f)
}
fmulti(f,temp,p,f); // f = f * l(b) / l'(b)
add(t,t,c,p,t); // t = 2t
if(array[j] == 1){
if(!evaluelinedivi(t,a,b,c,p,temp)){ // l is the line through t and a, l' throug t+a and -(t+a)
free(temp); freepoint(t);
return false;
}
fmulti(f,temp,p,f); // f = temp * f
add(t,a,c,p,t); // t = a + t
}
}
@ -560,7 +579,7 @@ lint findorder(POINT * po, CURVE * c, lint p)
if(i<6 && pequl(ppower(t,list[i],c,p,t),O)){
freepoint(t);
return list[i];
}else if(pequl(ppower(t,m*list[i%6],c,p,t),O)){
}else if(i >= 6 && pequl(ppower(t,m*list[i%6],c,p,t),O)){
freepoint(t);
return m*list[i%6];
}
@ -584,32 +603,25 @@ bool weilpairing(POINT * a, POINT * b, CURVE * c, lint p, FPOINT * result)
else if(m%n == 0)n = m;
else
return false;
POINT * S = newpoint(0,0,0,0), *temp = newpoint(0,0,0,0), *temp1 = newpoint(0,0,0,0), *temp2 = newpoint(0,0,0,0);
while(true){
freepoint(S);
S = randompoint(c,p); // random point on c
//phi(S,p,S);
showpoint(S);
if(!miller(a,add(S,b,c,p,temp),c,n,p,t1))continue; // t1 = f_a(S+b)
if(!miller(a,S,c,n,p,t2))continue; // t2 = f_a(S)
if(!miller(b,minus(a,S,c,p,temp),c,n,p,t3))continue; // t3 = f_b(a-S)
if(!miller(b,pneg(S,p,temp),c,m,p,t4))continue; // t4 = f_b(-S)
showpoint(S);
if(rand()%2)phi(S,p,S);
if(!miller(a,add(S,b,c,p,temp),c,p,n,t1))continue; // t1 = f_a(S+b)
if(!miller(a,S,c,p,n,t2))continue; // t2 = f_a(S)
if(!miller(b,minus(a,S,c,p,temp),c,p,n,t3))continue; // t3 = f_b(a-S)
if(!miller(b,pneg(S,p,temp),c,p,n,t4))continue; // t4 = f_b(-S)
assign(result,t1); fmulti(result,t4,p,result); // result = f_a(S+b) * f_b(-S)
fmulti(result,inverse(t2,p,t1),p,result); // result = f_a(S+b) * f_b(-S) / f_a(S)
fmulti(result,inverse(t3,p,t1),p,result); // result = f_a(S+b) * f_b(-S) / f_a(S) * f_b(a-S)
// l through a and -S, l' through a - 2S and 2S - a, evaluation at S + b
if(!evaluelinedivi(a,pneg(S,p,temp1),add(S,b,c,p,temp2),c,p,t1))continue;
@ -646,6 +658,8 @@ bool weilpairing(POINT * a, POINT * b, CURVE * c, lint p, FPOINT * result)
return true;
}
void init()
{
ONE = newfpoint(0,1);
@ -654,45 +668,39 @@ void init()
srand((int)time(0));
}
int main()
{
init();
lint p=11;
lint p=48611;
FPOINT * test = newfpoint(0,14);
FPOINT * test1;
CURVE * c = newcurve(0,1);
POINT * P1, * P2, * temp = newpoint(0,0,0,0);
POINT * P1, * P2, * P3, * temp = newpoint(0,0,0,0);
//add(P,P,c,p,P);
P1 = newpoint(0,0,0,1);
P2 = newpoint(0,9,0,2);
P1 = newpoint(0,35994,0,12884); //8
P2 = newpoint(0,28328,0,38900); //8
P3 = newpoint(0,41736,0,26322); //
showelement(primitroot(p));
showpoint(P1);showpoint(P2);showpoint(P3);
//phi(P2,p,P2);
//phi(P2,p,P1);
phi(P2,p,temp);
weilpairing(P1,P1,c,p,test);showelement(test);
weilpairing(P1,temp,c,p,test);showelement(test);
weilpairing(P2,temp,c,p,test);showelement(test);
weilpairing(add(P1,P2,c,p,P3),temp,c,p,test);showelement(test);
showpoint(P1);
showpoint(P2);
printf("%lld\n",findorder(P3,c,p));
//ppower(P1,2,c,p,P2);
printf("%lld\n",findorder(P1));
if(weilpairing(P1,P1,c,p,test))showelement(test);
else
printf("fail!\n");
fpower(test,6,p,test);showelement(test);
printf("%d\n",findorder(P1,c,p));
printf("%d\n",findorder(P2,c,p));
//pneg(P,p,P);
//passign(P,O);
//showelement(fpower(test,8,p,test));
return 0;
}