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Update Miller.cpp

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paul-wu
2015-05-15 18:13:53 +08:00
parent f53981d178
commit 57e9cc7f13
1 changed files with 250 additions and 17 deletions
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267
Miller.cpp
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@ -17,11 +17,11 @@ POINT * newpoint(int a, int b, int c, int d)
return result;
}
CURVE * newcurve(FPOINT * A, FPOINT * B)
CURVE * newcurve(int A, int B)
{
CURVE * result = (CURVE *)malloc(sizeof(curve));
result->A = A;
result->B = B;
result->A = newfpoint(0,A);
result->B = newfpoint(0,B);
return result;
}
@ -54,6 +54,21 @@ int gcdEx(int a, int b, int *x, int *y)
}
}
int powermod(int a, int n, int p)
{
int result, DB;
result = 1;
DB = a;
while(n>0){
if(n&1)result = (result*DB)%p;
DB = (DB*DB)%p;
n >>= 1;
}
return ABS(result,p);
}
//modulo inverse
int inver(int a, int p)
@ -63,6 +78,68 @@ int inver(int a, int p)
return ABS(s,p);
}
int randomnonq(int p)
{
int i, k = (p-1)>>1;
for(i = 1;i < p;i++){
if(powermod(i,k,p) != 1)break;
}
return i;
}
int modsquareroot(int a, int p)
{
if(powermod(a,(p-1)>>1,p) != 1)return -1;
int r = (p-1)>>1;
int b = randomnonq(p);
int x = r, y = 0;
while(!(x&1)){
x >>= 1; y >>= 1;
if(ABS(powermod(a,x,p)*powermod(b,y,p),p) != 1)y += r;
}
return ABS(powermod(a,(x+1)>>1,p)*powermod(b,y>>1,p),p);
}
bool millerrabin(int n, int r)
{
int s = 0, t = n - 1;
while(!(t&1)){
s++; t >>= 1;
}
while(r--){
int b = rand()%(n-1) + 2;
int r0 = powermod(b,t,n);
int s0 = s - 1;
if(r0 == 1 || r0 == n - 1)continue;
if(s0 < 1)return false;
while(s0--){
r0 = powermod(r0,2,n);
if(r0 == n-1)break;
if(s0 == 0)return false;
}
}
return true;
}
int largerandom(int n)
{
int a = rand()%10000, b = rand()%10000;
return (a+b*10000)%n;
}
int randomgoodprime(int n)
{
int p = 4;
while(!millerrabin(p,10))p = 12*largerandom(n)+11;
return p;
}
//field element equlity judgement
bool equl(FPOINT * a, FPOINT * b)
{
@ -81,6 +158,11 @@ bool pequl(POINT * a, POINT * b)
return equl(a->x,b->x)&&equl(a->y,b->y);
}
void showelement(FPOINT * p)
{
printf("(%d,%d)\n",p->x,p->y);
}
FPOINT * fneg(FPOINT * a, int p, FPOINT * result)
{
result->x = ABS(-a->x,p);
@ -158,6 +240,12 @@ FPOINT * fpower(FPOINT * a, int n, int p, FPOINT * result)
//field element inverse
FPOINT * inverse(FPOINT * a, int p, FPOINT * result)
{
if(a->x == 0){
result->x = 0;
result->y = inver(a->y,p);
return result;
}
int x = inver(ABS(-a->y*a->y*inver(a->x,p)-a->x,p),p);
int y = ABS(-a->y*inver(a->x,p)*x,p);
@ -205,6 +293,10 @@ void showpoint(POINT * p)
POINT * pneg(POINT * a, int p, POINT * result)
{
if(pequl(a,O)){
passign(result,O);
return result;
}
assign(result->x,a->x);
fneg(a->y,p,result->y);
@ -280,42 +372,183 @@ POINT * ppower(POINT * a, int n, CURVE * c, int p, POINT * result)
return result;
}
FPOINT * miller(POINT * a, POINT * b, CURVE * c, int p)
{
FPOINT * result = (FPOINT *)malloc(sizeof(fpoint));
POINT * randompoint(CURVE * c, int p)
{
POINT * result = newpoint(0,0,0,0);
//TODO
int x, y;
if((p-1)%3 && equl(c->A,ZERO)){
y = largerandom(p);
int r = inver(3,p-1);
x = powermod(y*y-1, r, p);
}else{
while(1){
x = largerandom(p);
y = ABS(powermod(x,3,p) + c->A->y*x + c->B->y,p);
if((y=modsquareroot(y,p)) != -1)break;
}
}
result->x = newfpoint(0,x);
result->y = newfpoint(0,y);
return result;
}
int main()
FPOINT * primitroot(int p)
{
int x, y;
y = inver(2,p);
if((x = modsquareroot(-3,p)) != -1){
y = ABS(x*y - y,p);
return newfpoint(0,y);
}
x = modsquareroot(ABS(y*y - y + 1,p),p);
return newfpoint(x,ABS(-y,p));
}
POINT * phi(POINT * a, int p, POINT * result)
{
fmulti(a->x,primitroot(p),p,result->x);
assign(result->y, a->y);
return result;
}
FPOINT * evalueline(POINT * a, POINT * b, POINT * in, int p, CURVE * c, FPOINT * result)
{
FPOINT * temp1, *temp2;
temp1 = newfpoint(0,0); temp2 = newfpoint(0,0);
if(pequl(a,b)){
fadd(fnmulti(fpower(a->x,2,p,temp1),3,p,temp1),c->A,p,temp1);
fminus(in->x,a->x,p,temp2);
fmulti(temp1,temp2,p,result);
fmulti(fnmulti(a->y,2,p,temp1),fminus(in->y,a->y,p,temp2),p,temp1);
fminus(result,temp1,p,result);
}else{
fmulti(fminus(in->x,b->x,p,temp1),fminus(a->y,b->y,p,temp2),p,result);
fmulti(fminus(a->x,b->x,p,temp1),fminus(in->y,b->y,p,temp2),p,temp1);
fminus(result,temp1,p,result);
}
free(temp1); free(temp2);
return result;
}
bool miller(POINT * a, POINT * b, CURVE * c, int m, int p, FPOINT * f)
{
FPOINT * temp = newfpoint(0,0);
POINT * t = newpoint(0,0,0,0), * tp = newpoint(0,0,0,0);
assign(f,ONE);
passign(t,a);
int i = 0, array[(int)logb((double)m)+1];
while(m){
if(m&1)array[i] = 1;
else
array[i] = 0;
m >>= 1;
i++;
}
for(int j = i - 1;j > 0; j--){
fmulti(f,f,p,f); fmulti(f,evalueline(t,t,b,p,c,temp),p,f);
if(equl(f,ZERO))return false;
add(t,t,c,p,t);
evalueline(t,pneg(t,p,tp),b,p,c,temp);
if(equl(temp,ZERO))return false;
fmulti(inverse(temp,p,temp),f,p,f);
if(array[i] == 1){
fmulti(f,evalueline(t,a,b,p,c,temp),p,f);
if(equl(f,ZERO))return false;
add(t,a,c,p,t);
evalueline(t,pneg(t,p,tp),b,p,c,temp);
if(equl(temp,ZERO))return false;
fmulti(inverse(temp,p,temp),f,p,f);
}
}
return true;
}
void init()
{
ONE = newfpoint(0,1);
ZERO = newfpoint(0,0);
O = newpoint(-1,-1,-1,-1);
srand((int)time(0));
}
int main()
{
init();
int p=23;
FPOINT * test = newfpoint(0,14);
FPOINT * test1;
int p=5;
FPOINT * test = newfpoint(0,3);
FPOINT * test1 = newfpoint(0,7);
CURVE * c = newcurve(0,1);
CURVE * c = newcurve(newfpoint(0,0),newfpoint(0,1));
POINT * P = newpoint(0,0,0,1);
POINT * P1, * P2, * temp = newpoint(0,0,0,0);
//add(P,P,c,p,P);
ppower(P,100,c,p,P);
P1 = randompoint(c,p);//newpoint(0,2,0,7);
P2 = randompoint(c,p);//newpoint(0,16,0,125);
miller(P1,P2,c,10,p,test);
showelement(test);
//passign(P2,P1);
showpoint(P1);
showpoint(P2);
ppower(P1,9,c,p,temp);
showpoint(temp);
phi(temp,p,temp);
showpoint(temp);
//minus(P,P,c,p,P);
//pneg(P,p,P);
//passign(P,O);
printf("%d\n",testpoint(P,c,p));
printf("%d\n",testpoint(temp,c,p));
showpoint(P);
//int a = 4;
//showelement(inverse(test,p,test1));
//test1 = primitroot(p);
//showelement(test1);
//fpower(test1,3,p,test1);
//showelement(test1);
//printf("%d\n",inver(14,p));
//printf("%d\n", modsquareroot(a,p));
printf("%d\n",millerrabin(10,10));
return 0;
}