mirror of
https://github.com/mii443/Weil-Pairing.git
synced 2025-08-22 16:35:30 +00:00
Update Miller.cpp
This commit is contained in:
paul-wu
317
Miller.cpp
317
Miller.cpp
@ -1,7 +1,6 @@
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#include"elliptic.h"
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FPOINT * newfpoint(int x, int y)
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FPOINT * newfpoint(lint x, lint y)
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{
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FPOINT * result = (FPOINT *)malloc(sizeof(fpoint));
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result->x = x;
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@ -9,7 +8,7 @@ FPOINT * newfpoint(int x, int y)
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return result;
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}
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POINT * newpoint(int a, int b, int c, int d)
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POINT * newpoint(lint a, lint b, lint c, lint d)
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{
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POINT * result = (POINT *)malloc(sizeof(point));
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result->x = newfpoint(a,b);
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@ -17,7 +16,7 @@ POINT * newpoint(int a, int b, int c, int d)
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return result;
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}
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CURVE * newcurve(int A, int B)
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CURVE * newcurve(lint A, lint B)
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{
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CURVE * result = (CURVE *)malloc(sizeof(curve));
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result->A = newfpoint(0,A);
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@ -33,30 +32,30 @@ void freepoint(POINT * a)
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}
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//absolute value modulo p
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int ABS(int a, int p)
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lint ABS(lint a, lint p)
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{
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return (a>=0)?a%p:(p-(-a)%p)%p;
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}
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//extended euclid algorithm
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int gcdEx(int a, int b, int *x, int *y)
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lint gcdEx(lint a, lint b, lint *x, lint *y)
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{
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if(b==0){
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*x = 1,*y = 0;
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return a;
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}
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else{
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int r = gcdEx(b, a%b, x, y);
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int t = *x;
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lint r = gcdEx(b, a%b, x, y);
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lint t = *x;
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*x = *y;
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*y = t - a/b * *y;
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return r;
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}
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}
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int powermod(int a, int n, int p)
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lint powermod(lint a, lint n, lint p)
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{
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int result, DB;
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lint result, DB;
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result = 1;
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DB = a;
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@ -71,29 +70,29 @@ int powermod(int a, int n, int p)
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}
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//modulo inverse
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int inver(int a, int p)
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lint inver(lint a, lint p)
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{
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int s,t;
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lint s,t;
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if(gcdEx(a,p,&s,&t)!=1)return 0;
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return ABS(s,p);
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}
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int randomnonq(int p)
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lint randomnonq(lint p)
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{
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int i, k = (p-1)>>1;
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lint i, k = (p-1)>>1;
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for(i = 1;i < p;i++){
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if(powermod(i,k,p) != 1)break;
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}
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return i;
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}
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int modsquareroot(int a, int p)
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lint modsquareroot(lint a, lint p)
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{
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if(powermod(a,(p-1)>>1,p) != 1)return -1;
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int r = (p-1)>>1;
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int b = randomnonq(p);
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int x = r, y = 0;
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lint r = (p-1)>>1;
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lint b = randomnonq(p);
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lint x = r, y = 0;
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while(!(x&1)){
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x >>= 1; y >>= 1;
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@ -103,17 +102,21 @@ int modsquareroot(int a, int p)
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return ABS(powermod(a,(x+1)>>1,p)*powermod(b,y>>1,p),p);
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}
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bool millerrabin(int n, int r)
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bool millerrabin(lint n, lint r)
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{
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int s = 0, t = n - 1;
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if(n <= 1)return false;
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lint s = 0, t = n - 1;
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while(!(t&1)){
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s++; t >>= 1;
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}
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while(r--){
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int b = rand()%(n-1) + 2;
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int r0 = powermod(b,t,n);
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int s0 = s - 1;
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lint b = rand()%(n-1) + 2;
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lint r0 = powermod(b,t,n);
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lint s0 = s - 1;
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lint c = powermod(b,n-1,n);
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if(r0 == 1 || r0 == n - 1)continue;
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if(s0 < 1)return false;
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@ -127,19 +130,28 @@ bool millerrabin(int n, int r)
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return true;
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}
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int largerandom(int n)
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lint largerandom(lint n)
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{
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int a = rand()%10000, b = rand()%10000;
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lint a = rand()%10000, b = rand()%10000;
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return (a+b*10000)%n;
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}
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int randomgoodprime(int n)
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lint randomgoodprime(lint n)
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{
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int p = 4;
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lint p = 4;
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while(!millerrabin(p,10))p = 12*largerandom(n)+11;
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return p;
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}
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lint randonsafeprime(lint n)
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{
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lint p;
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while(p = randomgoodprime(n)){
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if(millerrabin((p+1)/12,2))break;
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}
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return p;
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}
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//field element equlity judgement
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bool equl(FPOINT * a, FPOINT * b)
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{
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@ -147,7 +159,7 @@ bool equl(FPOINT * a, FPOINT * b)
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return false;
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}
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bool equln(FPOINT * a, FPOINT * b, int p)
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bool equln(FPOINT * a, FPOINT * b, lint p)
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{
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if(a->x == ABS(-b->x,p)&&a->y == ABS(-b->y,p))return true;
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return false;
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@ -160,10 +172,10 @@ bool pequl(POINT * a, POINT * b)
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void showelement(FPOINT * p)
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{
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printf("(%d,%d)\n",p->x,p->y);
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printf("(%lld,%lld)\n",p->x,p->y);
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}
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FPOINT * fneg(FPOINT * a, int p, FPOINT * result)
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FPOINT * fneg(FPOINT * a, lint p, FPOINT * result)
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{
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result->x = ABS(-a->x,p);
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result->y = ABS(-a->y,p);
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@ -172,10 +184,10 @@ FPOINT * fneg(FPOINT * a, int p, FPOINT * result)
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}
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//field elements addition
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FPOINT * fadd(FPOINT * a, FPOINT * b, int p, FPOINT * result)
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FPOINT * fadd(FPOINT * a, FPOINT * b, lint p, FPOINT * result)
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{
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int x = ABS(a->x + b->x,p);
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int y = ABS(a->y + b->y,p);
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lint x = ABS(a->x + b->x,p);
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lint y = ABS(a->y + b->y,p);
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result->x = x;
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result->y = y;
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@ -184,10 +196,10 @@ FPOINT * fadd(FPOINT * a, FPOINT * b, int p, FPOINT * result)
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}
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//field elements minus
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FPOINT * fminus(FPOINT * a, FPOINT * b, int p, FPOINT * result)
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FPOINT * fminus(FPOINT * a, FPOINT * b, lint p, FPOINT * result)
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{
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int x = ABS(a->x - b->x,p);
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int y = ABS(a->y - b->y,p);
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lint x = ABS(a->x - b->x,p);
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lint y = ABS(a->y - b->y,p);
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result->x = x;
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result->y = y;
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@ -196,10 +208,10 @@ FPOINT * fminus(FPOINT * a, FPOINT * b, int p, FPOINT * result)
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}
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//field elements multiplication
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FPOINT * fmulti(FPOINT * a, FPOINT * b, int p, FPOINT * result)
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FPOINT * fmulti(FPOINT * a, FPOINT * b, lint p, FPOINT * result)
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{
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int x = ABS(a->y*b->x + a->x*b->y,p);
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int y = ABS(a->y*b->y - a->x*b->x,p);
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lint x = ABS(a->y*b->x + a->x*b->y,p);
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lint y = ABS(a->y*b->y - a->x*b->x,p);
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result->x = x;
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result->y = y;
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@ -217,7 +229,7 @@ FPOINT * assign(FPOINT * a, FPOINT * b)
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//field element expontinal
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FPOINT * fpower(FPOINT * a, int n, int p, FPOINT * result)
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FPOINT * fpower(FPOINT * a, lint n, lint p, FPOINT * result)
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{
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n = n%(p*p - 1);
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@ -238,7 +250,7 @@ FPOINT * fpower(FPOINT * a, int n, int p, FPOINT * result)
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}
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//field element inverse
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FPOINT * inverse(FPOINT * a, int p, FPOINT * result)
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FPOINT * inverse(FPOINT * a, lint p, FPOINT * result)
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{
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if(a->x == 0){
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result->x = 0;
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@ -246,8 +258,8 @@ FPOINT * inverse(FPOINT * a, int p, FPOINT * result)
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return result;
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}
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int x = inver(ABS(-a->y*a->y*inver(a->x,p)-a->x,p),p);
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int y = ABS(-a->y*inver(a->x,p)*x,p);
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lint x = inver(ABS(-a->y*a->y*inver(a->x,p)-a->x,p),p);
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lint y = ABS(-a->y*inver(a->x,p)*x,p);
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result->x = x;
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result->y = y;
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@ -256,7 +268,7 @@ FPOINT * inverse(FPOINT * a, int p, FPOINT * result)
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}
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//multiply by number
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FPOINT * fnmulti(FPOINT * a, int b, int p, FPOINT * result)
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FPOINT * fnmulti(FPOINT * a, lint b, lint p, FPOINT * result)
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{
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result->x = ABS(a->x*b,p);
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result->y = ABS(a->y*b,p);
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@ -270,7 +282,7 @@ POINT * passign(POINT * a, POINT * b)
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return a;
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}
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bool testpoint(POINT * p, CURVE * c, int p1)
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bool testpoint(POINT * p, CURVE * c, lint p1)
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{
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if(pequl(p,O))return true;
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@ -288,10 +300,10 @@ bool testpoint(POINT * p, CURVE * c, int p1)
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void showpoint(POINT * p)
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{
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printf("\n[(%d,%d),(%d,%d)]\n",p->x->x,p->x->y,p->y->x,p->y->y);
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printf("\n[(%lld,%lld),(%lld,%lld)]\n",p->x->x,p->x->y,p->y->x,p->y->y);
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}
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POINT * pneg(POINT * a, int p, POINT * result)
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POINT * pneg(POINT * a, lint p, POINT * result)
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{
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if(pequl(a,O)){
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passign(result,O);
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@ -303,8 +315,8 @@ POINT * pneg(POINT * a, int p, POINT * result)
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return result;
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}
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//curve point additon
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POINT * add(POINT * p1, POINT * p2, CURVE * c, int p, POINT * result)
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//curve polint additon
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POINT * add(POINT * p1, POINT * p2, CURVE * c, lint p, POINT * result)
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{
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if(pequl(p1,O))return passign(result,p2);
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@ -341,7 +353,7 @@ POINT * add(POINT * p1, POINT * p2, CURVE * c, int p, POINT * result)
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return result;
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}
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POINT * minus(POINT * p1, POINT * p2, CURVE * c, int p, POINT * result)
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POINT * minus(POINT * p1, POINT * p2, CURVE * c, lint p, POINT * result)
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{
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POINT * temp = newpoint(0,0,0,0);
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add(pneg(p2,p,temp),p1,c,p,result);
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@ -352,7 +364,7 @@ POINT * minus(POINT * p1, POINT * p2, CURVE * c, int p, POINT * result)
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}
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//power of points addition
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POINT * ppower(POINT * a, int n, CURVE * c, int p, POINT * result)
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POINT * ppower(POINT * a, lint n, CURVE * c, lint p, POINT * result)
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{
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POINT * DB;
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@ -372,15 +384,15 @@ POINT * ppower(POINT * a, int n, CURVE * c, int p, POINT * result)
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return result;
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}
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POINT * randompoint(CURVE * c, int p)
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POINT * randompoint(CURVE * c, lint p)
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{
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POINT * result = newpoint(0,0,0,0);
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int x, y;
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lint x, y;
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if((p-1)%3 && equl(c->A,ZERO)){
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y = largerandom(p);
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int r = inver(3,p-1);
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lint r = inver(3,p-1);
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x = powermod(y*y-1, r, p);
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}else{
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@ -398,9 +410,9 @@ POINT * randompoint(CURVE * c, int p)
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return result;
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}
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FPOINT * primitroot(int p)
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FPOINT * primitroot(lint p)
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{
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int x, y;
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lint x, y;
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y = inver(2,p);
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@ -414,15 +426,25 @@ FPOINT * primitroot(int p)
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return newfpoint(x,ABS(-y,p));
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}
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POINT * phi(POINT * a, int p, POINT * result)
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POINT * phi(POINT * a, lint p, POINT * result)
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{
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fmulti(a->x,primitroot(p),p,result->x);
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if(pequl(a,O)){
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passign(result,a);
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return result;
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}
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FPOINT * temp = primitroot(p);
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fmulti(a->x,temp,p,result->x);
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assign(result->y, a->y);
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free(temp);
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return result;
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}
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FPOINT * evalueline(POINT * a, POINT * b, POINT * in, int p, CURVE * c, FPOINT * result)
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FPOINT * evalueline(POINT * a, POINT * b, POINT * in, lint p, CURVE * c, FPOINT * result)
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{
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FPOINT * temp1, *temp2;
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@ -446,15 +468,41 @@ FPOINT * evalueline(POINT * a, POINT * b, POINT * in, int p, CURVE * c, FPOINT *
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return result;
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}
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bool miller(POINT * a, POINT * b, CURVE * c, int m, int p, FPOINT * f)
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bool evaluelinedivi(POINT * a, POINT * b, POINT * in, CURVE * c, lint p, FPOINT * result)
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{
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FPOINT * temp = newfpoint(0,0);
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POINT * t = newpoint(0,0,0,0), * tp = newpoint(0,0,0,0);
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POINT * tp = newpoint(0,0,0,0), * tp1 = newpoint(0,0,0,0);
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assign(result,ONE);
|
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add(a,b,c,p,tp);
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fmulti(result,evalueline(a,b,in,p,c,temp),p,result);
|
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if(equl(result,ZERO)){
|
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free(temp); freepoint(tp); freepoint(tp1);
|
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return false;
|
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}
|
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|
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evalueline(tp,pneg(tp,p,tp1),in,p,c,temp);
|
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if(equl(temp,ZERO)){
|
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free(temp); freepoint(tp); freepoint(tp1);
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return false;
|
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}
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|
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fmulti(inverse(temp,p,temp),result,p,result);
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free(temp); freepoint(tp); freepoint(tp1);
|
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|
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return true;
|
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}
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|
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bool miller(POINT * a, POINT * b, CURVE * c, lint m, lint p, FPOINT * f)
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{
|
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FPOINT * temp = newfpoint(0,0);
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POINT * t = newpoint(0,0,0,0);
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assign(f,ONE);
|
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passign(t,a);
|
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int i = 0, array[(int)logb((double)m)+1];
|
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lint i = 0, array[(int)logb((double)m)+1];
|
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|
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while(m){
|
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if(m&1)array[i] = 1;
|
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@ -464,22 +512,99 @@ bool miller(POINT * a, POINT * b, CURVE * c, int m, int p, FPOINT * f)
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i++;
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}
|
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|
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for(int j = i - 1;j > 0; j--){
|
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fmulti(f,f,p,f); fmulti(f,evalueline(t,t,b,p,c,temp),p,f);
|
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if(equl(f,ZERO))return false;
|
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add(t,t,c,p,t);
|
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evalueline(t,pneg(t,p,tp),b,p,c,temp);
|
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if(equl(temp,ZERO))return false;
|
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fmulti(inverse(temp,p,temp),f,p,f);
|
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for(lint j = i - 1;j > 1; j--){
|
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fmulti(f,f,p,f);
|
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if(!evaluelinedivi(t,t,b,c,p,temp)){
|
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free(temp); freepoint(t);
|
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return false;
|
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}
|
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fmulti(f,temp,p,f);
|
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add(t,t,c,p,t); // double point t
|
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if(array[i] == 1){
|
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fmulti(f,evalueline(t,a,b,p,c,temp),p,f);
|
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if(equl(f,ZERO))return false;
|
||||
if(!evaluelinedivi(t,a,b,c,p,temp)){
|
||||
free(temp); freepoint(t);
|
||||
return false;
|
||||
}
|
||||
fmulti(f,temp,p,f);
|
||||
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);
|
||||
}
|
||||
}
|
||||
|
||||
free(temp); freepoint(t);
|
||||
|
||||
return true;
|
||||
}
|
||||
|
||||
//the following function works only for supersingular elliptic curve
|
||||
lint findorder(POINT * po, CURVE * c, lint p)
|
||||
{
|
||||
POINT * t = newpoint(0,0,0,0);
|
||||
lint m = (p+1)/12;
|
||||
lint list[6] = {1,2,3,4,6,12};
|
||||
|
||||
for(int i = 0;i < 12;i++){
|
||||
passign(t, po);
|
||||
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)){
|
||||
freepoint(t);
|
||||
return m*list[i%6];
|
||||
}
|
||||
}
|
||||
|
||||
freepoint(t);
|
||||
|
||||
return p+1;
|
||||
}
|
||||
|
||||
bool weilpairing(POINT * a, POINT * b, CURVE * c, lint p, FPOINT * result)
|
||||
{
|
||||
lint m = findorder(a,c,p);
|
||||
lint n = findorder(b,c,p);
|
||||
|
||||
FPOINT * t1, * t2, * t3, *t4;
|
||||
t1 = newfpoint(0,0); t2 = newfpoint(0,0); t3 = newfpoint(0,0); t4 = newfpoint(0,0);
|
||||
|
||||
|
||||
if(n%m == 0)m = n;
|
||||
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);
|
||||
|
||||
if(!miller(a,add(S,b,c,p,temp),c,n,p,t1))continue;
|
||||
if(!miller(a,S,c,n,p,t2))continue;
|
||||
if(!miller(b,minus(a,S,c,p,temp),c,n,p,t3))continue;
|
||||
if(!miller(b,pneg(S,p,temp),c,m,p,t4))continue;
|
||||
|
||||
assign(result,t1); fmulti(result,t4,p,result);
|
||||
fmulti(result,inverse(t2,p,t3),p,result);
|
||||
fmulti(result,inverse(t3,p,result),p,result);
|
||||
|
||||
if(!evaluelinedivi(minus(a,S,c,p,temp),pneg(S,p,temp1),add(S,b,c,p,temp2),c,p,t1))continue;
|
||||
if(!evaluelinedivi(minus(a,S,c,p,temp),pneg(S,p,temp1),S,c,p,t2))continue;
|
||||
if(!evaluelinedivi(add(S,b,c,p,temp),S,minus(a,S,c,p,temp2),c,p,t3))continue;
|
||||
if(!evaluelinedivi(add(S,b,c,p,temp),S,pneg(S,p,temp2),c,p,t4))continue;
|
||||
|
||||
fpower(t1,n,p,t1); fpower(t2,n,p,t2); fpower(t3,n,p,t3); fpower(t4,n,p,t4);
|
||||
inverse(result,p,result);
|
||||
|
||||
assign(result,t1); fmulti(result,t4,p,result);
|
||||
fmulti(result,inverse(t2,p,t3),p,result);
|
||||
fmulti(result,inverse(t3,p,result),p,result);
|
||||
|
||||
break;
|
||||
}
|
||||
|
||||
free(t1); free(t2); free(t3); free(t4);
|
||||
|
||||
freepoint(S); freepoint(temp); freepoint(temp1); freepoint(temp2);
|
||||
|
||||
return true;
|
||||
}
|
||||
|
||||
@ -494,7 +619,7 @@ void init()
|
||||
int main()
|
||||
{
|
||||
init();
|
||||
int p=23;
|
||||
lint p=46523;
|
||||
FPOINT * test = newfpoint(0,14);
|
||||
FPOINT * test1;
|
||||
|
||||
@ -504,51 +629,31 @@ int main()
|
||||
|
||||
//add(P,P,c,p,P);
|
||||
|
||||
P1 = randompoint(c,p);//newpoint(0,2,0,7);
|
||||
P2 = randompoint(c,p);//newpoint(0,16,0,125);
|
||||
P1 = newpoint(0,654,0,21925);
|
||||
P2 = newpoint(0,12416,0,39871);
|
||||
|
||||
miller(P1,P2,c,10,p,test);
|
||||
showelement(primitroot(p));
|
||||
|
||||
showelement(test);
|
||||
//phi(P2,p,P2);
|
||||
//phi(P1,p,P1);
|
||||
|
||||
//passign(P2,P1);
|
||||
|
||||
showpoint(P1);
|
||||
showpoint(P2);
|
||||
|
||||
ppower(P1,9,c,p,temp);
|
||||
ppower(P1,2,c,p,P2);
|
||||
|
||||
showpoint(temp);
|
||||
if(weilpairing(P1,P2,c,p,test))showelement(test);
|
||||
else
|
||||
printf("fail!\n");
|
||||
|
||||
phi(temp,p,temp);
|
||||
printf("%d\n",testpoint(P1,c,p));
|
||||
printf("%d\n",testpoint(P2,c,p));
|
||||
|
||||
showpoint(temp);
|
||||
//minus(P,P,c,p,P);
|
||||
|
||||
//pneg(P,p,P);
|
||||
|
||||
//passign(P,O);
|
||||
|
||||
printf("%d\n",testpoint(temp,c,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;
|
||||
}
|
||||
|
||||
|
||||
Reference in New Issue
Block a user