Create Miller.cpp

Miller.cpp

@@ -0,0 +1,321 @@
+#include"elliptic.h"
+
+
+FPOINT * newfpoint(int x, int y)
+{
+	FPOINT * result = (FPOINT *)malloc(sizeof(fpoint));
+	result->x = x;
+	result->y = y;
+	return result;
+}
+
+POINT * newpoint(int a, int b, int c, int d)
+{
+	POINT * result = (POINT *)malloc(sizeof(point));
+	result->x = newfpoint(a,b);
+	result->y = newfpoint(c,d);
+	return result;
+}
+
+CURVE * newcurve(FPOINT * A, FPOINT * B)
+{
+	CURVE * result = (CURVE *)malloc(sizeof(curve));
+	result->A = A;
+	result->B = B;
+	
+	return result;
+}
+
+void freepoint(POINT * a)
+{
+	free(a->x);
+	free(a->y);
+}
+
+//absolute value modulo p
+int ABS(int a, int p)
+{
+	return (a>=0)?a%p:(p-(-a)%p)%p;
+}
+
+//extended euclid algorithm
+int gcdEx(int a, int b, int *x, int *y) 
+{
+    if(b==0){
+        *x = 1,*y = 0;
+        return a;
+    }
+    else{
+        int r = gcdEx(b, a%b, x, y);
+        int t = *x;
+        *x = *y;
+        *y = t - a/b * *y;
+        return r;
+    }
+}
+
+
+//modulo inverse
+int inver(int a, int p)
+{
+	int s,t;
+	if(gcdEx(a,p,&s,&t)!=1)return 0;
+	return ABS(s,p);
+}
+
+//field element equlity judgement
+bool equl(FPOINT * a, FPOINT * b)
+{
+	if(a->x == b->x && a->y == b->y)return true;
+	return false;
+}
+
+bool equln(FPOINT * a, FPOINT * b, int p)
+{
+	if(a->x == ABS(-b->x,p)&&a->y == ABS(-b->y,p))return true;
+	return false;
+}
+
+bool pequl(POINT * a, POINT * b)
+{
+	return equl(a->x,b->x)&&equl(a->y,b->y);
+}
+
+FPOINT * fneg(FPOINT * a, int p, FPOINT * result)
+{
+	result->x = ABS(-a->x,p);
+	result->y = ABS(-a->y,p);
+	
+	return result;
+}
+
+//field elements addition
+FPOINT * fadd(FPOINT * a, FPOINT * b, int p, FPOINT * result)
+{
+	int x = ABS(a->x + b->x,p);
+	int y = ABS(a->y + b->y,p);
+	
+	result->x = x;
+	result->y = y;
+	
+	return result;
+}
+
+//field elements minus
+FPOINT * fminus(FPOINT * a, FPOINT * b, int p, FPOINT * result)
+{
+	int x = ABS(a->x - b->x,p);
+	int y = ABS(a->y - b->y,p);
+	
+	result->x = x;
+	result->y = y;
+	
+	return result;
+}
+
+//field elements multiplication
+FPOINT * fmulti(FPOINT * a, FPOINT * b, int p, FPOINT * result)
+{
+	int x = ABS(a->y*b->x + a->x*b->y,p);
+ 	int y = ABS(a->y*b->y - a->x*b->x,p);
+ 	
+ 	result->x = x;
+ 	result->y = y;
+ 	
+	return result;
+}
+
+//field assignment
+FPOINT * assign(FPOINT * a, FPOINT * b)
+{
+	a->x = b->x;
+	a->y = b->y;
+	return a;
+}
+
+
+//field element expontinal
+FPOINT * fpower(FPOINT * a, int n, int p, FPOINT * result)
+{
+	n = n%(p*p - 1);
+	
+	FPOINT * DB = newfpoint(0,0);
+	
+	assign(DB,a);
+	assign(result,ONE);
+
+	while(n > 0){
+		if(n&1)fmulti(DB,result,p,result);
+		fmulti(DB,DB,p,DB);
+		n >>= 1;	
+	}
+	
+	free(DB);
+	
+	return result;
+}
+
+//field element inverse
+FPOINT * inverse(FPOINT * a, int p, FPOINT * 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);
+	
+	result->x = x;
+	result->y = y;
+	
+	return result;
+}
+
+//multiply by number
+FPOINT * fnmulti(FPOINT * a, int b, int p, FPOINT * result)
+{
+	result->x = ABS(a->x*b,p);
+	result->y = ABS(a->y*b,p);
+	return result;
+}
+
+POINT * passign(POINT * a, POINT * b)
+{
+	assign(a->x,b->x);
+	assign(a->y,b->y);
+	return a;
+}
+
+bool testpoint(POINT * p, CURVE * c, int p1)
+{
+	if(pequl(p,O))return true;
+	
+	FPOINT * x = newfpoint(0,0);
+	FPOINT * y = newfpoint(0,0);
+	
+	assign(x,p->x);
+	
+	fadd(fadd(fpower(x,3,p1,x),fmulti(c->A,p->x,p1,y),p1,x),c->B,p1,x);
+	
+	fpower(p->y,2,p1,y);
+	
+	return equl(x,y);
+}
+
+void showpoint(POINT * p)
+{
+	printf("\n[(%d,%d),(%d,%d)]\n",p->x->x,p->x->y,p->y->x,p->y->y);
+}
+
+POINT * pneg(POINT * a, int p, POINT * result)
+{
+	assign(result->x,a->x);
+	fneg(a->y,p,result->y);
+	
+	return result;
+}
+
+//curve point additon
+POINT * add(POINT * p1, POINT * p2, CURVE * c, int p, POINT * result)
+{	
+	if(pequl(p1,O))return passign(result,p2);
+	
+	if(pequl(p2,O))return passign(result,p1);
+	
+	if(equl(p1->x,p2->x)&&equln(p1->y,p2->y,p)){
+		return passign(result,O);	
+	}
+	
+	FPOINT * x, * y, *lambda;
+	
+	x = newfpoint(0,0);
+	y = newfpoint(0,0);
+	lambda = (FPOINT *)malloc(sizeof(fpoint));
+	
+	if(equl(p1->x,p2->x)){
+		fadd(fnmulti(fpower(p1->x,2,p,lambda),3,p,lambda),c->A,p,lambda);
+		fmulti(lambda,inverse(fnmulti(p1->y,2,p,x),p,x),p,lambda);
+	}else{
+		fminus(p2->y,p1->y,p,lambda);
+		fmulti(lambda,inverse(fminus(p2->x,p1->x,p,x),p,x),p,lambda);
+	}
+	
+	fminus(fminus(fpower(lambda,2,p,x),p1->x,p,x),p2->x,p,x);
+	fminus(fmulti(fminus(p1->x,x,p,y),lambda,p,y),p1->y,p,y);
+	
+	assign(result->x,x);
+	assign(result->y,y); 
+	
+	free(lambda);
+	free(x);
+	free(y);
+	
+	return result;
+}
+
+POINT * minus(POINT * p1, POINT * p2, CURVE * c, int p, POINT * result)
+{
+	POINT * temp = newpoint(0,0,0,0);
+	add(pneg(p2,p,temp),p1,c,p,result);
+	
+	freepoint(temp);
+	
+	return result;
+}
+
+//power of points addition
+POINT * ppower(POINT * a, int n, CURVE * c, int p, POINT * result)
+{
+	POINT * DB;
+
+	DB = newpoint(0,0,0,0);
+	
+	passign(DB,a);
+	passign(result,O);
+	
+	while(n > 0){
+		if(n&1)add(DB,result,c,p,result);
+		add(DB,DB,c,p,DB);
+		n >>= 1;
+	}
+	
+	freepoint(DB);
+	
+	return result;
+}
+
+FPOINT * miller(POINT * a, POINT * b, CURVE * c, int p)
+{
+	FPOINT * result = (FPOINT *)malloc(sizeof(fpoint));
+	
+	//TODO
+	
+	return result;
+}
+
+int main()
+{
+	ONE = newfpoint(0,1);
+	ZERO = newfpoint(0,0);
+	O = newpoint(-1,-1,-1,-1);
+	
+	int p=5;
+	FPOINT * test = newfpoint(0,3);
+	FPOINT * test1 = newfpoint(0,7);
+	
+	CURVE * c = newcurve(newfpoint(0,0),newfpoint(0,1)); 
+	
+	POINT * P = newpoint(0,0,0,1);
+	
+	//add(P,P,c,p,P);
+	
+	ppower(P,100,c,p,P);
+	
+	//minus(P,P,c,p,P);
+
+	//pneg(P,p,P);
+	
+	//passign(P,O);
+	
+	printf("%d\n",testpoint(P,c,p));
+	
+	showpoint(P);
+	
+	return 0;
+}