Subversion Repositories planix.SVN

# Elliptic curve group operations in jacobian coordinates:
#       x=X/Z^2
#       x=Y/Z^3

jacobian_new(x,y,z, X,Y,Z) {
        X = x;
        Y = y;
        Z = z;
}
jacobian_inf(X,Y,Z) {
        X,Y,Z = jacobian_new(0,1,0);
}
jacobian_affine(p, X,Y,Z) mod(p) {
        if(Z != 0) {
                ZZ = Z^2;
                ZZZ = ZZ*Z;
                X = X / ZZ;
                Y = Y / ZZZ;
                Z = 1;
        }
}
jacobian_dbl(p,a, X1,Y1,Z1, X3,Y3,Z3) mod(p) {
        if(Y1 == 0) {
                X3,Y3,Z3 = jacobian_inf();
        } else {
                XX = X1^2;
                YY = Y1^2;
                YYYY = YY^2;
                ZZ = Z1^2;
                S = 2*((X1+YY)^2-XX-YYYY);
                M = 3*XX+a*ZZ^2;
                Z3 = (Y1+Z1)^2-YY-ZZ;   
                X3 = M^2-2*S;
                Y3 = M*(S-X3)-8*YYYY;
        }
}
jacobian_add(p,a, X1,Y1,Z1, X2,Y2,Z2, X3,Y3,Z3) mod(p) {
        Z1Z1 = Z1^2;
        Z2Z2 = Z2^2;
        U1 = X1*Z2Z2;
        U2 = X2*Z1Z1;
        S1 = Y1*Z2*Z2Z2;
        S2 = Y2*Z1*Z1Z1;
        if(U1 == U2) {
                if(S1 != S2) {
                        X3,Y3,Z3 = jacobian_inf();
                } else {
                        X3,Y3,Z3 = jacobian_dbl(p,a, X1,Y1,Z1);
                }
        } else {
                H = U2-U1;
                I = (2*H)^2;
                J = H*I;
                r = 2*(S2-S1);
                V = U1*I;
                X3 = r^2-J-2*V;
                Y3 = r*(V-X3)-2*S1*J;
                Z3 = ((Z1+Z2)^2-Z1Z1-Z2Z2)*H;
        }
}