}//projective
public static BigInteger GetFactorJacobian(BigInteger n, int B1, int B2)
{
BigInteger x, y, g;
var E = EllipticCurveWeierstrass.GenerateCurveRandom(n, out x, out y, out g, false);
var P = new PointJacobian(x, y, E);
if (g > 1 && g < n)
{
return(g);
}
//STEP 1
var P1 = P as IPoint;
var result = StageOneProjective(ref P1, n, B1);
if (result > 1 || result == 0)
{
return(result);
}
//STEP 2
result = StageTwoProjective(ref P1, n, B1, B2);
return(result);
}//jacobian
public static PointJacobian Double(PointJacobian P)//3M + 6S + 1*a + 4add + 2*2 + 1*3 + 1*4 + 1*8
{
if (P.IsInfinite())
{
return(new PointJacobian(0, 1, 0, P.E));
}
BigInteger XX = P.x * P.x;
BigInteger YY = P.y * P.y;
BigInteger ZZ = P.z * P.z;
BigInteger S = 4 * P.x * YY;
BigInteger M = 3 * XX + P.E.a * ZZ * ZZ;
BigInteger T = M * M - 2 * S;
BigInteger x = T % P.E.n;
BigInteger y = (M * (S - T) - 8 * YY * YY) % P.E.n;
BigInteger z = (2 * P.y * P.z) % P.E.n;
return(new PointJacobian(x, y, z, P.E));
}
public static PointJacobian operator *(BigInteger k, PointJacobian P)
{
PointJacobian R = new PointJacobian(0, 1, 0, P.E);
if (P.IsInfinite())
{
return(R);
}
while (k > 0)
{
if (k % 2 == 1)
{
R += P;
}
k /= 2;
P = Double(P);
}
return(R);
}
