}//first & second stage
public static BigInteger GetFactorProjective(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 PointProjective(x, y, E);
if (g > 1 && g < n)
{
return(g);
}
//STEP 1
var P1 = P as IPoint;
var result = StageOneEdwardsProjective(ref P1, n, B1);
if (result > 1 || result == 0)
{
return(result);
}
//STEP 2
result = StageTwoEdwardsProjective(ref P1, n, B1, B2);
return(result);
}//projective
public static PointProjective operator *(BigInteger k, PointProjective P)
{
PointProjective R = new PointProjective(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);
}
public static PointProjective Double(PointProjective P)//5M + 6S + 1*a + 7add + 3*2 + 1*3
{
if (P.IsInfinite())
{
return(new PointProjective(0, 1, 0, P.E));
}
BigInteger XX = P.x * P.x;
BigInteger ZZ = P.z * P.z;
BigInteger w = P.E.a * ZZ + 3 * XX;
BigInteger s = 2 * P.y * P.z;
BigInteger ss = s * s;
BigInteger sss = s * ss;
BigInteger R = P.y * s;
BigInteger RR = R * R;
BigInteger B = (P.x + R) * (P.x + R) - XX - RR;
BigInteger h = w * w - 2 * B;
BigInteger x = (h * s) % P.E.n;
BigInteger y = (w * (B - h) - 2 * RR) % P.E.n;
BigInteger z = sss % P.E.n;
return(new PointProjective(x, y, z, P.E));
}