public static PointAffine Double(PointAffine P)
{
if (P.y == 0)
{
return(new PointAffine(0, 1, 0, P.E));
}
BigInteger temp = (2 * P.y) % P.E.n;
if (temp < 0)
{
temp += P.E.n;
}
BigInteger inv;
BigInteger d;
Algorithms.ExtendedEuclidAlgorithm(temp, P.E.n, out inv, out d);
if (d > 1 && d < P.E.n)
{
return(new PointAffine(0, 0, temp, P.E)); //делитель найден, можно прекращать вычисления
}
BigInteger lambda = (3 * P.x * P.x + P.E.a) * inv;
BigInteger x = (lambda * lambda - 2 * P.x) % P.E.n;
BigInteger y = (lambda * (P.x - x) - P.y) % P.E.n;
return(new PointAffine(x, y, 1, P.E));
}
public static BigInteger GetFactorAffine(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 PointAffine(x, y, E);
if (g > 1 && g < n)
{
return(g);
}
//STEP 1
var P1 = P as IPoint;
var result = StageOneAffine(ref P1, n, B1);
if (result > 1 || result == 0)
{
return(result);
}
//STEP 2
P = P1 as PointAffine;
result = StageTwoAffine(ref P1, n, B1, B2);
return(result);
}//first & second stage
public static PointAffine operator *(BigInteger k, PointAffine P)
{
PointAffine R = new PointAffine(0, 1, 0, P.E);
if (P.IsInfinite())
{
return(R);
}
while (k > 0)
{
if (P.z > 1) //делитель найден, можно прекращать вычисления
{
return(P);
}
if (k % 2 == 1)
{
R = P + R;
}
k /= 2;
P = Double(P);//P = P + P;
}
return(R);
}