public static PointMontgomery Addition(PointMontgomery P, PointMontgomery Q, PointMontgomery P0)//4M + 2S + 6add
{
BigInteger t1 = (P.x - P.z) * (Q.x + Q.z);
BigInteger t2 = (P.x + P.z) * (Q.x - Q.z);
BigInteger a = t1 + t2;
BigInteger b = t1 - t2;
BigInteger x = (P0.z * a * a) % P.E.n;
BigInteger z = (P0.x * b * b) % P.E.n;
return(new PointMontgomery(x, 0, z, P.E));
}
public static PointMontgomery Double(PointMontgomery P)//2M + 2S + 1*a24 + 4add
{
BigInteger a = P.x + P.z;
BigInteger b = P.x - P.z;
BigInteger t1 = a * a;
BigInteger t2 = b * b;
BigInteger t = t1 - t2;
BigInteger x = (t1 * t2) % P.E.n;
BigInteger z = (t * (t2 + t * P.E.b)) % P.E.n;
return(new PointMontgomery(x, 0, z, P.E));
}
public static BigInteger GetFactorProjective(BigInteger n, int B1, int B2, TorsionType type)
{
BigInteger x;
BigInteger y;
var E = GenerateCurve(n, out x, out y, type);
var P = new PointMontgomery(x, y, E);
//STEP 1
var P1 = P as IPoint;
var result = StageOneProjective(ref P1, n, B1);
if (result > 1 || result == 0)
{
return(result);
}
//STEP 2
result = StageTwoProjective2(ref P1, n, B1, B2);
return(result);
}//Montgomery
public static PointMontgomery operator *(BigInteger k, PointMontgomery P)
{
if (k == 0)
{
return(new PointMontgomery(0, 1, 0, P.E));
}
else if (k == 1)
{
return(P);
}
PointMontgomery U = P;
PointMontgomery T = Double(P);
if (k == 2)
{
return(T);
}
var binary = new List <BigInteger>();
while (k >= 2)
{
binary.Add(k % 2);
k /= 2;
}
PointMontgomery R = P;
for (int i = binary.Count - 1; i >= 0; i--)
{
if (binary[i] == 1)
{
U = Addition(T, U, P);
T = Double(T);
}
else
{
T = Addition(T, U, P);
U = Double(U);
}
}
return(U);
}
