public static PointEdwardsExtended Double(PointEdwardsExtended P)//4M + 4S + 1*a + 6add + 1*2
{
BigInteger A = P.x * P.x;
BigInteger B = P.y * P.y;
BigInteger C = 2 * P.z * P.z;
BigInteger D = P.E.a * A;
BigInteger W = P.x + P.y;
BigInteger E = W * W - A - B;
BigInteger G = D + B;
BigInteger F = G - C;
BigInteger H = D - B;
BigInteger x = (E * F) % P.E.n;
BigInteger y = (G * H) % P.E.n;
BigInteger t = (E * H) % P.E.n;
BigInteger z = (F * G) % P.E.n;
return(new PointEdwardsExtended(x, y, z, t, P.E));
}
public static PointEdwardsExtended operator *(BigInteger k, PointEdwardsExtended P)
{
var R = new PointEdwardsExtended(0, 1, P.E);
if (P.IsInfinite())
{
return(R);
}
while (k > 0)
{
if (k % 2 == 1)
{
R += P;
}
k /= 2;
P = Double(P);
}
return(R);
}
}//inverted
public static BigInteger GetFactorExtended(BigInteger n, int B1, int B2, TorsionType type)
{
BigInteger x, y;
var E = GenerateCurve(n, out x, out y, type);
var P = new PointEdwardsExtended(x, y, E);
//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);
}//extended
public static PointEdwardsExtended Tripple(PointEdwardsExtended P)//4M + 4S + 1*a + 6add + 1*2
{
BigInteger YY = P.y * P.y;
BigInteger aXX = P.E.a * P.x * P.y;
BigInteger Ap = YY + aXX;
BigInteger B = 2 * (2 * P.z * P.z - Ap);
BigInteger xB = aXX * B;
BigInteger yB = YY * B;
BigInteger AA = Ap * (YY - aXX);
BigInteger F = AA - yB;
BigInteger G = AA + xB;
BigInteger xE = P.x * (yB + AA);
BigInteger yH = P.y * (xB - AA);
BigInteger zF = P.z * F;
BigInteger zG = P.z * G;
BigInteger x = (xE * zF) % P.E.n;
BigInteger y = (yH * zG) % P.E.n;
BigInteger z = (zF * zG) % P.E.n;
BigInteger t = (xE * yH) % P.E.n;
return(new PointEdwardsExtended(x, y, z, t, P.E));
}
