public static PointEdwardsInverted Double(PointEdwardsInverted P)//3M + 4S + 1*a + 1*d2 + 6add
{
BigInteger A = P.x * P.x;
BigInteger B = P.y * P.y;
BigInteger U = P.E.a * B;
BigInteger C = A + U;
BigInteger D = A - U;
BigInteger W = P.x + P.y;
BigInteger E = W * W - A - B;
BigInteger x = (C * D) % P.E.n;
BigInteger y = (E * (C - 2 * P.E.b * P.z * P.z)) % P.E.n;
BigInteger z = (D * E) % P.E.n;
return(new PointEdwardsInverted(x, y, z, P.E));
}
}//projective
public static BigInteger GetFactorInverted(BigInteger n, int B1, int B2, TorsionType type)
{
BigInteger x, y;
var E = GenerateCurve(n, out x, out y, type);
var P = new PointEdwardsInverted(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);
}//inverted
public static PointEdwardsInverted operator *(BigInteger k, PointEdwardsInverted P)
{
bool isFirst = true;
PointEdwardsInverted R = new PointEdwardsInverted(0, 1, 1, P.E);
while (k > 0)
{
if (k % 2 == 1 && isFirst)
{
R = new PointEdwardsInverted(P.x, P.y, P.z, P.E);
isFirst = false;
}
else if (k % 2 == 1)
{
R += P;
}
k /= 2;
P = Double(P);
}
return(R);
}