public static PointEdwardsProjective Tripple(PointEdwardsProjective P)//9M + 3S + 1*a + 7add + 2*2
{
BigInteger YY = P.y * P.y;
BigInteger aXX = P.E.a * P.x * P.x;
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 x = (P.x * (yB + AA) * F) % P.E.n;
BigInteger y = (P.y * (xB - AA) * G) % P.E.n;
BigInteger z = (P.z * F * G) % P.E.n;
return(new PointEdwardsProjective(x, y, z, P.E));
}
public static PointEdwardsProjective Double(PointEdwardsProjective P)//3M + 4S + 1*a + 6add + 1*2
{
BigInteger n = P.E.n;
BigInteger A = (P.x + P.y);
BigInteger B = A * A;
BigInteger C = P.x * P.x;
BigInteger D = P.y * P.y;
BigInteger E = P.E.a * C;
BigInteger F = E + D;
BigInteger H = P.z * P.z;
BigInteger J = F - 2 * H;
BigInteger x = ((B - C - D) * J) % P.E.n;
BigInteger y = (F * (E - D)) % P.E.n;
BigInteger z = (F * J) % P.E.n;
return(new PointEdwardsProjective(x, y, z, P.E));
}
public static BigInteger GetFactorProjective(BigInteger n, int B1, int B2, TorsionType type)
{
BigInteger x, y;
var E = GenerateCurve(n, out x, out y, type);
var P = new PointEdwardsProjective(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);
}//projective
public static PointEdwardsProjective operator *(BigInteger k, PointEdwardsProjective P)
{
bool isFirst = true;
var R = new PointEdwardsProjective(0, 1, 1, P.E);
while (k > 0)
{
if (k % 2 == 1 && isFirst)
{
R = new PointEdwardsProjective(P.x, P.y, P.z, P.E);
isFirst = false;
}
else if (k % 2 == 1)
{
R += P;
}
k /= 2;
P = Double(P);
}
return(R);
}