public PointMontgomery(BigInteger x, BigInteger y, EllipticCurveMontgomery E)
{
this.x = x;
this.y = y;
this.z = 1;
this.E = E;
}
public override bool Equals(Object obj)
{
if (obj == null)
{
return(false);
}
EllipticCurveMontgomery E = obj as EllipticCurveMontgomery;
return(new EllipticCurveMontgomery(this.An, this.Ad, this.n) == E);
}
public static PointMontgomeryBrent Double(PointMontgomeryBrent P)
{
EllipticCurveMontgomery E = P.E as EllipticCurveMontgomery;
BigInteger t1 = (P.x + P.z) * (P.x + P.z);
BigInteger t2 = (P.x - P.z) * (P.x - P.z);
BigInteger t = t1 - t2;
BigInteger x = (t1 * t2 * 4 * E.Ad) % P.E.n;
BigInteger z = ((4 * E.Ad * t2 + t * E.An) * t) % P.E.n;
return(new PointMontgomeryBrent(x, 0, z, P.E));
}
}//Montgomery
private static EllipticCurveMontgomery GenerateCurve(BigInteger n, out BigInteger x, out BigInteger y, TorsionType type)
{
switch (type)
{
case TorsionType.RandomCurve:
return(EllipticCurveMontgomery.GenerateCurveRandom(n, out x, out y));
case TorsionType.Curve6:
return(EllipticCurveMontgomery.GenerateCurve6(n, out x, out y));
default:
return(EllipticCurveMontgomery.GenerateCurveRandom(n, out x, out y));
}
}
public bool IsOnCurve()
{
EllipticCurveMontgomery E = this.E as EllipticCurveMontgomery;
return((x * x * x + (E.An / E.Ad - 2) * x * x * z + x * z * z) % E.n == 0);
}