public CurvePoint Add(CurvePoint p1, CurvePoint p2)
{
#if SAFE_MATH
CheckOnCurve(p1);
CheckOnCurve(p2);
#endif
// Special cases
if (p1.AtInfinity() && p2.AtInfinity())
{
return(new CurvePoint());
}
else if (p1.AtInfinity())
{
return(p2);
}
else if (p2.AtInfinity())
{
return(p1);
}
else if (p1.X == p2.X &&
p1.Y == Inverse(p2).Y
)
{
return(new CurvePoint());
}
BigInteger x3 = 0, y3 = 0;
if (type == CurveType.Weierstrass)
{
BigInteger slope = p1.X == p2.X && p1.Y == p2.Y ? Mod((3 * p1.X * p1.X + a) * MulInverse(2 * p1.Y)) : Mod(Mod(p2.Y - p1.Y) * MulInverse(p2.X - p1.X));
x3 = Mod((slope * slope) - p1.X - p2.X);
y3 = Mod(-((slope * x3) + p1.Y - (slope * p1.X)));
}
else if (type == CurveType.Montgomery)
{
if ((p1.X == p2.X && p1.Y == p2.Y))
{
BigInteger q = 3 * p1.X;
BigInteger w = q * p1.X;
BigInteger e = 2 * a;
BigInteger r = e * p1.X;
BigInteger t = 2 * b;
BigInteger y = t * p1.Y;
BigInteger u = MulInverse(y);
BigInteger o = w + e + 1;
BigInteger p = o * u;
}
BigInteger co = p1.X == p2.X && p1.Y == p2.Y ? Mod((3 * p1.X * p1.X + 2 * a * p1.X + 1) * MulInverse(2 * b * p1.Y)) : Mod(Mod(p2.Y - p1.Y) * MulInverse(p2.X - p1.X)); // Compute a commonly used coefficient
x3 = Mod(b * co * co - a - p1.X - p2.X);
y3 = Mod(((2 * p1.X + p2.X + a) * co) - (b * co * co * co) - p1.Y);
}
return(new CurvePoint(x3, y3));
}
public CurvePoint Multiply(CurvePoint p, BigInteger scalar)
{
if (scalar <= 0)
{
throw new System.Exception("Cannot multiply by a scalar which is <= 0");
}
if (p.AtInfinity())
{
return(new CurvePoint());
}
CurvePoint p1 = new CurvePoint(p.X, p.Y);
byte[] bytes = scalar.ToByteArray();
Int32 highBit = bytes.GetHighestBitSet();
// Double-and-add method
while (highBit >= 0)
{
p1 = Add(p1, p1); // Double
if (bytes.GetBit(highBit))
{
p1 = Add(p1, p); // Add
}
--highBit;
}
return(p1);
}
protected void CheckOnCurve(CurvePoint p)
{
if (!p.AtInfinity() && // The point at infinity is asserted to be on the curve
(type == CurveType.Weierstrass && Mod(p.Y * p.Y) != Mod((p.X * p.X * p.X) + (p.X * a) + b)) || // Weierstrass formula
(type == CurveType.Montgomery && Mod(b * p.Y * p.Y) != Mod((p.X * p.X * p.X) + (p.X * p.X * a) + p.X)) // Montgomery formula
)
{
throw new System.Exception("Point is not on curve");
}
}