/// <summary>
/// Negates a given point on the curve.
/// </summary>
/// <param name="point"><see cref="CurvePoint"/> to negate.</param>
/// <returns><see cref="CurvePoint"/> instance of the negation of <paramref name="point"/> on the curve.</returns>
public virtual CurvePoint Negate(CurvePoint point)
{
if (point.Equals(CurvePoint.PointAtInfinity))
{
return(point);
}
return(new CurvePoint(point.X, Field.Mod(-point.Y)));
}
/// <inheritdoc/>
public override CurvePoint Add(CurvePoint left, CurvePoint right)
{
BigInteger x1 = left.X;
BigInteger x2 = right.X;
BigInteger y1 = left.Y;
BigInteger y2 = right.Y;
BigInteger lambda;
if (left.Equals(right))
{
lambda = Field.Mod((3 * Field.Square(x1) + 2 * A * x1 + 1) * Field.InvertMult(2 * B * y1));
}
else
{
lambda = Field.Mod((y2 - y1) * Field.InvertMult(x2 - x1));
}
BigInteger x3 = Field.Mod(B * Field.Square(lambda) - x1 - x2 - A);
BigInteger y3 = Field.Mod(lambda * (x1 - x3) - y1);
CurvePoint result = CurvePoint.PointAtInfinity;
bool pointsAreNegations = AreNegations(left, right);
if (left.IsAtInfinity && right.IsAtInfinity)
{
result = CurvePoint.PointAtInfinity;
}
if (left.IsAtInfinity && !right.IsAtInfinity)
{
result = right.Clone();
}
if (right.IsAtInfinity && !left.IsAtInfinity)
{
result = left.Clone();
}
if (!left.IsAtInfinity && !right.IsAtInfinity && pointsAreNegations)
{
result = CurvePoint.PointAtInfinity;
}
if (!left.IsAtInfinity && !right.IsAtInfinity && !pointsAreNegations)
{
result = new CurvePoint(x3, y3);
}
return(result);
}