/// <summary>
/// Returns k * point computed using the double and <see cref="PointAdd"/> algorithm.
/// </summary>
/// <param name="k"></param>
/// <param name="point"></param>
/// <returns></returns>
public BigIntegerPoint ScalarMult(BigInteger k, BigIntegerPoint point)
{
if (EllipticCurveHelpers.MathMod(k, this.N) == 0 || point.IsEmpty())
{
return(BigIntegerPoint.GetEmpty());
}
if (k < 0)
{
return(this.ScalarMult(-k, this.NegatePoint(point)));
}
BigIntegerPoint result = BigIntegerPoint.GetEmpty();
BigIntegerPoint addend = point;
while (k > 0)
{
if ((k & 1) > 0)
{
result = this.PointAdd(result, addend);
}
addend = this.PointAdd(addend, addend);
k >>= 1;
}
return(result);
}
/// <summary>
/// Returns the result of lhs + rhs according to the group law.
/// </summary>
/// <param name="lhs"></param>
/// <param name="rhs"></param>
/// <returns></returns>
public BigIntegerPoint PointAdd(BigIntegerPoint lhs, BigIntegerPoint rhs)
{
if (lhs.IsEmpty())
{
return(rhs);
}
if (rhs.IsEmpty())
{
return(lhs);
}
BigInteger x1 = lhs.X, y1 = lhs.Y;
BigInteger x2 = rhs.X, y2 = rhs.Y;
if (x1 == x2 && y1 != y2)
{
return(BigIntegerPoint.GetEmpty());
}
BigInteger m;
if (x1 == x2)
{
m = (3 * x1 * x1 + this.A) * this.InverseMod(2 * y1, this.P);
}
else
{
m = (y1 - y2) * this.InverseMod(x1 - x2, this.P);
}
BigInteger x3 = m * m - x1 - x2;
BigInteger y3 = y1 + m * (x3 - x1);
BigIntegerPoint result = new BigIntegerPoint(EllipticCurveHelpers.MathMod(x3, this.P), EllipticCurveHelpers.MathMod(-y3, this.P));
return(result);
}
