/// <summary>
/// Based on the Fixed-base comb method (Algorithm 17 from https://link.springer.com/content/pdf/10.1007/3-540-44499-8_1.pdf)
/// </summary>
/// <param name="scalar"></param>
/// <returns></returns>
private EccPoint FastMultiply(BigInteger scalar)
{
var width = 4;
var degree = FieldSizeQ.ExactBitLength();
var d = degree.CeilingDivide(width);
var scalarBits = new BitString(scalar, degree).Bits;
var point = new EccPoint("infinity");
for (var i = d - 1; i >= 0; i--)
{
point = Double(point);
var index = 0;
for (var j = width - 1; j >= 0; j--)
{
index *= 2;
if (i + d * j >= degree)
{
continue;
}
if (scalarBits[i + d * j])
{
index++;
}
}
if (index != 0)
{
point = Add(point, _precomputedMultiplication[index]);
}
}
return(point);
}
public bool PointExistsInField(EccPoint point)
{
var m = FieldSizeQ.ExactBitLength();
if (point.X.ExactBitLength() == m || point.Y.ExactBitLength() == m)
{
return(false);
}
return(true);
}
