public EllipticCurvePoint ScalarMult(BigInteger k, EllipticCurvePoint point)
{
_curve.EnsureOnCurve(point);
var n = _curve.N;
if (k % n == 0 || EllipticCurvePoint.IsInfinityPoint(point))
{
return(EllipticCurvePoint.InfinityPoint);
}
// k * point = -k * (-point)
if (k < 0)
{
return(ScalarMult(-k, PointNeg(point)));
}
EllipticCurvePoint result = EllipticCurvePoint.InfinityPoint;
EllipticCurvePoint addend = point;
while (k != 0)
{
if ((k & 1) == 1)
{
result = Add(result, addend);
}
addend = Add(addend, addend);
k >>= 1;
}
_curve.EnsureOnCurve(result);
return(result);
}
public EllipticCurvePoint Add(EllipticCurvePoint point1, EllipticCurvePoint point2)
{
_curve.EnsureOnCurve(point1);
_curve.EnsureOnCurve(point2);
if (EllipticCurvePoint.IsInfinityPoint(point1))
{
return(point2);
}
if (EllipticCurvePoint.IsInfinityPoint(point2))
{
return(point1);
}
var x1 = point1.X;
var y1 = point1.Y;
var x2 = point2.X;
var y2 = point2.Y;
var p = _curve.P;
var a = _curve.A;
BigInteger m;
if (x1 == x2)
{
if (y1 != y2) // point1 + (-point1) = 0
{
return(EllipticCurvePoint.InfinityPoint);
}
// This is the case point1 == point2.
m = (3 * x1 * x1 + a) * InverseMod(2 * y1, p);
}
else // point1 != point2.
{
m = (y1 - y2) * InverseMod(x1 - x2, p);
}
BigInteger x3 = m * m - x1 - x2;
BigInteger y3 = y1 + m * (x3 - x1);
var result = new EllipticCurvePoint(Modular(x3, p), Modular(-y3, p));
return(result);
}
public EllipticCurvePoint PointNeg(EllipticCurvePoint point)
{
_curve.EnsureOnCurve(point);
// -0 = 0
if (EllipticCurvePoint.IsInfinityPoint(point))
{
return(point);
}
var x = point.X;
var y = point.Y;
var p = _curve.P;
var result = new EllipticCurvePoint(x, Modular(-y, p));
_curve.EnsureOnCurve(result);
return(result);
}