public Point Multiply(BigInteger k, Point point)
{
if (!IsOnCurve(point))
{
throw new PointIsNotOnCurveExceptioin("Point is not on the curve");
}
if (ModuloArithmetics.Mod(k, Parameters.SubGroupOrder) == 0 ||
point == Point.InfinityPoint)
{
return(Point.InfinityPoint);
}
if (k < 0)
{
return(Multiply(-k, Neg(point)));
}
BigInteger copy = k;
Point result = Point.InfinityPoint;
Point currentPow = point;
while (copy > 0)
{
if (copy % 2 == 1)
{
result = Add(result, currentPow);
}
currentPow = Add(currentPow, currentPow);
copy = copy / 2;
}
return(result);
}
public Point Add(Point first, Point second)
{
if (!IsOnCurve(first))
{
throw new PointIsNotOnCurveExceptioin("First point is not on the curve");
}
if (!IsOnCurve(second))
{
throw new PointIsNotOnCurveExceptioin("Second point is not on the curve");
}
if (first == Point.InfinityPoint)
{
return(new Point(second));
}
if (second == Point.InfinityPoint)
{
return(new Point(first));
}
BigInteger x1 = first.X ?? throw new ArgumentException();
BigInteger y1 = first.Y ?? throw new ArgumentException();
BigInteger x2 = second.X ?? throw new ArgumentException();
BigInteger y2 = second.Y ?? throw new ArgumentException();
BigInteger m = 0;
if (x1 == x2 && y1 != y2)
{
return(Point.InfinityPoint);
}
if (x1 == x2)
{
m = (3 * x1 * x1 + Parameters.A)
* ModuloArithmetics.Inverse(2 * y1, Parameters.FieldCharacteristic);
}
else
{
m = (y1 - y2) * ModuloArithmetics.Inverse(x1 - x2, Parameters.FieldCharacteristic);
}
var x = m * m - x1 - x2;
var y = y1 + m * (x - x1);
var point = new Point(
ModuloArithmetics.Mod(x, Parameters.FieldCharacteristic),
ModuloArithmetics.Mod(-y, Parameters.FieldCharacteristic));
if (!IsOnCurve(point))
{
throw new PointIsNotOnCurveExceptioin("Result point of adding is not on the curve");
}
return(point);
}
public bool IsOnCurve(Point point)
{
if (point == Point.InfinityPoint)
{
return(true);
}
// Stuff
var x = point.X ?? throw new ArgumentException();
var y = point.Y ?? throw new ArgumentException();
var a = Parameters.A;
var b = Parameters.B;
var p = Parameters.FieldCharacteristic;
return(ModuloArithmetics.Mod((y * y - x * x * x - a * x - b), p) == 0);
}
public Point Neg(Point point)
{
if (!IsOnCurve(point))
{
throw new PointIsNotOnCurveExceptioin("Point is not on the curve");
}
if (point == Point.InfinityPoint)
{
return(Point.InfinityPoint);
}
// Stuff
BigInteger y = point.Y ??
throw new ArgumentException();
return(new Point(point.X,
ModuloArithmetics.Mod(-y, Parameters.FieldCharacteristic)));
}