public EccPoint Add(EccPoint pointA, EccPoint pointB)
{
// Any point added to infinity is itself
if (pointA.Infinity)
{
return(pointB);
}
// Any point added to infinity is itself
if (pointB.Infinity)
{
return(pointA);
}
// Any point added to its inverse is infinity
if (pointA.Equals(Negate(pointB)))
{
return(new EccPoint("infinity"));
}
// Cannot add two identical points, use Double instead
if (pointA.Equals(pointB))
{
return(Double(pointA));
}
var numerator = _operator.Subtract(pointB.Y, pointA.Y);
var denominator = _operator.Subtract(pointB.X, pointA.X);
var lambda = _operator.Divide(numerator, denominator);
var x = _operator.Subtract(_operator.Subtract(_operator.Multiply(lambda, lambda), pointA.X), pointB.X);
var y = _operator.Subtract(_operator.Multiply(_operator.Subtract(pointA.X, x), lambda), pointA.Y);
return(new EccPoint(x, y));
}
public EccPoint Add(EccPoint pointA, EccPoint pointB)
{
// Any point added to infinity is itself
if (pointA.Infinity)
{
return(pointB);
}
// Any point added to infinity is itself
if (pointB.Infinity)
{
return(pointA);
}
// Any point added to its inverse is infinity
if (pointA.Equals(Negate(pointB)))
{
return(new EccPoint("infinity"));
}
// Cannot add two identical points, use Double instead
if (pointA.Equals(pointB))
{
return(Double(pointA));
}
var numerator = _operator.Add(pointA.Y, pointB.Y);
var denominator = _operator.Add(pointA.X, pointB.X);
if (denominator == 0)
{
return(new EccPoint("infinity"));
}
var lambda = _operator.Multiply(numerator, _operator.Inverse(denominator));
// x = lambda * lambda + lambda + x1 + x2 + a
var x = _operator.Add(_operator.Add(_operator.Add(_operator.Add(_operator.Multiply(lambda, lambda), lambda), pointA.X), pointB.X), CoefficientA);
// y = lambda * (x1 + x3) + x + y1
var y = _operator.Add(_operator.Add(_operator.Multiply(_operator.Add(pointA.X, x), lambda), x), pointA.Y);
return(new EccPoint(x, y));
}
public EccPoint Multiply(EccPoint startPoint, BigInteger scalar)
{
// Intentional normal modulo, this is what CAVS does
scalar %= OrderN;
if (startPoint.Equals(BasePointG) && HasPrecomputedValues)
{
return(FastMultiply(scalar));
}
else
{
return(Multiply(startPoint, new NonAdjacentBitString(scalar)));
}
}