/**
* Adds another <code>ECPoints.F2m</code> to <code>this</code> without
* checking if both points are on the same curve. Used by multiplication
* algorithms, because there all points are a multiple of the same point
* and hence the checks can be omitted.
* @param b The other <code>ECPoints.F2m</code> to add to
* <code>this</code>.
* @return <code>this + b</code>
*/
internal F2mPoint AddSimple(F2mPoint b)
{
if (this.IsInfinity)
{
return(b);
}
if (b.IsInfinity)
{
return(this);
}
F2mFieldElement x2 = (F2mFieldElement)b.X;
F2mFieldElement y2 = (F2mFieldElement)b.Y;
// Check if b == this or b == -this
if (this.x.Equals(x2))
{
// this == b, i.e. this must be doubled
if (this.y.Equals(y2))
{
return((F2mPoint)this.Twice());
}
// this = -other, i.e. the result is the point at infinity
return((F2mPoint)this.curve.Infinity);
}
ECFieldElement xSum = this.x.Add(x2);
F2mFieldElement lambda
= (F2mFieldElement)(this.y.Add(y2)).Divide(xSum);
F2mFieldElement x3
= (F2mFieldElement)lambda.Square().Add(lambda).Add(xSum).Add(this.curve.A);
F2mFieldElement y3
= (F2mFieldElement)lambda.Multiply(this.x.Add(x3)).Add(x3).Add(this.y);
return(new F2mPoint(curve, x3, y3, withCompression));
}
/* (non-Javadoc)
* @see Al.Security.Math.EC.ECPoint#twice()
*/
public override ECPoint Twice()
{
// Twice identity element (point at infinity) is identity
if (this.IsInfinity)
{
return(this);
}
// if x1 == 0, then (x1, y1) == (x1, x1 + y1)
// and hence this = -this and thus 2(x1, y1) == infinity
if (this.x.ToBigInteger().SignValue == 0)
{
return(this.curve.Infinity);
}
F2mFieldElement lambda = (F2mFieldElement)this.x.Add(this.y.Divide(this.x));
F2mFieldElement x2 = (F2mFieldElement)lambda.Square().Add(lambda).Add(this.curve.A);
ECFieldElement ONE = this.curve.FromBigInteger(BigInteger.One);
F2mFieldElement y2 = (F2mFieldElement)this.x.Square().Add(
x2.Multiply(lambda.Add(ONE)));
return(new F2mPoint(this.curve, x2, y2, withCompression));
}