/**
* Simple shift-and-add multiplication. Serves as reference implementation
* to verify (possibly faster) implementations, and for very small scalars.
*
* @param p
* The point to multiply.
* @param k
* The multiplier.
* @return The result of the point multiplication <code>kP</code>.
*/
public static ECPoint ReferenceMultiply(ECPoint p, BigInteger k)
{
BigInteger x = k.Abs();
ECPoint q = p.Curve.Infinity;
int t = x.BitLength;
if (t > 0)
{
if (x.TestBit(0))
{
q = p;
}
for (int i = 1; i < t; i++)
{
p = p.Twice();
if (x.TestBit(i))
{
q = q.Add(p);
}
}
}
return k.SignValue < 0 ? q.Negate() : q;
}
public override ECPoint TwicePlus(ECPoint b)
{
if (this.IsInfinity)
return b;
if (b.IsInfinity)
return Twice();
ECCurve curve = this.Curve;
ECFieldElement X1 = this.RawXCoord;
if (X1.IsZero)
{
// A point with X == 0 is it's own additive inverse
return b;
}
int coord = curve.CoordinateSystem;
switch (coord)
{
case ECCurve.COORD_LAMBDA_PROJECTIVE:
{
// NOTE: twicePlus() only optimized for lambda-affine argument
ECFieldElement X2 = b.RawXCoord, Z2 = b.RawZCoords[0];
if (X2.IsZero || !Z2.IsOne)
{
return Twice().Add(b);
}
ECFieldElement L1 = this.RawYCoord, Z1 = this.RawZCoords[0];
ECFieldElement L2 = b.RawYCoord;
ECFieldElement X1Sq = X1.Square();
ECFieldElement L1Sq = L1.Square();
ECFieldElement Z1Sq = Z1.Square();
ECFieldElement L1Z1 = L1.Multiply(Z1);
ECFieldElement T = curve.A.Multiply(Z1Sq).Add(L1Sq).Add(L1Z1);
ECFieldElement L2plus1 = L2.AddOne();
ECFieldElement A = curve.A.Add(L2plus1).Multiply(Z1Sq).Add(L1Sq).MultiplyPlusProduct(T, X1Sq, Z1Sq);
ECFieldElement X2Z1Sq = X2.Multiply(Z1Sq);
ECFieldElement B = X2Z1Sq.Add(T).Square();
if (B.IsZero)
{
if (A.IsZero)
{
return b.Twice();
}
return curve.Infinity;
}
if (A.IsZero)
{
return new F2mPoint(curve, A, curve.B.Sqrt(), IsCompressed);
}
ECFieldElement X3 = A.Square().Multiply(X2Z1Sq);
ECFieldElement Z3 = A.Multiply(B).Multiply(Z1Sq);
ECFieldElement L3 = A.Add(B).Square().MultiplyPlusProduct(T, L2plus1, Z3);
return new F2mPoint(curve, X3, L3, new ECFieldElement[] { Z3 }, IsCompressed);
}
default:
{
return Twice().Add(b);
}
}
}
