protected virtual ECFieldElement CalculateJacobianModifiedW(ECFieldElement Z, ECFieldElement ZSquared)
{
ECFieldElement a4 = this.Curve.A;
if (a4.IsZero)
{
return(a4);
}
if (ZSquared == null)
{
ZSquared = Z.Square();
}
ECFieldElement W = ZSquared.Square();
ECFieldElement a4Neg = a4.Negate();
if (a4Neg.BitLength < a4.BitLength)
{
W = W.Multiply(a4Neg).Negate();
}
else
{
W = W.Multiply(a4);
}
return(W);
}
protected override ECPoint DecompressPoint(int yTilde, BigInteger X1)
{
ECFieldElement x = FromBigInteger(X1);
ECFieldElement alpha = x.Square().Add(m_a).Multiply(x).Add(m_b);
ECFieldElement beta = alpha.Sqrt();
//
// if we can't find a sqrt we haven't got a point on the
// curve - run!
//
if (beta == null)
{
throw new ArithmeticException("Invalid point compression");
}
if (beta.TestBitZero() != (yTilde == 1))
{
// Use the other root
beta = beta.Negate();
}
return(new FpPoint(this, x, beta, true));
}
// B.3 pg 62
public override ECPoint Twice()
{
if (this.IsInfinity)
{
return(this);
}
ECCurve curve = this.Curve;
ECFieldElement Y1 = this.RawYCoord;
if (Y1.IsZero)
{
return(curve.Infinity);
}
int coord = curve.CoordinateSystem;
ECFieldElement X1 = this.RawXCoord;
switch (coord)
{
case ECCurve.COORD_AFFINE:
{
ECFieldElement X1Squared = X1.Square();
ECFieldElement gamma = Three(X1Squared).Add(this.Curve.A).Divide(Two(Y1));
ECFieldElement X3 = gamma.Square().Subtract(Two(X1));
ECFieldElement Y3 = gamma.Multiply(X1.Subtract(X3)).Subtract(Y1);
return(new FpPoint(Curve, X3, Y3, IsCompressed));
}
case ECCurve.COORD_HOMOGENEOUS:
{
ECFieldElement Z1 = this.RawZCoords[0];
bool Z1IsOne = Z1.IsOne;
// TODO Optimize for small negative a4 and -3
ECFieldElement w = curve.A;
if (!w.IsZero && !Z1IsOne)
{
w = w.Multiply(Z1.Square());
}
w = w.Add(Three(X1.Square()));
ECFieldElement s = Z1IsOne ? Y1 : Y1.Multiply(Z1);
ECFieldElement t = Z1IsOne ? Y1.Square() : s.Multiply(Y1);
ECFieldElement B = X1.Multiply(t);
ECFieldElement _4B = Four(B);
ECFieldElement h = w.Square().Subtract(Two(_4B));
ECFieldElement _2s = Two(s);
ECFieldElement X3 = h.Multiply(_2s);
ECFieldElement _2t = Two(t);
ECFieldElement Y3 = _4B.Subtract(h).Multiply(w).Subtract(Two(_2t.Square()));
ECFieldElement _4sSquared = Z1IsOne ? Two(_2t) : _2s.Square();
ECFieldElement Z3 = Two(_4sSquared).Multiply(s);
return(new FpPoint(curve, X3, Y3, new ECFieldElement[] { Z3 }, IsCompressed));
}
case ECCurve.COORD_JACOBIAN:
{
ECFieldElement Z1 = this.RawZCoords[0];
bool Z1IsOne = Z1.IsOne;
ECFieldElement Y1Squared = Y1.Square();
ECFieldElement T = Y1Squared.Square();
ECFieldElement a4 = curve.A;
ECFieldElement a4Neg = a4.Negate();
ECFieldElement M, S;
if (a4Neg.ToBigInteger().Equals(BigInteger.ValueOf(3)))
{
ECFieldElement Z1Squared = Z1IsOne ? Z1 : Z1.Square();
M = Three(X1.Add(Z1Squared).Multiply(X1.Subtract(Z1Squared)));
S = Four(Y1Squared.Multiply(X1));
}
else
{
ECFieldElement X1Squared = X1.Square();
M = Three(X1Squared);
if (Z1IsOne)
{
M = M.Add(a4);
}
else if (!a4.IsZero)
{
ECFieldElement Z1Squared = Z1IsOne ? Z1 : Z1.Square();
ECFieldElement Z1Pow4 = Z1Squared.Square();
if (a4Neg.BitLength < a4.BitLength)
{
M = M.Subtract(Z1Pow4.Multiply(a4Neg));
}
else
{
M = M.Add(Z1Pow4.Multiply(a4));
}
}
//S = two(doubleProductFromSquares(X1, Y1Squared, X1Squared, T));
S = Four(X1.Multiply(Y1Squared));
}
ECFieldElement X3 = M.Square().Subtract(Two(S));
ECFieldElement Y3 = S.Subtract(X3).Multiply(M).Subtract(Eight(T));
ECFieldElement Z3 = Two(Y1);
if (!Z1IsOne)
{
Z3 = Z3.Multiply(Z1);
}
// Alternative calculation of Z3 using fast square
//ECFieldElement Z3 = doubleProductFromSquares(Y1, Z1, Y1Squared, Z1Squared);
return(new FpPoint(curve, X3, Y3, new ECFieldElement[] { Z3 }, IsCompressed));
}
case ECCurve.COORD_JACOBIAN_MODIFIED:
{
return(TwiceJacobianModified(true));
}
default:
{
throw new InvalidOperationException("unsupported coordinate system");
}
}
}