public virtual bool Equals(ECPoint other)
{
if (this == other)
{
return(true);
}
if (null == other)
{
return(false);
}
ECCurve c1 = this.Curve, c2 = other.Curve;
bool n1 = (null == c1), n2 = (null == c2);
bool i1 = IsInfinity, i2 = other.IsInfinity;
if (i1 || i2)
{
return((i1 && i2) && (n1 || n2 || c1.Equals(c2)));
}
ECPoint p1 = this, p2 = other;
if (n1 && n2)
{
// Points with null curve are in affine form, so already normalized
}
else if (n1)
{
p2 = p2.Normalize();
}
else if (n2)
{
p1 = p1.Normalize();
}
else if (!c1.Equals(c2))
{
return(false);
}
else
{
// TODO Consider just requiring already normalized, to avoid silent performance degradation
ECPoint[] points = new ECPoint[] { this, c1.ImportPoint(p2) };
// TODO This is a little strong, really only requires coZNormalizeAll to get Zs equal
c1.NormalizeAll(points);
p1 = points[0];
p2 = points[1];
}
return(p1.XCoord.Equals(p2.XCoord) && p1.YCoord.Equals(p2.YCoord));
}
internal static ECPoint ImplShamirsTrick(ECPoint P, BigInteger k,
ECPoint Q, BigInteger l)
{
ECCurve curve = P.Curve;
ECPoint infinity = curve.Infinity;
// TODO conjugate co-Z addition (ZADDC) can return both of these
ECPoint PaddQ = P.Add(Q);
ECPoint PsubQ = P.Subtract(Q);
ECPoint[] points = new ECPoint[] { Q, PsubQ, P, PaddQ };
curve.NormalizeAll(points);
ECPoint[] table = new ECPoint[] {
points[3].Negate(), points[2].Negate(), points[1].Negate(),
points[0].Negate(), infinity, points[0],
points[1], points[2], points[3]
};
byte[] jsf = WNafUtilities.GenerateJsf(k, l);
ECPoint R = infinity;
int i = jsf.Length;
while (--i >= 0)
{
int jsfi = jsf[i];
// NOTE: The shifting ensures the sign is extended correctly
int kDigit = ((jsfi << 24) >> 28), lDigit = ((jsfi << 28) >> 28);
int index = 4 + (kDigit * 3) + lDigit;
R = R.TwicePlus(table[index]);
}
return(R);
}
public static WNafPreCompInfo Precompute(ECPoint p, int width, bool includeNegated)
{
ECCurve c = p.Curve;
WNafPreCompInfo wnafPreCompInfo = GetWNafPreCompInfo(c.GetPreCompInfo(p));
ECPoint[] preComp = wnafPreCompInfo.PreComp;
if (preComp == null)
{
preComp = new ECPoint[] { p };
}
int preCompLen = preComp.Length;
int reqPreCompLen = 1 << System.Math.Max(0, width - 2);
if (preCompLen < reqPreCompLen)
{
ECPoint twiceP = wnafPreCompInfo.Twice;
if (twiceP == null)
{
twiceP = preComp[0].Twice().Normalize();
wnafPreCompInfo.Twice = twiceP;
}
preComp = ResizeTable(preComp, reqPreCompLen);
/*
* TODO Okeya/Sakurai paper has precomputation trick and "Montgomery's Trick" to speed this up.
* Also, co-Z arithmetic could avoid the subsequent normalization too.
*/
for (int i = preCompLen; i < reqPreCompLen; i++)
{
/*
* Compute the new ECPoints for the precomputation array. The values 1, 3, 5, ...,
* 2^(width-1)-1 times p are computed
*/
preComp[i] = twiceP.Add(preComp[i - 1]);
}
/*
* Having oft-used operands in affine form makes operations faster.
*/
c.NormalizeAll(preComp);
}
wnafPreCompInfo.PreComp = preComp;
if (includeNegated)
{
ECPoint[] preCompNeg = wnafPreCompInfo.PreCompNeg;
int pos;
if (preCompNeg == null)
{
pos = 0;
preCompNeg = new ECPoint[reqPreCompLen];
}
else
{
pos = preCompNeg.Length;
if (pos < reqPreCompLen)
{
preCompNeg = ResizeTable(preCompNeg, reqPreCompLen);
}
}
while (pos < reqPreCompLen)
{
preCompNeg[pos] = preComp[pos].Negate();
++pos;
}
wnafPreCompInfo.PreCompNeg = preCompNeg;
}
c.SetPreCompInfo(p, wnafPreCompInfo);
return(wnafPreCompInfo);
}