private static ECPoint ImplSumOfMultiplies(bool[] negs, WNafPreCompInfo[] infos, byte[][] wnafs)
{
int len = 0, count = wnafs.Length;
for (int i = 0; i < count; ++i)
{
len = System.Math.Max(len, wnafs[i].Length);
}
ECCurve curve = infos[0].PreComp[0].Curve;
ECPoint infinity = curve.Infinity;
ECPoint R = infinity;
int zeroes = 0;
for (int i = len - 1; i >= 0; --i)
{
ECPoint r = infinity;
for (int j = 0; j < count; ++j)
{
byte[] wnaf = wnafs[j];
int wi = i < wnaf.Length ? (int)(sbyte)wnaf[i] : 0;
if (wi != 0)
{
int n = System.Math.Abs(wi);
WNafPreCompInfo info = infos[j];
ECPoint[] table = (wi < 0 == negs[j]) ? info.PreComp : info.PreCompNeg;
r = r.Add(table[n >> 1]);
}
}
if (r == infinity)
{
++zeroes;
continue;
}
if (zeroes > 0)
{
R = R.TimesPow2(zeroes);
zeroes = 0;
}
R = R.TwicePlus(r);
}
if (zeroes > 0)
{
R = R.TimesPow2(zeroes);
}
return R;
}
internal static ECPoint ImplSumOfMultiplies(ECPoint[] ps, BigInteger[] ks)
{
int count = ps.Length;
bool[] negs = new bool[count];
WNafPreCompInfo[] infos = new WNafPreCompInfo[count];
byte[][] wnafs = new byte[count][];
for (int i = 0; i < count; ++i)
{
BigInteger ki = ks[i]; negs[i] = ki.SignValue < 0; ki = ki.Abs();
int width = System.Math.Max(2, System.Math.Min(16, WNafUtilities.GetWindowSize(ki.BitLength)));
infos[i] = WNafUtilities.Precompute(ps[i], width, true);
wnafs[i] = WNafUtilities.GenerateWindowNaf(width, ki);
}
return ImplSumOfMultiplies(negs, infos, wnafs);
}
internal static ECPoint ImplSumOfMultiplies(ECPoint[] ps, ECPointMap pointMap, BigInteger[] ks)
{
int halfCount = ps.Length, fullCount = halfCount << 1;
bool[] negs = new bool[fullCount];
WNafPreCompInfo[] infos = new WNafPreCompInfo[fullCount];
byte[][] wnafs = new byte[fullCount][];
for (int i = 0; i < halfCount; ++i)
{
int j0 = i << 1, j1 = j0 + 1;
BigInteger kj0 = ks[j0]; negs[j0] = kj0.SignValue < 0; kj0 = kj0.Abs();
BigInteger kj1 = ks[j1]; negs[j1] = kj1.SignValue < 0; kj1 = kj1.Abs();
int width = System.Math.Max(2, System.Math.Min(16, WNafUtilities.GetWindowSize(System.Math.Max(kj0.BitLength, kj1.BitLength))));
ECPoint P = ps[i], Q = WNafUtilities.MapPointWithPrecomp(P, width, true, pointMap);
infos[j0] = WNafUtilities.GetWNafPreCompInfo(P);
infos[j1] = WNafUtilities.GetWNafPreCompInfo(Q);
wnafs[j0] = WNafUtilities.GenerateWindowNaf(width, kj0);
wnafs[j1] = WNafUtilities.GenerateWindowNaf(width, kj1);
}
return ImplSumOfMultiplies(negs, infos, wnafs);
}
public static WNafPreCompInfo Precompute(ECPoint p, int width, bool includeNegated)
{
ECCurve c = p.Curve;
WNafPreCompInfo wnafPreCompInfo = GetWNafPreCompInfo(c.GetPreCompInfo(p, PRECOMP_NAME));
int iniPreCompLen = 0, reqPreCompLen = 1 << System.Math.Max(0, width - 2);
ECPoint[] preComp = wnafPreCompInfo.PreComp;
if (preComp == null)
{
preComp = EMPTY_POINTS;
}
else
{
iniPreCompLen = preComp.Length;
}
if (iniPreCompLen < reqPreCompLen)
{
preComp = ResizeTable(preComp, reqPreCompLen);
if (reqPreCompLen == 1)
{
preComp[0] = p.Normalize();
}
else
{
int curPreCompLen = iniPreCompLen;
if (curPreCompLen == 0)
{
preComp[0] = p;
curPreCompLen = 1;
}
ECFieldElement iso = null;
if (reqPreCompLen == 2)
{
preComp[1] = p.ThreeTimes();
}
else
{
ECPoint twiceP = wnafPreCompInfo.Twice, last = preComp[curPreCompLen - 1];
if (twiceP == null)
{
twiceP = preComp[0].Twice();
wnafPreCompInfo.Twice = twiceP;
/*
* For Fp curves with Jacobian projective coordinates, use a (quasi-)isomorphism
* where 'twiceP' is "affine", so that the subsequent additions are cheaper. This
* also requires scaling the initial point's X, Y coordinates, and reversing the
* isomorphism as part of the subsequent normalization.
*
* NOTE: The correctness of this optimization depends on:
* 1) additions do not use the curve's A, B coefficients.
* 2) no special cases (i.e. Q +/- Q) when calculating 1P, 3P, 5P, ...
*/
if (ECAlgorithms.IsFpCurve(c) && c.FieldSize >= 64)
{
switch (c.CoordinateSystem)
{
case ECCurve.COORD_JACOBIAN:
case ECCurve.COORD_JACOBIAN_CHUDNOVSKY:
case ECCurve.COORD_JACOBIAN_MODIFIED:
{
iso = twiceP.GetZCoord(0);
twiceP = c.CreatePoint(twiceP.XCoord.ToBigInteger(),
twiceP.YCoord.ToBigInteger());
ECFieldElement iso2 = iso.Square(), iso3 = iso2.Multiply(iso);
last = last.ScaleX(iso2).ScaleY(iso3);
if (iniPreCompLen == 0)
{
preComp[0] = last;
}
break;
}
}
}
}
while (curPreCompLen < reqPreCompLen)
{
/*
* Compute the new ECPoints for the precomputation array. The values 1, 3,
* 5, ..., 2^(width-1)-1 times p are computed
*/
preComp[curPreCompLen++] = last = last.Add(twiceP);
}
}
/*
* Having oft-used operands in affine form makes operations faster.
*/
c.NormalizeAll(preComp, iniPreCompLen, reqPreCompLen - iniPreCompLen, iso);
}
}
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, PRECOMP_NAME, wnafPreCompInfo);
return(wnafPreCompInfo);
}