protected override ECPoint MultiplyPositive(ECPoint p, BigInteger k)
{
ECCurve curve = p.Curve;
int combSize = FixedPointUtilities.GetCombSize(curve);
if (k.BitLength > combSize)
{
throw new InvalidOperationException("fixed-point comb doesn't support scalars larger than the curve order");
}
int widthForCombSize = GetWidthForCombSize(combSize);
FixedPointPreCompInfo fixedPointPreCompInfo = FixedPointUtilities.Precompute(p, widthForCombSize);
ECPoint[] preComp = fixedPointPreCompInfo.PreComp;
int width = fixedPointPreCompInfo.Width;
int num = (combSize + width - 1) / width;
ECPoint eCPoint = curve.Infinity;
int num2 = num * width - 1;
for (int i = 0; i < num; i++)
{
int num3 = 0;
for (int num4 = num2 - i; num4 >= 0; num4 -= num)
{
num3 <<= 1;
if (k.TestBit(num4))
{
num3 |= 1;
}
}
eCPoint = eCPoint.TwicePlus(preComp[num3]);
}
return(eCPoint);
}
internal static ECPoint ImplShamirsTrickWNaf(ECPoint P, BigInteger k,
ECPoint Q, BigInteger l)
{
bool negK = k.SignValue < 0, negL = l.SignValue < 0;
BigInteger kAbs = k.Abs(), lAbs = l.Abs();
int minWidthP = WNafUtilities.GetWindowSize(kAbs.BitLength, 8);
int minWidthQ = WNafUtilities.GetWindowSize(lAbs.BitLength, 8);
WNafPreCompInfo infoP = WNafUtilities.Precompute(P, minWidthP, true);
WNafPreCompInfo infoQ = WNafUtilities.Precompute(Q, minWidthQ, true);
// When P, Q are 'promoted' (i.e. reused several times), switch to fixed-point algorithm
{
ECCurve c = P.Curve;
int combSize = FixedPointUtilities.GetCombSize(c);
if (!negK && !negL &&
k.BitLength <= combSize && l.BitLength <= combSize &&
infoP.IsPromoted && infoQ.IsPromoted)
{
return(ImplShamirsTrickFixedPoint(P, k, Q, l));
}
}
int widthP = System.Math.Min(8, infoP.Width);
int widthQ = System.Math.Min(8, infoQ.Width);
ECPoint[] preCompP = negK ? infoP.PreCompNeg : infoP.PreComp;
ECPoint[] preCompQ = negL ? infoQ.PreCompNeg : infoQ.PreComp;
ECPoint[] preCompNegP = negK ? infoP.PreComp : infoP.PreCompNeg;
ECPoint[] preCompNegQ = negL ? infoQ.PreComp : infoQ.PreCompNeg;
byte[] wnafP = WNafUtilities.GenerateWindowNaf(widthP, kAbs);
byte[] wnafQ = WNafUtilities.GenerateWindowNaf(widthQ, lAbs);
return(ImplShamirsTrickWNaf(preCompP, preCompNegP, wnafP, preCompQ, preCompNegQ, wnafQ));
}
private static ECPoint ImplShamirsTrickFixedPoint(ECPoint p, BigInteger k, ECPoint q, BigInteger l)
{
ECCurve c = p.Curve;
int combSize = FixedPointUtilities.GetCombSize(c);
if (k.BitLength > combSize || l.BitLength > combSize)
{
/*
* TODO The comb works best when the scalars are less than the (possibly unknown) order.
* Still, if we want to handle larger scalars, we could allow customization of the comb
* size, or alternatively we could deal with the 'extra' bits either by running the comb
* multiple times as necessary, or by using an alternative multiplier as prelude.
*/
throw new InvalidOperationException("fixed-point comb doesn't support scalars larger than the curve order");
}
FixedPointPreCompInfo infoP = FixedPointUtilities.Precompute(p);
FixedPointPreCompInfo infoQ = FixedPointUtilities.Precompute(q);
ECLookupTable lookupTableP = infoP.LookupTable;
ECLookupTable lookupTableQ = infoQ.LookupTable;
int widthP = infoP.Width;
int widthQ = infoQ.Width;
// TODO This shouldn't normally happen, but a better "solution" is desirable anyway
if (widthP != widthQ)
{
FixedPointCombMultiplier m = new FixedPointCombMultiplier();
ECPoint r1 = m.Multiply(p, k);
ECPoint r2 = m.Multiply(q, l);
return(r1.Add(r2));
}
int width = widthP;
int d = (combSize + width - 1) / width;
ECPoint R = c.Infinity;
int fullComb = d * width;
uint[] K = Nat.FromBigInteger(fullComb, k);
uint[] L = Nat.FromBigInteger(fullComb, l);
int top = fullComb - 1;
for (int i = 0; i < d; ++i)
{
uint secretIndexK = 0, secretIndexL = 0;
for (int j = top - i; j >= 0; j -= d)
{
uint secretBitK = K[j >> 5] >> (j & 0x1F);
secretIndexK ^= secretBitK >> 1;
secretIndexK <<= 1;
secretIndexK ^= secretBitK;
uint secretBitL = L[j >> 5] >> (j & 0x1F);
secretIndexL ^= secretBitL >> 1;
secretIndexL <<= 1;
secretIndexL ^= secretBitL;
}
ECPoint addP = lookupTableP.LookupVar((int)secretIndexK);
ECPoint addQ = lookupTableQ.LookupVar((int)secretIndexL);
ECPoint T = addP.Add(addQ);
R = R.TwicePlus(T);
}
return(R.Add(infoP.Offset).Add(infoQ.Offset));
}
