public PreCompInfo Precompute(PreCompInfo existing)
{
FixedPointPreCompInfo existingFP = (existing is FixedPointPreCompInfo) ? (FixedPointPreCompInfo)existing : null;
ECCurve c = m_p.Curve;
int bits = FixedPointUtilities.GetCombSize(c);
int minWidth = bits > 250 ? 6 : 5;
int n = 1 << minWidth;
if (CheckExisting(existingFP, n))
{
return(existingFP);
}
int d = (bits + minWidth - 1) / minWidth;
ECPoint[] pow2Table = new ECPoint[minWidth + 1];
pow2Table[0] = m_p;
for (int i = 1; i < minWidth; ++i)
{
pow2Table[i] = pow2Table[i - 1].TimesPow2(d);
}
// This will be the 'offset' value
pow2Table[minWidth] = pow2Table[0].Subtract(pow2Table[1]);
c.NormalizeAll(pow2Table);
ECPoint[] lookupTable = new ECPoint[n];
lookupTable[0] = pow2Table[0];
for (int bit = minWidth - 1; bit >= 0; --bit)
{
ECPoint pow2 = pow2Table[bit];
int step = 1 << bit;
for (int i = step; i < n; i += (step << 1))
{
lookupTable[i] = lookupTable[i - step].Add(pow2);
}
}
c.NormalizeAll(lookupTable);
FixedPointPreCompInfo result = new FixedPointPreCompInfo();
result.LookupTable = c.CreateCacheSafeLookupTable(lookupTable, 0, lookupTable.Length);
result.Offset = pow2Table[minWidth];
result.Width = minWidth;
return(result);
}
protected override ECPoint MultiplyPositive(ECPoint p, BigInteger k)
{
ECCurve c = p.Curve;
int size = FixedPointUtilities.GetCombSize(c);
if (k.BitLength > size)
{
/*
* 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 info = FixedPointUtilities.Precompute(p);
ECLookupTable lookupTable = info.LookupTable;
int width = info.Width;
int d = (size + width - 1) / width;
ECPoint R = c.Infinity;
int fullComb = d * width;
uint[] K = Nat.FromBigInteger(fullComb, k);
int top = fullComb - 1;
for (int i = 0; i < d; ++i)
{
uint secretIndex = 0;
for (int j = top - i; j >= 0; j -= d)
{
uint secretBit = K[j >> 5] >> (j & 0x1F);
secretIndex ^= secretBit >> 1;
secretIndex <<= 1;
secretIndex ^= secretBit;
}
ECPoint add = lookupTable.Lookup((int)secretIndex);
R = R.TwicePlus(add);
}
return(R.Add(info.Offset));
}
private bool CheckExisting(FixedPointPreCompInfo existingFP, int n)
{
return(existingFP != null && CheckTable(existingFP.LookupTable, n));
}