public static FixedPointPreCompInfo Precompute(ECPoint p, int minWidth) { ECCurve c = p.Curve; int n = 1 << minWidth; FixedPointPreCompInfo info = GetFixedPointPreCompInfo(c.GetPreCompInfo(p, PRECOMP_NAME)); ECPoint[] lookupTable = info.PreComp; if (lookupTable == null || lookupTable.Length < n) { int bits = GetCombSize(c); int d = (bits + minWidth - 1) / minWidth; ECPoint[] pow2Table = new ECPoint[minWidth]; pow2Table[0] = p; for (int i = 1; i < minWidth; ++i) { pow2Table[i] = pow2Table[i - 1].TimesPow2(d); } c.NormalizeAll(pow2Table); lookupTable = new ECPoint[n]; lookupTable[0] = c.Infinity; 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); info.PreComp = lookupTable; info.Width = minWidth; c.SetPreCompInfo(p, PRECOMP_NAME, info); } return(info); }
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"); } int minWidth = GetWidthForCombSize(size); FixedPointPreCompInfo info = FixedPointUtilities.Precompute(p, minWidth); ECPoint[] lookupTable = info.PreComp; int width = info.Width; int d = (size + width - 1) / width; ECPoint R = c.Infinity; int top = d * width - 1; for (int i = 0; i < d; ++i) { int index = 0; for (int j = top - i; j >= 0; j -= d) { index <<= 1; if (k.TestBit(j)) { index |= 1; } } R = R.TwicePlus(lookupTable[index]); } return(R); }