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); }
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 + 1]; pow2Table[0] = 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); 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); info.Offset = pow2Table[minWidth]; info.PreComp = lookupTable; info.Width = minWidth; c.SetPreCompInfo(p, PRECOMP_NAME, info); } return(info); }
public static FixedPointPreCompInfo Precompute(ECPoint p, int minWidth) { ECCurve curve = p.Curve; int num = 1 << minWidth; FixedPointPreCompInfo fixedPointPreCompInfo = GetFixedPointPreCompInfo(curve.GetPreCompInfo(p, PRECOMP_NAME)); ECPoint[] preComp = fixedPointPreCompInfo.PreComp; if (preComp == null || preComp.Length < num) { int combSize = GetCombSize(curve); int e = (combSize + minWidth - 1) / minWidth; ECPoint[] array = new ECPoint[minWidth]; array[0] = p; for (int i = 1; i < minWidth; i++) { array[i] = array[i - 1].TimesPow2(e); } curve.NormalizeAll(array); preComp = new ECPoint[num]; preComp[0] = curve.Infinity; for (int num2 = minWidth - 1; num2 >= 0; num2--) { ECPoint b = array[num2]; int num3 = 1 << num2; for (int j = num3; j < num; j += num3 << 1) { preComp[j] = preComp[j - num3].Add(b); } } curve.NormalizeAll(preComp); fixedPointPreCompInfo.PreComp = preComp; fixedPointPreCompInfo.Width = minWidth; curve.SetPreCompInfo(p, PRECOMP_NAME, fixedPointPreCompInfo); } return(fixedPointPreCompInfo); }
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)); }