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using System;
using Org.BouncyCastle.Math.EC.Multiplier;
using Org.BouncyCastle.Math.Field;
namespace Org.BouncyCastle.Math.EC
{
public class ECAlgorithms
{
public static bool IsF2mCurve(ECCurve c)
{
IFiniteField field = c.Field;
return field.Dimension > 1 && field.Characteristic.Equals(BigInteger.Two)
&& field is IPolynomialExtensionField;
}
public static bool IsFpCurve(ECCurve c)
{
return c.Field.Dimension == 1;
}
public static ECPoint SumOfTwoMultiplies(ECPoint P, BigInteger a, ECPoint Q, BigInteger b)
{
ECCurve cp = P.Curve;
Q = ImportPoint(cp, Q);
// Point multiplication for Koblitz curves (using WTNAF) beats Shamir's trick
if (cp is F2mCurve)
{
F2mCurve f2mCurve = (F2mCurve) cp;
if (f2mCurve.IsKoblitz)
{
return P.Multiply(a).Add(Q.Multiply(b));
}
}
return ImplShamirsTrickWNaf(P, a, Q, b);
}
/*
* "Shamir's Trick", originally due to E. G. Straus
* (Addition chains of vectors. American Mathematical Monthly,
* 71(7):806-808, Aug./Sept. 1964)
*
* Input: The points P, Q, scalar k = (km?, ... , k1, k0)
* and scalar l = (lm?, ... , l1, l0).
* Output: R = k * P + l * Q.
* 1: Z <- P + Q
* 2: R <- O
* 3: for i from m-1 down to 0 do
* 4: R <- R + R {point doubling}
* 5: if (ki = 1) and (li = 0) then R <- R + P end if
* 6: if (ki = 0) and (li = 1) then R <- R + Q end if
* 7: if (ki = 1) and (li = 1) then R <- R + Z end if
* 8: end for
* 9: return R
*/
public static ECPoint ShamirsTrick(ECPoint P, BigInteger k, ECPoint Q, BigInteger l)
{
ECCurve cp = P.Curve;
Q = ImportPoint(cp, Q);
return ImplShamirsTrickJsf(P, k, Q, l);
}
public static ECPoint ImportPoint(ECCurve c, ECPoint p)
{
ECCurve cp = p.Curve;
if (!c.Equals(cp))
throw new ArgumentException("Point must be on the same curve");
return c.ImportPoint(p);
}
public static void MontgomeryTrick(ECFieldElement[] zs, int off, int len)
{
/*
* Uses the "Montgomery Trick" to invert many field elements, with only a single actual
* field inversion. See e.g. the paper:
* "Fast Multi-scalar Multiplication Methods on Elliptic Curves with Precomputation Strategy Using Montgomery Trick"
* by Katsuyuki Okeya, Kouichi Sakurai.
*/
ECFieldElement[] c = new ECFieldElement[len];
c[0] = zs[off];
int i = 0;
while (++i < len)
{
c[i] = c[i - 1].Multiply(zs[off + i]);
}
ECFieldElement u = c[--i].Invert();
while (i > 0)
{
int j = off + i--;
ECFieldElement tmp = zs[j];
zs[j] = c[i].Multiply(u);
u = u.Multiply(tmp);
}
zs[off] = u;
}
internal static ECPoint ImplShamirsTrickJsf(ECPoint P, BigInteger k, ECPoint Q, BigInteger l)
{
ECCurve curve = P.Curve;
ECPoint infinity = curve.Infinity;
// TODO conjugate co-Z addition (ZADDC) can return both of these
ECPoint PaddQ = P.Add(Q);
ECPoint PsubQ = P.Subtract(Q);
ECPoint[] points = new ECPoint[] { Q, PsubQ, P, PaddQ };
curve.NormalizeAll(points);
ECPoint[] table = new ECPoint[] {
points[3].Negate(), points[2].Negate(), points[1].Negate(),
points[0].Negate(), infinity, points[0],
points[1], points[2], points[3] };
byte[] jsf = WNafUtilities.GenerateJsf(k, l);
ECPoint R = infinity;
int i = jsf.Length;
while (--i >= 0)
{
int jsfi = jsf[i];
// NOTE: The shifting ensures the sign is extended correctly
int kDigit = ((jsfi << 24) >> 28), lDigit = ((jsfi << 28) >> 28);
int index = 4 + (kDigit * 3) + lDigit;
R = R.TwicePlus(table[index]);
}
return R;
}
internal static ECPoint ImplShamirsTrickWNaf(ECPoint P, BigInteger k, ECPoint Q, BigInteger l)
{
int widthP = System.Math.Max(2, System.Math.Min(16, WNafUtilities.GetWindowSize(k.BitLength)));
int widthQ = System.Math.Max(2, System.Math.Min(16, WNafUtilities.GetWindowSize(l.BitLength)));
WNafPreCompInfo infoP = WNafUtilities.Precompute(P, widthP, true);
WNafPreCompInfo infoQ = WNafUtilities.Precompute(Q, widthQ, true);
ECPoint[] preCompP = infoP.PreComp;
ECPoint[] preCompQ = infoQ.PreComp;
ECPoint[] preCompNegP = infoP.PreCompNeg;
ECPoint[] preCompNegQ = infoQ.PreCompNeg;
byte[] wnafP = WNafUtilities.GenerateWindowNaf(widthP, k);
byte[] wnafQ = WNafUtilities.GenerateWindowNaf(widthQ, l);
int len = System.Math.Max(wnafP.Length, wnafQ.Length);
ECCurve curve = P.Curve;
ECPoint infinity = curve.Infinity;
ECPoint R = infinity;
int zeroes = 0;
for (int i = len - 1; i >= 0; --i)
{
int wiP = i < wnafP.Length ? (int)(sbyte)wnafP[i] : 0;
int wiQ = i < wnafQ.Length ? (int)(sbyte)wnafQ[i] : 0;
if ((wiP | wiQ) == 0)
{
++zeroes;
continue;
}
ECPoint r = infinity;
if (wiP != 0)
{
int nP = System.Math.Abs(wiP);
ECPoint[] tableP = wiP < 0 ? preCompNegP : preCompP;
r = r.Add(tableP[nP >> 1]);
}
if (wiQ != 0)
{
int nQ = System.Math.Abs(wiQ);
ECPoint[] tableQ = wiQ < 0 ? preCompNegQ : preCompQ;
r = r.Add(tableQ[nQ >> 1]);
}
if (zeroes > 0)
{
R = R.TimesPow2(zeroes);
zeroes = 0;
}
R = R.TwicePlus(r);
}
if (zeroes > 0)
{
R = R.TimesPow2(zeroes);
}
return R;
}
}
}
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