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using System;
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 ImplShamirsTrick(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 ImplShamirsTrick(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 ImplShamirsTrick(ECPoint P, BigInteger k,
ECPoint Q, BigInteger l)
{
int m = System.Math.Max(k.BitLength, l.BitLength);
ECPoint Z = P.Add(Q);
ECPoint R = P.Curve.Infinity;
for (int i = m - 1; i >= 0; --i)
{
R = R.Twice();
if (k.TestBit(i))
{
if (l.TestBit(i))
{
R = R.Add(Z);
}
else
{
R = R.Add(P);
}
}
else
{
if (l.TestBit(i))
{
R = R.Add(Q);
}
}
}
return R;
}
}
}
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