diff --git a/Crypto/src/math/ec/abc/Tnaf.cs b/Crypto/src/math/ec/abc/Tnaf.cs
new file mode 100644
index 000000000..225fc3075
--- /dev/null
+++ b/Crypto/src/math/ec/abc/Tnaf.cs
@@ -0,0 +1,834 @@
+using System;
+
+namespace Org.BouncyCastle.Math.EC.Abc
+{
+ /**
+ * Class holding methods for point multiplication based on the window
+ * τ-adic nonadjacent form (WTNAF). The algorithms are based on the
+ * paper "Improved Algorithms for Arithmetic on Anomalous Binary Curves"
+ * by Jerome A. Solinas. The paper first appeared in the Proceedings of
+ * Crypto 1997.
+ */
+ internal class Tnaf
+ {
+ private static readonly BigInteger MinusOne = BigInteger.One.Negate();
+ private static readonly BigInteger MinusTwo = BigInteger.Two.Negate();
+ private static readonly BigInteger MinusThree = BigInteger.Three.Negate();
+ private static readonly BigInteger Four = BigInteger.ValueOf(4);
+
+ /**
+ * The window width of WTNAF. The standard value of 4 is slightly less
+ * than optimal for running time, but keeps space requirements for
+ * precomputation low. For typical curves, a value of 5 or 6 results in
+ * a better running time. When changing this value, the
+ * <code>α<sub>u</sub></code>'s must be computed differently, see
+ * e.g. "Guide to Elliptic Curve Cryptography", Darrel Hankerson,
+ * Alfred Menezes, Scott Vanstone, Springer-Verlag New York Inc., 2004,
+ * p. 121-122
+ */
+ public const sbyte Width = 4;
+
+ /**
+ * 2<sup>4</sup>
+ */
+ public const sbyte Pow2Width = 16;
+
+ /**
+ * The <code>α<sub>u</sub></code>'s for <code>a=0</code> as an array
+ * of <code>ZTauElement</code>s.
+ */
+ public static readonly ZTauElement[] Alpha0 =
+ {
+ null,
+ new ZTauElement(BigInteger.One, BigInteger.Zero), null,
+ new ZTauElement(MinusThree, MinusOne), null,
+ new ZTauElement(MinusOne, MinusOne), null,
+ new ZTauElement(BigInteger.One, MinusOne), null
+ };
+
+ /**
+ * The <code>α<sub>u</sub></code>'s for <code>a=0</code> as an array
+ * of TNAFs.
+ */
+ public static readonly sbyte[][] Alpha0Tnaf =
+ {
+ null, new sbyte[]{1}, null, new sbyte[]{-1, 0, 1}, null, new sbyte[]{1, 0, 1}, null, new sbyte[]{-1, 0, 0, 1}
+ };
+
+ /**
+ * The <code>α<sub>u</sub></code>'s for <code>a=1</code> as an array
+ * of <code>ZTauElement</code>s.
+ */
+ public static readonly ZTauElement[] Alpha1 =
+ {
+ null,
+ new ZTauElement(BigInteger.One, BigInteger.Zero), null,
+ new ZTauElement(MinusThree, BigInteger.One), null,
+ new ZTauElement(MinusOne, BigInteger.One), null,
+ new ZTauElement(BigInteger.One, BigInteger.One), null
+ };
+
+ /**
+ * The <code>α<sub>u</sub></code>'s for <code>a=1</code> as an array
+ * of TNAFs.
+ */
+ public static readonly sbyte[][] Alpha1Tnaf =
+ {
+ null, new sbyte[]{1}, null, new sbyte[]{-1, 0, 1}, null, new sbyte[]{1, 0, 1}, null, new sbyte[]{-1, 0, 0, -1}
+ };
+
+ /**
+ * Computes the norm of an element <code>λ</code> of
+ * <code><b>Z</b>[τ]</code>.
+ * @param mu The parameter <code>μ</code> of the elliptic curve.
+ * @param lambda The element <code>λ</code> of
+ * <code><b>Z</b>[τ]</code>.
+ * @return The norm of <code>λ</code>.
+ */
+ public static BigInteger Norm(sbyte mu, ZTauElement lambda)
+ {
+ BigInteger norm;
+
+ // s1 = u^2
+ BigInteger s1 = lambda.u.Multiply(lambda.u);
+
+ // s2 = u * v
+ BigInteger s2 = lambda.u.Multiply(lambda.v);
+
+ // s3 = 2 * v^2
+ BigInteger s3 = lambda.v.Multiply(lambda.v).ShiftLeft(1);
+
+ if (mu == 1)
+ {
+ norm = s1.Add(s2).Add(s3);
+ }
+ else if (mu == -1)
+ {
+ norm = s1.Subtract(s2).Add(s3);
+ }
+ else
+ {
+ throw new ArgumentException("mu must be 1 or -1");
+ }
+
+ return norm;
+ }
+
+ /**
+ * Computes the norm of an element <code>λ</code> of
+ * <code><b>R</b>[τ]</code>, where <code>λ = u + vτ</code>
+ * and <code>u</code> and <code>u</code> are real numbers (elements of
+ * <code><b>R</b></code>).
+ * @param mu The parameter <code>μ</code> of the elliptic curve.
+ * @param u The real part of the element <code>λ</code> of
+ * <code><b>R</b>[τ]</code>.
+ * @param v The <code>τ</code>-adic part of the element
+ * <code>λ</code> of <code><b>R</b>[τ]</code>.
+ * @return The norm of <code>λ</code>.
+ */
+ public static SimpleBigDecimal Norm(sbyte mu, SimpleBigDecimal u, SimpleBigDecimal v)
+ {
+ SimpleBigDecimal norm;
+
+ // s1 = u^2
+ SimpleBigDecimal s1 = u.Multiply(u);
+
+ // s2 = u * v
+ SimpleBigDecimal s2 = u.Multiply(v);
+
+ // s3 = 2 * v^2
+ SimpleBigDecimal s3 = v.Multiply(v).ShiftLeft(1);
+
+ if (mu == 1)
+ {
+ norm = s1.Add(s2).Add(s3);
+ }
+ else if (mu == -1)
+ {
+ norm = s1.Subtract(s2).Add(s3);
+ }
+ else
+ {
+ throw new ArgumentException("mu must be 1 or -1");
+ }
+
+ return norm;
+ }
+
+ /**
+ * Rounds an element <code>λ</code> of <code><b>R</b>[τ]</code>
+ * to an element of <code><b>Z</b>[τ]</code>, such that their difference
+ * has minimal norm. <code>λ</code> is given as
+ * <code>λ = λ<sub>0</sub> + λ<sub>1</sub>τ</code>.
+ * @param lambda0 The component <code>λ<sub>0</sub></code>.
+ * @param lambda1 The component <code>λ<sub>1</sub></code>.
+ * @param mu The parameter <code>μ</code> of the elliptic curve. Must
+ * equal 1 or -1.
+ * @return The rounded element of <code><b>Z</b>[τ]</code>.
+ * @throws ArgumentException if <code>lambda0</code> and
+ * <code>lambda1</code> do not have same scale.
+ */
+ public static ZTauElement Round(SimpleBigDecimal lambda0,
+ SimpleBigDecimal lambda1, sbyte mu)
+ {
+ int scale = lambda0.Scale;
+ if (lambda1.Scale != scale)
+ throw new ArgumentException("lambda0 and lambda1 do not have same scale");
+
+ if (!((mu == 1) || (mu == -1)))
+ throw new ArgumentException("mu must be 1 or -1");
+
+ BigInteger f0 = lambda0.Round();
+ BigInteger f1 = lambda1.Round();
+
+ SimpleBigDecimal eta0 = lambda0.Subtract(f0);
+ SimpleBigDecimal eta1 = lambda1.Subtract(f1);
+
+ // eta = 2*eta0 + mu*eta1
+ SimpleBigDecimal eta = eta0.Add(eta0);
+ if (mu == 1)
+ {
+ eta = eta.Add(eta1);
+ }
+ else
+ {
+ // mu == -1
+ eta = eta.Subtract(eta1);
+ }
+
+ // check1 = eta0 - 3*mu*eta1
+ // check2 = eta0 + 4*mu*eta1
+ SimpleBigDecimal threeEta1 = eta1.Add(eta1).Add(eta1);
+ SimpleBigDecimal fourEta1 = threeEta1.Add(eta1);
+ SimpleBigDecimal check1;
+ SimpleBigDecimal check2;
+ if (mu == 1)
+ {
+ check1 = eta0.Subtract(threeEta1);
+ check2 = eta0.Add(fourEta1);
+ }
+ else
+ {
+ // mu == -1
+ check1 = eta0.Add(threeEta1);
+ check2 = eta0.Subtract(fourEta1);
+ }
+
+ sbyte h0 = 0;
+ sbyte h1 = 0;
+
+ // if eta >= 1
+ if (eta.CompareTo(BigInteger.One) >= 0)
+ {
+ if (check1.CompareTo(MinusOne) < 0)
+ {
+ h1 = mu;
+ }
+ else
+ {
+ h0 = 1;
+ }
+ }
+ else
+ {
+ // eta < 1
+ if (check2.CompareTo(BigInteger.Two) >= 0)
+ {
+ h1 = mu;
+ }
+ }
+
+ // if eta < -1
+ if (eta.CompareTo(MinusOne) < 0)
+ {
+ if (check1.CompareTo(BigInteger.One) >= 0)
+ {
+ h1 = (sbyte)-mu;
+ }
+ else
+ {
+ h0 = -1;
+ }
+ }
+ else
+ {
+ // eta >= -1
+ if (check2.CompareTo(MinusTwo) < 0)
+ {
+ h1 = (sbyte)-mu;
+ }
+ }
+
+ BigInteger q0 = f0.Add(BigInteger.ValueOf(h0));
+ BigInteger q1 = f1.Add(BigInteger.ValueOf(h1));
+ return new ZTauElement(q0, q1);
+ }
+
+ /**
+ * Approximate division by <code>n</code>. For an integer
+ * <code>k</code>, the value <code>λ = s k / n</code> is
+ * computed to <code>c</code> bits of accuracy.
+ * @param k The parameter <code>k</code>.
+ * @param s The curve parameter <code>s<sub>0</sub></code> or
+ * <code>s<sub>1</sub></code>.
+ * @param vm The Lucas Sequence element <code>V<sub>m</sub></code>.
+ * @param a The parameter <code>a</code> of the elliptic curve.
+ * @param m The bit length of the finite field
+ * <code><b>F</b><sub>m</sub></code>.
+ * @param c The number of bits of accuracy, i.e. the scale of the returned
+ * <code>SimpleBigDecimal</code>.
+ * @return The value <code>λ = s k / n</code> computed to
+ * <code>c</code> bits of accuracy.
+ */
+ public static SimpleBigDecimal ApproximateDivisionByN(BigInteger k,
+ BigInteger s, BigInteger vm, sbyte a, int m, int c)
+ {
+ int _k = (m + 5)/2 + c;
+ BigInteger ns = k.ShiftRight(m - _k - 2 + a);
+
+ BigInteger gs = s.Multiply(ns);
+
+ BigInteger hs = gs.ShiftRight(m);
+
+ BigInteger js = vm.Multiply(hs);
+
+ BigInteger gsPlusJs = gs.Add(js);
+ BigInteger ls = gsPlusJs.ShiftRight(_k-c);
+ if (gsPlusJs.TestBit(_k-c-1))
+ {
+ // round up
+ ls = ls.Add(BigInteger.One);
+ }
+
+ return new SimpleBigDecimal(ls, c);
+ }
+
+ /**
+ * Computes the <code>τ</code>-adic NAF (non-adjacent form) of an
+ * element <code>λ</code> of <code><b>Z</b>[τ]</code>.
+ * @param mu The parameter <code>μ</code> of the elliptic curve.
+ * @param lambda The element <code>λ</code> of
+ * <code><b>Z</b>[τ]</code>.
+ * @return The <code>τ</code>-adic NAF of <code>λ</code>.
+ */
+ public static sbyte[] TauAdicNaf(sbyte mu, ZTauElement lambda)
+ {
+ if (!((mu == 1) || (mu == -1)))
+ throw new ArgumentException("mu must be 1 or -1");
+
+ BigInteger norm = Norm(mu, lambda);
+
+ // Ceiling of log2 of the norm
+ int log2Norm = norm.BitLength;
+
+ // If length(TNAF) > 30, then length(TNAF) < log2Norm + 3.52
+ int maxLength = log2Norm > 30 ? log2Norm + 4 : 34;
+
+ // The array holding the TNAF
+ sbyte[] u = new sbyte[maxLength];
+ int i = 0;
+
+ // The actual length of the TNAF
+ int length = 0;
+
+ BigInteger r0 = lambda.u;
+ BigInteger r1 = lambda.v;
+
+ while(!((r0.Equals(BigInteger.Zero)) && (r1.Equals(BigInteger.Zero))))
+ {
+ // If r0 is odd
+ if (r0.TestBit(0))
+ {
+ u[i] = (sbyte) BigInteger.Two.Subtract((r0.Subtract(r1.ShiftLeft(1))).Mod(Four)).IntValue;
+
+ // r0 = r0 - u[i]
+ if (u[i] == 1)
+ {
+ r0 = r0.ClearBit(0);
+ }
+ else
+ {
+ // u[i] == -1
+ r0 = r0.Add(BigInteger.One);
+ }
+ length = i;
+ }
+ else
+ {
+ u[i] = 0;
+ }
+
+ BigInteger t = r0;
+ BigInteger s = r0.ShiftRight(1);
+ if (mu == 1)
+ {
+ r0 = r1.Add(s);
+ }
+ else
+ {
+ // mu == -1
+ r0 = r1.Subtract(s);
+ }
+
+ r1 = t.ShiftRight(1).Negate();
+ i++;
+ }
+
+ length++;
+
+ // Reduce the TNAF array to its actual length
+ sbyte[] tnaf = new sbyte[length];
+ Array.Copy(u, 0, tnaf, 0, length);
+ return tnaf;
+ }
+
+ /**
+ * Applies the operation <code>τ()</code> to an
+ * <code>F2mPoint</code>.
+ * @param p The F2mPoint to which <code>τ()</code> is applied.
+ * @return <code>τ(p)</code>
+ */
+ public static F2mPoint Tau(F2mPoint p)
+ {
+ if (p.IsInfinity)
+ return p;
+
+ ECFieldElement x = p.X;
+ ECFieldElement y = p.Y;
+
+ return new F2mPoint(p.Curve, x.Square(), y.Square(), p.IsCompressed);
+ }
+
+ /**
+ * Returns the parameter <code>μ</code> of the elliptic curve.
+ * @param curve The elliptic curve from which to obtain <code>μ</code>.
+ * The curve must be a Koblitz curve, i.e. <code>a</code> Equals
+ * <code>0</code> or <code>1</code> and <code>b</code> Equals
+ * <code>1</code>.
+ * @return <code>μ</code> of the elliptic curve.
+ * @throws ArgumentException if the given ECCurve is not a Koblitz
+ * curve.
+ */
+ public static sbyte GetMu(F2mCurve curve)
+ {
+ BigInteger a = curve.A.ToBigInteger();
+
+ sbyte mu;
+ if (a.SignValue == 0)
+ {
+ mu = -1;
+ }
+ else if (a.Equals(BigInteger.One))
+ {
+ mu = 1;
+ }
+ else
+ {
+ throw new ArgumentException("No Koblitz curve (ABC), TNAF multiplication not possible");
+ }
+ return mu;
+ }
+
+ /**
+ * Calculates the Lucas Sequence elements <code>U<sub>k-1</sub></code> and
+ * <code>U<sub>k</sub></code> or <code>V<sub>k-1</sub></code> and
+ * <code>V<sub>k</sub></code>.
+ * @param mu The parameter <code>μ</code> of the elliptic curve.
+ * @param k The index of the second element of the Lucas Sequence to be
+ * returned.
+ * @param doV If set to true, computes <code>V<sub>k-1</sub></code> and
+ * <code>V<sub>k</sub></code>, otherwise <code>U<sub>k-1</sub></code> and
+ * <code>U<sub>k</sub></code>.
+ * @return An array with 2 elements, containing <code>U<sub>k-1</sub></code>
+ * and <code>U<sub>k</sub></code> or <code>V<sub>k-1</sub></code>
+ * and <code>V<sub>k</sub></code>.
+ */
+ public static BigInteger[] GetLucas(sbyte mu, int k, bool doV)
+ {
+ if (!(mu == 1 || mu == -1))
+ throw new ArgumentException("mu must be 1 or -1");
+
+ BigInteger u0;
+ BigInteger u1;
+ BigInteger u2;
+
+ if (doV)
+ {
+ u0 = BigInteger.Two;
+ u1 = BigInteger.ValueOf(mu);
+ }
+ else
+ {
+ u0 = BigInteger.Zero;
+ u1 = BigInteger.One;
+ }
+
+ for (int i = 1; i < k; i++)
+ {
+ // u2 = mu*u1 - 2*u0;
+ BigInteger s = null;
+ if (mu == 1)
+ {
+ s = u1;
+ }
+ else
+ {
+ // mu == -1
+ s = u1.Negate();
+ }
+
+ u2 = s.Subtract(u0.ShiftLeft(1));
+ u0 = u1;
+ u1 = u2;
+ // System.out.println(i + ": " + u2);
+ // System.out.println();
+ }
+
+ BigInteger[] retVal = {u0, u1};
+ return retVal;
+ }
+
+ /**
+ * Computes the auxiliary value <code>t<sub>w</sub></code>. If the width is
+ * 4, then for <code>mu = 1</code>, <code>t<sub>w</sub> = 6</code> and for
+ * <code>mu = -1</code>, <code>t<sub>w</sub> = 10</code>
+ * @param mu The parameter <code>μ</code> of the elliptic curve.
+ * @param w The window width of the WTNAF.
+ * @return the auxiliary value <code>t<sub>w</sub></code>
+ */
+ public static BigInteger GetTw(sbyte mu, int w)
+ {
+ if (w == 4)
+ {
+ if (mu == 1)
+ {
+ return BigInteger.ValueOf(6);
+ }
+ else
+ {
+ // mu == -1
+ return BigInteger.ValueOf(10);
+ }
+ }
+ else
+ {
+ // For w <> 4, the values must be computed
+ BigInteger[] us = GetLucas(mu, w, false);
+ BigInteger twoToW = BigInteger.Zero.SetBit(w);
+ BigInteger u1invert = us[1].ModInverse(twoToW);
+ BigInteger tw;
+ tw = BigInteger.Two.Multiply(us[0]).Multiply(u1invert).Mod(twoToW);
+ //System.out.println("mu = " + mu);
+ //System.out.println("tw = " + tw);
+ return tw;
+ }
+ }
+
+ /**
+ * Computes the auxiliary values <code>s<sub>0</sub></code> and
+ * <code>s<sub>1</sub></code> used for partial modular reduction.
+ * @param curve The elliptic curve for which to compute
+ * <code>s<sub>0</sub></code> and <code>s<sub>1</sub></code>.
+ * @throws ArgumentException if <code>curve</code> is not a
+ * Koblitz curve (Anomalous Binary Curve, ABC).
+ */
+ public static BigInteger[] GetSi(F2mCurve curve)
+ {
+ if (!curve.IsKoblitz)
+ throw new ArgumentException("si is defined for Koblitz curves only");
+
+ int m = curve.M;
+ int a = curve.A.ToBigInteger().IntValue;
+ sbyte mu = curve.GetMu();
+ int h = curve.H.IntValue;
+ int index = m + 3 - a;
+ BigInteger[] ui = GetLucas(mu, index, false);
+
+ BigInteger dividend0;
+ BigInteger dividend1;
+ if (mu == 1)
+ {
+ dividend0 = BigInteger.One.Subtract(ui[1]);
+ dividend1 = BigInteger.One.Subtract(ui[0]);
+ }
+ else if (mu == -1)
+ {
+ dividend0 = BigInteger.One.Add(ui[1]);
+ dividend1 = BigInteger.One.Add(ui[0]);
+ }
+ else
+ {
+ throw new ArgumentException("mu must be 1 or -1");
+ }
+
+ BigInteger[] si = new BigInteger[2];
+
+ if (h == 2)
+ {
+ si[0] = dividend0.ShiftRight(1);
+ si[1] = dividend1.ShiftRight(1).Negate();
+ }
+ else if (h == 4)
+ {
+ si[0] = dividend0.ShiftRight(2);
+ si[1] = dividend1.ShiftRight(2).Negate();
+ }
+ else
+ {
+ throw new ArgumentException("h (Cofactor) must be 2 or 4");
+ }
+
+ return si;
+ }
+
+ /**
+ * Partial modular reduction modulo
+ * <code>(τ<sup>m</sup> - 1)/(τ - 1)</code>.
+ * @param k The integer to be reduced.
+ * @param m The bitlength of the underlying finite field.
+ * @param a The parameter <code>a</code> of the elliptic curve.
+ * @param s The auxiliary values <code>s<sub>0</sub></code> and
+ * <code>s<sub>1</sub></code>.
+ * @param mu The parameter μ of the elliptic curve.
+ * @param c The precision (number of bits of accuracy) of the partial
+ * modular reduction.
+ * @return <code>ρ := k partmod (τ<sup>m</sup> - 1)/(τ - 1)</code>
+ */
+ public static ZTauElement PartModReduction(BigInteger k, int m, sbyte a,
+ BigInteger[] s, sbyte mu, sbyte c)
+ {
+ // d0 = s[0] + mu*s[1]; mu is either 1 or -1
+ BigInteger d0;
+ if (mu == 1)
+ {
+ d0 = s[0].Add(s[1]);
+ }
+ else
+ {
+ d0 = s[0].Subtract(s[1]);
+ }
+
+ BigInteger[] v = GetLucas(mu, m, true);
+ BigInteger vm = v[1];
+
+ SimpleBigDecimal lambda0 = ApproximateDivisionByN(
+ k, s[0], vm, a, m, c);
+
+ SimpleBigDecimal lambda1 = ApproximateDivisionByN(
+ k, s[1], vm, a, m, c);
+
+ ZTauElement q = Round(lambda0, lambda1, mu);
+
+ // r0 = n - d0*q0 - 2*s1*q1
+ BigInteger r0 = k.Subtract(d0.Multiply(q.u)).Subtract(
+ BigInteger.ValueOf(2).Multiply(s[1]).Multiply(q.v));
+
+ // r1 = s1*q0 - s0*q1
+ BigInteger r1 = s[1].Multiply(q.u).Subtract(s[0].Multiply(q.v));
+
+ return new ZTauElement(r0, r1);
+ }
+
+ /**
+ * Multiplies a {@link org.bouncycastle.math.ec.F2mPoint F2mPoint}
+ * by a <code>BigInteger</code> using the reduced <code>τ</code>-adic
+ * NAF (RTNAF) method.
+ * @param p The F2mPoint to Multiply.
+ * @param k The <code>BigInteger</code> by which to Multiply <code>p</code>.
+ * @return <code>k * p</code>
+ */
+ public static F2mPoint MultiplyRTnaf(F2mPoint p, BigInteger k)
+ {
+ F2mCurve curve = (F2mCurve) p.Curve;
+ int m = curve.M;
+ sbyte a = (sbyte) curve.A.ToBigInteger().IntValue;
+ sbyte mu = curve.GetMu();
+ BigInteger[] s = curve.GetSi();
+ ZTauElement rho = PartModReduction(k, m, a, s, mu, (sbyte)10);
+
+ return MultiplyTnaf(p, rho);
+ }
+
+ /**
+ * Multiplies a {@link org.bouncycastle.math.ec.F2mPoint F2mPoint}
+ * by an element <code>λ</code> of <code><b>Z</b>[τ]</code>
+ * using the <code>τ</code>-adic NAF (TNAF) method.
+ * @param p The F2mPoint to Multiply.
+ * @param lambda The element <code>λ</code> of
+ * <code><b>Z</b>[τ]</code>.
+ * @return <code>λ * p</code>
+ */
+ public static F2mPoint MultiplyTnaf(F2mPoint p, ZTauElement lambda)
+ {
+ F2mCurve curve = (F2mCurve)p.Curve;
+ sbyte mu = curve.GetMu();
+ sbyte[] u = TauAdicNaf(mu, lambda);
+
+ F2mPoint q = MultiplyFromTnaf(p, u);
+
+ return q;
+ }
+
+ /**
+ * Multiplies a {@link org.bouncycastle.math.ec.F2mPoint F2mPoint}
+ * by an element <code>λ</code> of <code><b>Z</b>[τ]</code>
+ * using the <code>τ</code>-adic NAF (TNAF) method, given the TNAF
+ * of <code>λ</code>.
+ * @param p The F2mPoint to Multiply.
+ * @param u The the TNAF of <code>λ</code>..
+ * @return <code>λ * p</code>
+ */
+ public static F2mPoint MultiplyFromTnaf(F2mPoint p, sbyte[] u)
+ {
+ F2mCurve curve = (F2mCurve)p.Curve;
+ F2mPoint q = (F2mPoint) curve.Infinity;
+ for (int i = u.Length - 1; i >= 0; i--)
+ {
+ q = Tau(q);
+ if (u[i] == 1)
+ {
+ q = (F2mPoint)q.AddSimple(p);
+ }
+ else if (u[i] == -1)
+ {
+ q = (F2mPoint)q.SubtractSimple(p);
+ }
+ }
+ return q;
+ }
+
+ /**
+ * Computes the <code>[τ]</code>-adic window NAF of an element
+ * <code>λ</code> of <code><b>Z</b>[τ]</code>.
+ * @param mu The parameter μ of the elliptic curve.
+ * @param lambda The element <code>λ</code> of
+ * <code><b>Z</b>[τ]</code> of which to compute the
+ * <code>[τ]</code>-adic NAF.
+ * @param width The window width of the resulting WNAF.
+ * @param pow2w 2<sup>width</sup>.
+ * @param tw The auxiliary value <code>t<sub>w</sub></code>.
+ * @param alpha The <code>α<sub>u</sub></code>'s for the window width.
+ * @return The <code>[τ]</code>-adic window NAF of
+ * <code>λ</code>.
+ */
+ public static sbyte[] TauAdicWNaf(sbyte mu, ZTauElement lambda,
+ sbyte width, BigInteger pow2w, BigInteger tw, ZTauElement[] alpha)
+ {
+ if (!((mu == 1) || (mu == -1)))
+ throw new ArgumentException("mu must be 1 or -1");
+
+ BigInteger norm = Norm(mu, lambda);
+
+ // Ceiling of log2 of the norm
+ int log2Norm = norm.BitLength;
+
+ // If length(TNAF) > 30, then length(TNAF) < log2Norm + 3.52
+ int maxLength = log2Norm > 30 ? log2Norm + 4 + width : 34 + width;
+
+ // The array holding the TNAF
+ sbyte[] u = new sbyte[maxLength];
+
+ // 2^(width - 1)
+ BigInteger pow2wMin1 = pow2w.ShiftRight(1);
+
+ // Split lambda into two BigIntegers to simplify calculations
+ BigInteger r0 = lambda.u;
+ BigInteger r1 = lambda.v;
+ int i = 0;
+
+ // while lambda <> (0, 0)
+ while (!((r0.Equals(BigInteger.Zero))&&(r1.Equals(BigInteger.Zero))))
+ {
+ // if r0 is odd
+ if (r0.TestBit(0))
+ {
+ // uUnMod = r0 + r1*tw Mod 2^width
+ BigInteger uUnMod
+ = r0.Add(r1.Multiply(tw)).Mod(pow2w);
+
+ sbyte uLocal;
+ // if uUnMod >= 2^(width - 1)
+ if (uUnMod.CompareTo(pow2wMin1) >= 0)
+ {
+ uLocal = (sbyte) uUnMod.Subtract(pow2w).IntValue;
+ }
+ else
+ {
+ uLocal = (sbyte) uUnMod.IntValue;
+ }
+ // uLocal is now in [-2^(width-1), 2^(width-1)-1]
+
+ u[i] = uLocal;
+ bool s = true;
+ if (uLocal < 0)
+ {
+ s = false;
+ uLocal = (sbyte)-uLocal;
+ }
+ // uLocal is now >= 0
+
+ if (s)
+ {
+ r0 = r0.Subtract(alpha[uLocal].u);
+ r1 = r1.Subtract(alpha[uLocal].v);
+ }
+ else
+ {
+ r0 = r0.Add(alpha[uLocal].u);
+ r1 = r1.Add(alpha[uLocal].v);
+ }
+ }
+ else
+ {
+ u[i] = 0;
+ }
+
+ BigInteger t = r0;
+
+ if (mu == 1)
+ {
+ r0 = r1.Add(r0.ShiftRight(1));
+ }
+ else
+ {
+ // mu == -1
+ r0 = r1.Subtract(r0.ShiftRight(1));
+ }
+ r1 = t.ShiftRight(1).Negate();
+ i++;
+ }
+ return u;
+ }
+
+ /**
+ * Does the precomputation for WTNAF multiplication.
+ * @param p The <code>ECPoint</code> for which to do the precomputation.
+ * @param a The parameter <code>a</code> of the elliptic curve.
+ * @return The precomputation array for <code>p</code>.
+ */
+ public static F2mPoint[] GetPreComp(F2mPoint p, sbyte a)
+ {
+ F2mPoint[] pu;
+ pu = new F2mPoint[16];
+ pu[1] = p;
+ sbyte[][] alphaTnaf;
+ if (a == 0)
+ {
+ alphaTnaf = Tnaf.Alpha0Tnaf;
+ }
+ else
+ {
+ // a == 1
+ alphaTnaf = Tnaf.Alpha1Tnaf;
+ }
+
+ int precompLen = alphaTnaf.Length;
+ for (int i = 3; i < precompLen; i = i + 2)
+ {
+ pu[i] = Tnaf.MultiplyFromTnaf(p, alphaTnaf[i]);
+ }
+
+ return pu;
+ }
+ }
+}
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