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The Bouncy Castle Crypto package is a Java implementation of cryptographic algorithms. This jar contains JCE provider and lightweight API for the Bouncy Castle Cryptography APIs for JDK 1.5 to JDK 1.8 with debug enabled.

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package org.bouncycastle.math.ec;

import java.math.BigInteger;

/**
 * Class implementing the WTNAF (Window
 * τ-adic Non-Adjacent Form) algorithm.
 */
public class WTauNafMultiplier extends AbstractECMultiplier
{
    // TODO Create WTauNafUtil class and move various functionality into it
    static final String PRECOMP_NAME = "bc_wtnaf";

    /**
     * Multiplies a {@link org.bouncycastle.math.ec.ECPoint.AbstractF2m ECPoint.AbstractF2m}
     * by k using the reduced τ-adic NAF (RTNAF)
     * method.
     * @param point The ECPoint.AbstractF2m to multiply.
     * @param k The integer by which to multiply k.
     * @return p multiplied by k.
     */
    protected ECPoint multiplyPositive(ECPoint point, BigInteger k)
    {
        if (!(point instanceof ECPoint.AbstractF2m))
        {
            throw new IllegalArgumentException("Only ECPoint.AbstractF2m can be " +
                    "used in WTauNafMultiplier");
        }

        ECPoint.AbstractF2m p = (ECPoint.AbstractF2m)point;
        ECCurve.AbstractF2m curve = (ECCurve.AbstractF2m)p.getCurve();
        int m = curve.getFieldSize();
        byte a = curve.getA().toBigInteger().byteValue();
        byte mu = Tnaf.getMu(a);
        BigInteger[] s = curve.getSi();

        ZTauElement rho = Tnaf.partModReduction(k, m, a, s, mu, (byte)10);

        return multiplyWTnaf(p, rho, curve.getPreCompInfo(p, PRECOMP_NAME), a, mu);
    }

    /**
     * Multiplies a {@link org.bouncycastle.math.ec.ECPoint.AbstractF2m ECPoint.AbstractF2m}
     * by an element λ of Z[τ] using
     * the τ-adic NAF (TNAF) method.
     * @param p The ECPoint.AbstractF2m to multiply.
     * @param lambda The element λ of
     * Z[τ] of which to compute the
     * [τ]-adic NAF.
     * @return p multiplied by λ.
     */
    private ECPoint.AbstractF2m multiplyWTnaf(ECPoint.AbstractF2m p, ZTauElement lambda,
            PreCompInfo preCompInfo, byte a, byte mu)
    {
        ZTauElement[] alpha = (a == 0) ? Tnaf.alpha0 : Tnaf.alpha1;

        BigInteger tw = Tnaf.getTw(mu, Tnaf.WIDTH);

        byte[]u = Tnaf.tauAdicWNaf(mu, lambda, Tnaf.WIDTH,
            BigInteger.valueOf(Tnaf.POW_2_WIDTH), tw, alpha);

        return multiplyFromWTnaf(p, u, preCompInfo);
    }

    /**
     * Multiplies a {@link org.bouncycastle.math.ec.ECPoint.AbstractF2m ECPoint.AbstractF2m}
     * by an element λ of Z[τ]
     * using the window τ-adic NAF (TNAF) method, given the
     * WTNAF of λ.
     * @param p The ECPoint.AbstractF2m to multiply.
     * @param u The the WTNAF of λ..
     * @return λ * p
     */
    private static ECPoint.AbstractF2m multiplyFromWTnaf(ECPoint.AbstractF2m p, byte[] u, PreCompInfo preCompInfo)
    {
        ECCurve.AbstractF2m curve = (ECCurve.AbstractF2m)p.getCurve();
        byte a = curve.getA().toBigInteger().byteValue();

        ECPoint.AbstractF2m[] pu;
        if ((preCompInfo == null) || !(preCompInfo instanceof WTauNafPreCompInfo))
        {
            pu = Tnaf.getPreComp(p, a);

            WTauNafPreCompInfo pre = new WTauNafPreCompInfo();
            pre.setPreComp(pu);
            curve.setPreCompInfo(p, PRECOMP_NAME, pre);
        }
        else
        {
            pu = ((WTauNafPreCompInfo)preCompInfo).getPreComp();
        }

        // TODO Include negations in precomp (optionally) and use from here
        ECPoint.AbstractF2m[] puNeg = new ECPoint.AbstractF2m[pu.length];
        for (int i = 0; i < pu.length; ++i)
        {
            puNeg[i] = (ECPoint.AbstractF2m)pu[i].negate();
        }


        // q = infinity
        ECPoint.AbstractF2m q = (ECPoint.AbstractF2m) p.getCurve().getInfinity();

        int tauCount = 0;
        for (int i = u.length - 1; i >= 0; i--)
        {
            ++tauCount;
            int ui = u[i];
            if (ui != 0)
            {
                q = q.tauPow(tauCount);
                tauCount = 0;

                ECPoint x = ui > 0 ? pu[ui >>> 1] : puNeg[(-ui) >>> 1];
                q = (ECPoint.AbstractF2m)q.add(x);
            }
        }
        if (tauCount > 0)
        {
            q = q.tauPow(tauCount);
        }
        return q;
    }
}