1package org.bouncycastle.math.ec;
2
3import java.math.BigInteger;
4
5/**
6 * Class implementing the WTNAF (Window
7 * <code>&tau;</code>-adic Non-Adjacent Form) algorithm.
8 */
9public class WTauNafMultiplier extends AbstractECMultiplier
10{
11    // TODO Create WTauNafUtil class and move various functionality into it
12    static final String PRECOMP_NAME = "bc_wtnaf";
13
14    /**
15     * Multiplies a {@link org.bouncycastle.math.ec.ECPoint.F2m ECPoint.F2m}
16     * by <code>k</code> using the reduced <code>&tau;</code>-adic NAF (RTNAF)
17     * method.
18     * @param p The ECPoint.F2m to multiply.
19     * @param k The integer by which to multiply <code>k</code>.
20     * @return <code>p</code> multiplied by <code>k</code>.
21     */
22    protected ECPoint multiplyPositive(ECPoint point, BigInteger k)
23    {
24        if (!(point instanceof ECPoint.F2m))
25        {
26            throw new IllegalArgumentException("Only ECPoint.F2m can be " +
27                    "used in WTauNafMultiplier");
28        }
29
30        ECPoint.F2m p = (ECPoint.F2m)point;
31        ECCurve.F2m curve = (ECCurve.F2m)p.getCurve();
32        int m = curve.getM();
33        byte a = curve.getA().toBigInteger().byteValue();
34        byte mu = curve.getMu();
35        BigInteger[] s = curve.getSi();
36
37        ZTauElement rho = Tnaf.partModReduction(k, m, a, s, mu, (byte)10);
38
39        return multiplyWTnaf(p, rho, curve.getPreCompInfo(p, PRECOMP_NAME), a, mu);
40    }
41
42    /**
43     * Multiplies a {@link org.bouncycastle.math.ec.ECPoint.F2m ECPoint.F2m}
44     * by an element <code>&lambda;</code> of <code><b>Z</b>[&tau;]</code> using
45     * the <code>&tau;</code>-adic NAF (TNAF) method.
46     * @param p The ECPoint.F2m to multiply.
47     * @param lambda The element <code>&lambda;</code> of
48     * <code><b>Z</b>[&tau;]</code> of which to compute the
49     * <code>[&tau;]</code>-adic NAF.
50     * @return <code>p</code> multiplied by <code>&lambda;</code>.
51     */
52    private ECPoint.F2m multiplyWTnaf(ECPoint.F2m p, ZTauElement lambda,
53            PreCompInfo preCompInfo, byte a, byte mu)
54    {
55        ZTauElement[] alpha = (a == 0) ? Tnaf.alpha0 : Tnaf.alpha1;
56
57        BigInteger tw = Tnaf.getTw(mu, Tnaf.WIDTH);
58
59        byte[]u = Tnaf.tauAdicWNaf(mu, lambda, Tnaf.WIDTH,
60            BigInteger.valueOf(Tnaf.POW_2_WIDTH), tw, alpha);
61
62        return multiplyFromWTnaf(p, u, preCompInfo);
63    }
64
65    /**
66     * Multiplies a {@link org.bouncycastle.math.ec.ECPoint.F2m ECPoint.F2m}
67     * by an element <code>&lambda;</code> of <code><b>Z</b>[&tau;]</code>
68     * using the window <code>&tau;</code>-adic NAF (TNAF) method, given the
69     * WTNAF of <code>&lambda;</code>.
70     * @param p The ECPoint.F2m to multiply.
71     * @param u The the WTNAF of <code>&lambda;</code>..
72     * @return <code>&lambda; * p</code>
73     */
74    private static ECPoint.F2m multiplyFromWTnaf(ECPoint.F2m p, byte[] u, PreCompInfo preCompInfo)
75    {
76        ECCurve.F2m curve = (ECCurve.F2m)p.getCurve();
77        byte a = curve.getA().toBigInteger().byteValue();
78
79        ECPoint.F2m[] pu;
80        if ((preCompInfo == null) || !(preCompInfo instanceof WTauNafPreCompInfo))
81        {
82            pu = Tnaf.getPreComp(p, a);
83
84            WTauNafPreCompInfo pre = new WTauNafPreCompInfo();
85            pre.setPreComp(pu);
86            curve.setPreCompInfo(p, PRECOMP_NAME, pre);
87        }
88        else
89        {
90            pu = ((WTauNafPreCompInfo)preCompInfo).getPreComp();
91        }
92
93        // q = infinity
94        ECPoint.F2m q = (ECPoint.F2m) p.getCurve().getInfinity();
95        for (int i = u.length - 1; i >= 0; i--)
96        {
97            q = Tnaf.tau(q);
98            byte ui = u[i];
99            if (ui != 0)
100            {
101                if (ui > 0)
102                {
103                    q = q.addSimple(pu[ui]);
104                }
105                else
106                {
107                    q = q.subtractSimple(pu[-ui]);
108                }
109            }
110        }
111
112        return q;
113    }
114}
115