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    /**
12     * Multiplies a {@link org.bouncycastle.math.ec.ECPoint.F2m ECPoint.F2m}
13     * by <code>k</code> using the reduced <code>&tau;</code>-adic NAF (RTNAF)
14     * method.
15     * @param p The ECPoint.F2m to multiply.
16     * @param k The integer by which to multiply <code>k</code>.
17     * @return <code>p</code> multiplied by <code>k</code>.
18     */
19    protected ECPoint multiplyPositive(ECPoint point, BigInteger k)
20    {
21        if (!(point instanceof ECPoint.F2m))
22        {
23            throw new IllegalArgumentException("Only ECPoint.F2m can be " +
24                    "used in WTauNafMultiplier");
25        }
26
27        ECPoint.F2m p = (ECPoint.F2m)point;
28        ECCurve.F2m curve = (ECCurve.F2m)p.getCurve();
29        int m = curve.getM();
30        byte a = curve.getA().toBigInteger().byteValue();
31        byte mu = curve.getMu();
32        BigInteger[] s = curve.getSi();
33
34        ZTauElement rho = Tnaf.partModReduction(k, m, a, s, mu, (byte)10);
35
36        return multiplyWTnaf(p, rho, curve.getPreCompInfo(p), a, mu);
37    }
38
39    /**
40     * Multiplies a {@link org.bouncycastle.math.ec.ECPoint.F2m ECPoint.F2m}
41     * by an element <code>&lambda;</code> of <code><b>Z</b>[&tau;]</code> using
42     * the <code>&tau;</code>-adic NAF (TNAF) method.
43     * @param p The ECPoint.F2m to multiply.
44     * @param lambda The element <code>&lambda;</code> of
45     * <code><b>Z</b>[&tau;]</code> of which to compute the
46     * <code>[&tau;]</code>-adic NAF.
47     * @return <code>p</code> multiplied by <code>&lambda;</code>.
48     */
49    private ECPoint.F2m multiplyWTnaf(ECPoint.F2m p, ZTauElement lambda,
50            PreCompInfo preCompInfo, byte a, byte mu)
51    {
52        ZTauElement[] alpha;
53        if (a == 0)
54        {
55            alpha = Tnaf.alpha0;
56        }
57        else
58        {
59            // a == 1
60            alpha = Tnaf.alpha1;
61        }
62
63        BigInteger tw = Tnaf.getTw(mu, Tnaf.WIDTH);
64
65        byte[]u = Tnaf.tauAdicWNaf(mu, lambda, Tnaf.WIDTH,
66                BigInteger.valueOf(Tnaf.POW_2_WIDTH), tw, alpha);
67
68        return multiplyFromWTnaf(p, u, preCompInfo);
69    }
70
71    /**
72     * Multiplies a {@link org.bouncycastle.math.ec.ECPoint.F2m ECPoint.F2m}
73     * by an element <code>&lambda;</code> of <code><b>Z</b>[&tau;]</code>
74     * using the window <code>&tau;</code>-adic NAF (TNAF) method, given the
75     * WTNAF of <code>&lambda;</code>.
76     * @param p The ECPoint.F2m to multiply.
77     * @param u The the WTNAF of <code>&lambda;</code>..
78     * @return <code>&lambda; * p</code>
79     */
80    private static ECPoint.F2m multiplyFromWTnaf(ECPoint.F2m p, byte[] u,
81            PreCompInfo preCompInfo)
82    {
83        ECCurve.F2m curve = (ECCurve.F2m)p.getCurve();
84        byte a = curve.getA().toBigInteger().byteValue();
85
86        ECPoint.F2m[] pu;
87        if ((preCompInfo == null) || !(preCompInfo instanceof WTauNafPreCompInfo))
88        {
89            pu = Tnaf.getPreComp(p, a);
90            curve.setPreCompInfo(p, new WTauNafPreCompInfo(pu));
91        }
92        else
93        {
94            pu = ((WTauNafPreCompInfo)preCompInfo).getPreComp();
95        }
96
97        // q = infinity
98        ECPoint.F2m q = (ECPoint.F2m) p.getCurve().getInfinity();
99        for (int i = u.length - 1; i >= 0; i--)
100        {
101            q = Tnaf.tau(q);
102            if (u[i] != 0)
103            {
104                if (u[i] > 0)
105                {
106                    q = q.addSimple(pu[u[i]]);
107                }
108                else
109                {
110                    // u[i] < 0
111                    q = q.subtractSimple(pu[-u[i]]);
112                }
113            }
114        }
115
116        return q;
117    }
118}
119