WNafL2RMultiplier.java revision 5db505e1f6a68c8d5dfdb0fed0b8607dea7bed96 
1package org.bouncycastle.math.ec;
2
3import java.math.BigInteger;
4
5/**
6 * Class implementing the WNAF (Window Non-Adjacent Form) multiplication
7 * algorithm.
8 */
9public class WNafL2RMultiplier extends AbstractECMultiplier
10{
11    /**
12     * Multiplies <code>this</code> by an integer <code>k</code> using the
13     * Window NAF method.
14     * @param k The integer by which <code>this</code> is multiplied.
15     * @return A new <code>ECPoint</code> which equals <code>this</code>
16     * multiplied by <code>k</code>.
17     */
18    protected ECPoint multiplyPositive(ECPoint p, BigInteger k)
19    {
20        // Clamp the window width in the range [2, 16]
21        int width = Math.max(2, Math.min(16, getWindowSize(k.bitLength())));
22
23        WNafPreCompInfo wnafPreCompInfo = WNafUtil.precompute(p, width, true);
24        ECPoint[] preComp = wnafPreCompInfo.getPreComp();
25        ECPoint[] preCompNeg = wnafPreCompInfo.getPreCompNeg();
26
27        int[] wnaf = WNafUtil.generateCompactWindowNaf(width, k);
28
29        ECPoint R = p.getCurve().getInfinity();
30
31        int i = wnaf.length;
32
33        /*
34         * NOTE This code optimizes the first window using the precomputed points to substitute an
35         * addition for 2 or more doublings.
36         */
37        if (i > 1)
38        {
39            int wi = wnaf[--i];
40            int digit = wi >> 16, zeroes = wi & 0xFFFF;
41
42            int n = Math.abs(digit);
43            ECPoint[] table = digit < 0 ? preCompNeg : preComp;
44
45            /*
46             * NOTE: We use this optimization conservatively, since some coordinate systems have
47             * significantly cheaper doubling relative to addition.
48             *
49             * (n << 2) selects precomputed values in the lower half of the table
50             * (n << 3) selects precomputed values in the lower quarter of the table
51             */
52            //if ((n << 2) < (1 << width))
53            if ((n << 3) < (1 << width))
54            {
55                int highest = LongArray.bitLengths[n];
56                int lowBits =  n ^ (1 << (highest - 1));
57                int scale = width - highest;
58
59                int i1 = ((1 << (width - 1)) - 1);
60                int i2 = (lowBits << scale) + 1;
61                R = table[i1 >>> 1].add(table[i2 >>> 1]);
62
63                zeroes -= scale;
64
65//              System.out.println("Optimized: 2^" + scale + " * " + n + " = " + i1 + " + " + i2);
66            }
67            else
68            {
69                R = table[n >>> 1];
70            }
71
72            R = R.timesPow2(zeroes);
73        }
74
75        while (i > 0)
76        {
77            int wi = wnaf[--i];
78            int digit = wi >> 16, zeroes = wi & 0xFFFF;
79
80            int n = Math.abs(digit);
81            ECPoint[] table = digit < 0 ? preCompNeg : preComp;
82            ECPoint r = table[n >>> 1];
83
84            R = R.twicePlus(r);
85            R = R.timesPow2(zeroes);
86        }
87
88        return R;
89    }
90
91    /**
92     * Determine window width to use for a scalar multiplication of the given size.
93     *
94     * @param bits the bit-length of the scalar to multiply by
95     * @return the window size to use
96     */
97    protected int getWindowSize(int bits)
98    {
99        return WNafUtil.getWindowSize(bits);
100    }
101}
102