org.bouncycastle.math.ec.custom.sec.SecT131Field Maven / Gradle / Ivy

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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 and up.
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package org.bouncycastle.math.ec.custom.sec;

import java.math.BigInteger;

import org.bouncycastle.math.raw.Interleave;
import org.bouncycastle.math.raw.Nat;
import org.bouncycastle.math.raw.Nat192;

public class SecT131Field
{
    private static final long M03 = -1L >>> 61;
    private static final long M44 = -1L >>> 20;

    private static final long[] ROOT_Z = new long[]{ 0x26BC4D789AF13523L, 0x26BC4D789AF135E2L, 0x6L };

    public static void add(long[] x, long[] y, long[] z)
    {
        z[0] = x[0] ^ y[0];
        z[1] = x[1] ^ y[1];
        z[2] = x[2] ^ y[2];
    }

    public static void addExt(long[] xx, long[] yy, long[] zz)
    {
        zz[0] = xx[0] ^ yy[0];
        zz[1] = xx[1] ^ yy[1];
        zz[2] = xx[2] ^ yy[2];
        zz[3] = xx[3] ^ yy[3];
        zz[4] = xx[4] ^ yy[4];
    }

    public static void addOne(long[] x, long[] z)
    {
        z[0] = x[0] ^ 1L;
        z[1] = x[1];
        z[2] = x[2];
    }

    private static void addTo(long[] x, long[] z)
    {
        z[0] ^= x[0];
        z[1] ^= x[1];
        z[2] ^= x[2];
    }

    public static long[] fromBigInteger(BigInteger x)
    {
        return Nat.fromBigInteger64(131, x);
    }

    public static void halfTrace(long[] x, long[] z)
    {
        long[] tt = Nat.create64(5);

        Nat192.copy64(x, z);
        for (int i = 1; i < 131; i += 2)
        {
            implSquare(z, tt);
            reduce(tt, z);
            implSquare(z, tt);
            reduce(tt, z);
            addTo(x, z);
        }
    }

    public static void invert(long[] x, long[] z)
    {
        if (Nat192.isZero64(x))
        {
            throw new IllegalStateException();
        }

        // Itoh-Tsujii inversion

        long[] t0 = Nat192.create64();
        long[] t1 = Nat192.create64();

        square(x, t0);
        multiply(t0, x, t0);
        squareN(t0, 2, t1);
        multiply(t1, t0, t1);
        squareN(t1, 4, t0);
        multiply(t0, t1, t0);
        squareN(t0, 8, t1);
        multiply(t1, t0, t1);
        squareN(t1, 16, t0);
        multiply(t0, t1, t0);
        squareN(t0, 32, t1);
        multiply(t1, t0, t1);
        square(t1, t1);
        multiply(t1, x, t1);
        squareN(t1, 65, t0);
        multiply(t0, t1, t0);
        square(t0, z);
    }

    public static void multiply(long[] x, long[] y, long[] z)
    {
        long[] tt = new long[8];
        implMultiply(x, y, tt);
        reduce(tt, z);
    }

    public static void multiplyAddToExt(long[] x, long[] y, long[] zz)
    {
        long[] tt = new long[8];
        implMultiply(x, y, tt);
        addExt(zz, tt, zz);
    }

    public static void reduce(long[] xx, long[] z)
    {
        long x0 = xx[0], x1 = xx[1], x2 = xx[2], x3 = xx[3], x4 = xx[4];

        x1 ^= (x4 <<  61) ^ (x4 <<  63);
        x2 ^= (x4 >>>  3) ^ (x4 >>>  1) ^ x4 ^ (x4 <<   5);
        x3 ^=                                  (x4 >>> 59);

        x0 ^= (x3 <<  61) ^ (x3 <<  63);
        x1 ^= (x3 >>>  3) ^ (x3 >>>  1) ^ x3 ^ (x3 <<   5);
        x2 ^=                                  (x3 >>> 59);

        long t = x2 >>> 3;
        z[0]   = x0 ^ t ^ (t << 2) ^ (t << 3) ^ (t <<   8);
        z[1]   = x1                           ^ (t >>> 56);
        z[2]   = x2 & M03;
    }

    public static void reduce61(long[] z, int zOff)
    {
        long z2      = z[zOff + 2], t = z2 >>> 3;
        z[zOff    ] ^= t ^ (t << 2) ^ (t << 3) ^ (t <<   8);
        z[zOff + 1] ^=                           (t >>> 56);
        z[zOff + 2]  = z2 & M03;
    }

    public static void sqrt(long[] x, long[] z)
    {
        long[] odd = Nat192.create64();

        long u0, u1;
        u0 = Interleave.unshuffle(x[0]); u1 = Interleave.unshuffle(x[1]);
        long e0 = (u0 & 0x00000000FFFFFFFFL) | (u1 << 32);
        odd[0]  = (u0 >>> 32) | (u1 & 0xFFFFFFFF00000000L);

        u0 = Interleave.unshuffle(x[2]);
        long e1 = (u0 & 0x00000000FFFFFFFFL);
        odd[1]  = (u0 >>> 32);

        multiply(odd, ROOT_Z, z);

        z[0] ^= e0;
        z[1] ^= e1;
    }

    public static void square(long[] x, long[] z)
    {
        long[] tt = Nat.create64(5);
        implSquare(x, tt);
        reduce(tt, z);
    }

    public static void squareAddToExt(long[] x, long[] zz)
    {
        long[] tt = Nat.create64(5);
        implSquare(x, tt);
        addExt(zz, tt, zz);
    }

    public static void squareN(long[] x, int n, long[] z)
    {
//        assert n > 0;

        long[] tt = Nat.create64(5);
        implSquare(x, tt);
        reduce(tt, z);

        while (--n > 0)
        {
            implSquare(z, tt);
            reduce(tt, z);
        }
    }

    public static int trace(long[] x)
    {
        // Non-zero-trace bits: 0, 123, 129
        return (int)(x[0] ^ (x[1] >>> 59) ^ (x[2] >>> 1)) & 1;
    }

    protected static void implCompactExt(long[] zz)
    {
        long z0 = zz[0], z1 = zz[1], z2 = zz[2], z3 = zz[3], z4 = zz[4], z5 = zz[5];
        zz[0] =  z0         ^ (z1 << 44);
        zz[1] = (z1 >>> 20) ^ (z2 << 24);
        zz[2] = (z2 >>> 40) ^ (z3 <<  4)
                            ^ (z4 << 48);
        zz[3] = (z3 >>> 60) ^ (z5 << 28)
              ^ (z4 >>> 16);
        zz[4] = (z5 >>> 36);
        zz[5] = 0;
    }

    protected static void implMultiply(long[] x, long[] y, long[] zz)
    {
        /*
         * "Five-way recursion" as described in "Batch binary Edwards", Daniel J. Bernstein.
         */

        long f0 = x[0], f1 = x[1], f2 = x[2];
        f2  = ((f1 >>> 24) ^ (f2 << 40)) & M44;
        f1  = ((f0 >>> 44) ^ (f1 << 20)) & M44;
        f0 &= M44;

        long g0 = y[0], g1 = y[1], g2 = y[2];
        g2  = ((g1 >>> 24) ^ (g2 << 40)) & M44;
        g1  = ((g0 >>> 44) ^ (g1 << 20)) & M44;
        g0 &= M44;

        long[] u = zz;
        long[] H = new long[10];

        implMulw(u, f0, g0, H, 0);              // H(0)       44/43 bits
        implMulw(u, f2, g2, H, 2);              // H(INF)     44/41 bits

        long t0 = f0 ^ f1 ^ f2;
        long t1 = g0 ^ g1 ^ g2;

        implMulw(u, t0, t1, H, 4);              // H(1)       44/43 bits

        long t2 = (f1 << 1) ^ (f2 << 2);
        long t3 = (g1 << 1) ^ (g2 << 2);

        implMulw(u, f0 ^ t2, g0 ^ t3, H, 6);    // H(t)       44/45 bits
        implMulw(u, t0 ^ t2, t1 ^ t3, H, 8);    // H(t + 1)   44/45 bits

        long t4 = H[6] ^ H[8];
        long t5 = H[7] ^ H[9];

    //    assert t5 >>> 44 == 0;

        // Calculate V
        long v0 =      (t4 << 1) ^ H[6];
        long v1 = t4 ^ (t5 << 1) ^ H[7];
        long v2 = t5;

        // Calculate U
        long u0 = H[0];
        long u1 = H[1] ^ H[0] ^ H[4];
        long u2 =        H[1] ^ H[5];

        // Calculate W
        long w0 = u0 ^ v0 ^ (H[2] << 4) ^ (H[2] << 1);
        long w1 = u1 ^ v1 ^ (H[3] << 4) ^ (H[3] << 1);
        long w2 = u2 ^ v2;

        // Propagate carries
        w1 ^= (w0 >>> 44); w0 &= M44;
        w2 ^= (w1 >>> 44); w1 &= M44;

   //     assert (w0 & 1L) == 0;

        // Divide W by t

        w0 = (w0 >>> 1) ^ ((w1 & 1L) << 43);
        w1 = (w1 >>> 1) ^ ((w2 & 1L) << 43);
        w2 = (w2 >>> 1);

        // Divide W by (t + 1)

        w0 ^= (w0 << 1);
        w0 ^= (w0 << 2);
        w0 ^= (w0 << 4);
        w0 ^= (w0 << 8);
        w0 ^= (w0 << 16);
        w0 ^= (w0 << 32);

        w0 &= M44; w1 ^= (w0 >>> 43);

        w1 ^= (w1 << 1);
        w1 ^= (w1 << 2);
        w1 ^= (w1 << 4);
        w1 ^= (w1 << 8);
        w1 ^= (w1 << 16);
        w1 ^= (w1 << 32);

        w1 &= M44; w2 ^= (w1 >>> 43);

        w2 ^= (w2 << 1);
        w2 ^= (w2 << 2);
        w2 ^= (w2 << 4);
        w2 ^= (w2 << 8);
        w2 ^= (w2 << 16);
        w2 ^= (w2 << 32);

  //      assert w2 >>> 42 == 0;

        zz[0] = u0;
        zz[1] = u1 ^ w0      ^ H[2];
        zz[2] = u2 ^ w1 ^ w0 ^ H[3];
        zz[3] =      w2 ^ w1;
        zz[4] =           w2 ^ H[2];
        zz[5] =                H[3];

        implCompactExt(zz);
    }

    protected static void implMulw(long[] u, long x, long y, long[] z, int zOff)
    {
//        assert x >>> 45 == 0;
//        assert y >>> 45 == 0;

//      u[0] = 0;
        u[1] = y;
        u[2] = u[1] << 1;
        u[3] = u[2] ^  y;
        u[4] = u[2] << 1;
        u[5] = u[4] ^  y;
        u[6] = u[3] << 1;
        u[7] = u[6] ^  y;

        int j = (int)x;
        long g, h = 0, l = u[j & 7]
                         ^ u[(j >>>  3) & 7] <<  3
                         ^ u[(j >>>  6) & 7] <<  6
                         ^ u[(j >>>  9) & 7] <<  9
                         ^ u[(j >>> 12) & 7] << 12;
        int k = 30;
        do
        {
            j  = (int)(x >>> k);
            g  = u[j & 7]
               ^ u[(j >>>  3) & 7] <<  3
               ^ u[(j >>>  6) & 7] <<  6
               ^ u[(j >>>  9) & 7] <<  9
               ^ u[(j >>> 12) & 7] << 12;
            l ^= (g <<   k);
            h ^= (g >>> -k);
        }
        while ((k -= 15) > 0);

//        assert h >>> 25 == 0;

        z[zOff    ] = l & M44;
        z[zOff + 1] = (l >>> 44) ^ (h << 20);
    }

    protected static void implSquare(long[] x, long[] zz)
    {
        Interleave.expand64To128(x, 0, 2, zz, 0);
        zz[4] = Interleave.expand8to16((int)x[2]) & 0xFFFFFFFFL;
    }
}