bcprov/src/main/java/org/bouncycastle/math/ec/custom/sec/SecT193Field.java

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

import java.math.BigInteger;

import org.bouncycastle.math.raw.Interleave;
import org.bouncycastle.math.raw.Nat256;

public class SecT193Field
{
    private static final long M01 = 1L;
    private static final long M49 = -1L >>> 15;

    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];
        z[3] = x[3] ^ y[3];
    }

    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];
        zz[5] = xx[5] ^ yy[5];
        zz[6] = xx[6] ^ yy[6];
    }

    public static void addOne(long[] x, long[] z)
    {
        z[0] = x[0] ^ 1L;
        z[1] = x[1];
        z[2] = x[2];
        z[3] = x[3];
    }

    public static long[] fromBigInteger(BigInteger x)
    {
        long[] z = Nat256.fromBigInteger64(x);
        reduce63(z, 0);
        return z;
    }

    public static void invert(long[] x, long[] z)
    {
        if (Nat256.isZero64(x))
        {
            throw new IllegalStateException();
        }

        // Itoh-Tsujii inversion with bases { 2, 3 }

        long[] t0 = Nat256.create64();
        long[] t1 = Nat256.create64();

        square(x, t0);

        // 3 | 192
        squareN(t0, 1, t1);
        multiply(t0, t1, t0);
        squareN(t1, 1, t1);
        multiply(t0, t1, t0);

        // 2 | 64
        squareN(t0, 3, t1);
        multiply(t0, t1, t0);

        // 2 | 32
        squareN(t0, 6, t1);
        multiply(t0, t1, t0);

        // 2 | 16
        squareN(t0, 12, t1);
        multiply(t0, t1, t0);

        // 2 | 8
        squareN(t0, 24, t1);
        multiply(t0, t1, t0);

        // 2 | 4
        squareN(t0, 48, t1);
        multiply(t0, t1, t0);

        // 2 | 2
        squareN(t0, 96, t1);
        multiply(t0, t1, z);
    }

    public static void multiply(long[] x, long[] y, long[] z)
    {
        long[] tt = Nat256.createExt64();
        implMultiply(x, y, tt);
        reduce(tt, z);
    }

    public static void multiplyAddToExt(long[] x, long[] y, long[] zz)
    {
        long[] tt = Nat256.createExt64();
        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], x5 = xx[5], x6 = xx[6];

        x2 ^= (x6 <<  63);
        x3 ^= (x6 >>>  1) ^ (x6 <<  14);
        x4 ^= (x6 >>> 50);

        x1 ^= (x5 <<  63);
        x2 ^= (x5 >>>  1) ^ (x5 <<  14);
        x3 ^= (x5 >>> 50);

        x0 ^= (x4 <<  63);
        x1 ^= (x4 >>>  1) ^ (x4 <<  14);
        x2 ^= (x4 >>> 50);

        long t = x3 >>> 1;
        z[0]   = x0 ^ t ^ (t <<  15);
        z[1]   = x1     ^ (t >>> 49);
        z[2]   = x2;
        z[3]   = x3 & M01;
    }

    public static void reduce63(long[] z, int zOff)
    {
        long z3      = z[zOff + 3], t = z3 >>> 1;
        z[zOff    ] ^= t ^ (t <<  15);
        z[zOff + 1] ^=     (t >>> 49);
        z[zOff + 3]  = z3 & M01;
    }

    public static void sqrt(long[] x, long[] z)
    {
        long u0, u1;
        u0 = Interleave.unshuffle(x[0]); u1 = Interleave.unshuffle(x[1]);
        long e0 = (u0 & 0x00000000FFFFFFFFL) | (u1 << 32);
        long c0 = (u0 >>> 32) | (u1 & 0xFFFFFFFF00000000L);

        u0 = Interleave.unshuffle(x[2]);
        long e1 = (u0 & 0x00000000FFFFFFFFL) ^ (x[3] << 32);
        long c1 = (u0 >>> 32);

        z[0] = e0 ^ (c0 << 8);
        z[1] = e1 ^ (c1 << 8) ^ (c0 >>> 56) ^ (c0 << 33);
        z[2] =                  (c1 >>> 56) ^ (c1 << 33) ^ (c0 >>> 31);
        z[3] =                                             (c1 >>> 31);
    }

    public static void square(long[] x, long[] z)
    {
        long[] tt = Nat256.createExt64();
        implSquare(x, tt);
        reduce(tt, z);
    }

    public static void squareAddToExt(long[] x, long[] zz)
    {
        long[] tt = Nat256.createExt64();
        implSquare(x, tt);
        addExt(zz, tt, zz);
    }

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

        long[] tt = Nat256.createExt64();
        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
        return (int)(x[0]) & 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], z6 = zz[6], z7 = zz[7];
        zz[0] =  z0         ^ (z1 << 49);
        zz[1] = (z1 >>> 15) ^ (z2 << 34);
        zz[2] = (z2 >>> 30) ^ (z3 << 19);
        zz[3] = (z3 >>> 45) ^ (z4 <<  4)
                            ^ (z5 << 53);
        zz[4] = (z4 >>> 60) ^ (z6 << 38)
              ^ (z5 >>> 11);
        zz[5] = (z6 >>> 26) ^ (z7 << 23);
        zz[6] = (z7 >>> 41);
        zz[7] = 0;
    }

    protected static void implExpand(long[] x, long[] z)
    {
        long x0 = x[0], x1 = x[1], x2 = x[2], x3 = x[3];
        z[0] = x0 & M49;
        z[1] = ((x0 >>> 49) ^ (x1 << 15)) & M49;
        z[2] = ((x1 >>> 34) ^ (x2 << 30)) & M49;
        z[3] = ((x2 >>> 19) ^ (x3 << 45));
    }

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

        long[] f = new long[4], g = new long[4];
        implExpand(x, f);
        implExpand(y, g);

        implMulwAcc(f[0], g[0], zz, 0);
        implMulwAcc(f[1], g[1], zz, 1);
        implMulwAcc(f[2], g[2], zz, 2);
        implMulwAcc(f[3], g[3], zz, 3);

        // U *= (1 - t^n)
        for (int i = 5; i > 0; --i)
        {
            zz[i] ^= zz[i - 1];
        }

        implMulwAcc(f[0] ^ f[1], g[0] ^ g[1], zz, 1);
        implMulwAcc(f[2] ^ f[3], g[2] ^ g[3], zz, 3);

        // V *= (1 - t^2n)
        for (int i = 7; i > 1; --i)
        {
            zz[i] ^= zz[i - 2];
        }

        // Double-length recursion
        {
            long c0 = f[0] ^ f[2], c1 = f[1] ^ f[3];
            long d0 = g[0] ^ g[2], d1 = g[1] ^ g[3];
            implMulwAcc(c0 ^ c1, d0 ^ d1, zz, 3);
            long[] t = new long[3];
            implMulwAcc(c0, d0, t, 0);
            implMulwAcc(c1, d1, t, 1);
            long t0 = t[0], t1 = t[1], t2 = t[2];
            zz[2] ^= t0;
            zz[3] ^= t0 ^ t1;
            zz[4] ^= t2 ^ t1;
            zz[5] ^= t2;
        }

        implCompactExt(zz);
    }

    protected static void implMulwAcc(long x, long y, long[] z, int zOff)
    {
//        assert x >>> 49 == 0;
//        assert y >>> 49 == 0;

        long[] u = new long[8];
//        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);
        int k = 36;
        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 >>> 33 == 0;

        z[zOff    ] ^= l & M49;
        z[zOff + 1] ^= (l >>> 49) ^ (h << 15);
    }

    protected static void implSquare(long[] x, long[] zz)
    {
        Interleave.expand64To128(x[0], zz, 0);
        Interleave.expand64To128(x[1], zz, 2);
        Interleave.expand64To128(x[2], zz, 4);
        zz[6] = (x[3] & M01);
    }
}