bcprov/src/main/java/org/bouncycastle/math/ec/custom/sec/SecT409Field.java

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.Nat448;

public class SecT409Field
{
    private static final long M25 = -1L >>> 39;
    private static final long M59 = -1L >>> 5;

    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];
        z[4] = x[4] ^ y[4];
        z[5] = x[5] ^ y[5];
        z[6] = x[6] ^ y[6];
    }

    public static void addExt(long[] xx, long[] yy, long[] zz)
    {
        for (int i = 0; i < 13; ++i)
        {
            zz[i] = xx[i] ^ yy[i];
        }
    }

    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];
        z[4] = x[4];
        z[5] = x[5];
        z[6] = x[6];
    }

    public static long[] fromBigInteger(BigInteger x)
    {
        long[] z = Nat448.fromBigInteger64(x);
        reduce39(z, 0);
        return z;
    }

    public static void invert(long[] x, long[] z)
    {
        if (Nat448.isZero64(x))
        {
            throw new IllegalStateException();
        }

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

        long[] t0 = Nat448.create64();
        long[] t1 = Nat448.create64();
        long[] t2 = Nat448.create64();

        square(x, t0);

        // 3 | 408
        squareN(t0, 1, t1);
        multiply(t0, t1, t0);
        squareN(t1, 1, t1);
        multiply(t0, t1, t0);

        // 2 | 136
        squareN(t0, 3, t1);
        multiply(t0, t1, t0);

        // 2 | 68
        squareN(t0, 6, t1);
        multiply(t0, t1, t0);

        // 2 | 34
        squareN(t0, 12, t1);
        multiply(t0, t1, t2);

        // ! {2,3} | 17
        squareN(t2, 24, t0);
        squareN(t0, 24, t1);
        multiply(t0, t1, t0);

        // 2 | 8
        squareN(t0, 48, t1);
        multiply(t0, t1, t0);

        // 2 | 4
        squareN(t0, 96, t1);
        multiply(t0, t1, t0);

        // 2 | 2
        squareN(t0, 192, t1);
        multiply(t0, t1, t0);

        multiply(t0, t2, z);
    }

    public static void multiply(long[] x, long[] y, long[] z)
    {
        long[] tt = Nat448.createExt64();
        implMultiply(x, y, tt);
        reduce(tt, z);
    }

    public static void multiplyAddToExt(long[] x, long[] y, long[] zz)
    {
        long[] tt = Nat448.createExt64();
        implMultiply(x, y, tt);
        addExt(zz, tt, zz);
    }

    public static void reduce(long[] xx, long[] z)
    {
        long x00 = xx[0], x01 = xx[1], x02 = xx[2], x03 = xx[3];
        long x04 = xx[4], x05 = xx[5], x06 = xx[6], x07 = xx[7];

        long u = xx[12];
        x05 ^= (u <<  39);
        x06 ^= (u >>> 25) ^ (u <<  62);
        x07 ^= (u >>>  2);

        u = xx[11];
        x04 ^= (u <<  39);
        x05 ^= (u >>> 25) ^ (u <<  62);
        x06 ^= (u >>>  2);

        u = xx[10];
        x03 ^= (u <<  39);
        x04 ^= (u >>> 25) ^ (u <<  62);
        x05 ^= (u >>>  2);

        u = xx[9];
        x02 ^= (u <<  39);
        x03 ^= (u >>> 25) ^ (u <<  62);
        x04 ^= (u >>>  2);

        u = xx[8];
        x01 ^= (u <<  39);
        x02 ^= (u >>> 25) ^ (u <<  62);
        x03 ^= (u >>>  2);

        u = x07;
        x00 ^= (u <<  39);
        x01 ^= (u >>> 25) ^ (u <<  62);
        x02 ^= (u >>>  2);

        long t = x06 >>> 25;
        z[0]   = x00 ^ t;
        z[1]   = x01 ^ (t << 23);
        z[2]   = x02;
        z[3]   = x03;
        z[4]   = x04;
        z[5]   = x05;
        z[6]   = x06 & M25;
    }

    public static void reduce39(long[] z, int zOff)
    {
        long z6 = z[zOff + 6], t = z6 >>> 25;
        z[zOff    ] ^= t;
        z[zOff + 1] ^= (t << 23);
        z[zOff + 6]  = z6 & M25;
    }

    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]); u1 = Interleave.unshuffle(x[3]);
        long e1 = (u0 & 0x00000000FFFFFFFFL) | (u1 << 32);
        long c1 = (u0 >>> 32) | (u1 & 0xFFFFFFFF00000000L);

        u0 = Interleave.unshuffle(x[4]); u1 = Interleave.unshuffle(x[5]);
        long e2 = (u0 & 0x00000000FFFFFFFFL) | (u1 << 32);
        long c2 = (u0 >>> 32) | (u1 & 0xFFFFFFFF00000000L);

        u0 = Interleave.unshuffle(x[6]);
        long e3 = (u0 & 0x00000000FFFFFFFFL);
        long c3 = (u0 >>> 32);

        z[0] = e0 ^ (c0 << 44);
        z[1] = e1 ^ (c1 << 44) ^ (c0 >>> 20);
        z[2] = e2 ^ (c2 << 44) ^ (c1 >>> 20);
        z[3] = e3 ^ (c3 << 44) ^ (c2 >>> 20) ^ (c0 << 13);
        z[4] =                   (c3 >>> 20) ^ (c1 << 13) ^ (c0 >>> 51);
        z[5] =                                 (c2 << 13) ^ (c1 >>> 51);
        z[6] =                                 (c3 << 13) ^ (c2 >>> 51);
        
//        assert (c3 >>> 51) == 0;
    }

    public static void square(long[] x, long[] z)
    {
        long[] tt = Nat.create64(13);
        implSquare(x, tt);
        reduce(tt, z);
    }

    public static void squareAddToExt(long[] x, long[] zz)
    {
        long[] tt = Nat.create64(13);
        implSquare(x, tt);
        addExt(zz, tt, zz);
    }

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

        long[] tt = Nat.create64(13);
        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 z00 = zz[ 0], z01 = zz[ 1], z02 = zz[ 2], z03 = zz[ 3], z04 = zz[ 4], z05 = zz[ 5], z06 = zz[ 6];
        long z07 = zz[ 7], z08 = zz[ 8], z09 = zz[ 9], z10 = zz[10], z11 = zz[11], z12 = zz[12], z13 = zz[13];
        zz[ 0] =  z00         ^ (z01 << 59);
        zz[ 1] = (z01 >>>  5) ^ (z02 << 54);
        zz[ 2] = (z02 >>> 10) ^ (z03 << 49);
        zz[ 3] = (z03 >>> 15) ^ (z04 << 44);
        zz[ 4] = (z04 >>> 20) ^ (z05 << 39);
        zz[ 5] = (z05 >>> 25) ^ (z06 << 34);
        zz[ 6] = (z06 >>> 30) ^ (z07 << 29);
        zz[ 7] = (z07 >>> 35) ^ (z08 << 24);
        zz[ 8] = (z08 >>> 40) ^ (z09 << 19);
        zz[ 9] = (z09 >>> 45) ^ (z10 << 14);
        zz[10] = (z10 >>> 50) ^ (z11 <<  9);
        zz[11] = (z11 >>> 55) ^ (z12 <<  4)
                              ^ (z13 << 63);
        zz[12] = (z12 >>> 60)
               ^ (z13 >>> 1);
        zz[13] = 0;
    }

    protected static void implExpand(long[] x, long[] z)
    {
        long x0 = x[0], x1 = x[1], x2 = x[2], x3 = x[3], x4 = x[4], x5 = x[5], x6 = x[6];
        z[0] = x0 & M59;
        z[1] = ((x0 >>> 59) ^ (x1 <<  5)) & M59;
        z[2] = ((x1 >>> 54) ^ (x2 << 10)) & M59;
        z[3] = ((x2 >>> 49) ^ (x3 << 15)) & M59;
        z[4] = ((x3 >>> 44) ^ (x4 << 20)) & M59;
        z[5] = ((x4 >>> 39) ^ (x5 << 25)) & M59;
        z[6] = ((x5 >>> 34) ^ (x6 << 30));
    }

    protected static void implMultiply(long[] x, long[] y, long[] zz)
    {
        long[] a = new long[7], b = new long[7];
        implExpand(x, a);
        implExpand(y, b);

        for (int i = 0; i < 7; ++i)
        {
            implMulwAcc(a, b[i], zz, i);
        }

        implCompactExt(zz);
    }

    protected static void implMulwAcc(long[] xs, long y, long[] z, int zOff)
    {
//        assert y >>> 59 == 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;

        for (int i = 0; i < 7; ++i)
        {
            long x = xs[i];

//            assert x >>> 59 == 0;

            int j = (int)x;
            long g, h = 0, l = u[j & 7]
                             ^ (u[(j >>> 3) & 7] << 3);
            int k = 54;
            do
            {
                j  = (int)(x >>> k);
                g  = u[j & 7]
                   ^ u[(j >>> 3) & 7] << 3;
                l ^= (g <<   k);
                h ^= (g >>> -k);
            }
            while ((k -= 6) > 0);

//            assert h >>> 53 == 0;

            z[zOff + i    ] ^= l & M59;
            z[zOff + i + 1] ^= (l >>> 59) ^ (h << 5);
        }
    }

    protected static void implSquare(long[] x, long[] zz)
    {
        for (int i = 0; i < 6; ++i)
        {
            Interleave.expand64To128(x[i], zz, i << 1);
        }
        zz[12] = Interleave.expand32to64((int)x[6]);
    }
}