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422 lines
13 KiB
422 lines
13 KiB
using System;
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using System.Diagnostics;
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using Org.BouncyCastle.Math.Raw;
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namespace Org.BouncyCastle.Math.EC.Custom.Sec
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{
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internal class SecT283Field
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{
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private const ulong M27 = ulong.MaxValue >> 37;
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private const ulong M57 = ulong.MaxValue >> 7;
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private static readonly ulong[] ROOT_Z = new ulong[]{ 0x0C30C30C30C30808UL, 0x30C30C30C30C30C3UL,
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0x820820820820830CUL, 0x0820820820820820UL, 0x2082082UL };
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public static void Add(ulong[] x, ulong[] y, ulong[] z)
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{
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z[0] = x[0] ^ y[0];
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z[1] = x[1] ^ y[1];
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z[2] = x[2] ^ y[2];
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z[3] = x[3] ^ y[3];
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z[4] = x[4] ^ y[4];
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}
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public static void AddExt(ulong[] xx, ulong[] yy, ulong[] zz)
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{
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zz[0] = xx[0] ^ yy[0];
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zz[1] = xx[1] ^ yy[1];
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zz[2] = xx[2] ^ yy[2];
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zz[3] = xx[3] ^ yy[3];
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zz[4] = xx[4] ^ yy[4];
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zz[5] = xx[5] ^ yy[5];
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zz[6] = xx[6] ^ yy[6];
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zz[7] = xx[7] ^ yy[7];
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zz[8] = xx[8] ^ yy[8];
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}
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public static void AddOne(ulong[] x, ulong[] z)
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{
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z[0] = x[0] ^ 1UL;
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z[1] = x[1];
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z[2] = x[2];
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z[3] = x[3];
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z[4] = x[4];
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}
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private static void AddTo(ulong[] x, ulong[] z)
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{
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z[0] ^= x[0];
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z[1] ^= x[1];
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z[2] ^= x[2];
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z[3] ^= x[3];
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z[4] ^= x[4];
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}
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public static ulong[] FromBigInteger(BigInteger x)
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{
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return Nat.FromBigInteger64(283, x);
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}
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public static void HalfTrace(ulong[] x, ulong[] z)
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{
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ulong[] tt = Nat.Create64(9);
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Nat320.Copy64(x, z);
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for (int i = 1; i < 283; i += 2)
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{
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ImplSquare(z, tt);
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Reduce(tt, z);
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ImplSquare(z, tt);
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Reduce(tt, z);
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AddTo(x, z);
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}
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}
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public static void Invert(ulong[] x, ulong[] z)
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{
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if (Nat320.IsZero64(x))
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throw new InvalidOperationException();
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// Itoh-Tsujii inversion
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ulong[] t0 = Nat320.Create64();
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ulong[] t1 = Nat320.Create64();
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Square(x, t0);
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Multiply(t0, x, t0);
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SquareN(t0, 2, t1);
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Multiply(t1, t0, t1);
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SquareN(t1, 4, t0);
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Multiply(t0, t1, t0);
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SquareN(t0, 8, t1);
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Multiply(t1, t0, t1);
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Square(t1, t1);
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Multiply(t1, x, t1);
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SquareN(t1, 17, t0);
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Multiply(t0, t1, t0);
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Square(t0, t0);
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Multiply(t0, x, t0);
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SquareN(t0, 35, t1);
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Multiply(t1, t0, t1);
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SquareN(t1, 70, t0);
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Multiply(t0, t1, t0);
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Square(t0, t0);
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Multiply(t0, x, t0);
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SquareN(t0, 141, t1);
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Multiply(t1, t0, t1);
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Square(t1, z);
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}
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public static void Multiply(ulong[] x, ulong[] y, ulong[] z)
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{
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ulong[] tt = Nat320.CreateExt64();
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ImplMultiply(x, y, tt);
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Reduce(tt, z);
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}
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public static void MultiplyAddToExt(ulong[] x, ulong[] y, ulong[] zz)
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{
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ulong[] tt = Nat320.CreateExt64();
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ImplMultiply(x, y, tt);
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AddExt(zz, tt, zz);
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}
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public static void Reduce(ulong[] xx, ulong[] z)
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{
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ulong x0 = xx[0], x1 = xx[1], x2 = xx[2], x3 = xx[3], x4 = xx[4];
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ulong x5 = xx[5], x6 = xx[6], x7 = xx[7], x8 = xx[8];
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x3 ^= (x8 << 37) ^ (x8 << 42) ^ (x8 << 44) ^ (x8 << 49);
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x4 ^= (x8 >> 27) ^ (x8 >> 22) ^ (x8 >> 20) ^ (x8 >> 15);
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x2 ^= (x7 << 37) ^ (x7 << 42) ^ (x7 << 44) ^ (x7 << 49);
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x3 ^= (x7 >> 27) ^ (x7 >> 22) ^ (x7 >> 20) ^ (x7 >> 15);
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x1 ^= (x6 << 37) ^ (x6 << 42) ^ (x6 << 44) ^ (x6 << 49);
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x2 ^= (x6 >> 27) ^ (x6 >> 22) ^ (x6 >> 20) ^ (x6 >> 15);
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x0 ^= (x5 << 37) ^ (x5 << 42) ^ (x5 << 44) ^ (x5 << 49);
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x1 ^= (x5 >> 27) ^ (x5 >> 22) ^ (x5 >> 20) ^ (x5 >> 15);
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ulong t = x4 >> 27;
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z[0] = x0 ^ t ^ (t << 5) ^ (t << 7) ^ (t << 12);
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z[1] = x1;
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z[2] = x2;
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z[3] = x3;
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z[4] = x4 & M27;
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}
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public static void Reduce37(ulong[] z, int zOff)
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{
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ulong z4 = z[zOff + 4], t = z4 >> 27;
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z[zOff ] ^= t ^ (t << 5) ^ (t << 7) ^ (t << 12);
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z[zOff + 4] = z4 & M27;
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}
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public static void Sqrt(ulong[] x, ulong[] z)
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{
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ulong[] odd = Nat320.Create64();
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ulong u0, u1;
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u0 = Interleave.Unshuffle(x[0]); u1 = Interleave.Unshuffle(x[1]);
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ulong e0 = (u0 & 0x00000000FFFFFFFFUL) | (u1 << 32);
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odd[0] = (u0 >> 32) | (u1 & 0xFFFFFFFF00000000UL);
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u0 = Interleave.Unshuffle(x[2]); u1 = Interleave.Unshuffle(x[3]);
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ulong e1 = (u0 & 0x00000000FFFFFFFFUL) | (u1 << 32);
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odd[1] = (u0 >> 32) | (u1 & 0xFFFFFFFF00000000UL);
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u0 = Interleave.Unshuffle(x[4]);
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ulong e2 = (u0 & 0x00000000FFFFFFFFUL);
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odd[2] = (u0 >> 32);
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Multiply(odd, ROOT_Z, z);
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z[0] ^= e0;
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z[1] ^= e1;
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z[2] ^= e2;
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}
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public static void Square(ulong[] x, ulong[] z)
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{
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ulong[] tt = Nat.Create64(9);
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ImplSquare(x, tt);
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Reduce(tt, z);
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}
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public static void SquareAddToExt(ulong[] x, ulong[] zz)
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{
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ulong[] tt = Nat.Create64(9);
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ImplSquare(x, tt);
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AddExt(zz, tt, zz);
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}
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public static void SquareN(ulong[] x, int n, ulong[] z)
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{
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Debug.Assert(n > 0);
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ulong[] tt = Nat.Create64(9);
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ImplSquare(x, tt);
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Reduce(tt, z);
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while (--n > 0)
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{
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ImplSquare(z, tt);
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Reduce(tt, z);
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}
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}
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public static uint Trace(ulong[] x)
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{
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// Non-zero-trace bits: 0, 271
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return (uint)(x[0] ^ (x[4] >> 15)) & 1U;
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}
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protected static void ImplCompactExt(ulong[] zz)
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{
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ulong z0 = zz[0], z1 = zz[1], z2 = zz[2], z3 = zz[3], z4 = zz[4];
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ulong z5 = zz[5], z6 = zz[6], z7 = zz[7], z8 = zz[8], z9 = zz[9];
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zz[0] = z0 ^ (z1 << 57);
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zz[1] = (z1 >> 7) ^ (z2 << 50);
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zz[2] = (z2 >> 14) ^ (z3 << 43);
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zz[3] = (z3 >> 21) ^ (z4 << 36);
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zz[4] = (z4 >> 28) ^ (z5 << 29);
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zz[5] = (z5 >> 35) ^ (z6 << 22);
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zz[6] = (z6 >> 42) ^ (z7 << 15);
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zz[7] = (z7 >> 49) ^ (z8 << 8);
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zz[8] = (z8 >> 56) ^ (z9 << 1);
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zz[9] = (z9 >> 63); // Zero!
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}
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protected static void ImplExpand(ulong[] x, ulong[] z)
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{
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ulong x0 = x[0], x1 = x[1], x2 = x[2], x3 = x[3], x4 = x[4];
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z[0] = x0 & M57;
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z[1] = ((x0 >> 57) ^ (x1 << 7)) & M57;
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z[2] = ((x1 >> 50) ^ (x2 << 14)) & M57;
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z[3] = ((x2 >> 43) ^ (x3 << 21)) & M57;
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z[4] = ((x3 >> 36) ^ (x4 << 28));
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}
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//protected static void AddMs(ulong[] zz, int zOff, ulong[] p, params int[] ms)
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//{
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// ulong t0 = 0, t1 = 0;
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// foreach (int m in ms)
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// {
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// int i = (m - 1) << 1;
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// t0 ^= p[i ];
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// t1 ^= p[i + 1];
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// }
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// zz[zOff ] ^= t0;
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// zz[zOff + 1] ^= t1;
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//}
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protected static void ImplMultiply(ulong[] x, ulong[] y, ulong[] zz)
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{
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/*
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* Formula (17) from "Some New Results on Binary Polynomial Multiplication",
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* Murat Cenk and M. Anwar Hasan.
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*
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* The formula as given contained an error in the term t25, as noted below
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*/
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ulong[] a = new ulong[5], b = new ulong[5];
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ImplExpand(x, a);
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ImplExpand(y, b);
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ulong[] u = zz;
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ulong[] p = new ulong[26];
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ImplMulw(u, a[0], b[0], p, 0); // m1
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ImplMulw(u, a[1], b[1], p, 2); // m2
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ImplMulw(u, a[2], b[2], p, 4); // m3
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ImplMulw(u, a[3], b[3], p, 6); // m4
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ImplMulw(u, a[4], b[4], p, 8); // m5
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ulong u0 = a[0] ^ a[1], v0 = b[0] ^ b[1];
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ulong u1 = a[0] ^ a[2], v1 = b[0] ^ b[2];
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ulong u2 = a[2] ^ a[4], v2 = b[2] ^ b[4];
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ulong u3 = a[3] ^ a[4], v3 = b[3] ^ b[4];
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ImplMulw(u, u1 ^ a[3], v1 ^ b[3], p, 18); // m10
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ImplMulw(u, u2 ^ a[1], v2 ^ b[1], p, 20); // m11
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ulong A4 = u0 ^ u3 , B4 = v0 ^ v3;
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ulong A5 = A4 ^ a[2], B5 = B4 ^ b[2];
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ImplMulw(u, A4, B4, p, 22); // m12
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ImplMulw(u, A5, B5, p, 24); // m13
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ImplMulw(u, u0, v0, p, 10); // m6
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ImplMulw(u, u1, v1, p, 12); // m7
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ImplMulw(u, u2, v2, p, 14); // m8
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ImplMulw(u, u3, v3, p, 16); // m9
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// Original method, corresponding to formula (16)
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//AddMs(zz, 0, p, 1);
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//AddMs(zz, 1, p, 1, 2, 6);
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//AddMs(zz, 2, p, 1, 2, 3, 7);
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//AddMs(zz, 3, p, 1, 3, 4, 5, 8, 10, 12, 13);
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//AddMs(zz, 4, p, 1, 2, 4, 5, 6, 9, 10, 11, 13);
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//AddMs(zz, 5, p, 1, 2, 3, 5, 7, 11, 12, 13);
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//AddMs(zz, 6, p, 3, 4, 5, 8);
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//AddMs(zz, 7, p, 4, 5, 9);
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//AddMs(zz, 8, p, 5);
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// Improved method factors out common single-word terms
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// NOTE: p1,...,p26 in the paper maps to p[0],...,p[25] here
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zz[0] = p[ 0];
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zz[9] = p[ 9];
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ulong t1 = p[ 0] ^ p[ 1];
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ulong t2 = t1 ^ p[ 2];
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ulong t3 = t2 ^ p[10];
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zz[1] = t3;
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ulong t4 = p[ 3] ^ p[ 4];
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ulong t5 = p[11] ^ p[12];
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ulong t6 = t4 ^ t5;
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ulong t7 = t2 ^ t6;
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zz[2] = t7;
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ulong t8 = t1 ^ t4;
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ulong t9 = p[ 5] ^ p[ 6];
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ulong t10 = t8 ^ t9;
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ulong t11 = t10 ^ p[ 8];
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ulong t12 = p[13] ^ p[14];
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ulong t13 = t11 ^ t12;
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ulong t14 = p[18] ^ p[22];
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ulong t15 = t14 ^ p[24];
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ulong t16 = t13 ^ t15;
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zz[3] = t16;
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ulong t17 = p[ 7] ^ p[ 8];
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ulong t18 = t17 ^ p[ 9];
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ulong t19 = t18 ^ p[17];
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zz[8] = t19;
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ulong t20 = t18 ^ t9;
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ulong t21 = p[15] ^ p[16];
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ulong t22 = t20 ^ t21;
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zz[7] = t22;
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ulong t23 = t22 ^ t3;
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ulong t24 = p[19] ^ p[20];
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// ulong t25 = p[23] ^ p[24];
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ulong t25 = p[25] ^ p[24]; // Fixes an error in the paper: p[23] -> p{25]
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ulong t26 = p[18] ^ p[23];
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ulong t27 = t24 ^ t25;
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ulong t28 = t27 ^ t26;
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ulong t29 = t28 ^ t23;
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zz[4] = t29;
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ulong t30 = t7 ^ t19;
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ulong t31 = t27 ^ t30;
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ulong t32 = p[21] ^ p[22];
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ulong t33 = t31 ^ t32;
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zz[5] = t33;
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ulong t34 = t11 ^ p[0];
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ulong t35 = t34 ^ p[9];
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ulong t36 = t35 ^ t12;
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ulong t37 = t36 ^ p[21];
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ulong t38 = t37 ^ p[23];
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ulong t39 = t38 ^ p[25];
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zz[6] = t39;
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ImplCompactExt(zz);
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}
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protected static void ImplMulw(ulong[] u, ulong x, ulong y, ulong[] z, int zOff)
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{
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Debug.Assert(x >> 57 == 0);
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Debug.Assert(y >> 57 == 0);
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//u[0] = 0;
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u[1] = y;
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u[2] = u[1] << 1;
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u[3] = u[2] ^ y;
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u[4] = u[2] << 1;
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u[5] = u[4] ^ y;
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u[6] = u[3] << 1;
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u[7] = u[6] ^ y;
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uint j = (uint)x;
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ulong g, h = 0, l = u[j & 7];
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int k = 48;
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do
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{
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j = (uint)(x >> k);
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g = u[j & 7]
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^ u[(j >> 3) & 7] << 3
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^ u[(j >> 6) & 7] << 6;
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l ^= (g << k);
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h ^= (g >> -k);
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}
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while ((k -= 9) > 0);
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h ^= ((x & 0x0100804020100800L) & (ulong)(((long)y << 7) >> 63)) >> 8;
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Debug.Assert(h >> 49 == 0);
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z[zOff ] = l & M57;
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z[zOff + 1] = (l >> 57) ^ (h << 7);
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}
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protected static void ImplSquare(ulong[] x, ulong[] zz)
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{
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Interleave.Expand64To128(x, 0, 4, zz, 0);
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zz[8] = Interleave.Expand32to64((uint)x[4]);
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}
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}
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}
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