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325 lines
9.2 KiB
325 lines
9.2 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 SecT193Field
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{
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private const ulong M01 = 1UL;
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private const ulong M49 = ulong.MaxValue >> 15;
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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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}
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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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}
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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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}
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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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}
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public static ulong[] FromBigInteger(BigInteger x)
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{
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return Nat.FromBigInteger64(193, 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 = Nat256.CreateExt64();
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Nat256.Copy64(x, z);
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for (int i = 1; i < 193; 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 (Nat256.IsZero64(x))
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throw new InvalidOperationException();
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// Itoh-Tsujii inversion with bases { 2, 3 }
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ulong[] t0 = Nat256.Create64();
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ulong[] t1 = Nat256.Create64();
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Square(x, t0);
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// 3 | 192
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SquareN(t0, 1, t1);
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Multiply(t0, t1, t0);
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SquareN(t1, 1, t1);
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Multiply(t0, t1, t0);
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// 2 | 64
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SquareN(t0, 3, t1);
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Multiply(t0, t1, t0);
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// 2 | 32
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SquareN(t0, 6, t1);
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Multiply(t0, t1, t0);
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// 2 | 16
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SquareN(t0, 12, t1);
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Multiply(t0, t1, t0);
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// 2 | 8
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SquareN(t0, 24, t1);
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Multiply(t0, t1, t0);
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// 2 | 4
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SquareN(t0, 48, t1);
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Multiply(t0, t1, t0);
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// 2 | 2
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SquareN(t0, 96, t1);
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Multiply(t0, 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 = Nat256.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 = Nat256.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], x5 = xx[5], x6 = xx[6];
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x2 ^= (x6 << 63);
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x3 ^= (x6 >> 1) ^ (x6 << 14);
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x4 ^= (x6 >> 50);
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x1 ^= (x5 << 63);
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x2 ^= (x5 >> 1) ^ (x5 << 14);
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x3 ^= (x5 >> 50);
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x0 ^= (x4 << 63);
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x1 ^= (x4 >> 1) ^ (x4 << 14);
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x2 ^= (x4 >> 50);
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ulong t = x3 >> 1;
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z[0] = x0 ^ t ^ (t << 15);
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z[1] = x1 ^ (t >> 49);
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z[2] = x2;
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z[3] = x3 & M01;
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}
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public static void Reduce63(ulong[] z, int zOff)
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{
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ulong z3 = z[zOff + 3], t = z3 >> 1;
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z[zOff ] ^= t ^ (t << 15);
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z[zOff + 1] ^= (t >> 49);
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z[zOff + 3] = z3 & M01;
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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 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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ulong c0 = (u0 >> 32) | (u1 & 0xFFFFFFFF00000000UL);
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u0 = Interleave.Unshuffle(x[2]);
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ulong e1 = (u0 & 0x00000000FFFFFFFFUL) ^ (x[3] << 32);
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ulong c1 = (u0 >> 32);
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z[0] = e0 ^ (c0 << 8);
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z[1] = e1 ^ (c1 << 8) ^ (c0 >> 56) ^ (c0 << 33);
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z[2] = (c1 >> 56) ^ (c1 << 33) ^ (c0 >> 31);
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z[3] = (c1 >> 31);
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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 = Nat256.CreateExt64();
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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 = Nat256.CreateExt64();
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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 = Nat256.CreateExt64();
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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
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return (uint)(x[0]) & 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], z5 = zz[5], z6 = zz[6], z7 = zz[7];
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zz[0] = z0 ^ (z1 << 49);
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zz[1] = (z1 >> 15) ^ (z2 << 34);
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zz[2] = (z2 >> 30) ^ (z3 << 19);
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zz[3] = (z3 >> 45) ^ (z4 << 4)
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^ (z5 << 53);
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zz[4] = (z4 >> 60) ^ (z6 << 38)
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^ (z5 >> 11);
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zz[5] = (z6 >> 26) ^ (z7 << 23);
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zz[6] = (z7 >> 41);
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zz[7] = 0;
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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];
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z[0] = x0 & M49;
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z[1] = ((x0 >> 49) ^ (x1 << 15)) & M49;
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z[2] = ((x1 >> 34) ^ (x2 << 30)) & M49;
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z[3] = ((x2 >> 19) ^ (x3 << 45));
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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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* "Two-level seven-way recursion" as described in "Batch binary Edwards", Daniel J. Bernstein.
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*/
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ulong[] f = new ulong[4], g = new ulong[4];
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ImplExpand(x, f);
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ImplExpand(y, g);
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ulong[] u = new ulong[8];
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ImplMulwAcc(u, f[0], g[0], zz, 0);
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ImplMulwAcc(u, f[1], g[1], zz, 1);
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ImplMulwAcc(u, f[2], g[2], zz, 2);
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ImplMulwAcc(u, f[3], g[3], zz, 3);
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// U *= (1 - t^n)
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for (int i = 5; i > 0; --i)
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{
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zz[i] ^= zz[i - 1];
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}
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ImplMulwAcc(u, f[0] ^ f[1], g[0] ^ g[1], zz, 1);
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ImplMulwAcc(u, f[2] ^ f[3], g[2] ^ g[3], zz, 3);
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// V *= (1 - t^2n)
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for (int i = 7; i > 1; --i)
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{
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zz[i] ^= zz[i - 2];
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}
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// Double-length recursion
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{
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ulong c0 = f[0] ^ f[2], c1 = f[1] ^ f[3];
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ulong d0 = g[0] ^ g[2], d1 = g[1] ^ g[3];
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ImplMulwAcc(u, c0 ^ c1, d0 ^ d1, zz, 3);
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ulong[] t = new ulong[3];
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ImplMulwAcc(u, c0, d0, t, 0);
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ImplMulwAcc(u, c1, d1, t, 1);
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ulong t0 = t[0], t1 = t[1], t2 = t[2];
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zz[2] ^= t0;
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zz[3] ^= t0 ^ t1;
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zz[4] ^= t2 ^ t1;
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zz[5] ^= t2;
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}
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ImplCompactExt(zz);
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}
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protected static void ImplMulwAcc(ulong[] u, ulong x, ulong y, ulong[] z, int zOff)
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{
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Debug.Assert(x >> 49 == 0);
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Debug.Assert(y >> 49 == 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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^ (u[(j >> 3) & 7] << 3);
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int k = 36;
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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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^ u[(j >> 9) & 7] << 9
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^ u[(j >> 12) & 7] << 12;
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l ^= (g << k);
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h ^= (g >> -k);
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}
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while ((k -= 15) > 0);
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Debug.Assert(h >> 33 == 0);
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z[zOff ] ^= l & M49;
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z[zOff + 1] ^= (l >> 49) ^ (h << 15);
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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, 3, zz, 0);
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zz[6] = (x[3] & M01);
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}
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}
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}
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