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352 lines
10 KiB
352 lines
10 KiB
2 months ago
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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 SecT131Field
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{
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private const ulong M03 = ulong.MaxValue >> 61;
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private const ulong M44 = ulong.MaxValue >> 20;
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private static readonly ulong[] ROOT_Z = new ulong[]{ 0x26BC4D789AF13523UL, 0x26BC4D789AF135E2UL, 0x6UL };
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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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}
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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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}
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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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}
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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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}
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public static ulong[] FromBigInteger(BigInteger x)
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{
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return Nat.FromBigInteger64(131, 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(5);
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Nat192.Copy64(x, z);
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for (int i = 1; i < 131; 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 (Nat192.IsZero64(x))
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throw new InvalidOperationException();
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// Itoh-Tsujii inversion
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ulong[] t0 = Nat192.Create64();
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ulong[] t1 = Nat192.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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SquareN(t1, 16, t0);
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Multiply(t0, t1, t0);
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SquareN(t0, 32, 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, 65, t0);
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Multiply(t0, t1, t0);
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Square(t0, 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 = new ulong[8];
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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 = new ulong[8];
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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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x1 ^= (x4 << 61) ^ (x4 << 63);
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x2 ^= (x4 >> 3) ^ (x4 >> 1) ^ x4 ^ (x4 << 5);
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x3 ^= (x4 >> 59);
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x0 ^= (x3 << 61) ^ (x3 << 63);
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x1 ^= (x3 >> 3) ^ (x3 >> 1) ^ x3 ^ (x3 << 5);
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x2 ^= (x3 >> 59);
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ulong t = x2 >> 3;
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z[0] = x0 ^ t ^ (t << 2) ^ (t << 3) ^ (t << 8);
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z[1] = x1 ^ (t >> 56);
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z[2] = x2 & M03;
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}
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public static void Reduce61(ulong[] z, int zOff)
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{
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ulong z2 = z[zOff + 2], t = z2 >> 3;
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z[zOff ] ^= t ^ (t << 2) ^ (t << 3) ^ (t << 8);
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z[zOff + 1] ^= (t >> 56);
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z[zOff + 2] = z2 & M03;
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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 = Nat192.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]);
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ulong e1 = (u0 & 0x00000000FFFFFFFFUL);
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odd[1] = (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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}
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public static void Square(ulong[] x, ulong[] z)
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{
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ulong[] tt = Nat.Create64(5);
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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(5);
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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(5);
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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, 123, 129
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return (uint)(x[0] ^ (x[1] >> 59) ^ (x[2] >> 1)) & 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];
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zz[0] = z0 ^ (z1 << 44);
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zz[1] = (z1 >> 20) ^ (z2 << 24);
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zz[2] = (z2 >> 40) ^ (z3 << 4)
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^ (z4 << 48);
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zz[3] = (z3 >> 60) ^ (z5 << 28)
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^ (z4 >> 16);
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zz[4] = (z5 >> 36);
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zz[5] = 0;
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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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* "Five-way recursion" as described in "Batch binary Edwards", Daniel J. Bernstein.
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*/
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ulong f0 = x[0], f1 = x[1], f2 = x[2];
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f2 = ((f1 >> 24) ^ (f2 << 40)) & M44;
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f1 = ((f0 >> 44) ^ (f1 << 20)) & M44;
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f0 &= M44;
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ulong g0 = y[0], g1 = y[1], g2 = y[2];
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g2 = ((g1 >> 24) ^ (g2 << 40)) & M44;
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g1 = ((g0 >> 44) ^ (g1 << 20)) & M44;
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g0 &= M44;
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ulong[] u = zz;
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ulong[] H = new ulong[10];
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ImplMulw(u, f0, g0, H, 0); // H(0) 44/43 bits
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ImplMulw(u, f2, g2, H, 2); // H(INF) 44/41 bits
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ulong t0 = f0 ^ f1 ^ f2;
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ulong t1 = g0 ^ g1 ^ g2;
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ImplMulw(u, t0, t1, H, 4); // H(1) 44/43 bits
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ulong t2 = (f1 << 1) ^ (f2 << 2);
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ulong t3 = (g1 << 1) ^ (g2 << 2);
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ImplMulw(u, f0 ^ t2, g0 ^ t3, H, 6); // H(t) 44/45 bits
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ImplMulw(u, t0 ^ t2, t1 ^ t3, H, 8); // H(t + 1) 44/45 bits
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ulong t4 = H[6] ^ H[8];
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ulong t5 = H[7] ^ H[9];
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Debug.Assert(t5 >> 44 == 0);
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// Calculate V
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ulong v0 = (t4 << 1) ^ H[6];
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ulong v1 = t4 ^ (t5 << 1) ^ H[7];
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ulong v2 = t5;
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// Calculate U
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ulong u0 = H[0];
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ulong u1 = H[1] ^ H[0] ^ H[4];
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ulong u2 = H[1] ^ H[5];
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// Calculate W
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ulong w0 = u0 ^ v0 ^ (H[2] << 4) ^ (H[2] << 1);
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ulong w1 = u1 ^ v1 ^ (H[3] << 4) ^ (H[3] << 1);
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ulong w2 = u2 ^ v2;
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// Propagate carries
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w1 ^= (w0 >> 44); w0 &= M44;
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w2 ^= (w1 >> 44); w1 &= M44;
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Debug.Assert((w0 & 1UL) == 0);
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// Divide W by t
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w0 = (w0 >> 1) ^ ((w1 & 1UL) << 43);
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w1 = (w1 >> 1) ^ ((w2 & 1UL) << 43);
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w2 = (w2 >> 1);
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// Divide W by (t + 1)
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w0 ^= (w0 << 1);
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w0 ^= (w0 << 2);
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w0 ^= (w0 << 4);
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w0 ^= (w0 << 8);
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w0 ^= (w0 << 16);
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w0 ^= (w0 << 32);
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w0 &= M44; w1 ^= (w0 >> 43);
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w1 ^= (w1 << 1);
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w1 ^= (w1 << 2);
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w1 ^= (w1 << 4);
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w1 ^= (w1 << 8);
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w1 ^= (w1 << 16);
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w1 ^= (w1 << 32);
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w1 &= M44; w2 ^= (w1 >> 43);
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w2 ^= (w2 << 1);
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w2 ^= (w2 << 2);
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w2 ^= (w2 << 4);
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w2 ^= (w2 << 8);
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w2 ^= (w2 << 16);
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w2 ^= (w2 << 32);
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Debug.Assert(w2 >> 42 == 0);
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zz[0] = u0;
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zz[1] = u1 ^ w0 ^ H[2];
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zz[2] = u2 ^ w1 ^ w0 ^ H[3];
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zz[3] = w2 ^ w1;
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zz[4] = w2 ^ H[2];
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zz[5] = H[3];
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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 >> 45 == 0);
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Debug.Assert(y >> 45 == 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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^ 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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int k = 30;
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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 >> 25 == 0);
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z[zOff ] = l & M44;
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z[zOff + 1] = (l >> 44) ^ (h << 20);
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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, 2, zz, 0);
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zz[4] = Interleave.Expand8to16((uint)x[2]);
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}
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}
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}
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