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