#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