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using System;
using System.Diagnostics;
using Org.BouncyCastle.Math.Raw;
namespace Org.BouncyCastle.Math.EC.Custom.Sec
{
internal class SecT233Field
{
private const ulong M41 = ulong.MaxValue >> 23;
private const ulong M59 = ulong.MaxValue >> 5;
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];
}
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];
}
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];
}
private static void AddTo(ulong[] x, ulong[] z)
{
z[0] ^= x[0];
z[1] ^= x[1];
z[2] ^= x[2];
z[3] ^= x[3];
}
public static ulong[] FromBigInteger(BigInteger x)
{
return Nat.FromBigInteger64(233, x);
}
public static void HalfTrace(ulong[] x, ulong[] z)
{
ulong[] tt = Nat256.CreateExt64();
Nat256.Copy64(x, z);
for (int i = 1; i < 233; i += 2)
{
ImplSquare(z, tt);
Reduce(tt, z);
ImplSquare(z, tt);
Reduce(tt, z);
AddTo(x, z);
}
}
public static void Invert(ulong[] x, ulong[] z)
{
if (Nat256.IsZero64(x))
throw new InvalidOperationException();
// Itoh-Tsujii inversion
ulong[] t0 = Nat256.Create64();
ulong[] t1 = Nat256.Create64();
Square(x, t0);
Multiply(t0, x, t0);
Square(t0, t0);
Multiply(t0, x, t0);
SquareN(t0, 3, t1);
Multiply(t1, t0, t1);
Square(t1, t1);
Multiply(t1, x, t1);
SquareN(t1, 7, t0);
Multiply(t0, t1, t0);
SquareN(t0, 14, t1);
Multiply(t1, t0, t1);
Square(t1, t1);
Multiply(t1, x, t1);
SquareN(t1, 29, t0);
Multiply(t0, t1, t0);
SquareN(t0, 58, t1);
Multiply(t1, t0, t1);
SquareN(t1, 116, t0);
Multiply(t0, t1, t0);
Square(t0, z);
}
public static void Multiply(ulong[] x, ulong[] y, ulong[] z)
{
ulong[] tt = Nat256.CreateExt64();
ImplMultiply(x, y, tt);
Reduce(tt, z);
}
public static void MultiplyAddToExt(ulong[] x, ulong[] y, ulong[] zz)
{
ulong[] tt = Nat256.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];
ulong x4 = xx[4], x5 = xx[5], x6 = xx[6], x7 = xx[7];
x3 ^= (x7 << 23);
x4 ^= (x7 >> 41) ^ (x7 << 33);
x5 ^= (x7 >> 31);
x2 ^= (x6 << 23);
x3 ^= (x6 >> 41) ^ (x6 << 33);
x4 ^= (x6 >> 31);
x1 ^= (x5 << 23);
x2 ^= (x5 >> 41) ^ (x5 << 33);
x3 ^= (x5 >> 31);
x0 ^= (x4 << 23);
x1 ^= (x4 >> 41) ^ (x4 << 33);
x2 ^= (x4 >> 31);
ulong t = x3 >> 41;
z[0] = x0 ^ t;
z[1] = x1 ^ (t << 10);
z[2] = x2;
z[3] = x3 & M41;
}
public static void Reduce23(ulong[] z, int zOff)
{
ulong z3 = z[zOff + 3], t = z3 >> 41;
z[zOff ] ^= t;
z[zOff + 1] ^= (t << 10);
z[zOff + 3] = z3 & M41;
}
public static void Sqrt(ulong[] x, ulong[] z)
{
ulong u0, u1;
u0 = Interleave.Unshuffle(x[0]); u1 = Interleave.Unshuffle(x[1]);
ulong e0 = (u0 & 0x00000000FFFFFFFFUL) | (u1 << 32);
ulong c0 = (u0 >> 32) | (u1 & 0xFFFFFFFF00000000UL);
u0 = Interleave.Unshuffle(x[2]); u1 = Interleave.Unshuffle(x[3]);
ulong e1 = (u0 & 0x00000000FFFFFFFFUL) | (u1 << 32);
ulong c1 = (u0 >> 32) | (u1 & 0xFFFFFFFF00000000UL);
ulong c2;
c2 = (c1 >> 27);
c1 ^= (c0 >> 27) | (c1 << 37);
c0 ^= (c0 << 37);
ulong[] tt = Nat256.CreateExt64();
int[] shifts = { 32, 117, 191 };
for (int i = 0; i < shifts.Length; ++i)
{
int w = shifts[i] >> 6, s = shifts[i] & 63;
Debug.Assert(s != 0);
tt[w ] ^= (c0 << s);
tt[w + 1] ^= (c1 << s) | (c0 >> -s);
tt[w + 2] ^= (c2 << s) | (c1 >> -s);
tt[w + 3] ^= (c2 >> -s);
}
Reduce(tt, z);
z[0] ^= e0;
z[1] ^= e1;
}
public static void Square(ulong[] x, ulong[] z)
{
ulong[] tt = Nat256.CreateExt64();
ImplSquare(x, tt);
Reduce(tt, z);
}
public static void SquareAddToExt(ulong[] x, ulong[] zz)
{
ulong[] tt = Nat256.CreateExt64();
ImplSquare(x, tt);
AddExt(zz, tt, zz);
}
public static void SquareN(ulong[] x, int n, ulong[] z)
{
Debug.Assert(n > 0);
ulong[] tt = Nat256.CreateExt64();
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, 159
return (uint)(x[0] ^ (x[2] >> 31)) & 1U;
}
protected static void ImplCompactExt(ulong[] zz)
{
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];
zz[0] = z0 ^ (z1 << 59);
zz[1] = (z1 >> 5) ^ (z2 << 54);
zz[2] = (z2 >> 10) ^ (z3 << 49);
zz[3] = (z3 >> 15) ^ (z4 << 44);
zz[4] = (z4 >> 20) ^ (z5 << 39);
zz[5] = (z5 >> 25) ^ (z6 << 34);
zz[6] = (z6 >> 30) ^ (z7 << 29);
zz[7] = (z7 >> 35);
}
protected static void ImplExpand(ulong[] x, ulong[] z)
{
ulong x0 = x[0], x1 = x[1], x2 = x[2], x3 = x[3];
z[0] = x0 & M59;
z[1] = ((x0 >> 59) ^ (x1 << 5)) & M59;
z[2] = ((x1 >> 54) ^ (x2 << 10)) & M59;
z[3] = ((x2 >> 49) ^ (x3 << 15));
}
protected static void ImplMultiply(ulong[] x, ulong[] y, ulong[] zz)
{
/*
* "Two-level seven-way recursion" as described in "Batch binary Edwards", Daniel J. Bernstein.
*/
ulong[] f = new ulong[4], g = new ulong[4];
ImplExpand(x, f);
ImplExpand(y, g);
ulong[] u = new ulong[8];
ImplMulwAcc(u, f[0], g[0], zz, 0);
ImplMulwAcc(u, f[1], g[1], zz, 1);
ImplMulwAcc(u, f[2], g[2], zz, 2);
ImplMulwAcc(u, f[3], g[3], zz, 3);
// U *= (1 - t^n)
for (int i = 5; i > 0; --i)
{
zz[i] ^= zz[i - 1];
}
ImplMulwAcc(u, f[0] ^ f[1], g[0] ^ g[1], zz, 1);
ImplMulwAcc(u, f[2] ^ f[3], g[2] ^ g[3], zz, 3);
// V *= (1 - t^2n)
for (int i = 7; i > 1; --i)
{
zz[i] ^= zz[i - 2];
}
// Double-length recursion
{
ulong c0 = f[0] ^ f[2], c1 = f[1] ^ f[3];
ulong d0 = g[0] ^ g[2], d1 = g[1] ^ g[3];
ImplMulwAcc(u, c0 ^ c1, d0 ^ d1, zz, 3);
ulong[] t = new ulong[3];
ImplMulwAcc(u, c0, d0, t, 0);
ImplMulwAcc(u, c1, d1, t, 1);
ulong t0 = t[0], t1 = t[1], t2 = t[2];
zz[2] ^= t0;
zz[3] ^= t0 ^ t1;
zz[4] ^= t2 ^ t1;
zz[5] ^= t2;
}
ImplCompactExt(zz);
}
protected static void ImplMulwAcc(ulong[] u, ulong x, ulong y, ulong[] z, int zOff)
{
Debug.Assert(x >> 59 == 0);
Debug.Assert(y >> 59 == 0);
//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]
^ (u[(j >> 3) & 7] << 3);
int k = 54;
do
{
j = (uint)(x >> k);
g = u[j & 7]
^ u[(j >> 3) & 7] << 3;
l ^= (g << k);
h ^= (g >> -k);
}
while ((k -= 6) > 0);
Debug.Assert(h >> 53 == 0);
z[zOff ] ^= l & M59;
z[zOff + 1] ^= (l >> 59) ^ (h << 5);
}
protected static void ImplSquare(ulong[] x, ulong[] zz)
{
Interleave.Expand64To128(x, 0, 4, zz, 0);
}
}
}
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