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using System;
using System.Diagnostics;
using Org.BouncyCastle.Math.Raw;
namespace Org.BouncyCastle.Math.EC.Custom.Sec
{
internal class SecT113Field
{
private const ulong M49 = ulong.MaxValue >> 15;
private const ulong M57 = ulong.MaxValue >> 7;
public static void Add(ulong[] x, ulong[] y, ulong[] z)
{
z[0] = x[0] ^ y[0];
z[1] = x[1] ^ y[1];
}
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];
}
public static void AddOne(ulong[] x, ulong[] z)
{
z[0] = x[0] ^ 1UL;
z[1] = x[1];
}
public static ulong[] FromBigInteger(BigInteger x)
{
return Nat.FromBigInteger64(113, x);
}
public static void Invert(ulong[] x, ulong[] z)
{
if (Nat128.IsZero64(x))
throw new InvalidOperationException();
// Itoh-Tsujii inversion
ulong[] t0 = Nat128.Create64();
ulong[] t1 = Nat128.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);
SquareN(t1, 28, t0);
Multiply(t0, t1, t0);
SquareN(t0, 56, t1);
Multiply(t1, t0, t1);
Square(t1, z);
}
public static void Multiply(ulong[] x, ulong[] y, ulong[] z)
{
ulong[] tt = Nat128.CreateExt64();
ImplMultiply(x, y, tt);
Reduce(tt, z);
}
public static void MultiplyAddToExt(ulong[] x, ulong[] y, ulong[] zz)
{
ulong[] tt = Nat128.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];
x1 ^= (x3 << 15) ^ (x3 << 24);
x2 ^= (x3 >> 49) ^ (x3 >> 40);
x0 ^= (x2 << 15) ^ (x2 << 24);
x1 ^= (x2 >> 49) ^ (x2 >> 40);
ulong t = x1 >> 49;
z[0] = x0 ^ t ^ (t << 9);
z[1] = x1 & M49;
}
public static void Reduce15(ulong[] z, int zOff)
{
ulong z1 = z[zOff + 1], t = z1 >> 49;
z[zOff ] ^= t ^ (t << 9);
z[zOff + 1] = z1 & M49;
}
public static void Sqrt(ulong[] x, ulong[] z)
{
ulong u0 = Interleave.Unshuffle(x[0]), u1 = Interleave.Unshuffle(x[1]);
ulong e0 = (u0 & 0x00000000FFFFFFFFUL) | (u1 << 32);
ulong c0 = (u0 >> 32) | (u1 & 0xFFFFFFFF00000000UL);
z[0] = e0 ^ (c0 << 57) ^ (c0 << 5);
z[1] = (c0 >> 7) ^ (c0 >> 59);
}
public static void Square(ulong[] x, ulong[] z)
{
ulong[] tt = Nat128.CreateExt64();
ImplSquare(x, tt);
Reduce(tt, z);
}
public static void SquareAddToExt(ulong[] x, ulong[] zz)
{
ulong[] tt = Nat128.CreateExt64();
ImplSquare(x, tt);
AddExt(zz, tt, zz);
}
public static void SquareN(ulong[] x, int n, ulong[] z)
{
Debug.Assert(n > 0);
ulong[] tt = Nat128.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
return (uint)(x[0]) & 1U;
}
protected static void ImplMultiply(ulong[] x, ulong[] y, ulong[] zz)
{
/*
* "Three-way recursion" as described in "Batch binary Edwards", Daniel J. Bernstein.
*/
ulong f0 = x[0], f1 = x[1];
f1 = ((f0 >> 57) ^ (f1 << 7)) & M57;
f0 &= M57;
ulong g0 = y[0], g1 = y[1];
g1 = ((g0 >> 57) ^ (g1 << 7)) & M57;
g0 &= M57;
ulong[] H = new ulong[6];
ImplMulw(f0, g0, H, 0); // H(0) 57/56 bits
ImplMulw(f1, g1, H, 2); // H(INF) 57/54 bits
ImplMulw(f0 ^ f1, g0 ^ g1, H, 4); // H(1) 57/56 bits
ulong r = H[1] ^ H[2];
ulong z0 = H[0],
z3 = H[3],
z1 = H[4] ^ z0 ^ r,
z2 = H[5] ^ z3 ^ r;
zz[0] = z0 ^ (z1 << 57);
zz[1] = (z1 >> 7) ^ (z2 << 50);
zz[2] = (z2 >> 14) ^ (z3 << 43);
zz[3] = (z3 >> 21);
}
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 & 0x0100804020100800UL) & (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)
{
Interleave.Expand64To128(x[0], zz, 0);
Interleave.Expand64To128(x[1], zz, 2);
}
}
}
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