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using System;
using System.Diagnostics;
#if NETCOREAPP3_0_OR_GREATER
using System.Runtime.CompilerServices;
using System.Runtime.InteropServices;
using System.Runtime.Intrinsics;
using System.Runtime.Intrinsics.X86;
#endif
using Org.BouncyCastle.Math.Raw;
namespace Org.BouncyCastle.Math.EC.Custom.Sec
{
internal static class SecT113Field
{
private const ulong M49 = ulong.MaxValue >> 15;
private const ulong M57 = ulong.MaxValue >> 7;
#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
public static void Add(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> z)
#else
public static void Add(ulong[] x, ulong[] y, ulong[] z)
#endif
{
z[0] = x[0] ^ y[0];
z[1] = x[1] ^ y[1];
}
#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
public static void AddBothTo(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> z)
#else
public static void AddBothTo(ulong[] x, ulong[] y, ulong[] z)
#endif
{
z[0] ^= x[0] ^ y[0];
z[1] ^= x[1] ^ y[1];
}
#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
public static void AddExt(ReadOnlySpan<ulong> xx, ReadOnlySpan<ulong> yy, Span<ulong> zz)
#else
public static void AddExt(ulong[] xx, ulong[] yy, ulong[] zz)
#endif
{
zz[0] = xx[0] ^ yy[0];
zz[1] = xx[1] ^ yy[1];
zz[2] = xx[2] ^ yy[2];
zz[3] = xx[3] ^ yy[3];
}
#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
public static void AddOne(ReadOnlySpan<ulong> x, Span<ulong> z)
#else
public static void AddOne(ulong[] x, ulong[] z)
#endif
{
z[0] = x[0] ^ 1UL;
z[1] = x[1];
}
#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
public static void AddTo(ReadOnlySpan<ulong> x, Span<ulong> z)
#else
public static void AddTo(ulong[] x, ulong[] z)
#endif
{
z[0] ^= x[0];
z[1] ^= x[1];
}
public static ulong[] FromBigInteger(BigInteger x)
{
return Nat.FromBigInteger64(113, x);
}
#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
public static void HalfTrace(ReadOnlySpan<ulong> x, Span<ulong> z)
#else
public static void HalfTrace(ulong[] x, ulong[] z)
#endif
{
#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
Span<ulong> tt = stackalloc ulong[4];
#else
ulong[] tt = Nat128.CreateExt64();
#endif
Nat128.Copy64(x, z);
for (int i = 1; i < 113; i += 2)
{
ImplSquare(z, tt);
Reduce(tt, z);
ImplSquare(z, tt);
Reduce(tt, z);
AddTo(x, z);
}
}
#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
public static void Invert(ReadOnlySpan<ulong> x, Span<ulong> z)
#else
public static void Invert(ulong[] x, ulong[] z)
#endif
{
if (Nat128.IsZero64(x))
throw new InvalidOperationException();
// Itoh-Tsujii inversion
#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
Span<ulong> t0 = stackalloc ulong[2];
Span<ulong> t1 = stackalloc ulong[2];
#else
ulong[] t0 = Nat128.Create64();
ulong[] t1 = Nat128.Create64();
#endif
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);
}
#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
public static void Multiply(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> z)
#else
public static void Multiply(ulong[] x, ulong[] y, ulong[] z)
#endif
{
#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
Span<ulong> tt = stackalloc ulong[8];
#else
ulong[] tt = new ulong[8];
#endif
ImplMultiply(x, y, tt);
Reduce(tt, z);
}
#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
public static void MultiplyAddToExt(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> zz)
#else
public static void MultiplyAddToExt(ulong[] x, ulong[] y, ulong[] zz)
#endif
{
#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
Span<ulong> tt = stackalloc ulong[8];
#else
ulong[] tt = new ulong[8];
#endif
ImplMultiply(x, y, tt);
AddExt(zz, tt, zz);
}
#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
public static void MultiplyExt(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> zz)
#else
public static void MultiplyExt(ulong[] x, ulong[] y, ulong[] zz)
#endif
{
ImplMultiply(x, y, zz);
}
#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
public static void Reduce(ReadOnlySpan<ulong> xx, Span<ulong> z)
#else
public static void Reduce(ulong[] xx, ulong[] z)
#endif
{
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;
}
#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
public static void Sqrt(ReadOnlySpan<ulong> x, Span<ulong> z)
#else
public static void Sqrt(ulong[] x, ulong[] z)
#endif
{
ulong c0 = Interleave.Unshuffle(x[0], x[1], out ulong e0);
z[0] = e0 ^ (c0 << 57) ^ (c0 << 5);
z[1] = (c0 >> 7) ^ (c0 >> 59);
}
#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
public static void Square(ReadOnlySpan<ulong> x, Span<ulong> z)
#else
public static void Square(ulong[] x, ulong[] z)
#endif
{
#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
Span<ulong> tt = stackalloc ulong[4];
#else
ulong[] tt = Nat128.CreateExt64();
#endif
ImplSquare(x, tt);
Reduce(tt, z);
}
#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
public static void SquareAddToExt(ReadOnlySpan<ulong> x, Span<ulong> zz)
#else
public static void SquareAddToExt(ulong[] x, ulong[] zz)
#endif
{
#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
Span<ulong> tt = stackalloc ulong[4];
#else
ulong[] tt = Nat128.CreateExt64();
#endif
ImplSquare(x, tt);
AddExt(zz, tt, zz);
}
#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
public static void SquareExt(ReadOnlySpan<ulong> x, Span<ulong> zz)
#else
public static void SquareExt(ulong[] x, ulong[] zz)
#endif
{
ImplSquare(x, zz);
}
#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
public static void SquareN(ReadOnlySpan<ulong> x, int n, Span<ulong> z)
#else
public static void SquareN(ulong[] x, int n, ulong[] z)
#endif
{
Debug.Assert(n > 0);
#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
Span<ulong> tt = stackalloc ulong[4];
#else
ulong[] tt = Nat128.CreateExt64();
#endif
ImplSquare(x, tt);
Reduce(tt, z);
while (--n > 0)
{
ImplSquare(z, tt);
Reduce(tt, z);
}
}
#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
public static uint Trace(ReadOnlySpan<ulong> x)
#else
public static uint Trace(ulong[] x)
#endif
{
// Non-zero-trace bits: 0
return (uint)(x[0]) & 1U;
}
#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
private static void ImplMultiply(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> zz)
{
#if NETCOREAPP3_0_OR_GREATER
if (Org.BouncyCastle.Runtime.Intrinsics.X86.Pclmulqdq.IsEnabled &&
Org.BouncyCastle.Runtime.Intrinsics.Vector.IsPackedLittleEndian)
{
var X01 = Vector128.Create(x[0], x[1]);
var Y01 = Vector128.Create(y[0], y[1]);
var Z01 = Pclmulqdq.CarrylessMultiply(X01, Y01, 0x00);
var Z12 = Sse2.Xor(Pclmulqdq.CarrylessMultiply(X01, Y01, 0x01),
Pclmulqdq.CarrylessMultiply(X01, Y01, 0x10));
var Z23 = Pclmulqdq.CarrylessMultiply(X01, Y01, 0x11);
Z01 = Sse2.Xor(Z01, Sse2.ShiftLeftLogical128BitLane(Z12, 8));
Z23 = Sse2.Xor(Z23, Sse2.ShiftRightLogical128BitLane(Z12, 8));
Span<byte> zzBytes = MemoryMarshal.AsBytes(zz);
MemoryMarshal.Write(zzBytes[0x00..0x10], ref Z01);
MemoryMarshal.Write(zzBytes[0x10..0x20], ref Z23);
return;
}
#endif
/*
* "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;
Span<ulong> u = zz;
Span<ulong> H = stackalloc ulong[6];
ImplMulw(u, f0, g0, H[0..]); // H(0) 57/56 bits
ImplMulw(u, f1, g1, H[2..]); // H(INF) 57/54 bits
ImplMulw(u, 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);
}
#else
private 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[] u = zz;
ulong[] H = new ulong[6];
ImplMulw(u, f0, g0, H, 0); // H(0) 57/56 bits
ImplMulw(u, f1, g1, H, 2); // H(INF) 57/54 bits
ImplMulw(u, 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);
}
#endif
#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
private static void ImplMulw(Span<ulong> u, ulong x, ulong y, Span<ulong> z)
#else
private static void ImplMulw(ulong[] u, ulong x, ulong y, ulong[] z, int zOff)
#endif
{
Debug.Assert(x >> 57 == 0);
Debug.Assert(y >> 57 == 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[(int)j & 7];
int k = 48;
do
{
j = (uint)(x >> k);
g = u[(int)j & 7]
^ u[(int)(j >> 3) & 7] << 3
^ u[(int)(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);
#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
z[0] ^= l & M57;
z[1] ^= (l >> 57) ^ (h << 7);
#else
z[zOff ] = l & M57;
z[zOff + 1] = (l >> 57) ^ (h << 7);
#endif
}
#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
private static void ImplSquare(ReadOnlySpan<ulong> x, Span<ulong> zz)
#else
private static void ImplSquare(ulong[] x, ulong[] zz)
#endif
{
#if NETCOREAPP3_0_OR_GREATER
if (Org.BouncyCastle.Runtime.Intrinsics.X86.Bmi2.X64.IsEnabled)
{
zz[3] = Bmi2.X64.ParallelBitDeposit(x[1] >> 32, 0x5555555555555555UL);
zz[2] = Bmi2.X64.ParallelBitDeposit(x[1] , 0x5555555555555555UL);
zz[1] = Bmi2.X64.ParallelBitDeposit(x[0] >> 32, 0x5555555555555555UL);
zz[0] = Bmi2.X64.ParallelBitDeposit(x[0] , 0x5555555555555555UL);
return;
}
#endif
#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
Interleave.Expand64To128(x[..2], zz[..4]);
#else
Interleave.Expand64To128(x, 0, 2, zz, 0);
#endif
}
}
}
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