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using System;
using System.Diagnostics;
#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
using System.Runtime.CompilerServices;
using System.Runtime.InteropServices;
#endif
using Org.BouncyCastle.Math.Raw;
using Org.BouncyCastle.Utilities;
namespace Org.BouncyCastle.Math.EC.Rfc8032
{
internal static class Scalar25519
{
internal const int Size = 8;
private const int ScalarBytes = Size * 4;
private const long M08L = 0x000000FFL;
private const long M28L = 0x0FFFFFFFL;
private const long M32L = 0xFFFFFFFFL;
private const int TargetLength = 254;
private static readonly uint[] L = { 0x5CF5D3EDU, 0x5812631AU, 0xA2F79CD6U, 0x14DEF9DEU, 0x00000000U,
0x00000000U, 0x00000000U, 0x10000000U };
private static readonly uint[] LSq = { 0xAB128969U, 0xE2EDF685U, 0x2298A31DU, 0x68039276U, 0xD217F5BEU,
0x3DCEEC73U, 0x1B7C309AU, 0xA1B39941U, 0x4B9EBA7DU, 0xCB024C63U, 0xD45EF39AU, 0x029BDF3BU, 0x00000000U,
0x00000000U, 0x00000000U, 0x01000000U };
private const int L0 = -0x030A2C13; // L0:26/--
private const int L1 = 0x012631A6; // L1:24/22
private const int L2 = 0x079CD658; // L2:27/--
private const int L3 = -0x006215D1; // L3:23/--
private const int L4 = 0x000014DF; // L4:12/11
#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
internal static bool CheckVar(ReadOnlySpan<byte> s, Span<uint> n)
{
Decode(s, n);
return !Nat256.Gte(n, L);
}
#else
internal static bool CheckVar(byte[] s, uint[] n)
{
Decode(s, n);
return !Nat256.Gte(n, L);
}
#endif
#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
internal static void Decode(ReadOnlySpan<byte> k, Span<uint> n)
{
Codec.Decode32(k, n[..Size]);
}
#else
internal static void Decode(byte[] k, uint[] n)
{
Codec.Decode32(k, 0, n, 0, Size);
}
#endif
#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
internal static void GetOrderWnafVar(int width, Span<sbyte> ws)
#else
internal static void GetOrderWnafVar(int width, sbyte[] ws)
#endif
{
Wnaf.GetSignedVar(L, width, ws);
}
#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
internal static void Multiply128Var(ReadOnlySpan<uint> x, ReadOnlySpan<uint> y128, Span<uint> z)
{
Span<uint> tt = stackalloc uint[16];
Nat256.Mul128(x, y128, tt);
if ((int)y128[3] < 0)
{
Nat256.AddTo(L, tt[4..], 0U);
Nat256.SubFrom(x, tt[4..], 0);
}
Span<byte> r = MemoryMarshal.AsBytes(tt);
Reduce(r, r);
tt[..Size].CopyTo(z);
}
#else
internal static void Multiply128Var(uint[] x, uint[] y128, uint[] z)
{
uint[] tt = new uint[12];
Nat256.Mul128(x, y128, tt);
if ((int)y128[3] < 0)
{
Nat256.AddTo(L, 0, tt, 4, 0U);
Nat256.SubFrom(x, 0, tt, 4, 0);
}
byte[] bytes = new byte[64];
Codec.Encode32(tt, 0, 12, bytes, 0);
byte[] r = Reduce(bytes);
Decode(r, z);
}
#endif
internal static byte[] Reduce(byte[] n)
{
byte[] r = new byte[ScalarBytes];
#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
Reduce(n, r);
#else
long x00 = Codec.Decode32(n, 0) & M32L; // x00:32/--
long x01 = (Codec.Decode24(n, 4) << 4) & M32L; // x01:28/--
long x02 = Codec.Decode32(n, 7) & M32L; // x02:32/--
long x03 = (Codec.Decode24(n, 11) << 4) & M32L; // x03:28/--
long x04 = Codec.Decode32(n, 14) & M32L; // x04:32/--
long x05 = (Codec.Decode24(n, 18) << 4) & M32L; // x05:28/--
long x06 = Codec.Decode32(n, 21) & M32L; // x06:32/--
long x07 = (Codec.Decode24(n, 25) << 4) & M32L; // x07:28/--
long x08 = Codec.Decode32(n, 28) & M32L; // x08:32/--
long x09 = (Codec.Decode24(n, 32) << 4) & M32L; // x09:28/--
long x10 = Codec.Decode32(n, 35) & M32L; // x10:32/--
long x11 = (Codec.Decode24(n, 39) << 4) & M32L; // x11:28/--
long x12 = Codec.Decode32(n, 42) & M32L; // x12:32/--
long x13 = (Codec.Decode24(n, 46) << 4) & M32L; // x13:28/--
long x14 = Codec.Decode32(n, 49) & M32L; // x14:32/--
long x15 = (Codec.Decode24(n, 53) << 4) & M32L; // x15:28/--
long x16 = Codec.Decode32(n, 56) & M32L; // x16:32/--
long x17 = (Codec.Decode24(n, 60) << 4) & M32L; // x17:28/--
long x18 = n[63] & M08L; // x18:08/--
long t;
//x18 += (x17 >> 28); x17 &= M28L;
x09 -= x18 * L0; // x09:34/28
x10 -= x18 * L1; // x10:33/30
x11 -= x18 * L2; // x11:35/28
x12 -= x18 * L3; // x12:32/31
x13 -= x18 * L4; // x13:28/21
x17 += (x16 >> 28); x16 &= M28L; // x17:28/--, x16:28/--
x08 -= x17 * L0; // x08:54/32
x09 -= x17 * L1; // x09:52/51
x10 -= x17 * L2; // x10:55/34
x11 -= x17 * L3; // x11:51/36
x12 -= x17 * L4; // x12:41/--
//x16 += (x15 >> 28); x15 &= M28L;
x07 -= x16 * L0; // x07:54/28
x08 -= x16 * L1; // x08:54/53
x09 -= x16 * L2; // x09:55/53
x10 -= x16 * L3; // x10:55/52
x11 -= x16 * L4; // x11:51/41
x15 += (x14 >> 28); x14 &= M28L; // x15:28/--, x14:28/--
x06 -= x15 * L0; // x06:54/32
x07 -= x15 * L1; // x07:54/53
x08 -= x15 * L2; // x08:56/--
x09 -= x15 * L3; // x09:55/54
x10 -= x15 * L4; // x10:55/53
//x14 += (x13 >> 28); x13 &= M28L;
x05 -= x14 * L0; // x05:54/28
x06 -= x14 * L1; // x06:54/53
x07 -= x14 * L2; // x07:56/--
x08 -= x14 * L3; // x08:56/51
x09 -= x14 * L4; // x09:56/--
x13 += (x12 >> 28); x12 &= M28L; // x13:28/22, x12:28/--
x04 -= x13 * L0; // x04:54/49
x05 -= x13 * L1; // x05:54/53
x06 -= x13 * L2; // x06:56/--
x07 -= x13 * L3; // x07:56/52
x08 -= x13 * L4; // x08:56/52
x12 += (x11 >> 28); x11 &= M28L; // x12:28/24, x11:28/--
x03 -= x12 * L0; // x03:54/49
x04 -= x12 * L1; // x04:54/51
x05 -= x12 * L2; // x05:56/--
x06 -= x12 * L3; // x06:56/52
x07 -= x12 * L4; // x07:56/53
x11 += (x10 >> 28); x10 &= M28L; // x11:29/--, x10:28/--
x02 -= x11 * L0; // x02:55/32
x03 -= x11 * L1; // x03:55/--
x04 -= x11 * L2; // x04:56/55
x05 -= x11 * L3; // x05:56/52
x06 -= x11 * L4; // x06:56/53
x10 += (x09 >> 28); x09 &= M28L; // x10:29/--, x09:28/--
x01 -= x10 * L0; // x01:55/28
x02 -= x10 * L1; // x02:55/54
x03 -= x10 * L2; // x03:56/55
x04 -= x10 * L3; // x04:57/--
x05 -= x10 * L4; // x05:56/53
x08 += (x07 >> 28); x07 &= M28L; // x08:56/53, x07:28/--
x09 += (x08 >> 28); x08 &= M28L; // x09:29/25, x08:28/--
t = (x08 >> 27) & 1L;
x09 += t; // x09:29/26
x00 -= x09 * L0; // x00:55/53
x01 -= x09 * L1; // x01:55/54
x02 -= x09 * L2; // x02:57/--
x03 -= x09 * L3; // x03:57/--
x04 -= x09 * L4; // x04:57/42
x01 += (x00 >> 28); x00 &= M28L;
x02 += (x01 >> 28); x01 &= M28L;
x03 += (x02 >> 28); x02 &= M28L;
x04 += (x03 >> 28); x03 &= M28L;
x05 += (x04 >> 28); x04 &= M28L;
x06 += (x05 >> 28); x05 &= M28L;
x07 += (x06 >> 28); x06 &= M28L;
x08 += (x07 >> 28); x07 &= M28L;
x09 = (x08 >> 28); x08 &= M28L;
x09 -= t;
Debug.Assert(x09 == 0L || x09 == -1L);
x00 += x09 & L0;
x01 += x09 & L1;
x02 += x09 & L2;
x03 += x09 & L3;
x04 += x09 & L4;
x01 += (x00 >> 28); x00 &= M28L;
x02 += (x01 >> 28); x01 &= M28L;
x03 += (x02 >> 28); x02 &= M28L;
x04 += (x03 >> 28); x03 &= M28L;
x05 += (x04 >> 28); x04 &= M28L;
x06 += (x05 >> 28); x05 &= M28L;
x07 += (x06 >> 28); x06 &= M28L;
x08 += (x07 >> 28); x07 &= M28L;
Codec.Encode56((ulong)(x00 | (x01 << 28)), r, 0);
Codec.Encode56((ulong)(x02 | (x03 << 28)), r, 7);
Codec.Encode56((ulong)(x04 | (x05 << 28)), r, 14);
Codec.Encode56((ulong)(x06 | (x07 << 28)), r, 21);
Codec.Encode32((uint)x08, r, 28);
#endif
return r;
}
#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
internal static void Reduce(ReadOnlySpan<byte> n, Span<byte> r)
{
long x00 = Codec.Decode32(n[ 0..]) & M32L; // x00:32/--
long x01 = (Codec.Decode24(n[ 4..]) << 4) & M32L; // x01:28/--
long x02 = Codec.Decode32(n[ 7..]) & M32L; // x02:32/--
long x03 = (Codec.Decode24(n[11..]) << 4) & M32L; // x03:28/--
long x04 = Codec.Decode32(n[14..]) & M32L; // x04:32/--
long x05 = (Codec.Decode24(n[18..]) << 4) & M32L; // x05:28/--
long x06 = Codec.Decode32(n[21..]) & M32L; // x06:32/--
long x07 = (Codec.Decode24(n[25..]) << 4) & M32L; // x07:28/--
long x08 = Codec.Decode32(n[28..]) & M32L; // x08:32/--
long x09 = (Codec.Decode24(n[32..]) << 4) & M32L; // x09:28/--
long x10 = Codec.Decode32(n[35..]) & M32L; // x10:32/--
long x11 = (Codec.Decode24(n[39..]) << 4) & M32L; // x11:28/--
long x12 = Codec.Decode32(n[42..]) & M32L; // x12:32/--
long x13 = (Codec.Decode24(n[46..]) << 4) & M32L; // x13:28/--
long x14 = Codec.Decode32(n[49..]) & M32L; // x14:32/--
long x15 = (Codec.Decode24(n[53..]) << 4) & M32L; // x15:28/--
long x16 = Codec.Decode32(n[56..]) & M32L; // x16:32/--
long x17 = (Codec.Decode24(n[60..]) << 4) & M32L; // x17:28/--
long x18 = n[63] & M08L; // x18:08/--
long t;
//x18 += (x17 >> 28); x17 &= M28L;
x09 -= x18 * L0; // x09:34/28
x10 -= x18 * L1; // x10:33/30
x11 -= x18 * L2; // x11:35/28
x12 -= x18 * L3; // x12:32/31
x13 -= x18 * L4; // x13:28/21
x17 += (x16 >> 28); x16 &= M28L; // x17:28/--, x16:28/--
x08 -= x17 * L0; // x08:54/32
x09 -= x17 * L1; // x09:52/51
x10 -= x17 * L2; // x10:55/34
x11 -= x17 * L3; // x11:51/36
x12 -= x17 * L4; // x12:41/--
//x16 += (x15 >> 28); x15 &= M28L;
x07 -= x16 * L0; // x07:54/28
x08 -= x16 * L1; // x08:54/53
x09 -= x16 * L2; // x09:55/53
x10 -= x16 * L3; // x10:55/52
x11 -= x16 * L4; // x11:51/41
x15 += (x14 >> 28); x14 &= M28L; // x15:28/--, x14:28/--
x06 -= x15 * L0; // x06:54/32
x07 -= x15 * L1; // x07:54/53
x08 -= x15 * L2; // x08:56/--
x09 -= x15 * L3; // x09:55/54
x10 -= x15 * L4; // x10:55/53
//x14 += (x13 >> 28); x13 &= M28L;
x05 -= x14 * L0; // x05:54/28
x06 -= x14 * L1; // x06:54/53
x07 -= x14 * L2; // x07:56/--
x08 -= x14 * L3; // x08:56/51
x09 -= x14 * L4; // x09:56/--
x13 += (x12 >> 28); x12 &= M28L; // x13:28/22, x12:28/--
x04 -= x13 * L0; // x04:54/49
x05 -= x13 * L1; // x05:54/53
x06 -= x13 * L2; // x06:56/--
x07 -= x13 * L3; // x07:56/52
x08 -= x13 * L4; // x08:56/52
x12 += (x11 >> 28); x11 &= M28L; // x12:28/24, x11:28/--
x03 -= x12 * L0; // x03:54/49
x04 -= x12 * L1; // x04:54/51
x05 -= x12 * L2; // x05:56/--
x06 -= x12 * L3; // x06:56/52
x07 -= x12 * L4; // x07:56/53
x11 += (x10 >> 28); x10 &= M28L; // x11:29/--, x10:28/--
x02 -= x11 * L0; // x02:55/32
x03 -= x11 * L1; // x03:55/--
x04 -= x11 * L2; // x04:56/55
x05 -= x11 * L3; // x05:56/52
x06 -= x11 * L4; // x06:56/53
x10 += (x09 >> 28); x09 &= M28L; // x10:29/--, x09:28/--
x01 -= x10 * L0; // x01:55/28
x02 -= x10 * L1; // x02:55/54
x03 -= x10 * L2; // x03:56/55
x04 -= x10 * L3; // x04:57/--
x05 -= x10 * L4; // x05:56/53
x08 += (x07 >> 28); x07 &= M28L; // x08:56/53, x07:28/--
x09 += (x08 >> 28); x08 &= M28L; // x09:29/25, x08:28/--
t = (x08 >> 27) & 1L;
x09 += t; // x09:29/26
x00 -= x09 * L0; // x00:55/53
x01 -= x09 * L1; // x01:55/54
x02 -= x09 * L2; // x02:57/--
x03 -= x09 * L3; // x03:57/--
x04 -= x09 * L4; // x04:57/42
x01 += (x00 >> 28); x00 &= M28L;
x02 += (x01 >> 28); x01 &= M28L;
x03 += (x02 >> 28); x02 &= M28L;
x04 += (x03 >> 28); x03 &= M28L;
x05 += (x04 >> 28); x04 &= M28L;
x06 += (x05 >> 28); x05 &= M28L;
x07 += (x06 >> 28); x06 &= M28L;
x08 += (x07 >> 28); x07 &= M28L;
x09 = (x08 >> 28); x08 &= M28L;
x09 -= t;
Debug.Assert(x09 == 0L || x09 == -1L);
x00 += x09 & L0;
x01 += x09 & L1;
x02 += x09 & L2;
x03 += x09 & L3;
x04 += x09 & L4;
x01 += (x00 >> 28); x00 &= M28L;
x02 += (x01 >> 28); x01 &= M28L;
x03 += (x02 >> 28); x02 &= M28L;
x04 += (x03 >> 28); x03 &= M28L;
x05 += (x04 >> 28); x04 &= M28L;
x06 += (x05 >> 28); x05 &= M28L;
x07 += (x06 >> 28); x06 &= M28L;
x08 += (x07 >> 28); x07 &= M28L;
Codec.Encode56((ulong)(x00 | (x01 << 28)), r);
Codec.Encode56((ulong)(x02 | (x03 << 28)), r[7..]);
Codec.Encode56((ulong)(x04 | (x05 << 28)), r[14..]);
Codec.Encode56((ulong)(x06 | (x07 << 28)), r[21..]);
Codec.Encode32((uint)x08, r[28..]);
}
#endif
#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
internal static void ReduceBasisVar(ReadOnlySpan<uint> k, Span<uint> z0, Span<uint> z1)
{
/*
* Split scalar k into two half-size scalars z0 and z1, such that z1 * k == z0 mod L.
*
* See https://ia.cr/2020/454 (Pornin).
*/
Span<uint> Nu = stackalloc uint[16]; LSq.CopyTo(Nu);
Span<uint> Nv = stackalloc uint[16]; Nat256.Square(k, Nv); ++Nv[0];
Span<uint> p = stackalloc uint[16]; Nat256.Mul(L, k, p);
Span<uint> u0 = stackalloc uint[4]; u0.CopyFrom(L);
Span<uint> u1 = stackalloc uint[4];
Span<uint> v0 = stackalloc uint[4]; v0.CopyFrom(k);
Span<uint> v1 = stackalloc uint[4]; v1[0] = 1U;
int last = 15;
int len_Nv = ScalarUtilities.GetBitLengthPositive(last, Nv);
while (len_Nv > TargetLength)
{
int len_p = ScalarUtilities.GetBitLength(last, p);
int s = len_p - len_Nv;
s &= ~(s >> 31);
if ((int)p[last] < 0)
{
ScalarUtilities.AddShifted_NP(last, s, Nu, Nv, p);
ScalarUtilities.AddShifted_UV(last: 3, s, u0, u1, v0, v1);
}
else
{
ScalarUtilities.SubShifted_NP(last, s, Nu, Nv, p);
ScalarUtilities.SubShifted_UV(last: 3, s, u0, u1, v0, v1);
}
if (ScalarUtilities.LessThan(last, Nu, Nv))
{
ScalarUtilities.Swap(ref u0, ref v0);
ScalarUtilities.Swap(ref u1, ref v1);
ScalarUtilities.Swap(ref Nu, ref Nv);
last = len_Nv >> 5;
len_Nv = ScalarUtilities.GetBitLengthPositive(last, Nv);
}
}
// v1 * k == v0 mod L
v0.CopyTo(z0);
v1.CopyTo(z1);
}
#else
internal static void ReduceBasisVar(uint[] k, uint[] z0, uint[] z1)
{
/*
* Split scalar k into two half-size scalars z0 and z1, such that z1 * k == z0 mod L.
*
* See https://ia.cr/2020/454 (Pornin).
*/
uint[] Nu = new uint[16]; Array.Copy(LSq, Nu, 16);
uint[] Nv = new uint[16]; Nat256.Square(k, Nv); ++Nv[0];
uint[] p = new uint[16]; Nat256.Mul(L, k, p);
uint[] u0 = new uint[4]; Array.Copy(L, u0, 4);
uint[] u1 = new uint[4];
uint[] v0 = new uint[4]; Array.Copy(k, v0, 4);
uint[] v1 = new uint[4]; v1[0] = 1U;
int last = 15;
int len_Nv = ScalarUtilities.GetBitLengthPositive(last, Nv);
while (len_Nv > TargetLength)
{
int len_p = ScalarUtilities.GetBitLength(last, p);
int s = len_p - len_Nv;
s &= ~(s >> 31);
if ((int)p[last] < 0)
{
ScalarUtilities.AddShifted_NP(last, s, Nu, Nv, p);
ScalarUtilities.AddShifted_UV(last: 3, s, u0, u1, v0, v1);
}
else
{
ScalarUtilities.SubShifted_NP(last, s, Nu, Nv, p);
ScalarUtilities.SubShifted_UV(last: 3, s, u0, u1, v0, v1);
}
if (ScalarUtilities.LessThan(last, Nu, Nv))
{
ScalarUtilities.Swap(ref u0, ref v0);
ScalarUtilities.Swap(ref u1, ref v1);
ScalarUtilities.Swap(ref Nu, ref Nv);
last = len_Nv >> 5;
len_Nv = ScalarUtilities.GetBitLengthPositive(last, Nv);
}
}
// v1 * k == v0 mod L
Array.Copy(v0, z0, 4);
Array.Copy(v1, z1, 4);
}
#endif
#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
internal static void ToSignedDigits(int bits, Span<uint> z)
#else
internal static void ToSignedDigits(int bits, uint[] z)
#endif
{
Debug.Assert(bits == 256);
Debug.Assert(z.Length >= Size);
uint c1 = Nat.CAddTo(Size, ~(int)z[0] & 1, L, z); Debug.Assert(c1 == 0U);
uint c2 = Nat.ShiftDownBit(Size, z, 1U); Debug.Assert(c2 == (1U << 31));
}
}
}
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