diff options
Diffstat (limited to 'crypto/src/math/ec/rfc8032/Scalar448.cs')
| -rw-r--r-- | crypto/src/math/ec/rfc8032/Scalar448.cs | 819 |
1 files changed, 819 insertions, 0 deletions
diff --git a/crypto/src/math/ec/rfc8032/Scalar448.cs b/crypto/src/math/ec/rfc8032/Scalar448.cs new file mode 100644 index 000000000..e17f48a99 --- /dev/null +++ b/crypto/src/math/ec/rfc8032/Scalar448.cs @@ -0,0 +1,819 @@ +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.Crypto.Utilities; +using Org.BouncyCastle.Math.Raw; +using Org.BouncyCastle.Utilities; + +namespace Org.BouncyCastle.Math.EC.Rfc8032 +{ + internal static class Scalar448 + { + internal const int Size = 14; + + internal const int ScalarBytes = Size * 4 + 1; + + private const ulong M26UL = 0x03FFFFFFUL; + private const ulong M28UL = 0x0FFFFFFFUL; + + private const int TargetLength = 447; + + private static readonly uint[] L = { 0xAB5844F3U, 0x2378C292U, 0x8DC58F55U, 0x216CC272U, 0xAED63690U, + 0xC44EDB49U, 0x7CCA23E9U, 0xFFFFFFFFU, 0xFFFFFFFFU, 0xFFFFFFFFU, 0xFFFFFFFFU, 0xFFFFFFFFU, 0xFFFFFFFFU, + 0x3FFFFFFFU }; + private static readonly uint[] LSq = { 0x1BA1FEA9U, 0xC1ADFBB8U, 0x49E0A8B2U, 0xB91BF537U, 0xE764D815U, + 0x4525492BU, 0xA2B8716DU, 0x4AE17CF6U, 0xBA3C47C4U, 0xF1A9CC14U, 0x7E4D070AU, 0x92052BCBU, 0x9F823B72U, + 0xC3402A93U, 0x55AC2279U, 0x91BC6149U, 0x46E2C7AAU, 0x10B66139U, 0xD76B1B48U, 0xE2276DA4U, 0xBE6511F4U, + 0xFFFFFFFFU, 0xFFFFFFFFU, 0xFFFFFFFFU, 0xFFFFFFFFU, 0xFFFFFFFFU, 0xFFFFFFFFU, 0x0FFFFFFFU }; + + private const int L_0 = 0x04A7BB0D; // L_0:26/24 + private const int L_1 = 0x0873D6D5; // L_1:27/23 + private const int L_2 = 0x0A70AADC; // L_2:27/26 + private const int L_3 = 0x03D8D723; // L_3:26/-- + private const int L_4 = 0x096FDE93; // L_4:27/25 + private const int L_5 = 0x0B65129C; // L_5:27/26 + private const int L_6 = 0x063BB124; // L_6:27/-- + private const int L_7 = 0x08335DC1; // L_7:27/22 + + private const int L4_0 = 0x029EEC34; // L4_0:25/24 + private const int L4_1 = 0x01CF5B55; // L4_1:25/-- + private const int L4_2 = 0x09C2AB72; // L4_2:27/25 + private const int L4_3 = 0x0F635C8E; // L4_3:28/-- + private const int L4_4 = 0x05BF7A4C; // L4_4:26/25 + private const int L4_5 = 0x0D944A72; // L4_5:28/-- + private const int L4_6 = 0x08EEC492; // L4_6:27/24 + private const int L4_7 = 0x20CD7705; // L4_7:29/24 + +#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER + internal static bool CheckVar(ReadOnlySpan<byte> s, Span<uint> n) + { + if (s[ScalarBytes - 1] != 0x00) + return false; + + Decode(s, n); + return !Nat.Gte(Size, n, L); + } +#else + internal static bool CheckVar(byte[] s, uint[] n) + { + if (s[ScalarBytes - 1] != 0x00) + return false; + + Decode(s, n); + return !Nat.Gte(Size, n, L); + } +#endif + +#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER + internal static void Decode(ReadOnlySpan<byte> k, Span<uint> n) + { + Debug.Assert(k[ScalarBytes - 1] == 0x00); + + Codec.Decode32(k, n[..Size]); + } +#else + internal static void Decode(byte[] k, uint[] n) + { + Debug.Assert(k[ScalarBytes - 1] == 0x00); + + 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 Multiply225Var(ReadOnlySpan<uint> x, ReadOnlySpan<uint> y225, Span<uint> z) + { + Span<uint> tt = stackalloc uint[29]; + Nat.Mul(y225, x, tt); + + if ((int)y225[7] < 0) + { + Nat.AddTo(14, L, tt[8..]); + Nat.SubFrom(14, x, tt[8..]); + } + + Span<byte> r = MemoryMarshal.AsBytes(tt); + Reduce(r, r); + tt[..14].CopyTo(z); + } +#else + internal static void Multiply225Var(uint[] x, uint[] y225, uint[] z) + { + uint[] tt = new uint[22]; + Nat.Mul(y225, 0, 8, x, 0, 14, tt, 0); + + if ((int)y225[7] < 0) + { + Nat.AddTo(14, L, 0, tt, 8); + Nat.SubFrom(14, x, 0, tt, 8); + } + + byte[] bytes = new byte[114]; + Codec.Encode32(tt, 0, 22, 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 + ulong x00 = Codec.Decode32(n, 0); // x00:32/-- + ulong x01 = (Codec.Decode24(n, 4) << 4); // x01:28/-- + ulong x02 = Codec.Decode32(n, 7); // x02:32/-- + ulong x03 = (Codec.Decode24(n, 11) << 4); // x03:28/-- + ulong x04 = Codec.Decode32(n, 14); // x04:32/-- + ulong x05 = (Codec.Decode24(n, 18) << 4); // x05:28/-- + ulong x06 = Codec.Decode32(n, 21); // x06:32/-- + ulong x07 = (Codec.Decode24(n, 25) << 4); // x07:28/-- + ulong x08 = Codec.Decode32(n, 28); // x08:32/-- + ulong x09 = (Codec.Decode24(n, 32) << 4); // x09:28/-- + ulong x10 = Codec.Decode32(n, 35); // x10:32/-- + ulong x11 = (Codec.Decode24(n, 39) << 4); // x11:28/-- + ulong x12 = Codec.Decode32(n, 42); // x12:32/-- + ulong x13 = (Codec.Decode24(n, 46) << 4); // x13:28/-- + ulong x14 = Codec.Decode32(n, 49); // x14:32/-- + ulong x15 = (Codec.Decode24(n, 53) << 4); // x15:28/-- + ulong x16 = Codec.Decode32(n, 56); // x16:32/-- + ulong x17 = (Codec.Decode24(n, 60) << 4); // x17:28/-- + ulong x18 = Codec.Decode32(n, 63); // x18:32/-- + ulong x19 = (Codec.Decode24(n, 67) << 4); // x19:28/-- + ulong x20 = Codec.Decode32(n, 70); // x20:32/-- + ulong x21 = (Codec.Decode24(n, 74) << 4); // x21:28/-- + ulong x22 = Codec.Decode32(n, 77); // x22:32/-- + ulong x23 = (Codec.Decode24(n, 81) << 4); // x23:28/-- + ulong x24 = Codec.Decode32(n, 84); // x24:32/-- + ulong x25 = (Codec.Decode24(n, 88) << 4); // x25:28/-- + ulong x26 = Codec.Decode32(n, 91); // x26:32/-- + ulong x27 = (Codec.Decode24(n, 95) << 4); // x27:28/-- + ulong x28 = Codec.Decode32(n, 98); // x28:32/-- + ulong x29 = (Codec.Decode24(n, 102) << 4); // x29:28/-- + ulong x30 = Codec.Decode32(n, 105); // x30:32/-- + ulong x31 = (Codec.Decode24(n, 109) << 4); // x31:28/-- + ulong x32 = Codec.Decode16(n, 112); // x32:16/-- + + //x32 += (x31 >> 28); x31 &= M28UL; + x16 += x32 * L4_0; // x16:42/-- + x17 += x32 * L4_1; // x17:41/28 + x18 += x32 * L4_2; // x18:43/42 + x19 += x32 * L4_3; // x19:44/28 + x20 += x32 * L4_4; // x20:43/-- + x21 += x32 * L4_5; // x21:44/28 + x22 += x32 * L4_6; // x22:43/41 + x23 += x32 * L4_7; // x23:45/41 + + x31 += (x30 >> 28); x30 &= M28UL; // x31:28/--, x30:28/-- + x15 += x31 * L4_0; // x15:54/-- + x16 += x31 * L4_1; // x16:53/42 + x17 += x31 * L4_2; // x17:55/54 + x18 += x31 * L4_3; // x18:56/44 + x19 += x31 * L4_4; // x19:55/-- + x20 += x31 * L4_5; // x20:56/43 + x21 += x31 * L4_6; // x21:55/53 + x22 += x31 * L4_7; // x22:57/53 + + //x30 += (x29 >> 28); x29 &= M28UL; + x14 += x30 * L4_0; // x14:54/-- + x15 += x30 * L4_1; // x15:54/53 + x16 += x30 * L4_2; // x16:56/-- + x17 += x30 * L4_3; // x17:57/-- + x18 += x30 * L4_4; // x18:56/55 + x19 += x30 * L4_5; // x19:56/55 + x20 += x30 * L4_6; // x20:57/-- + x21 += x30 * L4_7; // x21:57/56 + + x29 += (x28 >> 28); x28 &= M28UL; // x29:28/--, x28:28/-- + x13 += x29 * L4_0; // x13:54/-- + x14 += x29 * L4_1; // x14:54/53 + x15 += x29 * L4_2; // x15:56/-- + x16 += x29 * L4_3; // x16:57/-- + x17 += x29 * L4_4; // x17:57/55 + x18 += x29 * L4_5; // x18:57/55 + x19 += x29 * L4_6; // x19:57/52 + x20 += x29 * L4_7; // x20:58/52 + + //x28 += (x27 >> 28); x27 &= M28UL; + x12 += x28 * L4_0; // x12:54/-- + x13 += x28 * L4_1; // x13:54/53 + x14 += x28 * L4_2; // x14:56/-- + x15 += x28 * L4_3; // x15:57/-- + x16 += x28 * L4_4; // x16:57/55 + x17 += x28 * L4_5; // x17:58/-- + x18 += x28 * L4_6; // x18:58/-- + x19 += x28 * L4_7; // x19:58/53 + + x27 += (x26 >> 28); x26 &= M28UL; // x27:28/--, x26:28/-- + x11 += x27 * L4_0; // x11:54/-- + x12 += x27 * L4_1; // x12:54/53 + x13 += x27 * L4_2; // x13:56/-- + x14 += x27 * L4_3; // x14:57/-- + x15 += x27 * L4_4; // x15:57/55 + x16 += x27 * L4_5; // x16:58/-- + x17 += x27 * L4_6; // x17:58/56 + x18 += x27 * L4_7; // x18:59/-- + + //x26 += (x25 >> 28); x25 &= M28UL; + x10 += x26 * L4_0; // x10:54/-- + x11 += x26 * L4_1; // x11:54/53 + x12 += x26 * L4_2; // x12:56/-- + x13 += x26 * L4_3; // x13:57/-- + x14 += x26 * L4_4; // x14:57/55 + x15 += x26 * L4_5; // x15:58/-- + x16 += x26 * L4_6; // x16:58/56 + x17 += x26 * L4_7; // x17:59/-- + + x25 += (x24 >> 28); x24 &= M28UL; // x25:28/--, x24:28/-- + x09 += x25 * L4_0; // x09:54/-- + x10 += x25 * L4_1; // x10:54/53 + x11 += x25 * L4_2; // x11:56/-- + x12 += x25 * L4_3; // x12:57/-- + x13 += x25 * L4_4; // x13:57/55 + x14 += x25 * L4_5; // x14:58/-- + x15 += x25 * L4_6; // x15:58/56 + x16 += x25 * L4_7; // x16:59/-- + + x21 += (x20 >> 28); x20 &= M28UL; // x21:58/--, x20:28/-- + x22 += (x21 >> 28); x21 &= M28UL; // x22:57/54, x21:28/-- + x23 += (x22 >> 28); x22 &= M28UL; // x23:45/42, x22:28/-- + x24 += (x23 >> 28); x23 &= M28UL; // x24:28/18, x23:28/-- + + x08 += x24 * L4_0; // x08:54/-- + x09 += x24 * L4_1; // x09:55/-- + x10 += x24 * L4_2; // x10:56/46 + x11 += x24 * L4_3; // x11:57/46 + x12 += x24 * L4_4; // x12:57/55 + x13 += x24 * L4_5; // x13:58/-- + x14 += x24 * L4_6; // x14:58/56 + x15 += x24 * L4_7; // x15:59/-- + + x07 += x23 * L4_0; // x07:54/-- + x08 += x23 * L4_1; // x08:54/53 + x09 += x23 * L4_2; // x09:56/53 + x10 += x23 * L4_3; // x10:57/46 + x11 += x23 * L4_4; // x11:57/55 + x12 += x23 * L4_5; // x12:58/-- + x13 += x23 * L4_6; // x13:58/56 + x14 += x23 * L4_7; // x14:59/-- + + x06 += x22 * L4_0; // x06:54/-- + x07 += x22 * L4_1; // x07:54/53 + x08 += x22 * L4_2; // x08:56/-- + x09 += x22 * L4_3; // x09:57/53 + x10 += x22 * L4_4; // x10:57/55 + x11 += x22 * L4_5; // x11:58/-- + x12 += x22 * L4_6; // x12:58/56 + x13 += x22 * L4_7; // x13:59/-- + + x18 += (x17 >> 28); x17 &= M28UL; // x18:59/31, x17:28/-- + x19 += (x18 >> 28); x18 &= M28UL; // x19:58/54, x18:28/-- + x20 += (x19 >> 28); x19 &= M28UL; // x20:30/29, x19:28/-- + x21 += (x20 >> 28); x20 &= M28UL; // x21:28/03, x20:28/-- + + x05 += x21 * L4_0; // x05:54/-- + x06 += x21 * L4_1; // x06:55/-- + x07 += x21 * L4_2; // x07:56/31 + x08 += x21 * L4_3; // x08:57/31 + x09 += x21 * L4_4; // x09:57/56 + x10 += x21 * L4_5; // x10:58/-- + x11 += x21 * L4_6; // x11:58/56 + x12 += x21 * L4_7; // x12:59/-- + + x04 += x20 * L4_0; // x04:54/-- + x05 += x20 * L4_1; // x05:54/53 + x06 += x20 * L4_2; // x06:56/53 + x07 += x20 * L4_3; // x07:57/31 + x08 += x20 * L4_4; // x08:57/55 + x09 += x20 * L4_5; // x09:58/-- + x10 += x20 * L4_6; // x10:58/56 + x11 += x20 * L4_7; // x11:59/-- + + x03 += x19 * L4_0; // x03:54/-- + x04 += x19 * L4_1; // x04:54/53 + x05 += x19 * L4_2; // x05:56/-- + x06 += x19 * L4_3; // x06:57/53 + x07 += x19 * L4_4; // x07:57/55 + x08 += x19 * L4_5; // x08:58/-- + x09 += x19 * L4_6; // x09:58/56 + x10 += x19 * L4_7; // x10:59/-- + + x15 += (x14 >> 28); x14 &= M28UL; // x15:59/31, x14:28/-- + x16 += (x15 >> 28); x15 &= M28UL; // x16:59/32, x15:28/-- + x17 += (x16 >> 28); x16 &= M28UL; // x17:31/29, x16:28/-- + x18 += (x17 >> 28); x17 &= M28UL; // x18:28/04, x17:28/-- + + x02 += x18 * L4_0; // x02:54/-- + x03 += x18 * L4_1; // x03:55/-- + x04 += x18 * L4_2; // x04:56/32 + x05 += x18 * L4_3; // x05:57/32 + x06 += x18 * L4_4; // x06:57/56 + x07 += x18 * L4_5; // x07:58/-- + x08 += x18 * L4_6; // x08:58/56 + x09 += x18 * L4_7; // x09:59/-- + + x01 += x17 * L4_0; // x01:54/-- + x02 += x17 * L4_1; // x02:54/53 + x03 += x17 * L4_2; // x03:56/53 + x04 += x17 * L4_3; // x04:57/32 + x05 += x17 * L4_4; // x05:57/55 + x06 += x17 * L4_5; // x06:58/-- + x07 += x17 * L4_6; // x07:58/56 + x08 += x17 * L4_7; // x08:59/-- + + x16 *= 4; + x16 += (x15 >> 26); x15 &= M26UL; + x16 += 1; // x16:30/01 + + x00 += x16 * L_0; + x01 += x16 * L_1; + x02 += x16 * L_2; + x03 += x16 * L_3; + x04 += x16 * L_4; + x05 += x16 * L_5; + x06 += x16 * L_6; + x07 += x16 * L_7; + + x01 += (x00 >> 28); x00 &= M28UL; + x02 += (x01 >> 28); x01 &= M28UL; + x03 += (x02 >> 28); x02 &= M28UL; + x04 += (x03 >> 28); x03 &= M28UL; + x05 += (x04 >> 28); x04 &= M28UL; + x06 += (x05 >> 28); x05 &= M28UL; + x07 += (x06 >> 28); x06 &= M28UL; + x08 += (x07 >> 28); x07 &= M28UL; + x09 += (x08 >> 28); x08 &= M28UL; + x10 += (x09 >> 28); x09 &= M28UL; + x11 += (x10 >> 28); x10 &= M28UL; + x12 += (x11 >> 28); x11 &= M28UL; + x13 += (x12 >> 28); x12 &= M28UL; + x14 += (x13 >> 28); x13 &= M28UL; + x15 += (x14 >> 28); x14 &= M28UL; + x16 = (x15 >> 26); x15 &= M26UL; + + x16 -= 1; + + Debug.Assert(x16 == 0UL || x16 == ulong.MaxValue); + + x00 -= x16 & L_0; + x01 -= x16 & L_1; + x02 -= x16 & L_2; + x03 -= x16 & L_3; + x04 -= x16 & L_4; + x05 -= x16 & L_5; + x06 -= x16 & L_6; + x07 -= x16 & L_7; + + x01 += (ulong)((long)x00 >> 28); x00 &= M28UL; + x02 += (ulong)((long)x01 >> 28); x01 &= M28UL; + x03 += (ulong)((long)x02 >> 28); x02 &= M28UL; + x04 += (ulong)((long)x03 >> 28); x03 &= M28UL; + x05 += (ulong)((long)x04 >> 28); x04 &= M28UL; + x06 += (ulong)((long)x05 >> 28); x05 &= M28UL; + x07 += (ulong)((long)x06 >> 28); x06 &= M28UL; + x08 += (ulong)((long)x07 >> 28); x07 &= M28UL; + x09 += (ulong)((long)x08 >> 28); x08 &= M28UL; + x10 += (ulong)((long)x09 >> 28); x09 &= M28UL; + x11 += (ulong)((long)x10 >> 28); x10 &= M28UL; + x12 += (ulong)((long)x11 >> 28); x11 &= M28UL; + x13 += (ulong)((long)x12 >> 28); x12 &= M28UL; + x14 += (ulong)((long)x13 >> 28); x13 &= M28UL; + x15 += (ulong)((long)x14 >> 28); x14 &= M28UL; + + Debug.Assert(x15 >> 26 == 0UL); + + Codec.Encode56(x00 | (x01 << 28), r, 0); + Codec.Encode56(x02 | (x03 << 28), r, 7); + Codec.Encode56(x04 | (x05 << 28), r, 14); + Codec.Encode56(x06 | (x07 << 28), r, 21); + Codec.Encode56(x08 | (x09 << 28), r, 28); + Codec.Encode56(x10 | (x11 << 28), r, 35); + Codec.Encode56(x12 | (x13 << 28), r, 42); + Codec.Encode56(x14 | (x15 << 28), r, 49); + //r[ScalarBytes - 1] = 0; +#endif + + return r; + } + +#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER + internal static void Reduce(ReadOnlySpan<byte> n, Span<byte> r) + { + ulong x00 = Codec.Decode32(n[ 0..]); // x00:32/-- + ulong x01 = (Codec.Decode24(n[ 4..]) << 4); // x01:28/-- + ulong x02 = Codec.Decode32(n[ 7..]); // x02:32/-- + ulong x03 = (Codec.Decode24(n[ 11..]) << 4); // x03:28/-- + ulong x04 = Codec.Decode32(n[ 14..]); // x04:32/-- + ulong x05 = (Codec.Decode24(n[ 18..]) << 4); // x05:28/-- + ulong x06 = Codec.Decode32(n[ 21..]); // x06:32/-- + ulong x07 = (Codec.Decode24(n[ 25..]) << 4); // x07:28/-- + ulong x08 = Codec.Decode32(n[ 28..]); // x08:32/-- + ulong x09 = (Codec.Decode24(n[ 32..]) << 4); // x09:28/-- + ulong x10 = Codec.Decode32(n[ 35..]); // x10:32/-- + ulong x11 = (Codec.Decode24(n[ 39..]) << 4); // x11:28/-- + ulong x12 = Codec.Decode32(n[ 42..]); // x12:32/-- + ulong x13 = (Codec.Decode24(n[ 46..]) << 4); // x13:28/-- + ulong x14 = Codec.Decode32(n[ 49..]); // x14:32/-- + ulong x15 = (Codec.Decode24(n[ 53..]) << 4); // x15:28/-- + ulong x16 = Codec.Decode32(n[ 56..]); // x16:32/-- + ulong x17 = (Codec.Decode24(n[ 60..]) << 4); // x17:28/-- + ulong x18 = Codec.Decode32(n[ 63..]); // x18:32/-- + ulong x19 = (Codec.Decode24(n[ 67..]) << 4); // x19:28/-- + ulong x20 = Codec.Decode32(n[ 70..]); // x20:32/-- + ulong x21 = (Codec.Decode24(n[ 74..]) << 4); // x21:28/-- + ulong x22 = Codec.Decode32(n[ 77..]); // x22:32/-- + ulong x23 = (Codec.Decode24(n[ 81..]) << 4); // x23:28/-- + ulong x24 = Codec.Decode32(n[ 84..]); // x24:32/-- + ulong x25 = (Codec.Decode24(n[ 88..]) << 4); // x25:28/-- + ulong x26 = Codec.Decode32(n[ 91..]); // x26:32/-- + ulong x27 = (Codec.Decode24(n[ 95..]) << 4); // x27:28/-- + ulong x28 = Codec.Decode32(n[ 98..]); // x28:32/-- + ulong x29 = (Codec.Decode24(n[102..]) << 4); // x29:28/-- + ulong x30 = Codec.Decode32(n[105..]); // x30:32/-- + ulong x31 = (Codec.Decode24(n[109..]) << 4); // x31:28/-- + ulong x32 = Codec.Decode16(n[112..]); // x32:16/-- + + //x32 += (x31 >> 28); x31 &= M28UL; + x16 += x32 * L4_0; // x16:42/-- + x17 += x32 * L4_1; // x17:41/28 + x18 += x32 * L4_2; // x18:43/42 + x19 += x32 * L4_3; // x19:44/28 + x20 += x32 * L4_4; // x20:43/-- + x21 += x32 * L4_5; // x21:44/28 + x22 += x32 * L4_6; // x22:43/41 + x23 += x32 * L4_7; // x23:45/41 + + x31 += (x30 >> 28); x30 &= M28UL; // x31:28/--, x30:28/-- + x15 += x31 * L4_0; // x15:54/-- + x16 += x31 * L4_1; // x16:53/42 + x17 += x31 * L4_2; // x17:55/54 + x18 += x31 * L4_3; // x18:56/44 + x19 += x31 * L4_4; // x19:55/-- + x20 += x31 * L4_5; // x20:56/43 + x21 += x31 * L4_6; // x21:55/53 + x22 += x31 * L4_7; // x22:57/53 + + //x30 += (x29 >> 28); x29 &= M28UL; + x14 += x30 * L4_0; // x14:54/-- + x15 += x30 * L4_1; // x15:54/53 + x16 += x30 * L4_2; // x16:56/-- + x17 += x30 * L4_3; // x17:57/-- + x18 += x30 * L4_4; // x18:56/55 + x19 += x30 * L4_5; // x19:56/55 + x20 += x30 * L4_6; // x20:57/-- + x21 += x30 * L4_7; // x21:57/56 + + x29 += (x28 >> 28); x28 &= M28UL; // x29:28/--, x28:28/-- + x13 += x29 * L4_0; // x13:54/-- + x14 += x29 * L4_1; // x14:54/53 + x15 += x29 * L4_2; // x15:56/-- + x16 += x29 * L4_3; // x16:57/-- + x17 += x29 * L4_4; // x17:57/55 + x18 += x29 * L4_5; // x18:57/55 + x19 += x29 * L4_6; // x19:57/52 + x20 += x29 * L4_7; // x20:58/52 + + //x28 += (x27 >> 28); x27 &= M28UL; + x12 += x28 * L4_0; // x12:54/-- + x13 += x28 * L4_1; // x13:54/53 + x14 += x28 * L4_2; // x14:56/-- + x15 += x28 * L4_3; // x15:57/-- + x16 += x28 * L4_4; // x16:57/55 + x17 += x28 * L4_5; // x17:58/-- + x18 += x28 * L4_6; // x18:58/-- + x19 += x28 * L4_7; // x19:58/53 + + x27 += (x26 >> 28); x26 &= M28UL; // x27:28/--, x26:28/-- + x11 += x27 * L4_0; // x11:54/-- + x12 += x27 * L4_1; // x12:54/53 + x13 += x27 * L4_2; // x13:56/-- + x14 += x27 * L4_3; // x14:57/-- + x15 += x27 * L4_4; // x15:57/55 + x16 += x27 * L4_5; // x16:58/-- + x17 += x27 * L4_6; // x17:58/56 + x18 += x27 * L4_7; // x18:59/-- + + //x26 += (x25 >> 28); x25 &= M28UL; + x10 += x26 * L4_0; // x10:54/-- + x11 += x26 * L4_1; // x11:54/53 + x12 += x26 * L4_2; // x12:56/-- + x13 += x26 * L4_3; // x13:57/-- + x14 += x26 * L4_4; // x14:57/55 + x15 += x26 * L4_5; // x15:58/-- + x16 += x26 * L4_6; // x16:58/56 + x17 += x26 * L4_7; // x17:59/-- + + x25 += (x24 >> 28); x24 &= M28UL; // x25:28/--, x24:28/-- + x09 += x25 * L4_0; // x09:54/-- + x10 += x25 * L4_1; // x10:54/53 + x11 += x25 * L4_2; // x11:56/-- + x12 += x25 * L4_3; // x12:57/-- + x13 += x25 * L4_4; // x13:57/55 + x14 += x25 * L4_5; // x14:58/-- + x15 += x25 * L4_6; // x15:58/56 + x16 += x25 * L4_7; // x16:59/-- + + x21 += (x20 >> 28); x20 &= M28UL; // x21:58/--, x20:28/-- + x22 += (x21 >> 28); x21 &= M28UL; // x22:57/54, x21:28/-- + x23 += (x22 >> 28); x22 &= M28UL; // x23:45/42, x22:28/-- + x24 += (x23 >> 28); x23 &= M28UL; // x24:28/18, x23:28/-- + + x08 += x24 * L4_0; // x08:54/-- + x09 += x24 * L4_1; // x09:55/-- + x10 += x24 * L4_2; // x10:56/46 + x11 += x24 * L4_3; // x11:57/46 + x12 += x24 * L4_4; // x12:57/55 + x13 += x24 * L4_5; // x13:58/-- + x14 += x24 * L4_6; // x14:58/56 + x15 += x24 * L4_7; // x15:59/-- + + x07 += x23 * L4_0; // x07:54/-- + x08 += x23 * L4_1; // x08:54/53 + x09 += x23 * L4_2; // x09:56/53 + x10 += x23 * L4_3; // x10:57/46 + x11 += x23 * L4_4; // x11:57/55 + x12 += x23 * L4_5; // x12:58/-- + x13 += x23 * L4_6; // x13:58/56 + x14 += x23 * L4_7; // x14:59/-- + + x06 += x22 * L4_0; // x06:54/-- + x07 += x22 * L4_1; // x07:54/53 + x08 += x22 * L4_2; // x08:56/-- + x09 += x22 * L4_3; // x09:57/53 + x10 += x22 * L4_4; // x10:57/55 + x11 += x22 * L4_5; // x11:58/-- + x12 += x22 * L4_6; // x12:58/56 + x13 += x22 * L4_7; // x13:59/-- + + x18 += (x17 >> 28); x17 &= M28UL; // x18:59/31, x17:28/-- + x19 += (x18 >> 28); x18 &= M28UL; // x19:58/54, x18:28/-- + x20 += (x19 >> 28); x19 &= M28UL; // x20:30/29, x19:28/-- + x21 += (x20 >> 28); x20 &= M28UL; // x21:28/03, x20:28/-- + + x05 += x21 * L4_0; // x05:54/-- + x06 += x21 * L4_1; // x06:55/-- + x07 += x21 * L4_2; // x07:56/31 + x08 += x21 * L4_3; // x08:57/31 + x09 += x21 * L4_4; // x09:57/56 + x10 += x21 * L4_5; // x10:58/-- + x11 += x21 * L4_6; // x11:58/56 + x12 += x21 * L4_7; // x12:59/-- + + x04 += x20 * L4_0; // x04:54/-- + x05 += x20 * L4_1; // x05:54/53 + x06 += x20 * L4_2; // x06:56/53 + x07 += x20 * L4_3; // x07:57/31 + x08 += x20 * L4_4; // x08:57/55 + x09 += x20 * L4_5; // x09:58/-- + x10 += x20 * L4_6; // x10:58/56 + x11 += x20 * L4_7; // x11:59/-- + + x03 += x19 * L4_0; // x03:54/-- + x04 += x19 * L4_1; // x04:54/53 + x05 += x19 * L4_2; // x05:56/-- + x06 += x19 * L4_3; // x06:57/53 + x07 += x19 * L4_4; // x07:57/55 + x08 += x19 * L4_5; // x08:58/-- + x09 += x19 * L4_6; // x09:58/56 + x10 += x19 * L4_7; // x10:59/-- + + x15 += (x14 >> 28); x14 &= M28UL; // x15:59/31, x14:28/-- + x16 += (x15 >> 28); x15 &= M28UL; // x16:59/32, x15:28/-- + x17 += (x16 >> 28); x16 &= M28UL; // x17:31/29, x16:28/-- + x18 += (x17 >> 28); x17 &= M28UL; // x18:28/04, x17:28/-- + + x02 += x18 * L4_0; // x02:54/-- + x03 += x18 * L4_1; // x03:55/-- + x04 += x18 * L4_2; // x04:56/32 + x05 += x18 * L4_3; // x05:57/32 + x06 += x18 * L4_4; // x06:57/56 + x07 += x18 * L4_5; // x07:58/-- + x08 += x18 * L4_6; // x08:58/56 + x09 += x18 * L4_7; // x09:59/-- + + x01 += x17 * L4_0; // x01:54/-- + x02 += x17 * L4_1; // x02:54/53 + x03 += x17 * L4_2; // x03:56/53 + x04 += x17 * L4_3; // x04:57/32 + x05 += x17 * L4_4; // x05:57/55 + x06 += x17 * L4_5; // x06:58/-- + x07 += x17 * L4_6; // x07:58/56 + x08 += x17 * L4_7; // x08:59/-- + + x16 *= 4; + x16 += (x15 >> 26); x15 &= M26UL; + x16 += 1; // x16:30/01 + + x00 += x16 * L_0; + x01 += x16 * L_1; + x02 += x16 * L_2; + x03 += x16 * L_3; + x04 += x16 * L_4; + x05 += x16 * L_5; + x06 += x16 * L_6; + x07 += x16 * L_7; + + x01 += (x00 >> 28); x00 &= M28UL; + x02 += (x01 >> 28); x01 &= M28UL; + x03 += (x02 >> 28); x02 &= M28UL; + x04 += (x03 >> 28); x03 &= M28UL; + x05 += (x04 >> 28); x04 &= M28UL; + x06 += (x05 >> 28); x05 &= M28UL; + x07 += (x06 >> 28); x06 &= M28UL; + x08 += (x07 >> 28); x07 &= M28UL; + x09 += (x08 >> 28); x08 &= M28UL; + x10 += (x09 >> 28); x09 &= M28UL; + x11 += (x10 >> 28); x10 &= M28UL; + x12 += (x11 >> 28); x11 &= M28UL; + x13 += (x12 >> 28); x12 &= M28UL; + x14 += (x13 >> 28); x13 &= M28UL; + x15 += (x14 >> 28); x14 &= M28UL; + x16 = (x15 >> 26); x15 &= M26UL; + + x16 -= 1; + + Debug.Assert(x16 == 0UL || x16 == ulong.MaxValue); + + x00 -= x16 & L_0; + x01 -= x16 & L_1; + x02 -= x16 & L_2; + x03 -= x16 & L_3; + x04 -= x16 & L_4; + x05 -= x16 & L_5; + x06 -= x16 & L_6; + x07 -= x16 & L_7; + + x01 += (ulong)((long)x00 >> 28); x00 &= M28UL; + x02 += (ulong)((long)x01 >> 28); x01 &= M28UL; + x03 += (ulong)((long)x02 >> 28); x02 &= M28UL; + x04 += (ulong)((long)x03 >> 28); x03 &= M28UL; + x05 += (ulong)((long)x04 >> 28); x04 &= M28UL; + x06 += (ulong)((long)x05 >> 28); x05 &= M28UL; + x07 += (ulong)((long)x06 >> 28); x06 &= M28UL; + x08 += (ulong)((long)x07 >> 28); x07 &= M28UL; + x09 += (ulong)((long)x08 >> 28); x08 &= M28UL; + x10 += (ulong)((long)x09 >> 28); x09 &= M28UL; + x11 += (ulong)((long)x10 >> 28); x10 &= M28UL; + x12 += (ulong)((long)x11 >> 28); x11 &= M28UL; + x13 += (ulong)((long)x12 >> 28); x12 &= M28UL; + x14 += (ulong)((long)x13 >> 28); x13 &= M28UL; + x15 += (ulong)((long)x14 >> 28); x14 &= M28UL; + + Debug.Assert(x15 >> 26 == 0UL); + + Codec.Encode56(x00 | (x01 << 28), r); + Codec.Encode56(x02 | (x03 << 28), r[7..]); + Codec.Encode56(x04 | (x05 << 28), r[14..]); + Codec.Encode56(x06 | (x07 << 28), r[21..]); + Codec.Encode56(x08 | (x09 << 28), r[28..]); + Codec.Encode56(x10 | (x11 << 28), r[35..]); + Codec.Encode56(x12 | (x13 << 28), r[42..]); + Codec.Encode56(x14 | (x15 << 28), r[49..]); + r[ScalarBytes - 1] = 0; + } +#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[28]; LSq.CopyTo(Nu); + Span<uint> Nv = stackalloc uint[28]; Nat.Square(14, k, Nv); Nat.AddWordTo(28, 1U, Nv); + Span<uint> p = stackalloc uint[28]; Nat.Mul(14, L, k, p); + Span<uint> u0 = stackalloc uint[8]; u0.CopyFrom(L); + Span<uint> u1 = stackalloc uint[8]; + Span<uint> v0 = stackalloc uint[8]; v0.CopyFrom(k); + Span<uint> v1 = stackalloc uint[8]; v1[0] = 1U; + + int last = 27; + 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: 7, s, u0, u1, v0, v1); + } + else + { + ScalarUtilities.SubShifted_NP(last, s, Nu, Nv, p); + ScalarUtilities.SubShifted_UV(last: 7, 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); + } + } + + Debug.Assert((int)v0[7] >> 31 == (int)v0[7] >> 1); + Debug.Assert((int)v1[7] >> 31 == (int)v1[7] >> 1); + + // 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[28]; Array.Copy(LSq, Nu, 28); + uint[] Nv = new uint[28]; Nat.Square(14, k, Nv); Nat.AddWordTo(28, 1U, Nv); + uint[] p = new uint[28]; Nat.Mul(14, L, k, p); + uint[] u0 = new uint[8]; Array.Copy(L, u0, 8); + uint[] u1 = new uint[8]; + uint[] v0 = new uint[8]; Array.Copy(k, v0, 8); + uint[] v1 = new uint[8]; v1[0] = 1U; + + int last = 27; + 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: 7, s, u0, u1, v0, v1); + } + else + { + ScalarUtilities.SubShifted_NP(last, s, Nu, Nv, p); + ScalarUtilities.SubShifted_UV(last: 7, 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); + } + } + + Debug.Assert((int)v0[7] >> 31 == (int)v0[7] >> 1); + Debug.Assert((int)v1[7] >> 31 == (int)v1[7] >> 1); + + // v1 * k == v0 mod L + Array.Copy(v0, z0, 8); + Array.Copy(v1, z1, 8); + } +#endif + +#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER + internal static void ToSignedDigits(int bits, ReadOnlySpan<uint> x, Span<uint> z) +#else + internal static void ToSignedDigits(int bits, uint[] x, uint[] z) +#endif + { + Debug.Assert(448 < bits && bits < 480); + Debug.Assert(z.Length > Size); + + z[Size] = (1U << (bits - 448)) + + Nat.CAdd(Size, ~(int)x[0] & 1, x, L, z); + uint c = Nat.ShiftDownBit(Size + 1, z, 0); + Debug.Assert(c == (1U << 31)); + } + } +} |