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 Scalar448 { internal const int Size = 14; private 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 s, Span 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 k, Span 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 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 x, ReadOnlySpan y225, Span z) { Debug.Assert((int)y225[7] >> 31 == (int)y225[7]); Span tt = stackalloc uint[22]; Nat.Mul(y225, x, tt); if ((int)y225[7] < 0) { Nat.AddTo(Size, L, tt[8..]); Nat.SubFrom(Size, x, tt[8..]); } if (BitConverter.IsLittleEndian) { Span r = MemoryMarshal.AsBytes(tt); Reduce704(r, r); tt[..Size].CopyTo(z); } else { Span r = stackalloc byte[88]; Codec.Encode32(tt, r); Reduce704(r, r); Decode(r, z); } } #else internal static void Multiply225Var(uint[] x, uint[] y225, uint[] z) { Debug.Assert((int)y225[7] >> 31 == (int)y225[7]); uint[] tt = new uint[22]; Nat.Mul(y225, 0, 8, x, 0, Size, tt, 0); if ((int)y225[7] < 0) { Nat.AddTo(Size, L, 0, tt, 8); Nat.SubFrom(Size, x, 0, tt, 8); } byte[] bytes = new byte[88]; Codec.Encode32(tt, 0, 22, bytes, 0); byte[] r = Reduce704(bytes); Decode(r, z); } #endif internal static byte[] Reduce704(byte[] n) { byte[] r = new byte[ScalarBytes]; #if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER Reduce704(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 = 0UL; // TODO Fix bounds calculations which were copied from Reduce912 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 Reduce704(ReadOnlySpan n, Span 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 = 0UL; // TODO Fix bounds calculations which were copied from Reduce912 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 internal static byte[] Reduce912(byte[] n) { byte[] r = new byte[ScalarBytes]; #if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER Reduce912(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 Reduce912(ReadOnlySpan n, Span 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 bool ReduceBasisVar(ReadOnlySpan k, Span z0, Span 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 Nu = stackalloc uint[28]; LSq.CopyTo(Nu); Span Nv = stackalloc uint[28]; Nat448.Square(k, Nv); ++Nv[0]; Span p = stackalloc uint[28]; Nat448.Mul(L, k, p); Span t = stackalloc uint[28]; Span u0 = stackalloc uint[8]; u0.CopyFrom(L); Span u1 = stackalloc uint[8]; Span v0 = stackalloc uint[8]; v0.CopyFrom(k); Span v1 = stackalloc uint[8]; v1[0] = 1U; // Conservative upper bound on the number of loop iterations needed int iterations = TargetLength * 4; int last = 27; int len_Nv = ScalarUtilities.GetBitLengthPositive(last, Nv); while (len_Nv > TargetLength) { if (--iterations < 0) return false; 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, t); ScalarUtilities.AddShifted_UV(last: 7, s, u0, u1, v0, v1); } else { ScalarUtilities.SubShifted_NP(last, s, Nu, Nv, p, t); 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]); Debug.Assert((int)v1[7] >> 31 == (int)v1[7]); // v1 * k == v0 mod L v0.CopyTo(z0); v1.CopyTo(z1); return true; } #else internal static bool 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]; Nat448.Square(k, Nv); ++Nv[0]; uint[] p = new uint[28]; Nat448.Mul(L, k, p); uint[] t = new uint[28]; 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; // Conservative upper bound on the number of loop iterations needed int iterations = TargetLength * 4; int last = 27; int len_Nv = ScalarUtilities.GetBitLengthPositive(last, Nv); while (len_Nv > TargetLength) { if (--iterations < 0) return false; 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, t); ScalarUtilities.AddShifted_UV(last: 7, s, u0, u1, v0, v1); } else { ScalarUtilities.SubShifted_NP(last, s, Nu, Nv, p, t); 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]); Debug.Assert((int)v1[7] >> 31 == (int)v1[7]); // v1 * k == v0 mod L Array.Copy(v0, z0, 8); Array.Copy(v1, z1, 8); return true; } #endif #if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER internal static void ToSignedDigits(int bits, ReadOnlySpan x, Span 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)); } } }