| 1 | /* |
| 2 | * Elliptic curves over GF(p): curve-specific data and functions |
| 3 | * |
| 4 | * Copyright (C) 2006-2015, ARM Limited, All Rights Reserved |
| 5 | * SPDX-License-Identifier: GPL-2.0 |
| 6 | * |
| 7 | * This program is free software; you can redistribute it and/or modify |
| 8 | * it under the terms of the GNU General Public License as published by |
| 9 | * the Free Software Foundation; either version 2 of the License, or |
| 10 | * (at your option) any later version. |
| 11 | * |
| 12 | * This program is distributed in the hope that it will be useful, |
| 13 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
| 14 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
| 15 | * GNU General Public License for more details. |
| 16 | * |
| 17 | * You should have received a copy of the GNU General Public License along |
| 18 | * with this program; if not, write to the Free Software Foundation, Inc., |
| 19 | * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. |
| 20 | * |
| 21 | * This file is part of mbed TLS (https://tls.mbed.org) |
| 22 | */ |
| 23 | |
| 24 | #if !defined(MBEDTLS_CONFIG_FILE) |
| 25 | #include "mbedtls/config.h" |
| 26 | #else |
| 27 | #include MBEDTLS_CONFIG_FILE |
| 28 | #endif |
| 29 | |
| 30 | #if defined(MBEDTLS_ECP_C) |
| 31 | |
| 32 | #include "mbedtls/ecp.h" |
| 33 | |
| 34 | #include <string.h> |
| 35 | |
| 36 | #if !defined(MBEDTLS_ECP_ALT) |
| 37 | |
| 38 | #if ( defined(__ARMCC_VERSION) || defined(_MSC_VER) ) && \ |
| 39 | !defined(inline) && !defined(__cplusplus) |
| 40 | #define inline __inline |
| 41 | #endif |
| 42 | |
| 43 | /* |
| 44 | * Conversion macros for embedded constants: |
| 45 | * build lists of mbedtls_mpi_uint's from lists of unsigned char's grouped by 8, 4 or 2 |
| 46 | */ |
| 47 | #if defined(MBEDTLS_HAVE_INT32) |
| 48 | |
| 49 | #define BYTES_TO_T_UINT_4( a, b, c, d ) \ |
| 50 | ( (mbedtls_mpi_uint) a << 0 ) | \ |
| 51 | ( (mbedtls_mpi_uint) b << 8 ) | \ |
| 52 | ( (mbedtls_mpi_uint) c << 16 ) | \ |
| 53 | ( (mbedtls_mpi_uint) d << 24 ) |
| 54 | |
| 55 | #define BYTES_TO_T_UINT_2( a, b ) \ |
| 56 | BYTES_TO_T_UINT_4( a, b, 0, 0 ) |
| 57 | |
| 58 | #define BYTES_TO_T_UINT_8( a, b, c, d, e, f, g, h ) \ |
| 59 | BYTES_TO_T_UINT_4( a, b, c, d ), \ |
| 60 | BYTES_TO_T_UINT_4( e, f, g, h ) |
| 61 | |
| 62 | #else /* 64-bits */ |
| 63 | |
| 64 | #define BYTES_TO_T_UINT_8( a, b, c, d, e, f, g, h ) \ |
| 65 | ( (mbedtls_mpi_uint) a << 0 ) | \ |
| 66 | ( (mbedtls_mpi_uint) b << 8 ) | \ |
| 67 | ( (mbedtls_mpi_uint) c << 16 ) | \ |
| 68 | ( (mbedtls_mpi_uint) d << 24 ) | \ |
| 69 | ( (mbedtls_mpi_uint) e << 32 ) | \ |
| 70 | ( (mbedtls_mpi_uint) f << 40 ) | \ |
| 71 | ( (mbedtls_mpi_uint) g << 48 ) | \ |
| 72 | ( (mbedtls_mpi_uint) h << 56 ) |
| 73 | |
| 74 | #define BYTES_TO_T_UINT_4( a, b, c, d ) \ |
| 75 | BYTES_TO_T_UINT_8( a, b, c, d, 0, 0, 0, 0 ) |
| 76 | |
| 77 | #define BYTES_TO_T_UINT_2( a, b ) \ |
| 78 | BYTES_TO_T_UINT_8( a, b, 0, 0, 0, 0, 0, 0 ) |
| 79 | |
| 80 | #endif /* bits in mbedtls_mpi_uint */ |
| 81 | |
| 82 | /* |
| 83 | * Note: the constants are in little-endian order |
| 84 | * to be directly usable in MPIs |
| 85 | */ |
| 86 | |
| 87 | /* |
| 88 | * Domain parameters for secp192r1 |
| 89 | */ |
| 90 | #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) |
| 91 | static const mbedtls_mpi_uint secp192r1_p[] = { |
| 92 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
| 93 | BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
| 94 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
| 95 | }; |
| 96 | static const mbedtls_mpi_uint secp192r1_b[] = { |
| 97 | BYTES_TO_T_UINT_8( 0xB1, 0xB9, 0x46, 0xC1, 0xEC, 0xDE, 0xB8, 0xFE ), |
| 98 | BYTES_TO_T_UINT_8( 0x49, 0x30, 0x24, 0x72, 0xAB, 0xE9, 0xA7, 0x0F ), |
| 99 | BYTES_TO_T_UINT_8( 0xE7, 0x80, 0x9C, 0xE5, 0x19, 0x05, 0x21, 0x64 ), |
| 100 | }; |
| 101 | static const mbedtls_mpi_uint secp192r1_gx[] = { |
| 102 | BYTES_TO_T_UINT_8( 0x12, 0x10, 0xFF, 0x82, 0xFD, 0x0A, 0xFF, 0xF4 ), |
| 103 | BYTES_TO_T_UINT_8( 0x00, 0x88, 0xA1, 0x43, 0xEB, 0x20, 0xBF, 0x7C ), |
| 104 | BYTES_TO_T_UINT_8( 0xF6, 0x90, 0x30, 0xB0, 0x0E, 0xA8, 0x8D, 0x18 ), |
| 105 | }; |
| 106 | static const mbedtls_mpi_uint secp192r1_gy[] = { |
| 107 | BYTES_TO_T_UINT_8( 0x11, 0x48, 0x79, 0x1E, 0xA1, 0x77, 0xF9, 0x73 ), |
| 108 | BYTES_TO_T_UINT_8( 0xD5, 0xCD, 0x24, 0x6B, 0xED, 0x11, 0x10, 0x63 ), |
| 109 | BYTES_TO_T_UINT_8( 0x78, 0xDA, 0xC8, 0xFF, 0x95, 0x2B, 0x19, 0x07 ), |
| 110 | }; |
| 111 | static const mbedtls_mpi_uint secp192r1_n[] = { |
| 112 | BYTES_TO_T_UINT_8( 0x31, 0x28, 0xD2, 0xB4, 0xB1, 0xC9, 0x6B, 0x14 ), |
| 113 | BYTES_TO_T_UINT_8( 0x36, 0xF8, 0xDE, 0x99, 0xFF, 0xFF, 0xFF, 0xFF ), |
| 114 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
| 115 | }; |
| 116 | #endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */ |
| 117 | |
| 118 | /* |
| 119 | * Domain parameters for secp224r1 |
| 120 | */ |
| 121 | #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) |
| 122 | static const mbedtls_mpi_uint secp224r1_p[] = { |
| 123 | BYTES_TO_T_UINT_8( 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ), |
| 124 | BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ), |
| 125 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
| 126 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ), |
| 127 | }; |
| 128 | static const mbedtls_mpi_uint secp224r1_b[] = { |
| 129 | BYTES_TO_T_UINT_8( 0xB4, 0xFF, 0x55, 0x23, 0x43, 0x39, 0x0B, 0x27 ), |
| 130 | BYTES_TO_T_UINT_8( 0xBA, 0xD8, 0xBF, 0xD7, 0xB7, 0xB0, 0x44, 0x50 ), |
| 131 | BYTES_TO_T_UINT_8( 0x56, 0x32, 0x41, 0xF5, 0xAB, 0xB3, 0x04, 0x0C ), |
| 132 | BYTES_TO_T_UINT_4( 0x85, 0x0A, 0x05, 0xB4 ), |
| 133 | }; |
| 134 | static const mbedtls_mpi_uint secp224r1_gx[] = { |
| 135 | BYTES_TO_T_UINT_8( 0x21, 0x1D, 0x5C, 0x11, 0xD6, 0x80, 0x32, 0x34 ), |
| 136 | BYTES_TO_T_UINT_8( 0x22, 0x11, 0xC2, 0x56, 0xD3, 0xC1, 0x03, 0x4A ), |
| 137 | BYTES_TO_T_UINT_8( 0xB9, 0x90, 0x13, 0x32, 0x7F, 0xBF, 0xB4, 0x6B ), |
| 138 | BYTES_TO_T_UINT_4( 0xBD, 0x0C, 0x0E, 0xB7 ), |
| 139 | }; |
| 140 | static const mbedtls_mpi_uint secp224r1_gy[] = { |
| 141 | BYTES_TO_T_UINT_8( 0x34, 0x7E, 0x00, 0x85, 0x99, 0x81, 0xD5, 0x44 ), |
| 142 | BYTES_TO_T_UINT_8( 0x64, 0x47, 0x07, 0x5A, 0xA0, 0x75, 0x43, 0xCD ), |
| 143 | BYTES_TO_T_UINT_8( 0xE6, 0xDF, 0x22, 0x4C, 0xFB, 0x23, 0xF7, 0xB5 ), |
| 144 | BYTES_TO_T_UINT_4( 0x88, 0x63, 0x37, 0xBD ), |
| 145 | }; |
| 146 | static const mbedtls_mpi_uint secp224r1_n[] = { |
| 147 | BYTES_TO_T_UINT_8( 0x3D, 0x2A, 0x5C, 0x5C, 0x45, 0x29, 0xDD, 0x13 ), |
| 148 | BYTES_TO_T_UINT_8( 0x3E, 0xF0, 0xB8, 0xE0, 0xA2, 0x16, 0xFF, 0xFF ), |
| 149 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
| 150 | BYTES_TO_T_UINT_4( 0xFF, 0xFF, 0xFF, 0xFF ), |
| 151 | }; |
| 152 | #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */ |
| 153 | |
| 154 | /* |
| 155 | * Domain parameters for secp256r1 |
| 156 | */ |
| 157 | #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) |
| 158 | static const mbedtls_mpi_uint secp256r1_p[] = { |
| 159 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
| 160 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ), |
| 161 | BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ), |
| 162 | BYTES_TO_T_UINT_8( 0x01, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ), |
| 163 | }; |
| 164 | static const mbedtls_mpi_uint secp256r1_b[] = { |
| 165 | BYTES_TO_T_UINT_8( 0x4B, 0x60, 0xD2, 0x27, 0x3E, 0x3C, 0xCE, 0x3B ), |
| 166 | BYTES_TO_T_UINT_8( 0xF6, 0xB0, 0x53, 0xCC, 0xB0, 0x06, 0x1D, 0x65 ), |
| 167 | BYTES_TO_T_UINT_8( 0xBC, 0x86, 0x98, 0x76, 0x55, 0xBD, 0xEB, 0xB3 ), |
| 168 | BYTES_TO_T_UINT_8( 0xE7, 0x93, 0x3A, 0xAA, 0xD8, 0x35, 0xC6, 0x5A ), |
| 169 | }; |
| 170 | static const mbedtls_mpi_uint secp256r1_gx[] = { |
| 171 | BYTES_TO_T_UINT_8( 0x96, 0xC2, 0x98, 0xD8, 0x45, 0x39, 0xA1, 0xF4 ), |
| 172 | BYTES_TO_T_UINT_8( 0xA0, 0x33, 0xEB, 0x2D, 0x81, 0x7D, 0x03, 0x77 ), |
| 173 | BYTES_TO_T_UINT_8( 0xF2, 0x40, 0xA4, 0x63, 0xE5, 0xE6, 0xBC, 0xF8 ), |
| 174 | BYTES_TO_T_UINT_8( 0x47, 0x42, 0x2C, 0xE1, 0xF2, 0xD1, 0x17, 0x6B ), |
| 175 | }; |
| 176 | static const mbedtls_mpi_uint secp256r1_gy[] = { |
| 177 | BYTES_TO_T_UINT_8( 0xF5, 0x51, 0xBF, 0x37, 0x68, 0x40, 0xB6, 0xCB ), |
| 178 | BYTES_TO_T_UINT_8( 0xCE, 0x5E, 0x31, 0x6B, 0x57, 0x33, 0xCE, 0x2B ), |
| 179 | BYTES_TO_T_UINT_8( 0x16, 0x9E, 0x0F, 0x7C, 0x4A, 0xEB, 0xE7, 0x8E ), |
| 180 | BYTES_TO_T_UINT_8( 0x9B, 0x7F, 0x1A, 0xFE, 0xE2, 0x42, 0xE3, 0x4F ), |
| 181 | }; |
| 182 | static const mbedtls_mpi_uint secp256r1_n[] = { |
| 183 | BYTES_TO_T_UINT_8( 0x51, 0x25, 0x63, 0xFC, 0xC2, 0xCA, 0xB9, 0xF3 ), |
| 184 | BYTES_TO_T_UINT_8( 0x84, 0x9E, 0x17, 0xA7, 0xAD, 0xFA, 0xE6, 0xBC ), |
| 185 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
| 186 | BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ), |
| 187 | }; |
| 188 | #endif /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */ |
| 189 | |
| 190 | /* |
| 191 | * Domain parameters for secp384r1 |
| 192 | */ |
| 193 | #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) |
| 194 | static const mbedtls_mpi_uint secp384r1_p[] = { |
| 195 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ), |
| 196 | BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ), |
| 197 | BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
| 198 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
| 199 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
| 200 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
| 201 | }; |
| 202 | static const mbedtls_mpi_uint secp384r1_b[] = { |
| 203 | BYTES_TO_T_UINT_8( 0xEF, 0x2A, 0xEC, 0xD3, 0xED, 0xC8, 0x85, 0x2A ), |
| 204 | BYTES_TO_T_UINT_8( 0x9D, 0xD1, 0x2E, 0x8A, 0x8D, 0x39, 0x56, 0xC6 ), |
| 205 | BYTES_TO_T_UINT_8( 0x5A, 0x87, 0x13, 0x50, 0x8F, 0x08, 0x14, 0x03 ), |
| 206 | BYTES_TO_T_UINT_8( 0x12, 0x41, 0x81, 0xFE, 0x6E, 0x9C, 0x1D, 0x18 ), |
| 207 | BYTES_TO_T_UINT_8( 0x19, 0x2D, 0xF8, 0xE3, 0x6B, 0x05, 0x8E, 0x98 ), |
| 208 | BYTES_TO_T_UINT_8( 0xE4, 0xE7, 0x3E, 0xE2, 0xA7, 0x2F, 0x31, 0xB3 ), |
| 209 | }; |
| 210 | static const mbedtls_mpi_uint secp384r1_gx[] = { |
| 211 | BYTES_TO_T_UINT_8( 0xB7, 0x0A, 0x76, 0x72, 0x38, 0x5E, 0x54, 0x3A ), |
| 212 | BYTES_TO_T_UINT_8( 0x6C, 0x29, 0x55, 0xBF, 0x5D, 0xF2, 0x02, 0x55 ), |
| 213 | BYTES_TO_T_UINT_8( 0x38, 0x2A, 0x54, 0x82, 0xE0, 0x41, 0xF7, 0x59 ), |
| 214 | BYTES_TO_T_UINT_8( 0x98, 0x9B, 0xA7, 0x8B, 0x62, 0x3B, 0x1D, 0x6E ), |
| 215 | BYTES_TO_T_UINT_8( 0x74, 0xAD, 0x20, 0xF3, 0x1E, 0xC7, 0xB1, 0x8E ), |
| 216 | BYTES_TO_T_UINT_8( 0x37, 0x05, 0x8B, 0xBE, 0x22, 0xCA, 0x87, 0xAA ), |
| 217 | }; |
| 218 | static const mbedtls_mpi_uint secp384r1_gy[] = { |
| 219 | BYTES_TO_T_UINT_8( 0x5F, 0x0E, 0xEA, 0x90, 0x7C, 0x1D, 0x43, 0x7A ), |
| 220 | BYTES_TO_T_UINT_8( 0x9D, 0x81, 0x7E, 0x1D, 0xCE, 0xB1, 0x60, 0x0A ), |
| 221 | BYTES_TO_T_UINT_8( 0xC0, 0xB8, 0xF0, 0xB5, 0x13, 0x31, 0xDA, 0xE9 ), |
| 222 | BYTES_TO_T_UINT_8( 0x7C, 0x14, 0x9A, 0x28, 0xBD, 0x1D, 0xF4, 0xF8 ), |
| 223 | BYTES_TO_T_UINT_8( 0x29, 0xDC, 0x92, 0x92, 0xBF, 0x98, 0x9E, 0x5D ), |
| 224 | BYTES_TO_T_UINT_8( 0x6F, 0x2C, 0x26, 0x96, 0x4A, 0xDE, 0x17, 0x36 ), |
| 225 | }; |
| 226 | static const mbedtls_mpi_uint secp384r1_n[] = { |
| 227 | BYTES_TO_T_UINT_8( 0x73, 0x29, 0xC5, 0xCC, 0x6A, 0x19, 0xEC, 0xEC ), |
| 228 | BYTES_TO_T_UINT_8( 0x7A, 0xA7, 0xB0, 0x48, 0xB2, 0x0D, 0x1A, 0x58 ), |
| 229 | BYTES_TO_T_UINT_8( 0xDF, 0x2D, 0x37, 0xF4, 0x81, 0x4D, 0x63, 0xC7 ), |
| 230 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
| 231 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
| 232 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
| 233 | }; |
| 234 | #endif /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */ |
| 235 | |
| 236 | /* |
| 237 | * Domain parameters for secp521r1 |
| 238 | */ |
| 239 | #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) |
| 240 | static const mbedtls_mpi_uint secp521r1_p[] = { |
| 241 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
| 242 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
| 243 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
| 244 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
| 245 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
| 246 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
| 247 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
| 248 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
| 249 | BYTES_TO_T_UINT_2( 0xFF, 0x01 ), |
| 250 | }; |
| 251 | static const mbedtls_mpi_uint secp521r1_b[] = { |
| 252 | BYTES_TO_T_UINT_8( 0x00, 0x3F, 0x50, 0x6B, 0xD4, 0x1F, 0x45, 0xEF ), |
| 253 | BYTES_TO_T_UINT_8( 0xF1, 0x34, 0x2C, 0x3D, 0x88, 0xDF, 0x73, 0x35 ), |
| 254 | BYTES_TO_T_UINT_8( 0x07, 0xBF, 0xB1, 0x3B, 0xBD, 0xC0, 0x52, 0x16 ), |
| 255 | BYTES_TO_T_UINT_8( 0x7B, 0x93, 0x7E, 0xEC, 0x51, 0x39, 0x19, 0x56 ), |
| 256 | BYTES_TO_T_UINT_8( 0xE1, 0x09, 0xF1, 0x8E, 0x91, 0x89, 0xB4, 0xB8 ), |
| 257 | BYTES_TO_T_UINT_8( 0xF3, 0x15, 0xB3, 0x99, 0x5B, 0x72, 0xDA, 0xA2 ), |
| 258 | BYTES_TO_T_UINT_8( 0xEE, 0x40, 0x85, 0xB6, 0xA0, 0x21, 0x9A, 0x92 ), |
| 259 | BYTES_TO_T_UINT_8( 0x1F, 0x9A, 0x1C, 0x8E, 0x61, 0xB9, 0x3E, 0x95 ), |
| 260 | BYTES_TO_T_UINT_2( 0x51, 0x00 ), |
| 261 | }; |
| 262 | static const mbedtls_mpi_uint secp521r1_gx[] = { |
| 263 | BYTES_TO_T_UINT_8( 0x66, 0xBD, 0xE5, 0xC2, 0x31, 0x7E, 0x7E, 0xF9 ), |
| 264 | BYTES_TO_T_UINT_8( 0x9B, 0x42, 0x6A, 0x85, 0xC1, 0xB3, 0x48, 0x33 ), |
| 265 | BYTES_TO_T_UINT_8( 0xDE, 0xA8, 0xFF, 0xA2, 0x27, 0xC1, 0x1D, 0xFE ), |
| 266 | BYTES_TO_T_UINT_8( 0x28, 0x59, 0xE7, 0xEF, 0x77, 0x5E, 0x4B, 0xA1 ), |
| 267 | BYTES_TO_T_UINT_8( 0xBA, 0x3D, 0x4D, 0x6B, 0x60, 0xAF, 0x28, 0xF8 ), |
| 268 | BYTES_TO_T_UINT_8( 0x21, 0xB5, 0x3F, 0x05, 0x39, 0x81, 0x64, 0x9C ), |
| 269 | BYTES_TO_T_UINT_8( 0x42, 0xB4, 0x95, 0x23, 0x66, 0xCB, 0x3E, 0x9E ), |
| 270 | BYTES_TO_T_UINT_8( 0xCD, 0xE9, 0x04, 0x04, 0xB7, 0x06, 0x8E, 0x85 ), |
| 271 | BYTES_TO_T_UINT_2( 0xC6, 0x00 ), |
| 272 | }; |
| 273 | static const mbedtls_mpi_uint secp521r1_gy[] = { |
| 274 | BYTES_TO_T_UINT_8( 0x50, 0x66, 0xD1, 0x9F, 0x76, 0x94, 0xBE, 0x88 ), |
| 275 | BYTES_TO_T_UINT_8( 0x40, 0xC2, 0x72, 0xA2, 0x86, 0x70, 0x3C, 0x35 ), |
| 276 | BYTES_TO_T_UINT_8( 0x61, 0x07, 0xAD, 0x3F, 0x01, 0xB9, 0x50, 0xC5 ), |
| 277 | BYTES_TO_T_UINT_8( 0x40, 0x26, 0xF4, 0x5E, 0x99, 0x72, 0xEE, 0x97 ), |
| 278 | BYTES_TO_T_UINT_8( 0x2C, 0x66, 0x3E, 0x27, 0x17, 0xBD, 0xAF, 0x17 ), |
| 279 | BYTES_TO_T_UINT_8( 0x68, 0x44, 0x9B, 0x57, 0x49, 0x44, 0xF5, 0x98 ), |
| 280 | BYTES_TO_T_UINT_8( 0xD9, 0x1B, 0x7D, 0x2C, 0xB4, 0x5F, 0x8A, 0x5C ), |
| 281 | BYTES_TO_T_UINT_8( 0x04, 0xC0, 0x3B, 0x9A, 0x78, 0x6A, 0x29, 0x39 ), |
| 282 | BYTES_TO_T_UINT_2( 0x18, 0x01 ), |
| 283 | }; |
| 284 | static const mbedtls_mpi_uint secp521r1_n[] = { |
| 285 | BYTES_TO_T_UINT_8( 0x09, 0x64, 0x38, 0x91, 0x1E, 0xB7, 0x6F, 0xBB ), |
| 286 | BYTES_TO_T_UINT_8( 0xAE, 0x47, 0x9C, 0x89, 0xB8, 0xC9, 0xB5, 0x3B ), |
| 287 | BYTES_TO_T_UINT_8( 0xD0, 0xA5, 0x09, 0xF7, 0x48, 0x01, 0xCC, 0x7F ), |
| 288 | BYTES_TO_T_UINT_8( 0x6B, 0x96, 0x2F, 0xBF, 0x83, 0x87, 0x86, 0x51 ), |
| 289 | BYTES_TO_T_UINT_8( 0xFA, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
| 290 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
| 291 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
| 292 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
| 293 | BYTES_TO_T_UINT_2( 0xFF, 0x01 ), |
| 294 | }; |
| 295 | #endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */ |
| 296 | |
| 297 | #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) |
| 298 | static const mbedtls_mpi_uint secp192k1_p[] = { |
| 299 | BYTES_TO_T_UINT_8( 0x37, 0xEE, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ), |
| 300 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
| 301 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
| 302 | }; |
| 303 | static const mbedtls_mpi_uint secp192k1_a[] = { |
| 304 | BYTES_TO_T_UINT_2( 0x00, 0x00 ), |
| 305 | }; |
| 306 | static const mbedtls_mpi_uint secp192k1_b[] = { |
| 307 | BYTES_TO_T_UINT_2( 0x03, 0x00 ), |
| 308 | }; |
| 309 | static const mbedtls_mpi_uint secp192k1_gx[] = { |
| 310 | BYTES_TO_T_UINT_8( 0x7D, 0x6C, 0xE0, 0xEA, 0xB1, 0xD1, 0xA5, 0x1D ), |
| 311 | BYTES_TO_T_UINT_8( 0x34, 0xF4, 0xB7, 0x80, 0x02, 0x7D, 0xB0, 0x26 ), |
| 312 | BYTES_TO_T_UINT_8( 0xAE, 0xE9, 0x57, 0xC0, 0x0E, 0xF1, 0x4F, 0xDB ), |
| 313 | }; |
| 314 | static const mbedtls_mpi_uint secp192k1_gy[] = { |
| 315 | BYTES_TO_T_UINT_8( 0x9D, 0x2F, 0x5E, 0xD9, 0x88, 0xAA, 0x82, 0x40 ), |
| 316 | BYTES_TO_T_UINT_8( 0x34, 0x86, 0xBE, 0x15, 0xD0, 0x63, 0x41, 0x84 ), |
| 317 | BYTES_TO_T_UINT_8( 0xA7, 0x28, 0x56, 0x9C, 0x6D, 0x2F, 0x2F, 0x9B ), |
| 318 | }; |
| 319 | static const mbedtls_mpi_uint secp192k1_n[] = { |
| 320 | BYTES_TO_T_UINT_8( 0x8D, 0xFD, 0xDE, 0x74, 0x6A, 0x46, 0x69, 0x0F ), |
| 321 | BYTES_TO_T_UINT_8( 0x17, 0xFC, 0xF2, 0x26, 0xFE, 0xFF, 0xFF, 0xFF ), |
| 322 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
| 323 | }; |
| 324 | #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */ |
| 325 | |
| 326 | #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) |
| 327 | static const mbedtls_mpi_uint secp224k1_p[] = { |
| 328 | BYTES_TO_T_UINT_8( 0x6D, 0xE5, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ), |
| 329 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
| 330 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
| 331 | BYTES_TO_T_UINT_4( 0xFF, 0xFF, 0xFF, 0xFF ), |
| 332 | }; |
| 333 | static const mbedtls_mpi_uint secp224k1_a[] = { |
| 334 | BYTES_TO_T_UINT_2( 0x00, 0x00 ), |
| 335 | }; |
| 336 | static const mbedtls_mpi_uint secp224k1_b[] = { |
| 337 | BYTES_TO_T_UINT_2( 0x05, 0x00 ), |
| 338 | }; |
| 339 | static const mbedtls_mpi_uint secp224k1_gx[] = { |
| 340 | BYTES_TO_T_UINT_8( 0x5C, 0xA4, 0xB7, 0xB6, 0x0E, 0x65, 0x7E, 0x0F ), |
| 341 | BYTES_TO_T_UINT_8( 0xA9, 0x75, 0x70, 0xE4, 0xE9, 0x67, 0xA4, 0x69 ), |
| 342 | BYTES_TO_T_UINT_8( 0xA1, 0x28, 0xFC, 0x30, 0xDF, 0x99, 0xF0, 0x4D ), |
| 343 | BYTES_TO_T_UINT_4( 0x33, 0x5B, 0x45, 0xA1 ), |
| 344 | }; |
| 345 | static const mbedtls_mpi_uint secp224k1_gy[] = { |
| 346 | BYTES_TO_T_UINT_8( 0xA5, 0x61, 0x6D, 0x55, 0xDB, 0x4B, 0xCA, 0xE2 ), |
| 347 | BYTES_TO_T_UINT_8( 0x59, 0xBD, 0xB0, 0xC0, 0xF7, 0x19, 0xE3, 0xF7 ), |
| 348 | BYTES_TO_T_UINT_8( 0xD6, 0xFB, 0xCA, 0x82, 0x42, 0x34, 0xBA, 0x7F ), |
| 349 | BYTES_TO_T_UINT_4( 0xED, 0x9F, 0x08, 0x7E ), |
| 350 | }; |
| 351 | static const mbedtls_mpi_uint secp224k1_n[] = { |
| 352 | BYTES_TO_T_UINT_8( 0xF7, 0xB1, 0x9F, 0x76, 0x71, 0xA9, 0xF0, 0xCA ), |
| 353 | BYTES_TO_T_UINT_8( 0x84, 0x61, 0xEC, 0xD2, 0xE8, 0xDC, 0x01, 0x00 ), |
| 354 | BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ), |
| 355 | BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ), |
| 356 | }; |
| 357 | #endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */ |
| 358 | |
| 359 | #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) |
| 360 | static const mbedtls_mpi_uint secp256k1_p[] = { |
| 361 | BYTES_TO_T_UINT_8( 0x2F, 0xFC, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ), |
| 362 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
| 363 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
| 364 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
| 365 | }; |
| 366 | static const mbedtls_mpi_uint secp256k1_a[] = { |
| 367 | BYTES_TO_T_UINT_2( 0x00, 0x00 ), |
| 368 | }; |
| 369 | static const mbedtls_mpi_uint secp256k1_b[] = { |
| 370 | BYTES_TO_T_UINT_2( 0x07, 0x00 ), |
| 371 | }; |
| 372 | static const mbedtls_mpi_uint secp256k1_gx[] = { |
| 373 | BYTES_TO_T_UINT_8( 0x98, 0x17, 0xF8, 0x16, 0x5B, 0x81, 0xF2, 0x59 ), |
| 374 | BYTES_TO_T_UINT_8( 0xD9, 0x28, 0xCE, 0x2D, 0xDB, 0xFC, 0x9B, 0x02 ), |
| 375 | BYTES_TO_T_UINT_8( 0x07, 0x0B, 0x87, 0xCE, 0x95, 0x62, 0xA0, 0x55 ), |
| 376 | BYTES_TO_T_UINT_8( 0xAC, 0xBB, 0xDC, 0xF9, 0x7E, 0x66, 0xBE, 0x79 ), |
| 377 | }; |
| 378 | static const mbedtls_mpi_uint secp256k1_gy[] = { |
| 379 | BYTES_TO_T_UINT_8( 0xB8, 0xD4, 0x10, 0xFB, 0x8F, 0xD0, 0x47, 0x9C ), |
| 380 | BYTES_TO_T_UINT_8( 0x19, 0x54, 0x85, 0xA6, 0x48, 0xB4, 0x17, 0xFD ), |
| 381 | BYTES_TO_T_UINT_8( 0xA8, 0x08, 0x11, 0x0E, 0xFC, 0xFB, 0xA4, 0x5D ), |
| 382 | BYTES_TO_T_UINT_8( 0x65, 0xC4, 0xA3, 0x26, 0x77, 0xDA, 0x3A, 0x48 ), |
| 383 | }; |
| 384 | static const mbedtls_mpi_uint secp256k1_n[] = { |
| 385 | BYTES_TO_T_UINT_8( 0x41, 0x41, 0x36, 0xD0, 0x8C, 0x5E, 0xD2, 0xBF ), |
| 386 | BYTES_TO_T_UINT_8( 0x3B, 0xA0, 0x48, 0xAF, 0xE6, 0xDC, 0xAE, 0xBA ), |
| 387 | BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
| 388 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
| 389 | }; |
| 390 | #endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */ |
| 391 | |
| 392 | /* |
| 393 | * Domain parameters for brainpoolP256r1 (RFC 5639 3.4) |
| 394 | */ |
| 395 | #if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) |
| 396 | static const mbedtls_mpi_uint brainpoolP256r1_p[] = { |
| 397 | BYTES_TO_T_UINT_8( 0x77, 0x53, 0x6E, 0x1F, 0x1D, 0x48, 0x13, 0x20 ), |
| 398 | BYTES_TO_T_UINT_8( 0x28, 0x20, 0x26, 0xD5, 0x23, 0xF6, 0x3B, 0x6E ), |
| 399 | BYTES_TO_T_UINT_8( 0x72, 0x8D, 0x83, 0x9D, 0x90, 0x0A, 0x66, 0x3E ), |
| 400 | BYTES_TO_T_UINT_8( 0xBC, 0xA9, 0xEE, 0xA1, 0xDB, 0x57, 0xFB, 0xA9 ), |
| 401 | }; |
| 402 | static const mbedtls_mpi_uint brainpoolP256r1_a[] = { |
| 403 | BYTES_TO_T_UINT_8( 0xD9, 0xB5, 0x30, 0xF3, 0x44, 0x4B, 0x4A, 0xE9 ), |
| 404 | BYTES_TO_T_UINT_8( 0x6C, 0x5C, 0xDC, 0x26, 0xC1, 0x55, 0x80, 0xFB ), |
| 405 | BYTES_TO_T_UINT_8( 0xE7, 0xFF, 0x7A, 0x41, 0x30, 0x75, 0xF6, 0xEE ), |
| 406 | BYTES_TO_T_UINT_8( 0x57, 0x30, 0x2C, 0xFC, 0x75, 0x09, 0x5A, 0x7D ), |
| 407 | }; |
| 408 | static const mbedtls_mpi_uint brainpoolP256r1_b[] = { |
| 409 | BYTES_TO_T_UINT_8( 0xB6, 0x07, 0x8C, 0xFF, 0x18, 0xDC, 0xCC, 0x6B ), |
| 410 | BYTES_TO_T_UINT_8( 0xCE, 0xE1, 0xF7, 0x5C, 0x29, 0x16, 0x84, 0x95 ), |
| 411 | BYTES_TO_T_UINT_8( 0xBF, 0x7C, 0xD7, 0xBB, 0xD9, 0xB5, 0x30, 0xF3 ), |
| 412 | BYTES_TO_T_UINT_8( 0x44, 0x4B, 0x4A, 0xE9, 0x6C, 0x5C, 0xDC, 0x26 ), |
| 413 | }; |
| 414 | static const mbedtls_mpi_uint brainpoolP256r1_gx[] = { |
| 415 | BYTES_TO_T_UINT_8( 0x62, 0x32, 0xCE, 0x9A, 0xBD, 0x53, 0x44, 0x3A ), |
| 416 | BYTES_TO_T_UINT_8( 0xC2, 0x23, 0xBD, 0xE3, 0xE1, 0x27, 0xDE, 0xB9 ), |
| 417 | BYTES_TO_T_UINT_8( 0xAF, 0xB7, 0x81, 0xFC, 0x2F, 0x48, 0x4B, 0x2C ), |
| 418 | BYTES_TO_T_UINT_8( 0xCB, 0x57, 0x7E, 0xCB, 0xB9, 0xAE, 0xD2, 0x8B ), |
| 419 | }; |
| 420 | static const mbedtls_mpi_uint brainpoolP256r1_gy[] = { |
| 421 | BYTES_TO_T_UINT_8( 0x97, 0x69, 0x04, 0x2F, 0xC7, 0x54, 0x1D, 0x5C ), |
| 422 | BYTES_TO_T_UINT_8( 0x54, 0x8E, 0xED, 0x2D, 0x13, 0x45, 0x77, 0xC2 ), |
| 423 | BYTES_TO_T_UINT_8( 0xC9, 0x1D, 0x61, 0x14, 0x1A, 0x46, 0xF8, 0x97 ), |
| 424 | BYTES_TO_T_UINT_8( 0xFD, 0xC4, 0xDA, 0xC3, 0x35, 0xF8, 0x7E, 0x54 ), |
| 425 | }; |
| 426 | static const mbedtls_mpi_uint brainpoolP256r1_n[] = { |
| 427 | BYTES_TO_T_UINT_8( 0xA7, 0x56, 0x48, 0x97, 0x82, 0x0E, 0x1E, 0x90 ), |
| 428 | BYTES_TO_T_UINT_8( 0xF7, 0xA6, 0x61, 0xB5, 0xA3, 0x7A, 0x39, 0x8C ), |
| 429 | BYTES_TO_T_UINT_8( 0x71, 0x8D, 0x83, 0x9D, 0x90, 0x0A, 0x66, 0x3E ), |
| 430 | BYTES_TO_T_UINT_8( 0xBC, 0xA9, 0xEE, 0xA1, 0xDB, 0x57, 0xFB, 0xA9 ), |
| 431 | }; |
| 432 | #endif /* MBEDTLS_ECP_DP_BP256R1_ENABLED */ |
| 433 | |
| 434 | /* |
| 435 | * Domain parameters for brainpoolP384r1 (RFC 5639 3.6) |
| 436 | */ |
| 437 | #if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) |
| 438 | static const mbedtls_mpi_uint brainpoolP384r1_p[] = { |
| 439 | BYTES_TO_T_UINT_8( 0x53, 0xEC, 0x07, 0x31, 0x13, 0x00, 0x47, 0x87 ), |
| 440 | BYTES_TO_T_UINT_8( 0x71, 0x1A, 0x1D, 0x90, 0x29, 0xA7, 0xD3, 0xAC ), |
| 441 | BYTES_TO_T_UINT_8( 0x23, 0x11, 0xB7, 0x7F, 0x19, 0xDA, 0xB1, 0x12 ), |
| 442 | BYTES_TO_T_UINT_8( 0xB4, 0x56, 0x54, 0xED, 0x09, 0x71, 0x2F, 0x15 ), |
| 443 | BYTES_TO_T_UINT_8( 0xDF, 0x41, 0xE6, 0x50, 0x7E, 0x6F, 0x5D, 0x0F ), |
| 444 | BYTES_TO_T_UINT_8( 0x28, 0x6D, 0x38, 0xA3, 0x82, 0x1E, 0xB9, 0x8C ), |
| 445 | }; |
| 446 | static const mbedtls_mpi_uint brainpoolP384r1_a[] = { |
| 447 | BYTES_TO_T_UINT_8( 0x26, 0x28, 0xCE, 0x22, 0xDD, 0xC7, 0xA8, 0x04 ), |
| 448 | BYTES_TO_T_UINT_8( 0xEB, 0xD4, 0x3A, 0x50, 0x4A, 0x81, 0xA5, 0x8A ), |
| 449 | BYTES_TO_T_UINT_8( 0x0F, 0xF9, 0x91, 0xBA, 0xEF, 0x65, 0x91, 0x13 ), |
| 450 | BYTES_TO_T_UINT_8( 0x87, 0x27, 0xB2, 0x4F, 0x8E, 0xA2, 0xBE, 0xC2 ), |
| 451 | BYTES_TO_T_UINT_8( 0xA0, 0xAF, 0x05, 0xCE, 0x0A, 0x08, 0x72, 0x3C ), |
| 452 | BYTES_TO_T_UINT_8( 0x0C, 0x15, 0x8C, 0x3D, 0xC6, 0x82, 0xC3, 0x7B ), |
| 453 | }; |
| 454 | static const mbedtls_mpi_uint brainpoolP384r1_b[] = { |
| 455 | BYTES_TO_T_UINT_8( 0x11, 0x4C, 0x50, 0xFA, 0x96, 0x86, 0xB7, 0x3A ), |
| 456 | BYTES_TO_T_UINT_8( 0x94, 0xC9, 0xDB, 0x95, 0x02, 0x39, 0xB4, 0x7C ), |
| 457 | BYTES_TO_T_UINT_8( 0xD5, 0x62, 0xEB, 0x3E, 0xA5, 0x0E, 0x88, 0x2E ), |
| 458 | BYTES_TO_T_UINT_8( 0xA6, 0xD2, 0xDC, 0x07, 0xE1, 0x7D, 0xB7, 0x2F ), |
| 459 | BYTES_TO_T_UINT_8( 0x7C, 0x44, 0xF0, 0x16, 0x54, 0xB5, 0x39, 0x8B ), |
| 460 | BYTES_TO_T_UINT_8( 0x26, 0x28, 0xCE, 0x22, 0xDD, 0xC7, 0xA8, 0x04 ), |
| 461 | }; |
| 462 | static const mbedtls_mpi_uint brainpoolP384r1_gx[] = { |
| 463 | BYTES_TO_T_UINT_8( 0x1E, 0xAF, 0xD4, 0x47, 0xE2, 0xB2, 0x87, 0xEF ), |
| 464 | BYTES_TO_T_UINT_8( 0xAA, 0x46, 0xD6, 0x36, 0x34, 0xE0, 0x26, 0xE8 ), |
| 465 | BYTES_TO_T_UINT_8( 0xE8, 0x10, 0xBD, 0x0C, 0xFE, 0xCA, 0x7F, 0xDB ), |
| 466 | BYTES_TO_T_UINT_8( 0xE3, 0x4F, 0xF1, 0x7E, 0xE7, 0xA3, 0x47, 0x88 ), |
| 467 | BYTES_TO_T_UINT_8( 0x6B, 0x3F, 0xC1, 0xB7, 0x81, 0x3A, 0xA6, 0xA2 ), |
| 468 | BYTES_TO_T_UINT_8( 0xFF, 0x45, 0xCF, 0x68, 0xF0, 0x64, 0x1C, 0x1D ), |
| 469 | }; |
| 470 | static const mbedtls_mpi_uint brainpoolP384r1_gy[] = { |
| 471 | BYTES_TO_T_UINT_8( 0x15, 0x53, 0x3C, 0x26, 0x41, 0x03, 0x82, 0x42 ), |
| 472 | BYTES_TO_T_UINT_8( 0x11, 0x81, 0x91, 0x77, 0x21, 0x46, 0x46, 0x0E ), |
| 473 | BYTES_TO_T_UINT_8( 0x28, 0x29, 0x91, 0xF9, 0x4F, 0x05, 0x9C, 0xE1 ), |
| 474 | BYTES_TO_T_UINT_8( 0x64, 0x58, 0xEC, 0xFE, 0x29, 0x0B, 0xB7, 0x62 ), |
| 475 | BYTES_TO_T_UINT_8( 0x52, 0xD5, 0xCF, 0x95, 0x8E, 0xEB, 0xB1, 0x5C ), |
| 476 | BYTES_TO_T_UINT_8( 0xA4, 0xC2, 0xF9, 0x20, 0x75, 0x1D, 0xBE, 0x8A ), |
| 477 | }; |
| 478 | static const mbedtls_mpi_uint brainpoolP384r1_n[] = { |
| 479 | BYTES_TO_T_UINT_8( 0x65, 0x65, 0x04, 0xE9, 0x02, 0x32, 0x88, 0x3B ), |
| 480 | BYTES_TO_T_UINT_8( 0x10, 0xC3, 0x7F, 0x6B, 0xAF, 0xB6, 0x3A, 0xCF ), |
| 481 | BYTES_TO_T_UINT_8( 0xA7, 0x25, 0x04, 0xAC, 0x6C, 0x6E, 0x16, 0x1F ), |
| 482 | BYTES_TO_T_UINT_8( 0xB3, 0x56, 0x54, 0xED, 0x09, 0x71, 0x2F, 0x15 ), |
| 483 | BYTES_TO_T_UINT_8( 0xDF, 0x41, 0xE6, 0x50, 0x7E, 0x6F, 0x5D, 0x0F ), |
| 484 | BYTES_TO_T_UINT_8( 0x28, 0x6D, 0x38, 0xA3, 0x82, 0x1E, 0xB9, 0x8C ), |
| 485 | }; |
| 486 | #endif /* MBEDTLS_ECP_DP_BP384R1_ENABLED */ |
| 487 | |
| 488 | /* |
| 489 | * Domain parameters for brainpoolP512r1 (RFC 5639 3.7) |
| 490 | */ |
| 491 | #if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) |
| 492 | static const mbedtls_mpi_uint brainpoolP512r1_p[] = { |
| 493 | BYTES_TO_T_UINT_8( 0xF3, 0x48, 0x3A, 0x58, 0x56, 0x60, 0xAA, 0x28 ), |
| 494 | BYTES_TO_T_UINT_8( 0x85, 0xC6, 0x82, 0x2D, 0x2F, 0xFF, 0x81, 0x28 ), |
| 495 | BYTES_TO_T_UINT_8( 0xE6, 0x80, 0xA3, 0xE6, 0x2A, 0xA1, 0xCD, 0xAE ), |
| 496 | BYTES_TO_T_UINT_8( 0x42, 0x68, 0xC6, 0x9B, 0x00, 0x9B, 0x4D, 0x7D ), |
| 497 | BYTES_TO_T_UINT_8( 0x71, 0x08, 0x33, 0x70, 0xCA, 0x9C, 0x63, 0xD6 ), |
| 498 | BYTES_TO_T_UINT_8( 0x0E, 0xD2, 0xC9, 0xB3, 0xB3, 0x8D, 0x30, 0xCB ), |
| 499 | BYTES_TO_T_UINT_8( 0x07, 0xFC, 0xC9, 0x33, 0xAE, 0xE6, 0xD4, 0x3F ), |
| 500 | BYTES_TO_T_UINT_8( 0x8B, 0xC4, 0xE9, 0xDB, 0xB8, 0x9D, 0xDD, 0xAA ), |
| 501 | }; |
| 502 | static const mbedtls_mpi_uint brainpoolP512r1_a[] = { |
| 503 | BYTES_TO_T_UINT_8( 0xCA, 0x94, 0xFC, 0x77, 0x4D, 0xAC, 0xC1, 0xE7 ), |
| 504 | BYTES_TO_T_UINT_8( 0xB9, 0xC7, 0xF2, 0x2B, 0xA7, 0x17, 0x11, 0x7F ), |
| 505 | BYTES_TO_T_UINT_8( 0xB5, 0xC8, 0x9A, 0x8B, 0xC9, 0xF1, 0x2E, 0x0A ), |
| 506 | BYTES_TO_T_UINT_8( 0xA1, 0x3A, 0x25, 0xA8, 0x5A, 0x5D, 0xED, 0x2D ), |
| 507 | BYTES_TO_T_UINT_8( 0xBC, 0x63, 0x98, 0xEA, 0xCA, 0x41, 0x34, 0xA8 ), |
| 508 | BYTES_TO_T_UINT_8( 0x10, 0x16, 0xF9, 0x3D, 0x8D, 0xDD, 0xCB, 0x94 ), |
| 509 | BYTES_TO_T_UINT_8( 0xC5, 0x4C, 0x23, 0xAC, 0x45, 0x71, 0x32, 0xE2 ), |
| 510 | BYTES_TO_T_UINT_8( 0x89, 0x3B, 0x60, 0x8B, 0x31, 0xA3, 0x30, 0x78 ), |
| 511 | }; |
| 512 | static const mbedtls_mpi_uint brainpoolP512r1_b[] = { |
| 513 | BYTES_TO_T_UINT_8( 0x23, 0xF7, 0x16, 0x80, 0x63, 0xBD, 0x09, 0x28 ), |
| 514 | BYTES_TO_T_UINT_8( 0xDD, 0xE5, 0xBA, 0x5E, 0xB7, 0x50, 0x40, 0x98 ), |
| 515 | BYTES_TO_T_UINT_8( 0x67, 0x3E, 0x08, 0xDC, 0xCA, 0x94, 0xFC, 0x77 ), |
| 516 | BYTES_TO_T_UINT_8( 0x4D, 0xAC, 0xC1, 0xE7, 0xB9, 0xC7, 0xF2, 0x2B ), |
| 517 | BYTES_TO_T_UINT_8( 0xA7, 0x17, 0x11, 0x7F, 0xB5, 0xC8, 0x9A, 0x8B ), |
| 518 | BYTES_TO_T_UINT_8( 0xC9, 0xF1, 0x2E, 0x0A, 0xA1, 0x3A, 0x25, 0xA8 ), |
| 519 | BYTES_TO_T_UINT_8( 0x5A, 0x5D, 0xED, 0x2D, 0xBC, 0x63, 0x98, 0xEA ), |
| 520 | BYTES_TO_T_UINT_8( 0xCA, 0x41, 0x34, 0xA8, 0x10, 0x16, 0xF9, 0x3D ), |
| 521 | }; |
| 522 | static const mbedtls_mpi_uint brainpoolP512r1_gx[] = { |
| 523 | BYTES_TO_T_UINT_8( 0x22, 0xF8, 0xB9, 0xBC, 0x09, 0x22, 0x35, 0x8B ), |
| 524 | BYTES_TO_T_UINT_8( 0x68, 0x5E, 0x6A, 0x40, 0x47, 0x50, 0x6D, 0x7C ), |
| 525 | BYTES_TO_T_UINT_8( 0x5F, 0x7D, 0xB9, 0x93, 0x7B, 0x68, 0xD1, 0x50 ), |
| 526 | BYTES_TO_T_UINT_8( 0x8D, 0xD4, 0xD0, 0xE2, 0x78, 0x1F, 0x3B, 0xFF ), |
| 527 | BYTES_TO_T_UINT_8( 0x8E, 0x09, 0xD0, 0xF4, 0xEE, 0x62, 0x3B, 0xB4 ), |
| 528 | BYTES_TO_T_UINT_8( 0xC1, 0x16, 0xD9, 0xB5, 0x70, 0x9F, 0xED, 0x85 ), |
| 529 | BYTES_TO_T_UINT_8( 0x93, 0x6A, 0x4C, 0x9C, 0x2E, 0x32, 0x21, 0x5A ), |
| 530 | BYTES_TO_T_UINT_8( 0x64, 0xD9, 0x2E, 0xD8, 0xBD, 0xE4, 0xAE, 0x81 ), |
| 531 | }; |
| 532 | static const mbedtls_mpi_uint brainpoolP512r1_gy[] = { |
| 533 | BYTES_TO_T_UINT_8( 0x92, 0x08, 0xD8, 0x3A, 0x0F, 0x1E, 0xCD, 0x78 ), |
| 534 | BYTES_TO_T_UINT_8( 0x06, 0x54, 0xF0, 0xA8, 0x2F, 0x2B, 0xCA, 0xD1 ), |
| 535 | BYTES_TO_T_UINT_8( 0xAE, 0x63, 0x27, 0x8A, 0xD8, 0x4B, 0xCA, 0x5B ), |
| 536 | BYTES_TO_T_UINT_8( 0x5E, 0x48, 0x5F, 0x4A, 0x49, 0xDE, 0xDC, 0xB2 ), |
| 537 | BYTES_TO_T_UINT_8( 0x11, 0x81, 0x1F, 0x88, 0x5B, 0xC5, 0x00, 0xA0 ), |
| 538 | BYTES_TO_T_UINT_8( 0x1A, 0x7B, 0xA5, 0x24, 0x00, 0xF7, 0x09, 0xF2 ), |
| 539 | BYTES_TO_T_UINT_8( 0xFD, 0x22, 0x78, 0xCF, 0xA9, 0xBF, 0xEA, 0xC0 ), |
| 540 | BYTES_TO_T_UINT_8( 0xEC, 0x32, 0x63, 0x56, 0x5D, 0x38, 0xDE, 0x7D ), |
| 541 | }; |
| 542 | static const mbedtls_mpi_uint brainpoolP512r1_n[] = { |
| 543 | BYTES_TO_T_UINT_8( 0x69, 0x00, 0xA9, 0x9C, 0x82, 0x96, 0x87, 0xB5 ), |
| 544 | BYTES_TO_T_UINT_8( 0xDD, 0xDA, 0x5D, 0x08, 0x81, 0xD3, 0xB1, 0x1D ), |
| 545 | BYTES_TO_T_UINT_8( 0x47, 0x10, 0xAC, 0x7F, 0x19, 0x61, 0x86, 0x41 ), |
| 546 | BYTES_TO_T_UINT_8( 0x19, 0x26, 0xA9, 0x4C, 0x41, 0x5C, 0x3E, 0x55 ), |
| 547 | BYTES_TO_T_UINT_8( 0x70, 0x08, 0x33, 0x70, 0xCA, 0x9C, 0x63, 0xD6 ), |
| 548 | BYTES_TO_T_UINT_8( 0x0E, 0xD2, 0xC9, 0xB3, 0xB3, 0x8D, 0x30, 0xCB ), |
| 549 | BYTES_TO_T_UINT_8( 0x07, 0xFC, 0xC9, 0x33, 0xAE, 0xE6, 0xD4, 0x3F ), |
| 550 | BYTES_TO_T_UINT_8( 0x8B, 0xC4, 0xE9, 0xDB, 0xB8, 0x9D, 0xDD, 0xAA ), |
| 551 | }; |
| 552 | #endif /* MBEDTLS_ECP_DP_BP512R1_ENABLED */ |
| 553 | |
| 554 | /* |
| 555 | * Create an MPI from embedded constants |
| 556 | * (assumes len is an exact multiple of sizeof mbedtls_mpi_uint) |
| 557 | */ |
| 558 | static inline void ecp_mpi_load( mbedtls_mpi *X, const mbedtls_mpi_uint *p, size_t len ) |
| 559 | { |
| 560 | X->s = 1; |
| 561 | X->n = len / sizeof( mbedtls_mpi_uint ); |
| 562 | X->p = (mbedtls_mpi_uint *) p; |
| 563 | } |
| 564 | |
| 565 | /* |
| 566 | * Set an MPI to static value 1 |
| 567 | */ |
| 568 | static inline void ecp_mpi_set1( mbedtls_mpi *X ) |
| 569 | { |
| 570 | static mbedtls_mpi_uint one[] = { 1 }; |
| 571 | X->s = 1; |
| 572 | X->n = 1; |
| 573 | X->p = one; |
| 574 | } |
| 575 | |
| 576 | /* |
| 577 | * Make group available from embedded constants |
| 578 | */ |
| 579 | static int ecp_group_load( mbedtls_ecp_group *grp, |
| 580 | const mbedtls_mpi_uint *p, size_t plen, |
| 581 | const mbedtls_mpi_uint *a, size_t alen, |
| 582 | const mbedtls_mpi_uint *b, size_t blen, |
| 583 | const mbedtls_mpi_uint *gx, size_t gxlen, |
| 584 | const mbedtls_mpi_uint *gy, size_t gylen, |
| 585 | const mbedtls_mpi_uint *n, size_t nlen) |
| 586 | { |
| 587 | ecp_mpi_load( &grp->P, p, plen ); |
| 588 | if( a != NULL ) |
| 589 | ecp_mpi_load( &grp->A, a, alen ); |
| 590 | ecp_mpi_load( &grp->B, b, blen ); |
| 591 | ecp_mpi_load( &grp->N, n, nlen ); |
| 592 | |
| 593 | ecp_mpi_load( &grp->G.X, gx, gxlen ); |
| 594 | ecp_mpi_load( &grp->G.Y, gy, gylen ); |
| 595 | ecp_mpi_set1( &grp->G.Z ); |
| 596 | |
| 597 | grp->pbits = mbedtls_mpi_bitlen( &grp->P ); |
| 598 | grp->nbits = mbedtls_mpi_bitlen( &grp->N ); |
| 599 | |
| 600 | grp->h = 1; |
| 601 | |
| 602 | return( 0 ); |
| 603 | } |
| 604 | |
| 605 | #if defined(MBEDTLS_ECP_NIST_OPTIM) |
| 606 | /* Forward declarations */ |
| 607 | #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) |
| 608 | static int ecp_mod_p192( mbedtls_mpi * ); |
| 609 | #endif |
| 610 | #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) |
| 611 | static int ecp_mod_p224( mbedtls_mpi * ); |
| 612 | #endif |
| 613 | #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) |
| 614 | static int ecp_mod_p256( mbedtls_mpi * ); |
| 615 | #endif |
| 616 | #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) |
| 617 | static int ecp_mod_p384( mbedtls_mpi * ); |
| 618 | #endif |
| 619 | #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) |
| 620 | static int ecp_mod_p521( mbedtls_mpi * ); |
| 621 | #endif |
| 622 | |
| 623 | #define NIST_MODP( P ) grp->modp = ecp_mod_ ## P; |
| 624 | #else |
| 625 | #define NIST_MODP( P ) |
| 626 | #endif /* MBEDTLS_ECP_NIST_OPTIM */ |
| 627 | |
| 628 | /* Additional forward declarations */ |
| 629 | #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) |
| 630 | static int ecp_mod_p255( mbedtls_mpi * ); |
| 631 | #endif |
| 632 | #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) |
| 633 | static int ecp_mod_p448( mbedtls_mpi * ); |
| 634 | #endif |
| 635 | #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) |
| 636 | static int ecp_mod_p192k1( mbedtls_mpi * ); |
| 637 | #endif |
| 638 | #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) |
| 639 | static int ecp_mod_p224k1( mbedtls_mpi * ); |
| 640 | #endif |
| 641 | #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) |
| 642 | static int ecp_mod_p256k1( mbedtls_mpi * ); |
| 643 | #endif |
| 644 | |
| 645 | #define LOAD_GROUP_A( G ) ecp_group_load( grp, \ |
| 646 | G ## _p, sizeof( G ## _p ), \ |
| 647 | G ## _a, sizeof( G ## _a ), \ |
| 648 | G ## _b, sizeof( G ## _b ), \ |
| 649 | G ## _gx, sizeof( G ## _gx ), \ |
| 650 | G ## _gy, sizeof( G ## _gy ), \ |
| 651 | G ## _n, sizeof( G ## _n ) ) |
| 652 | |
| 653 | #define LOAD_GROUP( G ) ecp_group_load( grp, \ |
| 654 | G ## _p, sizeof( G ## _p ), \ |
| 655 | NULL, 0, \ |
| 656 | G ## _b, sizeof( G ## _b ), \ |
| 657 | G ## _gx, sizeof( G ## _gx ), \ |
| 658 | G ## _gy, sizeof( G ## _gy ), \ |
| 659 | G ## _n, sizeof( G ## _n ) ) |
| 660 | |
| 661 | #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) |
| 662 | /* |
| 663 | * Specialized function for creating the Curve25519 group |
| 664 | */ |
| 665 | static int ecp_use_curve25519( mbedtls_ecp_group *grp ) |
| 666 | { |
| 667 | int ret; |
| 668 | |
| 669 | /* Actually ( A + 2 ) / 4 */ |
| 670 | MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &grp->A, 16, "01DB42" ) ); |
| 671 | |
| 672 | /* P = 2^255 - 19 */ |
| 673 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->P, 1 ) ); |
| 674 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &grp->P, 255 ) ); |
| 675 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &grp->P, &grp->P, 19 ) ); |
| 676 | grp->pbits = mbedtls_mpi_bitlen( &grp->P ); |
| 677 | |
| 678 | /* N = 2^252 + 27742317777372353535851937790883648493 */ |
| 679 | MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &grp->N, 16, |
| 680 | "14DEF9DEA2F79CD65812631A5CF5D3ED" ) ); |
| 681 | MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &grp->N, 252, 1 ) ); |
| 682 | |
| 683 | /* Y intentionally not set, since we use x/z coordinates. |
| 684 | * This is used as a marker to identify Montgomery curves! */ |
| 685 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.X, 9 ) ); |
| 686 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.Z, 1 ) ); |
| 687 | mbedtls_mpi_free( &grp->G.Y ); |
| 688 | |
| 689 | /* Actually, the required msb for private keys */ |
| 690 | grp->nbits = 254; |
| 691 | |
| 692 | cleanup: |
| 693 | if( ret != 0 ) |
| 694 | mbedtls_ecp_group_free( grp ); |
| 695 | |
| 696 | return( ret ); |
| 697 | } |
| 698 | #endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */ |
| 699 | |
| 700 | #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) |
| 701 | /* |
| 702 | * Specialized function for creating the Curve448 group |
| 703 | */ |
| 704 | static int ecp_use_curve448( mbedtls_ecp_group *grp ) |
| 705 | { |
| 706 | mbedtls_mpi Ns; |
| 707 | int ret; |
| 708 | |
| 709 | mbedtls_mpi_init( &Ns ); |
| 710 | |
| 711 | /* Actually ( A + 2 ) / 4 */ |
| 712 | MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &grp->A, 16, "98AA" ) ); |
| 713 | |
| 714 | /* P = 2^448 - 2^224 - 1 */ |
| 715 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->P, 1 ) ); |
| 716 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &grp->P, 224 ) ); |
| 717 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &grp->P, &grp->P, 1 ) ); |
| 718 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &grp->P, 224 ) ); |
| 719 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &grp->P, &grp->P, 1 ) ); |
| 720 | grp->pbits = mbedtls_mpi_bitlen( &grp->P ); |
| 721 | |
| 722 | /* Y intentionally not set, since we use x/z coordinates. |
| 723 | * This is used as a marker to identify Montgomery curves! */ |
| 724 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.X, 5 ) ); |
| 725 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.Z, 1 ) ); |
| 726 | mbedtls_mpi_free( &grp->G.Y ); |
| 727 | |
| 728 | /* N = 2^446 - 13818066809895115352007386748515426880336692474882178609894547503885 */ |
| 729 | MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &grp->N, 446, 1 ) ); |
| 730 | MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &Ns, 16, |
| 731 | "8335DC163BB124B65129C96FDE933D8D723A70AADC873D6D54A7BB0D" ) ); |
| 732 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &grp->N, &grp->N, &Ns ) ); |
| 733 | |
| 734 | /* Actually, the required msb for private keys */ |
| 735 | grp->nbits = 447; |
| 736 | |
| 737 | cleanup: |
| 738 | mbedtls_mpi_free( &Ns ); |
| 739 | if( ret != 0 ) |
| 740 | mbedtls_ecp_group_free( grp ); |
| 741 | |
| 742 | return( ret ); |
| 743 | } |
| 744 | #endif /* MBEDTLS_ECP_DP_CURVE448_ENABLED */ |
| 745 | |
| 746 | /* |
| 747 | * Set a group using well-known domain parameters |
| 748 | */ |
| 749 | int mbedtls_ecp_group_load( mbedtls_ecp_group *grp, mbedtls_ecp_group_id id ) |
| 750 | { |
| 751 | mbedtls_ecp_group_free( grp ); |
| 752 | |
| 753 | grp->id = id; |
| 754 | |
| 755 | switch( id ) |
| 756 | { |
| 757 | #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) |
| 758 | case MBEDTLS_ECP_DP_SECP192R1: |
| 759 | NIST_MODP( p192 ); |
| 760 | return( LOAD_GROUP( secp192r1 ) ); |
| 761 | #endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */ |
| 762 | |
| 763 | #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) |
| 764 | case MBEDTLS_ECP_DP_SECP224R1: |
| 765 | NIST_MODP( p224 ); |
| 766 | return( LOAD_GROUP( secp224r1 ) ); |
| 767 | #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */ |
| 768 | |
| 769 | #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) |
| 770 | case MBEDTLS_ECP_DP_SECP256R1: |
| 771 | NIST_MODP( p256 ); |
| 772 | return( LOAD_GROUP( secp256r1 ) ); |
| 773 | #endif /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */ |
| 774 | |
| 775 | #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) |
| 776 | case MBEDTLS_ECP_DP_SECP384R1: |
| 777 | NIST_MODP( p384 ); |
| 778 | return( LOAD_GROUP( secp384r1 ) ); |
| 779 | #endif /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */ |
| 780 | |
| 781 | #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) |
| 782 | case MBEDTLS_ECP_DP_SECP521R1: |
| 783 | NIST_MODP( p521 ); |
| 784 | return( LOAD_GROUP( secp521r1 ) ); |
| 785 | #endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */ |
| 786 | |
| 787 | #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) |
| 788 | case MBEDTLS_ECP_DP_SECP192K1: |
| 789 | grp->modp = ecp_mod_p192k1; |
| 790 | return( LOAD_GROUP_A( secp192k1 ) ); |
| 791 | #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */ |
| 792 | |
| 793 | #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) |
| 794 | case MBEDTLS_ECP_DP_SECP224K1: |
| 795 | grp->modp = ecp_mod_p224k1; |
| 796 | return( LOAD_GROUP_A( secp224k1 ) ); |
| 797 | #endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */ |
| 798 | |
| 799 | #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) |
| 800 | case MBEDTLS_ECP_DP_SECP256K1: |
| 801 | grp->modp = ecp_mod_p256k1; |
| 802 | return( LOAD_GROUP_A( secp256k1 ) ); |
| 803 | #endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */ |
| 804 | |
| 805 | #if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) |
| 806 | case MBEDTLS_ECP_DP_BP256R1: |
| 807 | return( LOAD_GROUP_A( brainpoolP256r1 ) ); |
| 808 | #endif /* MBEDTLS_ECP_DP_BP256R1_ENABLED */ |
| 809 | |
| 810 | #if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) |
| 811 | case MBEDTLS_ECP_DP_BP384R1: |
| 812 | return( LOAD_GROUP_A( brainpoolP384r1 ) ); |
| 813 | #endif /* MBEDTLS_ECP_DP_BP384R1_ENABLED */ |
| 814 | |
| 815 | #if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) |
| 816 | case MBEDTLS_ECP_DP_BP512R1: |
| 817 | return( LOAD_GROUP_A( brainpoolP512r1 ) ); |
| 818 | #endif /* MBEDTLS_ECP_DP_BP512R1_ENABLED */ |
| 819 | |
| 820 | #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) |
| 821 | case MBEDTLS_ECP_DP_CURVE25519: |
| 822 | grp->modp = ecp_mod_p255; |
| 823 | return( ecp_use_curve25519( grp ) ); |
| 824 | #endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */ |
| 825 | |
| 826 | #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) |
| 827 | case MBEDTLS_ECP_DP_CURVE448: |
| 828 | grp->modp = ecp_mod_p448; |
| 829 | return( ecp_use_curve448( grp ) ); |
| 830 | #endif /* MBEDTLS_ECP_DP_CURVE448_ENABLED */ |
| 831 | |
| 832 | default: |
| 833 | mbedtls_ecp_group_free( grp ); |
| 834 | return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE ); |
| 835 | } |
| 836 | } |
| 837 | |
| 838 | #if defined(MBEDTLS_ECP_NIST_OPTIM) |
| 839 | /* |
| 840 | * Fast reduction modulo the primes used by the NIST curves. |
| 841 | * |
| 842 | * These functions are critical for speed, but not needed for correct |
| 843 | * operations. So, we make the choice to heavily rely on the internals of our |
| 844 | * bignum library, which creates a tight coupling between these functions and |
| 845 | * our MPI implementation. However, the coupling between the ECP module and |
| 846 | * MPI remains loose, since these functions can be deactivated at will. |
| 847 | */ |
| 848 | |
| 849 | #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) |
| 850 | /* |
| 851 | * Compared to the way things are presented in FIPS 186-3 D.2, |
| 852 | * we proceed in columns, from right (least significant chunk) to left, |
| 853 | * adding chunks to N in place, and keeping a carry for the next chunk. |
| 854 | * This avoids moving things around in memory, and uselessly adding zeros, |
| 855 | * compared to the more straightforward, line-oriented approach. |
| 856 | * |
| 857 | * For this prime we need to handle data in chunks of 64 bits. |
| 858 | * Since this is always a multiple of our basic mbedtls_mpi_uint, we can |
| 859 | * use a mbedtls_mpi_uint * to designate such a chunk, and small loops to handle it. |
| 860 | */ |
| 861 | |
| 862 | /* Add 64-bit chunks (dst += src) and update carry */ |
| 863 | static inline void add64( mbedtls_mpi_uint *dst, mbedtls_mpi_uint *src, mbedtls_mpi_uint *carry ) |
| 864 | { |
| 865 | unsigned char i; |
| 866 | mbedtls_mpi_uint c = 0; |
| 867 | for( i = 0; i < 8 / sizeof( mbedtls_mpi_uint ); i++, dst++, src++ ) |
| 868 | { |
| 869 | *dst += c; c = ( *dst < c ); |
| 870 | *dst += *src; c += ( *dst < *src ); |
| 871 | } |
| 872 | *carry += c; |
| 873 | } |
| 874 | |
| 875 | /* Add carry to a 64-bit chunk and update carry */ |
| 876 | static inline void carry64( mbedtls_mpi_uint *dst, mbedtls_mpi_uint *carry ) |
| 877 | { |
| 878 | unsigned char i; |
| 879 | for( i = 0; i < 8 / sizeof( mbedtls_mpi_uint ); i++, dst++ ) |
| 880 | { |
| 881 | *dst += *carry; |
| 882 | *carry = ( *dst < *carry ); |
| 883 | } |
| 884 | } |
| 885 | |
| 886 | #define WIDTH 8 / sizeof( mbedtls_mpi_uint ) |
| 887 | #define A( i ) N->p + i * WIDTH |
| 888 | #define ADD( i ) add64( p, A( i ), &c ) |
| 889 | #define NEXT p += WIDTH; carry64( p, &c ) |
| 890 | #define LAST p += WIDTH; *p = c; while( ++p < end ) *p = 0 |
| 891 | |
| 892 | /* |
| 893 | * Fast quasi-reduction modulo p192 (FIPS 186-3 D.2.1) |
| 894 | */ |
| 895 | static int ecp_mod_p192( mbedtls_mpi *N ) |
| 896 | { |
| 897 | int ret; |
| 898 | mbedtls_mpi_uint c = 0; |
| 899 | mbedtls_mpi_uint *p, *end; |
| 900 | |
| 901 | /* Make sure we have enough blocks so that A(5) is legal */ |
| 902 | MBEDTLS_MPI_CHK( mbedtls_mpi_grow( N, 6 * WIDTH ) ); |
| 903 | |
| 904 | p = N->p; |
| 905 | end = p + N->n; |
| 906 | |
| 907 | ADD( 3 ); ADD( 5 ); NEXT; // A0 += A3 + A5 |
| 908 | ADD( 3 ); ADD( 4 ); ADD( 5 ); NEXT; // A1 += A3 + A4 + A5 |
| 909 | ADD( 4 ); ADD( 5 ); LAST; // A2 += A4 + A5 |
| 910 | |
| 911 | cleanup: |
| 912 | return( ret ); |
| 913 | } |
| 914 | |
| 915 | #undef WIDTH |
| 916 | #undef A |
| 917 | #undef ADD |
| 918 | #undef NEXT |
| 919 | #undef LAST |
| 920 | #endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */ |
| 921 | |
| 922 | #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) || \ |
| 923 | defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) || \ |
| 924 | defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) |
| 925 | /* |
| 926 | * The reader is advised to first understand ecp_mod_p192() since the same |
| 927 | * general structure is used here, but with additional complications: |
| 928 | * (1) chunks of 32 bits, and (2) subtractions. |
| 929 | */ |
| 930 | |
| 931 | /* |
| 932 | * For these primes, we need to handle data in chunks of 32 bits. |
| 933 | * This makes it more complicated if we use 64 bits limbs in MPI, |
| 934 | * which prevents us from using a uniform access method as for p192. |
| 935 | * |
| 936 | * So, we define a mini abstraction layer to access 32 bit chunks, |
| 937 | * load them in 'cur' for work, and store them back from 'cur' when done. |
| 938 | * |
| 939 | * While at it, also define the size of N in terms of 32-bit chunks. |
| 940 | */ |
| 941 | #define LOAD32 cur = A( i ); |
| 942 | |
| 943 | #if defined(MBEDTLS_HAVE_INT32) /* 32 bit */ |
| 944 | |
| 945 | #define MAX32 N->n |
| 946 | #define A( j ) N->p[j] |
| 947 | #define STORE32 N->p[i] = cur; |
| 948 | |
| 949 | #else /* 64-bit */ |
| 950 | |
| 951 | #define MAX32 N->n * 2 |
| 952 | #define A( j ) j % 2 ? (uint32_t)( N->p[j/2] >> 32 ) : (uint32_t)( N->p[j/2] ) |
| 953 | #define STORE32 \ |
| 954 | if( i % 2 ) { \ |
| 955 | N->p[i/2] &= 0x00000000FFFFFFFF; \ |
| 956 | N->p[i/2] |= ((mbedtls_mpi_uint) cur) << 32; \ |
| 957 | } else { \ |
| 958 | N->p[i/2] &= 0xFFFFFFFF00000000; \ |
| 959 | N->p[i/2] |= (mbedtls_mpi_uint) cur; \ |
| 960 | } |
| 961 | |
| 962 | #endif /* sizeof( mbedtls_mpi_uint ) */ |
| 963 | |
| 964 | /* |
| 965 | * Helpers for addition and subtraction of chunks, with signed carry. |
| 966 | */ |
| 967 | static inline void add32( uint32_t *dst, uint32_t src, signed char *carry ) |
| 968 | { |
| 969 | *dst += src; |
| 970 | *carry += ( *dst < src ); |
| 971 | } |
| 972 | |
| 973 | static inline void sub32( uint32_t *dst, uint32_t src, signed char *carry ) |
| 974 | { |
| 975 | *carry -= ( *dst < src ); |
| 976 | *dst -= src; |
| 977 | } |
| 978 | |
| 979 | #define ADD( j ) add32( &cur, A( j ), &c ); |
| 980 | #define SUB( j ) sub32( &cur, A( j ), &c ); |
| 981 | |
| 982 | /* |
| 983 | * Helpers for the main 'loop' |
| 984 | * (see fix_negative for the motivation of C) |
| 985 | */ |
| 986 | #define INIT( b ) \ |
| 987 | int ret; \ |
| 988 | signed char c = 0, cc; \ |
| 989 | uint32_t cur; \ |
| 990 | size_t i = 0, bits = b; \ |
| 991 | mbedtls_mpi C; \ |
| 992 | mbedtls_mpi_uint Cp[ b / 8 / sizeof( mbedtls_mpi_uint) + 1 ]; \ |
| 993 | \ |
| 994 | C.s = 1; \ |
| 995 | C.n = b / 8 / sizeof( mbedtls_mpi_uint) + 1; \ |
| 996 | C.p = Cp; \ |
| 997 | memset( Cp, 0, C.n * sizeof( mbedtls_mpi_uint ) ); \ |
| 998 | \ |
| 999 | MBEDTLS_MPI_CHK( mbedtls_mpi_grow( N, b * 2 / 8 / sizeof( mbedtls_mpi_uint ) ) ); \ |
| 1000 | LOAD32; |
| 1001 | |
| 1002 | #define NEXT \ |
| 1003 | STORE32; i++; LOAD32; \ |
| 1004 | cc = c; c = 0; \ |
| 1005 | if( cc < 0 ) \ |
| 1006 | sub32( &cur, -cc, &c ); \ |
| 1007 | else \ |
| 1008 | add32( &cur, cc, &c ); \ |
| 1009 | |
| 1010 | #define LAST \ |
| 1011 | STORE32; i++; \ |
| 1012 | cur = c > 0 ? c : 0; STORE32; \ |
| 1013 | cur = 0; while( ++i < MAX32 ) { STORE32; } \ |
| 1014 | if( c < 0 ) fix_negative( N, c, &C, bits ); |
| 1015 | |
| 1016 | /* |
| 1017 | * If the result is negative, we get it in the form |
| 1018 | * c * 2^(bits + 32) + N, with c negative and N positive shorter than 'bits' |
| 1019 | */ |
| 1020 | static inline int fix_negative( mbedtls_mpi *N, signed char c, mbedtls_mpi *C, size_t bits ) |
| 1021 | { |
| 1022 | int ret; |
| 1023 | |
| 1024 | /* C = - c * 2^(bits + 32) */ |
| 1025 | #if !defined(MBEDTLS_HAVE_INT64) |
| 1026 | ((void) bits); |
| 1027 | #else |
| 1028 | if( bits == 224 ) |
| 1029 | C->p[ C->n - 1 ] = ((mbedtls_mpi_uint) -c) << 32; |
| 1030 | else |
| 1031 | #endif |
| 1032 | C->p[ C->n - 1 ] = (mbedtls_mpi_uint) -c; |
| 1033 | |
| 1034 | /* N = - ( C - N ) */ |
| 1035 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( N, C, N ) ); |
| 1036 | N->s = -1; |
| 1037 | |
| 1038 | cleanup: |
| 1039 | |
| 1040 | return( ret ); |
| 1041 | } |
| 1042 | |
| 1043 | #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) |
| 1044 | /* |
| 1045 | * Fast quasi-reduction modulo p224 (FIPS 186-3 D.2.2) |
| 1046 | */ |
| 1047 | static int ecp_mod_p224( mbedtls_mpi *N ) |
| 1048 | { |
| 1049 | INIT( 224 ); |
| 1050 | |
| 1051 | SUB( 7 ); SUB( 11 ); NEXT; // A0 += -A7 - A11 |
| 1052 | SUB( 8 ); SUB( 12 ); NEXT; // A1 += -A8 - A12 |
| 1053 | SUB( 9 ); SUB( 13 ); NEXT; // A2 += -A9 - A13 |
| 1054 | SUB( 10 ); ADD( 7 ); ADD( 11 ); NEXT; // A3 += -A10 + A7 + A11 |
| 1055 | SUB( 11 ); ADD( 8 ); ADD( 12 ); NEXT; // A4 += -A11 + A8 + A12 |
| 1056 | SUB( 12 ); ADD( 9 ); ADD( 13 ); NEXT; // A5 += -A12 + A9 + A13 |
| 1057 | SUB( 13 ); ADD( 10 ); LAST; // A6 += -A13 + A10 |
| 1058 | |
| 1059 | cleanup: |
| 1060 | return( ret ); |
| 1061 | } |
| 1062 | #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */ |
| 1063 | |
| 1064 | #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) |
| 1065 | /* |
| 1066 | * Fast quasi-reduction modulo p256 (FIPS 186-3 D.2.3) |
| 1067 | */ |
| 1068 | static int ecp_mod_p256( mbedtls_mpi *N ) |
| 1069 | { |
| 1070 | INIT( 256 ); |
| 1071 | |
| 1072 | ADD( 8 ); ADD( 9 ); |
| 1073 | SUB( 11 ); SUB( 12 ); SUB( 13 ); SUB( 14 ); NEXT; // A0 |
| 1074 | |
| 1075 | ADD( 9 ); ADD( 10 ); |
| 1076 | SUB( 12 ); SUB( 13 ); SUB( 14 ); SUB( 15 ); NEXT; // A1 |
| 1077 | |
| 1078 | ADD( 10 ); ADD( 11 ); |
| 1079 | SUB( 13 ); SUB( 14 ); SUB( 15 ); NEXT; // A2 |
| 1080 | |
| 1081 | ADD( 11 ); ADD( 11 ); ADD( 12 ); ADD( 12 ); ADD( 13 ); |
| 1082 | SUB( 15 ); SUB( 8 ); SUB( 9 ); NEXT; // A3 |
| 1083 | |
| 1084 | ADD( 12 ); ADD( 12 ); ADD( 13 ); ADD( 13 ); ADD( 14 ); |
| 1085 | SUB( 9 ); SUB( 10 ); NEXT; // A4 |
| 1086 | |
| 1087 | ADD( 13 ); ADD( 13 ); ADD( 14 ); ADD( 14 ); ADD( 15 ); |
| 1088 | SUB( 10 ); SUB( 11 ); NEXT; // A5 |
| 1089 | |
| 1090 | ADD( 14 ); ADD( 14 ); ADD( 15 ); ADD( 15 ); ADD( 14 ); ADD( 13 ); |
| 1091 | SUB( 8 ); SUB( 9 ); NEXT; // A6 |
| 1092 | |
| 1093 | ADD( 15 ); ADD( 15 ); ADD( 15 ); ADD( 8 ); |
| 1094 | SUB( 10 ); SUB( 11 ); SUB( 12 ); SUB( 13 ); LAST; // A7 |
| 1095 | |
| 1096 | cleanup: |
| 1097 | return( ret ); |
| 1098 | } |
| 1099 | #endif /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */ |
| 1100 | |
| 1101 | #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) |
| 1102 | /* |
| 1103 | * Fast quasi-reduction modulo p384 (FIPS 186-3 D.2.4) |
| 1104 | */ |
| 1105 | static int ecp_mod_p384( mbedtls_mpi *N ) |
| 1106 | { |
| 1107 | INIT( 384 ); |
| 1108 | |
| 1109 | ADD( 12 ); ADD( 21 ); ADD( 20 ); |
| 1110 | SUB( 23 ); NEXT; // A0 |
| 1111 | |
| 1112 | ADD( 13 ); ADD( 22 ); ADD( 23 ); |
| 1113 | SUB( 12 ); SUB( 20 ); NEXT; // A2 |
| 1114 | |
| 1115 | ADD( 14 ); ADD( 23 ); |
| 1116 | SUB( 13 ); SUB( 21 ); NEXT; // A2 |
| 1117 | |
| 1118 | ADD( 15 ); ADD( 12 ); ADD( 20 ); ADD( 21 ); |
| 1119 | SUB( 14 ); SUB( 22 ); SUB( 23 ); NEXT; // A3 |
| 1120 | |
| 1121 | ADD( 21 ); ADD( 21 ); ADD( 16 ); ADD( 13 ); ADD( 12 ); ADD( 20 ); ADD( 22 ); |
| 1122 | SUB( 15 ); SUB( 23 ); SUB( 23 ); NEXT; // A4 |
| 1123 | |
| 1124 | ADD( 22 ); ADD( 22 ); ADD( 17 ); ADD( 14 ); ADD( 13 ); ADD( 21 ); ADD( 23 ); |
| 1125 | SUB( 16 ); NEXT; // A5 |
| 1126 | |
| 1127 | ADD( 23 ); ADD( 23 ); ADD( 18 ); ADD( 15 ); ADD( 14 ); ADD( 22 ); |
| 1128 | SUB( 17 ); NEXT; // A6 |
| 1129 | |
| 1130 | ADD( 19 ); ADD( 16 ); ADD( 15 ); ADD( 23 ); |
| 1131 | SUB( 18 ); NEXT; // A7 |
| 1132 | |
| 1133 | ADD( 20 ); ADD( 17 ); ADD( 16 ); |
| 1134 | SUB( 19 ); NEXT; // A8 |
| 1135 | |
| 1136 | ADD( 21 ); ADD( 18 ); ADD( 17 ); |
| 1137 | SUB( 20 ); NEXT; // A9 |
| 1138 | |
| 1139 | ADD( 22 ); ADD( 19 ); ADD( 18 ); |
| 1140 | SUB( 21 ); NEXT; // A10 |
| 1141 | |
| 1142 | ADD( 23 ); ADD( 20 ); ADD( 19 ); |
| 1143 | SUB( 22 ); LAST; // A11 |
| 1144 | |
| 1145 | cleanup: |
| 1146 | return( ret ); |
| 1147 | } |
| 1148 | #endif /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */ |
| 1149 | |
| 1150 | #undef A |
| 1151 | #undef LOAD32 |
| 1152 | #undef STORE32 |
| 1153 | #undef MAX32 |
| 1154 | #undef INIT |
| 1155 | #undef NEXT |
| 1156 | #undef LAST |
| 1157 | |
| 1158 | #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED || |
| 1159 | MBEDTLS_ECP_DP_SECP256R1_ENABLED || |
| 1160 | MBEDTLS_ECP_DP_SECP384R1_ENABLED */ |
| 1161 | |
| 1162 | #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) |
| 1163 | /* |
| 1164 | * Here we have an actual Mersenne prime, so things are more straightforward. |
| 1165 | * However, chunks are aligned on a 'weird' boundary (521 bits). |
| 1166 | */ |
| 1167 | |
| 1168 | /* Size of p521 in terms of mbedtls_mpi_uint */ |
| 1169 | #define P521_WIDTH ( 521 / 8 / sizeof( mbedtls_mpi_uint ) + 1 ) |
| 1170 | |
| 1171 | /* Bits to keep in the most significant mbedtls_mpi_uint */ |
| 1172 | #define P521_MASK 0x01FF |
| 1173 | |
| 1174 | /* |
| 1175 | * Fast quasi-reduction modulo p521 (FIPS 186-3 D.2.5) |
| 1176 | * Write N as A1 + 2^521 A0, return A0 + A1 |
| 1177 | */ |
| 1178 | static int ecp_mod_p521( mbedtls_mpi *N ) |
| 1179 | { |
| 1180 | int ret; |
| 1181 | size_t i; |
| 1182 | mbedtls_mpi M; |
| 1183 | mbedtls_mpi_uint Mp[P521_WIDTH + 1]; |
| 1184 | /* Worst case for the size of M is when mbedtls_mpi_uint is 16 bits: |
| 1185 | * we need to hold bits 513 to 1056, which is 34 limbs, that is |
| 1186 | * P521_WIDTH + 1. Otherwise P521_WIDTH is enough. */ |
| 1187 | |
| 1188 | if( N->n < P521_WIDTH ) |
| 1189 | return( 0 ); |
| 1190 | |
| 1191 | /* M = A1 */ |
| 1192 | M.s = 1; |
| 1193 | M.n = N->n - ( P521_WIDTH - 1 ); |
| 1194 | if( M.n > P521_WIDTH + 1 ) |
| 1195 | M.n = P521_WIDTH + 1; |
| 1196 | M.p = Mp; |
| 1197 | memcpy( Mp, N->p + P521_WIDTH - 1, M.n * sizeof( mbedtls_mpi_uint ) ); |
| 1198 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, 521 % ( 8 * sizeof( mbedtls_mpi_uint ) ) ) ); |
| 1199 | |
| 1200 | /* N = A0 */ |
| 1201 | N->p[P521_WIDTH - 1] &= P521_MASK; |
| 1202 | for( i = P521_WIDTH; i < N->n; i++ ) |
| 1203 | N->p[i] = 0; |
| 1204 | |
| 1205 | /* N = A0 + A1 */ |
| 1206 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) ); |
| 1207 | |
| 1208 | cleanup: |
| 1209 | return( ret ); |
| 1210 | } |
| 1211 | |
| 1212 | #undef P521_WIDTH |
| 1213 | #undef P521_MASK |
| 1214 | #endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */ |
| 1215 | |
| 1216 | #endif /* MBEDTLS_ECP_NIST_OPTIM */ |
| 1217 | |
| 1218 | #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) |
| 1219 | |
| 1220 | /* Size of p255 in terms of mbedtls_mpi_uint */ |
| 1221 | #define P255_WIDTH ( 255 / 8 / sizeof( mbedtls_mpi_uint ) + 1 ) |
| 1222 | |
| 1223 | /* |
| 1224 | * Fast quasi-reduction modulo p255 = 2^255 - 19 |
| 1225 | * Write N as A0 + 2^255 A1, return A0 + 19 * A1 |
| 1226 | */ |
| 1227 | static int ecp_mod_p255( mbedtls_mpi *N ) |
| 1228 | { |
| 1229 | int ret; |
| 1230 | size_t i; |
| 1231 | mbedtls_mpi M; |
| 1232 | mbedtls_mpi_uint Mp[P255_WIDTH + 2]; |
| 1233 | |
| 1234 | if( N->n < P255_WIDTH ) |
| 1235 | return( 0 ); |
| 1236 | |
| 1237 | /* M = A1 */ |
| 1238 | M.s = 1; |
| 1239 | M.n = N->n - ( P255_WIDTH - 1 ); |
| 1240 | if( M.n > P255_WIDTH + 1 ) |
| 1241 | return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); |
| 1242 | M.p = Mp; |
| 1243 | memset( Mp, 0, sizeof Mp ); |
| 1244 | memcpy( Mp, N->p + P255_WIDTH - 1, M.n * sizeof( mbedtls_mpi_uint ) ); |
| 1245 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, 255 % ( 8 * sizeof( mbedtls_mpi_uint ) ) ) ); |
| 1246 | M.n++; /* Make room for multiplication by 19 */ |
| 1247 | |
| 1248 | /* N = A0 */ |
| 1249 | MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( N, 255, 0 ) ); |
| 1250 | for( i = P255_WIDTH; i < N->n; i++ ) |
| 1251 | N->p[i] = 0; |
| 1252 | |
| 1253 | /* N = A0 + 19 * A1 */ |
| 1254 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &M, 19 ) ); |
| 1255 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) ); |
| 1256 | |
| 1257 | cleanup: |
| 1258 | return( ret ); |
| 1259 | } |
| 1260 | #endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */ |
| 1261 | |
| 1262 | #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) |
| 1263 | |
| 1264 | /* Size of p448 in terms of mbedtls_mpi_uint */ |
| 1265 | #define P448_WIDTH ( 448 / 8 / sizeof( mbedtls_mpi_uint ) ) |
| 1266 | |
| 1267 | /* Number of limbs fully occupied by 2^224 (max), and limbs used by it (min) */ |
| 1268 | #define DIV_ROUND_UP( X, Y ) ( ( ( X ) + ( Y ) - 1 ) / ( Y ) ) |
| 1269 | #define P224_WIDTH_MIN ( 28 / sizeof( mbedtls_mpi_uint ) ) |
| 1270 | #define P224_WIDTH_MAX DIV_ROUND_UP( 28, sizeof( mbedtls_mpi_uint ) ) |
| 1271 | #define P224_UNUSED_BITS ( ( P224_WIDTH_MAX * sizeof( mbedtls_mpi_uint ) * 8 ) - 224 ) |
| 1272 | |
| 1273 | /* |
| 1274 | * Fast quasi-reduction modulo p448 = 2^448 - 2^224 - 1 |
| 1275 | * Write N as A0 + 2^448 A1 and A1 as B0 + 2^224 B1, and return |
| 1276 | * A0 + A1 + B1 + (B0 + B1) * 2^224. This is different to the reference |
| 1277 | * implementation of Curve448, which uses its own special 56-bit limbs rather |
| 1278 | * than a generic bignum library. We could squeeze some extra speed out on |
| 1279 | * 32-bit machines by splitting N up into 32-bit limbs and doing the |
| 1280 | * arithmetic using the limbs directly as we do for the NIST primes above, |
| 1281 | * but for 64-bit targets it should use half the number of operations if we do |
| 1282 | * the reduction with 224-bit limbs, since mpi_add_mpi will then use 64-bit adds. |
| 1283 | */ |
| 1284 | static int ecp_mod_p448( mbedtls_mpi *N ) |
| 1285 | { |
| 1286 | int ret; |
| 1287 | size_t i; |
| 1288 | mbedtls_mpi M, Q; |
| 1289 | mbedtls_mpi_uint Mp[P448_WIDTH + 1], Qp[P448_WIDTH]; |
| 1290 | |
| 1291 | if( N->n <= P448_WIDTH ) |
| 1292 | return( 0 ); |
| 1293 | |
| 1294 | /* M = A1 */ |
| 1295 | M.s = 1; |
| 1296 | M.n = N->n - ( P448_WIDTH ); |
| 1297 | if( M.n > P448_WIDTH ) |
| 1298 | /* Shouldn't be called with N larger than 2^896! */ |
| 1299 | return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); |
| 1300 | M.p = Mp; |
| 1301 | memset( Mp, 0, sizeof( Mp ) ); |
| 1302 | memcpy( Mp, N->p + P448_WIDTH, M.n * sizeof( mbedtls_mpi_uint ) ); |
| 1303 | |
| 1304 | /* N = A0 */ |
| 1305 | for( i = P448_WIDTH; i < N->n; i++ ) |
| 1306 | N->p[i] = 0; |
| 1307 | |
| 1308 | /* N += A1 */ |
| 1309 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &M ) ); |
| 1310 | |
| 1311 | /* Q = B1, N += B1 */ |
| 1312 | Q = M; |
| 1313 | Q.p = Qp; |
| 1314 | memcpy( Qp, Mp, sizeof( Qp ) ); |
| 1315 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &Q, 224 ) ); |
| 1316 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &Q ) ); |
| 1317 | |
| 1318 | /* M = (B0 + B1) * 2^224, N += M */ |
| 1319 | if( sizeof( mbedtls_mpi_uint ) > 4 ) |
| 1320 | Mp[P224_WIDTH_MIN] &= ( (mbedtls_mpi_uint)-1 ) >> ( P224_UNUSED_BITS ); |
| 1321 | for( i = P224_WIDTH_MAX; i < M.n; ++i ) |
| 1322 | Mp[i] = 0; |
| 1323 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &M, &M, &Q ) ); |
| 1324 | M.n = P448_WIDTH + 1; /* Make room for shifted carry bit from the addition */ |
| 1325 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &M, 224 ) ); |
| 1326 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &M ) ); |
| 1327 | |
| 1328 | cleanup: |
| 1329 | return( ret ); |
| 1330 | } |
| 1331 | #endif /* MBEDTLS_ECP_DP_CURVE448_ENABLED */ |
| 1332 | |
| 1333 | #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) || \ |
| 1334 | defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) || \ |
| 1335 | defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) |
| 1336 | /* |
| 1337 | * Fast quasi-reduction modulo P = 2^s - R, |
| 1338 | * with R about 33 bits, used by the Koblitz curves. |
| 1339 | * |
| 1340 | * Write N as A0 + 2^224 A1, return A0 + R * A1. |
| 1341 | * Actually do two passes, since R is big. |
| 1342 | */ |
| 1343 | #define P_KOBLITZ_MAX ( 256 / 8 / sizeof( mbedtls_mpi_uint ) ) // Max limbs in P |
| 1344 | #define P_KOBLITZ_R ( 8 / sizeof( mbedtls_mpi_uint ) ) // Limbs in R |
| 1345 | static inline int ecp_mod_koblitz( mbedtls_mpi *N, mbedtls_mpi_uint *Rp, size_t p_limbs, |
| 1346 | size_t adjust, size_t shift, mbedtls_mpi_uint mask ) |
| 1347 | { |
| 1348 | int ret; |
| 1349 | size_t i; |
| 1350 | mbedtls_mpi M, R; |
| 1351 | mbedtls_mpi_uint Mp[P_KOBLITZ_MAX + P_KOBLITZ_R + 1]; |
| 1352 | |
| 1353 | if( N->n < p_limbs ) |
| 1354 | return( 0 ); |
| 1355 | |
| 1356 | /* Init R */ |
| 1357 | R.s = 1; |
| 1358 | R.p = Rp; |
| 1359 | R.n = P_KOBLITZ_R; |
| 1360 | |
| 1361 | /* Common setup for M */ |
| 1362 | M.s = 1; |
| 1363 | M.p = Mp; |
| 1364 | |
| 1365 | /* M = A1 */ |
| 1366 | M.n = N->n - ( p_limbs - adjust ); |
| 1367 | if( M.n > p_limbs + adjust ) |
| 1368 | M.n = p_limbs + adjust; |
| 1369 | memset( Mp, 0, sizeof Mp ); |
| 1370 | memcpy( Mp, N->p + p_limbs - adjust, M.n * sizeof( mbedtls_mpi_uint ) ); |
| 1371 | if( shift != 0 ) |
| 1372 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, shift ) ); |
| 1373 | M.n += R.n; /* Make room for multiplication by R */ |
| 1374 | |
| 1375 | /* N = A0 */ |
| 1376 | if( mask != 0 ) |
| 1377 | N->p[p_limbs - 1] &= mask; |
| 1378 | for( i = p_limbs; i < N->n; i++ ) |
| 1379 | N->p[i] = 0; |
| 1380 | |
| 1381 | /* N = A0 + R * A1 */ |
| 1382 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &M, &M, &R ) ); |
| 1383 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) ); |
| 1384 | |
| 1385 | /* Second pass */ |
| 1386 | |
| 1387 | /* M = A1 */ |
| 1388 | M.n = N->n - ( p_limbs - adjust ); |
| 1389 | if( M.n > p_limbs + adjust ) |
| 1390 | M.n = p_limbs + adjust; |
| 1391 | memset( Mp, 0, sizeof Mp ); |
| 1392 | memcpy( Mp, N->p + p_limbs - adjust, M.n * sizeof( mbedtls_mpi_uint ) ); |
| 1393 | if( shift != 0 ) |
| 1394 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, shift ) ); |
| 1395 | M.n += R.n; /* Make room for multiplication by R */ |
| 1396 | |
| 1397 | /* N = A0 */ |
| 1398 | if( mask != 0 ) |
| 1399 | N->p[p_limbs - 1] &= mask; |
| 1400 | for( i = p_limbs; i < N->n; i++ ) |
| 1401 | N->p[i] = 0; |
| 1402 | |
| 1403 | /* N = A0 + R * A1 */ |
| 1404 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &M, &M, &R ) ); |
| 1405 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) ); |
| 1406 | |
| 1407 | cleanup: |
| 1408 | return( ret ); |
| 1409 | } |
| 1410 | #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED) || |
| 1411 | MBEDTLS_ECP_DP_SECP224K1_ENABLED) || |
| 1412 | MBEDTLS_ECP_DP_SECP256K1_ENABLED) */ |
| 1413 | |
| 1414 | #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) |
| 1415 | /* |
| 1416 | * Fast quasi-reduction modulo p192k1 = 2^192 - R, |
| 1417 | * with R = 2^32 + 2^12 + 2^8 + 2^7 + 2^6 + 2^3 + 1 = 0x0100001119 |
| 1418 | */ |
| 1419 | static int ecp_mod_p192k1( mbedtls_mpi *N ) |
| 1420 | { |
| 1421 | static mbedtls_mpi_uint Rp[] = { |
| 1422 | BYTES_TO_T_UINT_8( 0xC9, 0x11, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) }; |
| 1423 | |
| 1424 | return( ecp_mod_koblitz( N, Rp, 192 / 8 / sizeof( mbedtls_mpi_uint ), 0, 0, 0 ) ); |
| 1425 | } |
| 1426 | #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */ |
| 1427 | |
| 1428 | #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) |
| 1429 | /* |
| 1430 | * Fast quasi-reduction modulo p224k1 = 2^224 - R, |
| 1431 | * with R = 2^32 + 2^12 + 2^11 + 2^9 + 2^7 + 2^4 + 2 + 1 = 0x0100001A93 |
| 1432 | */ |
| 1433 | static int ecp_mod_p224k1( mbedtls_mpi *N ) |
| 1434 | { |
| 1435 | static mbedtls_mpi_uint Rp[] = { |
| 1436 | BYTES_TO_T_UINT_8( 0x93, 0x1A, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) }; |
| 1437 | |
| 1438 | #if defined(MBEDTLS_HAVE_INT64) |
| 1439 | return( ecp_mod_koblitz( N, Rp, 4, 1, 32, 0xFFFFFFFF ) ); |
| 1440 | #else |
| 1441 | return( ecp_mod_koblitz( N, Rp, 224 / 8 / sizeof( mbedtls_mpi_uint ), 0, 0, 0 ) ); |
| 1442 | #endif |
| 1443 | } |
| 1444 | |
| 1445 | #endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */ |
| 1446 | |
| 1447 | #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) |
| 1448 | /* |
| 1449 | * Fast quasi-reduction modulo p256k1 = 2^256 - R, |
| 1450 | * with R = 2^32 + 2^9 + 2^8 + 2^7 + 2^6 + 2^4 + 1 = 0x01000003D1 |
| 1451 | */ |
| 1452 | static int ecp_mod_p256k1( mbedtls_mpi *N ) |
| 1453 | { |
| 1454 | static mbedtls_mpi_uint Rp[] = { |
| 1455 | BYTES_TO_T_UINT_8( 0xD1, 0x03, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) }; |
| 1456 | return( ecp_mod_koblitz( N, Rp, 256 / 8 / sizeof( mbedtls_mpi_uint ), 0, 0, 0 ) ); |
| 1457 | } |
| 1458 | #endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */ |
| 1459 | |
| 1460 | #endif /* !MBEDTLS_ECP_ALT */ |
| 1461 | |
| 1462 | #endif /* MBEDTLS_ECP_C */ |