1 // SPDX-License-Identifier: Apache-2.0 2 /* 3 * Elliptic curves over GF(p): curve-specific data and functions 4 * 5 * Copyright (C) 2006-2015, ARM Limited, All Rights Reserved 6 * 7 * Licensed under the Apache License, Version 2.0 (the "License"); you may 8 * not use this file except in compliance with the License. 9 * You may obtain a copy of the License at 10 * 11 * http://www.apache.org/licenses/LICENSE-2.0 12 * 13 * Unless required by applicable law or agreed to in writing, software 14 * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT 15 * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 16 * See the License for the specific language governing permissions and 17 * limitations under the License. 18 * 19 * This file is part of mbed TLS (https://tls.mbed.org) 20 */ 21 22 #if !defined(MBEDTLS_CONFIG_FILE) 23 #include "mbedtls/config.h" 24 #else 25 #include MBEDTLS_CONFIG_FILE 26 #endif 27 28 #if defined(MBEDTLS_ECP_C) 29 30 #include "mbedtls/ecp.h" 31 #include "mbedtls/platform_util.h" 32 #include "mbedtls/error.h" 33 34 #include <string.h> 35 36 #if !defined(MBEDTLS_ECP_ALT) 37 38 /* Parameter validation macros based on platform_util.h */ 39 #define ECP_VALIDATE_RET( cond ) \ 40 MBEDTLS_INTERNAL_VALIDATE_RET( cond, MBEDTLS_ERR_ECP_BAD_INPUT_DATA ) 41 #define ECP_VALIDATE( cond ) \ 42 MBEDTLS_INTERNAL_VALIDATE( cond ) 43 44 #if ( defined(__ARMCC_VERSION) || defined(_MSC_VER) ) && \ 45 !defined(inline) && !defined(__cplusplus) 46 #define inline __inline 47 #endif 48 49 /* 50 * Conversion macros for embedded constants: 51 * build lists of mbedtls_mpi_uint's from lists of unsigned char's grouped by 8, 4 or 2 52 */ 53 #if defined(MBEDTLS_HAVE_INT32) 54 55 #define BYTES_TO_T_UINT_4( a, b, c, d ) \ 56 ( (mbedtls_mpi_uint) (a) << 0 ) | \ 57 ( (mbedtls_mpi_uint) (b) << 8 ) | \ 58 ( (mbedtls_mpi_uint) (c) << 16 ) | \ 59 ( (mbedtls_mpi_uint) (d) << 24 ) 60 61 #define BYTES_TO_T_UINT_2( a, b ) \ 62 BYTES_TO_T_UINT_4( a, b, 0, 0 ) 63 64 #define BYTES_TO_T_UINT_8( a, b, c, d, e, f, g, h ) \ 65 BYTES_TO_T_UINT_4( a, b, c, d ), \ 66 BYTES_TO_T_UINT_4( e, f, g, h ) 67 68 #else /* 64-bits */ 69 70 #define BYTES_TO_T_UINT_8( a, b, c, d, e, f, g, h ) \ 71 ( (mbedtls_mpi_uint) (a) << 0 ) | \ 72 ( (mbedtls_mpi_uint) (b) << 8 ) | \ 73 ( (mbedtls_mpi_uint) (c) << 16 ) | \ 74 ( (mbedtls_mpi_uint) (d) << 24 ) | \ 75 ( (mbedtls_mpi_uint) (e) << 32 ) | \ 76 ( (mbedtls_mpi_uint) (f) << 40 ) | \ 77 ( (mbedtls_mpi_uint) (g) << 48 ) | \ 78 ( (mbedtls_mpi_uint) (h) << 56 ) 79 80 #define BYTES_TO_T_UINT_4( a, b, c, d ) \ 81 BYTES_TO_T_UINT_8( a, b, c, d, 0, 0, 0, 0 ) 82 83 #define BYTES_TO_T_UINT_2( a, b ) \ 84 BYTES_TO_T_UINT_8( a, b, 0, 0, 0, 0, 0, 0 ) 85 86 #endif /* bits in mbedtls_mpi_uint */ 87 88 /* 89 * Note: the constants are in little-endian order 90 * to be directly usable in MPIs 91 */ 92 93 /* 94 * Domain parameters for secp192r1 95 */ 96 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) 97 static const mbedtls_mpi_uint secp192r1_p[] = { 98 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 99 BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 100 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 101 }; 102 static const mbedtls_mpi_uint secp192r1_b[] = { 103 BYTES_TO_T_UINT_8( 0xB1, 0xB9, 0x46, 0xC1, 0xEC, 0xDE, 0xB8, 0xFE ), 104 BYTES_TO_T_UINT_8( 0x49, 0x30, 0x24, 0x72, 0xAB, 0xE9, 0xA7, 0x0F ), 105 BYTES_TO_T_UINT_8( 0xE7, 0x80, 0x9C, 0xE5, 0x19, 0x05, 0x21, 0x64 ), 106 }; 107 static const mbedtls_mpi_uint secp192r1_gx[] = { 108 BYTES_TO_T_UINT_8( 0x12, 0x10, 0xFF, 0x82, 0xFD, 0x0A, 0xFF, 0xF4 ), 109 BYTES_TO_T_UINT_8( 0x00, 0x88, 0xA1, 0x43, 0xEB, 0x20, 0xBF, 0x7C ), 110 BYTES_TO_T_UINT_8( 0xF6, 0x90, 0x30, 0xB0, 0x0E, 0xA8, 0x8D, 0x18 ), 111 }; 112 static const mbedtls_mpi_uint secp192r1_gy[] = { 113 BYTES_TO_T_UINT_8( 0x11, 0x48, 0x79, 0x1E, 0xA1, 0x77, 0xF9, 0x73 ), 114 BYTES_TO_T_UINT_8( 0xD5, 0xCD, 0x24, 0x6B, 0xED, 0x11, 0x10, 0x63 ), 115 BYTES_TO_T_UINT_8( 0x78, 0xDA, 0xC8, 0xFF, 0x95, 0x2B, 0x19, 0x07 ), 116 }; 117 static const mbedtls_mpi_uint secp192r1_n[] = { 118 BYTES_TO_T_UINT_8( 0x31, 0x28, 0xD2, 0xB4, 0xB1, 0xC9, 0x6B, 0x14 ), 119 BYTES_TO_T_UINT_8( 0x36, 0xF8, 0xDE, 0x99, 0xFF, 0xFF, 0xFF, 0xFF ), 120 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 121 }; 122 #endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */ 123 124 /* 125 * Domain parameters for secp224r1 126 */ 127 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) 128 static const mbedtls_mpi_uint secp224r1_p[] = { 129 BYTES_TO_T_UINT_8( 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ), 130 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ), 131 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 132 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ), 133 }; 134 static const mbedtls_mpi_uint secp224r1_b[] = { 135 BYTES_TO_T_UINT_8( 0xB4, 0xFF, 0x55, 0x23, 0x43, 0x39, 0x0B, 0x27 ), 136 BYTES_TO_T_UINT_8( 0xBA, 0xD8, 0xBF, 0xD7, 0xB7, 0xB0, 0x44, 0x50 ), 137 BYTES_TO_T_UINT_8( 0x56, 0x32, 0x41, 0xF5, 0xAB, 0xB3, 0x04, 0x0C ), 138 BYTES_TO_T_UINT_4( 0x85, 0x0A, 0x05, 0xB4 ), 139 }; 140 static const mbedtls_mpi_uint secp224r1_gx[] = { 141 BYTES_TO_T_UINT_8( 0x21, 0x1D, 0x5C, 0x11, 0xD6, 0x80, 0x32, 0x34 ), 142 BYTES_TO_T_UINT_8( 0x22, 0x11, 0xC2, 0x56, 0xD3, 0xC1, 0x03, 0x4A ), 143 BYTES_TO_T_UINT_8( 0xB9, 0x90, 0x13, 0x32, 0x7F, 0xBF, 0xB4, 0x6B ), 144 BYTES_TO_T_UINT_4( 0xBD, 0x0C, 0x0E, 0xB7 ), 145 }; 146 static const mbedtls_mpi_uint secp224r1_gy[] = { 147 BYTES_TO_T_UINT_8( 0x34, 0x7E, 0x00, 0x85, 0x99, 0x81, 0xD5, 0x44 ), 148 BYTES_TO_T_UINT_8( 0x64, 0x47, 0x07, 0x5A, 0xA0, 0x75, 0x43, 0xCD ), 149 BYTES_TO_T_UINT_8( 0xE6, 0xDF, 0x22, 0x4C, 0xFB, 0x23, 0xF7, 0xB5 ), 150 BYTES_TO_T_UINT_4( 0x88, 0x63, 0x37, 0xBD ), 151 }; 152 static const mbedtls_mpi_uint secp224r1_n[] = { 153 BYTES_TO_T_UINT_8( 0x3D, 0x2A, 0x5C, 0x5C, 0x45, 0x29, 0xDD, 0x13 ), 154 BYTES_TO_T_UINT_8( 0x3E, 0xF0, 0xB8, 0xE0, 0xA2, 0x16, 0xFF, 0xFF ), 155 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 156 BYTES_TO_T_UINT_4( 0xFF, 0xFF, 0xFF, 0xFF ), 157 }; 158 #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */ 159 160 /* 161 * Domain parameters for secp256r1 162 */ 163 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) 164 static const mbedtls_mpi_uint secp256r1_p[] = { 165 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 166 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ), 167 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ), 168 BYTES_TO_T_UINT_8( 0x01, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ), 169 }; 170 static const mbedtls_mpi_uint secp256r1_b[] = { 171 BYTES_TO_T_UINT_8( 0x4B, 0x60, 0xD2, 0x27, 0x3E, 0x3C, 0xCE, 0x3B ), 172 BYTES_TO_T_UINT_8( 0xF6, 0xB0, 0x53, 0xCC, 0xB0, 0x06, 0x1D, 0x65 ), 173 BYTES_TO_T_UINT_8( 0xBC, 0x86, 0x98, 0x76, 0x55, 0xBD, 0xEB, 0xB3 ), 174 BYTES_TO_T_UINT_8( 0xE7, 0x93, 0x3A, 0xAA, 0xD8, 0x35, 0xC6, 0x5A ), 175 }; 176 static const mbedtls_mpi_uint secp256r1_gx[] = { 177 BYTES_TO_T_UINT_8( 0x96, 0xC2, 0x98, 0xD8, 0x45, 0x39, 0xA1, 0xF4 ), 178 BYTES_TO_T_UINT_8( 0xA0, 0x33, 0xEB, 0x2D, 0x81, 0x7D, 0x03, 0x77 ), 179 BYTES_TO_T_UINT_8( 0xF2, 0x40, 0xA4, 0x63, 0xE5, 0xE6, 0xBC, 0xF8 ), 180 BYTES_TO_T_UINT_8( 0x47, 0x42, 0x2C, 0xE1, 0xF2, 0xD1, 0x17, 0x6B ), 181 }; 182 static const mbedtls_mpi_uint secp256r1_gy[] = { 183 BYTES_TO_T_UINT_8( 0xF5, 0x51, 0xBF, 0x37, 0x68, 0x40, 0xB6, 0xCB ), 184 BYTES_TO_T_UINT_8( 0xCE, 0x5E, 0x31, 0x6B, 0x57, 0x33, 0xCE, 0x2B ), 185 BYTES_TO_T_UINT_8( 0x16, 0x9E, 0x0F, 0x7C, 0x4A, 0xEB, 0xE7, 0x8E ), 186 BYTES_TO_T_UINT_8( 0x9B, 0x7F, 0x1A, 0xFE, 0xE2, 0x42, 0xE3, 0x4F ), 187 }; 188 static const mbedtls_mpi_uint secp256r1_n[] = { 189 BYTES_TO_T_UINT_8( 0x51, 0x25, 0x63, 0xFC, 0xC2, 0xCA, 0xB9, 0xF3 ), 190 BYTES_TO_T_UINT_8( 0x84, 0x9E, 0x17, 0xA7, 0xAD, 0xFA, 0xE6, 0xBC ), 191 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 192 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ), 193 }; 194 #endif /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */ 195 196 /* 197 * Domain parameters for secp384r1 198 */ 199 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) 200 static const mbedtls_mpi_uint secp384r1_p[] = { 201 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ), 202 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ), 203 BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 204 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 205 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 206 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 207 }; 208 static const mbedtls_mpi_uint secp384r1_b[] = { 209 BYTES_TO_T_UINT_8( 0xEF, 0x2A, 0xEC, 0xD3, 0xED, 0xC8, 0x85, 0x2A ), 210 BYTES_TO_T_UINT_8( 0x9D, 0xD1, 0x2E, 0x8A, 0x8D, 0x39, 0x56, 0xC6 ), 211 BYTES_TO_T_UINT_8( 0x5A, 0x87, 0x13, 0x50, 0x8F, 0x08, 0x14, 0x03 ), 212 BYTES_TO_T_UINT_8( 0x12, 0x41, 0x81, 0xFE, 0x6E, 0x9C, 0x1D, 0x18 ), 213 BYTES_TO_T_UINT_8( 0x19, 0x2D, 0xF8, 0xE3, 0x6B, 0x05, 0x8E, 0x98 ), 214 BYTES_TO_T_UINT_8( 0xE4, 0xE7, 0x3E, 0xE2, 0xA7, 0x2F, 0x31, 0xB3 ), 215 }; 216 static const mbedtls_mpi_uint secp384r1_gx[] = { 217 BYTES_TO_T_UINT_8( 0xB7, 0x0A, 0x76, 0x72, 0x38, 0x5E, 0x54, 0x3A ), 218 BYTES_TO_T_UINT_8( 0x6C, 0x29, 0x55, 0xBF, 0x5D, 0xF2, 0x02, 0x55 ), 219 BYTES_TO_T_UINT_8( 0x38, 0x2A, 0x54, 0x82, 0xE0, 0x41, 0xF7, 0x59 ), 220 BYTES_TO_T_UINT_8( 0x98, 0x9B, 0xA7, 0x8B, 0x62, 0x3B, 0x1D, 0x6E ), 221 BYTES_TO_T_UINT_8( 0x74, 0xAD, 0x20, 0xF3, 0x1E, 0xC7, 0xB1, 0x8E ), 222 BYTES_TO_T_UINT_8( 0x37, 0x05, 0x8B, 0xBE, 0x22, 0xCA, 0x87, 0xAA ), 223 }; 224 static const mbedtls_mpi_uint secp384r1_gy[] = { 225 BYTES_TO_T_UINT_8( 0x5F, 0x0E, 0xEA, 0x90, 0x7C, 0x1D, 0x43, 0x7A ), 226 BYTES_TO_T_UINT_8( 0x9D, 0x81, 0x7E, 0x1D, 0xCE, 0xB1, 0x60, 0x0A ), 227 BYTES_TO_T_UINT_8( 0xC0, 0xB8, 0xF0, 0xB5, 0x13, 0x31, 0xDA, 0xE9 ), 228 BYTES_TO_T_UINT_8( 0x7C, 0x14, 0x9A, 0x28, 0xBD, 0x1D, 0xF4, 0xF8 ), 229 BYTES_TO_T_UINT_8( 0x29, 0xDC, 0x92, 0x92, 0xBF, 0x98, 0x9E, 0x5D ), 230 BYTES_TO_T_UINT_8( 0x6F, 0x2C, 0x26, 0x96, 0x4A, 0xDE, 0x17, 0x36 ), 231 }; 232 static const mbedtls_mpi_uint secp384r1_n[] = { 233 BYTES_TO_T_UINT_8( 0x73, 0x29, 0xC5, 0xCC, 0x6A, 0x19, 0xEC, 0xEC ), 234 BYTES_TO_T_UINT_8( 0x7A, 0xA7, 0xB0, 0x48, 0xB2, 0x0D, 0x1A, 0x58 ), 235 BYTES_TO_T_UINT_8( 0xDF, 0x2D, 0x37, 0xF4, 0x81, 0x4D, 0x63, 0xC7 ), 236 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 237 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 238 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 239 }; 240 #endif /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */ 241 242 /* 243 * Domain parameters for secp521r1 244 */ 245 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) 246 static const mbedtls_mpi_uint secp521r1_p[] = { 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_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 250 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 251 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 252 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 253 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 254 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 255 BYTES_TO_T_UINT_2( 0xFF, 0x01 ), 256 }; 257 static const mbedtls_mpi_uint secp521r1_b[] = { 258 BYTES_TO_T_UINT_8( 0x00, 0x3F, 0x50, 0x6B, 0xD4, 0x1F, 0x45, 0xEF ), 259 BYTES_TO_T_UINT_8( 0xF1, 0x34, 0x2C, 0x3D, 0x88, 0xDF, 0x73, 0x35 ), 260 BYTES_TO_T_UINT_8( 0x07, 0xBF, 0xB1, 0x3B, 0xBD, 0xC0, 0x52, 0x16 ), 261 BYTES_TO_T_UINT_8( 0x7B, 0x93, 0x7E, 0xEC, 0x51, 0x39, 0x19, 0x56 ), 262 BYTES_TO_T_UINT_8( 0xE1, 0x09, 0xF1, 0x8E, 0x91, 0x89, 0xB4, 0xB8 ), 263 BYTES_TO_T_UINT_8( 0xF3, 0x15, 0xB3, 0x99, 0x5B, 0x72, 0xDA, 0xA2 ), 264 BYTES_TO_T_UINT_8( 0xEE, 0x40, 0x85, 0xB6, 0xA0, 0x21, 0x9A, 0x92 ), 265 BYTES_TO_T_UINT_8( 0x1F, 0x9A, 0x1C, 0x8E, 0x61, 0xB9, 0x3E, 0x95 ), 266 BYTES_TO_T_UINT_2( 0x51, 0x00 ), 267 }; 268 static const mbedtls_mpi_uint secp521r1_gx[] = { 269 BYTES_TO_T_UINT_8( 0x66, 0xBD, 0xE5, 0xC2, 0x31, 0x7E, 0x7E, 0xF9 ), 270 BYTES_TO_T_UINT_8( 0x9B, 0x42, 0x6A, 0x85, 0xC1, 0xB3, 0x48, 0x33 ), 271 BYTES_TO_T_UINT_8( 0xDE, 0xA8, 0xFF, 0xA2, 0x27, 0xC1, 0x1D, 0xFE ), 272 BYTES_TO_T_UINT_8( 0x28, 0x59, 0xE7, 0xEF, 0x77, 0x5E, 0x4B, 0xA1 ), 273 BYTES_TO_T_UINT_8( 0xBA, 0x3D, 0x4D, 0x6B, 0x60, 0xAF, 0x28, 0xF8 ), 274 BYTES_TO_T_UINT_8( 0x21, 0xB5, 0x3F, 0x05, 0x39, 0x81, 0x64, 0x9C ), 275 BYTES_TO_T_UINT_8( 0x42, 0xB4, 0x95, 0x23, 0x66, 0xCB, 0x3E, 0x9E ), 276 BYTES_TO_T_UINT_8( 0xCD, 0xE9, 0x04, 0x04, 0xB7, 0x06, 0x8E, 0x85 ), 277 BYTES_TO_T_UINT_2( 0xC6, 0x00 ), 278 }; 279 static const mbedtls_mpi_uint secp521r1_gy[] = { 280 BYTES_TO_T_UINT_8( 0x50, 0x66, 0xD1, 0x9F, 0x76, 0x94, 0xBE, 0x88 ), 281 BYTES_TO_T_UINT_8( 0x40, 0xC2, 0x72, 0xA2, 0x86, 0x70, 0x3C, 0x35 ), 282 BYTES_TO_T_UINT_8( 0x61, 0x07, 0xAD, 0x3F, 0x01, 0xB9, 0x50, 0xC5 ), 283 BYTES_TO_T_UINT_8( 0x40, 0x26, 0xF4, 0x5E, 0x99, 0x72, 0xEE, 0x97 ), 284 BYTES_TO_T_UINT_8( 0x2C, 0x66, 0x3E, 0x27, 0x17, 0xBD, 0xAF, 0x17 ), 285 BYTES_TO_T_UINT_8( 0x68, 0x44, 0x9B, 0x57, 0x49, 0x44, 0xF5, 0x98 ), 286 BYTES_TO_T_UINT_8( 0xD9, 0x1B, 0x7D, 0x2C, 0xB4, 0x5F, 0x8A, 0x5C ), 287 BYTES_TO_T_UINT_8( 0x04, 0xC0, 0x3B, 0x9A, 0x78, 0x6A, 0x29, 0x39 ), 288 BYTES_TO_T_UINT_2( 0x18, 0x01 ), 289 }; 290 static const mbedtls_mpi_uint secp521r1_n[] = { 291 BYTES_TO_T_UINT_8( 0x09, 0x64, 0x38, 0x91, 0x1E, 0xB7, 0x6F, 0xBB ), 292 BYTES_TO_T_UINT_8( 0xAE, 0x47, 0x9C, 0x89, 0xB8, 0xC9, 0xB5, 0x3B ), 293 BYTES_TO_T_UINT_8( 0xD0, 0xA5, 0x09, 0xF7, 0x48, 0x01, 0xCC, 0x7F ), 294 BYTES_TO_T_UINT_8( 0x6B, 0x96, 0x2F, 0xBF, 0x83, 0x87, 0x86, 0x51 ), 295 BYTES_TO_T_UINT_8( 0xFA, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 296 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 297 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 298 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 299 BYTES_TO_T_UINT_2( 0xFF, 0x01 ), 300 }; 301 #endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */ 302 303 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) 304 static const mbedtls_mpi_uint secp192k1_p[] = { 305 BYTES_TO_T_UINT_8( 0x37, 0xEE, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ), 306 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 307 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 308 }; 309 static const mbedtls_mpi_uint secp192k1_a[] = { 310 BYTES_TO_T_UINT_2( 0x00, 0x00 ), 311 }; 312 static const mbedtls_mpi_uint secp192k1_b[] = { 313 BYTES_TO_T_UINT_2( 0x03, 0x00 ), 314 }; 315 static const mbedtls_mpi_uint secp192k1_gx[] = { 316 BYTES_TO_T_UINT_8( 0x7D, 0x6C, 0xE0, 0xEA, 0xB1, 0xD1, 0xA5, 0x1D ), 317 BYTES_TO_T_UINT_8( 0x34, 0xF4, 0xB7, 0x80, 0x02, 0x7D, 0xB0, 0x26 ), 318 BYTES_TO_T_UINT_8( 0xAE, 0xE9, 0x57, 0xC0, 0x0E, 0xF1, 0x4F, 0xDB ), 319 }; 320 static const mbedtls_mpi_uint secp192k1_gy[] = { 321 BYTES_TO_T_UINT_8( 0x9D, 0x2F, 0x5E, 0xD9, 0x88, 0xAA, 0x82, 0x40 ), 322 BYTES_TO_T_UINT_8( 0x34, 0x86, 0xBE, 0x15, 0xD0, 0x63, 0x41, 0x84 ), 323 BYTES_TO_T_UINT_8( 0xA7, 0x28, 0x56, 0x9C, 0x6D, 0x2F, 0x2F, 0x9B ), 324 }; 325 static const mbedtls_mpi_uint secp192k1_n[] = { 326 BYTES_TO_T_UINT_8( 0x8D, 0xFD, 0xDE, 0x74, 0x6A, 0x46, 0x69, 0x0F ), 327 BYTES_TO_T_UINT_8( 0x17, 0xFC, 0xF2, 0x26, 0xFE, 0xFF, 0xFF, 0xFF ), 328 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 329 }; 330 #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */ 331 332 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) 333 static const mbedtls_mpi_uint secp224k1_p[] = { 334 BYTES_TO_T_UINT_8( 0x6D, 0xE5, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ), 335 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 336 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 337 BYTES_TO_T_UINT_4( 0xFF, 0xFF, 0xFF, 0xFF ), 338 }; 339 static const mbedtls_mpi_uint secp224k1_a[] = { 340 BYTES_TO_T_UINT_2( 0x00, 0x00 ), 341 }; 342 static const mbedtls_mpi_uint secp224k1_b[] = { 343 BYTES_TO_T_UINT_2( 0x05, 0x00 ), 344 }; 345 static const mbedtls_mpi_uint secp224k1_gx[] = { 346 BYTES_TO_T_UINT_8( 0x5C, 0xA4, 0xB7, 0xB6, 0x0E, 0x65, 0x7E, 0x0F ), 347 BYTES_TO_T_UINT_8( 0xA9, 0x75, 0x70, 0xE4, 0xE9, 0x67, 0xA4, 0x69 ), 348 BYTES_TO_T_UINT_8( 0xA1, 0x28, 0xFC, 0x30, 0xDF, 0x99, 0xF0, 0x4D ), 349 BYTES_TO_T_UINT_4( 0x33, 0x5B, 0x45, 0xA1 ), 350 }; 351 static const mbedtls_mpi_uint secp224k1_gy[] = { 352 BYTES_TO_T_UINT_8( 0xA5, 0x61, 0x6D, 0x55, 0xDB, 0x4B, 0xCA, 0xE2 ), 353 BYTES_TO_T_UINT_8( 0x59, 0xBD, 0xB0, 0xC0, 0xF7, 0x19, 0xE3, 0xF7 ), 354 BYTES_TO_T_UINT_8( 0xD6, 0xFB, 0xCA, 0x82, 0x42, 0x34, 0xBA, 0x7F ), 355 BYTES_TO_T_UINT_4( 0xED, 0x9F, 0x08, 0x7E ), 356 }; 357 static const mbedtls_mpi_uint secp224k1_n[] = { 358 BYTES_TO_T_UINT_8( 0xF7, 0xB1, 0x9F, 0x76, 0x71, 0xA9, 0xF0, 0xCA ), 359 BYTES_TO_T_UINT_8( 0x84, 0x61, 0xEC, 0xD2, 0xE8, 0xDC, 0x01, 0x00 ), 360 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ), 361 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ), 362 }; 363 #endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */ 364 365 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) 366 static const mbedtls_mpi_uint secp256k1_p[] = { 367 BYTES_TO_T_UINT_8( 0x2F, 0xFC, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ), 368 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 369 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 370 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 371 }; 372 static const mbedtls_mpi_uint secp256k1_a[] = { 373 BYTES_TO_T_UINT_2( 0x00, 0x00 ), 374 }; 375 static const mbedtls_mpi_uint secp256k1_b[] = { 376 BYTES_TO_T_UINT_2( 0x07, 0x00 ), 377 }; 378 static const mbedtls_mpi_uint secp256k1_gx[] = { 379 BYTES_TO_T_UINT_8( 0x98, 0x17, 0xF8, 0x16, 0x5B, 0x81, 0xF2, 0x59 ), 380 BYTES_TO_T_UINT_8( 0xD9, 0x28, 0xCE, 0x2D, 0xDB, 0xFC, 0x9B, 0x02 ), 381 BYTES_TO_T_UINT_8( 0x07, 0x0B, 0x87, 0xCE, 0x95, 0x62, 0xA0, 0x55 ), 382 BYTES_TO_T_UINT_8( 0xAC, 0xBB, 0xDC, 0xF9, 0x7E, 0x66, 0xBE, 0x79 ), 383 }; 384 static const mbedtls_mpi_uint secp256k1_gy[] = { 385 BYTES_TO_T_UINT_8( 0xB8, 0xD4, 0x10, 0xFB, 0x8F, 0xD0, 0x47, 0x9C ), 386 BYTES_TO_T_UINT_8( 0x19, 0x54, 0x85, 0xA6, 0x48, 0xB4, 0x17, 0xFD ), 387 BYTES_TO_T_UINT_8( 0xA8, 0x08, 0x11, 0x0E, 0xFC, 0xFB, 0xA4, 0x5D ), 388 BYTES_TO_T_UINT_8( 0x65, 0xC4, 0xA3, 0x26, 0x77, 0xDA, 0x3A, 0x48 ), 389 }; 390 static const mbedtls_mpi_uint secp256k1_n[] = { 391 BYTES_TO_T_UINT_8( 0x41, 0x41, 0x36, 0xD0, 0x8C, 0x5E, 0xD2, 0xBF ), 392 BYTES_TO_T_UINT_8( 0x3B, 0xA0, 0x48, 0xAF, 0xE6, 0xDC, 0xAE, 0xBA ), 393 BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 394 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 395 }; 396 #endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */ 397 398 /* 399 * Domain parameters for brainpoolP256r1 (RFC 5639 3.4) 400 */ 401 #if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) 402 static const mbedtls_mpi_uint brainpoolP256r1_p[] = { 403 BYTES_TO_T_UINT_8( 0x77, 0x53, 0x6E, 0x1F, 0x1D, 0x48, 0x13, 0x20 ), 404 BYTES_TO_T_UINT_8( 0x28, 0x20, 0x26, 0xD5, 0x23, 0xF6, 0x3B, 0x6E ), 405 BYTES_TO_T_UINT_8( 0x72, 0x8D, 0x83, 0x9D, 0x90, 0x0A, 0x66, 0x3E ), 406 BYTES_TO_T_UINT_8( 0xBC, 0xA9, 0xEE, 0xA1, 0xDB, 0x57, 0xFB, 0xA9 ), 407 }; 408 static const mbedtls_mpi_uint brainpoolP256r1_a[] = { 409 BYTES_TO_T_UINT_8( 0xD9, 0xB5, 0x30, 0xF3, 0x44, 0x4B, 0x4A, 0xE9 ), 410 BYTES_TO_T_UINT_8( 0x6C, 0x5C, 0xDC, 0x26, 0xC1, 0x55, 0x80, 0xFB ), 411 BYTES_TO_T_UINT_8( 0xE7, 0xFF, 0x7A, 0x41, 0x30, 0x75, 0xF6, 0xEE ), 412 BYTES_TO_T_UINT_8( 0x57, 0x30, 0x2C, 0xFC, 0x75, 0x09, 0x5A, 0x7D ), 413 }; 414 static const mbedtls_mpi_uint brainpoolP256r1_b[] = { 415 BYTES_TO_T_UINT_8( 0xB6, 0x07, 0x8C, 0xFF, 0x18, 0xDC, 0xCC, 0x6B ), 416 BYTES_TO_T_UINT_8( 0xCE, 0xE1, 0xF7, 0x5C, 0x29, 0x16, 0x84, 0x95 ), 417 BYTES_TO_T_UINT_8( 0xBF, 0x7C, 0xD7, 0xBB, 0xD9, 0xB5, 0x30, 0xF3 ), 418 BYTES_TO_T_UINT_8( 0x44, 0x4B, 0x4A, 0xE9, 0x6C, 0x5C, 0xDC, 0x26 ), 419 }; 420 static const mbedtls_mpi_uint brainpoolP256r1_gx[] = { 421 BYTES_TO_T_UINT_8( 0x62, 0x32, 0xCE, 0x9A, 0xBD, 0x53, 0x44, 0x3A ), 422 BYTES_TO_T_UINT_8( 0xC2, 0x23, 0xBD, 0xE3, 0xE1, 0x27, 0xDE, 0xB9 ), 423 BYTES_TO_T_UINT_8( 0xAF, 0xB7, 0x81, 0xFC, 0x2F, 0x48, 0x4B, 0x2C ), 424 BYTES_TO_T_UINT_8( 0xCB, 0x57, 0x7E, 0xCB, 0xB9, 0xAE, 0xD2, 0x8B ), 425 }; 426 static const mbedtls_mpi_uint brainpoolP256r1_gy[] = { 427 BYTES_TO_T_UINT_8( 0x97, 0x69, 0x04, 0x2F, 0xC7, 0x54, 0x1D, 0x5C ), 428 BYTES_TO_T_UINT_8( 0x54, 0x8E, 0xED, 0x2D, 0x13, 0x45, 0x77, 0xC2 ), 429 BYTES_TO_T_UINT_8( 0xC9, 0x1D, 0x61, 0x14, 0x1A, 0x46, 0xF8, 0x97 ), 430 BYTES_TO_T_UINT_8( 0xFD, 0xC4, 0xDA, 0xC3, 0x35, 0xF8, 0x7E, 0x54 ), 431 }; 432 static const mbedtls_mpi_uint brainpoolP256r1_n[] = { 433 BYTES_TO_T_UINT_8( 0xA7, 0x56, 0x48, 0x97, 0x82, 0x0E, 0x1E, 0x90 ), 434 BYTES_TO_T_UINT_8( 0xF7, 0xA6, 0x61, 0xB5, 0xA3, 0x7A, 0x39, 0x8C ), 435 BYTES_TO_T_UINT_8( 0x71, 0x8D, 0x83, 0x9D, 0x90, 0x0A, 0x66, 0x3E ), 436 BYTES_TO_T_UINT_8( 0xBC, 0xA9, 0xEE, 0xA1, 0xDB, 0x57, 0xFB, 0xA9 ), 437 }; 438 #endif /* MBEDTLS_ECP_DP_BP256R1_ENABLED */ 439 440 /* 441 * Domain parameters for brainpoolP384r1 (RFC 5639 3.6) 442 */ 443 #if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) 444 static const mbedtls_mpi_uint brainpoolP384r1_p[] = { 445 BYTES_TO_T_UINT_8( 0x53, 0xEC, 0x07, 0x31, 0x13, 0x00, 0x47, 0x87 ), 446 BYTES_TO_T_UINT_8( 0x71, 0x1A, 0x1D, 0x90, 0x29, 0xA7, 0xD3, 0xAC ), 447 BYTES_TO_T_UINT_8( 0x23, 0x11, 0xB7, 0x7F, 0x19, 0xDA, 0xB1, 0x12 ), 448 BYTES_TO_T_UINT_8( 0xB4, 0x56, 0x54, 0xED, 0x09, 0x71, 0x2F, 0x15 ), 449 BYTES_TO_T_UINT_8( 0xDF, 0x41, 0xE6, 0x50, 0x7E, 0x6F, 0x5D, 0x0F ), 450 BYTES_TO_T_UINT_8( 0x28, 0x6D, 0x38, 0xA3, 0x82, 0x1E, 0xB9, 0x8C ), 451 }; 452 static const mbedtls_mpi_uint brainpoolP384r1_a[] = { 453 BYTES_TO_T_UINT_8( 0x26, 0x28, 0xCE, 0x22, 0xDD, 0xC7, 0xA8, 0x04 ), 454 BYTES_TO_T_UINT_8( 0xEB, 0xD4, 0x3A, 0x50, 0x4A, 0x81, 0xA5, 0x8A ), 455 BYTES_TO_T_UINT_8( 0x0F, 0xF9, 0x91, 0xBA, 0xEF, 0x65, 0x91, 0x13 ), 456 BYTES_TO_T_UINT_8( 0x87, 0x27, 0xB2, 0x4F, 0x8E, 0xA2, 0xBE, 0xC2 ), 457 BYTES_TO_T_UINT_8( 0xA0, 0xAF, 0x05, 0xCE, 0x0A, 0x08, 0x72, 0x3C ), 458 BYTES_TO_T_UINT_8( 0x0C, 0x15, 0x8C, 0x3D, 0xC6, 0x82, 0xC3, 0x7B ), 459 }; 460 static const mbedtls_mpi_uint brainpoolP384r1_b[] = { 461 BYTES_TO_T_UINT_8( 0x11, 0x4C, 0x50, 0xFA, 0x96, 0x86, 0xB7, 0x3A ), 462 BYTES_TO_T_UINT_8( 0x94, 0xC9, 0xDB, 0x95, 0x02, 0x39, 0xB4, 0x7C ), 463 BYTES_TO_T_UINT_8( 0xD5, 0x62, 0xEB, 0x3E, 0xA5, 0x0E, 0x88, 0x2E ), 464 BYTES_TO_T_UINT_8( 0xA6, 0xD2, 0xDC, 0x07, 0xE1, 0x7D, 0xB7, 0x2F ), 465 BYTES_TO_T_UINT_8( 0x7C, 0x44, 0xF0, 0x16, 0x54, 0xB5, 0x39, 0x8B ), 466 BYTES_TO_T_UINT_8( 0x26, 0x28, 0xCE, 0x22, 0xDD, 0xC7, 0xA8, 0x04 ), 467 }; 468 static const mbedtls_mpi_uint brainpoolP384r1_gx[] = { 469 BYTES_TO_T_UINT_8( 0x1E, 0xAF, 0xD4, 0x47, 0xE2, 0xB2, 0x87, 0xEF ), 470 BYTES_TO_T_UINT_8( 0xAA, 0x46, 0xD6, 0x36, 0x34, 0xE0, 0x26, 0xE8 ), 471 BYTES_TO_T_UINT_8( 0xE8, 0x10, 0xBD, 0x0C, 0xFE, 0xCA, 0x7F, 0xDB ), 472 BYTES_TO_T_UINT_8( 0xE3, 0x4F, 0xF1, 0x7E, 0xE7, 0xA3, 0x47, 0x88 ), 473 BYTES_TO_T_UINT_8( 0x6B, 0x3F, 0xC1, 0xB7, 0x81, 0x3A, 0xA6, 0xA2 ), 474 BYTES_TO_T_UINT_8( 0xFF, 0x45, 0xCF, 0x68, 0xF0, 0x64, 0x1C, 0x1D ), 475 }; 476 static const mbedtls_mpi_uint brainpoolP384r1_gy[] = { 477 BYTES_TO_T_UINT_8( 0x15, 0x53, 0x3C, 0x26, 0x41, 0x03, 0x82, 0x42 ), 478 BYTES_TO_T_UINT_8( 0x11, 0x81, 0x91, 0x77, 0x21, 0x46, 0x46, 0x0E ), 479 BYTES_TO_T_UINT_8( 0x28, 0x29, 0x91, 0xF9, 0x4F, 0x05, 0x9C, 0xE1 ), 480 BYTES_TO_T_UINT_8( 0x64, 0x58, 0xEC, 0xFE, 0x29, 0x0B, 0xB7, 0x62 ), 481 BYTES_TO_T_UINT_8( 0x52, 0xD5, 0xCF, 0x95, 0x8E, 0xEB, 0xB1, 0x5C ), 482 BYTES_TO_T_UINT_8( 0xA4, 0xC2, 0xF9, 0x20, 0x75, 0x1D, 0xBE, 0x8A ), 483 }; 484 static const mbedtls_mpi_uint brainpoolP384r1_n[] = { 485 BYTES_TO_T_UINT_8( 0x65, 0x65, 0x04, 0xE9, 0x02, 0x32, 0x88, 0x3B ), 486 BYTES_TO_T_UINT_8( 0x10, 0xC3, 0x7F, 0x6B, 0xAF, 0xB6, 0x3A, 0xCF ), 487 BYTES_TO_T_UINT_8( 0xA7, 0x25, 0x04, 0xAC, 0x6C, 0x6E, 0x16, 0x1F ), 488 BYTES_TO_T_UINT_8( 0xB3, 0x56, 0x54, 0xED, 0x09, 0x71, 0x2F, 0x15 ), 489 BYTES_TO_T_UINT_8( 0xDF, 0x41, 0xE6, 0x50, 0x7E, 0x6F, 0x5D, 0x0F ), 490 BYTES_TO_T_UINT_8( 0x28, 0x6D, 0x38, 0xA3, 0x82, 0x1E, 0xB9, 0x8C ), 491 }; 492 #endif /* MBEDTLS_ECP_DP_BP384R1_ENABLED */ 493 494 /* 495 * Domain parameters for brainpoolP512r1 (RFC 5639 3.7) 496 */ 497 #if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) 498 static const mbedtls_mpi_uint brainpoolP512r1_p[] = { 499 BYTES_TO_T_UINT_8( 0xF3, 0x48, 0x3A, 0x58, 0x56, 0x60, 0xAA, 0x28 ), 500 BYTES_TO_T_UINT_8( 0x85, 0xC6, 0x82, 0x2D, 0x2F, 0xFF, 0x81, 0x28 ), 501 BYTES_TO_T_UINT_8( 0xE6, 0x80, 0xA3, 0xE6, 0x2A, 0xA1, 0xCD, 0xAE ), 502 BYTES_TO_T_UINT_8( 0x42, 0x68, 0xC6, 0x9B, 0x00, 0x9B, 0x4D, 0x7D ), 503 BYTES_TO_T_UINT_8( 0x71, 0x08, 0x33, 0x70, 0xCA, 0x9C, 0x63, 0xD6 ), 504 BYTES_TO_T_UINT_8( 0x0E, 0xD2, 0xC9, 0xB3, 0xB3, 0x8D, 0x30, 0xCB ), 505 BYTES_TO_T_UINT_8( 0x07, 0xFC, 0xC9, 0x33, 0xAE, 0xE6, 0xD4, 0x3F ), 506 BYTES_TO_T_UINT_8( 0x8B, 0xC4, 0xE9, 0xDB, 0xB8, 0x9D, 0xDD, 0xAA ), 507 }; 508 static const mbedtls_mpi_uint brainpoolP512r1_a[] = { 509 BYTES_TO_T_UINT_8( 0xCA, 0x94, 0xFC, 0x77, 0x4D, 0xAC, 0xC1, 0xE7 ), 510 BYTES_TO_T_UINT_8( 0xB9, 0xC7, 0xF2, 0x2B, 0xA7, 0x17, 0x11, 0x7F ), 511 BYTES_TO_T_UINT_8( 0xB5, 0xC8, 0x9A, 0x8B, 0xC9, 0xF1, 0x2E, 0x0A ), 512 BYTES_TO_T_UINT_8( 0xA1, 0x3A, 0x25, 0xA8, 0x5A, 0x5D, 0xED, 0x2D ), 513 BYTES_TO_T_UINT_8( 0xBC, 0x63, 0x98, 0xEA, 0xCA, 0x41, 0x34, 0xA8 ), 514 BYTES_TO_T_UINT_8( 0x10, 0x16, 0xF9, 0x3D, 0x8D, 0xDD, 0xCB, 0x94 ), 515 BYTES_TO_T_UINT_8( 0xC5, 0x4C, 0x23, 0xAC, 0x45, 0x71, 0x32, 0xE2 ), 516 BYTES_TO_T_UINT_8( 0x89, 0x3B, 0x60, 0x8B, 0x31, 0xA3, 0x30, 0x78 ), 517 }; 518 static const mbedtls_mpi_uint brainpoolP512r1_b[] = { 519 BYTES_TO_T_UINT_8( 0x23, 0xF7, 0x16, 0x80, 0x63, 0xBD, 0x09, 0x28 ), 520 BYTES_TO_T_UINT_8( 0xDD, 0xE5, 0xBA, 0x5E, 0xB7, 0x50, 0x40, 0x98 ), 521 BYTES_TO_T_UINT_8( 0x67, 0x3E, 0x08, 0xDC, 0xCA, 0x94, 0xFC, 0x77 ), 522 BYTES_TO_T_UINT_8( 0x4D, 0xAC, 0xC1, 0xE7, 0xB9, 0xC7, 0xF2, 0x2B ), 523 BYTES_TO_T_UINT_8( 0xA7, 0x17, 0x11, 0x7F, 0xB5, 0xC8, 0x9A, 0x8B ), 524 BYTES_TO_T_UINT_8( 0xC9, 0xF1, 0x2E, 0x0A, 0xA1, 0x3A, 0x25, 0xA8 ), 525 BYTES_TO_T_UINT_8( 0x5A, 0x5D, 0xED, 0x2D, 0xBC, 0x63, 0x98, 0xEA ), 526 BYTES_TO_T_UINT_8( 0xCA, 0x41, 0x34, 0xA8, 0x10, 0x16, 0xF9, 0x3D ), 527 }; 528 static const mbedtls_mpi_uint brainpoolP512r1_gx[] = { 529 BYTES_TO_T_UINT_8( 0x22, 0xF8, 0xB9, 0xBC, 0x09, 0x22, 0x35, 0x8B ), 530 BYTES_TO_T_UINT_8( 0x68, 0x5E, 0x6A, 0x40, 0x47, 0x50, 0x6D, 0x7C ), 531 BYTES_TO_T_UINT_8( 0x5F, 0x7D, 0xB9, 0x93, 0x7B, 0x68, 0xD1, 0x50 ), 532 BYTES_TO_T_UINT_8( 0x8D, 0xD4, 0xD0, 0xE2, 0x78, 0x1F, 0x3B, 0xFF ), 533 BYTES_TO_T_UINT_8( 0x8E, 0x09, 0xD0, 0xF4, 0xEE, 0x62, 0x3B, 0xB4 ), 534 BYTES_TO_T_UINT_8( 0xC1, 0x16, 0xD9, 0xB5, 0x70, 0x9F, 0xED, 0x85 ), 535 BYTES_TO_T_UINT_8( 0x93, 0x6A, 0x4C, 0x9C, 0x2E, 0x32, 0x21, 0x5A ), 536 BYTES_TO_T_UINT_8( 0x64, 0xD9, 0x2E, 0xD8, 0xBD, 0xE4, 0xAE, 0x81 ), 537 }; 538 static const mbedtls_mpi_uint brainpoolP512r1_gy[] = { 539 BYTES_TO_T_UINT_8( 0x92, 0x08, 0xD8, 0x3A, 0x0F, 0x1E, 0xCD, 0x78 ), 540 BYTES_TO_T_UINT_8( 0x06, 0x54, 0xF0, 0xA8, 0x2F, 0x2B, 0xCA, 0xD1 ), 541 BYTES_TO_T_UINT_8( 0xAE, 0x63, 0x27, 0x8A, 0xD8, 0x4B, 0xCA, 0x5B ), 542 BYTES_TO_T_UINT_8( 0x5E, 0x48, 0x5F, 0x4A, 0x49, 0xDE, 0xDC, 0xB2 ), 543 BYTES_TO_T_UINT_8( 0x11, 0x81, 0x1F, 0x88, 0x5B, 0xC5, 0x00, 0xA0 ), 544 BYTES_TO_T_UINT_8( 0x1A, 0x7B, 0xA5, 0x24, 0x00, 0xF7, 0x09, 0xF2 ), 545 BYTES_TO_T_UINT_8( 0xFD, 0x22, 0x78, 0xCF, 0xA9, 0xBF, 0xEA, 0xC0 ), 546 BYTES_TO_T_UINT_8( 0xEC, 0x32, 0x63, 0x56, 0x5D, 0x38, 0xDE, 0x7D ), 547 }; 548 static const mbedtls_mpi_uint brainpoolP512r1_n[] = { 549 BYTES_TO_T_UINT_8( 0x69, 0x00, 0xA9, 0x9C, 0x82, 0x96, 0x87, 0xB5 ), 550 BYTES_TO_T_UINT_8( 0xDD, 0xDA, 0x5D, 0x08, 0x81, 0xD3, 0xB1, 0x1D ), 551 BYTES_TO_T_UINT_8( 0x47, 0x10, 0xAC, 0x7F, 0x19, 0x61, 0x86, 0x41 ), 552 BYTES_TO_T_UINT_8( 0x19, 0x26, 0xA9, 0x4C, 0x41, 0x5C, 0x3E, 0x55 ), 553 BYTES_TO_T_UINT_8( 0x70, 0x08, 0x33, 0x70, 0xCA, 0x9C, 0x63, 0xD6 ), 554 BYTES_TO_T_UINT_8( 0x0E, 0xD2, 0xC9, 0xB3, 0xB3, 0x8D, 0x30, 0xCB ), 555 BYTES_TO_T_UINT_8( 0x07, 0xFC, 0xC9, 0x33, 0xAE, 0xE6, 0xD4, 0x3F ), 556 BYTES_TO_T_UINT_8( 0x8B, 0xC4, 0xE9, 0xDB, 0xB8, 0x9D, 0xDD, 0xAA ), 557 }; 558 #endif /* MBEDTLS_ECP_DP_BP512R1_ENABLED */ 559 560 /* 561 * Domain parameters for SM2 (GM/T 0003 Part 5) 562 */ 563 #if defined(MBEDTLS_ECP_DP_SM2_ENABLED) 564 static const mbedtls_mpi_uint sm2_p[] = { 565 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 566 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ), 567 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 568 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ), 569 }; 570 static const mbedtls_mpi_uint sm2_a[] = { 571 BYTES_TO_T_UINT_8( 0xFC, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 572 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ), 573 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 574 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ), 575 }; 576 static const mbedtls_mpi_uint sm2_b[] = { 577 BYTES_TO_T_UINT_8( 0x93, 0x0E, 0x94, 0x4D, 0x41, 0xBD, 0xBC, 0xDD ), 578 BYTES_TO_T_UINT_8( 0x92, 0x8F, 0xAB, 0x15, 0xF5, 0x89, 0x97, 0xF3 ), 579 BYTES_TO_T_UINT_8( 0xA7, 0x09, 0x65, 0xCF, 0x4B, 0x9E, 0x5A, 0x4D ), 580 BYTES_TO_T_UINT_8( 0x34, 0x5E, 0x9F, 0x9D, 0x9E, 0xFA, 0xE9, 0x28 ), 581 }; 582 static const mbedtls_mpi_uint sm2_gx[] = { 583 BYTES_TO_T_UINT_8( 0xC7, 0x74, 0x4C, 0x33, 0x89, 0x45, 0x5A, 0x71 ), 584 BYTES_TO_T_UINT_8( 0xE1, 0x0B, 0x66, 0xF2, 0xBF, 0x0B, 0xE3, 0x8F ), 585 BYTES_TO_T_UINT_8( 0x94, 0xC9, 0x39, 0x6A, 0x46, 0x04, 0x99, 0x5F ), 586 BYTES_TO_T_UINT_8( 0x19, 0x81, 0x19, 0x1F, 0x2C, 0xAE, 0xC4, 0x32 ), 587 }; 588 static const mbedtls_mpi_uint sm2_gy[] = { 589 BYTES_TO_T_UINT_8( 0xA0, 0xF0, 0x39, 0x21, 0xE5, 0x32, 0xDF, 0x02 ), 590 BYTES_TO_T_UINT_8( 0x40, 0x47, 0x2A, 0xC6, 0x7C, 0x87, 0xA9, 0xD0 ), 591 BYTES_TO_T_UINT_8( 0x53, 0x21, 0x69, 0x6B, 0xE3, 0xCE, 0xBD, 0x59 ), 592 BYTES_TO_T_UINT_8( 0x9C, 0x77, 0xF6, 0xF4, 0xA2, 0x36, 0x37, 0xBC ), 593 }; 594 static const mbedtls_mpi_uint sm2_n[] = { 595 BYTES_TO_T_UINT_8( 0x23, 0x41, 0xD5, 0x39, 0x09, 0xF4, 0xBB, 0x53 ), 596 BYTES_TO_T_UINT_8( 0x2B, 0x05, 0xC6, 0x21, 0x6B, 0xDF, 0x03, 0x72 ), 597 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 598 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ), 599 }; 600 #endif /* MBEDTLS_ECP_DP_SM2_ENABLED */ 601 /* 602 * Create an MPI from embedded constants 603 * (assumes len is an exact multiple of sizeof mbedtls_mpi_uint) 604 */ 605 static inline void ecp_mpi_load( mbedtls_mpi *X, const mbedtls_mpi_uint *p, size_t len ) 606 { 607 X->s = 1; 608 X->n = len / sizeof( mbedtls_mpi_uint ); 609 X->p = (mbedtls_mpi_uint *) p; 610 } 611 612 /* 613 * Set an MPI to static value 1 614 */ 615 static inline void ecp_mpi_set1( mbedtls_mpi *X ) 616 { 617 static mbedtls_mpi_uint one[] = { 1 }; 618 X->s = 1; 619 X->n = 1; 620 X->p = one; 621 } 622 623 /* 624 * Make group available from embedded constants 625 */ 626 static int ecp_group_load( mbedtls_ecp_group *grp, 627 const mbedtls_mpi_uint *p, size_t plen, 628 const mbedtls_mpi_uint *a, size_t alen, 629 const mbedtls_mpi_uint *b, size_t blen, 630 const mbedtls_mpi_uint *gx, size_t gxlen, 631 const mbedtls_mpi_uint *gy, size_t gylen, 632 const mbedtls_mpi_uint *n, size_t nlen) 633 { 634 ecp_mpi_load( &grp->P, p, plen ); 635 if( a != NULL ) 636 ecp_mpi_load( &grp->A, a, alen ); 637 ecp_mpi_load( &grp->B, b, blen ); 638 ecp_mpi_load( &grp->N, n, nlen ); 639 640 ecp_mpi_load( &grp->G.X, gx, gxlen ); 641 ecp_mpi_load( &grp->G.Y, gy, gylen ); 642 ecp_mpi_set1( &grp->G.Z ); 643 644 grp->pbits = mbedtls_mpi_bitlen( &grp->P ); 645 grp->nbits = mbedtls_mpi_bitlen( &grp->N ); 646 647 grp->h = 1; 648 649 return( 0 ); 650 } 651 652 #if defined(MBEDTLS_ECP_NIST_OPTIM) 653 /* Forward declarations */ 654 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) 655 static int ecp_mod_p192( mbedtls_mpi * ); 656 #endif 657 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) 658 static int ecp_mod_p224( mbedtls_mpi * ); 659 #endif 660 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) 661 static int ecp_mod_p256( mbedtls_mpi * ); 662 #endif 663 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) 664 static int ecp_mod_p384( mbedtls_mpi * ); 665 #endif 666 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) 667 static int ecp_mod_p521( mbedtls_mpi * ); 668 #endif 669 670 #define NIST_MODP( P ) grp->modp = ecp_mod_ ## P; 671 #else 672 #define NIST_MODP( P ) 673 #endif /* MBEDTLS_ECP_NIST_OPTIM */ 674 675 /* Additional forward declarations */ 676 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) 677 static int ecp_mod_p255( mbedtls_mpi * ); 678 #endif 679 #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) 680 static int ecp_mod_p448( mbedtls_mpi * ); 681 #endif 682 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) 683 static int ecp_mod_p192k1( mbedtls_mpi * ); 684 #endif 685 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) 686 static int ecp_mod_p224k1( mbedtls_mpi * ); 687 #endif 688 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) 689 static int ecp_mod_p256k1( mbedtls_mpi * ); 690 #endif 691 692 #define LOAD_GROUP_A( G ) ecp_group_load( grp, \ 693 G ## _p, sizeof( G ## _p ), \ 694 G ## _a, sizeof( G ## _a ), \ 695 G ## _b, sizeof( G ## _b ), \ 696 G ## _gx, sizeof( G ## _gx ), \ 697 G ## _gy, sizeof( G ## _gy ), \ 698 G ## _n, sizeof( G ## _n ) ) 699 700 #define LOAD_GROUP( G ) ecp_group_load( grp, \ 701 G ## _p, sizeof( G ## _p ), \ 702 NULL, 0, \ 703 G ## _b, sizeof( G ## _b ), \ 704 G ## _gx, sizeof( G ## _gx ), \ 705 G ## _gy, sizeof( G ## _gy ), \ 706 G ## _n, sizeof( G ## _n ) ) 707 708 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) 709 /* 710 * Specialized function for creating the Curve25519 group 711 */ 712 static int ecp_use_curve25519( mbedtls_ecp_group *grp ) 713 { 714 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 715 716 /* Actually ( A + 2 ) / 4 */ 717 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &grp->A, 16, "01DB42" ) ); 718 719 /* P = 2^255 - 19 */ 720 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->P, 1 ) ); 721 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &grp->P, 255 ) ); 722 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &grp->P, &grp->P, 19 ) ); 723 grp->pbits = mbedtls_mpi_bitlen( &grp->P ); 724 725 /* N = 2^252 + 27742317777372353535851937790883648493 */ 726 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &grp->N, 16, 727 "14DEF9DEA2F79CD65812631A5CF5D3ED" ) ); 728 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &grp->N, 252, 1 ) ); 729 730 /* Y intentionally not set, since we use x/z coordinates. 731 * This is used as a marker to identify Montgomery curves! */ 732 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.X, 9 ) ); 733 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.Z, 1 ) ); 734 mbedtls_mpi_free( &grp->G.Y ); 735 736 /* Actually, the required msb for private keys */ 737 grp->nbits = 254; 738 739 cleanup: 740 if( ret != 0 ) 741 mbedtls_ecp_group_free( grp ); 742 743 return( ret ); 744 } 745 #endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */ 746 747 #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) 748 /* 749 * Specialized function for creating the Curve448 group 750 */ 751 static int ecp_use_curve448( mbedtls_ecp_group *grp ) 752 { 753 mbedtls_mpi Ns; 754 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 755 756 mbedtls_mpi_init( &Ns ); 757 758 /* Actually ( A + 2 ) / 4 */ 759 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &grp->A, 16, "98AA" ) ); 760 761 /* P = 2^448 - 2^224 - 1 */ 762 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->P, 1 ) ); 763 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &grp->P, 224 ) ); 764 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &grp->P, &grp->P, 1 ) ); 765 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &grp->P, 224 ) ); 766 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &grp->P, &grp->P, 1 ) ); 767 grp->pbits = mbedtls_mpi_bitlen( &grp->P ); 768 769 /* Y intentionally not set, since we use x/z coordinates. 770 * This is used as a marker to identify Montgomery curves! */ 771 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.X, 5 ) ); 772 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.Z, 1 ) ); 773 mbedtls_mpi_free( &grp->G.Y ); 774 775 /* N = 2^446 - 13818066809895115352007386748515426880336692474882178609894547503885 */ 776 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &grp->N, 446, 1 ) ); 777 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &Ns, 16, 778 "8335DC163BB124B65129C96FDE933D8D723A70AADC873D6D54A7BB0D" ) ); 779 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &grp->N, &grp->N, &Ns ) ); 780 781 /* Actually, the required msb for private keys */ 782 grp->nbits = 447; 783 784 cleanup: 785 mbedtls_mpi_free( &Ns ); 786 if( ret != 0 ) 787 mbedtls_ecp_group_free( grp ); 788 789 return( ret ); 790 } 791 #endif /* MBEDTLS_ECP_DP_CURVE448_ENABLED */ 792 793 /* 794 * Set a group using well-known domain parameters 795 */ 796 int mbedtls_ecp_group_load( mbedtls_ecp_group *grp, mbedtls_ecp_group_id id ) 797 { 798 ECP_VALIDATE_RET( grp != NULL ); 799 mbedtls_ecp_group_free( grp ); 800 801 grp->id = id; 802 803 switch( id ) 804 { 805 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) 806 case MBEDTLS_ECP_DP_SECP192R1: 807 NIST_MODP( p192 ); 808 return( LOAD_GROUP( secp192r1 ) ); 809 #endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */ 810 811 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) 812 case MBEDTLS_ECP_DP_SECP224R1: 813 NIST_MODP( p224 ); 814 return( LOAD_GROUP( secp224r1 ) ); 815 #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */ 816 817 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) 818 case MBEDTLS_ECP_DP_SECP256R1: 819 NIST_MODP( p256 ); 820 return( LOAD_GROUP( secp256r1 ) ); 821 #endif /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */ 822 823 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) 824 case MBEDTLS_ECP_DP_SECP384R1: 825 NIST_MODP( p384 ); 826 return( LOAD_GROUP( secp384r1 ) ); 827 #endif /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */ 828 829 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) 830 case MBEDTLS_ECP_DP_SECP521R1: 831 NIST_MODP( p521 ); 832 return( LOAD_GROUP( secp521r1 ) ); 833 #endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */ 834 835 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) 836 case MBEDTLS_ECP_DP_SECP192K1: 837 grp->modp = ecp_mod_p192k1; 838 return( LOAD_GROUP_A( secp192k1 ) ); 839 #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */ 840 841 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) 842 case MBEDTLS_ECP_DP_SECP224K1: 843 grp->modp = ecp_mod_p224k1; 844 return( LOAD_GROUP_A( secp224k1 ) ); 845 #endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */ 846 847 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) 848 case MBEDTLS_ECP_DP_SECP256K1: 849 grp->modp = ecp_mod_p256k1; 850 return( LOAD_GROUP_A( secp256k1 ) ); 851 #endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */ 852 853 #if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) 854 case MBEDTLS_ECP_DP_BP256R1: 855 return( LOAD_GROUP_A( brainpoolP256r1 ) ); 856 #endif /* MBEDTLS_ECP_DP_BP256R1_ENABLED */ 857 858 #if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) 859 case MBEDTLS_ECP_DP_BP384R1: 860 return( LOAD_GROUP_A( brainpoolP384r1 ) ); 861 #endif /* MBEDTLS_ECP_DP_BP384R1_ENABLED */ 862 863 #if defined(MBEDTLS_ECP_DP_SM2_ENABLED) 864 case MBEDTLS_ECP_DP_SM2: 865 return( LOAD_GROUP_A( sm2 ) ); 866 #endif /* MBEDTLS_ECP_DP_SM2_ENABLED */ 867 868 #if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) 869 case MBEDTLS_ECP_DP_BP512R1: 870 return( LOAD_GROUP_A( brainpoolP512r1 ) ); 871 #endif /* MBEDTLS_ECP_DP_BP512R1_ENABLED */ 872 873 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) 874 case MBEDTLS_ECP_DP_CURVE25519: 875 grp->modp = ecp_mod_p255; 876 return( ecp_use_curve25519( grp ) ); 877 #endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */ 878 879 #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) 880 case MBEDTLS_ECP_DP_CURVE448: 881 grp->modp = ecp_mod_p448; 882 return( ecp_use_curve448( grp ) ); 883 #endif /* MBEDTLS_ECP_DP_CURVE448_ENABLED */ 884 885 default: 886 grp->id = MBEDTLS_ECP_DP_NONE; 887 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE ); 888 } 889 } 890 891 #if defined(MBEDTLS_ECP_NIST_OPTIM) 892 /* 893 * Fast reduction modulo the primes used by the NIST curves. 894 * 895 * These functions are critical for speed, but not needed for correct 896 * operations. So, we make the choice to heavily rely on the internals of our 897 * bignum library, which creates a tight coupling between these functions and 898 * our MPI implementation. However, the coupling between the ECP module and 899 * MPI remains loose, since these functions can be deactivated at will. 900 */ 901 902 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) 903 /* 904 * Compared to the way things are presented in FIPS 186-3 D.2, 905 * we proceed in columns, from right (least significant chunk) to left, 906 * adding chunks to N in place, and keeping a carry for the next chunk. 907 * This avoids moving things around in memory, and uselessly adding zeros, 908 * compared to the more straightforward, line-oriented approach. 909 * 910 * For this prime we need to handle data in chunks of 64 bits. 911 * Since this is always a multiple of our basic mbedtls_mpi_uint, we can 912 * use a mbedtls_mpi_uint * to designate such a chunk, and small loops to handle it. 913 */ 914 915 /* Add 64-bit chunks (dst += src) and update carry */ 916 static inline void add64( mbedtls_mpi_uint *dst, mbedtls_mpi_uint *src, mbedtls_mpi_uint *carry ) 917 { 918 unsigned char i; 919 mbedtls_mpi_uint c = 0; 920 for( i = 0; i < 8 / sizeof( mbedtls_mpi_uint ); i++, dst++, src++ ) 921 { 922 *dst += c; c = ( *dst < c ); 923 *dst += *src; c += ( *dst < *src ); 924 } 925 *carry += c; 926 } 927 928 /* Add carry to a 64-bit chunk and update carry */ 929 static inline void carry64( mbedtls_mpi_uint *dst, mbedtls_mpi_uint *carry ) 930 { 931 unsigned char i; 932 for( i = 0; i < 8 / sizeof( mbedtls_mpi_uint ); i++, dst++ ) 933 { 934 *dst += *carry; 935 *carry = ( *dst < *carry ); 936 } 937 } 938 939 #define WIDTH 8 / sizeof( mbedtls_mpi_uint ) 940 #define A( i ) N->p + (i) * WIDTH 941 #define ADD( i ) add64( p, A( i ), &c ) 942 #define NEXT p += WIDTH; carry64( p, &c ) 943 #define LAST p += WIDTH; *p = c; while( ++p < end ) *p = 0 944 945 /* 946 * Fast quasi-reduction modulo p192 (FIPS 186-3 D.2.1) 947 */ 948 static int ecp_mod_p192( mbedtls_mpi *N ) 949 { 950 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 951 mbedtls_mpi_uint c = 0; 952 mbedtls_mpi_uint *p, *end; 953 954 /* Make sure we have enough blocks so that A(5) is legal */ 955 MBEDTLS_MPI_CHK( mbedtls_mpi_grow( N, 6 * WIDTH ) ); 956 957 p = N->p; 958 end = p + N->n; 959 960 ADD( 3 ); ADD( 5 ); NEXT; // A0 += A3 + A5 961 ADD( 3 ); ADD( 4 ); ADD( 5 ); NEXT; // A1 += A3 + A4 + A5 962 ADD( 4 ); ADD( 5 ); LAST; // A2 += A4 + A5 963 964 cleanup: 965 return( ret ); 966 } 967 968 #undef WIDTH 969 #undef A 970 #undef ADD 971 #undef NEXT 972 #undef LAST 973 #endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */ 974 975 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) || \ 976 defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) || \ 977 defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) 978 /* 979 * The reader is advised to first understand ecp_mod_p192() since the same 980 * general structure is used here, but with additional complications: 981 * (1) chunks of 32 bits, and (2) subtractions. 982 */ 983 984 /* 985 * For these primes, we need to handle data in chunks of 32 bits. 986 * This makes it more complicated if we use 64 bits limbs in MPI, 987 * which prevents us from using a uniform access method as for p192. 988 * 989 * So, we define a mini abstraction layer to access 32 bit chunks, 990 * load them in 'cur' for work, and store them back from 'cur' when done. 991 * 992 * While at it, also define the size of N in terms of 32-bit chunks. 993 */ 994 #define LOAD32 cur = A( i ); 995 996 #if defined(MBEDTLS_HAVE_INT32) /* 32 bit */ 997 998 #define MAX32 N->n 999 #define A( j ) N->p[j] 1000 #define STORE32 N->p[i] = cur; 1001 1002 #else /* 64-bit */ 1003 1004 #define MAX32 N->n * 2 1005 #define A( j ) (j) % 2 ? (uint32_t)( N->p[(j)/2] >> 32 ) : \ 1006 (uint32_t)( N->p[(j)/2] ) 1007 #define STORE32 \ 1008 if( i % 2 ) { \ 1009 N->p[i/2] &= 0x00000000FFFFFFFF; \ 1010 N->p[i/2] |= ((mbedtls_mpi_uint) cur) << 32; \ 1011 } else { \ 1012 N->p[i/2] &= 0xFFFFFFFF00000000; \ 1013 N->p[i/2] |= (mbedtls_mpi_uint) cur; \ 1014 } 1015 1016 #endif /* sizeof( mbedtls_mpi_uint ) */ 1017 1018 /* 1019 * Helpers for addition and subtraction of chunks, with signed carry. 1020 */ 1021 static inline void add32( uint32_t *dst, uint32_t src, signed char *carry ) 1022 { 1023 *dst += src; 1024 *carry += ( *dst < src ); 1025 } 1026 1027 static inline void sub32( uint32_t *dst, uint32_t src, signed char *carry ) 1028 { 1029 *carry -= ( *dst < src ); 1030 *dst -= src; 1031 } 1032 1033 #define ADD( j ) add32( &cur, A( j ), &c ); 1034 #define SUB( j ) sub32( &cur, A( j ), &c ); 1035 1036 /* 1037 * Helpers for the main 'loop' 1038 * (see fix_negative for the motivation of C) 1039 */ 1040 #define INIT( b ) \ 1041 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; \ 1042 signed char c = 0, cc; \ 1043 uint32_t cur; \ 1044 size_t i = 0, bits = (b); \ 1045 mbedtls_mpi C; \ 1046 mbedtls_mpi_uint Cp[ (b) / 8 / sizeof( mbedtls_mpi_uint) + 1 ]; \ 1047 \ 1048 C.s = 1; \ 1049 C.n = (b) / 8 / sizeof( mbedtls_mpi_uint) + 1; \ 1050 C.p = Cp; \ 1051 memset( Cp, 0, C.n * sizeof( mbedtls_mpi_uint ) ); \ 1052 \ 1053 MBEDTLS_MPI_CHK( mbedtls_mpi_grow( N, (b) * 2 / 8 / \ 1054 sizeof( mbedtls_mpi_uint ) ) ); \ 1055 LOAD32; 1056 1057 #define NEXT \ 1058 STORE32; i++; LOAD32; \ 1059 cc = c; c = 0; \ 1060 if( cc < 0 ) \ 1061 sub32( &cur, -cc, &c ); \ 1062 else \ 1063 add32( &cur, cc, &c ); \ 1064 1065 #define LAST \ 1066 STORE32; i++; \ 1067 cur = c > 0 ? c : 0; STORE32; \ 1068 cur = 0; while( ++i < MAX32 ) { STORE32; } \ 1069 if( c < 0 ) fix_negative( N, c, &C, bits ); 1070 1071 /* 1072 * If the result is negative, we get it in the form 1073 * c * 2^(bits + 32) + N, with c negative and N positive shorter than 'bits' 1074 */ 1075 static inline int fix_negative( mbedtls_mpi *N, signed char c, mbedtls_mpi *C, size_t bits ) 1076 { 1077 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 1078 1079 /* C = - c * 2^(bits + 32) */ 1080 #if !defined(MBEDTLS_HAVE_INT64) 1081 ((void) bits); 1082 #else 1083 if( bits == 224 ) 1084 C->p[ C->n - 1 ] = ((mbedtls_mpi_uint) -c) << 32; 1085 else 1086 #endif 1087 C->p[ C->n - 1 ] = (mbedtls_mpi_uint) -c; 1088 1089 /* N = - ( C - N ) */ 1090 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( N, C, N ) ); 1091 N->s = -1; 1092 1093 cleanup: 1094 1095 return( ret ); 1096 } 1097 1098 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) 1099 /* 1100 * Fast quasi-reduction modulo p224 (FIPS 186-3 D.2.2) 1101 */ 1102 static int ecp_mod_p224( mbedtls_mpi *N ) 1103 { 1104 INIT( 224 ); 1105 1106 SUB( 7 ); SUB( 11 ); NEXT; // A0 += -A7 - A11 1107 SUB( 8 ); SUB( 12 ); NEXT; // A1 += -A8 - A12 1108 SUB( 9 ); SUB( 13 ); NEXT; // A2 += -A9 - A13 1109 SUB( 10 ); ADD( 7 ); ADD( 11 ); NEXT; // A3 += -A10 + A7 + A11 1110 SUB( 11 ); ADD( 8 ); ADD( 12 ); NEXT; // A4 += -A11 + A8 + A12 1111 SUB( 12 ); ADD( 9 ); ADD( 13 ); NEXT; // A5 += -A12 + A9 + A13 1112 SUB( 13 ); ADD( 10 ); LAST; // A6 += -A13 + A10 1113 1114 cleanup: 1115 return( ret ); 1116 } 1117 #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */ 1118 1119 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) 1120 /* 1121 * Fast quasi-reduction modulo p256 (FIPS 186-3 D.2.3) 1122 */ 1123 static int ecp_mod_p256( mbedtls_mpi *N ) 1124 { 1125 INIT( 256 ); 1126 1127 ADD( 8 ); ADD( 9 ); 1128 SUB( 11 ); SUB( 12 ); SUB( 13 ); SUB( 14 ); NEXT; // A0 1129 1130 ADD( 9 ); ADD( 10 ); 1131 SUB( 12 ); SUB( 13 ); SUB( 14 ); SUB( 15 ); NEXT; // A1 1132 1133 ADD( 10 ); ADD( 11 ); 1134 SUB( 13 ); SUB( 14 ); SUB( 15 ); NEXT; // A2 1135 1136 ADD( 11 ); ADD( 11 ); ADD( 12 ); ADD( 12 ); ADD( 13 ); 1137 SUB( 15 ); SUB( 8 ); SUB( 9 ); NEXT; // A3 1138 1139 ADD( 12 ); ADD( 12 ); ADD( 13 ); ADD( 13 ); ADD( 14 ); 1140 SUB( 9 ); SUB( 10 ); NEXT; // A4 1141 1142 ADD( 13 ); ADD( 13 ); ADD( 14 ); ADD( 14 ); ADD( 15 ); 1143 SUB( 10 ); SUB( 11 ); NEXT; // A5 1144 1145 ADD( 14 ); ADD( 14 ); ADD( 15 ); ADD( 15 ); ADD( 14 ); ADD( 13 ); 1146 SUB( 8 ); SUB( 9 ); NEXT; // A6 1147 1148 ADD( 15 ); ADD( 15 ); ADD( 15 ); ADD( 8 ); 1149 SUB( 10 ); SUB( 11 ); SUB( 12 ); SUB( 13 ); LAST; // A7 1150 1151 cleanup: 1152 return( ret ); 1153 } 1154 #endif /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */ 1155 1156 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) 1157 /* 1158 * Fast quasi-reduction modulo p384 (FIPS 186-3 D.2.4) 1159 */ 1160 static int ecp_mod_p384( mbedtls_mpi *N ) 1161 { 1162 INIT( 384 ); 1163 1164 ADD( 12 ); ADD( 21 ); ADD( 20 ); 1165 SUB( 23 ); NEXT; // A0 1166 1167 ADD( 13 ); ADD( 22 ); ADD( 23 ); 1168 SUB( 12 ); SUB( 20 ); NEXT; // A2 1169 1170 ADD( 14 ); ADD( 23 ); 1171 SUB( 13 ); SUB( 21 ); NEXT; // A2 1172 1173 ADD( 15 ); ADD( 12 ); ADD( 20 ); ADD( 21 ); 1174 SUB( 14 ); SUB( 22 ); SUB( 23 ); NEXT; // A3 1175 1176 ADD( 21 ); ADD( 21 ); ADD( 16 ); ADD( 13 ); ADD( 12 ); ADD( 20 ); ADD( 22 ); 1177 SUB( 15 ); SUB( 23 ); SUB( 23 ); NEXT; // A4 1178 1179 ADD( 22 ); ADD( 22 ); ADD( 17 ); ADD( 14 ); ADD( 13 ); ADD( 21 ); ADD( 23 ); 1180 SUB( 16 ); NEXT; // A5 1181 1182 ADD( 23 ); ADD( 23 ); ADD( 18 ); ADD( 15 ); ADD( 14 ); ADD( 22 ); 1183 SUB( 17 ); NEXT; // A6 1184 1185 ADD( 19 ); ADD( 16 ); ADD( 15 ); ADD( 23 ); 1186 SUB( 18 ); NEXT; // A7 1187 1188 ADD( 20 ); ADD( 17 ); ADD( 16 ); 1189 SUB( 19 ); NEXT; // A8 1190 1191 ADD( 21 ); ADD( 18 ); ADD( 17 ); 1192 SUB( 20 ); NEXT; // A9 1193 1194 ADD( 22 ); ADD( 19 ); ADD( 18 ); 1195 SUB( 21 ); NEXT; // A10 1196 1197 ADD( 23 ); ADD( 20 ); ADD( 19 ); 1198 SUB( 22 ); LAST; // A11 1199 1200 cleanup: 1201 return( ret ); 1202 } 1203 #endif /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */ 1204 1205 #undef A 1206 #undef LOAD32 1207 #undef STORE32 1208 #undef MAX32 1209 #undef INIT 1210 #undef NEXT 1211 #undef LAST 1212 1213 #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED || 1214 MBEDTLS_ECP_DP_SECP256R1_ENABLED || 1215 MBEDTLS_ECP_DP_SECP384R1_ENABLED */ 1216 1217 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) 1218 /* 1219 * Here we have an actual Mersenne prime, so things are more straightforward. 1220 * However, chunks are aligned on a 'weird' boundary (521 bits). 1221 */ 1222 1223 /* Size of p521 in terms of mbedtls_mpi_uint */ 1224 #define P521_WIDTH ( 521 / 8 / sizeof( mbedtls_mpi_uint ) + 1 ) 1225 1226 /* Bits to keep in the most significant mbedtls_mpi_uint */ 1227 #define P521_MASK 0x01FF 1228 1229 /* 1230 * Fast quasi-reduction modulo p521 (FIPS 186-3 D.2.5) 1231 * Write N as A1 + 2^521 A0, return A0 + A1 1232 */ 1233 static int ecp_mod_p521( mbedtls_mpi *N ) 1234 { 1235 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 1236 size_t i; 1237 mbedtls_mpi M; 1238 mbedtls_mpi_uint Mp[P521_WIDTH + 1]; 1239 /* Worst case for the size of M is when mbedtls_mpi_uint is 16 bits: 1240 * we need to hold bits 513 to 1056, which is 34 limbs, that is 1241 * P521_WIDTH + 1. Otherwise P521_WIDTH is enough. */ 1242 1243 if( N->n < P521_WIDTH ) 1244 return( 0 ); 1245 1246 /* M = A1 */ 1247 M.s = 1; 1248 M.n = N->n - ( P521_WIDTH - 1 ); 1249 if( M.n > P521_WIDTH + 1 ) 1250 M.n = P521_WIDTH + 1; 1251 M.p = Mp; 1252 memcpy( Mp, N->p + P521_WIDTH - 1, M.n * sizeof( mbedtls_mpi_uint ) ); 1253 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, 521 % ( 8 * sizeof( mbedtls_mpi_uint ) ) ) ); 1254 1255 /* N = A0 */ 1256 N->p[P521_WIDTH - 1] &= P521_MASK; 1257 for( i = P521_WIDTH; i < N->n; i++ ) 1258 N->p[i] = 0; 1259 1260 /* N = A0 + A1 */ 1261 MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) ); 1262 1263 cleanup: 1264 return( ret ); 1265 } 1266 1267 #undef P521_WIDTH 1268 #undef P521_MASK 1269 #endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */ 1270 1271 #endif /* MBEDTLS_ECP_NIST_OPTIM */ 1272 1273 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) 1274 1275 /* Size of p255 in terms of mbedtls_mpi_uint */ 1276 #define P255_WIDTH ( 255 / 8 / sizeof( mbedtls_mpi_uint ) + 1 ) 1277 1278 /* 1279 * Fast quasi-reduction modulo p255 = 2^255 - 19 1280 * Write N as A0 + 2^255 A1, return A0 + 19 * A1 1281 */ 1282 static int ecp_mod_p255( mbedtls_mpi *N ) 1283 { 1284 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 1285 size_t i; 1286 mbedtls_mpi M; 1287 mbedtls_mpi_uint Mp[P255_WIDTH + 2]; 1288 1289 if( N->n < P255_WIDTH ) 1290 return( 0 ); 1291 1292 /* M = A1 */ 1293 M.s = 1; 1294 M.n = N->n - ( P255_WIDTH - 1 ); 1295 if( M.n > P255_WIDTH + 1 ) 1296 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); 1297 M.p = Mp; 1298 memset( Mp, 0, sizeof Mp ); 1299 memcpy( Mp, N->p + P255_WIDTH - 1, M.n * sizeof( mbedtls_mpi_uint ) ); 1300 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, 255 % ( 8 * sizeof( mbedtls_mpi_uint ) ) ) ); 1301 M.n++; /* Make room for multiplication by 19 */ 1302 1303 /* N = A0 */ 1304 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( N, 255, 0 ) ); 1305 for( i = P255_WIDTH; i < N->n; i++ ) 1306 N->p[i] = 0; 1307 1308 /* N = A0 + 19 * A1 */ 1309 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &M, 19 ) ); 1310 MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) ); 1311 1312 cleanup: 1313 return( ret ); 1314 } 1315 #endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */ 1316 1317 #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) 1318 1319 /* Size of p448 in terms of mbedtls_mpi_uint */ 1320 #define P448_WIDTH ( 448 / 8 / sizeof( mbedtls_mpi_uint ) ) 1321 1322 /* Number of limbs fully occupied by 2^224 (max), and limbs used by it (min) */ 1323 #define DIV_ROUND_UP( X, Y ) ( ( ( X ) + ( Y ) - 1 ) / ( Y ) ) 1324 #define P224_WIDTH_MIN ( 28 / sizeof( mbedtls_mpi_uint ) ) 1325 #define P224_WIDTH_MAX DIV_ROUND_UP( 28, sizeof( mbedtls_mpi_uint ) ) 1326 #define P224_UNUSED_BITS ( ( P224_WIDTH_MAX * sizeof( mbedtls_mpi_uint ) * 8 ) - 224 ) 1327 1328 /* 1329 * Fast quasi-reduction modulo p448 = 2^448 - 2^224 - 1 1330 * Write N as A0 + 2^448 A1 and A1 as B0 + 2^224 B1, and return 1331 * A0 + A1 + B1 + (B0 + B1) * 2^224. This is different to the reference 1332 * implementation of Curve448, which uses its own special 56-bit limbs rather 1333 * than a generic bignum library. We could squeeze some extra speed out on 1334 * 32-bit machines by splitting N up into 32-bit limbs and doing the 1335 * arithmetic using the limbs directly as we do for the NIST primes above, 1336 * but for 64-bit targets it should use half the number of operations if we do 1337 * the reduction with 224-bit limbs, since mpi_add_mpi will then use 64-bit adds. 1338 */ 1339 static int ecp_mod_p448( mbedtls_mpi *N ) 1340 { 1341 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 1342 size_t i; 1343 mbedtls_mpi M, Q; 1344 mbedtls_mpi_uint Mp[P448_WIDTH + 1], Qp[P448_WIDTH]; 1345 1346 if( N->n <= P448_WIDTH ) 1347 return( 0 ); 1348 1349 /* M = A1 */ 1350 M.s = 1; 1351 M.n = N->n - ( P448_WIDTH ); 1352 if( M.n > P448_WIDTH ) 1353 /* Shouldn't be called with N larger than 2^896! */ 1354 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); 1355 M.p = Mp; 1356 memset( Mp, 0, sizeof( Mp ) ); 1357 memcpy( Mp, N->p + P448_WIDTH, M.n * sizeof( mbedtls_mpi_uint ) ); 1358 1359 /* N = A0 */ 1360 for( i = P448_WIDTH; i < N->n; i++ ) 1361 N->p[i] = 0; 1362 1363 /* N += A1 */ 1364 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &M ) ); 1365 1366 /* Q = B1, N += B1 */ 1367 Q = M; 1368 Q.p = Qp; 1369 memcpy( Qp, Mp, sizeof( Qp ) ); 1370 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &Q, 224 ) ); 1371 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &Q ) ); 1372 1373 /* M = (B0 + B1) * 2^224, N += M */ 1374 if( sizeof( mbedtls_mpi_uint ) > 4 ) 1375 Mp[P224_WIDTH_MIN] &= ( (mbedtls_mpi_uint)-1 ) >> ( P224_UNUSED_BITS ); 1376 for( i = P224_WIDTH_MAX; i < M.n; ++i ) 1377 Mp[i] = 0; 1378 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &M, &M, &Q ) ); 1379 M.n = P448_WIDTH + 1; /* Make room for shifted carry bit from the addition */ 1380 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &M, 224 ) ); 1381 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &M ) ); 1382 1383 cleanup: 1384 return( ret ); 1385 } 1386 #endif /* MBEDTLS_ECP_DP_CURVE448_ENABLED */ 1387 1388 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) || \ 1389 defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) || \ 1390 defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) 1391 /* 1392 * Fast quasi-reduction modulo P = 2^s - R, 1393 * with R about 33 bits, used by the Koblitz curves. 1394 * 1395 * Write N as A0 + 2^224 A1, return A0 + R * A1. 1396 * Actually do two passes, since R is big. 1397 */ 1398 #define P_KOBLITZ_MAX ( 256 / 8 / sizeof( mbedtls_mpi_uint ) ) // Max limbs in P 1399 #define P_KOBLITZ_R ( 8 / sizeof( mbedtls_mpi_uint ) ) // Limbs in R 1400 static inline int ecp_mod_koblitz( mbedtls_mpi *N, mbedtls_mpi_uint *Rp, size_t p_limbs, 1401 size_t adjust, size_t shift, mbedtls_mpi_uint mask ) 1402 { 1403 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; 1404 size_t i; 1405 mbedtls_mpi M, R; 1406 mbedtls_mpi_uint Mp[P_KOBLITZ_MAX + P_KOBLITZ_R + 1]; 1407 1408 if( N->n < p_limbs ) 1409 return( 0 ); 1410 1411 /* Init R */ 1412 R.s = 1; 1413 R.p = Rp; 1414 R.n = P_KOBLITZ_R; 1415 1416 /* Common setup for M */ 1417 M.s = 1; 1418 M.p = Mp; 1419 1420 /* M = A1 */ 1421 M.n = N->n - ( p_limbs - adjust ); 1422 if( M.n > p_limbs + adjust ) 1423 M.n = p_limbs + adjust; 1424 memset( Mp, 0, sizeof Mp ); 1425 memcpy( Mp, N->p + p_limbs - adjust, M.n * sizeof( mbedtls_mpi_uint ) ); 1426 if( shift != 0 ) 1427 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, shift ) ); 1428 M.n += R.n; /* Make room for multiplication by R */ 1429 1430 /* N = A0 */ 1431 if( mask != 0 ) 1432 N->p[p_limbs - 1] &= mask; 1433 for( i = p_limbs; i < N->n; i++ ) 1434 N->p[i] = 0; 1435 1436 /* N = A0 + R * A1 */ 1437 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &M, &M, &R ) ); 1438 MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) ); 1439 1440 /* Second pass */ 1441 1442 /* M = A1 */ 1443 M.n = N->n - ( p_limbs - adjust ); 1444 if( M.n > p_limbs + adjust ) 1445 M.n = p_limbs + adjust; 1446 memset( Mp, 0, sizeof Mp ); 1447 memcpy( Mp, N->p + p_limbs - adjust, M.n * sizeof( mbedtls_mpi_uint ) ); 1448 if( shift != 0 ) 1449 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, shift ) ); 1450 M.n += R.n; /* Make room for multiplication by R */ 1451 1452 /* N = A0 */ 1453 if( mask != 0 ) 1454 N->p[p_limbs - 1] &= mask; 1455 for( i = p_limbs; i < N->n; i++ ) 1456 N->p[i] = 0; 1457 1458 /* N = A0 + R * A1 */ 1459 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &M, &M, &R ) ); 1460 MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) ); 1461 1462 cleanup: 1463 return( ret ); 1464 } 1465 #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED) || 1466 MBEDTLS_ECP_DP_SECP224K1_ENABLED) || 1467 MBEDTLS_ECP_DP_SECP256K1_ENABLED) */ 1468 1469 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) 1470 /* 1471 * Fast quasi-reduction modulo p192k1 = 2^192 - R, 1472 * with R = 2^32 + 2^12 + 2^8 + 2^7 + 2^6 + 2^3 + 1 = 0x0100001119 1473 */ 1474 static int ecp_mod_p192k1( mbedtls_mpi *N ) 1475 { 1476 static mbedtls_mpi_uint Rp[] = { 1477 BYTES_TO_T_UINT_8( 0xC9, 0x11, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) }; 1478 1479 return( ecp_mod_koblitz( N, Rp, 192 / 8 / sizeof( mbedtls_mpi_uint ), 0, 0, 0 ) ); 1480 } 1481 #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */ 1482 1483 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) 1484 /* 1485 * Fast quasi-reduction modulo p224k1 = 2^224 - R, 1486 * with R = 2^32 + 2^12 + 2^11 + 2^9 + 2^7 + 2^4 + 2 + 1 = 0x0100001A93 1487 */ 1488 static int ecp_mod_p224k1( mbedtls_mpi *N ) 1489 { 1490 static mbedtls_mpi_uint Rp[] = { 1491 BYTES_TO_T_UINT_8( 0x93, 0x1A, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) }; 1492 1493 #if defined(MBEDTLS_HAVE_INT64) 1494 return( ecp_mod_koblitz( N, Rp, 4, 1, 32, 0xFFFFFFFF ) ); 1495 #else 1496 return( ecp_mod_koblitz( N, Rp, 224 / 8 / sizeof( mbedtls_mpi_uint ), 0, 0, 0 ) ); 1497 #endif 1498 } 1499 1500 #endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */ 1501 1502 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) 1503 /* 1504 * Fast quasi-reduction modulo p256k1 = 2^256 - R, 1505 * with R = 2^32 + 2^9 + 2^8 + 2^7 + 2^6 + 2^4 + 1 = 0x01000003D1 1506 */ 1507 static int ecp_mod_p256k1( mbedtls_mpi *N ) 1508 { 1509 static mbedtls_mpi_uint Rp[] = { 1510 BYTES_TO_T_UINT_8( 0xD1, 0x03, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) }; 1511 return( ecp_mod_koblitz( N, Rp, 256 / 8 / sizeof( mbedtls_mpi_uint ), 0, 0, 0 ) ); 1512 } 1513 #endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */ 1514 1515 #endif /* !MBEDTLS_ECP_ALT */ 1516 1517 #endif /* MBEDTLS_ECP_C */ 1518