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 32 #include <string.h> 33 34 #if !defined(MBEDTLS_ECP_ALT) 35 36 #if ( defined(__ARMCC_VERSION) || defined(_MSC_VER) ) && \ 37 !defined(inline) && !defined(__cplusplus) 38 #define inline __inline 39 #endif 40 41 /* 42 * Conversion macros for embedded constants: 43 * build lists of mbedtls_mpi_uint's from lists of unsigned char's grouped by 8, 4 or 2 44 */ 45 #if defined(MBEDTLS_HAVE_INT32) 46 47 #define BYTES_TO_T_UINT_4( a, b, c, d ) \ 48 ( (mbedtls_mpi_uint) a << 0 ) | \ 49 ( (mbedtls_mpi_uint) b << 8 ) | \ 50 ( (mbedtls_mpi_uint) c << 16 ) | \ 51 ( (mbedtls_mpi_uint) d << 24 ) 52 53 #define BYTES_TO_T_UINT_2( a, b ) \ 54 BYTES_TO_T_UINT_4( a, b, 0, 0 ) 55 56 #define BYTES_TO_T_UINT_8( a, b, c, d, e, f, g, h ) \ 57 BYTES_TO_T_UINT_4( a, b, c, d ), \ 58 BYTES_TO_T_UINT_4( e, f, g, h ) 59 60 #else /* 64-bits */ 61 62 #define BYTES_TO_T_UINT_8( a, b, c, d, e, f, g, h ) \ 63 ( (mbedtls_mpi_uint) a << 0 ) | \ 64 ( (mbedtls_mpi_uint) b << 8 ) | \ 65 ( (mbedtls_mpi_uint) c << 16 ) | \ 66 ( (mbedtls_mpi_uint) d << 24 ) | \ 67 ( (mbedtls_mpi_uint) e << 32 ) | \ 68 ( (mbedtls_mpi_uint) f << 40 ) | \ 69 ( (mbedtls_mpi_uint) g << 48 ) | \ 70 ( (mbedtls_mpi_uint) h << 56 ) 71 72 #define BYTES_TO_T_UINT_4( a, b, c, d ) \ 73 BYTES_TO_T_UINT_8( a, b, c, d, 0, 0, 0, 0 ) 74 75 #define BYTES_TO_T_UINT_2( a, b ) \ 76 BYTES_TO_T_UINT_8( a, b, 0, 0, 0, 0, 0, 0 ) 77 78 #endif /* bits in mbedtls_mpi_uint */ 79 80 /* 81 * Note: the constants are in little-endian order 82 * to be directly usable in MPIs 83 */ 84 85 /* 86 * Domain parameters for secp192r1 87 */ 88 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) 89 static const mbedtls_mpi_uint secp192r1_p[] = { 90 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 91 BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 92 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 93 }; 94 static const mbedtls_mpi_uint secp192r1_b[] = { 95 BYTES_TO_T_UINT_8( 0xB1, 0xB9, 0x46, 0xC1, 0xEC, 0xDE, 0xB8, 0xFE ), 96 BYTES_TO_T_UINT_8( 0x49, 0x30, 0x24, 0x72, 0xAB, 0xE9, 0xA7, 0x0F ), 97 BYTES_TO_T_UINT_8( 0xE7, 0x80, 0x9C, 0xE5, 0x19, 0x05, 0x21, 0x64 ), 98 }; 99 static const mbedtls_mpi_uint secp192r1_gx[] = { 100 BYTES_TO_T_UINT_8( 0x12, 0x10, 0xFF, 0x82, 0xFD, 0x0A, 0xFF, 0xF4 ), 101 BYTES_TO_T_UINT_8( 0x00, 0x88, 0xA1, 0x43, 0xEB, 0x20, 0xBF, 0x7C ), 102 BYTES_TO_T_UINT_8( 0xF6, 0x90, 0x30, 0xB0, 0x0E, 0xA8, 0x8D, 0x18 ), 103 }; 104 static const mbedtls_mpi_uint secp192r1_gy[] = { 105 BYTES_TO_T_UINT_8( 0x11, 0x48, 0x79, 0x1E, 0xA1, 0x77, 0xF9, 0x73 ), 106 BYTES_TO_T_UINT_8( 0xD5, 0xCD, 0x24, 0x6B, 0xED, 0x11, 0x10, 0x63 ), 107 BYTES_TO_T_UINT_8( 0x78, 0xDA, 0xC8, 0xFF, 0x95, 0x2B, 0x19, 0x07 ), 108 }; 109 static const mbedtls_mpi_uint secp192r1_n[] = { 110 BYTES_TO_T_UINT_8( 0x31, 0x28, 0xD2, 0xB4, 0xB1, 0xC9, 0x6B, 0x14 ), 111 BYTES_TO_T_UINT_8( 0x36, 0xF8, 0xDE, 0x99, 0xFF, 0xFF, 0xFF, 0xFF ), 112 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 113 }; 114 #endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */ 115 116 /* 117 * Domain parameters for secp224r1 118 */ 119 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) 120 static const mbedtls_mpi_uint secp224r1_p[] = { 121 BYTES_TO_T_UINT_8( 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ), 122 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ), 123 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 124 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ), 125 }; 126 static const mbedtls_mpi_uint secp224r1_b[] = { 127 BYTES_TO_T_UINT_8( 0xB4, 0xFF, 0x55, 0x23, 0x43, 0x39, 0x0B, 0x27 ), 128 BYTES_TO_T_UINT_8( 0xBA, 0xD8, 0xBF, 0xD7, 0xB7, 0xB0, 0x44, 0x50 ), 129 BYTES_TO_T_UINT_8( 0x56, 0x32, 0x41, 0xF5, 0xAB, 0xB3, 0x04, 0x0C ), 130 BYTES_TO_T_UINT_4( 0x85, 0x0A, 0x05, 0xB4 ), 131 }; 132 static const mbedtls_mpi_uint secp224r1_gx[] = { 133 BYTES_TO_T_UINT_8( 0x21, 0x1D, 0x5C, 0x11, 0xD6, 0x80, 0x32, 0x34 ), 134 BYTES_TO_T_UINT_8( 0x22, 0x11, 0xC2, 0x56, 0xD3, 0xC1, 0x03, 0x4A ), 135 BYTES_TO_T_UINT_8( 0xB9, 0x90, 0x13, 0x32, 0x7F, 0xBF, 0xB4, 0x6B ), 136 BYTES_TO_T_UINT_4( 0xBD, 0x0C, 0x0E, 0xB7 ), 137 }; 138 static const mbedtls_mpi_uint secp224r1_gy[] = { 139 BYTES_TO_T_UINT_8( 0x34, 0x7E, 0x00, 0x85, 0x99, 0x81, 0xD5, 0x44 ), 140 BYTES_TO_T_UINT_8( 0x64, 0x47, 0x07, 0x5A, 0xA0, 0x75, 0x43, 0xCD ), 141 BYTES_TO_T_UINT_8( 0xE6, 0xDF, 0x22, 0x4C, 0xFB, 0x23, 0xF7, 0xB5 ), 142 BYTES_TO_T_UINT_4( 0x88, 0x63, 0x37, 0xBD ), 143 }; 144 static const mbedtls_mpi_uint secp224r1_n[] = { 145 BYTES_TO_T_UINT_8( 0x3D, 0x2A, 0x5C, 0x5C, 0x45, 0x29, 0xDD, 0x13 ), 146 BYTES_TO_T_UINT_8( 0x3E, 0xF0, 0xB8, 0xE0, 0xA2, 0x16, 0xFF, 0xFF ), 147 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 148 BYTES_TO_T_UINT_4( 0xFF, 0xFF, 0xFF, 0xFF ), 149 }; 150 #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */ 151 152 /* 153 * Domain parameters for secp256r1 154 */ 155 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) 156 static const mbedtls_mpi_uint secp256r1_p[] = { 157 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 158 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ), 159 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ), 160 BYTES_TO_T_UINT_8( 0x01, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ), 161 }; 162 static const mbedtls_mpi_uint secp256r1_b[] = { 163 BYTES_TO_T_UINT_8( 0x4B, 0x60, 0xD2, 0x27, 0x3E, 0x3C, 0xCE, 0x3B ), 164 BYTES_TO_T_UINT_8( 0xF6, 0xB0, 0x53, 0xCC, 0xB0, 0x06, 0x1D, 0x65 ), 165 BYTES_TO_T_UINT_8( 0xBC, 0x86, 0x98, 0x76, 0x55, 0xBD, 0xEB, 0xB3 ), 166 BYTES_TO_T_UINT_8( 0xE7, 0x93, 0x3A, 0xAA, 0xD8, 0x35, 0xC6, 0x5A ), 167 }; 168 static const mbedtls_mpi_uint secp256r1_gx[] = { 169 BYTES_TO_T_UINT_8( 0x96, 0xC2, 0x98, 0xD8, 0x45, 0x39, 0xA1, 0xF4 ), 170 BYTES_TO_T_UINT_8( 0xA0, 0x33, 0xEB, 0x2D, 0x81, 0x7D, 0x03, 0x77 ), 171 BYTES_TO_T_UINT_8( 0xF2, 0x40, 0xA4, 0x63, 0xE5, 0xE6, 0xBC, 0xF8 ), 172 BYTES_TO_T_UINT_8( 0x47, 0x42, 0x2C, 0xE1, 0xF2, 0xD1, 0x17, 0x6B ), 173 }; 174 static const mbedtls_mpi_uint secp256r1_gy[] = { 175 BYTES_TO_T_UINT_8( 0xF5, 0x51, 0xBF, 0x37, 0x68, 0x40, 0xB6, 0xCB ), 176 BYTES_TO_T_UINT_8( 0xCE, 0x5E, 0x31, 0x6B, 0x57, 0x33, 0xCE, 0x2B ), 177 BYTES_TO_T_UINT_8( 0x16, 0x9E, 0x0F, 0x7C, 0x4A, 0xEB, 0xE7, 0x8E ), 178 BYTES_TO_T_UINT_8( 0x9B, 0x7F, 0x1A, 0xFE, 0xE2, 0x42, 0xE3, 0x4F ), 179 }; 180 static const mbedtls_mpi_uint secp256r1_n[] = { 181 BYTES_TO_T_UINT_8( 0x51, 0x25, 0x63, 0xFC, 0xC2, 0xCA, 0xB9, 0xF3 ), 182 BYTES_TO_T_UINT_8( 0x84, 0x9E, 0x17, 0xA7, 0xAD, 0xFA, 0xE6, 0xBC ), 183 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 184 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ), 185 }; 186 #endif /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */ 187 188 /* 189 * Domain parameters for secp384r1 190 */ 191 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) 192 static const mbedtls_mpi_uint secp384r1_p[] = { 193 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ), 194 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ), 195 BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 196 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 197 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 198 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 199 }; 200 static const mbedtls_mpi_uint secp384r1_b[] = { 201 BYTES_TO_T_UINT_8( 0xEF, 0x2A, 0xEC, 0xD3, 0xED, 0xC8, 0x85, 0x2A ), 202 BYTES_TO_T_UINT_8( 0x9D, 0xD1, 0x2E, 0x8A, 0x8D, 0x39, 0x56, 0xC6 ), 203 BYTES_TO_T_UINT_8( 0x5A, 0x87, 0x13, 0x50, 0x8F, 0x08, 0x14, 0x03 ), 204 BYTES_TO_T_UINT_8( 0x12, 0x41, 0x81, 0xFE, 0x6E, 0x9C, 0x1D, 0x18 ), 205 BYTES_TO_T_UINT_8( 0x19, 0x2D, 0xF8, 0xE3, 0x6B, 0x05, 0x8E, 0x98 ), 206 BYTES_TO_T_UINT_8( 0xE4, 0xE7, 0x3E, 0xE2, 0xA7, 0x2F, 0x31, 0xB3 ), 207 }; 208 static const mbedtls_mpi_uint secp384r1_gx[] = { 209 BYTES_TO_T_UINT_8( 0xB7, 0x0A, 0x76, 0x72, 0x38, 0x5E, 0x54, 0x3A ), 210 BYTES_TO_T_UINT_8( 0x6C, 0x29, 0x55, 0xBF, 0x5D, 0xF2, 0x02, 0x55 ), 211 BYTES_TO_T_UINT_8( 0x38, 0x2A, 0x54, 0x82, 0xE0, 0x41, 0xF7, 0x59 ), 212 BYTES_TO_T_UINT_8( 0x98, 0x9B, 0xA7, 0x8B, 0x62, 0x3B, 0x1D, 0x6E ), 213 BYTES_TO_T_UINT_8( 0x74, 0xAD, 0x20, 0xF3, 0x1E, 0xC7, 0xB1, 0x8E ), 214 BYTES_TO_T_UINT_8( 0x37, 0x05, 0x8B, 0xBE, 0x22, 0xCA, 0x87, 0xAA ), 215 }; 216 static const mbedtls_mpi_uint secp384r1_gy[] = { 217 BYTES_TO_T_UINT_8( 0x5F, 0x0E, 0xEA, 0x90, 0x7C, 0x1D, 0x43, 0x7A ), 218 BYTES_TO_T_UINT_8( 0x9D, 0x81, 0x7E, 0x1D, 0xCE, 0xB1, 0x60, 0x0A ), 219 BYTES_TO_T_UINT_8( 0xC0, 0xB8, 0xF0, 0xB5, 0x13, 0x31, 0xDA, 0xE9 ), 220 BYTES_TO_T_UINT_8( 0x7C, 0x14, 0x9A, 0x28, 0xBD, 0x1D, 0xF4, 0xF8 ), 221 BYTES_TO_T_UINT_8( 0x29, 0xDC, 0x92, 0x92, 0xBF, 0x98, 0x9E, 0x5D ), 222 BYTES_TO_T_UINT_8( 0x6F, 0x2C, 0x26, 0x96, 0x4A, 0xDE, 0x17, 0x36 ), 223 }; 224 static const mbedtls_mpi_uint secp384r1_n[] = { 225 BYTES_TO_T_UINT_8( 0x73, 0x29, 0xC5, 0xCC, 0x6A, 0x19, 0xEC, 0xEC ), 226 BYTES_TO_T_UINT_8( 0x7A, 0xA7, 0xB0, 0x48, 0xB2, 0x0D, 0x1A, 0x58 ), 227 BYTES_TO_T_UINT_8( 0xDF, 0x2D, 0x37, 0xF4, 0x81, 0x4D, 0x63, 0xC7 ), 228 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 229 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 230 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 231 }; 232 #endif /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */ 233 234 /* 235 * Domain parameters for secp521r1 236 */ 237 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) 238 static const mbedtls_mpi_uint secp521r1_p[] = { 239 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 240 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 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_2( 0xFF, 0x01 ), 248 }; 249 static const mbedtls_mpi_uint secp521r1_b[] = { 250 BYTES_TO_T_UINT_8( 0x00, 0x3F, 0x50, 0x6B, 0xD4, 0x1F, 0x45, 0xEF ), 251 BYTES_TO_T_UINT_8( 0xF1, 0x34, 0x2C, 0x3D, 0x88, 0xDF, 0x73, 0x35 ), 252 BYTES_TO_T_UINT_8( 0x07, 0xBF, 0xB1, 0x3B, 0xBD, 0xC0, 0x52, 0x16 ), 253 BYTES_TO_T_UINT_8( 0x7B, 0x93, 0x7E, 0xEC, 0x51, 0x39, 0x19, 0x56 ), 254 BYTES_TO_T_UINT_8( 0xE1, 0x09, 0xF1, 0x8E, 0x91, 0x89, 0xB4, 0xB8 ), 255 BYTES_TO_T_UINT_8( 0xF3, 0x15, 0xB3, 0x99, 0x5B, 0x72, 0xDA, 0xA2 ), 256 BYTES_TO_T_UINT_8( 0xEE, 0x40, 0x85, 0xB6, 0xA0, 0x21, 0x9A, 0x92 ), 257 BYTES_TO_T_UINT_8( 0x1F, 0x9A, 0x1C, 0x8E, 0x61, 0xB9, 0x3E, 0x95 ), 258 BYTES_TO_T_UINT_2( 0x51, 0x00 ), 259 }; 260 static const mbedtls_mpi_uint secp521r1_gx[] = { 261 BYTES_TO_T_UINT_8( 0x66, 0xBD, 0xE5, 0xC2, 0x31, 0x7E, 0x7E, 0xF9 ), 262 BYTES_TO_T_UINT_8( 0x9B, 0x42, 0x6A, 0x85, 0xC1, 0xB3, 0x48, 0x33 ), 263 BYTES_TO_T_UINT_8( 0xDE, 0xA8, 0xFF, 0xA2, 0x27, 0xC1, 0x1D, 0xFE ), 264 BYTES_TO_T_UINT_8( 0x28, 0x59, 0xE7, 0xEF, 0x77, 0x5E, 0x4B, 0xA1 ), 265 BYTES_TO_T_UINT_8( 0xBA, 0x3D, 0x4D, 0x6B, 0x60, 0xAF, 0x28, 0xF8 ), 266 BYTES_TO_T_UINT_8( 0x21, 0xB5, 0x3F, 0x05, 0x39, 0x81, 0x64, 0x9C ), 267 BYTES_TO_T_UINT_8( 0x42, 0xB4, 0x95, 0x23, 0x66, 0xCB, 0x3E, 0x9E ), 268 BYTES_TO_T_UINT_8( 0xCD, 0xE9, 0x04, 0x04, 0xB7, 0x06, 0x8E, 0x85 ), 269 BYTES_TO_T_UINT_2( 0xC6, 0x00 ), 270 }; 271 static const mbedtls_mpi_uint secp521r1_gy[] = { 272 BYTES_TO_T_UINT_8( 0x50, 0x66, 0xD1, 0x9F, 0x76, 0x94, 0xBE, 0x88 ), 273 BYTES_TO_T_UINT_8( 0x40, 0xC2, 0x72, 0xA2, 0x86, 0x70, 0x3C, 0x35 ), 274 BYTES_TO_T_UINT_8( 0x61, 0x07, 0xAD, 0x3F, 0x01, 0xB9, 0x50, 0xC5 ), 275 BYTES_TO_T_UINT_8( 0x40, 0x26, 0xF4, 0x5E, 0x99, 0x72, 0xEE, 0x97 ), 276 BYTES_TO_T_UINT_8( 0x2C, 0x66, 0x3E, 0x27, 0x17, 0xBD, 0xAF, 0x17 ), 277 BYTES_TO_T_UINT_8( 0x68, 0x44, 0x9B, 0x57, 0x49, 0x44, 0xF5, 0x98 ), 278 BYTES_TO_T_UINT_8( 0xD9, 0x1B, 0x7D, 0x2C, 0xB4, 0x5F, 0x8A, 0x5C ), 279 BYTES_TO_T_UINT_8( 0x04, 0xC0, 0x3B, 0x9A, 0x78, 0x6A, 0x29, 0x39 ), 280 BYTES_TO_T_UINT_2( 0x18, 0x01 ), 281 }; 282 static const mbedtls_mpi_uint secp521r1_n[] = { 283 BYTES_TO_T_UINT_8( 0x09, 0x64, 0x38, 0x91, 0x1E, 0xB7, 0x6F, 0xBB ), 284 BYTES_TO_T_UINT_8( 0xAE, 0x47, 0x9C, 0x89, 0xB8, 0xC9, 0xB5, 0x3B ), 285 BYTES_TO_T_UINT_8( 0xD0, 0xA5, 0x09, 0xF7, 0x48, 0x01, 0xCC, 0x7F ), 286 BYTES_TO_T_UINT_8( 0x6B, 0x96, 0x2F, 0xBF, 0x83, 0x87, 0x86, 0x51 ), 287 BYTES_TO_T_UINT_8( 0xFA, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 288 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 289 BYTES_TO_T_UINT_8( 0xFF, 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_2( 0xFF, 0x01 ), 292 }; 293 #endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */ 294 295 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) 296 static const mbedtls_mpi_uint secp192k1_p[] = { 297 BYTES_TO_T_UINT_8( 0x37, 0xEE, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ), 298 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 299 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 300 }; 301 static const mbedtls_mpi_uint secp192k1_a[] = { 302 BYTES_TO_T_UINT_2( 0x00, 0x00 ), 303 }; 304 static const mbedtls_mpi_uint secp192k1_b[] = { 305 BYTES_TO_T_UINT_2( 0x03, 0x00 ), 306 }; 307 static const mbedtls_mpi_uint secp192k1_gx[] = { 308 BYTES_TO_T_UINT_8( 0x7D, 0x6C, 0xE0, 0xEA, 0xB1, 0xD1, 0xA5, 0x1D ), 309 BYTES_TO_T_UINT_8( 0x34, 0xF4, 0xB7, 0x80, 0x02, 0x7D, 0xB0, 0x26 ), 310 BYTES_TO_T_UINT_8( 0xAE, 0xE9, 0x57, 0xC0, 0x0E, 0xF1, 0x4F, 0xDB ), 311 }; 312 static const mbedtls_mpi_uint secp192k1_gy[] = { 313 BYTES_TO_T_UINT_8( 0x9D, 0x2F, 0x5E, 0xD9, 0x88, 0xAA, 0x82, 0x40 ), 314 BYTES_TO_T_UINT_8( 0x34, 0x86, 0xBE, 0x15, 0xD0, 0x63, 0x41, 0x84 ), 315 BYTES_TO_T_UINT_8( 0xA7, 0x28, 0x56, 0x9C, 0x6D, 0x2F, 0x2F, 0x9B ), 316 }; 317 static const mbedtls_mpi_uint secp192k1_n[] = { 318 BYTES_TO_T_UINT_8( 0x8D, 0xFD, 0xDE, 0x74, 0x6A, 0x46, 0x69, 0x0F ), 319 BYTES_TO_T_UINT_8( 0x17, 0xFC, 0xF2, 0x26, 0xFE, 0xFF, 0xFF, 0xFF ), 320 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 321 }; 322 #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */ 323 324 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) 325 static const mbedtls_mpi_uint secp224k1_p[] = { 326 BYTES_TO_T_UINT_8( 0x6D, 0xE5, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ), 327 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 328 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 329 BYTES_TO_T_UINT_4( 0xFF, 0xFF, 0xFF, 0xFF ), 330 }; 331 static const mbedtls_mpi_uint secp224k1_a[] = { 332 BYTES_TO_T_UINT_2( 0x00, 0x00 ), 333 }; 334 static const mbedtls_mpi_uint secp224k1_b[] = { 335 BYTES_TO_T_UINT_2( 0x05, 0x00 ), 336 }; 337 static const mbedtls_mpi_uint secp224k1_gx[] = { 338 BYTES_TO_T_UINT_8( 0x5C, 0xA4, 0xB7, 0xB6, 0x0E, 0x65, 0x7E, 0x0F ), 339 BYTES_TO_T_UINT_8( 0xA9, 0x75, 0x70, 0xE4, 0xE9, 0x67, 0xA4, 0x69 ), 340 BYTES_TO_T_UINT_8( 0xA1, 0x28, 0xFC, 0x30, 0xDF, 0x99, 0xF0, 0x4D ), 341 BYTES_TO_T_UINT_4( 0x33, 0x5B, 0x45, 0xA1 ), 342 }; 343 static const mbedtls_mpi_uint secp224k1_gy[] = { 344 BYTES_TO_T_UINT_8( 0xA5, 0x61, 0x6D, 0x55, 0xDB, 0x4B, 0xCA, 0xE2 ), 345 BYTES_TO_T_UINT_8( 0x59, 0xBD, 0xB0, 0xC0, 0xF7, 0x19, 0xE3, 0xF7 ), 346 BYTES_TO_T_UINT_8( 0xD6, 0xFB, 0xCA, 0x82, 0x42, 0x34, 0xBA, 0x7F ), 347 BYTES_TO_T_UINT_4( 0xED, 0x9F, 0x08, 0x7E ), 348 }; 349 static const mbedtls_mpi_uint secp224k1_n[] = { 350 BYTES_TO_T_UINT_8( 0xF7, 0xB1, 0x9F, 0x76, 0x71, 0xA9, 0xF0, 0xCA ), 351 BYTES_TO_T_UINT_8( 0x84, 0x61, 0xEC, 0xD2, 0xE8, 0xDC, 0x01, 0x00 ), 352 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ), 353 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ), 354 }; 355 #endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */ 356 357 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) 358 static const mbedtls_mpi_uint secp256k1_p[] = { 359 BYTES_TO_T_UINT_8( 0x2F, 0xFC, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ), 360 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 361 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 362 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 363 }; 364 static const mbedtls_mpi_uint secp256k1_a[] = { 365 BYTES_TO_T_UINT_2( 0x00, 0x00 ), 366 }; 367 static const mbedtls_mpi_uint secp256k1_b[] = { 368 BYTES_TO_T_UINT_2( 0x07, 0x00 ), 369 }; 370 static const mbedtls_mpi_uint secp256k1_gx[] = { 371 BYTES_TO_T_UINT_8( 0x98, 0x17, 0xF8, 0x16, 0x5B, 0x81, 0xF2, 0x59 ), 372 BYTES_TO_T_UINT_8( 0xD9, 0x28, 0xCE, 0x2D, 0xDB, 0xFC, 0x9B, 0x02 ), 373 BYTES_TO_T_UINT_8( 0x07, 0x0B, 0x87, 0xCE, 0x95, 0x62, 0xA0, 0x55 ), 374 BYTES_TO_T_UINT_8( 0xAC, 0xBB, 0xDC, 0xF9, 0x7E, 0x66, 0xBE, 0x79 ), 375 }; 376 static const mbedtls_mpi_uint secp256k1_gy[] = { 377 BYTES_TO_T_UINT_8( 0xB8, 0xD4, 0x10, 0xFB, 0x8F, 0xD0, 0x47, 0x9C ), 378 BYTES_TO_T_UINT_8( 0x19, 0x54, 0x85, 0xA6, 0x48, 0xB4, 0x17, 0xFD ), 379 BYTES_TO_T_UINT_8( 0xA8, 0x08, 0x11, 0x0E, 0xFC, 0xFB, 0xA4, 0x5D ), 380 BYTES_TO_T_UINT_8( 0x65, 0xC4, 0xA3, 0x26, 0x77, 0xDA, 0x3A, 0x48 ), 381 }; 382 static const mbedtls_mpi_uint secp256k1_n[] = { 383 BYTES_TO_T_UINT_8( 0x41, 0x41, 0x36, 0xD0, 0x8C, 0x5E, 0xD2, 0xBF ), 384 BYTES_TO_T_UINT_8( 0x3B, 0xA0, 0x48, 0xAF, 0xE6, 0xDC, 0xAE, 0xBA ), 385 BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 386 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 387 }; 388 #endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */ 389 390 /* 391 * Domain parameters for brainpoolP256r1 (RFC 5639 3.4) 392 */ 393 #if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) 394 static const mbedtls_mpi_uint brainpoolP256r1_p[] = { 395 BYTES_TO_T_UINT_8( 0x77, 0x53, 0x6E, 0x1F, 0x1D, 0x48, 0x13, 0x20 ), 396 BYTES_TO_T_UINT_8( 0x28, 0x20, 0x26, 0xD5, 0x23, 0xF6, 0x3B, 0x6E ), 397 BYTES_TO_T_UINT_8( 0x72, 0x8D, 0x83, 0x9D, 0x90, 0x0A, 0x66, 0x3E ), 398 BYTES_TO_T_UINT_8( 0xBC, 0xA9, 0xEE, 0xA1, 0xDB, 0x57, 0xFB, 0xA9 ), 399 }; 400 static const mbedtls_mpi_uint brainpoolP256r1_a[] = { 401 BYTES_TO_T_UINT_8( 0xD9, 0xB5, 0x30, 0xF3, 0x44, 0x4B, 0x4A, 0xE9 ), 402 BYTES_TO_T_UINT_8( 0x6C, 0x5C, 0xDC, 0x26, 0xC1, 0x55, 0x80, 0xFB ), 403 BYTES_TO_T_UINT_8( 0xE7, 0xFF, 0x7A, 0x41, 0x30, 0x75, 0xF6, 0xEE ), 404 BYTES_TO_T_UINT_8( 0x57, 0x30, 0x2C, 0xFC, 0x75, 0x09, 0x5A, 0x7D ), 405 }; 406 static const mbedtls_mpi_uint brainpoolP256r1_b[] = { 407 BYTES_TO_T_UINT_8( 0xB6, 0x07, 0x8C, 0xFF, 0x18, 0xDC, 0xCC, 0x6B ), 408 BYTES_TO_T_UINT_8( 0xCE, 0xE1, 0xF7, 0x5C, 0x29, 0x16, 0x84, 0x95 ), 409 BYTES_TO_T_UINT_8( 0xBF, 0x7C, 0xD7, 0xBB, 0xD9, 0xB5, 0x30, 0xF3 ), 410 BYTES_TO_T_UINT_8( 0x44, 0x4B, 0x4A, 0xE9, 0x6C, 0x5C, 0xDC, 0x26 ), 411 }; 412 static const mbedtls_mpi_uint brainpoolP256r1_gx[] = { 413 BYTES_TO_T_UINT_8( 0x62, 0x32, 0xCE, 0x9A, 0xBD, 0x53, 0x44, 0x3A ), 414 BYTES_TO_T_UINT_8( 0xC2, 0x23, 0xBD, 0xE3, 0xE1, 0x27, 0xDE, 0xB9 ), 415 BYTES_TO_T_UINT_8( 0xAF, 0xB7, 0x81, 0xFC, 0x2F, 0x48, 0x4B, 0x2C ), 416 BYTES_TO_T_UINT_8( 0xCB, 0x57, 0x7E, 0xCB, 0xB9, 0xAE, 0xD2, 0x8B ), 417 }; 418 static const mbedtls_mpi_uint brainpoolP256r1_gy[] = { 419 BYTES_TO_T_UINT_8( 0x97, 0x69, 0x04, 0x2F, 0xC7, 0x54, 0x1D, 0x5C ), 420 BYTES_TO_T_UINT_8( 0x54, 0x8E, 0xED, 0x2D, 0x13, 0x45, 0x77, 0xC2 ), 421 BYTES_TO_T_UINT_8( 0xC9, 0x1D, 0x61, 0x14, 0x1A, 0x46, 0xF8, 0x97 ), 422 BYTES_TO_T_UINT_8( 0xFD, 0xC4, 0xDA, 0xC3, 0x35, 0xF8, 0x7E, 0x54 ), 423 }; 424 static const mbedtls_mpi_uint brainpoolP256r1_n[] = { 425 BYTES_TO_T_UINT_8( 0xA7, 0x56, 0x48, 0x97, 0x82, 0x0E, 0x1E, 0x90 ), 426 BYTES_TO_T_UINT_8( 0xF7, 0xA6, 0x61, 0xB5, 0xA3, 0x7A, 0x39, 0x8C ), 427 BYTES_TO_T_UINT_8( 0x71, 0x8D, 0x83, 0x9D, 0x90, 0x0A, 0x66, 0x3E ), 428 BYTES_TO_T_UINT_8( 0xBC, 0xA9, 0xEE, 0xA1, 0xDB, 0x57, 0xFB, 0xA9 ), 429 }; 430 #endif /* MBEDTLS_ECP_DP_BP256R1_ENABLED */ 431 432 /* 433 * Domain parameters for brainpoolP384r1 (RFC 5639 3.6) 434 */ 435 #if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) 436 static const mbedtls_mpi_uint brainpoolP384r1_p[] = { 437 BYTES_TO_T_UINT_8( 0x53, 0xEC, 0x07, 0x31, 0x13, 0x00, 0x47, 0x87 ), 438 BYTES_TO_T_UINT_8( 0x71, 0x1A, 0x1D, 0x90, 0x29, 0xA7, 0xD3, 0xAC ), 439 BYTES_TO_T_UINT_8( 0x23, 0x11, 0xB7, 0x7F, 0x19, 0xDA, 0xB1, 0x12 ), 440 BYTES_TO_T_UINT_8( 0xB4, 0x56, 0x54, 0xED, 0x09, 0x71, 0x2F, 0x15 ), 441 BYTES_TO_T_UINT_8( 0xDF, 0x41, 0xE6, 0x50, 0x7E, 0x6F, 0x5D, 0x0F ), 442 BYTES_TO_T_UINT_8( 0x28, 0x6D, 0x38, 0xA3, 0x82, 0x1E, 0xB9, 0x8C ), 443 }; 444 static const mbedtls_mpi_uint brainpoolP384r1_a[] = { 445 BYTES_TO_T_UINT_8( 0x26, 0x28, 0xCE, 0x22, 0xDD, 0xC7, 0xA8, 0x04 ), 446 BYTES_TO_T_UINT_8( 0xEB, 0xD4, 0x3A, 0x50, 0x4A, 0x81, 0xA5, 0x8A ), 447 BYTES_TO_T_UINT_8( 0x0F, 0xF9, 0x91, 0xBA, 0xEF, 0x65, 0x91, 0x13 ), 448 BYTES_TO_T_UINT_8( 0x87, 0x27, 0xB2, 0x4F, 0x8E, 0xA2, 0xBE, 0xC2 ), 449 BYTES_TO_T_UINT_8( 0xA0, 0xAF, 0x05, 0xCE, 0x0A, 0x08, 0x72, 0x3C ), 450 BYTES_TO_T_UINT_8( 0x0C, 0x15, 0x8C, 0x3D, 0xC6, 0x82, 0xC3, 0x7B ), 451 }; 452 static const mbedtls_mpi_uint brainpoolP384r1_b[] = { 453 BYTES_TO_T_UINT_8( 0x11, 0x4C, 0x50, 0xFA, 0x96, 0x86, 0xB7, 0x3A ), 454 BYTES_TO_T_UINT_8( 0x94, 0xC9, 0xDB, 0x95, 0x02, 0x39, 0xB4, 0x7C ), 455 BYTES_TO_T_UINT_8( 0xD5, 0x62, 0xEB, 0x3E, 0xA5, 0x0E, 0x88, 0x2E ), 456 BYTES_TO_T_UINT_8( 0xA6, 0xD2, 0xDC, 0x07, 0xE1, 0x7D, 0xB7, 0x2F ), 457 BYTES_TO_T_UINT_8( 0x7C, 0x44, 0xF0, 0x16, 0x54, 0xB5, 0x39, 0x8B ), 458 BYTES_TO_T_UINT_8( 0x26, 0x28, 0xCE, 0x22, 0xDD, 0xC7, 0xA8, 0x04 ), 459 }; 460 static const mbedtls_mpi_uint brainpoolP384r1_gx[] = { 461 BYTES_TO_T_UINT_8( 0x1E, 0xAF, 0xD4, 0x47, 0xE2, 0xB2, 0x87, 0xEF ), 462 BYTES_TO_T_UINT_8( 0xAA, 0x46, 0xD6, 0x36, 0x34, 0xE0, 0x26, 0xE8 ), 463 BYTES_TO_T_UINT_8( 0xE8, 0x10, 0xBD, 0x0C, 0xFE, 0xCA, 0x7F, 0xDB ), 464 BYTES_TO_T_UINT_8( 0xE3, 0x4F, 0xF1, 0x7E, 0xE7, 0xA3, 0x47, 0x88 ), 465 BYTES_TO_T_UINT_8( 0x6B, 0x3F, 0xC1, 0xB7, 0x81, 0x3A, 0xA6, 0xA2 ), 466 BYTES_TO_T_UINT_8( 0xFF, 0x45, 0xCF, 0x68, 0xF0, 0x64, 0x1C, 0x1D ), 467 }; 468 static const mbedtls_mpi_uint brainpoolP384r1_gy[] = { 469 BYTES_TO_T_UINT_8( 0x15, 0x53, 0x3C, 0x26, 0x41, 0x03, 0x82, 0x42 ), 470 BYTES_TO_T_UINT_8( 0x11, 0x81, 0x91, 0x77, 0x21, 0x46, 0x46, 0x0E ), 471 BYTES_TO_T_UINT_8( 0x28, 0x29, 0x91, 0xF9, 0x4F, 0x05, 0x9C, 0xE1 ), 472 BYTES_TO_T_UINT_8( 0x64, 0x58, 0xEC, 0xFE, 0x29, 0x0B, 0xB7, 0x62 ), 473 BYTES_TO_T_UINT_8( 0x52, 0xD5, 0xCF, 0x95, 0x8E, 0xEB, 0xB1, 0x5C ), 474 BYTES_TO_T_UINT_8( 0xA4, 0xC2, 0xF9, 0x20, 0x75, 0x1D, 0xBE, 0x8A ), 475 }; 476 static const mbedtls_mpi_uint brainpoolP384r1_n[] = { 477 BYTES_TO_T_UINT_8( 0x65, 0x65, 0x04, 0xE9, 0x02, 0x32, 0x88, 0x3B ), 478 BYTES_TO_T_UINT_8( 0x10, 0xC3, 0x7F, 0x6B, 0xAF, 0xB6, 0x3A, 0xCF ), 479 BYTES_TO_T_UINT_8( 0xA7, 0x25, 0x04, 0xAC, 0x6C, 0x6E, 0x16, 0x1F ), 480 BYTES_TO_T_UINT_8( 0xB3, 0x56, 0x54, 0xED, 0x09, 0x71, 0x2F, 0x15 ), 481 BYTES_TO_T_UINT_8( 0xDF, 0x41, 0xE6, 0x50, 0x7E, 0x6F, 0x5D, 0x0F ), 482 BYTES_TO_T_UINT_8( 0x28, 0x6D, 0x38, 0xA3, 0x82, 0x1E, 0xB9, 0x8C ), 483 }; 484 #endif /* MBEDTLS_ECP_DP_BP384R1_ENABLED */ 485 486 /* 487 * Domain parameters for brainpoolP512r1 (RFC 5639 3.7) 488 */ 489 #if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) 490 static const mbedtls_mpi_uint brainpoolP512r1_p[] = { 491 BYTES_TO_T_UINT_8( 0xF3, 0x48, 0x3A, 0x58, 0x56, 0x60, 0xAA, 0x28 ), 492 BYTES_TO_T_UINT_8( 0x85, 0xC6, 0x82, 0x2D, 0x2F, 0xFF, 0x81, 0x28 ), 493 BYTES_TO_T_UINT_8( 0xE6, 0x80, 0xA3, 0xE6, 0x2A, 0xA1, 0xCD, 0xAE ), 494 BYTES_TO_T_UINT_8( 0x42, 0x68, 0xC6, 0x9B, 0x00, 0x9B, 0x4D, 0x7D ), 495 BYTES_TO_T_UINT_8( 0x71, 0x08, 0x33, 0x70, 0xCA, 0x9C, 0x63, 0xD6 ), 496 BYTES_TO_T_UINT_8( 0x0E, 0xD2, 0xC9, 0xB3, 0xB3, 0x8D, 0x30, 0xCB ), 497 BYTES_TO_T_UINT_8( 0x07, 0xFC, 0xC9, 0x33, 0xAE, 0xE6, 0xD4, 0x3F ), 498 BYTES_TO_T_UINT_8( 0x8B, 0xC4, 0xE9, 0xDB, 0xB8, 0x9D, 0xDD, 0xAA ), 499 }; 500 static const mbedtls_mpi_uint brainpoolP512r1_a[] = { 501 BYTES_TO_T_UINT_8( 0xCA, 0x94, 0xFC, 0x77, 0x4D, 0xAC, 0xC1, 0xE7 ), 502 BYTES_TO_T_UINT_8( 0xB9, 0xC7, 0xF2, 0x2B, 0xA7, 0x17, 0x11, 0x7F ), 503 BYTES_TO_T_UINT_8( 0xB5, 0xC8, 0x9A, 0x8B, 0xC9, 0xF1, 0x2E, 0x0A ), 504 BYTES_TO_T_UINT_8( 0xA1, 0x3A, 0x25, 0xA8, 0x5A, 0x5D, 0xED, 0x2D ), 505 BYTES_TO_T_UINT_8( 0xBC, 0x63, 0x98, 0xEA, 0xCA, 0x41, 0x34, 0xA8 ), 506 BYTES_TO_T_UINT_8( 0x10, 0x16, 0xF9, 0x3D, 0x8D, 0xDD, 0xCB, 0x94 ), 507 BYTES_TO_T_UINT_8( 0xC5, 0x4C, 0x23, 0xAC, 0x45, 0x71, 0x32, 0xE2 ), 508 BYTES_TO_T_UINT_8( 0x89, 0x3B, 0x60, 0x8B, 0x31, 0xA3, 0x30, 0x78 ), 509 }; 510 static const mbedtls_mpi_uint brainpoolP512r1_b[] = { 511 BYTES_TO_T_UINT_8( 0x23, 0xF7, 0x16, 0x80, 0x63, 0xBD, 0x09, 0x28 ), 512 BYTES_TO_T_UINT_8( 0xDD, 0xE5, 0xBA, 0x5E, 0xB7, 0x50, 0x40, 0x98 ), 513 BYTES_TO_T_UINT_8( 0x67, 0x3E, 0x08, 0xDC, 0xCA, 0x94, 0xFC, 0x77 ), 514 BYTES_TO_T_UINT_8( 0x4D, 0xAC, 0xC1, 0xE7, 0xB9, 0xC7, 0xF2, 0x2B ), 515 BYTES_TO_T_UINT_8( 0xA7, 0x17, 0x11, 0x7F, 0xB5, 0xC8, 0x9A, 0x8B ), 516 BYTES_TO_T_UINT_8( 0xC9, 0xF1, 0x2E, 0x0A, 0xA1, 0x3A, 0x25, 0xA8 ), 517 BYTES_TO_T_UINT_8( 0x5A, 0x5D, 0xED, 0x2D, 0xBC, 0x63, 0x98, 0xEA ), 518 BYTES_TO_T_UINT_8( 0xCA, 0x41, 0x34, 0xA8, 0x10, 0x16, 0xF9, 0x3D ), 519 }; 520 static const mbedtls_mpi_uint brainpoolP512r1_gx[] = { 521 BYTES_TO_T_UINT_8( 0x22, 0xF8, 0xB9, 0xBC, 0x09, 0x22, 0x35, 0x8B ), 522 BYTES_TO_T_UINT_8( 0x68, 0x5E, 0x6A, 0x40, 0x47, 0x50, 0x6D, 0x7C ), 523 BYTES_TO_T_UINT_8( 0x5F, 0x7D, 0xB9, 0x93, 0x7B, 0x68, 0xD1, 0x50 ), 524 BYTES_TO_T_UINT_8( 0x8D, 0xD4, 0xD0, 0xE2, 0x78, 0x1F, 0x3B, 0xFF ), 525 BYTES_TO_T_UINT_8( 0x8E, 0x09, 0xD0, 0xF4, 0xEE, 0x62, 0x3B, 0xB4 ), 526 BYTES_TO_T_UINT_8( 0xC1, 0x16, 0xD9, 0xB5, 0x70, 0x9F, 0xED, 0x85 ), 527 BYTES_TO_T_UINT_8( 0x93, 0x6A, 0x4C, 0x9C, 0x2E, 0x32, 0x21, 0x5A ), 528 BYTES_TO_T_UINT_8( 0x64, 0xD9, 0x2E, 0xD8, 0xBD, 0xE4, 0xAE, 0x81 ), 529 }; 530 static const mbedtls_mpi_uint brainpoolP512r1_gy[] = { 531 BYTES_TO_T_UINT_8( 0x92, 0x08, 0xD8, 0x3A, 0x0F, 0x1E, 0xCD, 0x78 ), 532 BYTES_TO_T_UINT_8( 0x06, 0x54, 0xF0, 0xA8, 0x2F, 0x2B, 0xCA, 0xD1 ), 533 BYTES_TO_T_UINT_8( 0xAE, 0x63, 0x27, 0x8A, 0xD8, 0x4B, 0xCA, 0x5B ), 534 BYTES_TO_T_UINT_8( 0x5E, 0x48, 0x5F, 0x4A, 0x49, 0xDE, 0xDC, 0xB2 ), 535 BYTES_TO_T_UINT_8( 0x11, 0x81, 0x1F, 0x88, 0x5B, 0xC5, 0x00, 0xA0 ), 536 BYTES_TO_T_UINT_8( 0x1A, 0x7B, 0xA5, 0x24, 0x00, 0xF7, 0x09, 0xF2 ), 537 BYTES_TO_T_UINT_8( 0xFD, 0x22, 0x78, 0xCF, 0xA9, 0xBF, 0xEA, 0xC0 ), 538 BYTES_TO_T_UINT_8( 0xEC, 0x32, 0x63, 0x56, 0x5D, 0x38, 0xDE, 0x7D ), 539 }; 540 static const mbedtls_mpi_uint brainpoolP512r1_n[] = { 541 BYTES_TO_T_UINT_8( 0x69, 0x00, 0xA9, 0x9C, 0x82, 0x96, 0x87, 0xB5 ), 542 BYTES_TO_T_UINT_8( 0xDD, 0xDA, 0x5D, 0x08, 0x81, 0xD3, 0xB1, 0x1D ), 543 BYTES_TO_T_UINT_8( 0x47, 0x10, 0xAC, 0x7F, 0x19, 0x61, 0x86, 0x41 ), 544 BYTES_TO_T_UINT_8( 0x19, 0x26, 0xA9, 0x4C, 0x41, 0x5C, 0x3E, 0x55 ), 545 BYTES_TO_T_UINT_8( 0x70, 0x08, 0x33, 0x70, 0xCA, 0x9C, 0x63, 0xD6 ), 546 BYTES_TO_T_UINT_8( 0x0E, 0xD2, 0xC9, 0xB3, 0xB3, 0x8D, 0x30, 0xCB ), 547 BYTES_TO_T_UINT_8( 0x07, 0xFC, 0xC9, 0x33, 0xAE, 0xE6, 0xD4, 0x3F ), 548 BYTES_TO_T_UINT_8( 0x8B, 0xC4, 0xE9, 0xDB, 0xB8, 0x9D, 0xDD, 0xAA ), 549 }; 550 #endif /* MBEDTLS_ECP_DP_BP512R1_ENABLED */ 551 552 /* 553 * Create an MPI from embedded constants 554 * (assumes len is an exact multiple of sizeof mbedtls_mpi_uint) 555 */ 556 static inline void ecp_mpi_load( mbedtls_mpi *X, const mbedtls_mpi_uint *p, size_t len ) 557 { 558 X->s = 1; 559 X->n = len / sizeof( mbedtls_mpi_uint ); 560 X->p = (mbedtls_mpi_uint *) p; 561 } 562 563 /* 564 * Set an MPI to static value 1 565 */ 566 static inline void ecp_mpi_set1( mbedtls_mpi *X ) 567 { 568 static mbedtls_mpi_uint one[] = { 1 }; 569 X->s = 1; 570 X->n = 1; 571 X->p = one; 572 } 573 574 /* 575 * Make group available from embedded constants 576 */ 577 static int ecp_group_load( mbedtls_ecp_group *grp, 578 const mbedtls_mpi_uint *p, size_t plen, 579 const mbedtls_mpi_uint *a, size_t alen, 580 const mbedtls_mpi_uint *b, size_t blen, 581 const mbedtls_mpi_uint *gx, size_t gxlen, 582 const mbedtls_mpi_uint *gy, size_t gylen, 583 const mbedtls_mpi_uint *n, size_t nlen) 584 { 585 ecp_mpi_load( &grp->P, p, plen ); 586 if( a != NULL ) 587 ecp_mpi_load( &grp->A, a, alen ); 588 ecp_mpi_load( &grp->B, b, blen ); 589 ecp_mpi_load( &grp->N, n, nlen ); 590 591 ecp_mpi_load( &grp->G.X, gx, gxlen ); 592 ecp_mpi_load( &grp->G.Y, gy, gylen ); 593 ecp_mpi_set1( &grp->G.Z ); 594 595 grp->pbits = mbedtls_mpi_bitlen( &grp->P ); 596 grp->nbits = mbedtls_mpi_bitlen( &grp->N ); 597 598 grp->h = 1; 599 600 return( 0 ); 601 } 602 603 #if defined(MBEDTLS_ECP_NIST_OPTIM) 604 /* Forward declarations */ 605 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) 606 static int ecp_mod_p192( mbedtls_mpi * ); 607 #endif 608 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) 609 static int ecp_mod_p224( mbedtls_mpi * ); 610 #endif 611 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) 612 static int ecp_mod_p256( mbedtls_mpi * ); 613 #endif 614 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) 615 static int ecp_mod_p384( mbedtls_mpi * ); 616 #endif 617 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) 618 static int ecp_mod_p521( mbedtls_mpi * ); 619 #endif 620 621 #define NIST_MODP( P ) grp->modp = ecp_mod_ ## P; 622 #else 623 #define NIST_MODP( P ) 624 #endif /* MBEDTLS_ECP_NIST_OPTIM */ 625 626 /* Additional forward declarations */ 627 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) 628 static int ecp_mod_p255( mbedtls_mpi * ); 629 #endif 630 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) 631 static int ecp_mod_p192k1( mbedtls_mpi * ); 632 #endif 633 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) 634 static int ecp_mod_p224k1( mbedtls_mpi * ); 635 #endif 636 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) 637 static int ecp_mod_p256k1( mbedtls_mpi * ); 638 #endif 639 640 #define LOAD_GROUP_A( G ) ecp_group_load( grp, \ 641 G ## _p, sizeof( G ## _p ), \ 642 G ## _a, sizeof( G ## _a ), \ 643 G ## _b, sizeof( G ## _b ), \ 644 G ## _gx, sizeof( G ## _gx ), \ 645 G ## _gy, sizeof( G ## _gy ), \ 646 G ## _n, sizeof( G ## _n ) ) 647 648 #define LOAD_GROUP( G ) ecp_group_load( grp, \ 649 G ## _p, sizeof( G ## _p ), \ 650 NULL, 0, \ 651 G ## _b, sizeof( G ## _b ), \ 652 G ## _gx, sizeof( G ## _gx ), \ 653 G ## _gy, sizeof( G ## _gy ), \ 654 G ## _n, sizeof( G ## _n ) ) 655 656 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) 657 /* 658 * Specialized function for creating the Curve25519 group 659 */ 660 static int ecp_use_curve25519( mbedtls_ecp_group *grp ) 661 { 662 int ret; 663 664 /* Actually ( A + 2 ) / 4 */ 665 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &grp->A, 16, "01DB42" ) ); 666 667 /* P = 2^255 - 19 */ 668 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->P, 1 ) ); 669 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &grp->P, 255 ) ); 670 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &grp->P, &grp->P, 19 ) ); 671 grp->pbits = mbedtls_mpi_bitlen( &grp->P ); 672 673 /* Y intentionaly not set, since we use x/z coordinates. 674 * This is used as a marker to identify Montgomery curves! */ 675 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.X, 9 ) ); 676 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.Z, 1 ) ); 677 mbedtls_mpi_free( &grp->G.Y ); 678 679 /* Actually, the required msb for private keys */ 680 grp->nbits = 254; 681 682 cleanup: 683 if( ret != 0 ) 684 mbedtls_ecp_group_free( grp ); 685 686 return( ret ); 687 } 688 #endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */ 689 690 /* 691 * Set a group using well-known domain parameters 692 */ 693 int mbedtls_ecp_group_load( mbedtls_ecp_group *grp, mbedtls_ecp_group_id id ) 694 { 695 mbedtls_ecp_group_free( grp ); 696 697 grp->id = id; 698 699 switch( id ) 700 { 701 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) 702 case MBEDTLS_ECP_DP_SECP192R1: 703 NIST_MODP( p192 ); 704 return( LOAD_GROUP( secp192r1 ) ); 705 #endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */ 706 707 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) 708 case MBEDTLS_ECP_DP_SECP224R1: 709 NIST_MODP( p224 ); 710 return( LOAD_GROUP( secp224r1 ) ); 711 #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */ 712 713 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) 714 case MBEDTLS_ECP_DP_SECP256R1: 715 NIST_MODP( p256 ); 716 return( LOAD_GROUP( secp256r1 ) ); 717 #endif /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */ 718 719 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) 720 case MBEDTLS_ECP_DP_SECP384R1: 721 NIST_MODP( p384 ); 722 return( LOAD_GROUP( secp384r1 ) ); 723 #endif /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */ 724 725 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) 726 case MBEDTLS_ECP_DP_SECP521R1: 727 NIST_MODP( p521 ); 728 return( LOAD_GROUP( secp521r1 ) ); 729 #endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */ 730 731 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) 732 case MBEDTLS_ECP_DP_SECP192K1: 733 grp->modp = ecp_mod_p192k1; 734 return( LOAD_GROUP_A( secp192k1 ) ); 735 #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */ 736 737 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) 738 case MBEDTLS_ECP_DP_SECP224K1: 739 grp->modp = ecp_mod_p224k1; 740 return( LOAD_GROUP_A( secp224k1 ) ); 741 #endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */ 742 743 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) 744 case MBEDTLS_ECP_DP_SECP256K1: 745 grp->modp = ecp_mod_p256k1; 746 return( LOAD_GROUP_A( secp256k1 ) ); 747 #endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */ 748 749 #if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) 750 case MBEDTLS_ECP_DP_BP256R1: 751 return( LOAD_GROUP_A( brainpoolP256r1 ) ); 752 #endif /* MBEDTLS_ECP_DP_BP256R1_ENABLED */ 753 754 #if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) 755 case MBEDTLS_ECP_DP_BP384R1: 756 return( LOAD_GROUP_A( brainpoolP384r1 ) ); 757 #endif /* MBEDTLS_ECP_DP_BP384R1_ENABLED */ 758 759 #if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) 760 case MBEDTLS_ECP_DP_BP512R1: 761 return( LOAD_GROUP_A( brainpoolP512r1 ) ); 762 #endif /* MBEDTLS_ECP_DP_BP512R1_ENABLED */ 763 764 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) 765 case MBEDTLS_ECP_DP_CURVE25519: 766 grp->modp = ecp_mod_p255; 767 return( ecp_use_curve25519( grp ) ); 768 #endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */ 769 770 default: 771 mbedtls_ecp_group_free( grp ); 772 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE ); 773 } 774 } 775 776 #if defined(MBEDTLS_ECP_NIST_OPTIM) 777 /* 778 * Fast reduction modulo the primes used by the NIST curves. 779 * 780 * These functions are critical for speed, but not needed for correct 781 * operations. So, we make the choice to heavily rely on the internals of our 782 * bignum library, which creates a tight coupling between these functions and 783 * our MPI implementation. However, the coupling between the ECP module and 784 * MPI remains loose, since these functions can be deactivated at will. 785 */ 786 787 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) 788 /* 789 * Compared to the way things are presented in FIPS 186-3 D.2, 790 * we proceed in columns, from right (least significant chunk) to left, 791 * adding chunks to N in place, and keeping a carry for the next chunk. 792 * This avoids moving things around in memory, and uselessly adding zeros, 793 * compared to the more straightforward, line-oriented approach. 794 * 795 * For this prime we need to handle data in chunks of 64 bits. 796 * Since this is always a multiple of our basic mbedtls_mpi_uint, we can 797 * use a mbedtls_mpi_uint * to designate such a chunk, and small loops to handle it. 798 */ 799 800 /* Add 64-bit chunks (dst += src) and update carry */ 801 static inline void add64( mbedtls_mpi_uint *dst, mbedtls_mpi_uint *src, mbedtls_mpi_uint *carry ) 802 { 803 unsigned char i; 804 mbedtls_mpi_uint c = 0; 805 for( i = 0; i < 8 / sizeof( mbedtls_mpi_uint ); i++, dst++, src++ ) 806 { 807 *dst += c; c = ( *dst < c ); 808 *dst += *src; c += ( *dst < *src ); 809 } 810 *carry += c; 811 } 812 813 /* Add carry to a 64-bit chunk and update carry */ 814 static inline void carry64( mbedtls_mpi_uint *dst, mbedtls_mpi_uint *carry ) 815 { 816 unsigned char i; 817 for( i = 0; i < 8 / sizeof( mbedtls_mpi_uint ); i++, dst++ ) 818 { 819 *dst += *carry; 820 *carry = ( *dst < *carry ); 821 } 822 } 823 824 #define WIDTH 8 / sizeof( mbedtls_mpi_uint ) 825 #define A( i ) N->p + i * WIDTH 826 #define ADD( i ) add64( p, A( i ), &c ) 827 #define NEXT p += WIDTH; carry64( p, &c ) 828 #define LAST p += WIDTH; *p = c; while( ++p < end ) *p = 0 829 830 /* 831 * Fast quasi-reduction modulo p192 (FIPS 186-3 D.2.1) 832 */ 833 static int ecp_mod_p192( mbedtls_mpi *N ) 834 { 835 int ret; 836 mbedtls_mpi_uint c = 0; 837 mbedtls_mpi_uint *p, *end; 838 839 /* Make sure we have enough blocks so that A(5) is legal */ 840 MBEDTLS_MPI_CHK( mbedtls_mpi_grow( N, 6 * WIDTH ) ); 841 842 p = N->p; 843 end = p + N->n; 844 845 ADD( 3 ); ADD( 5 ); NEXT; // A0 += A3 + A5 846 ADD( 3 ); ADD( 4 ); ADD( 5 ); NEXT; // A1 += A3 + A4 + A5 847 ADD( 4 ); ADD( 5 ); LAST; // A2 += A4 + A5 848 849 cleanup: 850 return( ret ); 851 } 852 853 #undef WIDTH 854 #undef A 855 #undef ADD 856 #undef NEXT 857 #undef LAST 858 #endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */ 859 860 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) || \ 861 defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) || \ 862 defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) 863 /* 864 * The reader is advised to first understand ecp_mod_p192() since the same 865 * general structure is used here, but with additional complications: 866 * (1) chunks of 32 bits, and (2) subtractions. 867 */ 868 869 /* 870 * For these primes, we need to handle data in chunks of 32 bits. 871 * This makes it more complicated if we use 64 bits limbs in MPI, 872 * which prevents us from using a uniform access method as for p192. 873 * 874 * So, we define a mini abstraction layer to access 32 bit chunks, 875 * load them in 'cur' for work, and store them back from 'cur' when done. 876 * 877 * While at it, also define the size of N in terms of 32-bit chunks. 878 */ 879 #define LOAD32 cur = A( i ); 880 881 #if defined(MBEDTLS_HAVE_INT32) /* 32 bit */ 882 883 #define MAX32 N->n 884 #define A( j ) N->p[j] 885 #define STORE32 N->p[i] = cur; 886 887 #else /* 64-bit */ 888 889 #define MAX32 N->n * 2 890 #define A( j ) j % 2 ? (uint32_t)( N->p[j/2] >> 32 ) : (uint32_t)( N->p[j/2] ) 891 #define STORE32 \ 892 if( i % 2 ) { \ 893 N->p[i/2] &= 0x00000000FFFFFFFF; \ 894 N->p[i/2] |= ((mbedtls_mpi_uint) cur) << 32; \ 895 } else { \ 896 N->p[i/2] &= 0xFFFFFFFF00000000; \ 897 N->p[i/2] |= (mbedtls_mpi_uint) cur; \ 898 } 899 900 #endif /* sizeof( mbedtls_mpi_uint ) */ 901 902 /* 903 * Helpers for addition and subtraction of chunks, with signed carry. 904 */ 905 static inline void add32( uint32_t *dst, uint32_t src, signed char *carry ) 906 { 907 *dst += src; 908 *carry += ( *dst < src ); 909 } 910 911 static inline void sub32( uint32_t *dst, uint32_t src, signed char *carry ) 912 { 913 *carry -= ( *dst < src ); 914 *dst -= src; 915 } 916 917 #define ADD( j ) add32( &cur, A( j ), &c ); 918 #define SUB( j ) sub32( &cur, A( j ), &c ); 919 920 /* 921 * Helpers for the main 'loop' 922 * (see fix_negative for the motivation of C) 923 */ 924 #define INIT( b ) \ 925 int ret; \ 926 signed char c = 0, cc; \ 927 uint32_t cur; \ 928 size_t i = 0, bits = b; \ 929 mbedtls_mpi C; \ 930 mbedtls_mpi_uint Cp[ b / 8 / sizeof( mbedtls_mpi_uint) + 1 ]; \ 931 \ 932 C.s = 1; \ 933 C.n = b / 8 / sizeof( mbedtls_mpi_uint) + 1; \ 934 C.p = Cp; \ 935 memset( Cp, 0, C.n * sizeof( mbedtls_mpi_uint ) ); \ 936 \ 937 MBEDTLS_MPI_CHK( mbedtls_mpi_grow( N, b * 2 / 8 / sizeof( mbedtls_mpi_uint ) ) ); \ 938 LOAD32; 939 940 #define NEXT \ 941 STORE32; i++; LOAD32; \ 942 cc = c; c = 0; \ 943 if( cc < 0 ) \ 944 sub32( &cur, -cc, &c ); \ 945 else \ 946 add32( &cur, cc, &c ); \ 947 948 #define LAST \ 949 STORE32; i++; \ 950 cur = c > 0 ? c : 0; STORE32; \ 951 cur = 0; while( ++i < MAX32 ) { STORE32; } \ 952 if( c < 0 ) fix_negative( N, c, &C, bits ); 953 954 /* 955 * If the result is negative, we get it in the form 956 * c * 2^(bits + 32) + N, with c negative and N positive shorter than 'bits' 957 */ 958 static inline int fix_negative( mbedtls_mpi *N, signed char c, mbedtls_mpi *C, size_t bits ) 959 { 960 int ret; 961 962 /* C = - c * 2^(bits + 32) */ 963 #if !defined(MBEDTLS_HAVE_INT64) 964 ((void) bits); 965 #else 966 if( bits == 224 ) 967 C->p[ C->n - 1 ] = ((mbedtls_mpi_uint) -c) << 32; 968 else 969 #endif 970 C->p[ C->n - 1 ] = (mbedtls_mpi_uint) -c; 971 972 /* N = - ( C - N ) */ 973 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( N, C, N ) ); 974 N->s = -1; 975 976 cleanup: 977 978 return( ret ); 979 } 980 981 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) 982 /* 983 * Fast quasi-reduction modulo p224 (FIPS 186-3 D.2.2) 984 */ 985 static int ecp_mod_p224( mbedtls_mpi *N ) 986 { 987 INIT( 224 ); 988 989 SUB( 7 ); SUB( 11 ); NEXT; // A0 += -A7 - A11 990 SUB( 8 ); SUB( 12 ); NEXT; // A1 += -A8 - A12 991 SUB( 9 ); SUB( 13 ); NEXT; // A2 += -A9 - A13 992 SUB( 10 ); ADD( 7 ); ADD( 11 ); NEXT; // A3 += -A10 + A7 + A11 993 SUB( 11 ); ADD( 8 ); ADD( 12 ); NEXT; // A4 += -A11 + A8 + A12 994 SUB( 12 ); ADD( 9 ); ADD( 13 ); NEXT; // A5 += -A12 + A9 + A13 995 SUB( 13 ); ADD( 10 ); LAST; // A6 += -A13 + A10 996 997 cleanup: 998 return( ret ); 999 } 1000 #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */ 1001 1002 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) 1003 /* 1004 * Fast quasi-reduction modulo p256 (FIPS 186-3 D.2.3) 1005 */ 1006 static int ecp_mod_p256( mbedtls_mpi *N ) 1007 { 1008 INIT( 256 ); 1009 1010 ADD( 8 ); ADD( 9 ); 1011 SUB( 11 ); SUB( 12 ); SUB( 13 ); SUB( 14 ); NEXT; // A0 1012 1013 ADD( 9 ); ADD( 10 ); 1014 SUB( 12 ); SUB( 13 ); SUB( 14 ); SUB( 15 ); NEXT; // A1 1015 1016 ADD( 10 ); ADD( 11 ); 1017 SUB( 13 ); SUB( 14 ); SUB( 15 ); NEXT; // A2 1018 1019 ADD( 11 ); ADD( 11 ); ADD( 12 ); ADD( 12 ); ADD( 13 ); 1020 SUB( 15 ); SUB( 8 ); SUB( 9 ); NEXT; // A3 1021 1022 ADD( 12 ); ADD( 12 ); ADD( 13 ); ADD( 13 ); ADD( 14 ); 1023 SUB( 9 ); SUB( 10 ); NEXT; // A4 1024 1025 ADD( 13 ); ADD( 13 ); ADD( 14 ); ADD( 14 ); ADD( 15 ); 1026 SUB( 10 ); SUB( 11 ); NEXT; // A5 1027 1028 ADD( 14 ); ADD( 14 ); ADD( 15 ); ADD( 15 ); ADD( 14 ); ADD( 13 ); 1029 SUB( 8 ); SUB( 9 ); NEXT; // A6 1030 1031 ADD( 15 ); ADD( 15 ); ADD( 15 ); ADD( 8 ); 1032 SUB( 10 ); SUB( 11 ); SUB( 12 ); SUB( 13 ); LAST; // A7 1033 1034 cleanup: 1035 return( ret ); 1036 } 1037 #endif /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */ 1038 1039 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) 1040 /* 1041 * Fast quasi-reduction modulo p384 (FIPS 186-3 D.2.4) 1042 */ 1043 static int ecp_mod_p384( mbedtls_mpi *N ) 1044 { 1045 INIT( 384 ); 1046 1047 ADD( 12 ); ADD( 21 ); ADD( 20 ); 1048 SUB( 23 ); NEXT; // A0 1049 1050 ADD( 13 ); ADD( 22 ); ADD( 23 ); 1051 SUB( 12 ); SUB( 20 ); NEXT; // A2 1052 1053 ADD( 14 ); ADD( 23 ); 1054 SUB( 13 ); SUB( 21 ); NEXT; // A2 1055 1056 ADD( 15 ); ADD( 12 ); ADD( 20 ); ADD( 21 ); 1057 SUB( 14 ); SUB( 22 ); SUB( 23 ); NEXT; // A3 1058 1059 ADD( 21 ); ADD( 21 ); ADD( 16 ); ADD( 13 ); ADD( 12 ); ADD( 20 ); ADD( 22 ); 1060 SUB( 15 ); SUB( 23 ); SUB( 23 ); NEXT; // A4 1061 1062 ADD( 22 ); ADD( 22 ); ADD( 17 ); ADD( 14 ); ADD( 13 ); ADD( 21 ); ADD( 23 ); 1063 SUB( 16 ); NEXT; // A5 1064 1065 ADD( 23 ); ADD( 23 ); ADD( 18 ); ADD( 15 ); ADD( 14 ); ADD( 22 ); 1066 SUB( 17 ); NEXT; // A6 1067 1068 ADD( 19 ); ADD( 16 ); ADD( 15 ); ADD( 23 ); 1069 SUB( 18 ); NEXT; // A7 1070 1071 ADD( 20 ); ADD( 17 ); ADD( 16 ); 1072 SUB( 19 ); NEXT; // A8 1073 1074 ADD( 21 ); ADD( 18 ); ADD( 17 ); 1075 SUB( 20 ); NEXT; // A9 1076 1077 ADD( 22 ); ADD( 19 ); ADD( 18 ); 1078 SUB( 21 ); NEXT; // A10 1079 1080 ADD( 23 ); ADD( 20 ); ADD( 19 ); 1081 SUB( 22 ); LAST; // A11 1082 1083 cleanup: 1084 return( ret ); 1085 } 1086 #endif /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */ 1087 1088 #undef A 1089 #undef LOAD32 1090 #undef STORE32 1091 #undef MAX32 1092 #undef INIT 1093 #undef NEXT 1094 #undef LAST 1095 1096 #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED || 1097 MBEDTLS_ECP_DP_SECP256R1_ENABLED || 1098 MBEDTLS_ECP_DP_SECP384R1_ENABLED */ 1099 1100 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) 1101 /* 1102 * Here we have an actual Mersenne prime, so things are more straightforward. 1103 * However, chunks are aligned on a 'weird' boundary (521 bits). 1104 */ 1105 1106 /* Size of p521 in terms of mbedtls_mpi_uint */ 1107 #define P521_WIDTH ( 521 / 8 / sizeof( mbedtls_mpi_uint ) + 1 ) 1108 1109 /* Bits to keep in the most significant mbedtls_mpi_uint */ 1110 #define P521_MASK 0x01FF 1111 1112 /* 1113 * Fast quasi-reduction modulo p521 (FIPS 186-3 D.2.5) 1114 * Write N as A1 + 2^521 A0, return A0 + A1 1115 */ 1116 static int ecp_mod_p521( mbedtls_mpi *N ) 1117 { 1118 int ret; 1119 size_t i; 1120 mbedtls_mpi M; 1121 mbedtls_mpi_uint Mp[P521_WIDTH + 1]; 1122 /* Worst case for the size of M is when mbedtls_mpi_uint is 16 bits: 1123 * we need to hold bits 513 to 1056, which is 34 limbs, that is 1124 * P521_WIDTH + 1. Otherwise P521_WIDTH is enough. */ 1125 1126 if( N->n < P521_WIDTH ) 1127 return( 0 ); 1128 1129 /* M = A1 */ 1130 M.s = 1; 1131 M.n = N->n - ( P521_WIDTH - 1 ); 1132 if( M.n > P521_WIDTH + 1 ) 1133 M.n = P521_WIDTH + 1; 1134 M.p = Mp; 1135 memcpy( Mp, N->p + P521_WIDTH - 1, M.n * sizeof( mbedtls_mpi_uint ) ); 1136 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, 521 % ( 8 * sizeof( mbedtls_mpi_uint ) ) ) ); 1137 1138 /* N = A0 */ 1139 N->p[P521_WIDTH - 1] &= P521_MASK; 1140 for( i = P521_WIDTH; i < N->n; i++ ) 1141 N->p[i] = 0; 1142 1143 /* N = A0 + A1 */ 1144 MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) ); 1145 1146 cleanup: 1147 return( ret ); 1148 } 1149 1150 #undef P521_WIDTH 1151 #undef P521_MASK 1152 #endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */ 1153 1154 #endif /* MBEDTLS_ECP_NIST_OPTIM */ 1155 1156 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) 1157 1158 /* Size of p255 in terms of mbedtls_mpi_uint */ 1159 #define P255_WIDTH ( 255 / 8 / sizeof( mbedtls_mpi_uint ) + 1 ) 1160 1161 /* 1162 * Fast quasi-reduction modulo p255 = 2^255 - 19 1163 * Write N as A0 + 2^255 A1, return A0 + 19 * A1 1164 */ 1165 static int ecp_mod_p255( mbedtls_mpi *N ) 1166 { 1167 int ret; 1168 size_t i; 1169 mbedtls_mpi M; 1170 mbedtls_mpi_uint Mp[P255_WIDTH + 2]; 1171 1172 if( N->n < P255_WIDTH ) 1173 return( 0 ); 1174 1175 /* M = A1 */ 1176 M.s = 1; 1177 M.n = N->n - ( P255_WIDTH - 1 ); 1178 if( M.n > P255_WIDTH + 1 ) 1179 M.n = P255_WIDTH + 1; 1180 M.p = Mp; 1181 memset( Mp, 0, sizeof Mp ); 1182 memcpy( Mp, N->p + P255_WIDTH - 1, M.n * sizeof( mbedtls_mpi_uint ) ); 1183 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, 255 % ( 8 * sizeof( mbedtls_mpi_uint ) ) ) ); 1184 M.n++; /* Make room for multiplication by 19 */ 1185 1186 /* N = A0 */ 1187 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( N, 255, 0 ) ); 1188 for( i = P255_WIDTH; i < N->n; i++ ) 1189 N->p[i] = 0; 1190 1191 /* N = A0 + 19 * A1 */ 1192 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &M, 19 ) ); 1193 MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) ); 1194 1195 cleanup: 1196 return( ret ); 1197 } 1198 #endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */ 1199 1200 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) || \ 1201 defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) || \ 1202 defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) 1203 /* 1204 * Fast quasi-reduction modulo P = 2^s - R, 1205 * with R about 33 bits, used by the Koblitz curves. 1206 * 1207 * Write N as A0 + 2^224 A1, return A0 + R * A1. 1208 * Actually do two passes, since R is big. 1209 */ 1210 #define P_KOBLITZ_MAX ( 256 / 8 / sizeof( mbedtls_mpi_uint ) ) // Max limbs in P 1211 #define P_KOBLITZ_R ( 8 / sizeof( mbedtls_mpi_uint ) ) // Limbs in R 1212 static inline int ecp_mod_koblitz( mbedtls_mpi *N, mbedtls_mpi_uint *Rp, size_t p_limbs, 1213 size_t adjust, size_t shift, mbedtls_mpi_uint mask ) 1214 { 1215 int ret; 1216 size_t i; 1217 mbedtls_mpi M, R; 1218 mbedtls_mpi_uint Mp[P_KOBLITZ_MAX + P_KOBLITZ_R + 1]; 1219 1220 if( N->n < p_limbs ) 1221 return( 0 ); 1222 1223 /* Init R */ 1224 R.s = 1; 1225 R.p = Rp; 1226 R.n = P_KOBLITZ_R; 1227 1228 /* Common setup for M */ 1229 M.s = 1; 1230 M.p = Mp; 1231 1232 /* M = A1 */ 1233 M.n = N->n - ( p_limbs - adjust ); 1234 if( M.n > p_limbs + adjust ) 1235 M.n = p_limbs + adjust; 1236 memset( Mp, 0, sizeof Mp ); 1237 memcpy( Mp, N->p + p_limbs - adjust, M.n * sizeof( mbedtls_mpi_uint ) ); 1238 if( shift != 0 ) 1239 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, shift ) ); 1240 M.n += R.n; /* Make room for multiplication by R */ 1241 1242 /* N = A0 */ 1243 if( mask != 0 ) 1244 N->p[p_limbs - 1] &= mask; 1245 for( i = p_limbs; i < N->n; i++ ) 1246 N->p[i] = 0; 1247 1248 /* N = A0 + R * A1 */ 1249 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &M, &M, &R ) ); 1250 MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) ); 1251 1252 /* Second pass */ 1253 1254 /* M = A1 */ 1255 M.n = N->n - ( p_limbs - adjust ); 1256 if( M.n > p_limbs + adjust ) 1257 M.n = p_limbs + adjust; 1258 memset( Mp, 0, sizeof Mp ); 1259 memcpy( Mp, N->p + p_limbs - adjust, M.n * sizeof( mbedtls_mpi_uint ) ); 1260 if( shift != 0 ) 1261 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, shift ) ); 1262 M.n += R.n; /* Make room for multiplication by R */ 1263 1264 /* N = A0 */ 1265 if( mask != 0 ) 1266 N->p[p_limbs - 1] &= mask; 1267 for( i = p_limbs; i < N->n; i++ ) 1268 N->p[i] = 0; 1269 1270 /* N = A0 + R * A1 */ 1271 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &M, &M, &R ) ); 1272 MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) ); 1273 1274 cleanup: 1275 return( ret ); 1276 } 1277 #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED) || 1278 MBEDTLS_ECP_DP_SECP224K1_ENABLED) || 1279 MBEDTLS_ECP_DP_SECP256K1_ENABLED) */ 1280 1281 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) 1282 /* 1283 * Fast quasi-reduction modulo p192k1 = 2^192 - R, 1284 * with R = 2^32 + 2^12 + 2^8 + 2^7 + 2^6 + 2^3 + 1 = 0x0100001119 1285 */ 1286 static int ecp_mod_p192k1( mbedtls_mpi *N ) 1287 { 1288 static mbedtls_mpi_uint Rp[] = { 1289 BYTES_TO_T_UINT_8( 0xC9, 0x11, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) }; 1290 1291 return( ecp_mod_koblitz( N, Rp, 192 / 8 / sizeof( mbedtls_mpi_uint ), 0, 0, 0 ) ); 1292 } 1293 #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */ 1294 1295 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) 1296 /* 1297 * Fast quasi-reduction modulo p224k1 = 2^224 - R, 1298 * with R = 2^32 + 2^12 + 2^11 + 2^9 + 2^7 + 2^4 + 2 + 1 = 0x0100001A93 1299 */ 1300 static int ecp_mod_p224k1( mbedtls_mpi *N ) 1301 { 1302 static mbedtls_mpi_uint Rp[] = { 1303 BYTES_TO_T_UINT_8( 0x93, 0x1A, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) }; 1304 1305 #if defined(MBEDTLS_HAVE_INT64) 1306 return( ecp_mod_koblitz( N, Rp, 4, 1, 32, 0xFFFFFFFF ) ); 1307 #else 1308 return( ecp_mod_koblitz( N, Rp, 224 / 8 / sizeof( mbedtls_mpi_uint ), 0, 0, 0 ) ); 1309 #endif 1310 } 1311 1312 #endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */ 1313 1314 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) 1315 /* 1316 * Fast quasi-reduction modulo p256k1 = 2^256 - R, 1317 * with R = 2^32 + 2^9 + 2^8 + 2^7 + 2^6 + 2^4 + 1 = 0x01000003D1 1318 */ 1319 static int ecp_mod_p256k1( mbedtls_mpi *N ) 1320 { 1321 static mbedtls_mpi_uint Rp[] = { 1322 BYTES_TO_T_UINT_8( 0xD1, 0x03, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) }; 1323 return( ecp_mod_koblitz( N, Rp, 256 / 8 / sizeof( mbedtls_mpi_uint ), 0, 0, 0 ) ); 1324 } 1325 #endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */ 1326 1327 #endif /* !MBEDTLS_ECP_ALT */ 1328 1329 #endif /* MBEDTLS_ECP_C */ 1330