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 33 #include <string.h> 34 35 #if !defined(MBEDTLS_ECP_ALT) 36 37 /* Parameter validation macros based on platform_util.h */ 38 #define ECP_VALIDATE_RET( cond ) \ 39 MBEDTLS_INTERNAL_VALIDATE_RET( cond, MBEDTLS_ERR_ECP_BAD_INPUT_DATA ) 40 #define ECP_VALIDATE( cond ) \ 41 MBEDTLS_INTERNAL_VALIDATE( cond ) 42 43 #if ( defined(__ARMCC_VERSION) || defined(_MSC_VER) ) && \ 44 !defined(inline) && !defined(__cplusplus) 45 #define inline __inline 46 #endif 47 48 /* 49 * Conversion macros for embedded constants: 50 * build lists of mbedtls_mpi_uint's from lists of unsigned char's grouped by 8, 4 or 2 51 */ 52 #if defined(MBEDTLS_HAVE_INT32) 53 54 #define BYTES_TO_T_UINT_4( a, b, c, d ) \ 55 ( (mbedtls_mpi_uint) a << 0 ) | \ 56 ( (mbedtls_mpi_uint) b << 8 ) | \ 57 ( (mbedtls_mpi_uint) c << 16 ) | \ 58 ( (mbedtls_mpi_uint) d << 24 ) 59 60 #define BYTES_TO_T_UINT_2( a, b ) \ 61 BYTES_TO_T_UINT_4( a, b, 0, 0 ) 62 63 #define BYTES_TO_T_UINT_8( a, b, c, d, e, f, g, h ) \ 64 BYTES_TO_T_UINT_4( a, b, c, d ), \ 65 BYTES_TO_T_UINT_4( e, f, g, h ) 66 67 #else /* 64-bits */ 68 69 #define BYTES_TO_T_UINT_8( a, b, c, d, e, f, g, h ) \ 70 ( (mbedtls_mpi_uint) a << 0 ) | \ 71 ( (mbedtls_mpi_uint) b << 8 ) | \ 72 ( (mbedtls_mpi_uint) c << 16 ) | \ 73 ( (mbedtls_mpi_uint) d << 24 ) | \ 74 ( (mbedtls_mpi_uint) e << 32 ) | \ 75 ( (mbedtls_mpi_uint) f << 40 ) | \ 76 ( (mbedtls_mpi_uint) g << 48 ) | \ 77 ( (mbedtls_mpi_uint) h << 56 ) 78 79 #define BYTES_TO_T_UINT_4( a, b, c, d ) \ 80 BYTES_TO_T_UINT_8( a, b, c, d, 0, 0, 0, 0 ) 81 82 #define BYTES_TO_T_UINT_2( a, b ) \ 83 BYTES_TO_T_UINT_8( a, b, 0, 0, 0, 0, 0, 0 ) 84 85 #endif /* bits in mbedtls_mpi_uint */ 86 87 /* 88 * Note: the constants are in little-endian order 89 * to be directly usable in MPIs 90 */ 91 92 /* 93 * Domain parameters for secp192r1 94 */ 95 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) 96 static const mbedtls_mpi_uint secp192r1_p[] = { 97 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 98 BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 99 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 100 }; 101 static const mbedtls_mpi_uint secp192r1_b[] = { 102 BYTES_TO_T_UINT_8( 0xB1, 0xB9, 0x46, 0xC1, 0xEC, 0xDE, 0xB8, 0xFE ), 103 BYTES_TO_T_UINT_8( 0x49, 0x30, 0x24, 0x72, 0xAB, 0xE9, 0xA7, 0x0F ), 104 BYTES_TO_T_UINT_8( 0xE7, 0x80, 0x9C, 0xE5, 0x19, 0x05, 0x21, 0x64 ), 105 }; 106 static const mbedtls_mpi_uint secp192r1_gx[] = { 107 BYTES_TO_T_UINT_8( 0x12, 0x10, 0xFF, 0x82, 0xFD, 0x0A, 0xFF, 0xF4 ), 108 BYTES_TO_T_UINT_8( 0x00, 0x88, 0xA1, 0x43, 0xEB, 0x20, 0xBF, 0x7C ), 109 BYTES_TO_T_UINT_8( 0xF6, 0x90, 0x30, 0xB0, 0x0E, 0xA8, 0x8D, 0x18 ), 110 }; 111 static const mbedtls_mpi_uint secp192r1_gy[] = { 112 BYTES_TO_T_UINT_8( 0x11, 0x48, 0x79, 0x1E, 0xA1, 0x77, 0xF9, 0x73 ), 113 BYTES_TO_T_UINT_8( 0xD5, 0xCD, 0x24, 0x6B, 0xED, 0x11, 0x10, 0x63 ), 114 BYTES_TO_T_UINT_8( 0x78, 0xDA, 0xC8, 0xFF, 0x95, 0x2B, 0x19, 0x07 ), 115 }; 116 static const mbedtls_mpi_uint secp192r1_n[] = { 117 BYTES_TO_T_UINT_8( 0x31, 0x28, 0xD2, 0xB4, 0xB1, 0xC9, 0x6B, 0x14 ), 118 BYTES_TO_T_UINT_8( 0x36, 0xF8, 0xDE, 0x99, 0xFF, 0xFF, 0xFF, 0xFF ), 119 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 120 }; 121 #endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */ 122 123 /* 124 * Domain parameters for secp224r1 125 */ 126 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) 127 static const mbedtls_mpi_uint secp224r1_p[] = { 128 BYTES_TO_T_UINT_8( 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ), 129 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ), 130 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 131 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ), 132 }; 133 static const mbedtls_mpi_uint secp224r1_b[] = { 134 BYTES_TO_T_UINT_8( 0xB4, 0xFF, 0x55, 0x23, 0x43, 0x39, 0x0B, 0x27 ), 135 BYTES_TO_T_UINT_8( 0xBA, 0xD8, 0xBF, 0xD7, 0xB7, 0xB0, 0x44, 0x50 ), 136 BYTES_TO_T_UINT_8( 0x56, 0x32, 0x41, 0xF5, 0xAB, 0xB3, 0x04, 0x0C ), 137 BYTES_TO_T_UINT_4( 0x85, 0x0A, 0x05, 0xB4 ), 138 }; 139 static const mbedtls_mpi_uint secp224r1_gx[] = { 140 BYTES_TO_T_UINT_8( 0x21, 0x1D, 0x5C, 0x11, 0xD6, 0x80, 0x32, 0x34 ), 141 BYTES_TO_T_UINT_8( 0x22, 0x11, 0xC2, 0x56, 0xD3, 0xC1, 0x03, 0x4A ), 142 BYTES_TO_T_UINT_8( 0xB9, 0x90, 0x13, 0x32, 0x7F, 0xBF, 0xB4, 0x6B ), 143 BYTES_TO_T_UINT_4( 0xBD, 0x0C, 0x0E, 0xB7 ), 144 }; 145 static const mbedtls_mpi_uint secp224r1_gy[] = { 146 BYTES_TO_T_UINT_8( 0x34, 0x7E, 0x00, 0x85, 0x99, 0x81, 0xD5, 0x44 ), 147 BYTES_TO_T_UINT_8( 0x64, 0x47, 0x07, 0x5A, 0xA0, 0x75, 0x43, 0xCD ), 148 BYTES_TO_T_UINT_8( 0xE6, 0xDF, 0x22, 0x4C, 0xFB, 0x23, 0xF7, 0xB5 ), 149 BYTES_TO_T_UINT_4( 0x88, 0x63, 0x37, 0xBD ), 150 }; 151 static const mbedtls_mpi_uint secp224r1_n[] = { 152 BYTES_TO_T_UINT_8( 0x3D, 0x2A, 0x5C, 0x5C, 0x45, 0x29, 0xDD, 0x13 ), 153 BYTES_TO_T_UINT_8( 0x3E, 0xF0, 0xB8, 0xE0, 0xA2, 0x16, 0xFF, 0xFF ), 154 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 155 BYTES_TO_T_UINT_4( 0xFF, 0xFF, 0xFF, 0xFF ), 156 }; 157 #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */ 158 159 /* 160 * Domain parameters for secp256r1 161 */ 162 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) 163 static const mbedtls_mpi_uint secp256r1_p[] = { 164 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 165 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ), 166 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ), 167 BYTES_TO_T_UINT_8( 0x01, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ), 168 }; 169 static const mbedtls_mpi_uint secp256r1_b[] = { 170 BYTES_TO_T_UINT_8( 0x4B, 0x60, 0xD2, 0x27, 0x3E, 0x3C, 0xCE, 0x3B ), 171 BYTES_TO_T_UINT_8( 0xF6, 0xB0, 0x53, 0xCC, 0xB0, 0x06, 0x1D, 0x65 ), 172 BYTES_TO_T_UINT_8( 0xBC, 0x86, 0x98, 0x76, 0x55, 0xBD, 0xEB, 0xB3 ), 173 BYTES_TO_T_UINT_8( 0xE7, 0x93, 0x3A, 0xAA, 0xD8, 0x35, 0xC6, 0x5A ), 174 }; 175 static const mbedtls_mpi_uint secp256r1_gx[] = { 176 BYTES_TO_T_UINT_8( 0x96, 0xC2, 0x98, 0xD8, 0x45, 0x39, 0xA1, 0xF4 ), 177 BYTES_TO_T_UINT_8( 0xA0, 0x33, 0xEB, 0x2D, 0x81, 0x7D, 0x03, 0x77 ), 178 BYTES_TO_T_UINT_8( 0xF2, 0x40, 0xA4, 0x63, 0xE5, 0xE6, 0xBC, 0xF8 ), 179 BYTES_TO_T_UINT_8( 0x47, 0x42, 0x2C, 0xE1, 0xF2, 0xD1, 0x17, 0x6B ), 180 }; 181 static const mbedtls_mpi_uint secp256r1_gy[] = { 182 BYTES_TO_T_UINT_8( 0xF5, 0x51, 0xBF, 0x37, 0x68, 0x40, 0xB6, 0xCB ), 183 BYTES_TO_T_UINT_8( 0xCE, 0x5E, 0x31, 0x6B, 0x57, 0x33, 0xCE, 0x2B ), 184 BYTES_TO_T_UINT_8( 0x16, 0x9E, 0x0F, 0x7C, 0x4A, 0xEB, 0xE7, 0x8E ), 185 BYTES_TO_T_UINT_8( 0x9B, 0x7F, 0x1A, 0xFE, 0xE2, 0x42, 0xE3, 0x4F ), 186 }; 187 static const mbedtls_mpi_uint secp256r1_n[] = { 188 BYTES_TO_T_UINT_8( 0x51, 0x25, 0x63, 0xFC, 0xC2, 0xCA, 0xB9, 0xF3 ), 189 BYTES_TO_T_UINT_8( 0x84, 0x9E, 0x17, 0xA7, 0xAD, 0xFA, 0xE6, 0xBC ), 190 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 191 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ), 192 }; 193 #endif /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */ 194 195 /* 196 * Domain parameters for secp384r1 197 */ 198 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) 199 static const mbedtls_mpi_uint secp384r1_p[] = { 200 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ), 201 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ), 202 BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 203 BYTES_TO_T_UINT_8( 0xFF, 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 }; 207 static const mbedtls_mpi_uint secp384r1_b[] = { 208 BYTES_TO_T_UINT_8( 0xEF, 0x2A, 0xEC, 0xD3, 0xED, 0xC8, 0x85, 0x2A ), 209 BYTES_TO_T_UINT_8( 0x9D, 0xD1, 0x2E, 0x8A, 0x8D, 0x39, 0x56, 0xC6 ), 210 BYTES_TO_T_UINT_8( 0x5A, 0x87, 0x13, 0x50, 0x8F, 0x08, 0x14, 0x03 ), 211 BYTES_TO_T_UINT_8( 0x12, 0x41, 0x81, 0xFE, 0x6E, 0x9C, 0x1D, 0x18 ), 212 BYTES_TO_T_UINT_8( 0x19, 0x2D, 0xF8, 0xE3, 0x6B, 0x05, 0x8E, 0x98 ), 213 BYTES_TO_T_UINT_8( 0xE4, 0xE7, 0x3E, 0xE2, 0xA7, 0x2F, 0x31, 0xB3 ), 214 }; 215 static const mbedtls_mpi_uint secp384r1_gx[] = { 216 BYTES_TO_T_UINT_8( 0xB7, 0x0A, 0x76, 0x72, 0x38, 0x5E, 0x54, 0x3A ), 217 BYTES_TO_T_UINT_8( 0x6C, 0x29, 0x55, 0xBF, 0x5D, 0xF2, 0x02, 0x55 ), 218 BYTES_TO_T_UINT_8( 0x38, 0x2A, 0x54, 0x82, 0xE0, 0x41, 0xF7, 0x59 ), 219 BYTES_TO_T_UINT_8( 0x98, 0x9B, 0xA7, 0x8B, 0x62, 0x3B, 0x1D, 0x6E ), 220 BYTES_TO_T_UINT_8( 0x74, 0xAD, 0x20, 0xF3, 0x1E, 0xC7, 0xB1, 0x8E ), 221 BYTES_TO_T_UINT_8( 0x37, 0x05, 0x8B, 0xBE, 0x22, 0xCA, 0x87, 0xAA ), 222 }; 223 static const mbedtls_mpi_uint secp384r1_gy[] = { 224 BYTES_TO_T_UINT_8( 0x5F, 0x0E, 0xEA, 0x90, 0x7C, 0x1D, 0x43, 0x7A ), 225 BYTES_TO_T_UINT_8( 0x9D, 0x81, 0x7E, 0x1D, 0xCE, 0xB1, 0x60, 0x0A ), 226 BYTES_TO_T_UINT_8( 0xC0, 0xB8, 0xF0, 0xB5, 0x13, 0x31, 0xDA, 0xE9 ), 227 BYTES_TO_T_UINT_8( 0x7C, 0x14, 0x9A, 0x28, 0xBD, 0x1D, 0xF4, 0xF8 ), 228 BYTES_TO_T_UINT_8( 0x29, 0xDC, 0x92, 0x92, 0xBF, 0x98, 0x9E, 0x5D ), 229 BYTES_TO_T_UINT_8( 0x6F, 0x2C, 0x26, 0x96, 0x4A, 0xDE, 0x17, 0x36 ), 230 }; 231 static const mbedtls_mpi_uint secp384r1_n[] = { 232 BYTES_TO_T_UINT_8( 0x73, 0x29, 0xC5, 0xCC, 0x6A, 0x19, 0xEC, 0xEC ), 233 BYTES_TO_T_UINT_8( 0x7A, 0xA7, 0xB0, 0x48, 0xB2, 0x0D, 0x1A, 0x58 ), 234 BYTES_TO_T_UINT_8( 0xDF, 0x2D, 0x37, 0xF4, 0x81, 0x4D, 0x63, 0xC7 ), 235 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 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 }; 239 #endif /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */ 240 241 /* 242 * Domain parameters for secp521r1 243 */ 244 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) 245 static const mbedtls_mpi_uint secp521r1_p[] = { 246 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 247 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 248 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 249 BYTES_TO_T_UINT_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_2( 0xFF, 0x01 ), 255 }; 256 static const mbedtls_mpi_uint secp521r1_b[] = { 257 BYTES_TO_T_UINT_8( 0x00, 0x3F, 0x50, 0x6B, 0xD4, 0x1F, 0x45, 0xEF ), 258 BYTES_TO_T_UINT_8( 0xF1, 0x34, 0x2C, 0x3D, 0x88, 0xDF, 0x73, 0x35 ), 259 BYTES_TO_T_UINT_8( 0x07, 0xBF, 0xB1, 0x3B, 0xBD, 0xC0, 0x52, 0x16 ), 260 BYTES_TO_T_UINT_8( 0x7B, 0x93, 0x7E, 0xEC, 0x51, 0x39, 0x19, 0x56 ), 261 BYTES_TO_T_UINT_8( 0xE1, 0x09, 0xF1, 0x8E, 0x91, 0x89, 0xB4, 0xB8 ), 262 BYTES_TO_T_UINT_8( 0xF3, 0x15, 0xB3, 0x99, 0x5B, 0x72, 0xDA, 0xA2 ), 263 BYTES_TO_T_UINT_8( 0xEE, 0x40, 0x85, 0xB6, 0xA0, 0x21, 0x9A, 0x92 ), 264 BYTES_TO_T_UINT_8( 0x1F, 0x9A, 0x1C, 0x8E, 0x61, 0xB9, 0x3E, 0x95 ), 265 BYTES_TO_T_UINT_2( 0x51, 0x00 ), 266 }; 267 static const mbedtls_mpi_uint secp521r1_gx[] = { 268 BYTES_TO_T_UINT_8( 0x66, 0xBD, 0xE5, 0xC2, 0x31, 0x7E, 0x7E, 0xF9 ), 269 BYTES_TO_T_UINT_8( 0x9B, 0x42, 0x6A, 0x85, 0xC1, 0xB3, 0x48, 0x33 ), 270 BYTES_TO_T_UINT_8( 0xDE, 0xA8, 0xFF, 0xA2, 0x27, 0xC1, 0x1D, 0xFE ), 271 BYTES_TO_T_UINT_8( 0x28, 0x59, 0xE7, 0xEF, 0x77, 0x5E, 0x4B, 0xA1 ), 272 BYTES_TO_T_UINT_8( 0xBA, 0x3D, 0x4D, 0x6B, 0x60, 0xAF, 0x28, 0xF8 ), 273 BYTES_TO_T_UINT_8( 0x21, 0xB5, 0x3F, 0x05, 0x39, 0x81, 0x64, 0x9C ), 274 BYTES_TO_T_UINT_8( 0x42, 0xB4, 0x95, 0x23, 0x66, 0xCB, 0x3E, 0x9E ), 275 BYTES_TO_T_UINT_8( 0xCD, 0xE9, 0x04, 0x04, 0xB7, 0x06, 0x8E, 0x85 ), 276 BYTES_TO_T_UINT_2( 0xC6, 0x00 ), 277 }; 278 static const mbedtls_mpi_uint secp521r1_gy[] = { 279 BYTES_TO_T_UINT_8( 0x50, 0x66, 0xD1, 0x9F, 0x76, 0x94, 0xBE, 0x88 ), 280 BYTES_TO_T_UINT_8( 0x40, 0xC2, 0x72, 0xA2, 0x86, 0x70, 0x3C, 0x35 ), 281 BYTES_TO_T_UINT_8( 0x61, 0x07, 0xAD, 0x3F, 0x01, 0xB9, 0x50, 0xC5 ), 282 BYTES_TO_T_UINT_8( 0x40, 0x26, 0xF4, 0x5E, 0x99, 0x72, 0xEE, 0x97 ), 283 BYTES_TO_T_UINT_8( 0x2C, 0x66, 0x3E, 0x27, 0x17, 0xBD, 0xAF, 0x17 ), 284 BYTES_TO_T_UINT_8( 0x68, 0x44, 0x9B, 0x57, 0x49, 0x44, 0xF5, 0x98 ), 285 BYTES_TO_T_UINT_8( 0xD9, 0x1B, 0x7D, 0x2C, 0xB4, 0x5F, 0x8A, 0x5C ), 286 BYTES_TO_T_UINT_8( 0x04, 0xC0, 0x3B, 0x9A, 0x78, 0x6A, 0x29, 0x39 ), 287 BYTES_TO_T_UINT_2( 0x18, 0x01 ), 288 }; 289 static const mbedtls_mpi_uint secp521r1_n[] = { 290 BYTES_TO_T_UINT_8( 0x09, 0x64, 0x38, 0x91, 0x1E, 0xB7, 0x6F, 0xBB ), 291 BYTES_TO_T_UINT_8( 0xAE, 0x47, 0x9C, 0x89, 0xB8, 0xC9, 0xB5, 0x3B ), 292 BYTES_TO_T_UINT_8( 0xD0, 0xA5, 0x09, 0xF7, 0x48, 0x01, 0xCC, 0x7F ), 293 BYTES_TO_T_UINT_8( 0x6B, 0x96, 0x2F, 0xBF, 0x83, 0x87, 0x86, 0x51 ), 294 BYTES_TO_T_UINT_8( 0xFA, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 295 BYTES_TO_T_UINT_8( 0xFF, 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_2( 0xFF, 0x01 ), 299 }; 300 #endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */ 301 302 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) 303 static const mbedtls_mpi_uint secp192k1_p[] = { 304 BYTES_TO_T_UINT_8( 0x37, 0xEE, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ), 305 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 306 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 307 }; 308 static const mbedtls_mpi_uint secp192k1_a[] = { 309 BYTES_TO_T_UINT_2( 0x00, 0x00 ), 310 }; 311 static const mbedtls_mpi_uint secp192k1_b[] = { 312 BYTES_TO_T_UINT_2( 0x03, 0x00 ), 313 }; 314 static const mbedtls_mpi_uint secp192k1_gx[] = { 315 BYTES_TO_T_UINT_8( 0x7D, 0x6C, 0xE0, 0xEA, 0xB1, 0xD1, 0xA5, 0x1D ), 316 BYTES_TO_T_UINT_8( 0x34, 0xF4, 0xB7, 0x80, 0x02, 0x7D, 0xB0, 0x26 ), 317 BYTES_TO_T_UINT_8( 0xAE, 0xE9, 0x57, 0xC0, 0x0E, 0xF1, 0x4F, 0xDB ), 318 }; 319 static const mbedtls_mpi_uint secp192k1_gy[] = { 320 BYTES_TO_T_UINT_8( 0x9D, 0x2F, 0x5E, 0xD9, 0x88, 0xAA, 0x82, 0x40 ), 321 BYTES_TO_T_UINT_8( 0x34, 0x86, 0xBE, 0x15, 0xD0, 0x63, 0x41, 0x84 ), 322 BYTES_TO_T_UINT_8( 0xA7, 0x28, 0x56, 0x9C, 0x6D, 0x2F, 0x2F, 0x9B ), 323 }; 324 static const mbedtls_mpi_uint secp192k1_n[] = { 325 BYTES_TO_T_UINT_8( 0x8D, 0xFD, 0xDE, 0x74, 0x6A, 0x46, 0x69, 0x0F ), 326 BYTES_TO_T_UINT_8( 0x17, 0xFC, 0xF2, 0x26, 0xFE, 0xFF, 0xFF, 0xFF ), 327 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 328 }; 329 #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */ 330 331 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) 332 static const mbedtls_mpi_uint secp224k1_p[] = { 333 BYTES_TO_T_UINT_8( 0x6D, 0xE5, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ), 334 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 335 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 336 BYTES_TO_T_UINT_4( 0xFF, 0xFF, 0xFF, 0xFF ), 337 }; 338 static const mbedtls_mpi_uint secp224k1_a[] = { 339 BYTES_TO_T_UINT_2( 0x00, 0x00 ), 340 }; 341 static const mbedtls_mpi_uint secp224k1_b[] = { 342 BYTES_TO_T_UINT_2( 0x05, 0x00 ), 343 }; 344 static const mbedtls_mpi_uint secp224k1_gx[] = { 345 BYTES_TO_T_UINT_8( 0x5C, 0xA4, 0xB7, 0xB6, 0x0E, 0x65, 0x7E, 0x0F ), 346 BYTES_TO_T_UINT_8( 0xA9, 0x75, 0x70, 0xE4, 0xE9, 0x67, 0xA4, 0x69 ), 347 BYTES_TO_T_UINT_8( 0xA1, 0x28, 0xFC, 0x30, 0xDF, 0x99, 0xF0, 0x4D ), 348 BYTES_TO_T_UINT_4( 0x33, 0x5B, 0x45, 0xA1 ), 349 }; 350 static const mbedtls_mpi_uint secp224k1_gy[] = { 351 BYTES_TO_T_UINT_8( 0xA5, 0x61, 0x6D, 0x55, 0xDB, 0x4B, 0xCA, 0xE2 ), 352 BYTES_TO_T_UINT_8( 0x59, 0xBD, 0xB0, 0xC0, 0xF7, 0x19, 0xE3, 0xF7 ), 353 BYTES_TO_T_UINT_8( 0xD6, 0xFB, 0xCA, 0x82, 0x42, 0x34, 0xBA, 0x7F ), 354 BYTES_TO_T_UINT_4( 0xED, 0x9F, 0x08, 0x7E ), 355 }; 356 static const mbedtls_mpi_uint secp224k1_n[] = { 357 BYTES_TO_T_UINT_8( 0xF7, 0xB1, 0x9F, 0x76, 0x71, 0xA9, 0xF0, 0xCA ), 358 BYTES_TO_T_UINT_8( 0x84, 0x61, 0xEC, 0xD2, 0xE8, 0xDC, 0x01, 0x00 ), 359 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ), 360 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ), 361 }; 362 #endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */ 363 364 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) 365 static const mbedtls_mpi_uint secp256k1_p[] = { 366 BYTES_TO_T_UINT_8( 0x2F, 0xFC, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ), 367 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 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 }; 371 static const mbedtls_mpi_uint secp256k1_a[] = { 372 BYTES_TO_T_UINT_2( 0x00, 0x00 ), 373 }; 374 static const mbedtls_mpi_uint secp256k1_b[] = { 375 BYTES_TO_T_UINT_2( 0x07, 0x00 ), 376 }; 377 static const mbedtls_mpi_uint secp256k1_gx[] = { 378 BYTES_TO_T_UINT_8( 0x98, 0x17, 0xF8, 0x16, 0x5B, 0x81, 0xF2, 0x59 ), 379 BYTES_TO_T_UINT_8( 0xD9, 0x28, 0xCE, 0x2D, 0xDB, 0xFC, 0x9B, 0x02 ), 380 BYTES_TO_T_UINT_8( 0x07, 0x0B, 0x87, 0xCE, 0x95, 0x62, 0xA0, 0x55 ), 381 BYTES_TO_T_UINT_8( 0xAC, 0xBB, 0xDC, 0xF9, 0x7E, 0x66, 0xBE, 0x79 ), 382 }; 383 static const mbedtls_mpi_uint secp256k1_gy[] = { 384 BYTES_TO_T_UINT_8( 0xB8, 0xD4, 0x10, 0xFB, 0x8F, 0xD0, 0x47, 0x9C ), 385 BYTES_TO_T_UINT_8( 0x19, 0x54, 0x85, 0xA6, 0x48, 0xB4, 0x17, 0xFD ), 386 BYTES_TO_T_UINT_8( 0xA8, 0x08, 0x11, 0x0E, 0xFC, 0xFB, 0xA4, 0x5D ), 387 BYTES_TO_T_UINT_8( 0x65, 0xC4, 0xA3, 0x26, 0x77, 0xDA, 0x3A, 0x48 ), 388 }; 389 static const mbedtls_mpi_uint secp256k1_n[] = { 390 BYTES_TO_T_UINT_8( 0x41, 0x41, 0x36, 0xD0, 0x8C, 0x5E, 0xD2, 0xBF ), 391 BYTES_TO_T_UINT_8( 0x3B, 0xA0, 0x48, 0xAF, 0xE6, 0xDC, 0xAE, 0xBA ), 392 BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 393 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 394 }; 395 #endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */ 396 397 /* 398 * Domain parameters for brainpoolP256r1 (RFC 5639 3.4) 399 */ 400 #if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) 401 static const mbedtls_mpi_uint brainpoolP256r1_p[] = { 402 BYTES_TO_T_UINT_8( 0x77, 0x53, 0x6E, 0x1F, 0x1D, 0x48, 0x13, 0x20 ), 403 BYTES_TO_T_UINT_8( 0x28, 0x20, 0x26, 0xD5, 0x23, 0xF6, 0x3B, 0x6E ), 404 BYTES_TO_T_UINT_8( 0x72, 0x8D, 0x83, 0x9D, 0x90, 0x0A, 0x66, 0x3E ), 405 BYTES_TO_T_UINT_8( 0xBC, 0xA9, 0xEE, 0xA1, 0xDB, 0x57, 0xFB, 0xA9 ), 406 }; 407 static const mbedtls_mpi_uint brainpoolP256r1_a[] = { 408 BYTES_TO_T_UINT_8( 0xD9, 0xB5, 0x30, 0xF3, 0x44, 0x4B, 0x4A, 0xE9 ), 409 BYTES_TO_T_UINT_8( 0x6C, 0x5C, 0xDC, 0x26, 0xC1, 0x55, 0x80, 0xFB ), 410 BYTES_TO_T_UINT_8( 0xE7, 0xFF, 0x7A, 0x41, 0x30, 0x75, 0xF6, 0xEE ), 411 BYTES_TO_T_UINT_8( 0x57, 0x30, 0x2C, 0xFC, 0x75, 0x09, 0x5A, 0x7D ), 412 }; 413 static const mbedtls_mpi_uint brainpoolP256r1_b[] = { 414 BYTES_TO_T_UINT_8( 0xB6, 0x07, 0x8C, 0xFF, 0x18, 0xDC, 0xCC, 0x6B ), 415 BYTES_TO_T_UINT_8( 0xCE, 0xE1, 0xF7, 0x5C, 0x29, 0x16, 0x84, 0x95 ), 416 BYTES_TO_T_UINT_8( 0xBF, 0x7C, 0xD7, 0xBB, 0xD9, 0xB5, 0x30, 0xF3 ), 417 BYTES_TO_T_UINT_8( 0x44, 0x4B, 0x4A, 0xE9, 0x6C, 0x5C, 0xDC, 0x26 ), 418 }; 419 static const mbedtls_mpi_uint brainpoolP256r1_gx[] = { 420 BYTES_TO_T_UINT_8( 0x62, 0x32, 0xCE, 0x9A, 0xBD, 0x53, 0x44, 0x3A ), 421 BYTES_TO_T_UINT_8( 0xC2, 0x23, 0xBD, 0xE3, 0xE1, 0x27, 0xDE, 0xB9 ), 422 BYTES_TO_T_UINT_8( 0xAF, 0xB7, 0x81, 0xFC, 0x2F, 0x48, 0x4B, 0x2C ), 423 BYTES_TO_T_UINT_8( 0xCB, 0x57, 0x7E, 0xCB, 0xB9, 0xAE, 0xD2, 0x8B ), 424 }; 425 static const mbedtls_mpi_uint brainpoolP256r1_gy[] = { 426 BYTES_TO_T_UINT_8( 0x97, 0x69, 0x04, 0x2F, 0xC7, 0x54, 0x1D, 0x5C ), 427 BYTES_TO_T_UINT_8( 0x54, 0x8E, 0xED, 0x2D, 0x13, 0x45, 0x77, 0xC2 ), 428 BYTES_TO_T_UINT_8( 0xC9, 0x1D, 0x61, 0x14, 0x1A, 0x46, 0xF8, 0x97 ), 429 BYTES_TO_T_UINT_8( 0xFD, 0xC4, 0xDA, 0xC3, 0x35, 0xF8, 0x7E, 0x54 ), 430 }; 431 static const mbedtls_mpi_uint brainpoolP256r1_n[] = { 432 BYTES_TO_T_UINT_8( 0xA7, 0x56, 0x48, 0x97, 0x82, 0x0E, 0x1E, 0x90 ), 433 BYTES_TO_T_UINT_8( 0xF7, 0xA6, 0x61, 0xB5, 0xA3, 0x7A, 0x39, 0x8C ), 434 BYTES_TO_T_UINT_8( 0x71, 0x8D, 0x83, 0x9D, 0x90, 0x0A, 0x66, 0x3E ), 435 BYTES_TO_T_UINT_8( 0xBC, 0xA9, 0xEE, 0xA1, 0xDB, 0x57, 0xFB, 0xA9 ), 436 }; 437 #endif /* MBEDTLS_ECP_DP_BP256R1_ENABLED */ 438 439 /* 440 * Domain parameters for brainpoolP384r1 (RFC 5639 3.6) 441 */ 442 #if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) 443 static const mbedtls_mpi_uint brainpoolP384r1_p[] = { 444 BYTES_TO_T_UINT_8( 0x53, 0xEC, 0x07, 0x31, 0x13, 0x00, 0x47, 0x87 ), 445 BYTES_TO_T_UINT_8( 0x71, 0x1A, 0x1D, 0x90, 0x29, 0xA7, 0xD3, 0xAC ), 446 BYTES_TO_T_UINT_8( 0x23, 0x11, 0xB7, 0x7F, 0x19, 0xDA, 0xB1, 0x12 ), 447 BYTES_TO_T_UINT_8( 0xB4, 0x56, 0x54, 0xED, 0x09, 0x71, 0x2F, 0x15 ), 448 BYTES_TO_T_UINT_8( 0xDF, 0x41, 0xE6, 0x50, 0x7E, 0x6F, 0x5D, 0x0F ), 449 BYTES_TO_T_UINT_8( 0x28, 0x6D, 0x38, 0xA3, 0x82, 0x1E, 0xB9, 0x8C ), 450 }; 451 static const mbedtls_mpi_uint brainpoolP384r1_a[] = { 452 BYTES_TO_T_UINT_8( 0x26, 0x28, 0xCE, 0x22, 0xDD, 0xC7, 0xA8, 0x04 ), 453 BYTES_TO_T_UINT_8( 0xEB, 0xD4, 0x3A, 0x50, 0x4A, 0x81, 0xA5, 0x8A ), 454 BYTES_TO_T_UINT_8( 0x0F, 0xF9, 0x91, 0xBA, 0xEF, 0x65, 0x91, 0x13 ), 455 BYTES_TO_T_UINT_8( 0x87, 0x27, 0xB2, 0x4F, 0x8E, 0xA2, 0xBE, 0xC2 ), 456 BYTES_TO_T_UINT_8( 0xA0, 0xAF, 0x05, 0xCE, 0x0A, 0x08, 0x72, 0x3C ), 457 BYTES_TO_T_UINT_8( 0x0C, 0x15, 0x8C, 0x3D, 0xC6, 0x82, 0xC3, 0x7B ), 458 }; 459 static const mbedtls_mpi_uint brainpoolP384r1_b[] = { 460 BYTES_TO_T_UINT_8( 0x11, 0x4C, 0x50, 0xFA, 0x96, 0x86, 0xB7, 0x3A ), 461 BYTES_TO_T_UINT_8( 0x94, 0xC9, 0xDB, 0x95, 0x02, 0x39, 0xB4, 0x7C ), 462 BYTES_TO_T_UINT_8( 0xD5, 0x62, 0xEB, 0x3E, 0xA5, 0x0E, 0x88, 0x2E ), 463 BYTES_TO_T_UINT_8( 0xA6, 0xD2, 0xDC, 0x07, 0xE1, 0x7D, 0xB7, 0x2F ), 464 BYTES_TO_T_UINT_8( 0x7C, 0x44, 0xF0, 0x16, 0x54, 0xB5, 0x39, 0x8B ), 465 BYTES_TO_T_UINT_8( 0x26, 0x28, 0xCE, 0x22, 0xDD, 0xC7, 0xA8, 0x04 ), 466 }; 467 static const mbedtls_mpi_uint brainpoolP384r1_gx[] = { 468 BYTES_TO_T_UINT_8( 0x1E, 0xAF, 0xD4, 0x47, 0xE2, 0xB2, 0x87, 0xEF ), 469 BYTES_TO_T_UINT_8( 0xAA, 0x46, 0xD6, 0x36, 0x34, 0xE0, 0x26, 0xE8 ), 470 BYTES_TO_T_UINT_8( 0xE8, 0x10, 0xBD, 0x0C, 0xFE, 0xCA, 0x7F, 0xDB ), 471 BYTES_TO_T_UINT_8( 0xE3, 0x4F, 0xF1, 0x7E, 0xE7, 0xA3, 0x47, 0x88 ), 472 BYTES_TO_T_UINT_8( 0x6B, 0x3F, 0xC1, 0xB7, 0x81, 0x3A, 0xA6, 0xA2 ), 473 BYTES_TO_T_UINT_8( 0xFF, 0x45, 0xCF, 0x68, 0xF0, 0x64, 0x1C, 0x1D ), 474 }; 475 static const mbedtls_mpi_uint brainpoolP384r1_gy[] = { 476 BYTES_TO_T_UINT_8( 0x15, 0x53, 0x3C, 0x26, 0x41, 0x03, 0x82, 0x42 ), 477 BYTES_TO_T_UINT_8( 0x11, 0x81, 0x91, 0x77, 0x21, 0x46, 0x46, 0x0E ), 478 BYTES_TO_T_UINT_8( 0x28, 0x29, 0x91, 0xF9, 0x4F, 0x05, 0x9C, 0xE1 ), 479 BYTES_TO_T_UINT_8( 0x64, 0x58, 0xEC, 0xFE, 0x29, 0x0B, 0xB7, 0x62 ), 480 BYTES_TO_T_UINT_8( 0x52, 0xD5, 0xCF, 0x95, 0x8E, 0xEB, 0xB1, 0x5C ), 481 BYTES_TO_T_UINT_8( 0xA4, 0xC2, 0xF9, 0x20, 0x75, 0x1D, 0xBE, 0x8A ), 482 }; 483 static const mbedtls_mpi_uint brainpoolP384r1_n[] = { 484 BYTES_TO_T_UINT_8( 0x65, 0x65, 0x04, 0xE9, 0x02, 0x32, 0x88, 0x3B ), 485 BYTES_TO_T_UINT_8( 0x10, 0xC3, 0x7F, 0x6B, 0xAF, 0xB6, 0x3A, 0xCF ), 486 BYTES_TO_T_UINT_8( 0xA7, 0x25, 0x04, 0xAC, 0x6C, 0x6E, 0x16, 0x1F ), 487 BYTES_TO_T_UINT_8( 0xB3, 0x56, 0x54, 0xED, 0x09, 0x71, 0x2F, 0x15 ), 488 BYTES_TO_T_UINT_8( 0xDF, 0x41, 0xE6, 0x50, 0x7E, 0x6F, 0x5D, 0x0F ), 489 BYTES_TO_T_UINT_8( 0x28, 0x6D, 0x38, 0xA3, 0x82, 0x1E, 0xB9, 0x8C ), 490 }; 491 #endif /* MBEDTLS_ECP_DP_BP384R1_ENABLED */ 492 493 /* 494 * Domain parameters for brainpoolP512r1 (RFC 5639 3.7) 495 */ 496 #if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) 497 static const mbedtls_mpi_uint brainpoolP512r1_p[] = { 498 BYTES_TO_T_UINT_8( 0xF3, 0x48, 0x3A, 0x58, 0x56, 0x60, 0xAA, 0x28 ), 499 BYTES_TO_T_UINT_8( 0x85, 0xC6, 0x82, 0x2D, 0x2F, 0xFF, 0x81, 0x28 ), 500 BYTES_TO_T_UINT_8( 0xE6, 0x80, 0xA3, 0xE6, 0x2A, 0xA1, 0xCD, 0xAE ), 501 BYTES_TO_T_UINT_8( 0x42, 0x68, 0xC6, 0x9B, 0x00, 0x9B, 0x4D, 0x7D ), 502 BYTES_TO_T_UINT_8( 0x71, 0x08, 0x33, 0x70, 0xCA, 0x9C, 0x63, 0xD6 ), 503 BYTES_TO_T_UINT_8( 0x0E, 0xD2, 0xC9, 0xB3, 0xB3, 0x8D, 0x30, 0xCB ), 504 BYTES_TO_T_UINT_8( 0x07, 0xFC, 0xC9, 0x33, 0xAE, 0xE6, 0xD4, 0x3F ), 505 BYTES_TO_T_UINT_8( 0x8B, 0xC4, 0xE9, 0xDB, 0xB8, 0x9D, 0xDD, 0xAA ), 506 }; 507 static const mbedtls_mpi_uint brainpoolP512r1_a[] = { 508 BYTES_TO_T_UINT_8( 0xCA, 0x94, 0xFC, 0x77, 0x4D, 0xAC, 0xC1, 0xE7 ), 509 BYTES_TO_T_UINT_8( 0xB9, 0xC7, 0xF2, 0x2B, 0xA7, 0x17, 0x11, 0x7F ), 510 BYTES_TO_T_UINT_8( 0xB5, 0xC8, 0x9A, 0x8B, 0xC9, 0xF1, 0x2E, 0x0A ), 511 BYTES_TO_T_UINT_8( 0xA1, 0x3A, 0x25, 0xA8, 0x5A, 0x5D, 0xED, 0x2D ), 512 BYTES_TO_T_UINT_8( 0xBC, 0x63, 0x98, 0xEA, 0xCA, 0x41, 0x34, 0xA8 ), 513 BYTES_TO_T_UINT_8( 0x10, 0x16, 0xF9, 0x3D, 0x8D, 0xDD, 0xCB, 0x94 ), 514 BYTES_TO_T_UINT_8( 0xC5, 0x4C, 0x23, 0xAC, 0x45, 0x71, 0x32, 0xE2 ), 515 BYTES_TO_T_UINT_8( 0x89, 0x3B, 0x60, 0x8B, 0x31, 0xA3, 0x30, 0x78 ), 516 }; 517 static const mbedtls_mpi_uint brainpoolP512r1_b[] = { 518 BYTES_TO_T_UINT_8( 0x23, 0xF7, 0x16, 0x80, 0x63, 0xBD, 0x09, 0x28 ), 519 BYTES_TO_T_UINT_8( 0xDD, 0xE5, 0xBA, 0x5E, 0xB7, 0x50, 0x40, 0x98 ), 520 BYTES_TO_T_UINT_8( 0x67, 0x3E, 0x08, 0xDC, 0xCA, 0x94, 0xFC, 0x77 ), 521 BYTES_TO_T_UINT_8( 0x4D, 0xAC, 0xC1, 0xE7, 0xB9, 0xC7, 0xF2, 0x2B ), 522 BYTES_TO_T_UINT_8( 0xA7, 0x17, 0x11, 0x7F, 0xB5, 0xC8, 0x9A, 0x8B ), 523 BYTES_TO_T_UINT_8( 0xC9, 0xF1, 0x2E, 0x0A, 0xA1, 0x3A, 0x25, 0xA8 ), 524 BYTES_TO_T_UINT_8( 0x5A, 0x5D, 0xED, 0x2D, 0xBC, 0x63, 0x98, 0xEA ), 525 BYTES_TO_T_UINT_8( 0xCA, 0x41, 0x34, 0xA8, 0x10, 0x16, 0xF9, 0x3D ), 526 }; 527 static const mbedtls_mpi_uint brainpoolP512r1_gx[] = { 528 BYTES_TO_T_UINT_8( 0x22, 0xF8, 0xB9, 0xBC, 0x09, 0x22, 0x35, 0x8B ), 529 BYTES_TO_T_UINT_8( 0x68, 0x5E, 0x6A, 0x40, 0x47, 0x50, 0x6D, 0x7C ), 530 BYTES_TO_T_UINT_8( 0x5F, 0x7D, 0xB9, 0x93, 0x7B, 0x68, 0xD1, 0x50 ), 531 BYTES_TO_T_UINT_8( 0x8D, 0xD4, 0xD0, 0xE2, 0x78, 0x1F, 0x3B, 0xFF ), 532 BYTES_TO_T_UINT_8( 0x8E, 0x09, 0xD0, 0xF4, 0xEE, 0x62, 0x3B, 0xB4 ), 533 BYTES_TO_T_UINT_8( 0xC1, 0x16, 0xD9, 0xB5, 0x70, 0x9F, 0xED, 0x85 ), 534 BYTES_TO_T_UINT_8( 0x93, 0x6A, 0x4C, 0x9C, 0x2E, 0x32, 0x21, 0x5A ), 535 BYTES_TO_T_UINT_8( 0x64, 0xD9, 0x2E, 0xD8, 0xBD, 0xE4, 0xAE, 0x81 ), 536 }; 537 static const mbedtls_mpi_uint brainpoolP512r1_gy[] = { 538 BYTES_TO_T_UINT_8( 0x92, 0x08, 0xD8, 0x3A, 0x0F, 0x1E, 0xCD, 0x78 ), 539 BYTES_TO_T_UINT_8( 0x06, 0x54, 0xF0, 0xA8, 0x2F, 0x2B, 0xCA, 0xD1 ), 540 BYTES_TO_T_UINT_8( 0xAE, 0x63, 0x27, 0x8A, 0xD8, 0x4B, 0xCA, 0x5B ), 541 BYTES_TO_T_UINT_8( 0x5E, 0x48, 0x5F, 0x4A, 0x49, 0xDE, 0xDC, 0xB2 ), 542 BYTES_TO_T_UINT_8( 0x11, 0x81, 0x1F, 0x88, 0x5B, 0xC5, 0x00, 0xA0 ), 543 BYTES_TO_T_UINT_8( 0x1A, 0x7B, 0xA5, 0x24, 0x00, 0xF7, 0x09, 0xF2 ), 544 BYTES_TO_T_UINT_8( 0xFD, 0x22, 0x78, 0xCF, 0xA9, 0xBF, 0xEA, 0xC0 ), 545 BYTES_TO_T_UINT_8( 0xEC, 0x32, 0x63, 0x56, 0x5D, 0x38, 0xDE, 0x7D ), 546 }; 547 static const mbedtls_mpi_uint brainpoolP512r1_n[] = { 548 BYTES_TO_T_UINT_8( 0x69, 0x00, 0xA9, 0x9C, 0x82, 0x96, 0x87, 0xB5 ), 549 BYTES_TO_T_UINT_8( 0xDD, 0xDA, 0x5D, 0x08, 0x81, 0xD3, 0xB1, 0x1D ), 550 BYTES_TO_T_UINT_8( 0x47, 0x10, 0xAC, 0x7F, 0x19, 0x61, 0x86, 0x41 ), 551 BYTES_TO_T_UINT_8( 0x19, 0x26, 0xA9, 0x4C, 0x41, 0x5C, 0x3E, 0x55 ), 552 BYTES_TO_T_UINT_8( 0x70, 0x08, 0x33, 0x70, 0xCA, 0x9C, 0x63, 0xD6 ), 553 BYTES_TO_T_UINT_8( 0x0E, 0xD2, 0xC9, 0xB3, 0xB3, 0x8D, 0x30, 0xCB ), 554 BYTES_TO_T_UINT_8( 0x07, 0xFC, 0xC9, 0x33, 0xAE, 0xE6, 0xD4, 0x3F ), 555 BYTES_TO_T_UINT_8( 0x8B, 0xC4, 0xE9, 0xDB, 0xB8, 0x9D, 0xDD, 0xAA ), 556 }; 557 #endif /* MBEDTLS_ECP_DP_BP512R1_ENABLED */ 558 559 /* 560 * Create an MPI from embedded constants 561 * (assumes len is an exact multiple of sizeof mbedtls_mpi_uint) 562 */ 563 static inline void ecp_mpi_load( mbedtls_mpi *X, const mbedtls_mpi_uint *p, size_t len ) 564 { 565 X->s = 1; 566 X->n = len / sizeof( mbedtls_mpi_uint ); 567 X->p = (mbedtls_mpi_uint *) p; 568 } 569 570 /* 571 * Set an MPI to static value 1 572 */ 573 static inline void ecp_mpi_set1( mbedtls_mpi *X ) 574 { 575 static mbedtls_mpi_uint one[] = { 1 }; 576 X->s = 1; 577 X->n = 1; 578 X->p = one; 579 } 580 581 /* 582 * Make group available from embedded constants 583 */ 584 static int ecp_group_load( mbedtls_ecp_group *grp, 585 const mbedtls_mpi_uint *p, size_t plen, 586 const mbedtls_mpi_uint *a, size_t alen, 587 const mbedtls_mpi_uint *b, size_t blen, 588 const mbedtls_mpi_uint *gx, size_t gxlen, 589 const mbedtls_mpi_uint *gy, size_t gylen, 590 const mbedtls_mpi_uint *n, size_t nlen) 591 { 592 ecp_mpi_load( &grp->P, p, plen ); 593 if( a != NULL ) 594 ecp_mpi_load( &grp->A, a, alen ); 595 ecp_mpi_load( &grp->B, b, blen ); 596 ecp_mpi_load( &grp->N, n, nlen ); 597 598 ecp_mpi_load( &grp->G.X, gx, gxlen ); 599 ecp_mpi_load( &grp->G.Y, gy, gylen ); 600 ecp_mpi_set1( &grp->G.Z ); 601 602 grp->pbits = mbedtls_mpi_bitlen( &grp->P ); 603 grp->nbits = mbedtls_mpi_bitlen( &grp->N ); 604 605 grp->h = 1; 606 607 return( 0 ); 608 } 609 610 #if defined(MBEDTLS_ECP_NIST_OPTIM) 611 /* Forward declarations */ 612 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) 613 static int ecp_mod_p192( mbedtls_mpi * ); 614 #endif 615 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) 616 static int ecp_mod_p224( mbedtls_mpi * ); 617 #endif 618 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) 619 static int ecp_mod_p256( mbedtls_mpi * ); 620 #endif 621 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) 622 static int ecp_mod_p384( mbedtls_mpi * ); 623 #endif 624 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) 625 static int ecp_mod_p521( mbedtls_mpi * ); 626 #endif 627 628 #define NIST_MODP( P ) grp->modp = ecp_mod_ ## P; 629 #else 630 #define NIST_MODP( P ) 631 #endif /* MBEDTLS_ECP_NIST_OPTIM */ 632 633 /* Additional forward declarations */ 634 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) 635 static int ecp_mod_p255( mbedtls_mpi * ); 636 #endif 637 #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) 638 static int ecp_mod_p448( mbedtls_mpi * ); 639 #endif 640 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) 641 static int ecp_mod_p192k1( mbedtls_mpi * ); 642 #endif 643 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) 644 static int ecp_mod_p224k1( mbedtls_mpi * ); 645 #endif 646 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) 647 static int ecp_mod_p256k1( mbedtls_mpi * ); 648 #endif 649 650 #define LOAD_GROUP_A( G ) ecp_group_load( grp, \ 651 G ## _p, sizeof( G ## _p ), \ 652 G ## _a, sizeof( G ## _a ), \ 653 G ## _b, sizeof( G ## _b ), \ 654 G ## _gx, sizeof( G ## _gx ), \ 655 G ## _gy, sizeof( G ## _gy ), \ 656 G ## _n, sizeof( G ## _n ) ) 657 658 #define LOAD_GROUP( G ) ecp_group_load( grp, \ 659 G ## _p, sizeof( G ## _p ), \ 660 NULL, 0, \ 661 G ## _b, sizeof( G ## _b ), \ 662 G ## _gx, sizeof( G ## _gx ), \ 663 G ## _gy, sizeof( G ## _gy ), \ 664 G ## _n, sizeof( G ## _n ) ) 665 666 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) 667 /* 668 * Specialized function for creating the Curve25519 group 669 */ 670 static int ecp_use_curve25519( mbedtls_ecp_group *grp ) 671 { 672 int ret; 673 674 /* Actually ( A + 2 ) / 4 */ 675 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &grp->A, 16, "01DB42" ) ); 676 677 /* P = 2^255 - 19 */ 678 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->P, 1 ) ); 679 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &grp->P, 255 ) ); 680 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &grp->P, &grp->P, 19 ) ); 681 grp->pbits = mbedtls_mpi_bitlen( &grp->P ); 682 683 /* N = 2^252 + 27742317777372353535851937790883648493 */ 684 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &grp->N, 16, 685 "14DEF9DEA2F79CD65812631A5CF5D3ED" ) ); 686 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &grp->N, 252, 1 ) ); 687 688 /* Y intentionally not set, since we use x/z coordinates. 689 * This is used as a marker to identify Montgomery curves! */ 690 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.X, 9 ) ); 691 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.Z, 1 ) ); 692 mbedtls_mpi_free( &grp->G.Y ); 693 694 /* Actually, the required msb for private keys */ 695 grp->nbits = 254; 696 697 cleanup: 698 if( ret != 0 ) 699 mbedtls_ecp_group_free( grp ); 700 701 return( ret ); 702 } 703 #endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */ 704 705 #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) 706 /* 707 * Specialized function for creating the Curve448 group 708 */ 709 static int ecp_use_curve448( mbedtls_ecp_group *grp ) 710 { 711 mbedtls_mpi Ns; 712 int ret; 713 714 mbedtls_mpi_init( &Ns ); 715 716 /* Actually ( A + 2 ) / 4 */ 717 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &grp->A, 16, "98AA" ) ); 718 719 /* P = 2^448 - 2^224 - 1 */ 720 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->P, 1 ) ); 721 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &grp->P, 224 ) ); 722 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &grp->P, &grp->P, 1 ) ); 723 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &grp->P, 224 ) ); 724 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &grp->P, &grp->P, 1 ) ); 725 grp->pbits = mbedtls_mpi_bitlen( &grp->P ); 726 727 /* Y intentionally not set, since we use x/z coordinates. 728 * This is used as a marker to identify Montgomery curves! */ 729 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.X, 5 ) ); 730 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.Z, 1 ) ); 731 mbedtls_mpi_free( &grp->G.Y ); 732 733 /* N = 2^446 - 13818066809895115352007386748515426880336692474882178609894547503885 */ 734 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &grp->N, 446, 1 ) ); 735 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &Ns, 16, 736 "8335DC163BB124B65129C96FDE933D8D723A70AADC873D6D54A7BB0D" ) ); 737 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &grp->N, &grp->N, &Ns ) ); 738 739 /* Actually, the required msb for private keys */ 740 grp->nbits = 447; 741 742 cleanup: 743 mbedtls_mpi_free( &Ns ); 744 if( ret != 0 ) 745 mbedtls_ecp_group_free( grp ); 746 747 return( ret ); 748 } 749 #endif /* MBEDTLS_ECP_DP_CURVE448_ENABLED */ 750 751 /* 752 * Set a group using well-known domain parameters 753 */ 754 int mbedtls_ecp_group_load( mbedtls_ecp_group *grp, mbedtls_ecp_group_id id ) 755 { 756 ECP_VALIDATE_RET( grp != NULL ); 757 mbedtls_ecp_group_free( grp ); 758 759 grp->id = id; 760 761 switch( id ) 762 { 763 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) 764 case MBEDTLS_ECP_DP_SECP192R1: 765 NIST_MODP( p192 ); 766 return( LOAD_GROUP( secp192r1 ) ); 767 #endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */ 768 769 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) 770 case MBEDTLS_ECP_DP_SECP224R1: 771 NIST_MODP( p224 ); 772 return( LOAD_GROUP( secp224r1 ) ); 773 #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */ 774 775 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) 776 case MBEDTLS_ECP_DP_SECP256R1: 777 NIST_MODP( p256 ); 778 return( LOAD_GROUP( secp256r1 ) ); 779 #endif /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */ 780 781 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) 782 case MBEDTLS_ECP_DP_SECP384R1: 783 NIST_MODP( p384 ); 784 return( LOAD_GROUP( secp384r1 ) ); 785 #endif /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */ 786 787 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) 788 case MBEDTLS_ECP_DP_SECP521R1: 789 NIST_MODP( p521 ); 790 return( LOAD_GROUP( secp521r1 ) ); 791 #endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */ 792 793 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) 794 case MBEDTLS_ECP_DP_SECP192K1: 795 grp->modp = ecp_mod_p192k1; 796 return( LOAD_GROUP_A( secp192k1 ) ); 797 #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */ 798 799 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) 800 case MBEDTLS_ECP_DP_SECP224K1: 801 grp->modp = ecp_mod_p224k1; 802 return( LOAD_GROUP_A( secp224k1 ) ); 803 #endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */ 804 805 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) 806 case MBEDTLS_ECP_DP_SECP256K1: 807 grp->modp = ecp_mod_p256k1; 808 return( LOAD_GROUP_A( secp256k1 ) ); 809 #endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */ 810 811 #if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) 812 case MBEDTLS_ECP_DP_BP256R1: 813 return( LOAD_GROUP_A( brainpoolP256r1 ) ); 814 #endif /* MBEDTLS_ECP_DP_BP256R1_ENABLED */ 815 816 #if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) 817 case MBEDTLS_ECP_DP_BP384R1: 818 return( LOAD_GROUP_A( brainpoolP384r1 ) ); 819 #endif /* MBEDTLS_ECP_DP_BP384R1_ENABLED */ 820 821 #if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) 822 case MBEDTLS_ECP_DP_BP512R1: 823 return( LOAD_GROUP_A( brainpoolP512r1 ) ); 824 #endif /* MBEDTLS_ECP_DP_BP512R1_ENABLED */ 825 826 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) 827 case MBEDTLS_ECP_DP_CURVE25519: 828 grp->modp = ecp_mod_p255; 829 return( ecp_use_curve25519( grp ) ); 830 #endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */ 831 832 #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) 833 case MBEDTLS_ECP_DP_CURVE448: 834 grp->modp = ecp_mod_p448; 835 return( ecp_use_curve448( grp ) ); 836 #endif /* MBEDTLS_ECP_DP_CURVE448_ENABLED */ 837 838 default: 839 mbedtls_ecp_group_free( grp ); 840 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE ); 841 } 842 } 843 844 #if defined(MBEDTLS_ECP_NIST_OPTIM) 845 /* 846 * Fast reduction modulo the primes used by the NIST curves. 847 * 848 * These functions are critical for speed, but not needed for correct 849 * operations. So, we make the choice to heavily rely on the internals of our 850 * bignum library, which creates a tight coupling between these functions and 851 * our MPI implementation. However, the coupling between the ECP module and 852 * MPI remains loose, since these functions can be deactivated at will. 853 */ 854 855 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) 856 /* 857 * Compared to the way things are presented in FIPS 186-3 D.2, 858 * we proceed in columns, from right (least significant chunk) to left, 859 * adding chunks to N in place, and keeping a carry for the next chunk. 860 * This avoids moving things around in memory, and uselessly adding zeros, 861 * compared to the more straightforward, line-oriented approach. 862 * 863 * For this prime we need to handle data in chunks of 64 bits. 864 * Since this is always a multiple of our basic mbedtls_mpi_uint, we can 865 * use a mbedtls_mpi_uint * to designate such a chunk, and small loops to handle it. 866 */ 867 868 /* Add 64-bit chunks (dst += src) and update carry */ 869 static inline void add64( mbedtls_mpi_uint *dst, mbedtls_mpi_uint *src, mbedtls_mpi_uint *carry ) 870 { 871 unsigned char i; 872 mbedtls_mpi_uint c = 0; 873 for( i = 0; i < 8 / sizeof( mbedtls_mpi_uint ); i++, dst++, src++ ) 874 { 875 *dst += c; c = ( *dst < c ); 876 *dst += *src; c += ( *dst < *src ); 877 } 878 *carry += c; 879 } 880 881 /* Add carry to a 64-bit chunk and update carry */ 882 static inline void carry64( mbedtls_mpi_uint *dst, mbedtls_mpi_uint *carry ) 883 { 884 unsigned char i; 885 for( i = 0; i < 8 / sizeof( mbedtls_mpi_uint ); i++, dst++ ) 886 { 887 *dst += *carry; 888 *carry = ( *dst < *carry ); 889 } 890 } 891 892 #define WIDTH 8 / sizeof( mbedtls_mpi_uint ) 893 #define A( i ) N->p + i * WIDTH 894 #define ADD( i ) add64( p, A( i ), &c ) 895 #define NEXT p += WIDTH; carry64( p, &c ) 896 #define LAST p += WIDTH; *p = c; while( ++p < end ) *p = 0 897 898 /* 899 * Fast quasi-reduction modulo p192 (FIPS 186-3 D.2.1) 900 */ 901 static int ecp_mod_p192( mbedtls_mpi *N ) 902 { 903 int ret; 904 mbedtls_mpi_uint c = 0; 905 mbedtls_mpi_uint *p, *end; 906 907 /* Make sure we have enough blocks so that A(5) is legal */ 908 MBEDTLS_MPI_CHK( mbedtls_mpi_grow( N, 6 * WIDTH ) ); 909 910 p = N->p; 911 end = p + N->n; 912 913 ADD( 3 ); ADD( 5 ); NEXT; // A0 += A3 + A5 914 ADD( 3 ); ADD( 4 ); ADD( 5 ); NEXT; // A1 += A3 + A4 + A5 915 ADD( 4 ); ADD( 5 ); LAST; // A2 += A4 + A5 916 917 cleanup: 918 return( ret ); 919 } 920 921 #undef WIDTH 922 #undef A 923 #undef ADD 924 #undef NEXT 925 #undef LAST 926 #endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */ 927 928 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) || \ 929 defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) || \ 930 defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) 931 /* 932 * The reader is advised to first understand ecp_mod_p192() since the same 933 * general structure is used here, but with additional complications: 934 * (1) chunks of 32 bits, and (2) subtractions. 935 */ 936 937 /* 938 * For these primes, we need to handle data in chunks of 32 bits. 939 * This makes it more complicated if we use 64 bits limbs in MPI, 940 * which prevents us from using a uniform access method as for p192. 941 * 942 * So, we define a mini abstraction layer to access 32 bit chunks, 943 * load them in 'cur' for work, and store them back from 'cur' when done. 944 * 945 * While at it, also define the size of N in terms of 32-bit chunks. 946 */ 947 #define LOAD32 cur = A( i ); 948 949 #if defined(MBEDTLS_HAVE_INT32) /* 32 bit */ 950 951 #define MAX32 N->n 952 #define A( j ) N->p[j] 953 #define STORE32 N->p[i] = cur; 954 955 #else /* 64-bit */ 956 957 #define MAX32 N->n * 2 958 #define A( j ) j % 2 ? (uint32_t)( N->p[j/2] >> 32 ) : (uint32_t)( N->p[j/2] ) 959 #define STORE32 \ 960 if( i % 2 ) { \ 961 N->p[i/2] &= 0x00000000FFFFFFFF; \ 962 N->p[i/2] |= ((mbedtls_mpi_uint) cur) << 32; \ 963 } else { \ 964 N->p[i/2] &= 0xFFFFFFFF00000000; \ 965 N->p[i/2] |= (mbedtls_mpi_uint) cur; \ 966 } 967 968 #endif /* sizeof( mbedtls_mpi_uint ) */ 969 970 /* 971 * Helpers for addition and subtraction of chunks, with signed carry. 972 */ 973 static inline void add32( uint32_t *dst, uint32_t src, signed char *carry ) 974 { 975 *dst += src; 976 *carry += ( *dst < src ); 977 } 978 979 static inline void sub32( uint32_t *dst, uint32_t src, signed char *carry ) 980 { 981 *carry -= ( *dst < src ); 982 *dst -= src; 983 } 984 985 #define ADD( j ) add32( &cur, A( j ), &c ); 986 #define SUB( j ) sub32( &cur, A( j ), &c ); 987 988 /* 989 * Helpers for the main 'loop' 990 * (see fix_negative for the motivation of C) 991 */ 992 #define INIT( b ) \ 993 int ret; \ 994 signed char c = 0, cc; \ 995 uint32_t cur; \ 996 size_t i = 0, bits = b; \ 997 mbedtls_mpi C; \ 998 mbedtls_mpi_uint Cp[ b / 8 / sizeof( mbedtls_mpi_uint) + 1 ]; \ 999 \ 1000 C.s = 1; \ 1001 C.n = b / 8 / sizeof( mbedtls_mpi_uint) + 1; \ 1002 C.p = Cp; \ 1003 memset( Cp, 0, C.n * sizeof( mbedtls_mpi_uint ) ); \ 1004 \ 1005 MBEDTLS_MPI_CHK( mbedtls_mpi_grow( N, b * 2 / 8 / sizeof( mbedtls_mpi_uint ) ) ); \ 1006 LOAD32; 1007 1008 #define NEXT \ 1009 STORE32; i++; LOAD32; \ 1010 cc = c; c = 0; \ 1011 if( cc < 0 ) \ 1012 sub32( &cur, -cc, &c ); \ 1013 else \ 1014 add32( &cur, cc, &c ); \ 1015 1016 #define LAST \ 1017 STORE32; i++; \ 1018 cur = c > 0 ? c : 0; STORE32; \ 1019 cur = 0; while( ++i < MAX32 ) { STORE32; } \ 1020 if( c < 0 ) fix_negative( N, c, &C, bits ); 1021 1022 /* 1023 * If the result is negative, we get it in the form 1024 * c * 2^(bits + 32) + N, with c negative and N positive shorter than 'bits' 1025 */ 1026 static inline int fix_negative( mbedtls_mpi *N, signed char c, mbedtls_mpi *C, size_t bits ) 1027 { 1028 int ret; 1029 1030 /* C = - c * 2^(bits + 32) */ 1031 #if !defined(MBEDTLS_HAVE_INT64) 1032 ((void) bits); 1033 #else 1034 if( bits == 224 ) 1035 C->p[ C->n - 1 ] = ((mbedtls_mpi_uint) -c) << 32; 1036 else 1037 #endif 1038 C->p[ C->n - 1 ] = (mbedtls_mpi_uint) -c; 1039 1040 /* N = - ( C - N ) */ 1041 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( N, C, N ) ); 1042 N->s = -1; 1043 1044 cleanup: 1045 1046 return( ret ); 1047 } 1048 1049 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) 1050 /* 1051 * Fast quasi-reduction modulo p224 (FIPS 186-3 D.2.2) 1052 */ 1053 static int ecp_mod_p224( mbedtls_mpi *N ) 1054 { 1055 INIT( 224 ); 1056 1057 SUB( 7 ); SUB( 11 ); NEXT; // A0 += -A7 - A11 1058 SUB( 8 ); SUB( 12 ); NEXT; // A1 += -A8 - A12 1059 SUB( 9 ); SUB( 13 ); NEXT; // A2 += -A9 - A13 1060 SUB( 10 ); ADD( 7 ); ADD( 11 ); NEXT; // A3 += -A10 + A7 + A11 1061 SUB( 11 ); ADD( 8 ); ADD( 12 ); NEXT; // A4 += -A11 + A8 + A12 1062 SUB( 12 ); ADD( 9 ); ADD( 13 ); NEXT; // A5 += -A12 + A9 + A13 1063 SUB( 13 ); ADD( 10 ); LAST; // A6 += -A13 + A10 1064 1065 cleanup: 1066 return( ret ); 1067 } 1068 #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */ 1069 1070 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) 1071 /* 1072 * Fast quasi-reduction modulo p256 (FIPS 186-3 D.2.3) 1073 */ 1074 static int ecp_mod_p256( mbedtls_mpi *N ) 1075 { 1076 INIT( 256 ); 1077 1078 ADD( 8 ); ADD( 9 ); 1079 SUB( 11 ); SUB( 12 ); SUB( 13 ); SUB( 14 ); NEXT; // A0 1080 1081 ADD( 9 ); ADD( 10 ); 1082 SUB( 12 ); SUB( 13 ); SUB( 14 ); SUB( 15 ); NEXT; // A1 1083 1084 ADD( 10 ); ADD( 11 ); 1085 SUB( 13 ); SUB( 14 ); SUB( 15 ); NEXT; // A2 1086 1087 ADD( 11 ); ADD( 11 ); ADD( 12 ); ADD( 12 ); ADD( 13 ); 1088 SUB( 15 ); SUB( 8 ); SUB( 9 ); NEXT; // A3 1089 1090 ADD( 12 ); ADD( 12 ); ADD( 13 ); ADD( 13 ); ADD( 14 ); 1091 SUB( 9 ); SUB( 10 ); NEXT; // A4 1092 1093 ADD( 13 ); ADD( 13 ); ADD( 14 ); ADD( 14 ); ADD( 15 ); 1094 SUB( 10 ); SUB( 11 ); NEXT; // A5 1095 1096 ADD( 14 ); ADD( 14 ); ADD( 15 ); ADD( 15 ); ADD( 14 ); ADD( 13 ); 1097 SUB( 8 ); SUB( 9 ); NEXT; // A6 1098 1099 ADD( 15 ); ADD( 15 ); ADD( 15 ); ADD( 8 ); 1100 SUB( 10 ); SUB( 11 ); SUB( 12 ); SUB( 13 ); LAST; // A7 1101 1102 cleanup: 1103 return( ret ); 1104 } 1105 #endif /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */ 1106 1107 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) 1108 /* 1109 * Fast quasi-reduction modulo p384 (FIPS 186-3 D.2.4) 1110 */ 1111 static int ecp_mod_p384( mbedtls_mpi *N ) 1112 { 1113 INIT( 384 ); 1114 1115 ADD( 12 ); ADD( 21 ); ADD( 20 ); 1116 SUB( 23 ); NEXT; // A0 1117 1118 ADD( 13 ); ADD( 22 ); ADD( 23 ); 1119 SUB( 12 ); SUB( 20 ); NEXT; // A2 1120 1121 ADD( 14 ); ADD( 23 ); 1122 SUB( 13 ); SUB( 21 ); NEXT; // A2 1123 1124 ADD( 15 ); ADD( 12 ); ADD( 20 ); ADD( 21 ); 1125 SUB( 14 ); SUB( 22 ); SUB( 23 ); NEXT; // A3 1126 1127 ADD( 21 ); ADD( 21 ); ADD( 16 ); ADD( 13 ); ADD( 12 ); ADD( 20 ); ADD( 22 ); 1128 SUB( 15 ); SUB( 23 ); SUB( 23 ); NEXT; // A4 1129 1130 ADD( 22 ); ADD( 22 ); ADD( 17 ); ADD( 14 ); ADD( 13 ); ADD( 21 ); ADD( 23 ); 1131 SUB( 16 ); NEXT; // A5 1132 1133 ADD( 23 ); ADD( 23 ); ADD( 18 ); ADD( 15 ); ADD( 14 ); ADD( 22 ); 1134 SUB( 17 ); NEXT; // A6 1135 1136 ADD( 19 ); ADD( 16 ); ADD( 15 ); ADD( 23 ); 1137 SUB( 18 ); NEXT; // A7 1138 1139 ADD( 20 ); ADD( 17 ); ADD( 16 ); 1140 SUB( 19 ); NEXT; // A8 1141 1142 ADD( 21 ); ADD( 18 ); ADD( 17 ); 1143 SUB( 20 ); NEXT; // A9 1144 1145 ADD( 22 ); ADD( 19 ); ADD( 18 ); 1146 SUB( 21 ); NEXT; // A10 1147 1148 ADD( 23 ); ADD( 20 ); ADD( 19 ); 1149 SUB( 22 ); LAST; // A11 1150 1151 cleanup: 1152 return( ret ); 1153 } 1154 #endif /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */ 1155 1156 #undef A 1157 #undef LOAD32 1158 #undef STORE32 1159 #undef MAX32 1160 #undef INIT 1161 #undef NEXT 1162 #undef LAST 1163 1164 #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED || 1165 MBEDTLS_ECP_DP_SECP256R1_ENABLED || 1166 MBEDTLS_ECP_DP_SECP384R1_ENABLED */ 1167 1168 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) 1169 /* 1170 * Here we have an actual Mersenne prime, so things are more straightforward. 1171 * However, chunks are aligned on a 'weird' boundary (521 bits). 1172 */ 1173 1174 /* Size of p521 in terms of mbedtls_mpi_uint */ 1175 #define P521_WIDTH ( 521 / 8 / sizeof( mbedtls_mpi_uint ) + 1 ) 1176 1177 /* Bits to keep in the most significant mbedtls_mpi_uint */ 1178 #define P521_MASK 0x01FF 1179 1180 /* 1181 * Fast quasi-reduction modulo p521 (FIPS 186-3 D.2.5) 1182 * Write N as A1 + 2^521 A0, return A0 + A1 1183 */ 1184 static int ecp_mod_p521( mbedtls_mpi *N ) 1185 { 1186 int ret; 1187 size_t i; 1188 mbedtls_mpi M; 1189 mbedtls_mpi_uint Mp[P521_WIDTH + 1]; 1190 /* Worst case for the size of M is when mbedtls_mpi_uint is 16 bits: 1191 * we need to hold bits 513 to 1056, which is 34 limbs, that is 1192 * P521_WIDTH + 1. Otherwise P521_WIDTH is enough. */ 1193 1194 if( N->n < P521_WIDTH ) 1195 return( 0 ); 1196 1197 /* M = A1 */ 1198 M.s = 1; 1199 M.n = N->n - ( P521_WIDTH - 1 ); 1200 if( M.n > P521_WIDTH + 1 ) 1201 M.n = P521_WIDTH + 1; 1202 M.p = Mp; 1203 memcpy( Mp, N->p + P521_WIDTH - 1, M.n * sizeof( mbedtls_mpi_uint ) ); 1204 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, 521 % ( 8 * sizeof( mbedtls_mpi_uint ) ) ) ); 1205 1206 /* N = A0 */ 1207 N->p[P521_WIDTH - 1] &= P521_MASK; 1208 for( i = P521_WIDTH; i < N->n; i++ ) 1209 N->p[i] = 0; 1210 1211 /* N = A0 + A1 */ 1212 MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) ); 1213 1214 cleanup: 1215 return( ret ); 1216 } 1217 1218 #undef P521_WIDTH 1219 #undef P521_MASK 1220 #endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */ 1221 1222 #endif /* MBEDTLS_ECP_NIST_OPTIM */ 1223 1224 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) 1225 1226 /* Size of p255 in terms of mbedtls_mpi_uint */ 1227 #define P255_WIDTH ( 255 / 8 / sizeof( mbedtls_mpi_uint ) + 1 ) 1228 1229 /* 1230 * Fast quasi-reduction modulo p255 = 2^255 - 19 1231 * Write N as A0 + 2^255 A1, return A0 + 19 * A1 1232 */ 1233 static int ecp_mod_p255( mbedtls_mpi *N ) 1234 { 1235 int ret; 1236 size_t i; 1237 mbedtls_mpi M; 1238 mbedtls_mpi_uint Mp[P255_WIDTH + 2]; 1239 1240 if( N->n < P255_WIDTH ) 1241 return( 0 ); 1242 1243 /* M = A1 */ 1244 M.s = 1; 1245 M.n = N->n - ( P255_WIDTH - 1 ); 1246 if( M.n > P255_WIDTH + 1 ) 1247 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); 1248 M.p = Mp; 1249 memset( Mp, 0, sizeof Mp ); 1250 memcpy( Mp, N->p + P255_WIDTH - 1, M.n * sizeof( mbedtls_mpi_uint ) ); 1251 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, 255 % ( 8 * sizeof( mbedtls_mpi_uint ) ) ) ); 1252 M.n++; /* Make room for multiplication by 19 */ 1253 1254 /* N = A0 */ 1255 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( N, 255, 0 ) ); 1256 for( i = P255_WIDTH; i < N->n; i++ ) 1257 N->p[i] = 0; 1258 1259 /* N = A0 + 19 * A1 */ 1260 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &M, 19 ) ); 1261 MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) ); 1262 1263 cleanup: 1264 return( ret ); 1265 } 1266 #endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */ 1267 1268 #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) 1269 1270 /* Size of p448 in terms of mbedtls_mpi_uint */ 1271 #define P448_WIDTH ( 448 / 8 / sizeof( mbedtls_mpi_uint ) ) 1272 1273 /* Number of limbs fully occupied by 2^224 (max), and limbs used by it (min) */ 1274 #define DIV_ROUND_UP( X, Y ) ( ( ( X ) + ( Y ) - 1 ) / ( Y ) ) 1275 #define P224_WIDTH_MIN ( 28 / sizeof( mbedtls_mpi_uint ) ) 1276 #define P224_WIDTH_MAX DIV_ROUND_UP( 28, sizeof( mbedtls_mpi_uint ) ) 1277 #define P224_UNUSED_BITS ( ( P224_WIDTH_MAX * sizeof( mbedtls_mpi_uint ) * 8 ) - 224 ) 1278 1279 /* 1280 * Fast quasi-reduction modulo p448 = 2^448 - 2^224 - 1 1281 * Write N as A0 + 2^448 A1 and A1 as B0 + 2^224 B1, and return 1282 * A0 + A1 + B1 + (B0 + B1) * 2^224. This is different to the reference 1283 * implementation of Curve448, which uses its own special 56-bit limbs rather 1284 * than a generic bignum library. We could squeeze some extra speed out on 1285 * 32-bit machines by splitting N up into 32-bit limbs and doing the 1286 * arithmetic using the limbs directly as we do for the NIST primes above, 1287 * but for 64-bit targets it should use half the number of operations if we do 1288 * the reduction with 224-bit limbs, since mpi_add_mpi will then use 64-bit adds. 1289 */ 1290 static int ecp_mod_p448( mbedtls_mpi *N ) 1291 { 1292 int ret; 1293 size_t i; 1294 mbedtls_mpi M, Q; 1295 mbedtls_mpi_uint Mp[P448_WIDTH + 1], Qp[P448_WIDTH]; 1296 1297 if( N->n <= P448_WIDTH ) 1298 return( 0 ); 1299 1300 /* M = A1 */ 1301 M.s = 1; 1302 M.n = N->n - ( P448_WIDTH ); 1303 if( M.n > P448_WIDTH ) 1304 /* Shouldn't be called with N larger than 2^896! */ 1305 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); 1306 M.p = Mp; 1307 memset( Mp, 0, sizeof( Mp ) ); 1308 memcpy( Mp, N->p + P448_WIDTH, M.n * sizeof( mbedtls_mpi_uint ) ); 1309 1310 /* N = A0 */ 1311 for( i = P448_WIDTH; i < N->n; i++ ) 1312 N->p[i] = 0; 1313 1314 /* N += A1 */ 1315 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &M ) ); 1316 1317 /* Q = B1, N += B1 */ 1318 Q = M; 1319 Q.p = Qp; 1320 memcpy( Qp, Mp, sizeof( Qp ) ); 1321 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &Q, 224 ) ); 1322 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &Q ) ); 1323 1324 /* M = (B0 + B1) * 2^224, N += M */ 1325 if( sizeof( mbedtls_mpi_uint ) > 4 ) 1326 Mp[P224_WIDTH_MIN] &= ( (mbedtls_mpi_uint)-1 ) >> ( P224_UNUSED_BITS ); 1327 for( i = P224_WIDTH_MAX; i < M.n; ++i ) 1328 Mp[i] = 0; 1329 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &M, &M, &Q ) ); 1330 M.n = P448_WIDTH + 1; /* Make room for shifted carry bit from the addition */ 1331 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &M, 224 ) ); 1332 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &M ) ); 1333 1334 cleanup: 1335 return( ret ); 1336 } 1337 #endif /* MBEDTLS_ECP_DP_CURVE448_ENABLED */ 1338 1339 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) || \ 1340 defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) || \ 1341 defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) 1342 /* 1343 * Fast quasi-reduction modulo P = 2^s - R, 1344 * with R about 33 bits, used by the Koblitz curves. 1345 * 1346 * Write N as A0 + 2^224 A1, return A0 + R * A1. 1347 * Actually do two passes, since R is big. 1348 */ 1349 #define P_KOBLITZ_MAX ( 256 / 8 / sizeof( mbedtls_mpi_uint ) ) // Max limbs in P 1350 #define P_KOBLITZ_R ( 8 / sizeof( mbedtls_mpi_uint ) ) // Limbs in R 1351 static inline int ecp_mod_koblitz( mbedtls_mpi *N, mbedtls_mpi_uint *Rp, size_t p_limbs, 1352 size_t adjust, size_t shift, mbedtls_mpi_uint mask ) 1353 { 1354 int ret; 1355 size_t i; 1356 mbedtls_mpi M, R; 1357 mbedtls_mpi_uint Mp[P_KOBLITZ_MAX + P_KOBLITZ_R + 1]; 1358 1359 if( N->n < p_limbs ) 1360 return( 0 ); 1361 1362 /* Init R */ 1363 R.s = 1; 1364 R.p = Rp; 1365 R.n = P_KOBLITZ_R; 1366 1367 /* Common setup for M */ 1368 M.s = 1; 1369 M.p = Mp; 1370 1371 /* M = A1 */ 1372 M.n = N->n - ( p_limbs - adjust ); 1373 if( M.n > p_limbs + adjust ) 1374 M.n = p_limbs + adjust; 1375 memset( Mp, 0, sizeof Mp ); 1376 memcpy( Mp, N->p + p_limbs - adjust, M.n * sizeof( mbedtls_mpi_uint ) ); 1377 if( shift != 0 ) 1378 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, shift ) ); 1379 M.n += R.n; /* Make room for multiplication by R */ 1380 1381 /* N = A0 */ 1382 if( mask != 0 ) 1383 N->p[p_limbs - 1] &= mask; 1384 for( i = p_limbs; i < N->n; i++ ) 1385 N->p[i] = 0; 1386 1387 /* N = A0 + R * A1 */ 1388 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &M, &M, &R ) ); 1389 MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) ); 1390 1391 /* Second pass */ 1392 1393 /* M = A1 */ 1394 M.n = N->n - ( p_limbs - adjust ); 1395 if( M.n > p_limbs + adjust ) 1396 M.n = p_limbs + adjust; 1397 memset( Mp, 0, sizeof Mp ); 1398 memcpy( Mp, N->p + p_limbs - adjust, M.n * sizeof( mbedtls_mpi_uint ) ); 1399 if( shift != 0 ) 1400 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, shift ) ); 1401 M.n += R.n; /* Make room for multiplication by R */ 1402 1403 /* N = A0 */ 1404 if( mask != 0 ) 1405 N->p[p_limbs - 1] &= mask; 1406 for( i = p_limbs; i < N->n; i++ ) 1407 N->p[i] = 0; 1408 1409 /* N = A0 + R * A1 */ 1410 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &M, &M, &R ) ); 1411 MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) ); 1412 1413 cleanup: 1414 return( ret ); 1415 } 1416 #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED) || 1417 MBEDTLS_ECP_DP_SECP224K1_ENABLED) || 1418 MBEDTLS_ECP_DP_SECP256K1_ENABLED) */ 1419 1420 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) 1421 /* 1422 * Fast quasi-reduction modulo p192k1 = 2^192 - R, 1423 * with R = 2^32 + 2^12 + 2^8 + 2^7 + 2^6 + 2^3 + 1 = 0x0100001119 1424 */ 1425 static int ecp_mod_p192k1( mbedtls_mpi *N ) 1426 { 1427 static mbedtls_mpi_uint Rp[] = { 1428 BYTES_TO_T_UINT_8( 0xC9, 0x11, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) }; 1429 1430 return( ecp_mod_koblitz( N, Rp, 192 / 8 / sizeof( mbedtls_mpi_uint ), 0, 0, 0 ) ); 1431 } 1432 #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */ 1433 1434 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) 1435 /* 1436 * Fast quasi-reduction modulo p224k1 = 2^224 - R, 1437 * with R = 2^32 + 2^12 + 2^11 + 2^9 + 2^7 + 2^4 + 2 + 1 = 0x0100001A93 1438 */ 1439 static int ecp_mod_p224k1( mbedtls_mpi *N ) 1440 { 1441 static mbedtls_mpi_uint Rp[] = { 1442 BYTES_TO_T_UINT_8( 0x93, 0x1A, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) }; 1443 1444 #if defined(MBEDTLS_HAVE_INT64) 1445 return( ecp_mod_koblitz( N, Rp, 4, 1, 32, 0xFFFFFFFF ) ); 1446 #else 1447 return( ecp_mod_koblitz( N, Rp, 224 / 8 / sizeof( mbedtls_mpi_uint ), 0, 0, 0 ) ); 1448 #endif 1449 } 1450 1451 #endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */ 1452 1453 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) 1454 /* 1455 * Fast quasi-reduction modulo p256k1 = 2^256 - R, 1456 * with R = 2^32 + 2^9 + 2^8 + 2^7 + 2^6 + 2^4 + 1 = 0x01000003D1 1457 */ 1458 static int ecp_mod_p256k1( mbedtls_mpi *N ) 1459 { 1460 static mbedtls_mpi_uint Rp[] = { 1461 BYTES_TO_T_UINT_8( 0xD1, 0x03, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) }; 1462 return( ecp_mod_koblitz( N, Rp, 256 / 8 / sizeof( mbedtls_mpi_uint ), 0, 0, 0 ) ); 1463 } 1464 #endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */ 1465 1466 #endif /* !MBEDTLS_ECP_ALT */ 1467 1468 #endif /* MBEDTLS_ECP_C */ 1469