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ecp_curves.c
00001 /* 00002 * Elliptic curves over GF(p): curve-specific data and functions 00003 * 00004 * Copyright (C) 2006-2015, ARM Limited, All Rights Reserved 00005 * SPDX-License-Identifier: Apache-2.0 00006 * 00007 * Licensed under the Apache License, Version 2.0 (the "License"); you may 00008 * not use this file except in compliance with the License. 00009 * You may obtain a copy of the License at 00010 * 00011 * http://www.apache.org/licenses/LICENSE-2.0 00012 * 00013 * Unless required by applicable law or agreed to in writing, software 00014 * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT 00015 * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 00016 * See the License for the specific language governing permissions and 00017 * limitations under the License. 00018 * 00019 * This file is part of mbed TLS (https://tls.mbed.org) 00020 */ 00021 00022 #if !defined(MBEDTLS_CONFIG_FILE) 00023 #include "mbedtls/config.h" 00024 #else 00025 #include MBEDTLS_CONFIG_FILE 00026 #endif 00027 00028 #if defined(MBEDTLS_ECP_C) 00029 00030 #include "mbedtls/ecp.h" 00031 00032 #include <string.h> 00033 00034 #if !defined(MBEDTLS_ECP_ALT) 00035 00036 #if ( defined(__ARMCC_VERSION) || defined(_MSC_VER) ) && \ 00037 !defined(inline) && !defined(__cplusplus) 00038 #define inline __inline 00039 #endif 00040 00041 /* 00042 * Conversion macros for embedded constants: 00043 * build lists of mbedtls_mpi_uint's from lists of unsigned char's grouped by 8, 4 or 2 00044 */ 00045 #if defined(MBEDTLS_HAVE_INT32) 00046 00047 #define BYTES_TO_T_UINT_4( a, b, c, d ) \ 00048 ( (mbedtls_mpi_uint) a << 0 ) | \ 00049 ( (mbedtls_mpi_uint) b << 8 ) | \ 00050 ( (mbedtls_mpi_uint) c << 16 ) | \ 00051 ( (mbedtls_mpi_uint) d << 24 ) 00052 00053 #define BYTES_TO_T_UINT_2( a, b ) \ 00054 BYTES_TO_T_UINT_4( a, b, 0, 0 ) 00055 00056 #define BYTES_TO_T_UINT_8( a, b, c, d, e, f, g, h ) \ 00057 BYTES_TO_T_UINT_4( a, b, c, d ), \ 00058 BYTES_TO_T_UINT_4( e, f, g, h ) 00059 00060 #else /* 64-bits */ 00061 00062 #define BYTES_TO_T_UINT_8( a, b, c, d, e, f, g, h ) \ 00063 ( (mbedtls_mpi_uint) a << 0 ) | \ 00064 ( (mbedtls_mpi_uint) b << 8 ) | \ 00065 ( (mbedtls_mpi_uint) c << 16 ) | \ 00066 ( (mbedtls_mpi_uint) d << 24 ) | \ 00067 ( (mbedtls_mpi_uint) e << 32 ) | \ 00068 ( (mbedtls_mpi_uint) f << 40 ) | \ 00069 ( (mbedtls_mpi_uint) g << 48 ) | \ 00070 ( (mbedtls_mpi_uint) h << 56 ) 00071 00072 #define BYTES_TO_T_UINT_4( a, b, c, d ) \ 00073 BYTES_TO_T_UINT_8( a, b, c, d, 0, 0, 0, 0 ) 00074 00075 #define BYTES_TO_T_UINT_2( a, b ) \ 00076 BYTES_TO_T_UINT_8( a, b, 0, 0, 0, 0, 0, 0 ) 00077 00078 #endif /* bits in mbedtls_mpi_uint */ 00079 00080 /* 00081 * Note: the constants are in little-endian order 00082 * to be directly usable in MPIs 00083 */ 00084 00085 /* 00086 * Domain parameters for secp192r1 00087 */ 00088 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) 00089 static const mbedtls_mpi_uint secp192r1_p[] = { 00090 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00091 BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00092 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00093 }; 00094 static const mbedtls_mpi_uint secp192r1_b[] = { 00095 BYTES_TO_T_UINT_8( 0xB1, 0xB9, 0x46, 0xC1, 0xEC, 0xDE, 0xB8, 0xFE ), 00096 BYTES_TO_T_UINT_8( 0x49, 0x30, 0x24, 0x72, 0xAB, 0xE9, 0xA7, 0x0F ), 00097 BYTES_TO_T_UINT_8( 0xE7, 0x80, 0x9C, 0xE5, 0x19, 0x05, 0x21, 0x64 ), 00098 }; 00099 static const mbedtls_mpi_uint secp192r1_gx[] = { 00100 BYTES_TO_T_UINT_8( 0x12, 0x10, 0xFF, 0x82, 0xFD, 0x0A, 0xFF, 0xF4 ), 00101 BYTES_TO_T_UINT_8( 0x00, 0x88, 0xA1, 0x43, 0xEB, 0x20, 0xBF, 0x7C ), 00102 BYTES_TO_T_UINT_8( 0xF6, 0x90, 0x30, 0xB0, 0x0E, 0xA8, 0x8D, 0x18 ), 00103 }; 00104 static const mbedtls_mpi_uint secp192r1_gy[] = { 00105 BYTES_TO_T_UINT_8( 0x11, 0x48, 0x79, 0x1E, 0xA1, 0x77, 0xF9, 0x73 ), 00106 BYTES_TO_T_UINT_8( 0xD5, 0xCD, 0x24, 0x6B, 0xED, 0x11, 0x10, 0x63 ), 00107 BYTES_TO_T_UINT_8( 0x78, 0xDA, 0xC8, 0xFF, 0x95, 0x2B, 0x19, 0x07 ), 00108 }; 00109 static const mbedtls_mpi_uint secp192r1_n[] = { 00110 BYTES_TO_T_UINT_8( 0x31, 0x28, 0xD2, 0xB4, 0xB1, 0xC9, 0x6B, 0x14 ), 00111 BYTES_TO_T_UINT_8( 0x36, 0xF8, 0xDE, 0x99, 0xFF, 0xFF, 0xFF, 0xFF ), 00112 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00113 }; 00114 #endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */ 00115 00116 /* 00117 * Domain parameters for secp224r1 00118 */ 00119 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) 00120 static const mbedtls_mpi_uint secp224r1_p[] = { 00121 BYTES_TO_T_UINT_8( 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ), 00122 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ), 00123 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00124 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ), 00125 }; 00126 static const mbedtls_mpi_uint secp224r1_b[] = { 00127 BYTES_TO_T_UINT_8( 0xB4, 0xFF, 0x55, 0x23, 0x43, 0x39, 0x0B, 0x27 ), 00128 BYTES_TO_T_UINT_8( 0xBA, 0xD8, 0xBF, 0xD7, 0xB7, 0xB0, 0x44, 0x50 ), 00129 BYTES_TO_T_UINT_8( 0x56, 0x32, 0x41, 0xF5, 0xAB, 0xB3, 0x04, 0x0C ), 00130 BYTES_TO_T_UINT_4( 0x85, 0x0A, 0x05, 0xB4 ), 00131 }; 00132 static const mbedtls_mpi_uint secp224r1_gx[] = { 00133 BYTES_TO_T_UINT_8( 0x21, 0x1D, 0x5C, 0x11, 0xD6, 0x80, 0x32, 0x34 ), 00134 BYTES_TO_T_UINT_8( 0x22, 0x11, 0xC2, 0x56, 0xD3, 0xC1, 0x03, 0x4A ), 00135 BYTES_TO_T_UINT_8( 0xB9, 0x90, 0x13, 0x32, 0x7F, 0xBF, 0xB4, 0x6B ), 00136 BYTES_TO_T_UINT_4( 0xBD, 0x0C, 0x0E, 0xB7 ), 00137 }; 00138 static const mbedtls_mpi_uint secp224r1_gy[] = { 00139 BYTES_TO_T_UINT_8( 0x34, 0x7E, 0x00, 0x85, 0x99, 0x81, 0xD5, 0x44 ), 00140 BYTES_TO_T_UINT_8( 0x64, 0x47, 0x07, 0x5A, 0xA0, 0x75, 0x43, 0xCD ), 00141 BYTES_TO_T_UINT_8( 0xE6, 0xDF, 0x22, 0x4C, 0xFB, 0x23, 0xF7, 0xB5 ), 00142 BYTES_TO_T_UINT_4( 0x88, 0x63, 0x37, 0xBD ), 00143 }; 00144 static const mbedtls_mpi_uint secp224r1_n[] = { 00145 BYTES_TO_T_UINT_8( 0x3D, 0x2A, 0x5C, 0x5C, 0x45, 0x29, 0xDD, 0x13 ), 00146 BYTES_TO_T_UINT_8( 0x3E, 0xF0, 0xB8, 0xE0, 0xA2, 0x16, 0xFF, 0xFF ), 00147 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00148 BYTES_TO_T_UINT_4( 0xFF, 0xFF, 0xFF, 0xFF ), 00149 }; 00150 #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */ 00151 00152 /* 00153 * Domain parameters for secp256r1 00154 */ 00155 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) 00156 static const mbedtls_mpi_uint secp256r1_p[] = { 00157 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00158 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ), 00159 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ), 00160 BYTES_TO_T_UINT_8( 0x01, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ), 00161 }; 00162 static const mbedtls_mpi_uint secp256r1_b[] = { 00163 BYTES_TO_T_UINT_8( 0x4B, 0x60, 0xD2, 0x27, 0x3E, 0x3C, 0xCE, 0x3B ), 00164 BYTES_TO_T_UINT_8( 0xF6, 0xB0, 0x53, 0xCC, 0xB0, 0x06, 0x1D, 0x65 ), 00165 BYTES_TO_T_UINT_8( 0xBC, 0x86, 0x98, 0x76, 0x55, 0xBD, 0xEB, 0xB3 ), 00166 BYTES_TO_T_UINT_8( 0xE7, 0x93, 0x3A, 0xAA, 0xD8, 0x35, 0xC6, 0x5A ), 00167 }; 00168 static const mbedtls_mpi_uint secp256r1_gx[] = { 00169 BYTES_TO_T_UINT_8( 0x96, 0xC2, 0x98, 0xD8, 0x45, 0x39, 0xA1, 0xF4 ), 00170 BYTES_TO_T_UINT_8( 0xA0, 0x33, 0xEB, 0x2D, 0x81, 0x7D, 0x03, 0x77 ), 00171 BYTES_TO_T_UINT_8( 0xF2, 0x40, 0xA4, 0x63, 0xE5, 0xE6, 0xBC, 0xF8 ), 00172 BYTES_TO_T_UINT_8( 0x47, 0x42, 0x2C, 0xE1, 0xF2, 0xD1, 0x17, 0x6B ), 00173 }; 00174 static const mbedtls_mpi_uint secp256r1_gy[] = { 00175 BYTES_TO_T_UINT_8( 0xF5, 0x51, 0xBF, 0x37, 0x68, 0x40, 0xB6, 0xCB ), 00176 BYTES_TO_T_UINT_8( 0xCE, 0x5E, 0x31, 0x6B, 0x57, 0x33, 0xCE, 0x2B ), 00177 BYTES_TO_T_UINT_8( 0x16, 0x9E, 0x0F, 0x7C, 0x4A, 0xEB, 0xE7, 0x8E ), 00178 BYTES_TO_T_UINT_8( 0x9B, 0x7F, 0x1A, 0xFE, 0xE2, 0x42, 0xE3, 0x4F ), 00179 }; 00180 static const mbedtls_mpi_uint secp256r1_n[] = { 00181 BYTES_TO_T_UINT_8( 0x51, 0x25, 0x63, 0xFC, 0xC2, 0xCA, 0xB9, 0xF3 ), 00182 BYTES_TO_T_UINT_8( 0x84, 0x9E, 0x17, 0xA7, 0xAD, 0xFA, 0xE6, 0xBC ), 00183 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00184 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ), 00185 }; 00186 #endif /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */ 00187 00188 /* 00189 * Domain parameters for secp384r1 00190 */ 00191 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) 00192 static const mbedtls_mpi_uint secp384r1_p[] = { 00193 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ), 00194 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ), 00195 BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00196 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00197 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00198 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00199 }; 00200 static const mbedtls_mpi_uint secp384r1_b[] = { 00201 BYTES_TO_T_UINT_8( 0xEF, 0x2A, 0xEC, 0xD3, 0xED, 0xC8, 0x85, 0x2A ), 00202 BYTES_TO_T_UINT_8( 0x9D, 0xD1, 0x2E, 0x8A, 0x8D, 0x39, 0x56, 0xC6 ), 00203 BYTES_TO_T_UINT_8( 0x5A, 0x87, 0x13, 0x50, 0x8F, 0x08, 0x14, 0x03 ), 00204 BYTES_TO_T_UINT_8( 0x12, 0x41, 0x81, 0xFE, 0x6E, 0x9C, 0x1D, 0x18 ), 00205 BYTES_TO_T_UINT_8( 0x19, 0x2D, 0xF8, 0xE3, 0x6B, 0x05, 0x8E, 0x98 ), 00206 BYTES_TO_T_UINT_8( 0xE4, 0xE7, 0x3E, 0xE2, 0xA7, 0x2F, 0x31, 0xB3 ), 00207 }; 00208 static const mbedtls_mpi_uint secp384r1_gx[] = { 00209 BYTES_TO_T_UINT_8( 0xB7, 0x0A, 0x76, 0x72, 0x38, 0x5E, 0x54, 0x3A ), 00210 BYTES_TO_T_UINT_8( 0x6C, 0x29, 0x55, 0xBF, 0x5D, 0xF2, 0x02, 0x55 ), 00211 BYTES_TO_T_UINT_8( 0x38, 0x2A, 0x54, 0x82, 0xE0, 0x41, 0xF7, 0x59 ), 00212 BYTES_TO_T_UINT_8( 0x98, 0x9B, 0xA7, 0x8B, 0x62, 0x3B, 0x1D, 0x6E ), 00213 BYTES_TO_T_UINT_8( 0x74, 0xAD, 0x20, 0xF3, 0x1E, 0xC7, 0xB1, 0x8E ), 00214 BYTES_TO_T_UINT_8( 0x37, 0x05, 0x8B, 0xBE, 0x22, 0xCA, 0x87, 0xAA ), 00215 }; 00216 static const mbedtls_mpi_uint secp384r1_gy[] = { 00217 BYTES_TO_T_UINT_8( 0x5F, 0x0E, 0xEA, 0x90, 0x7C, 0x1D, 0x43, 0x7A ), 00218 BYTES_TO_T_UINT_8( 0x9D, 0x81, 0x7E, 0x1D, 0xCE, 0xB1, 0x60, 0x0A ), 00219 BYTES_TO_T_UINT_8( 0xC0, 0xB8, 0xF0, 0xB5, 0x13, 0x31, 0xDA, 0xE9 ), 00220 BYTES_TO_T_UINT_8( 0x7C, 0x14, 0x9A, 0x28, 0xBD, 0x1D, 0xF4, 0xF8 ), 00221 BYTES_TO_T_UINT_8( 0x29, 0xDC, 0x92, 0x92, 0xBF, 0x98, 0x9E, 0x5D ), 00222 BYTES_TO_T_UINT_8( 0x6F, 0x2C, 0x26, 0x96, 0x4A, 0xDE, 0x17, 0x36 ), 00223 }; 00224 static const mbedtls_mpi_uint secp384r1_n[] = { 00225 BYTES_TO_T_UINT_8( 0x73, 0x29, 0xC5, 0xCC, 0x6A, 0x19, 0xEC, 0xEC ), 00226 BYTES_TO_T_UINT_8( 0x7A, 0xA7, 0xB0, 0x48, 0xB2, 0x0D, 0x1A, 0x58 ), 00227 BYTES_TO_T_UINT_8( 0xDF, 0x2D, 0x37, 0xF4, 0x81, 0x4D, 0x63, 0xC7 ), 00228 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00229 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00230 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00231 }; 00232 #endif /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */ 00233 00234 /* 00235 * Domain parameters for secp521r1 00236 */ 00237 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) 00238 static const mbedtls_mpi_uint secp521r1_p[] = { 00239 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00240 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00241 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00242 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00243 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00244 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00245 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00246 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00247 BYTES_TO_T_UINT_2( 0xFF, 0x01 ), 00248 }; 00249 static const mbedtls_mpi_uint secp521r1_b[] = { 00250 BYTES_TO_T_UINT_8( 0x00, 0x3F, 0x50, 0x6B, 0xD4, 0x1F, 0x45, 0xEF ), 00251 BYTES_TO_T_UINT_8( 0xF1, 0x34, 0x2C, 0x3D, 0x88, 0xDF, 0x73, 0x35 ), 00252 BYTES_TO_T_UINT_8( 0x07, 0xBF, 0xB1, 0x3B, 0xBD, 0xC0, 0x52, 0x16 ), 00253 BYTES_TO_T_UINT_8( 0x7B, 0x93, 0x7E, 0xEC, 0x51, 0x39, 0x19, 0x56 ), 00254 BYTES_TO_T_UINT_8( 0xE1, 0x09, 0xF1, 0x8E, 0x91, 0x89, 0xB4, 0xB8 ), 00255 BYTES_TO_T_UINT_8( 0xF3, 0x15, 0xB3, 0x99, 0x5B, 0x72, 0xDA, 0xA2 ), 00256 BYTES_TO_T_UINT_8( 0xEE, 0x40, 0x85, 0xB6, 0xA0, 0x21, 0x9A, 0x92 ), 00257 BYTES_TO_T_UINT_8( 0x1F, 0x9A, 0x1C, 0x8E, 0x61, 0xB9, 0x3E, 0x95 ), 00258 BYTES_TO_T_UINT_2( 0x51, 0x00 ), 00259 }; 00260 static const mbedtls_mpi_uint secp521r1_gx[] = { 00261 BYTES_TO_T_UINT_8( 0x66, 0xBD, 0xE5, 0xC2, 0x31, 0x7E, 0x7E, 0xF9 ), 00262 BYTES_TO_T_UINT_8( 0x9B, 0x42, 0x6A, 0x85, 0xC1, 0xB3, 0x48, 0x33 ), 00263 BYTES_TO_T_UINT_8( 0xDE, 0xA8, 0xFF, 0xA2, 0x27, 0xC1, 0x1D, 0xFE ), 00264 BYTES_TO_T_UINT_8( 0x28, 0x59, 0xE7, 0xEF, 0x77, 0x5E, 0x4B, 0xA1 ), 00265 BYTES_TO_T_UINT_8( 0xBA, 0x3D, 0x4D, 0x6B, 0x60, 0xAF, 0x28, 0xF8 ), 00266 BYTES_TO_T_UINT_8( 0x21, 0xB5, 0x3F, 0x05, 0x39, 0x81, 0x64, 0x9C ), 00267 BYTES_TO_T_UINT_8( 0x42, 0xB4, 0x95, 0x23, 0x66, 0xCB, 0x3E, 0x9E ), 00268 BYTES_TO_T_UINT_8( 0xCD, 0xE9, 0x04, 0x04, 0xB7, 0x06, 0x8E, 0x85 ), 00269 BYTES_TO_T_UINT_2( 0xC6, 0x00 ), 00270 }; 00271 static const mbedtls_mpi_uint secp521r1_gy[] = { 00272 BYTES_TO_T_UINT_8( 0x50, 0x66, 0xD1, 0x9F, 0x76, 0x94, 0xBE, 0x88 ), 00273 BYTES_TO_T_UINT_8( 0x40, 0xC2, 0x72, 0xA2, 0x86, 0x70, 0x3C, 0x35 ), 00274 BYTES_TO_T_UINT_8( 0x61, 0x07, 0xAD, 0x3F, 0x01, 0xB9, 0x50, 0xC5 ), 00275 BYTES_TO_T_UINT_8( 0x40, 0x26, 0xF4, 0x5E, 0x99, 0x72, 0xEE, 0x97 ), 00276 BYTES_TO_T_UINT_8( 0x2C, 0x66, 0x3E, 0x27, 0x17, 0xBD, 0xAF, 0x17 ), 00277 BYTES_TO_T_UINT_8( 0x68, 0x44, 0x9B, 0x57, 0x49, 0x44, 0xF5, 0x98 ), 00278 BYTES_TO_T_UINT_8( 0xD9, 0x1B, 0x7D, 0x2C, 0xB4, 0x5F, 0x8A, 0x5C ), 00279 BYTES_TO_T_UINT_8( 0x04, 0xC0, 0x3B, 0x9A, 0x78, 0x6A, 0x29, 0x39 ), 00280 BYTES_TO_T_UINT_2( 0x18, 0x01 ), 00281 }; 00282 static const mbedtls_mpi_uint secp521r1_n[] = { 00283 BYTES_TO_T_UINT_8( 0x09, 0x64, 0x38, 0x91, 0x1E, 0xB7, 0x6F, 0xBB ), 00284 BYTES_TO_T_UINT_8( 0xAE, 0x47, 0x9C, 0x89, 0xB8, 0xC9, 0xB5, 0x3B ), 00285 BYTES_TO_T_UINT_8( 0xD0, 0xA5, 0x09, 0xF7, 0x48, 0x01, 0xCC, 0x7F ), 00286 BYTES_TO_T_UINT_8( 0x6B, 0x96, 0x2F, 0xBF, 0x83, 0x87, 0x86, 0x51 ), 00287 BYTES_TO_T_UINT_8( 0xFA, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00288 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00289 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00290 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00291 BYTES_TO_T_UINT_2( 0xFF, 0x01 ), 00292 }; 00293 #endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */ 00294 00295 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) 00296 static const mbedtls_mpi_uint secp192k1_p[] = { 00297 BYTES_TO_T_UINT_8( 0x37, 0xEE, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ), 00298 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00299 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00300 }; 00301 static const mbedtls_mpi_uint secp192k1_a[] = { 00302 BYTES_TO_T_UINT_2( 0x00, 0x00 ), 00303 }; 00304 static const mbedtls_mpi_uint secp192k1_b[] = { 00305 BYTES_TO_T_UINT_2( 0x03, 0x00 ), 00306 }; 00307 static const mbedtls_mpi_uint secp192k1_gx[] = { 00308 BYTES_TO_T_UINT_8( 0x7D, 0x6C, 0xE0, 0xEA, 0xB1, 0xD1, 0xA5, 0x1D ), 00309 BYTES_TO_T_UINT_8( 0x34, 0xF4, 0xB7, 0x80, 0x02, 0x7D, 0xB0, 0x26 ), 00310 BYTES_TO_T_UINT_8( 0xAE, 0xE9, 0x57, 0xC0, 0x0E, 0xF1, 0x4F, 0xDB ), 00311 }; 00312 static const mbedtls_mpi_uint secp192k1_gy[] = { 00313 BYTES_TO_T_UINT_8( 0x9D, 0x2F, 0x5E, 0xD9, 0x88, 0xAA, 0x82, 0x40 ), 00314 BYTES_TO_T_UINT_8( 0x34, 0x86, 0xBE, 0x15, 0xD0, 0x63, 0x41, 0x84 ), 00315 BYTES_TO_T_UINT_8( 0xA7, 0x28, 0x56, 0x9C, 0x6D, 0x2F, 0x2F, 0x9B ), 00316 }; 00317 static const mbedtls_mpi_uint secp192k1_n[] = { 00318 BYTES_TO_T_UINT_8( 0x8D, 0xFD, 0xDE, 0x74, 0x6A, 0x46, 0x69, 0x0F ), 00319 BYTES_TO_T_UINT_8( 0x17, 0xFC, 0xF2, 0x26, 0xFE, 0xFF, 0xFF, 0xFF ), 00320 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00321 }; 00322 #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */ 00323 00324 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) 00325 static const mbedtls_mpi_uint secp224k1_p[] = { 00326 BYTES_TO_T_UINT_8( 0x6D, 0xE5, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ), 00327 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00328 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00329 BYTES_TO_T_UINT_4( 0xFF, 0xFF, 0xFF, 0xFF ), 00330 }; 00331 static const mbedtls_mpi_uint secp224k1_a[] = { 00332 BYTES_TO_T_UINT_2( 0x00, 0x00 ), 00333 }; 00334 static const mbedtls_mpi_uint secp224k1_b[] = { 00335 BYTES_TO_T_UINT_2( 0x05, 0x00 ), 00336 }; 00337 static const mbedtls_mpi_uint secp224k1_gx[] = { 00338 BYTES_TO_T_UINT_8( 0x5C, 0xA4, 0xB7, 0xB6, 0x0E, 0x65, 0x7E, 0x0F ), 00339 BYTES_TO_T_UINT_8( 0xA9, 0x75, 0x70, 0xE4, 0xE9, 0x67, 0xA4, 0x69 ), 00340 BYTES_TO_T_UINT_8( 0xA1, 0x28, 0xFC, 0x30, 0xDF, 0x99, 0xF0, 0x4D ), 00341 BYTES_TO_T_UINT_4( 0x33, 0x5B, 0x45, 0xA1 ), 00342 }; 00343 static const mbedtls_mpi_uint secp224k1_gy[] = { 00344 BYTES_TO_T_UINT_8( 0xA5, 0x61, 0x6D, 0x55, 0xDB, 0x4B, 0xCA, 0xE2 ), 00345 BYTES_TO_T_UINT_8( 0x59, 0xBD, 0xB0, 0xC0, 0xF7, 0x19, 0xE3, 0xF7 ), 00346 BYTES_TO_T_UINT_8( 0xD6, 0xFB, 0xCA, 0x82, 0x42, 0x34, 0xBA, 0x7F ), 00347 BYTES_TO_T_UINT_4( 0xED, 0x9F, 0x08, 0x7E ), 00348 }; 00349 static const mbedtls_mpi_uint secp224k1_n[] = { 00350 BYTES_TO_T_UINT_8( 0xF7, 0xB1, 0x9F, 0x76, 0x71, 0xA9, 0xF0, 0xCA ), 00351 BYTES_TO_T_UINT_8( 0x84, 0x61, 0xEC, 0xD2, 0xE8, 0xDC, 0x01, 0x00 ), 00352 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ), 00353 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ), 00354 }; 00355 #endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */ 00356 00357 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) 00358 static const mbedtls_mpi_uint secp256k1_p[] = { 00359 BYTES_TO_T_UINT_8( 0x2F, 0xFC, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ), 00360 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00361 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00362 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00363 }; 00364 static const mbedtls_mpi_uint secp256k1_a[] = { 00365 BYTES_TO_T_UINT_2( 0x00, 0x00 ), 00366 }; 00367 static const mbedtls_mpi_uint secp256k1_b[] = { 00368 BYTES_TO_T_UINT_2( 0x07, 0x00 ), 00369 }; 00370 static const mbedtls_mpi_uint secp256k1_gx[] = { 00371 BYTES_TO_T_UINT_8( 0x98, 0x17, 0xF8, 0x16, 0x5B, 0x81, 0xF2, 0x59 ), 00372 BYTES_TO_T_UINT_8( 0xD9, 0x28, 0xCE, 0x2D, 0xDB, 0xFC, 0x9B, 0x02 ), 00373 BYTES_TO_T_UINT_8( 0x07, 0x0B, 0x87, 0xCE, 0x95, 0x62, 0xA0, 0x55 ), 00374 BYTES_TO_T_UINT_8( 0xAC, 0xBB, 0xDC, 0xF9, 0x7E, 0x66, 0xBE, 0x79 ), 00375 }; 00376 static const mbedtls_mpi_uint secp256k1_gy[] = { 00377 BYTES_TO_T_UINT_8( 0xB8, 0xD4, 0x10, 0xFB, 0x8F, 0xD0, 0x47, 0x9C ), 00378 BYTES_TO_T_UINT_8( 0x19, 0x54, 0x85, 0xA6, 0x48, 0xB4, 0x17, 0xFD ), 00379 BYTES_TO_T_UINT_8( 0xA8, 0x08, 0x11, 0x0E, 0xFC, 0xFB, 0xA4, 0x5D ), 00380 BYTES_TO_T_UINT_8( 0x65, 0xC4, 0xA3, 0x26, 0x77, 0xDA, 0x3A, 0x48 ), 00381 }; 00382 static const mbedtls_mpi_uint secp256k1_n[] = { 00383 BYTES_TO_T_UINT_8( 0x41, 0x41, 0x36, 0xD0, 0x8C, 0x5E, 0xD2, 0xBF ), 00384 BYTES_TO_T_UINT_8( 0x3B, 0xA0, 0x48, 0xAF, 0xE6, 0xDC, 0xAE, 0xBA ), 00385 BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00386 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00387 }; 00388 #endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */ 00389 00390 /* 00391 * Domain parameters for brainpoolP256r1 (RFC 5639 3.4) 00392 */ 00393 #if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) 00394 static const mbedtls_mpi_uint brainpoolP256r1_p[] = { 00395 BYTES_TO_T_UINT_8( 0x77, 0x53, 0x6E, 0x1F, 0x1D, 0x48, 0x13, 0x20 ), 00396 BYTES_TO_T_UINT_8( 0x28, 0x20, 0x26, 0xD5, 0x23, 0xF6, 0x3B, 0x6E ), 00397 BYTES_TO_T_UINT_8( 0x72, 0x8D, 0x83, 0x9D, 0x90, 0x0A, 0x66, 0x3E ), 00398 BYTES_TO_T_UINT_8( 0xBC, 0xA9, 0xEE, 0xA1, 0xDB, 0x57, 0xFB, 0xA9 ), 00399 }; 00400 static const mbedtls_mpi_uint brainpoolP256r1_a[] = { 00401 BYTES_TO_T_UINT_8( 0xD9, 0xB5, 0x30, 0xF3, 0x44, 0x4B, 0x4A, 0xE9 ), 00402 BYTES_TO_T_UINT_8( 0x6C, 0x5C, 0xDC, 0x26, 0xC1, 0x55, 0x80, 0xFB ), 00403 BYTES_TO_T_UINT_8( 0xE7, 0xFF, 0x7A, 0x41, 0x30, 0x75, 0xF6, 0xEE ), 00404 BYTES_TO_T_UINT_8( 0x57, 0x30, 0x2C, 0xFC, 0x75, 0x09, 0x5A, 0x7D ), 00405 }; 00406 static const mbedtls_mpi_uint brainpoolP256r1_b[] = { 00407 BYTES_TO_T_UINT_8( 0xB6, 0x07, 0x8C, 0xFF, 0x18, 0xDC, 0xCC, 0x6B ), 00408 BYTES_TO_T_UINT_8( 0xCE, 0xE1, 0xF7, 0x5C, 0x29, 0x16, 0x84, 0x95 ), 00409 BYTES_TO_T_UINT_8( 0xBF, 0x7C, 0xD7, 0xBB, 0xD9, 0xB5, 0x30, 0xF3 ), 00410 BYTES_TO_T_UINT_8( 0x44, 0x4B, 0x4A, 0xE9, 0x6C, 0x5C, 0xDC, 0x26 ), 00411 }; 00412 static const mbedtls_mpi_uint brainpoolP256r1_gx[] = { 00413 BYTES_TO_T_UINT_8( 0x62, 0x32, 0xCE, 0x9A, 0xBD, 0x53, 0x44, 0x3A ), 00414 BYTES_TO_T_UINT_8( 0xC2, 0x23, 0xBD, 0xE3, 0xE1, 0x27, 0xDE, 0xB9 ), 00415 BYTES_TO_T_UINT_8( 0xAF, 0xB7, 0x81, 0xFC, 0x2F, 0x48, 0x4B, 0x2C ), 00416 BYTES_TO_T_UINT_8( 0xCB, 0x57, 0x7E, 0xCB, 0xB9, 0xAE, 0xD2, 0x8B ), 00417 }; 00418 static const mbedtls_mpi_uint brainpoolP256r1_gy[] = { 00419 BYTES_TO_T_UINT_8( 0x97, 0x69, 0x04, 0x2F, 0xC7, 0x54, 0x1D, 0x5C ), 00420 BYTES_TO_T_UINT_8( 0x54, 0x8E, 0xED, 0x2D, 0x13, 0x45, 0x77, 0xC2 ), 00421 BYTES_TO_T_UINT_8( 0xC9, 0x1D, 0x61, 0x14, 0x1A, 0x46, 0xF8, 0x97 ), 00422 BYTES_TO_T_UINT_8( 0xFD, 0xC4, 0xDA, 0xC3, 0x35, 0xF8, 0x7E, 0x54 ), 00423 }; 00424 static const mbedtls_mpi_uint brainpoolP256r1_n[] = { 00425 BYTES_TO_T_UINT_8( 0xA7, 0x56, 0x48, 0x97, 0x82, 0x0E, 0x1E, 0x90 ), 00426 BYTES_TO_T_UINT_8( 0xF7, 0xA6, 0x61, 0xB5, 0xA3, 0x7A, 0x39, 0x8C ), 00427 BYTES_TO_T_UINT_8( 0x71, 0x8D, 0x83, 0x9D, 0x90, 0x0A, 0x66, 0x3E ), 00428 BYTES_TO_T_UINT_8( 0xBC, 0xA9, 0xEE, 0xA1, 0xDB, 0x57, 0xFB, 0xA9 ), 00429 }; 00430 #endif /* MBEDTLS_ECP_DP_BP256R1_ENABLED */ 00431 00432 /* 00433 * Domain parameters for brainpoolP384r1 (RFC 5639 3.6) 00434 */ 00435 #if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) 00436 static const mbedtls_mpi_uint brainpoolP384r1_p[] = { 00437 BYTES_TO_T_UINT_8( 0x53, 0xEC, 0x07, 0x31, 0x13, 0x00, 0x47, 0x87 ), 00438 BYTES_TO_T_UINT_8( 0x71, 0x1A, 0x1D, 0x90, 0x29, 0xA7, 0xD3, 0xAC ), 00439 BYTES_TO_T_UINT_8( 0x23, 0x11, 0xB7, 0x7F, 0x19, 0xDA, 0xB1, 0x12 ), 00440 BYTES_TO_T_UINT_8( 0xB4, 0x56, 0x54, 0xED, 0x09, 0x71, 0x2F, 0x15 ), 00441 BYTES_TO_T_UINT_8( 0xDF, 0x41, 0xE6, 0x50, 0x7E, 0x6F, 0x5D, 0x0F ), 00442 BYTES_TO_T_UINT_8( 0x28, 0x6D, 0x38, 0xA3, 0x82, 0x1E, 0xB9, 0x8C ), 00443 }; 00444 static const mbedtls_mpi_uint brainpoolP384r1_a[] = { 00445 BYTES_TO_T_UINT_8( 0x26, 0x28, 0xCE, 0x22, 0xDD, 0xC7, 0xA8, 0x04 ), 00446 BYTES_TO_T_UINT_8( 0xEB, 0xD4, 0x3A, 0x50, 0x4A, 0x81, 0xA5, 0x8A ), 00447 BYTES_TO_T_UINT_8( 0x0F, 0xF9, 0x91, 0xBA, 0xEF, 0x65, 0x91, 0x13 ), 00448 BYTES_TO_T_UINT_8( 0x87, 0x27, 0xB2, 0x4F, 0x8E, 0xA2, 0xBE, 0xC2 ), 00449 BYTES_TO_T_UINT_8( 0xA0, 0xAF, 0x05, 0xCE, 0x0A, 0x08, 0x72, 0x3C ), 00450 BYTES_TO_T_UINT_8( 0x0C, 0x15, 0x8C, 0x3D, 0xC6, 0x82, 0xC3, 0x7B ), 00451 }; 00452 static const mbedtls_mpi_uint brainpoolP384r1_b[] = { 00453 BYTES_TO_T_UINT_8( 0x11, 0x4C, 0x50, 0xFA, 0x96, 0x86, 0xB7, 0x3A ), 00454 BYTES_TO_T_UINT_8( 0x94, 0xC9, 0xDB, 0x95, 0x02, 0x39, 0xB4, 0x7C ), 00455 BYTES_TO_T_UINT_8( 0xD5, 0x62, 0xEB, 0x3E, 0xA5, 0x0E, 0x88, 0x2E ), 00456 BYTES_TO_T_UINT_8( 0xA6, 0xD2, 0xDC, 0x07, 0xE1, 0x7D, 0xB7, 0x2F ), 00457 BYTES_TO_T_UINT_8( 0x7C, 0x44, 0xF0, 0x16, 0x54, 0xB5, 0x39, 0x8B ), 00458 BYTES_TO_T_UINT_8( 0x26, 0x28, 0xCE, 0x22, 0xDD, 0xC7, 0xA8, 0x04 ), 00459 }; 00460 static const mbedtls_mpi_uint brainpoolP384r1_gx[] = { 00461 BYTES_TO_T_UINT_8( 0x1E, 0xAF, 0xD4, 0x47, 0xE2, 0xB2, 0x87, 0xEF ), 00462 BYTES_TO_T_UINT_8( 0xAA, 0x46, 0xD6, 0x36, 0x34, 0xE0, 0x26, 0xE8 ), 00463 BYTES_TO_T_UINT_8( 0xE8, 0x10, 0xBD, 0x0C, 0xFE, 0xCA, 0x7F, 0xDB ), 00464 BYTES_TO_T_UINT_8( 0xE3, 0x4F, 0xF1, 0x7E, 0xE7, 0xA3, 0x47, 0x88 ), 00465 BYTES_TO_T_UINT_8( 0x6B, 0x3F, 0xC1, 0xB7, 0x81, 0x3A, 0xA6, 0xA2 ), 00466 BYTES_TO_T_UINT_8( 0xFF, 0x45, 0xCF, 0x68, 0xF0, 0x64, 0x1C, 0x1D ), 00467 }; 00468 static const mbedtls_mpi_uint brainpoolP384r1_gy[] = { 00469 BYTES_TO_T_UINT_8( 0x15, 0x53, 0x3C, 0x26, 0x41, 0x03, 0x82, 0x42 ), 00470 BYTES_TO_T_UINT_8( 0x11, 0x81, 0x91, 0x77, 0x21, 0x46, 0x46, 0x0E ), 00471 BYTES_TO_T_UINT_8( 0x28, 0x29, 0x91, 0xF9, 0x4F, 0x05, 0x9C, 0xE1 ), 00472 BYTES_TO_T_UINT_8( 0x64, 0x58, 0xEC, 0xFE, 0x29, 0x0B, 0xB7, 0x62 ), 00473 BYTES_TO_T_UINT_8( 0x52, 0xD5, 0xCF, 0x95, 0x8E, 0xEB, 0xB1, 0x5C ), 00474 BYTES_TO_T_UINT_8( 0xA4, 0xC2, 0xF9, 0x20, 0x75, 0x1D, 0xBE, 0x8A ), 00475 }; 00476 static const mbedtls_mpi_uint brainpoolP384r1_n[] = { 00477 BYTES_TO_T_UINT_8( 0x65, 0x65, 0x04, 0xE9, 0x02, 0x32, 0x88, 0x3B ), 00478 BYTES_TO_T_UINT_8( 0x10, 0xC3, 0x7F, 0x6B, 0xAF, 0xB6, 0x3A, 0xCF ), 00479 BYTES_TO_T_UINT_8( 0xA7, 0x25, 0x04, 0xAC, 0x6C, 0x6E, 0x16, 0x1F ), 00480 BYTES_TO_T_UINT_8( 0xB3, 0x56, 0x54, 0xED, 0x09, 0x71, 0x2F, 0x15 ), 00481 BYTES_TO_T_UINT_8( 0xDF, 0x41, 0xE6, 0x50, 0x7E, 0x6F, 0x5D, 0x0F ), 00482 BYTES_TO_T_UINT_8( 0x28, 0x6D, 0x38, 0xA3, 0x82, 0x1E, 0xB9, 0x8C ), 00483 }; 00484 #endif /* MBEDTLS_ECP_DP_BP384R1_ENABLED */ 00485 00486 /* 00487 * Domain parameters for brainpoolP512r1 (RFC 5639 3.7) 00488 */ 00489 #if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) 00490 static const mbedtls_mpi_uint brainpoolP512r1_p[] = { 00491 BYTES_TO_T_UINT_8( 0xF3, 0x48, 0x3A, 0x58, 0x56, 0x60, 0xAA, 0x28 ), 00492 BYTES_TO_T_UINT_8( 0x85, 0xC6, 0x82, 0x2D, 0x2F, 0xFF, 0x81, 0x28 ), 00493 BYTES_TO_T_UINT_8( 0xE6, 0x80, 0xA3, 0xE6, 0x2A, 0xA1, 0xCD, 0xAE ), 00494 BYTES_TO_T_UINT_8( 0x42, 0x68, 0xC6, 0x9B, 0x00, 0x9B, 0x4D, 0x7D ), 00495 BYTES_TO_T_UINT_8( 0x71, 0x08, 0x33, 0x70, 0xCA, 0x9C, 0x63, 0xD6 ), 00496 BYTES_TO_T_UINT_8( 0x0E, 0xD2, 0xC9, 0xB3, 0xB3, 0x8D, 0x30, 0xCB ), 00497 BYTES_TO_T_UINT_8( 0x07, 0xFC, 0xC9, 0x33, 0xAE, 0xE6, 0xD4, 0x3F ), 00498 BYTES_TO_T_UINT_8( 0x8B, 0xC4, 0xE9, 0xDB, 0xB8, 0x9D, 0xDD, 0xAA ), 00499 }; 00500 static const mbedtls_mpi_uint brainpoolP512r1_a[] = { 00501 BYTES_TO_T_UINT_8( 0xCA, 0x94, 0xFC, 0x77, 0x4D, 0xAC, 0xC1, 0xE7 ), 00502 BYTES_TO_T_UINT_8( 0xB9, 0xC7, 0xF2, 0x2B, 0xA7, 0x17, 0x11, 0x7F ), 00503 BYTES_TO_T_UINT_8( 0xB5, 0xC8, 0x9A, 0x8B, 0xC9, 0xF1, 0x2E, 0x0A ), 00504 BYTES_TO_T_UINT_8( 0xA1, 0x3A, 0x25, 0xA8, 0x5A, 0x5D, 0xED, 0x2D ), 00505 BYTES_TO_T_UINT_8( 0xBC, 0x63, 0x98, 0xEA, 0xCA, 0x41, 0x34, 0xA8 ), 00506 BYTES_TO_T_UINT_8( 0x10, 0x16, 0xF9, 0x3D, 0x8D, 0xDD, 0xCB, 0x94 ), 00507 BYTES_TO_T_UINT_8( 0xC5, 0x4C, 0x23, 0xAC, 0x45, 0x71, 0x32, 0xE2 ), 00508 BYTES_TO_T_UINT_8( 0x89, 0x3B, 0x60, 0x8B, 0x31, 0xA3, 0x30, 0x78 ), 00509 }; 00510 static const mbedtls_mpi_uint brainpoolP512r1_b[] = { 00511 BYTES_TO_T_UINT_8( 0x23, 0xF7, 0x16, 0x80, 0x63, 0xBD, 0x09, 0x28 ), 00512 BYTES_TO_T_UINT_8( 0xDD, 0xE5, 0xBA, 0x5E, 0xB7, 0x50, 0x40, 0x98 ), 00513 BYTES_TO_T_UINT_8( 0x67, 0x3E, 0x08, 0xDC, 0xCA, 0x94, 0xFC, 0x77 ), 00514 BYTES_TO_T_UINT_8( 0x4D, 0xAC, 0xC1, 0xE7, 0xB9, 0xC7, 0xF2, 0x2B ), 00515 BYTES_TO_T_UINT_8( 0xA7, 0x17, 0x11, 0x7F, 0xB5, 0xC8, 0x9A, 0x8B ), 00516 BYTES_TO_T_UINT_8( 0xC9, 0xF1, 0x2E, 0x0A, 0xA1, 0x3A, 0x25, 0xA8 ), 00517 BYTES_TO_T_UINT_8( 0x5A, 0x5D, 0xED, 0x2D, 0xBC, 0x63, 0x98, 0xEA ), 00518 BYTES_TO_T_UINT_8( 0xCA, 0x41, 0x34, 0xA8, 0x10, 0x16, 0xF9, 0x3D ), 00519 }; 00520 static const mbedtls_mpi_uint brainpoolP512r1_gx[] = { 00521 BYTES_TO_T_UINT_8( 0x22, 0xF8, 0xB9, 0xBC, 0x09, 0x22, 0x35, 0x8B ), 00522 BYTES_TO_T_UINT_8( 0x68, 0x5E, 0x6A, 0x40, 0x47, 0x50, 0x6D, 0x7C ), 00523 BYTES_TO_T_UINT_8( 0x5F, 0x7D, 0xB9, 0x93, 0x7B, 0x68, 0xD1, 0x50 ), 00524 BYTES_TO_T_UINT_8( 0x8D, 0xD4, 0xD0, 0xE2, 0x78, 0x1F, 0x3B, 0xFF ), 00525 BYTES_TO_T_UINT_8( 0x8E, 0x09, 0xD0, 0xF4, 0xEE, 0x62, 0x3B, 0xB4 ), 00526 BYTES_TO_T_UINT_8( 0xC1, 0x16, 0xD9, 0xB5, 0x70, 0x9F, 0xED, 0x85 ), 00527 BYTES_TO_T_UINT_8( 0x93, 0x6A, 0x4C, 0x9C, 0x2E, 0x32, 0x21, 0x5A ), 00528 BYTES_TO_T_UINT_8( 0x64, 0xD9, 0x2E, 0xD8, 0xBD, 0xE4, 0xAE, 0x81 ), 00529 }; 00530 static const mbedtls_mpi_uint brainpoolP512r1_gy[] = { 00531 BYTES_TO_T_UINT_8( 0x92, 0x08, 0xD8, 0x3A, 0x0F, 0x1E, 0xCD, 0x78 ), 00532 BYTES_TO_T_UINT_8( 0x06, 0x54, 0xF0, 0xA8, 0x2F, 0x2B, 0xCA, 0xD1 ), 00533 BYTES_TO_T_UINT_8( 0xAE, 0x63, 0x27, 0x8A, 0xD8, 0x4B, 0xCA, 0x5B ), 00534 BYTES_TO_T_UINT_8( 0x5E, 0x48, 0x5F, 0x4A, 0x49, 0xDE, 0xDC, 0xB2 ), 00535 BYTES_TO_T_UINT_8( 0x11, 0x81, 0x1F, 0x88, 0x5B, 0xC5, 0x00, 0xA0 ), 00536 BYTES_TO_T_UINT_8( 0x1A, 0x7B, 0xA5, 0x24, 0x00, 0xF7, 0x09, 0xF2 ), 00537 BYTES_TO_T_UINT_8( 0xFD, 0x22, 0x78, 0xCF, 0xA9, 0xBF, 0xEA, 0xC0 ), 00538 BYTES_TO_T_UINT_8( 0xEC, 0x32, 0x63, 0x56, 0x5D, 0x38, 0xDE, 0x7D ), 00539 }; 00540 static const mbedtls_mpi_uint brainpoolP512r1_n[] = { 00541 BYTES_TO_T_UINT_8( 0x69, 0x00, 0xA9, 0x9C, 0x82, 0x96, 0x87, 0xB5 ), 00542 BYTES_TO_T_UINT_8( 0xDD, 0xDA, 0x5D, 0x08, 0x81, 0xD3, 0xB1, 0x1D ), 00543 BYTES_TO_T_UINT_8( 0x47, 0x10, 0xAC, 0x7F, 0x19, 0x61, 0x86, 0x41 ), 00544 BYTES_TO_T_UINT_8( 0x19, 0x26, 0xA9, 0x4C, 0x41, 0x5C, 0x3E, 0x55 ), 00545 BYTES_TO_T_UINT_8( 0x70, 0x08, 0x33, 0x70, 0xCA, 0x9C, 0x63, 0xD6 ), 00546 BYTES_TO_T_UINT_8( 0x0E, 0xD2, 0xC9, 0xB3, 0xB3, 0x8D, 0x30, 0xCB ), 00547 BYTES_TO_T_UINT_8( 0x07, 0xFC, 0xC9, 0x33, 0xAE, 0xE6, 0xD4, 0x3F ), 00548 BYTES_TO_T_UINT_8( 0x8B, 0xC4, 0xE9, 0xDB, 0xB8, 0x9D, 0xDD, 0xAA ), 00549 }; 00550 #endif /* MBEDTLS_ECP_DP_BP512R1_ENABLED */ 00551 00552 /* 00553 * Create an MPI from embedded constants 00554 * (assumes len is an exact multiple of sizeof mbedtls_mpi_uint) 00555 */ 00556 static inline void ecp_mpi_load( mbedtls_mpi *X, const mbedtls_mpi_uint *p, size_t len ) 00557 { 00558 X->s = 1; 00559 X->n = len / sizeof( mbedtls_mpi_uint ); 00560 X->p = (mbedtls_mpi_uint *) p; 00561 } 00562 00563 /* 00564 * Set an MPI to static value 1 00565 */ 00566 static inline void ecp_mpi_set1( mbedtls_mpi *X ) 00567 { 00568 static mbedtls_mpi_uint one[] = { 1 }; 00569 X->s = 1; 00570 X->n = 1; 00571 X->p = one; 00572 } 00573 00574 /* 00575 * Make group available from embedded constants 00576 */ 00577 static int ecp_group_load( mbedtls_ecp_group *grp, 00578 const mbedtls_mpi_uint *p, size_t plen, 00579 const mbedtls_mpi_uint *a, size_t alen, 00580 const mbedtls_mpi_uint *b, size_t blen, 00581 const mbedtls_mpi_uint *gx, size_t gxlen, 00582 const mbedtls_mpi_uint *gy, size_t gylen, 00583 const mbedtls_mpi_uint *n, size_t nlen) 00584 { 00585 ecp_mpi_load( &grp->P , p, plen ); 00586 if( a != NULL ) 00587 ecp_mpi_load( &grp->A , a, alen ); 00588 ecp_mpi_load( &grp->B , b, blen ); 00589 ecp_mpi_load( &grp->N , n, nlen ); 00590 00591 ecp_mpi_load( &grp->G .X , gx, gxlen ); 00592 ecp_mpi_load( &grp->G .Y , gy, gylen ); 00593 ecp_mpi_set1( &grp->G .Z ); 00594 00595 grp->pbits = mbedtls_mpi_bitlen( &grp->P ); 00596 grp->nbits = mbedtls_mpi_bitlen( &grp->N ); 00597 00598 grp->h = 1; 00599 00600 return( 0 ); 00601 } 00602 00603 #if defined(MBEDTLS_ECP_NIST_OPTIM) 00604 /* Forward declarations */ 00605 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) 00606 static int ecp_mod_p192( mbedtls_mpi * ); 00607 #endif 00608 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) 00609 static int ecp_mod_p224( mbedtls_mpi * ); 00610 #endif 00611 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) 00612 static int ecp_mod_p256( mbedtls_mpi * ); 00613 #endif 00614 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) 00615 static int ecp_mod_p384( mbedtls_mpi * ); 00616 #endif 00617 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) 00618 static int ecp_mod_p521( mbedtls_mpi * ); 00619 #endif 00620 00621 #define NIST_MODP( P ) grp->modp = ecp_mod_ ## P; 00622 #else 00623 #define NIST_MODP( P ) 00624 #endif /* MBEDTLS_ECP_NIST_OPTIM */ 00625 00626 /* Additional forward declarations */ 00627 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) 00628 static int ecp_mod_p255( mbedtls_mpi * ); 00629 #endif 00630 #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) 00631 static int ecp_mod_p448( mbedtls_mpi * ); 00632 #endif 00633 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) 00634 static int ecp_mod_p192k1( mbedtls_mpi * ); 00635 #endif 00636 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) 00637 static int ecp_mod_p224k1( mbedtls_mpi * ); 00638 #endif 00639 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) 00640 static int ecp_mod_p256k1( mbedtls_mpi * ); 00641 #endif 00642 00643 #define LOAD_GROUP_A( G ) ecp_group_load( grp, \ 00644 G ## _p, sizeof( G ## _p ), \ 00645 G ## _a, sizeof( G ## _a ), \ 00646 G ## _b, sizeof( G ## _b ), \ 00647 G ## _gx, sizeof( G ## _gx ), \ 00648 G ## _gy, sizeof( G ## _gy ), \ 00649 G ## _n, sizeof( G ## _n ) ) 00650 00651 #define LOAD_GROUP( G ) ecp_group_load( grp, \ 00652 G ## _p, sizeof( G ## _p ), \ 00653 NULL, 0, \ 00654 G ## _b, sizeof( G ## _b ), \ 00655 G ## _gx, sizeof( G ## _gx ), \ 00656 G ## _gy, sizeof( G ## _gy ), \ 00657 G ## _n, sizeof( G ## _n ) ) 00658 00659 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) 00660 /* 00661 * Specialized function for creating the Curve25519 group 00662 */ 00663 static int ecp_use_curve25519( mbedtls_ecp_group *grp ) 00664 { 00665 int ret; 00666 00667 /* Actually ( A + 2 ) / 4 */ 00668 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &grp->A , 16, "01DB42" ) ); 00669 00670 /* P = 2^255 - 19 */ 00671 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->P , 1 ) ); 00672 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &grp->P , 255 ) ); 00673 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &grp->P , &grp->P , 19 ) ); 00674 grp->pbits = mbedtls_mpi_bitlen( &grp->P ); 00675 00676 /* N = 2^252 + 27742317777372353535851937790883648493 */ 00677 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &grp->N , 16, 00678 "14DEF9DEA2F79CD65812631A5CF5D3ED" ) ); 00679 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &grp->N , 252, 1 ) ); 00680 00681 /* Y intentionally not set, since we use x/z coordinates. 00682 * This is used as a marker to identify Montgomery curves! */ 00683 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G .X , 9 ) ); 00684 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G .Z , 1 ) ); 00685 mbedtls_mpi_free( &grp->G .Y ); 00686 00687 /* Actually, the required msb for private keys */ 00688 grp->nbits = 254; 00689 00690 cleanup: 00691 if( ret != 0 ) 00692 mbedtls_ecp_group_free( grp ); 00693 00694 return( ret ); 00695 } 00696 #endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */ 00697 00698 #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) 00699 /* 00700 * Specialized function for creating the Curve448 group 00701 */ 00702 static int ecp_use_curve448( mbedtls_ecp_group *grp ) 00703 { 00704 mbedtls_mpi Ns; 00705 int ret; 00706 00707 mbedtls_mpi_init( &Ns ); 00708 00709 /* Actually ( A + 2 ) / 4 */ 00710 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &grp->A , 16, "98AA" ) ); 00711 00712 /* P = 2^448 - 2^224 - 1 */ 00713 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->P , 1 ) ); 00714 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &grp->P , 224 ) ); 00715 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &grp->P , &grp->P , 1 ) ); 00716 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &grp->P , 224 ) ); 00717 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &grp->P , &grp->P , 1 ) ); 00718 grp->pbits = mbedtls_mpi_bitlen( &grp->P ); 00719 00720 /* Y intentionally not set, since we use x/z coordinates. 00721 * This is used as a marker to identify Montgomery curves! */ 00722 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G .X , 5 ) ); 00723 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G .Z , 1 ) ); 00724 mbedtls_mpi_free( &grp->G .Y ); 00725 00726 /* N = 2^446 - 13818066809895115352007386748515426880336692474882178609894547503885 */ 00727 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &grp->N , 446, 1 ) ); 00728 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &Ns, 16, 00729 "8335DC163BB124B65129C96FDE933D8D723A70AADC873D6D54A7BB0D" ) ); 00730 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &grp->N , &grp->N , &Ns ) ); 00731 00732 /* Actually, the required msb for private keys */ 00733 grp->nbits = 447; 00734 00735 cleanup: 00736 mbedtls_mpi_free( &Ns ); 00737 if( ret != 0 ) 00738 mbedtls_ecp_group_free( grp ); 00739 00740 return( ret ); 00741 } 00742 #endif /* MBEDTLS_ECP_DP_CURVE448_ENABLED */ 00743 00744 /* 00745 * Set a group using well-known domain parameters 00746 */ 00747 int mbedtls_ecp_group_load( mbedtls_ecp_group *grp, mbedtls_ecp_group_id id ) 00748 { 00749 mbedtls_ecp_group_free( grp ); 00750 00751 grp->id = id; 00752 00753 switch( id ) 00754 { 00755 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) 00756 case MBEDTLS_ECP_DP_SECP192R1: 00757 NIST_MODP( p192 ); 00758 return( LOAD_GROUP( secp192r1 ) ); 00759 #endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */ 00760 00761 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) 00762 case MBEDTLS_ECP_DP_SECP224R1: 00763 NIST_MODP( p224 ); 00764 return( LOAD_GROUP( secp224r1 ) ); 00765 #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */ 00766 00767 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) 00768 case MBEDTLS_ECP_DP_SECP256R1: 00769 NIST_MODP( p256 ); 00770 return( LOAD_GROUP( secp256r1 ) ); 00771 #endif /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */ 00772 00773 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) 00774 case MBEDTLS_ECP_DP_SECP384R1: 00775 NIST_MODP( p384 ); 00776 return( LOAD_GROUP( secp384r1 ) ); 00777 #endif /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */ 00778 00779 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) 00780 case MBEDTLS_ECP_DP_SECP521R1: 00781 NIST_MODP( p521 ); 00782 return( LOAD_GROUP( secp521r1 ) ); 00783 #endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */ 00784 00785 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) 00786 case MBEDTLS_ECP_DP_SECP192K1: 00787 grp->modp = ecp_mod_p192k1; 00788 return( LOAD_GROUP_A( secp192k1 ) ); 00789 #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */ 00790 00791 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) 00792 case MBEDTLS_ECP_DP_SECP224K1: 00793 grp->modp = ecp_mod_p224k1; 00794 return( LOAD_GROUP_A( secp224k1 ) ); 00795 #endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */ 00796 00797 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) 00798 case MBEDTLS_ECP_DP_SECP256K1: 00799 grp->modp = ecp_mod_p256k1; 00800 return( LOAD_GROUP_A( secp256k1 ) ); 00801 #endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */ 00802 00803 #if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) 00804 case MBEDTLS_ECP_DP_BP256R1: 00805 return( LOAD_GROUP_A( brainpoolP256r1 ) ); 00806 #endif /* MBEDTLS_ECP_DP_BP256R1_ENABLED */ 00807 00808 #if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) 00809 case MBEDTLS_ECP_DP_BP384R1: 00810 return( LOAD_GROUP_A( brainpoolP384r1 ) ); 00811 #endif /* MBEDTLS_ECP_DP_BP384R1_ENABLED */ 00812 00813 #if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) 00814 case MBEDTLS_ECP_DP_BP512R1: 00815 return( LOAD_GROUP_A( brainpoolP512r1 ) ); 00816 #endif /* MBEDTLS_ECP_DP_BP512R1_ENABLED */ 00817 00818 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) 00819 case MBEDTLS_ECP_DP_CURVE25519: 00820 grp->modp = ecp_mod_p255; 00821 return( ecp_use_curve25519( grp ) ); 00822 #endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */ 00823 00824 #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) 00825 case MBEDTLS_ECP_DP_CURVE448: 00826 grp->modp = ecp_mod_p448; 00827 return( ecp_use_curve448( grp ) ); 00828 #endif /* MBEDTLS_ECP_DP_CURVE448_ENABLED */ 00829 00830 default: 00831 mbedtls_ecp_group_free( grp ); 00832 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE ); 00833 } 00834 } 00835 00836 #if defined(MBEDTLS_ECP_NIST_OPTIM) 00837 /* 00838 * Fast reduction modulo the primes used by the NIST curves. 00839 * 00840 * These functions are critical for speed, but not needed for correct 00841 * operations. So, we make the choice to heavily rely on the internals of our 00842 * bignum library, which creates a tight coupling between these functions and 00843 * our MPI implementation. However, the coupling between the ECP module and 00844 * MPI remains loose, since these functions can be deactivated at will. 00845 */ 00846 00847 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) 00848 /* 00849 * Compared to the way things are presented in FIPS 186-3 D.2, 00850 * we proceed in columns, from right (least significant chunk) to left, 00851 * adding chunks to N in place, and keeping a carry for the next chunk. 00852 * This avoids moving things around in memory, and uselessly adding zeros, 00853 * compared to the more straightforward, line-oriented approach. 00854 * 00855 * For this prime we need to handle data in chunks of 64 bits. 00856 * Since this is always a multiple of our basic mbedtls_mpi_uint, we can 00857 * use a mbedtls_mpi_uint * to designate such a chunk, and small loops to handle it. 00858 */ 00859 00860 /* Add 64-bit chunks (dst += src) and update carry */ 00861 static inline void add64( mbedtls_mpi_uint *dst, mbedtls_mpi_uint *src, mbedtls_mpi_uint *carry ) 00862 { 00863 unsigned char i; 00864 mbedtls_mpi_uint c = 0; 00865 for( i = 0; i < 8 / sizeof( mbedtls_mpi_uint ); i++, dst++, src++ ) 00866 { 00867 *dst += c; c = ( *dst < c ); 00868 *dst += *src; c += ( *dst < *src ); 00869 } 00870 *carry += c; 00871 } 00872 00873 /* Add carry to a 64-bit chunk and update carry */ 00874 static inline void carry64( mbedtls_mpi_uint *dst, mbedtls_mpi_uint *carry ) 00875 { 00876 unsigned char i; 00877 for( i = 0; i < 8 / sizeof( mbedtls_mpi_uint ); i++, dst++ ) 00878 { 00879 *dst += *carry; 00880 *carry = ( *dst < *carry ); 00881 } 00882 } 00883 00884 #define WIDTH 8 / sizeof( mbedtls_mpi_uint ) 00885 #define A( i ) N->p + i * WIDTH 00886 #define ADD( i ) add64( p, A( i ), &c ) 00887 #define NEXT p += WIDTH; carry64( p, &c ) 00888 #define LAST p += WIDTH; *p = c; while( ++p < end ) *p = 0 00889 00890 /* 00891 * Fast quasi-reduction modulo p192 (FIPS 186-3 D.2.1) 00892 */ 00893 static int ecp_mod_p192( mbedtls_mpi *N ) 00894 { 00895 int ret; 00896 mbedtls_mpi_uint c = 0; 00897 mbedtls_mpi_uint *p, *end; 00898 00899 /* Make sure we have enough blocks so that A(5) is legal */ 00900 MBEDTLS_MPI_CHK( mbedtls_mpi_grow( N, 6 * WIDTH ) ); 00901 00902 p = N->p ; 00903 end = p + N->n ; 00904 00905 ADD( 3 ); ADD( 5 ); NEXT; // A0 += A3 + A5 00906 ADD( 3 ); ADD( 4 ); ADD( 5 ); NEXT; // A1 += A3 + A4 + A5 00907 ADD( 4 ); ADD( 5 ); LAST; // A2 += A4 + A5 00908 00909 cleanup: 00910 return( ret ); 00911 } 00912 00913 #undef WIDTH 00914 #undef A 00915 #undef ADD 00916 #undef NEXT 00917 #undef LAST 00918 #endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */ 00919 00920 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) || \ 00921 defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) || \ 00922 defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) 00923 /* 00924 * The reader is advised to first understand ecp_mod_p192() since the same 00925 * general structure is used here, but with additional complications: 00926 * (1) chunks of 32 bits, and (2) subtractions. 00927 */ 00928 00929 /* 00930 * For these primes, we need to handle data in chunks of 32 bits. 00931 * This makes it more complicated if we use 64 bits limbs in MPI, 00932 * which prevents us from using a uniform access method as for p192. 00933 * 00934 * So, we define a mini abstraction layer to access 32 bit chunks, 00935 * load them in 'cur' for work, and store them back from 'cur' when done. 00936 * 00937 * While at it, also define the size of N in terms of 32-bit chunks. 00938 */ 00939 #define LOAD32 cur = A( i ); 00940 00941 #if defined(MBEDTLS_HAVE_INT32) /* 32 bit */ 00942 00943 #define MAX32 N->n 00944 #define A( j ) N->p[j] 00945 #define STORE32 N->p[i] = cur; 00946 00947 #else /* 64-bit */ 00948 00949 #define MAX32 N->n * 2 00950 #define A( j ) j % 2 ? (uint32_t)( N->p[j/2] >> 32 ) : (uint32_t)( N->p[j/2] ) 00951 #define STORE32 \ 00952 if( i % 2 ) { \ 00953 N->p[i/2] &= 0x00000000FFFFFFFF; \ 00954 N->p[i/2] |= ((mbedtls_mpi_uint) cur) << 32; \ 00955 } else { \ 00956 N->p[i/2] &= 0xFFFFFFFF00000000; \ 00957 N->p[i/2] |= (mbedtls_mpi_uint) cur; \ 00958 } 00959 00960 #endif /* sizeof( mbedtls_mpi_uint ) */ 00961 00962 /* 00963 * Helpers for addition and subtraction of chunks, with signed carry. 00964 */ 00965 static inline void add32( uint32_t *dst, uint32_t src, signed char *carry ) 00966 { 00967 *dst += src; 00968 *carry += ( *dst < src ); 00969 } 00970 00971 static inline void sub32( uint32_t *dst, uint32_t src, signed char *carry ) 00972 { 00973 *carry -= ( *dst < src ); 00974 *dst -= src; 00975 } 00976 00977 #define ADD( j ) add32( &cur, A( j ), &c ); 00978 #define SUB( j ) sub32( &cur, A( j ), &c ); 00979 00980 /* 00981 * Helpers for the main 'loop' 00982 * (see fix_negative for the motivation of C) 00983 */ 00984 #define INIT( b ) \ 00985 int ret; \ 00986 signed char c = 0, cc; \ 00987 uint32_t cur; \ 00988 size_t i = 0, bits = b; \ 00989 mbedtls_mpi C; \ 00990 mbedtls_mpi_uint Cp[ b / 8 / sizeof( mbedtls_mpi_uint) + 1 ]; \ 00991 \ 00992 C.s = 1; \ 00993 C.n = b / 8 / sizeof( mbedtls_mpi_uint) + 1; \ 00994 C.p = Cp; \ 00995 memset( Cp, 0, C.n * sizeof( mbedtls_mpi_uint ) ); \ 00996 \ 00997 MBEDTLS_MPI_CHK( mbedtls_mpi_grow( N, b * 2 / 8 / sizeof( mbedtls_mpi_uint ) ) ); \ 00998 LOAD32; 00999 01000 #define NEXT \ 01001 STORE32; i++; LOAD32; \ 01002 cc = c; c = 0; \ 01003 if( cc < 0 ) \ 01004 sub32( &cur, -cc, &c ); \ 01005 else \ 01006 add32( &cur, cc, &c ); \ 01007 01008 #define LAST \ 01009 STORE32; i++; \ 01010 cur = c > 0 ? c : 0; STORE32; \ 01011 cur = 0; while( ++i < MAX32 ) { STORE32; } \ 01012 if( c < 0 ) fix_negative( N, c, &C, bits ); 01013 01014 /* 01015 * If the result is negative, we get it in the form 01016 * c * 2^(bits + 32) + N, with c negative and N positive shorter than 'bits' 01017 */ 01018 static inline int fix_negative( mbedtls_mpi *N, signed char c, mbedtls_mpi *C, size_t bits ) 01019 { 01020 int ret; 01021 01022 /* C = - c * 2^(bits + 32) */ 01023 #if !defined(MBEDTLS_HAVE_INT64) 01024 ((void) bits); 01025 #else 01026 if( bits == 224 ) 01027 C->p [ C->n - 1 ] = ((mbedtls_mpi_uint) -c) << 32; 01028 else 01029 #endif 01030 C->p [ C->n - 1 ] = (mbedtls_mpi_uint) -c; 01031 01032 /* N = - ( C - N ) */ 01033 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( N, C, N ) ); 01034 N->s = -1; 01035 01036 cleanup: 01037 01038 return( ret ); 01039 } 01040 01041 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) 01042 /* 01043 * Fast quasi-reduction modulo p224 (FIPS 186-3 D.2.2) 01044 */ 01045 static int ecp_mod_p224( mbedtls_mpi *N ) 01046 { 01047 INIT( 224 ); 01048 01049 SUB( 7 ); SUB( 11 ); NEXT; // A0 += -A7 - A11 01050 SUB( 8 ); SUB( 12 ); NEXT; // A1 += -A8 - A12 01051 SUB( 9 ); SUB( 13 ); NEXT; // A2 += -A9 - A13 01052 SUB( 10 ); ADD( 7 ); ADD( 11 ); NEXT; // A3 += -A10 + A7 + A11 01053 SUB( 11 ); ADD( 8 ); ADD( 12 ); NEXT; // A4 += -A11 + A8 + A12 01054 SUB( 12 ); ADD( 9 ); ADD( 13 ); NEXT; // A5 += -A12 + A9 + A13 01055 SUB( 13 ); ADD( 10 ); LAST; // A6 += -A13 + A10 01056 01057 cleanup: 01058 return( ret ); 01059 } 01060 #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */ 01061 01062 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) 01063 /* 01064 * Fast quasi-reduction modulo p256 (FIPS 186-3 D.2.3) 01065 */ 01066 static int ecp_mod_p256( mbedtls_mpi *N ) 01067 { 01068 INIT( 256 ); 01069 01070 ADD( 8 ); ADD( 9 ); 01071 SUB( 11 ); SUB( 12 ); SUB( 13 ); SUB( 14 ); NEXT; // A0 01072 01073 ADD( 9 ); ADD( 10 ); 01074 SUB( 12 ); SUB( 13 ); SUB( 14 ); SUB( 15 ); NEXT; // A1 01075 01076 ADD( 10 ); ADD( 11 ); 01077 SUB( 13 ); SUB( 14 ); SUB( 15 ); NEXT; // A2 01078 01079 ADD( 11 ); ADD( 11 ); ADD( 12 ); ADD( 12 ); ADD( 13 ); 01080 SUB( 15 ); SUB( 8 ); SUB( 9 ); NEXT; // A3 01081 01082 ADD( 12 ); ADD( 12 ); ADD( 13 ); ADD( 13 ); ADD( 14 ); 01083 SUB( 9 ); SUB( 10 ); NEXT; // A4 01084 01085 ADD( 13 ); ADD( 13 ); ADD( 14 ); ADD( 14 ); ADD( 15 ); 01086 SUB( 10 ); SUB( 11 ); NEXT; // A5 01087 01088 ADD( 14 ); ADD( 14 ); ADD( 15 ); ADD( 15 ); ADD( 14 ); ADD( 13 ); 01089 SUB( 8 ); SUB( 9 ); NEXT; // A6 01090 01091 ADD( 15 ); ADD( 15 ); ADD( 15 ); ADD( 8 ); 01092 SUB( 10 ); SUB( 11 ); SUB( 12 ); SUB( 13 ); LAST; // A7 01093 01094 cleanup: 01095 return( ret ); 01096 } 01097 #endif /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */ 01098 01099 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) 01100 /* 01101 * Fast quasi-reduction modulo p384 (FIPS 186-3 D.2.4) 01102 */ 01103 static int ecp_mod_p384( mbedtls_mpi *N ) 01104 { 01105 INIT( 384 ); 01106 01107 ADD( 12 ); ADD( 21 ); ADD( 20 ); 01108 SUB( 23 ); NEXT; // A0 01109 01110 ADD( 13 ); ADD( 22 ); ADD( 23 ); 01111 SUB( 12 ); SUB( 20 ); NEXT; // A2 01112 01113 ADD( 14 ); ADD( 23 ); 01114 SUB( 13 ); SUB( 21 ); NEXT; // A2 01115 01116 ADD( 15 ); ADD( 12 ); ADD( 20 ); ADD( 21 ); 01117 SUB( 14 ); SUB( 22 ); SUB( 23 ); NEXT; // A3 01118 01119 ADD( 21 ); ADD( 21 ); ADD( 16 ); ADD( 13 ); ADD( 12 ); ADD( 20 ); ADD( 22 ); 01120 SUB( 15 ); SUB( 23 ); SUB( 23 ); NEXT; // A4 01121 01122 ADD( 22 ); ADD( 22 ); ADD( 17 ); ADD( 14 ); ADD( 13 ); ADD( 21 ); ADD( 23 ); 01123 SUB( 16 ); NEXT; // A5 01124 01125 ADD( 23 ); ADD( 23 ); ADD( 18 ); ADD( 15 ); ADD( 14 ); ADD( 22 ); 01126 SUB( 17 ); NEXT; // A6 01127 01128 ADD( 19 ); ADD( 16 ); ADD( 15 ); ADD( 23 ); 01129 SUB( 18 ); NEXT; // A7 01130 01131 ADD( 20 ); ADD( 17 ); ADD( 16 ); 01132 SUB( 19 ); NEXT; // A8 01133 01134 ADD( 21 ); ADD( 18 ); ADD( 17 ); 01135 SUB( 20 ); NEXT; // A9 01136 01137 ADD( 22 ); ADD( 19 ); ADD( 18 ); 01138 SUB( 21 ); NEXT; // A10 01139 01140 ADD( 23 ); ADD( 20 ); ADD( 19 ); 01141 SUB( 22 ); LAST; // A11 01142 01143 cleanup: 01144 return( ret ); 01145 } 01146 #endif /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */ 01147 01148 #undef A 01149 #undef LOAD32 01150 #undef STORE32 01151 #undef MAX32 01152 #undef INIT 01153 #undef NEXT 01154 #undef LAST 01155 01156 #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED || 01157 MBEDTLS_ECP_DP_SECP256R1_ENABLED || 01158 MBEDTLS_ECP_DP_SECP384R1_ENABLED */ 01159 01160 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) 01161 /* 01162 * Here we have an actual Mersenne prime, so things are more straightforward. 01163 * However, chunks are aligned on a 'weird' boundary (521 bits). 01164 */ 01165 01166 /* Size of p521 in terms of mbedtls_mpi_uint */ 01167 #define P521_WIDTH ( 521 / 8 / sizeof( mbedtls_mpi_uint ) + 1 ) 01168 01169 /* Bits to keep in the most significant mbedtls_mpi_uint */ 01170 #define P521_MASK 0x01FF 01171 01172 /* 01173 * Fast quasi-reduction modulo p521 (FIPS 186-3 D.2.5) 01174 * Write N as A1 + 2^521 A0, return A0 + A1 01175 */ 01176 static int ecp_mod_p521( mbedtls_mpi *N ) 01177 { 01178 int ret; 01179 size_t i; 01180 mbedtls_mpi M; 01181 mbedtls_mpi_uint Mp[P521_WIDTH + 1]; 01182 /* Worst case for the size of M is when mbedtls_mpi_uint is 16 bits: 01183 * we need to hold bits 513 to 1056, which is 34 limbs, that is 01184 * P521_WIDTH + 1. Otherwise P521_WIDTH is enough. */ 01185 01186 if( N->n < P521_WIDTH ) 01187 return( 0 ); 01188 01189 /* M = A1 */ 01190 M.s = 1; 01191 M.n = N->n - ( P521_WIDTH - 1 ); 01192 if( M.n > P521_WIDTH + 1 ) 01193 M.n = P521_WIDTH + 1; 01194 M.p = Mp; 01195 memcpy( Mp, N->p + P521_WIDTH - 1, M.n * sizeof( mbedtls_mpi_uint ) ); 01196 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, 521 % ( 8 * sizeof( mbedtls_mpi_uint ) ) ) ); 01197 01198 /* N = A0 */ 01199 N->p [P521_WIDTH - 1] &= P521_MASK; 01200 for( i = P521_WIDTH; i < N->n ; i++ ) 01201 N->p [i] = 0; 01202 01203 /* N = A0 + A1 */ 01204 MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) ); 01205 01206 cleanup: 01207 return( ret ); 01208 } 01209 01210 #undef P521_WIDTH 01211 #undef P521_MASK 01212 #endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */ 01213 01214 #endif /* MBEDTLS_ECP_NIST_OPTIM */ 01215 01216 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) 01217 01218 /* Size of p255 in terms of mbedtls_mpi_uint */ 01219 #define P255_WIDTH ( 255 / 8 / sizeof( mbedtls_mpi_uint ) + 1 ) 01220 01221 /* 01222 * Fast quasi-reduction modulo p255 = 2^255 - 19 01223 * Write N as A0 + 2^255 A1, return A0 + 19 * A1 01224 */ 01225 static int ecp_mod_p255( mbedtls_mpi *N ) 01226 { 01227 int ret; 01228 size_t i; 01229 mbedtls_mpi M; 01230 mbedtls_mpi_uint Mp[P255_WIDTH + 2]; 01231 01232 if( N->n < P255_WIDTH ) 01233 return( 0 ); 01234 01235 /* M = A1 */ 01236 M.s = 1; 01237 M.n = N->n - ( P255_WIDTH - 1 ); 01238 if( M.n > P255_WIDTH + 1 ) 01239 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); 01240 M.p = Mp; 01241 memset( Mp, 0, sizeof Mp ); 01242 memcpy( Mp, N->p + P255_WIDTH - 1, M.n * sizeof( mbedtls_mpi_uint ) ); 01243 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, 255 % ( 8 * sizeof( mbedtls_mpi_uint ) ) ) ); 01244 M.n ++; /* Make room for multiplication by 19 */ 01245 01246 /* N = A0 */ 01247 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( N, 255, 0 ) ); 01248 for( i = P255_WIDTH; i < N->n ; i++ ) 01249 N->p [i] = 0; 01250 01251 /* N = A0 + 19 * A1 */ 01252 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &M, 19 ) ); 01253 MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) ); 01254 01255 cleanup: 01256 return( ret ); 01257 } 01258 #endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */ 01259 01260 #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) 01261 01262 /* Size of p448 in terms of mbedtls_mpi_uint */ 01263 #define P448_WIDTH ( 448 / 8 / sizeof( mbedtls_mpi_uint ) ) 01264 01265 /* Number of limbs fully occupied by 2^224 (max), and limbs used by it (min) */ 01266 #define DIV_ROUND_UP( X, Y ) ( ( ( X ) + ( Y ) - 1 ) / ( Y ) ) 01267 #define P224_WIDTH_MIN ( 28 / sizeof( mbedtls_mpi_uint ) ) 01268 #define P224_WIDTH_MAX DIV_ROUND_UP( 28, sizeof( mbedtls_mpi_uint ) ) 01269 #define P224_UNUSED_BITS ( ( P224_WIDTH_MAX * sizeof( mbedtls_mpi_uint ) * 8 ) - 224 ) 01270 01271 /* 01272 * Fast quasi-reduction modulo p448 = 2^448 - 2^224 - 1 01273 * Write N as A0 + 2^448 A1 and A1 as B0 + 2^224 B1, and return 01274 * A0 + A1 + B1 + (B0 + B1) * 2^224. This is different to the reference 01275 * implementation of Curve448, which uses its own special 56-bit limbs rather 01276 * than a generic bignum library. We could squeeze some extra speed out on 01277 * 32-bit machines by splitting N up into 32-bit limbs and doing the 01278 * arithmetic using the limbs directly as we do for the NIST primes above, 01279 * but for 64-bit targets it should use half the number of operations if we do 01280 * the reduction with 224-bit limbs, since mpi_add_mpi will then use 64-bit adds. 01281 */ 01282 static int ecp_mod_p448( mbedtls_mpi *N ) 01283 { 01284 int ret; 01285 size_t i; 01286 mbedtls_mpi M, Q; 01287 mbedtls_mpi_uint Mp[P448_WIDTH + 1], Qp[P448_WIDTH]; 01288 01289 if( N->n <= P448_WIDTH ) 01290 return( 0 ); 01291 01292 /* M = A1 */ 01293 M.s = 1; 01294 M.n = N->n - ( P448_WIDTH ); 01295 if( M.n > P448_WIDTH ) 01296 /* Shouldn't be called with N larger than 2^896! */ 01297 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); 01298 M.p = Mp; 01299 memset( Mp, 0, sizeof( Mp ) ); 01300 memcpy( Mp, N->p + P448_WIDTH, M.n * sizeof( mbedtls_mpi_uint ) ); 01301 01302 /* N = A0 */ 01303 for( i = P448_WIDTH; i < N->n ; i++ ) 01304 N->p [i] = 0; 01305 01306 /* N += A1 */ 01307 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &M ) ); 01308 01309 /* Q = B1, N += B1 */ 01310 Q = M; 01311 Q.p = Qp; 01312 memcpy( Qp, Mp, sizeof( Qp ) ); 01313 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &Q, 224 ) ); 01314 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &Q ) ); 01315 01316 /* M = (B0 + B1) * 2^224, N += M */ 01317 if( sizeof( mbedtls_mpi_uint ) > 4 ) 01318 Mp[P224_WIDTH_MIN] &= ( (mbedtls_mpi_uint)-1 ) >> ( P224_UNUSED_BITS ); 01319 for( i = P224_WIDTH_MAX; i < M.n ; ++i ) 01320 Mp[i] = 0; 01321 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &M, &M, &Q ) ); 01322 M.n = P448_WIDTH + 1; /* Make room for shifted carry bit from the addition */ 01323 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &M, 224 ) ); 01324 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &M ) ); 01325 01326 cleanup: 01327 return( ret ); 01328 } 01329 #endif /* MBEDTLS_ECP_DP_CURVE448_ENABLED */ 01330 01331 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) || \ 01332 defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) || \ 01333 defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) 01334 /* 01335 * Fast quasi-reduction modulo P = 2^s - R, 01336 * with R about 33 bits, used by the Koblitz curves. 01337 * 01338 * Write N as A0 + 2^224 A1, return A0 + R * A1. 01339 * Actually do two passes, since R is big. 01340 */ 01341 #define P_KOBLITZ_MAX ( 256 / 8 / sizeof( mbedtls_mpi_uint ) ) // Max limbs in P 01342 #define P_KOBLITZ_R ( 8 / sizeof( mbedtls_mpi_uint ) ) // Limbs in R 01343 static inline int ecp_mod_koblitz( mbedtls_mpi *N, mbedtls_mpi_uint *Rp, size_t p_limbs, 01344 size_t adjust, size_t shift, mbedtls_mpi_uint mask ) 01345 { 01346 int ret; 01347 size_t i; 01348 mbedtls_mpi M, R; 01349 mbedtls_mpi_uint Mp[P_KOBLITZ_MAX + P_KOBLITZ_R + 1]; 01350 01351 if( N->n < p_limbs ) 01352 return( 0 ); 01353 01354 /* Init R */ 01355 R.s = 1; 01356 R.p = Rp; 01357 R.n = P_KOBLITZ_R; 01358 01359 /* Common setup for M */ 01360 M.s = 1; 01361 M.p = Mp; 01362 01363 /* M = A1 */ 01364 M.n = N->n - ( p_limbs - adjust ); 01365 if( M.n > p_limbs + adjust ) 01366 M.n = p_limbs + adjust; 01367 memset( Mp, 0, sizeof Mp ); 01368 memcpy( Mp, N->p + p_limbs - adjust, M.n * sizeof( mbedtls_mpi_uint ) ); 01369 if( shift != 0 ) 01370 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, shift ) ); 01371 M.n += R.n ; /* Make room for multiplication by R */ 01372 01373 /* N = A0 */ 01374 if( mask != 0 ) 01375 N->p [p_limbs - 1] &= mask; 01376 for( i = p_limbs; i < N->n ; i++ ) 01377 N->p [i] = 0; 01378 01379 /* N = A0 + R * A1 */ 01380 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &M, &M, &R ) ); 01381 MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) ); 01382 01383 /* Second pass */ 01384 01385 /* M = A1 */ 01386 M.n = N->n - ( p_limbs - adjust ); 01387 if( M.n > p_limbs + adjust ) 01388 M.n = p_limbs + adjust; 01389 memset( Mp, 0, sizeof Mp ); 01390 memcpy( Mp, N->p + p_limbs - adjust, M.n * sizeof( mbedtls_mpi_uint ) ); 01391 if( shift != 0 ) 01392 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, shift ) ); 01393 M.n += R.n ; /* Make room for multiplication by R */ 01394 01395 /* N = A0 */ 01396 if( mask != 0 ) 01397 N->p [p_limbs - 1] &= mask; 01398 for( i = p_limbs; i < N->n ; i++ ) 01399 N->p [i] = 0; 01400 01401 /* N = A0 + R * A1 */ 01402 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &M, &M, &R ) ); 01403 MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) ); 01404 01405 cleanup: 01406 return( ret ); 01407 } 01408 #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED) || 01409 MBEDTLS_ECP_DP_SECP224K1_ENABLED) || 01410 MBEDTLS_ECP_DP_SECP256K1_ENABLED) */ 01411 01412 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) 01413 /* 01414 * Fast quasi-reduction modulo p192k1 = 2^192 - R, 01415 * with R = 2^32 + 2^12 + 2^8 + 2^7 + 2^6 + 2^3 + 1 = 0x0100001119 01416 */ 01417 static int ecp_mod_p192k1( mbedtls_mpi *N ) 01418 { 01419 static mbedtls_mpi_uint Rp[] = { 01420 BYTES_TO_T_UINT_8( 0xC9, 0x11, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) }; 01421 01422 return( ecp_mod_koblitz( N, Rp, 192 / 8 / sizeof( mbedtls_mpi_uint ), 0, 0, 0 ) ); 01423 } 01424 #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */ 01425 01426 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) 01427 /* 01428 * Fast quasi-reduction modulo p224k1 = 2^224 - R, 01429 * with R = 2^32 + 2^12 + 2^11 + 2^9 + 2^7 + 2^4 + 2 + 1 = 0x0100001A93 01430 */ 01431 static int ecp_mod_p224k1( mbedtls_mpi *N ) 01432 { 01433 static mbedtls_mpi_uint Rp[] = { 01434 BYTES_TO_T_UINT_8( 0x93, 0x1A, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) }; 01435 01436 #if defined(MBEDTLS_HAVE_INT64) 01437 return( ecp_mod_koblitz( N, Rp, 4, 1, 32, 0xFFFFFFFF ) ); 01438 #else 01439 return( ecp_mod_koblitz( N, Rp, 224 / 8 / sizeof( mbedtls_mpi_uint ), 0, 0, 0 ) ); 01440 #endif 01441 } 01442 01443 #endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */ 01444 01445 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) 01446 /* 01447 * Fast quasi-reduction modulo p256k1 = 2^256 - R, 01448 * with R = 2^32 + 2^9 + 2^8 + 2^7 + 2^6 + 2^4 + 1 = 0x01000003D1 01449 */ 01450 static int ecp_mod_p256k1( mbedtls_mpi *N ) 01451 { 01452 static mbedtls_mpi_uint Rp[] = { 01453 BYTES_TO_T_UINT_8( 0xD1, 0x03, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) }; 01454 return( ecp_mod_koblitz( N, Rp, 256 / 8 / sizeof( mbedtls_mpi_uint ), 0, 0, 0 ) ); 01455 } 01456 #endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */ 01457 01458 #endif /* !MBEDTLS_ECP_ALT */ 01459 01460 #endif /* MBEDTLS_ECP_C */
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