Doug Anson
mbed TLS library
Dependents: HTTPClient-SSL WS_SERVER
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ecp_curves.c
00001 /* 00002 * Elliptic curves over GF(p): curve-specific data and functions 00003 * 00004 * Copyright (C) 2006-2014, ARM Limited, All Rights Reserved 00005 * 00006 * This file is part of mbed TLS (https://tls.mbed.org) 00007 * 00008 * This program is free software; you can redistribute it and/or modify 00009 * it under the terms of the GNU General Public License as published by 00010 * the Free Software Foundation; either version 2 of the License, or 00011 * (at your option) any later version. 00012 * 00013 * This program is distributed in the hope that it will be useful, 00014 * but WITHOUT ANY WARRANTY; without even the implied warranty of 00015 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 00016 * GNU General Public License for more details. 00017 * 00018 * You should have received a copy of the GNU General Public License along 00019 * with this program; if not, write to the Free Software Foundation, Inc., 00020 * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. 00021 */ 00022 00023 #if !defined(POLARSSL_CONFIG_FILE) 00024 #include "polarssl/config.h" 00025 #else 00026 #include POLARSSL_CONFIG_FILE 00027 #endif 00028 00029 #if defined(POLARSSL_ECP_C) 00030 00031 #include "polarssl/ecp.h" 00032 00033 #include <string.h> 00034 00035 #if defined(_MSC_VER) && !defined(inline) 00036 #define inline _inline 00037 #else 00038 #if defined(__ARMCC_VERSION) && !defined(inline) 00039 #define inline __inline 00040 #endif /* __ARMCC_VERSION */ 00041 #endif /*_MSC_VER */ 00042 00043 /* 00044 * Conversion macros for embedded constants: 00045 * build lists of t_uint's from lists of unsigned char's grouped by 8, 4 or 2 00046 */ 00047 #if defined(POLARSSL_HAVE_INT8) 00048 00049 #define BYTES_TO_T_UINT_8( a, b, c, d, e, f, g, h ) \ 00050 a, b, c, d, e, f, g, h 00051 00052 #define BYTES_TO_T_UINT_4( a, b, c, d ) \ 00053 a, b, c, d 00054 00055 #define BYTES_TO_T_UINT_2( a, b ) \ 00056 a, b 00057 00058 #elif defined(POLARSSL_HAVE_INT16) 00059 00060 #define BYTES_TO_T_UINT_2( a, b ) \ 00061 ( (t_uint) a << 0 ) | \ 00062 ( (t_uint) b << 8 ) 00063 00064 #define BYTES_TO_T_UINT_4( a, b, c, d ) \ 00065 BYTES_TO_T_UINT_2( a, b ), \ 00066 BYTES_TO_T_UINT_2( c, d ) 00067 00068 #define BYTES_TO_T_UINT_8( a, b, c, d, e, f, g, h ) \ 00069 BYTES_TO_T_UINT_2( a, b ), \ 00070 BYTES_TO_T_UINT_2( c, d ), \ 00071 BYTES_TO_T_UINT_2( e, f ), \ 00072 BYTES_TO_T_UINT_2( g, h ) 00073 00074 #elif defined(POLARSSL_HAVE_INT32) 00075 00076 #define BYTES_TO_T_UINT_4( a, b, c, d ) \ 00077 ( (t_uint) a << 0 ) | \ 00078 ( (t_uint) b << 8 ) | \ 00079 ( (t_uint) c << 16 ) | \ 00080 ( (t_uint) d << 24 ) 00081 00082 #define BYTES_TO_T_UINT_2( a, b ) \ 00083 BYTES_TO_T_UINT_4( a, b, 0, 0 ) 00084 00085 #define BYTES_TO_T_UINT_8( a, b, c, d, e, f, g, h ) \ 00086 BYTES_TO_T_UINT_4( a, b, c, d ), \ 00087 BYTES_TO_T_UINT_4( e, f, g, h ) 00088 00089 #else /* 64-bits */ 00090 00091 #define BYTES_TO_T_UINT_8( a, b, c, d, e, f, g, h ) \ 00092 ( (t_uint) a << 0 ) | \ 00093 ( (t_uint) b << 8 ) | \ 00094 ( (t_uint) c << 16 ) | \ 00095 ( (t_uint) d << 24 ) | \ 00096 ( (t_uint) e << 32 ) | \ 00097 ( (t_uint) f << 40 ) | \ 00098 ( (t_uint) g << 48 ) | \ 00099 ( (t_uint) h << 56 ) 00100 00101 #define BYTES_TO_T_UINT_4( a, b, c, d ) \ 00102 BYTES_TO_T_UINT_8( a, b, c, d, 0, 0, 0, 0 ) 00103 00104 #define BYTES_TO_T_UINT_2( a, b ) \ 00105 BYTES_TO_T_UINT_8( a, b, 0, 0, 0, 0, 0, 0 ) 00106 00107 #endif /* bits in t_uint */ 00108 00109 /* 00110 * Note: the constants are in little-endian order 00111 * to be directly usable in MPIs 00112 */ 00113 00114 /* 00115 * Domain parameters for secp192r1 00116 */ 00117 #if defined(POLARSSL_ECP_DP_SECP192R1_ENABLED) 00118 static const t_uint secp192r1_p[] = { 00119 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00120 BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00121 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00122 }; 00123 static const t_uint secp192r1_b[] = { 00124 BYTES_TO_T_UINT_8( 0xB1, 0xB9, 0x46, 0xC1, 0xEC, 0xDE, 0xB8, 0xFE ), 00125 BYTES_TO_T_UINT_8( 0x49, 0x30, 0x24, 0x72, 0xAB, 0xE9, 0xA7, 0x0F ), 00126 BYTES_TO_T_UINT_8( 0xE7, 0x80, 0x9C, 0xE5, 0x19, 0x05, 0x21, 0x64 ), 00127 }; 00128 static const t_uint secp192r1_gx[] = { 00129 BYTES_TO_T_UINT_8( 0x12, 0x10, 0xFF, 0x82, 0xFD, 0x0A, 0xFF, 0xF4 ), 00130 BYTES_TO_T_UINT_8( 0x00, 0x88, 0xA1, 0x43, 0xEB, 0x20, 0xBF, 0x7C ), 00131 BYTES_TO_T_UINT_8( 0xF6, 0x90, 0x30, 0xB0, 0x0E, 0xA8, 0x8D, 0x18 ), 00132 }; 00133 static const t_uint secp192r1_gy[] = { 00134 BYTES_TO_T_UINT_8( 0x11, 0x48, 0x79, 0x1E, 0xA1, 0x77, 0xF9, 0x73 ), 00135 BYTES_TO_T_UINT_8( 0xD5, 0xCD, 0x24, 0x6B, 0xED, 0x11, 0x10, 0x63 ), 00136 BYTES_TO_T_UINT_8( 0x78, 0xDA, 0xC8, 0xFF, 0x95, 0x2B, 0x19, 0x07 ), 00137 }; 00138 static const t_uint secp192r1_n[] = { 00139 BYTES_TO_T_UINT_8( 0x31, 0x28, 0xD2, 0xB4, 0xB1, 0xC9, 0x6B, 0x14 ), 00140 BYTES_TO_T_UINT_8( 0x36, 0xF8, 0xDE, 0x99, 0xFF, 0xFF, 0xFF, 0xFF ), 00141 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00142 }; 00143 #endif /* POLARSSL_ECP_DP_SECP192R1_ENABLED */ 00144 00145 /* 00146 * Domain parameters for secp224r1 00147 */ 00148 #if defined(POLARSSL_ECP_DP_SECP224R1_ENABLED) 00149 static const t_uint secp224r1_p[] = { 00150 BYTES_TO_T_UINT_8( 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ), 00151 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ), 00152 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00153 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ), 00154 }; 00155 static const t_uint secp224r1_b[] = { 00156 BYTES_TO_T_UINT_8( 0xB4, 0xFF, 0x55, 0x23, 0x43, 0x39, 0x0B, 0x27 ), 00157 BYTES_TO_T_UINT_8( 0xBA, 0xD8, 0xBF, 0xD7, 0xB7, 0xB0, 0x44, 0x50 ), 00158 BYTES_TO_T_UINT_8( 0x56, 0x32, 0x41, 0xF5, 0xAB, 0xB3, 0x04, 0x0C ), 00159 BYTES_TO_T_UINT_4( 0x85, 0x0A, 0x05, 0xB4 ), 00160 }; 00161 static const t_uint secp224r1_gx[] = { 00162 BYTES_TO_T_UINT_8( 0x21, 0x1D, 0x5C, 0x11, 0xD6, 0x80, 0x32, 0x34 ), 00163 BYTES_TO_T_UINT_8( 0x22, 0x11, 0xC2, 0x56, 0xD3, 0xC1, 0x03, 0x4A ), 00164 BYTES_TO_T_UINT_8( 0xB9, 0x90, 0x13, 0x32, 0x7F, 0xBF, 0xB4, 0x6B ), 00165 BYTES_TO_T_UINT_4( 0xBD, 0x0C, 0x0E, 0xB7 ), 00166 }; 00167 static const t_uint secp224r1_gy[] = { 00168 BYTES_TO_T_UINT_8( 0x34, 0x7E, 0x00, 0x85, 0x99, 0x81, 0xD5, 0x44 ), 00169 BYTES_TO_T_UINT_8( 0x64, 0x47, 0x07, 0x5A, 0xA0, 0x75, 0x43, 0xCD ), 00170 BYTES_TO_T_UINT_8( 0xE6, 0xDF, 0x22, 0x4C, 0xFB, 0x23, 0xF7, 0xB5 ), 00171 BYTES_TO_T_UINT_4( 0x88, 0x63, 0x37, 0xBD ), 00172 }; 00173 static const t_uint secp224r1_n[] = { 00174 BYTES_TO_T_UINT_8( 0x3D, 0x2A, 0x5C, 0x5C, 0x45, 0x29, 0xDD, 0x13 ), 00175 BYTES_TO_T_UINT_8( 0x3E, 0xF0, 0xB8, 0xE0, 0xA2, 0x16, 0xFF, 0xFF ), 00176 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00177 BYTES_TO_T_UINT_4( 0xFF, 0xFF, 0xFF, 0xFF ), 00178 }; 00179 #endif /* POLARSSL_ECP_DP_SECP224R1_ENABLED */ 00180 00181 /* 00182 * Domain parameters for secp256r1 00183 */ 00184 #if defined(POLARSSL_ECP_DP_SECP256R1_ENABLED) 00185 static const t_uint secp256r1_p[] = { 00186 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00187 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ), 00188 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ), 00189 BYTES_TO_T_UINT_8( 0x01, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ), 00190 }; 00191 static const t_uint secp256r1_b[] = { 00192 BYTES_TO_T_UINT_8( 0x4B, 0x60, 0xD2, 0x27, 0x3E, 0x3C, 0xCE, 0x3B ), 00193 BYTES_TO_T_UINT_8( 0xF6, 0xB0, 0x53, 0xCC, 0xB0, 0x06, 0x1D, 0x65 ), 00194 BYTES_TO_T_UINT_8( 0xBC, 0x86, 0x98, 0x76, 0x55, 0xBD, 0xEB, 0xB3 ), 00195 BYTES_TO_T_UINT_8( 0xE7, 0x93, 0x3A, 0xAA, 0xD8, 0x35, 0xC6, 0x5A ), 00196 }; 00197 static const t_uint secp256r1_gx[] = { 00198 BYTES_TO_T_UINT_8( 0x96, 0xC2, 0x98, 0xD8, 0x45, 0x39, 0xA1, 0xF4 ), 00199 BYTES_TO_T_UINT_8( 0xA0, 0x33, 0xEB, 0x2D, 0x81, 0x7D, 0x03, 0x77 ), 00200 BYTES_TO_T_UINT_8( 0xF2, 0x40, 0xA4, 0x63, 0xE5, 0xE6, 0xBC, 0xF8 ), 00201 BYTES_TO_T_UINT_8( 0x47, 0x42, 0x2C, 0xE1, 0xF2, 0xD1, 0x17, 0x6B ), 00202 }; 00203 static const t_uint secp256r1_gy[] = { 00204 BYTES_TO_T_UINT_8( 0xF5, 0x51, 0xBF, 0x37, 0x68, 0x40, 0xB6, 0xCB ), 00205 BYTES_TO_T_UINT_8( 0xCE, 0x5E, 0x31, 0x6B, 0x57, 0x33, 0xCE, 0x2B ), 00206 BYTES_TO_T_UINT_8( 0x16, 0x9E, 0x0F, 0x7C, 0x4A, 0xEB, 0xE7, 0x8E ), 00207 BYTES_TO_T_UINT_8( 0x9B, 0x7F, 0x1A, 0xFE, 0xE2, 0x42, 0xE3, 0x4F ), 00208 }; 00209 static const t_uint secp256r1_n[] = { 00210 BYTES_TO_T_UINT_8( 0x51, 0x25, 0x63, 0xFC, 0xC2, 0xCA, 0xB9, 0xF3 ), 00211 BYTES_TO_T_UINT_8( 0x84, 0x9E, 0x17, 0xA7, 0xAD, 0xFA, 0xE6, 0xBC ), 00212 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00213 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ), 00214 }; 00215 #endif /* POLARSSL_ECP_DP_SECP256R1_ENABLED */ 00216 00217 /* 00218 * Domain parameters for secp384r1 00219 */ 00220 #if defined(POLARSSL_ECP_DP_SECP384R1_ENABLED) 00221 static const t_uint secp384r1_p[] = { 00222 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ), 00223 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ), 00224 BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00225 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00226 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00227 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00228 }; 00229 static const t_uint secp384r1_b[] = { 00230 BYTES_TO_T_UINT_8( 0xEF, 0x2A, 0xEC, 0xD3, 0xED, 0xC8, 0x85, 0x2A ), 00231 BYTES_TO_T_UINT_8( 0x9D, 0xD1, 0x2E, 0x8A, 0x8D, 0x39, 0x56, 0xC6 ), 00232 BYTES_TO_T_UINT_8( 0x5A, 0x87, 0x13, 0x50, 0x8F, 0x08, 0x14, 0x03 ), 00233 BYTES_TO_T_UINT_8( 0x12, 0x41, 0x81, 0xFE, 0x6E, 0x9C, 0x1D, 0x18 ), 00234 BYTES_TO_T_UINT_8( 0x19, 0x2D, 0xF8, 0xE3, 0x6B, 0x05, 0x8E, 0x98 ), 00235 BYTES_TO_T_UINT_8( 0xE4, 0xE7, 0x3E, 0xE2, 0xA7, 0x2F, 0x31, 0xB3 ), 00236 }; 00237 static const t_uint secp384r1_gx[] = { 00238 BYTES_TO_T_UINT_8( 0xB7, 0x0A, 0x76, 0x72, 0x38, 0x5E, 0x54, 0x3A ), 00239 BYTES_TO_T_UINT_8( 0x6C, 0x29, 0x55, 0xBF, 0x5D, 0xF2, 0x02, 0x55 ), 00240 BYTES_TO_T_UINT_8( 0x38, 0x2A, 0x54, 0x82, 0xE0, 0x41, 0xF7, 0x59 ), 00241 BYTES_TO_T_UINT_8( 0x98, 0x9B, 0xA7, 0x8B, 0x62, 0x3B, 0x1D, 0x6E ), 00242 BYTES_TO_T_UINT_8( 0x74, 0xAD, 0x20, 0xF3, 0x1E, 0xC7, 0xB1, 0x8E ), 00243 BYTES_TO_T_UINT_8( 0x37, 0x05, 0x8B, 0xBE, 0x22, 0xCA, 0x87, 0xAA ), 00244 }; 00245 static const t_uint secp384r1_gy[] = { 00246 BYTES_TO_T_UINT_8( 0x5F, 0x0E, 0xEA, 0x90, 0x7C, 0x1D, 0x43, 0x7A ), 00247 BYTES_TO_T_UINT_8( 0x9D, 0x81, 0x7E, 0x1D, 0xCE, 0xB1, 0x60, 0x0A ), 00248 BYTES_TO_T_UINT_8( 0xC0, 0xB8, 0xF0, 0xB5, 0x13, 0x31, 0xDA, 0xE9 ), 00249 BYTES_TO_T_UINT_8( 0x7C, 0x14, 0x9A, 0x28, 0xBD, 0x1D, 0xF4, 0xF8 ), 00250 BYTES_TO_T_UINT_8( 0x29, 0xDC, 0x92, 0x92, 0xBF, 0x98, 0x9E, 0x5D ), 00251 BYTES_TO_T_UINT_8( 0x6F, 0x2C, 0x26, 0x96, 0x4A, 0xDE, 0x17, 0x36 ), 00252 }; 00253 static const t_uint secp384r1_n[] = { 00254 BYTES_TO_T_UINT_8( 0x73, 0x29, 0xC5, 0xCC, 0x6A, 0x19, 0xEC, 0xEC ), 00255 BYTES_TO_T_UINT_8( 0x7A, 0xA7, 0xB0, 0x48, 0xB2, 0x0D, 0x1A, 0x58 ), 00256 BYTES_TO_T_UINT_8( 0xDF, 0x2D, 0x37, 0xF4, 0x81, 0x4D, 0x63, 0xC7 ), 00257 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00258 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00259 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00260 }; 00261 #endif /* POLARSSL_ECP_DP_SECP384R1_ENABLED */ 00262 00263 /* 00264 * Domain parameters for secp521r1 00265 */ 00266 #if defined(POLARSSL_ECP_DP_SECP521R1_ENABLED) 00267 static const t_uint secp521r1_p[] = { 00268 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00269 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00270 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00271 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00272 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00273 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00274 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00275 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00276 BYTES_TO_T_UINT_2( 0xFF, 0x01 ), 00277 }; 00278 static const t_uint secp521r1_b[] = { 00279 BYTES_TO_T_UINT_8( 0x00, 0x3F, 0x50, 0x6B, 0xD4, 0x1F, 0x45, 0xEF ), 00280 BYTES_TO_T_UINT_8( 0xF1, 0x34, 0x2C, 0x3D, 0x88, 0xDF, 0x73, 0x35 ), 00281 BYTES_TO_T_UINT_8( 0x07, 0xBF, 0xB1, 0x3B, 0xBD, 0xC0, 0x52, 0x16 ), 00282 BYTES_TO_T_UINT_8( 0x7B, 0x93, 0x7E, 0xEC, 0x51, 0x39, 0x19, 0x56 ), 00283 BYTES_TO_T_UINT_8( 0xE1, 0x09, 0xF1, 0x8E, 0x91, 0x89, 0xB4, 0xB8 ), 00284 BYTES_TO_T_UINT_8( 0xF3, 0x15, 0xB3, 0x99, 0x5B, 0x72, 0xDA, 0xA2 ), 00285 BYTES_TO_T_UINT_8( 0xEE, 0x40, 0x85, 0xB6, 0xA0, 0x21, 0x9A, 0x92 ), 00286 BYTES_TO_T_UINT_8( 0x1F, 0x9A, 0x1C, 0x8E, 0x61, 0xB9, 0x3E, 0x95 ), 00287 BYTES_TO_T_UINT_2( 0x51, 0x00 ), 00288 }; 00289 static const t_uint secp521r1_gx[] = { 00290 BYTES_TO_T_UINT_8( 0x66, 0xBD, 0xE5, 0xC2, 0x31, 0x7E, 0x7E, 0xF9 ), 00291 BYTES_TO_T_UINT_8( 0x9B, 0x42, 0x6A, 0x85, 0xC1, 0xB3, 0x48, 0x33 ), 00292 BYTES_TO_T_UINT_8( 0xDE, 0xA8, 0xFF, 0xA2, 0x27, 0xC1, 0x1D, 0xFE ), 00293 BYTES_TO_T_UINT_8( 0x28, 0x59, 0xE7, 0xEF, 0x77, 0x5E, 0x4B, 0xA1 ), 00294 BYTES_TO_T_UINT_8( 0xBA, 0x3D, 0x4D, 0x6B, 0x60, 0xAF, 0x28, 0xF8 ), 00295 BYTES_TO_T_UINT_8( 0x21, 0xB5, 0x3F, 0x05, 0x39, 0x81, 0x64, 0x9C ), 00296 BYTES_TO_T_UINT_8( 0x42, 0xB4, 0x95, 0x23, 0x66, 0xCB, 0x3E, 0x9E ), 00297 BYTES_TO_T_UINT_8( 0xCD, 0xE9, 0x04, 0x04, 0xB7, 0x06, 0x8E, 0x85 ), 00298 BYTES_TO_T_UINT_2( 0xC6, 0x00 ), 00299 }; 00300 static const t_uint secp521r1_gy[] = { 00301 BYTES_TO_T_UINT_8( 0x50, 0x66, 0xD1, 0x9F, 0x76, 0x94, 0xBE, 0x88 ), 00302 BYTES_TO_T_UINT_8( 0x40, 0xC2, 0x72, 0xA2, 0x86, 0x70, 0x3C, 0x35 ), 00303 BYTES_TO_T_UINT_8( 0x61, 0x07, 0xAD, 0x3F, 0x01, 0xB9, 0x50, 0xC5 ), 00304 BYTES_TO_T_UINT_8( 0x40, 0x26, 0xF4, 0x5E, 0x99, 0x72, 0xEE, 0x97 ), 00305 BYTES_TO_T_UINT_8( 0x2C, 0x66, 0x3E, 0x27, 0x17, 0xBD, 0xAF, 0x17 ), 00306 BYTES_TO_T_UINT_8( 0x68, 0x44, 0x9B, 0x57, 0x49, 0x44, 0xF5, 0x98 ), 00307 BYTES_TO_T_UINT_8( 0xD9, 0x1B, 0x7D, 0x2C, 0xB4, 0x5F, 0x8A, 0x5C ), 00308 BYTES_TO_T_UINT_8( 0x04, 0xC0, 0x3B, 0x9A, 0x78, 0x6A, 0x29, 0x39 ), 00309 BYTES_TO_T_UINT_2( 0x18, 0x01 ), 00310 }; 00311 static const t_uint secp521r1_n[] = { 00312 BYTES_TO_T_UINT_8( 0x09, 0x64, 0x38, 0x91, 0x1E, 0xB7, 0x6F, 0xBB ), 00313 BYTES_TO_T_UINT_8( 0xAE, 0x47, 0x9C, 0x89, 0xB8, 0xC9, 0xB5, 0x3B ), 00314 BYTES_TO_T_UINT_8( 0xD0, 0xA5, 0x09, 0xF7, 0x48, 0x01, 0xCC, 0x7F ), 00315 BYTES_TO_T_UINT_8( 0x6B, 0x96, 0x2F, 0xBF, 0x83, 0x87, 0x86, 0x51 ), 00316 BYTES_TO_T_UINT_8( 0xFA, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00317 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00318 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00319 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00320 BYTES_TO_T_UINT_2( 0xFF, 0x01 ), 00321 }; 00322 #endif /* POLARSSL_ECP_DP_SECP521R1_ENABLED */ 00323 00324 #if defined(POLARSSL_ECP_DP_SECP192K1_ENABLED) 00325 static const t_uint secp192k1_p[] = { 00326 BYTES_TO_T_UINT_8( 0x37, 0xEE, 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 }; 00330 static const t_uint secp192k1_a[] = { 00331 BYTES_TO_T_UINT_2( 0x00, 0x00 ), 00332 }; 00333 static const t_uint secp192k1_b[] = { 00334 BYTES_TO_T_UINT_2( 0x03, 0x00 ), 00335 }; 00336 static const t_uint secp192k1_gx[] = { 00337 BYTES_TO_T_UINT_8( 0x7D, 0x6C, 0xE0, 0xEA, 0xB1, 0xD1, 0xA5, 0x1D ), 00338 BYTES_TO_T_UINT_8( 0x34, 0xF4, 0xB7, 0x80, 0x02, 0x7D, 0xB0, 0x26 ), 00339 BYTES_TO_T_UINT_8( 0xAE, 0xE9, 0x57, 0xC0, 0x0E, 0xF1, 0x4F, 0xDB ), 00340 }; 00341 static const t_uint secp192k1_gy[] = { 00342 BYTES_TO_T_UINT_8( 0x9D, 0x2F, 0x5E, 0xD9, 0x88, 0xAA, 0x82, 0x40 ), 00343 BYTES_TO_T_UINT_8( 0x34, 0x86, 0xBE, 0x15, 0xD0, 0x63, 0x41, 0x84 ), 00344 BYTES_TO_T_UINT_8( 0xA7, 0x28, 0x56, 0x9C, 0x6D, 0x2F, 0x2F, 0x9B ), 00345 }; 00346 static const t_uint secp192k1_n[] = { 00347 BYTES_TO_T_UINT_8( 0x8D, 0xFD, 0xDE, 0x74, 0x6A, 0x46, 0x69, 0x0F ), 00348 BYTES_TO_T_UINT_8( 0x17, 0xFC, 0xF2, 0x26, 0xFE, 0xFF, 0xFF, 0xFF ), 00349 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00350 }; 00351 #endif /* POLARSSL_ECP_DP_SECP192K1_ENABLED */ 00352 00353 #if defined(POLARSSL_ECP_DP_SECP224K1_ENABLED) 00354 static const t_uint secp224k1_p[] = { 00355 BYTES_TO_T_UINT_8( 0x6D, 0xE5, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ), 00356 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00357 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00358 BYTES_TO_T_UINT_4( 0xFF, 0xFF, 0xFF, 0xFF ), 00359 }; 00360 static const t_uint secp224k1_a[] = { 00361 BYTES_TO_T_UINT_2( 0x00, 0x00 ), 00362 }; 00363 static const t_uint secp224k1_b[] = { 00364 BYTES_TO_T_UINT_2( 0x05, 0x00 ), 00365 }; 00366 static const t_uint secp224k1_gx[] = { 00367 BYTES_TO_T_UINT_8( 0x5C, 0xA4, 0xB7, 0xB6, 0x0E, 0x65, 0x7E, 0x0F ), 00368 BYTES_TO_T_UINT_8( 0xA9, 0x75, 0x70, 0xE4, 0xE9, 0x67, 0xA4, 0x69 ), 00369 BYTES_TO_T_UINT_8( 0xA1, 0x28, 0xFC, 0x30, 0xDF, 0x99, 0xF0, 0x4D ), 00370 BYTES_TO_T_UINT_4( 0x33, 0x5B, 0x45, 0xA1 ), 00371 }; 00372 static const t_uint secp224k1_gy[] = { 00373 BYTES_TO_T_UINT_8( 0xA5, 0x61, 0x6D, 0x55, 0xDB, 0x4B, 0xCA, 0xE2 ), 00374 BYTES_TO_T_UINT_8( 0x59, 0xBD, 0xB0, 0xC0, 0xF7, 0x19, 0xE3, 0xF7 ), 00375 BYTES_TO_T_UINT_8( 0xD6, 0xFB, 0xCA, 0x82, 0x42, 0x34, 0xBA, 0x7F ), 00376 BYTES_TO_T_UINT_4( 0xED, 0x9F, 0x08, 0x7E ), 00377 }; 00378 static const t_uint secp224k1_n[] = { 00379 BYTES_TO_T_UINT_8( 0xF7, 0xB1, 0x9F, 0x76, 0x71, 0xA9, 0xF0, 0xCA ), 00380 BYTES_TO_T_UINT_8( 0x84, 0x61, 0xEC, 0xD2, 0xE8, 0xDC, 0x01, 0x00 ), 00381 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ), 00382 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ), 00383 }; 00384 #endif /* POLARSSL_ECP_DP_SECP224K1_ENABLED */ 00385 00386 #if defined(POLARSSL_ECP_DP_SECP256K1_ENABLED) 00387 static const t_uint secp256k1_p[] = { 00388 BYTES_TO_T_UINT_8( 0x2F, 0xFC, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ), 00389 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00390 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00391 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00392 }; 00393 static const t_uint secp256k1_a[] = { 00394 BYTES_TO_T_UINT_2( 0x00, 0x00 ), 00395 }; 00396 static const t_uint secp256k1_b[] = { 00397 BYTES_TO_T_UINT_2( 0x07, 0x00 ), 00398 }; 00399 static const t_uint secp256k1_gx[] = { 00400 BYTES_TO_T_UINT_8( 0x98, 0x17, 0xF8, 0x16, 0x5B, 0x81, 0xF2, 0x59 ), 00401 BYTES_TO_T_UINT_8( 0xD9, 0x28, 0xCE, 0x2D, 0xDB, 0xFC, 0x9B, 0x02 ), 00402 BYTES_TO_T_UINT_8( 0x07, 0x0B, 0x87, 0xCE, 0x95, 0x62, 0xA0, 0x55 ), 00403 BYTES_TO_T_UINT_8( 0xAC, 0xBB, 0xDC, 0xF9, 0x7E, 0x66, 0xBE, 0x79 ), 00404 }; 00405 static const t_uint secp256k1_gy[] = { 00406 BYTES_TO_T_UINT_8( 0xB8, 0xD4, 0x10, 0xFB, 0x8F, 0xD0, 0x47, 0x9C ), 00407 BYTES_TO_T_UINT_8( 0x19, 0x54, 0x85, 0xA6, 0x48, 0xB4, 0x17, 0xFD ), 00408 BYTES_TO_T_UINT_8( 0xA8, 0x08, 0x11, 0x0E, 0xFC, 0xFB, 0xA4, 0x5D ), 00409 BYTES_TO_T_UINT_8( 0x65, 0xC4, 0xA3, 0x26, 0x77, 0xDA, 0x3A, 0x48 ), 00410 }; 00411 static const t_uint secp256k1_n[] = { 00412 BYTES_TO_T_UINT_8( 0x41, 0x41, 0x36, 0xD0, 0x8C, 0x5E, 0xD2, 0xBF ), 00413 BYTES_TO_T_UINT_8( 0x3B, 0xA0, 0x48, 0xAF, 0xE6, 0xDC, 0xAE, 0xBA ), 00414 BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00415 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), 00416 }; 00417 #endif /* POLARSSL_ECP_DP_SECP256K1_ENABLED */ 00418 00419 /* 00420 * Domain parameters for brainpoolP256r1 (RFC 5639 3.4) 00421 */ 00422 #if defined(POLARSSL_ECP_DP_BP256R1_ENABLED) 00423 static const t_uint brainpoolP256r1_p[] = { 00424 BYTES_TO_T_UINT_8( 0x77, 0x53, 0x6E, 0x1F, 0x1D, 0x48, 0x13, 0x20 ), 00425 BYTES_TO_T_UINT_8( 0x28, 0x20, 0x26, 0xD5, 0x23, 0xF6, 0x3B, 0x6E ), 00426 BYTES_TO_T_UINT_8( 0x72, 0x8D, 0x83, 0x9D, 0x90, 0x0A, 0x66, 0x3E ), 00427 BYTES_TO_T_UINT_8( 0xBC, 0xA9, 0xEE, 0xA1, 0xDB, 0x57, 0xFB, 0xA9 ), 00428 }; 00429 static const t_uint brainpoolP256r1_a[] = { 00430 BYTES_TO_T_UINT_8( 0xD9, 0xB5, 0x30, 0xF3, 0x44, 0x4B, 0x4A, 0xE9 ), 00431 BYTES_TO_T_UINT_8( 0x6C, 0x5C, 0xDC, 0x26, 0xC1, 0x55, 0x80, 0xFB ), 00432 BYTES_TO_T_UINT_8( 0xE7, 0xFF, 0x7A, 0x41, 0x30, 0x75, 0xF6, 0xEE ), 00433 BYTES_TO_T_UINT_8( 0x57, 0x30, 0x2C, 0xFC, 0x75, 0x09, 0x5A, 0x7D ), 00434 }; 00435 static const t_uint brainpoolP256r1_b[] = { 00436 BYTES_TO_T_UINT_8( 0xB6, 0x07, 0x8C, 0xFF, 0x18, 0xDC, 0xCC, 0x6B ), 00437 BYTES_TO_T_UINT_8( 0xCE, 0xE1, 0xF7, 0x5C, 0x29, 0x16, 0x84, 0x95 ), 00438 BYTES_TO_T_UINT_8( 0xBF, 0x7C, 0xD7, 0xBB, 0xD9, 0xB5, 0x30, 0xF3 ), 00439 BYTES_TO_T_UINT_8( 0x44, 0x4B, 0x4A, 0xE9, 0x6C, 0x5C, 0xDC, 0x26 ), 00440 }; 00441 static const t_uint brainpoolP256r1_gx[] = { 00442 BYTES_TO_T_UINT_8( 0x62, 0x32, 0xCE, 0x9A, 0xBD, 0x53, 0x44, 0x3A ), 00443 BYTES_TO_T_UINT_8( 0xC2, 0x23, 0xBD, 0xE3, 0xE1, 0x27, 0xDE, 0xB9 ), 00444 BYTES_TO_T_UINT_8( 0xAF, 0xB7, 0x81, 0xFC, 0x2F, 0x48, 0x4B, 0x2C ), 00445 BYTES_TO_T_UINT_8( 0xCB, 0x57, 0x7E, 0xCB, 0xB9, 0xAE, 0xD2, 0x8B ), 00446 }; 00447 static const t_uint brainpoolP256r1_gy[] = { 00448 BYTES_TO_T_UINT_8( 0x97, 0x69, 0x04, 0x2F, 0xC7, 0x54, 0x1D, 0x5C ), 00449 BYTES_TO_T_UINT_8( 0x54, 0x8E, 0xED, 0x2D, 0x13, 0x45, 0x77, 0xC2 ), 00450 BYTES_TO_T_UINT_8( 0xC9, 0x1D, 0x61, 0x14, 0x1A, 0x46, 0xF8, 0x97 ), 00451 BYTES_TO_T_UINT_8( 0xFD, 0xC4, 0xDA, 0xC3, 0x35, 0xF8, 0x7E, 0x54 ), 00452 }; 00453 static const t_uint brainpoolP256r1_n[] = { 00454 BYTES_TO_T_UINT_8( 0xA7, 0x56, 0x48, 0x97, 0x82, 0x0E, 0x1E, 0x90 ), 00455 BYTES_TO_T_UINT_8( 0xF7, 0xA6, 0x61, 0xB5, 0xA3, 0x7A, 0x39, 0x8C ), 00456 BYTES_TO_T_UINT_8( 0x71, 0x8D, 0x83, 0x9D, 0x90, 0x0A, 0x66, 0x3E ), 00457 BYTES_TO_T_UINT_8( 0xBC, 0xA9, 0xEE, 0xA1, 0xDB, 0x57, 0xFB, 0xA9 ), 00458 }; 00459 #endif /* POLARSSL_ECP_DP_BP256R1_ENABLED */ 00460 00461 /* 00462 * Domain parameters for brainpoolP384r1 (RFC 5639 3.6) 00463 */ 00464 #if defined(POLARSSL_ECP_DP_BP384R1_ENABLED) 00465 static const t_uint brainpoolP384r1_p[] = { 00466 BYTES_TO_T_UINT_8( 0x53, 0xEC, 0x07, 0x31, 0x13, 0x00, 0x47, 0x87 ), 00467 BYTES_TO_T_UINT_8( 0x71, 0x1A, 0x1D, 0x90, 0x29, 0xA7, 0xD3, 0xAC ), 00468 BYTES_TO_T_UINT_8( 0x23, 0x11, 0xB7, 0x7F, 0x19, 0xDA, 0xB1, 0x12 ), 00469 BYTES_TO_T_UINT_8( 0xB4, 0x56, 0x54, 0xED, 0x09, 0x71, 0x2F, 0x15 ), 00470 BYTES_TO_T_UINT_8( 0xDF, 0x41, 0xE6, 0x50, 0x7E, 0x6F, 0x5D, 0x0F ), 00471 BYTES_TO_T_UINT_8( 0x28, 0x6D, 0x38, 0xA3, 0x82, 0x1E, 0xB9, 0x8C ), 00472 }; 00473 static const t_uint brainpoolP384r1_a[] = { 00474 BYTES_TO_T_UINT_8( 0x26, 0x28, 0xCE, 0x22, 0xDD, 0xC7, 0xA8, 0x04 ), 00475 BYTES_TO_T_UINT_8( 0xEB, 0xD4, 0x3A, 0x50, 0x4A, 0x81, 0xA5, 0x8A ), 00476 BYTES_TO_T_UINT_8( 0x0F, 0xF9, 0x91, 0xBA, 0xEF, 0x65, 0x91, 0x13 ), 00477 BYTES_TO_T_UINT_8( 0x87, 0x27, 0xB2, 0x4F, 0x8E, 0xA2, 0xBE, 0xC2 ), 00478 BYTES_TO_T_UINT_8( 0xA0, 0xAF, 0x05, 0xCE, 0x0A, 0x08, 0x72, 0x3C ), 00479 BYTES_TO_T_UINT_8( 0x0C, 0x15, 0x8C, 0x3D, 0xC6, 0x82, 0xC3, 0x7B ), 00480 }; 00481 static const t_uint brainpoolP384r1_b[] = { 00482 BYTES_TO_T_UINT_8( 0x11, 0x4C, 0x50, 0xFA, 0x96, 0x86, 0xB7, 0x3A ), 00483 BYTES_TO_T_UINT_8( 0x94, 0xC9, 0xDB, 0x95, 0x02, 0x39, 0xB4, 0x7C ), 00484 BYTES_TO_T_UINT_8( 0xD5, 0x62, 0xEB, 0x3E, 0xA5, 0x0E, 0x88, 0x2E ), 00485 BYTES_TO_T_UINT_8( 0xA6, 0xD2, 0xDC, 0x07, 0xE1, 0x7D, 0xB7, 0x2F ), 00486 BYTES_TO_T_UINT_8( 0x7C, 0x44, 0xF0, 0x16, 0x54, 0xB5, 0x39, 0x8B ), 00487 BYTES_TO_T_UINT_8( 0x26, 0x28, 0xCE, 0x22, 0xDD, 0xC7, 0xA8, 0x04 ), 00488 }; 00489 static const t_uint brainpoolP384r1_gx[] = { 00490 BYTES_TO_T_UINT_8( 0x1E, 0xAF, 0xD4, 0x47, 0xE2, 0xB2, 0x87, 0xEF ), 00491 BYTES_TO_T_UINT_8( 0xAA, 0x46, 0xD6, 0x36, 0x34, 0xE0, 0x26, 0xE8 ), 00492 BYTES_TO_T_UINT_8( 0xE8, 0x10, 0xBD, 0x0C, 0xFE, 0xCA, 0x7F, 0xDB ), 00493 BYTES_TO_T_UINT_8( 0xE3, 0x4F, 0xF1, 0x7E, 0xE7, 0xA3, 0x47, 0x88 ), 00494 BYTES_TO_T_UINT_8( 0x6B, 0x3F, 0xC1, 0xB7, 0x81, 0x3A, 0xA6, 0xA2 ), 00495 BYTES_TO_T_UINT_8( 0xFF, 0x45, 0xCF, 0x68, 0xF0, 0x64, 0x1C, 0x1D ), 00496 }; 00497 static const t_uint brainpoolP384r1_gy[] = { 00498 BYTES_TO_T_UINT_8( 0x15, 0x53, 0x3C, 0x26, 0x41, 0x03, 0x82, 0x42 ), 00499 BYTES_TO_T_UINT_8( 0x11, 0x81, 0x91, 0x77, 0x21, 0x46, 0x46, 0x0E ), 00500 BYTES_TO_T_UINT_8( 0x28, 0x29, 0x91, 0xF9, 0x4F, 0x05, 0x9C, 0xE1 ), 00501 BYTES_TO_T_UINT_8( 0x64, 0x58, 0xEC, 0xFE, 0x29, 0x0B, 0xB7, 0x62 ), 00502 BYTES_TO_T_UINT_8( 0x52, 0xD5, 0xCF, 0x95, 0x8E, 0xEB, 0xB1, 0x5C ), 00503 BYTES_TO_T_UINT_8( 0xA4, 0xC2, 0xF9, 0x20, 0x75, 0x1D, 0xBE, 0x8A ), 00504 }; 00505 static const t_uint brainpoolP384r1_n[] = { 00506 BYTES_TO_T_UINT_8( 0x65, 0x65, 0x04, 0xE9, 0x02, 0x32, 0x88, 0x3B ), 00507 BYTES_TO_T_UINT_8( 0x10, 0xC3, 0x7F, 0x6B, 0xAF, 0xB6, 0x3A, 0xCF ), 00508 BYTES_TO_T_UINT_8( 0xA7, 0x25, 0x04, 0xAC, 0x6C, 0x6E, 0x16, 0x1F ), 00509 BYTES_TO_T_UINT_8( 0xB3, 0x56, 0x54, 0xED, 0x09, 0x71, 0x2F, 0x15 ), 00510 BYTES_TO_T_UINT_8( 0xDF, 0x41, 0xE6, 0x50, 0x7E, 0x6F, 0x5D, 0x0F ), 00511 BYTES_TO_T_UINT_8( 0x28, 0x6D, 0x38, 0xA3, 0x82, 0x1E, 0xB9, 0x8C ), 00512 }; 00513 #endif /* POLARSSL_ECP_DP_BP384R1_ENABLED */ 00514 00515 /* 00516 * Domain parameters for brainpoolP512r1 (RFC 5639 3.7) 00517 */ 00518 #if defined(POLARSSL_ECP_DP_BP512R1_ENABLED) 00519 static const t_uint brainpoolP512r1_p[] = { 00520 BYTES_TO_T_UINT_8( 0xF3, 0x48, 0x3A, 0x58, 0x56, 0x60, 0xAA, 0x28 ), 00521 BYTES_TO_T_UINT_8( 0x85, 0xC6, 0x82, 0x2D, 0x2F, 0xFF, 0x81, 0x28 ), 00522 BYTES_TO_T_UINT_8( 0xE6, 0x80, 0xA3, 0xE6, 0x2A, 0xA1, 0xCD, 0xAE ), 00523 BYTES_TO_T_UINT_8( 0x42, 0x68, 0xC6, 0x9B, 0x00, 0x9B, 0x4D, 0x7D ), 00524 BYTES_TO_T_UINT_8( 0x71, 0x08, 0x33, 0x70, 0xCA, 0x9C, 0x63, 0xD6 ), 00525 BYTES_TO_T_UINT_8( 0x0E, 0xD2, 0xC9, 0xB3, 0xB3, 0x8D, 0x30, 0xCB ), 00526 BYTES_TO_T_UINT_8( 0x07, 0xFC, 0xC9, 0x33, 0xAE, 0xE6, 0xD4, 0x3F ), 00527 BYTES_TO_T_UINT_8( 0x8B, 0xC4, 0xE9, 0xDB, 0xB8, 0x9D, 0xDD, 0xAA ), 00528 }; 00529 static const t_uint brainpoolP512r1_a[] = { 00530 BYTES_TO_T_UINT_8( 0xCA, 0x94, 0xFC, 0x77, 0x4D, 0xAC, 0xC1, 0xE7 ), 00531 BYTES_TO_T_UINT_8( 0xB9, 0xC7, 0xF2, 0x2B, 0xA7, 0x17, 0x11, 0x7F ), 00532 BYTES_TO_T_UINT_8( 0xB5, 0xC8, 0x9A, 0x8B, 0xC9, 0xF1, 0x2E, 0x0A ), 00533 BYTES_TO_T_UINT_8( 0xA1, 0x3A, 0x25, 0xA8, 0x5A, 0x5D, 0xED, 0x2D ), 00534 BYTES_TO_T_UINT_8( 0xBC, 0x63, 0x98, 0xEA, 0xCA, 0x41, 0x34, 0xA8 ), 00535 BYTES_TO_T_UINT_8( 0x10, 0x16, 0xF9, 0x3D, 0x8D, 0xDD, 0xCB, 0x94 ), 00536 BYTES_TO_T_UINT_8( 0xC5, 0x4C, 0x23, 0xAC, 0x45, 0x71, 0x32, 0xE2 ), 00537 BYTES_TO_T_UINT_8( 0x89, 0x3B, 0x60, 0x8B, 0x31, 0xA3, 0x30, 0x78 ), 00538 }; 00539 static const t_uint brainpoolP512r1_b[] = { 00540 BYTES_TO_T_UINT_8( 0x23, 0xF7, 0x16, 0x80, 0x63, 0xBD, 0x09, 0x28 ), 00541 BYTES_TO_T_UINT_8( 0xDD, 0xE5, 0xBA, 0x5E, 0xB7, 0x50, 0x40, 0x98 ), 00542 BYTES_TO_T_UINT_8( 0x67, 0x3E, 0x08, 0xDC, 0xCA, 0x94, 0xFC, 0x77 ), 00543 BYTES_TO_T_UINT_8( 0x4D, 0xAC, 0xC1, 0xE7, 0xB9, 0xC7, 0xF2, 0x2B ), 00544 BYTES_TO_T_UINT_8( 0xA7, 0x17, 0x11, 0x7F, 0xB5, 0xC8, 0x9A, 0x8B ), 00545 BYTES_TO_T_UINT_8( 0xC9, 0xF1, 0x2E, 0x0A, 0xA1, 0x3A, 0x25, 0xA8 ), 00546 BYTES_TO_T_UINT_8( 0x5A, 0x5D, 0xED, 0x2D, 0xBC, 0x63, 0x98, 0xEA ), 00547 BYTES_TO_T_UINT_8( 0xCA, 0x41, 0x34, 0xA8, 0x10, 0x16, 0xF9, 0x3D ), 00548 }; 00549 static const t_uint brainpoolP512r1_gx[] = { 00550 BYTES_TO_T_UINT_8( 0x22, 0xF8, 0xB9, 0xBC, 0x09, 0x22, 0x35, 0x8B ), 00551 BYTES_TO_T_UINT_8( 0x68, 0x5E, 0x6A, 0x40, 0x47, 0x50, 0x6D, 0x7C ), 00552 BYTES_TO_T_UINT_8( 0x5F, 0x7D, 0xB9, 0x93, 0x7B, 0x68, 0xD1, 0x50 ), 00553 BYTES_TO_T_UINT_8( 0x8D, 0xD4, 0xD0, 0xE2, 0x78, 0x1F, 0x3B, 0xFF ), 00554 BYTES_TO_T_UINT_8( 0x8E, 0x09, 0xD0, 0xF4, 0xEE, 0x62, 0x3B, 0xB4 ), 00555 BYTES_TO_T_UINT_8( 0xC1, 0x16, 0xD9, 0xB5, 0x70, 0x9F, 0xED, 0x85 ), 00556 BYTES_TO_T_UINT_8( 0x93, 0x6A, 0x4C, 0x9C, 0x2E, 0x32, 0x21, 0x5A ), 00557 BYTES_TO_T_UINT_8( 0x64, 0xD9, 0x2E, 0xD8, 0xBD, 0xE4, 0xAE, 0x81 ), 00558 }; 00559 static const t_uint brainpoolP512r1_gy[] = { 00560 BYTES_TO_T_UINT_8( 0x92, 0x08, 0xD8, 0x3A, 0x0F, 0x1E, 0xCD, 0x78 ), 00561 BYTES_TO_T_UINT_8( 0x06, 0x54, 0xF0, 0xA8, 0x2F, 0x2B, 0xCA, 0xD1 ), 00562 BYTES_TO_T_UINT_8( 0xAE, 0x63, 0x27, 0x8A, 0xD8, 0x4B, 0xCA, 0x5B ), 00563 BYTES_TO_T_UINT_8( 0x5E, 0x48, 0x5F, 0x4A, 0x49, 0xDE, 0xDC, 0xB2 ), 00564 BYTES_TO_T_UINT_8( 0x11, 0x81, 0x1F, 0x88, 0x5B, 0xC5, 0x00, 0xA0 ), 00565 BYTES_TO_T_UINT_8( 0x1A, 0x7B, 0xA5, 0x24, 0x00, 0xF7, 0x09, 0xF2 ), 00566 BYTES_TO_T_UINT_8( 0xFD, 0x22, 0x78, 0xCF, 0xA9, 0xBF, 0xEA, 0xC0 ), 00567 BYTES_TO_T_UINT_8( 0xEC, 0x32, 0x63, 0x56, 0x5D, 0x38, 0xDE, 0x7D ), 00568 }; 00569 static const t_uint brainpoolP512r1_n[] = { 00570 BYTES_TO_T_UINT_8( 0x69, 0x00, 0xA9, 0x9C, 0x82, 0x96, 0x87, 0xB5 ), 00571 BYTES_TO_T_UINT_8( 0xDD, 0xDA, 0x5D, 0x08, 0x81, 0xD3, 0xB1, 0x1D ), 00572 BYTES_TO_T_UINT_8( 0x47, 0x10, 0xAC, 0x7F, 0x19, 0x61, 0x86, 0x41 ), 00573 BYTES_TO_T_UINT_8( 0x19, 0x26, 0xA9, 0x4C, 0x41, 0x5C, 0x3E, 0x55 ), 00574 BYTES_TO_T_UINT_8( 0x70, 0x08, 0x33, 0x70, 0xCA, 0x9C, 0x63, 0xD6 ), 00575 BYTES_TO_T_UINT_8( 0x0E, 0xD2, 0xC9, 0xB3, 0xB3, 0x8D, 0x30, 0xCB ), 00576 BYTES_TO_T_UINT_8( 0x07, 0xFC, 0xC9, 0x33, 0xAE, 0xE6, 0xD4, 0x3F ), 00577 BYTES_TO_T_UINT_8( 0x8B, 0xC4, 0xE9, 0xDB, 0xB8, 0x9D, 0xDD, 0xAA ), 00578 }; 00579 #endif /* POLARSSL_ECP_DP_BP512R1_ENABLED */ 00580 00581 /* 00582 * Create an MPI from embedded constants 00583 * (assumes len is an exact multiple of sizeof t_uint) 00584 */ 00585 static inline void ecp_mpi_load( mpi *X, const t_uint *p, size_t len ) 00586 { 00587 X->s = 1; 00588 X->n = len / sizeof( t_uint ); 00589 X->p = (t_uint *) p; 00590 } 00591 00592 /* 00593 * Set an MPI to static value 1 00594 */ 00595 static inline void ecp_mpi_set1( mpi *X ) 00596 { 00597 static t_uint one[] = { 1 }; 00598 X->s = 1; 00599 X->n = 1; 00600 X->p = one; 00601 } 00602 00603 /* 00604 * Make group available from embedded constants 00605 */ 00606 static int ecp_group_load( ecp_group *grp, 00607 const t_uint *p, size_t plen, 00608 const t_uint *a, size_t alen, 00609 const t_uint *b, size_t blen, 00610 const t_uint *gx, size_t gxlen, 00611 const t_uint *gy, size_t gylen, 00612 const t_uint *n, size_t nlen) 00613 { 00614 ecp_mpi_load( &grp->P , p, plen ); 00615 if( a != NULL ) 00616 ecp_mpi_load( &grp->A , a, alen ); 00617 ecp_mpi_load( &grp->B , b, blen ); 00618 ecp_mpi_load( &grp->N , n, nlen ); 00619 00620 ecp_mpi_load( &grp->G .X , gx, gxlen ); 00621 ecp_mpi_load( &grp->G .Y , gy, gylen ); 00622 ecp_mpi_set1( &grp->G .Z ); 00623 00624 grp->pbits = mpi_msb( &grp->P ); 00625 grp->nbits = mpi_msb( &grp->N ); 00626 00627 grp->h = 1; 00628 00629 return( 0 ); 00630 } 00631 00632 #if defined(POLARSSL_ECP_NIST_OPTIM) 00633 /* Forward declarations */ 00634 #if defined(POLARSSL_ECP_DP_SECP192R1_ENABLED) 00635 static int ecp_mod_p192( mpi * ); 00636 #endif 00637 #if defined(POLARSSL_ECP_DP_SECP224R1_ENABLED) 00638 static int ecp_mod_p224( mpi * ); 00639 #endif 00640 #if defined(POLARSSL_ECP_DP_SECP256R1_ENABLED) 00641 static int ecp_mod_p256( mpi * ); 00642 #endif 00643 #if defined(POLARSSL_ECP_DP_SECP384R1_ENABLED) 00644 static int ecp_mod_p384( mpi * ); 00645 #endif 00646 #if defined(POLARSSL_ECP_DP_SECP521R1_ENABLED) 00647 static int ecp_mod_p521( mpi * ); 00648 #endif 00649 00650 #define NIST_MODP( P ) grp->modp = ecp_mod_ ## P; 00651 #else 00652 #define NIST_MODP( P ) 00653 #endif /* POLARSSL_ECP_NIST_OPTIM */ 00654 00655 /* Additional forward declarations */ 00656 #if defined(POLARSSL_ECP_DP_M255_ENABLED) 00657 static int ecp_mod_p255( mpi * ); 00658 #endif 00659 #if defined(POLARSSL_ECP_DP_SECP192K1_ENABLED) 00660 static int ecp_mod_p192k1( mpi * ); 00661 #endif 00662 #if defined(POLARSSL_ECP_DP_SECP224K1_ENABLED) 00663 static int ecp_mod_p224k1( mpi * ); 00664 #endif 00665 #if defined(POLARSSL_ECP_DP_SECP256K1_ENABLED) 00666 static int ecp_mod_p256k1( mpi * ); 00667 #endif 00668 00669 #define LOAD_GROUP_A( G ) ecp_group_load( grp, \ 00670 G ## _p, sizeof( G ## _p ), \ 00671 G ## _a, sizeof( G ## _a ), \ 00672 G ## _b, sizeof( G ## _b ), \ 00673 G ## _gx, sizeof( G ## _gx ), \ 00674 G ## _gy, sizeof( G ## _gy ), \ 00675 G ## _n, sizeof( G ## _n ) ) 00676 00677 #define LOAD_GROUP( G ) ecp_group_load( grp, \ 00678 G ## _p, sizeof( G ## _p ), \ 00679 NULL, 0, \ 00680 G ## _b, sizeof( G ## _b ), \ 00681 G ## _gx, sizeof( G ## _gx ), \ 00682 G ## _gy, sizeof( G ## _gy ), \ 00683 G ## _n, sizeof( G ## _n ) ) 00684 00685 #if defined(POLARSSL_ECP_DP_M255_ENABLED) 00686 /* 00687 * Specialized function for creating the Curve25519 group 00688 */ 00689 static int ecp_use_curve25519( ecp_group *grp ) 00690 { 00691 int ret; 00692 00693 /* Actually ( A + 2 ) / 4 */ 00694 MPI_CHK( mpi_read_string( &grp->A , 16, "01DB42" ) ); 00695 00696 /* P = 2^255 - 19 */ 00697 MPI_CHK( mpi_lset( &grp->P , 1 ) ); 00698 MPI_CHK( mpi_shift_l( &grp->P , 255 ) ); 00699 MPI_CHK( mpi_sub_int( &grp->P , &grp->P , 19 ) ); 00700 grp->pbits = mpi_msb( &grp->P ); 00701 00702 /* Y intentionaly not set, since we use x/z coordinates. 00703 * This is used as a marker to identify Montgomery curves! */ 00704 MPI_CHK( mpi_lset( &grp->G .X , 9 ) ); 00705 MPI_CHK( mpi_lset( &grp->G .Z , 1 ) ); 00706 mpi_free( &grp->G .Y ); 00707 00708 /* Actually, the required msb for private keys */ 00709 grp->nbits = 254; 00710 00711 cleanup: 00712 if( ret != 0 ) 00713 ecp_group_free( grp ); 00714 00715 return( ret ); 00716 } 00717 #endif /* POLARSSL_ECP_DP_M255_ENABLED */ 00718 00719 /* 00720 * Set a group using well-known domain parameters 00721 */ 00722 int ecp_use_known_dp( ecp_group *grp, ecp_group_id id ) 00723 { 00724 ecp_group_free( grp ); 00725 00726 grp->id = id; 00727 00728 switch( id ) 00729 { 00730 #if defined(POLARSSL_ECP_DP_SECP192R1_ENABLED) 00731 case POLARSSL_ECP_DP_SECP192R1 : 00732 NIST_MODP( p192 ); 00733 return( LOAD_GROUP( secp192r1 ) ); 00734 #endif /* POLARSSL_ECP_DP_SECP192R1_ENABLED */ 00735 00736 #if defined(POLARSSL_ECP_DP_SECP224R1_ENABLED) 00737 case POLARSSL_ECP_DP_SECP224R1 : 00738 NIST_MODP( p224 ); 00739 return( LOAD_GROUP( secp224r1 ) ); 00740 #endif /* POLARSSL_ECP_DP_SECP224R1_ENABLED */ 00741 00742 #if defined(POLARSSL_ECP_DP_SECP256R1_ENABLED) 00743 case POLARSSL_ECP_DP_SECP256R1 : 00744 NIST_MODP( p256 ); 00745 return( LOAD_GROUP( secp256r1 ) ); 00746 #endif /* POLARSSL_ECP_DP_SECP256R1_ENABLED */ 00747 00748 #if defined(POLARSSL_ECP_DP_SECP384R1_ENABLED) 00749 case POLARSSL_ECP_DP_SECP384R1 : 00750 NIST_MODP( p384 ); 00751 return( LOAD_GROUP( secp384r1 ) ); 00752 #endif /* POLARSSL_ECP_DP_SECP384R1_ENABLED */ 00753 00754 #if defined(POLARSSL_ECP_DP_SECP521R1_ENABLED) 00755 case POLARSSL_ECP_DP_SECP521R1 : 00756 NIST_MODP( p521 ); 00757 return( LOAD_GROUP( secp521r1 ) ); 00758 #endif /* POLARSSL_ECP_DP_SECP521R1_ENABLED */ 00759 00760 #if defined(POLARSSL_ECP_DP_SECP192K1_ENABLED) 00761 case POLARSSL_ECP_DP_SECP192K1 : 00762 grp->modp = ecp_mod_p192k1; 00763 return( LOAD_GROUP_A( secp192k1 ) ); 00764 #endif /* POLARSSL_ECP_DP_SECP192K1_ENABLED */ 00765 00766 #if defined(POLARSSL_ECP_DP_SECP224K1_ENABLED) 00767 case POLARSSL_ECP_DP_SECP224K1 : 00768 grp->modp = ecp_mod_p224k1; 00769 return( LOAD_GROUP_A( secp224k1 ) ); 00770 #endif /* POLARSSL_ECP_DP_SECP224K1_ENABLED */ 00771 00772 #if defined(POLARSSL_ECP_DP_SECP256K1_ENABLED) 00773 case POLARSSL_ECP_DP_SECP256K1 : 00774 grp->modp = ecp_mod_p256k1; 00775 return( LOAD_GROUP_A( secp256k1 ) ); 00776 #endif /* POLARSSL_ECP_DP_SECP256K1_ENABLED */ 00777 00778 #if defined(POLARSSL_ECP_DP_BP256R1_ENABLED) 00779 case POLARSSL_ECP_DP_BP256R1 : 00780 return( LOAD_GROUP_A( brainpoolP256r1 ) ); 00781 #endif /* POLARSSL_ECP_DP_BP256R1_ENABLED */ 00782 00783 #if defined(POLARSSL_ECP_DP_BP384R1_ENABLED) 00784 case POLARSSL_ECP_DP_BP384R1 : 00785 return( LOAD_GROUP_A( brainpoolP384r1 ) ); 00786 #endif /* POLARSSL_ECP_DP_BP384R1_ENABLED */ 00787 00788 #if defined(POLARSSL_ECP_DP_BP512R1_ENABLED) 00789 case POLARSSL_ECP_DP_BP512R1 : 00790 return( LOAD_GROUP_A( brainpoolP512r1 ) ); 00791 #endif /* POLARSSL_ECP_DP_BP512R1_ENABLED */ 00792 00793 #if defined(POLARSSL_ECP_DP_M255_ENABLED) 00794 case POLARSSL_ECP_DP_M255 : 00795 grp->modp = ecp_mod_p255; 00796 return( ecp_use_curve25519( grp ) ); 00797 #endif /* POLARSSL_ECP_DP_M255_ENABLED */ 00798 00799 default: 00800 ecp_group_free( grp ); 00801 return( POLARSSL_ERR_ECP_FEATURE_UNAVAILABLE ); 00802 } 00803 } 00804 00805 #if defined(POLARSSL_ECP_NIST_OPTIM) 00806 /* 00807 * Fast reduction modulo the primes used by the NIST curves. 00808 * 00809 * These functions are critical for speed, but not needed for correct 00810 * operations. So, we make the choice to heavily rely on the internals of our 00811 * bignum library, which creates a tight coupling between these functions and 00812 * our MPI implementation. However, the coupling between the ECP module and 00813 * MPI remains loose, since these functions can be deactivated at will. 00814 */ 00815 00816 #if defined(POLARSSL_ECP_DP_SECP192R1_ENABLED) 00817 /* 00818 * Compared to the way things are presented in FIPS 186-3 D.2, 00819 * we proceed in columns, from right (least significant chunk) to left, 00820 * adding chunks to N in place, and keeping a carry for the next chunk. 00821 * This avoids moving things around in memory, and uselessly adding zeros, 00822 * compared to the more straightforward, line-oriented approach. 00823 * 00824 * For this prime we need to handle data in chunks of 64 bits. 00825 * Since this is always a multiple of our basic t_uint, we can 00826 * use a t_uint * to designate such a chunk, and small loops to handle it. 00827 */ 00828 00829 /* Add 64-bit chunks (dst += src) and update carry */ 00830 static inline void add64( t_uint *dst, t_uint *src, t_uint *carry ) 00831 { 00832 unsigned char i; 00833 t_uint c = 0; 00834 for( i = 0; i < 8 / sizeof( t_uint ); i++, dst++, src++ ) 00835 { 00836 *dst += c; c = ( *dst < c ); 00837 *dst += *src; c += ( *dst < *src ); 00838 } 00839 *carry += c; 00840 } 00841 00842 /* Add carry to a 64-bit chunk and update carry */ 00843 static inline void carry64( t_uint *dst, t_uint *carry ) 00844 { 00845 unsigned char i; 00846 for( i = 0; i < 8 / sizeof( t_uint ); i++, dst++ ) 00847 { 00848 *dst += *carry; 00849 *carry = ( *dst < *carry ); 00850 } 00851 } 00852 00853 #define WIDTH 8 / sizeof( t_uint ) 00854 #define A( i ) N->p + i * WIDTH 00855 #define ADD( i ) add64( p, A( i ), &c ) 00856 #define NEXT p += WIDTH; carry64( p, &c ) 00857 #define LAST p += WIDTH; *p = c; while( ++p < end ) *p = 0 00858 00859 /* 00860 * Fast quasi-reduction modulo p192 (FIPS 186-3 D.2.1) 00861 */ 00862 static int ecp_mod_p192( mpi *N ) 00863 { 00864 int ret; 00865 t_uint c = 0; 00866 t_uint *p, *end; 00867 00868 /* Make sure we have enough blocks so that A(5) is legal */ 00869 MPI_CHK( mpi_grow( N, 6 * WIDTH ) ); 00870 00871 p = N->p ; 00872 end = p + N->n ; 00873 00874 ADD( 3 ); ADD( 5 ); NEXT; // A0 += A3 + A5 00875 ADD( 3 ); ADD( 4 ); ADD( 5 ); NEXT; // A1 += A3 + A4 + A5 00876 ADD( 4 ); ADD( 5 ); LAST; // A2 += A4 + A5 00877 00878 cleanup: 00879 return( ret ); 00880 } 00881 00882 #undef WIDTH 00883 #undef A 00884 #undef ADD 00885 #undef NEXT 00886 #undef LAST 00887 #endif /* POLARSSL_ECP_DP_SECP192R1_ENABLED */ 00888 00889 #if defined(POLARSSL_ECP_DP_SECP224R1_ENABLED) || \ 00890 defined(POLARSSL_ECP_DP_SECP256R1_ENABLED) || \ 00891 defined(POLARSSL_ECP_DP_SECP384R1_ENABLED) 00892 /* 00893 * The reader is advised to first understand ecp_mod_p192() since the same 00894 * general structure is used here, but with additional complications: 00895 * (1) chunks of 32 bits, and (2) subtractions. 00896 */ 00897 00898 /* 00899 * For these primes, we need to handle data in chunks of 32 bits. 00900 * This makes it more complicated if we use 64 bits limbs in MPI, 00901 * which prevents us from using a uniform access method as for p192. 00902 * 00903 * So, we define a mini abstraction layer to access 32 bit chunks, 00904 * load them in 'cur' for work, and store them back from 'cur' when done. 00905 * 00906 * While at it, also define the size of N in terms of 32-bit chunks. 00907 */ 00908 #define LOAD32 cur = A( i ); 00909 00910 #if defined(POLARSSL_HAVE_INT8) /* 8 bit */ 00911 00912 #define MAX32 N->n / 4 00913 #define A( j ) (uint32_t)( N->p[4*j+0] ) | \ 00914 ( N->p[4*j+1] << 8 ) | \ 00915 ( N->p[4*j+2] << 16 ) | \ 00916 ( N->p[4*j+3] << 24 ) 00917 #define STORE32 N->p[4*i+0] = (t_uint)( cur ); \ 00918 N->p[4*i+1] = (t_uint)( cur >> 8 ); \ 00919 N->p[4*i+2] = (t_uint)( cur >> 16 ); \ 00920 N->p[4*i+3] = (t_uint)( cur >> 24 ); 00921 00922 #elif defined(POLARSSL_HAVE_INT16) /* 16 bit */ 00923 00924 #define MAX32 N->n / 2 00925 #define A( j ) (uint32_t)( N->p[2*j] ) | ( N->p[2*j+1] << 16 ) 00926 #define STORE32 N->p[2*i+0] = (t_uint)( cur ); \ 00927 N->p[2*i+1] = (t_uint)( cur >> 16 ); 00928 00929 #elif defined(POLARSSL_HAVE_INT32) /* 32 bit */ 00930 00931 #define MAX32 N->n 00932 #define A( j ) N->p[j] 00933 #define STORE32 N->p[i] = cur; 00934 00935 #else /* 64-bit */ 00936 00937 #define MAX32 N->n * 2 00938 #define A( j ) j % 2 ? (uint32_t)( N->p[j/2] >> 32 ) : (uint32_t)( N->p[j/2] ) 00939 #define STORE32 \ 00940 if( i % 2 ) { \ 00941 N->p[i/2] &= 0x00000000FFFFFFFF; \ 00942 N->p[i/2] |= ((t_uint) cur) << 32; \ 00943 } else { \ 00944 N->p[i/2] &= 0xFFFFFFFF00000000; \ 00945 N->p[i/2] |= (t_uint) cur; \ 00946 } 00947 00948 #endif /* sizeof( t_uint ) */ 00949 00950 /* 00951 * Helpers for addition and subtraction of chunks, with signed carry. 00952 */ 00953 static inline void add32( uint32_t *dst, uint32_t src, signed char *carry ) 00954 { 00955 *dst += src; 00956 *carry += ( *dst < src ); 00957 } 00958 00959 static inline void sub32( uint32_t *dst, uint32_t src, signed char *carry ) 00960 { 00961 *carry -= ( *dst < src ); 00962 *dst -= src; 00963 } 00964 00965 #define ADD( j ) add32( &cur, A( j ), &c ); 00966 #define SUB( j ) sub32( &cur, A( j ), &c ); 00967 00968 /* 00969 * Helpers for the main 'loop' 00970 * (see fix_negative for the motivation of C) 00971 */ 00972 #define INIT( b ) \ 00973 int ret; \ 00974 signed char c = 0, cc; \ 00975 uint32_t cur; \ 00976 size_t i = 0, bits = b; \ 00977 mpi C; \ 00978 t_uint Cp[ b / 8 / sizeof( t_uint) + 1 ]; \ 00979 \ 00980 C.s = 1; \ 00981 C.n = b / 8 / sizeof( t_uint) + 1; \ 00982 C.p = Cp; \ 00983 memset( Cp, 0, C.n * sizeof( t_uint ) ); \ 00984 \ 00985 MPI_CHK( mpi_grow( N, b * 2 / 8 / sizeof( t_uint ) ) ); \ 00986 LOAD32; 00987 00988 #define NEXT \ 00989 STORE32; i++; LOAD32; \ 00990 cc = c; c = 0; \ 00991 if( cc < 0 ) \ 00992 sub32( &cur, -cc, &c ); \ 00993 else \ 00994 add32( &cur, cc, &c ); \ 00995 00996 #define LAST \ 00997 STORE32; i++; \ 00998 cur = c > 0 ? c : 0; STORE32; \ 00999 cur = 0; while( ++i < MAX32 ) { STORE32; } \ 01000 if( c < 0 ) fix_negative( N, c, &C, bits ); 01001 01002 /* 01003 * If the result is negative, we get it in the form 01004 * c * 2^(bits + 32) + N, with c negative and N positive shorter than 'bits' 01005 */ 01006 static inline int fix_negative( mpi *N, signed char c, mpi *C, size_t bits ) 01007 { 01008 int ret; 01009 01010 /* C = - c * 2^(bits + 32) */ 01011 #if !defined(POLARSSL_HAVE_INT64) 01012 ((void) bits); 01013 #else 01014 if( bits == 224 ) 01015 C->p [ C->n - 1 ] = ((t_uint) -c) << 32; 01016 else 01017 #endif 01018 C->p [ C->n - 1 ] = (t_uint) -c; 01019 01020 /* N = - ( C - N ) */ 01021 MPI_CHK( mpi_sub_abs( N, C, N ) ); 01022 N->s = -1; 01023 01024 cleanup: 01025 01026 return( ret ); 01027 } 01028 01029 #if defined(POLARSSL_ECP_DP_SECP224R1_ENABLED) 01030 /* 01031 * Fast quasi-reduction modulo p224 (FIPS 186-3 D.2.2) 01032 */ 01033 static int ecp_mod_p224( mpi *N ) 01034 { 01035 INIT( 224 ); 01036 01037 SUB( 7 ); SUB( 11 ); NEXT; // A0 += -A7 - A11 01038 SUB( 8 ); SUB( 12 ); NEXT; // A1 += -A8 - A12 01039 SUB( 9 ); SUB( 13 ); NEXT; // A2 += -A9 - A13 01040 SUB( 10 ); ADD( 7 ); ADD( 11 ); NEXT; // A3 += -A10 + A7 + A11 01041 SUB( 11 ); ADD( 8 ); ADD( 12 ); NEXT; // A4 += -A11 + A8 + A12 01042 SUB( 12 ); ADD( 9 ); ADD( 13 ); NEXT; // A5 += -A12 + A9 + A13 01043 SUB( 13 ); ADD( 10 ); LAST; // A6 += -A13 + A10 01044 01045 cleanup: 01046 return( ret ); 01047 } 01048 #endif /* POLARSSL_ECP_DP_SECP224R1_ENABLED */ 01049 01050 #if defined(POLARSSL_ECP_DP_SECP256R1_ENABLED) 01051 /* 01052 * Fast quasi-reduction modulo p256 (FIPS 186-3 D.2.3) 01053 */ 01054 static int ecp_mod_p256( mpi *N ) 01055 { 01056 INIT( 256 ); 01057 01058 ADD( 8 ); ADD( 9 ); 01059 SUB( 11 ); SUB( 12 ); SUB( 13 ); SUB( 14 ); NEXT; // A0 01060 01061 ADD( 9 ); ADD( 10 ); 01062 SUB( 12 ); SUB( 13 ); SUB( 14 ); SUB( 15 ); NEXT; // A1 01063 01064 ADD( 10 ); ADD( 11 ); 01065 SUB( 13 ); SUB( 14 ); SUB( 15 ); NEXT; // A2 01066 01067 ADD( 11 ); ADD( 11 ); ADD( 12 ); ADD( 12 ); ADD( 13 ); 01068 SUB( 15 ); SUB( 8 ); SUB( 9 ); NEXT; // A3 01069 01070 ADD( 12 ); ADD( 12 ); ADD( 13 ); ADD( 13 ); ADD( 14 ); 01071 SUB( 9 ); SUB( 10 ); NEXT; // A4 01072 01073 ADD( 13 ); ADD( 13 ); ADD( 14 ); ADD( 14 ); ADD( 15 ); 01074 SUB( 10 ); SUB( 11 ); NEXT; // A5 01075 01076 ADD( 14 ); ADD( 14 ); ADD( 15 ); ADD( 15 ); ADD( 14 ); ADD( 13 ); 01077 SUB( 8 ); SUB( 9 ); NEXT; // A6 01078 01079 ADD( 15 ); ADD( 15 ); ADD( 15 ); ADD( 8 ); 01080 SUB( 10 ); SUB( 11 ); SUB( 12 ); SUB( 13 ); LAST; // A7 01081 01082 cleanup: 01083 return( ret ); 01084 } 01085 #endif /* POLARSSL_ECP_DP_SECP256R1_ENABLED */ 01086 01087 #if defined(POLARSSL_ECP_DP_SECP384R1_ENABLED) 01088 /* 01089 * Fast quasi-reduction modulo p384 (FIPS 186-3 D.2.4) 01090 */ 01091 static int ecp_mod_p384( mpi *N ) 01092 { 01093 INIT( 384 ); 01094 01095 ADD( 12 ); ADD( 21 ); ADD( 20 ); 01096 SUB( 23 ); NEXT; // A0 01097 01098 ADD( 13 ); ADD( 22 ); ADD( 23 ); 01099 SUB( 12 ); SUB( 20 ); NEXT; // A2 01100 01101 ADD( 14 ); ADD( 23 ); 01102 SUB( 13 ); SUB( 21 ); NEXT; // A2 01103 01104 ADD( 15 ); ADD( 12 ); ADD( 20 ); ADD( 21 ); 01105 SUB( 14 ); SUB( 22 ); SUB( 23 ); NEXT; // A3 01106 01107 ADD( 21 ); ADD( 21 ); ADD( 16 ); ADD( 13 ); ADD( 12 ); ADD( 20 ); ADD( 22 ); 01108 SUB( 15 ); SUB( 23 ); SUB( 23 ); NEXT; // A4 01109 01110 ADD( 22 ); ADD( 22 ); ADD( 17 ); ADD( 14 ); ADD( 13 ); ADD( 21 ); ADD( 23 ); 01111 SUB( 16 ); NEXT; // A5 01112 01113 ADD( 23 ); ADD( 23 ); ADD( 18 ); ADD( 15 ); ADD( 14 ); ADD( 22 ); 01114 SUB( 17 ); NEXT; // A6 01115 01116 ADD( 19 ); ADD( 16 ); ADD( 15 ); ADD( 23 ); 01117 SUB( 18 ); NEXT; // A7 01118 01119 ADD( 20 ); ADD( 17 ); ADD( 16 ); 01120 SUB( 19 ); NEXT; // A8 01121 01122 ADD( 21 ); ADD( 18 ); ADD( 17 ); 01123 SUB( 20 ); NEXT; // A9 01124 01125 ADD( 22 ); ADD( 19 ); ADD( 18 ); 01126 SUB( 21 ); NEXT; // A10 01127 01128 ADD( 23 ); ADD( 20 ); ADD( 19 ); 01129 SUB( 22 ); LAST; // A11 01130 01131 cleanup: 01132 return( ret ); 01133 } 01134 #endif /* POLARSSL_ECP_DP_SECP384R1_ENABLED */ 01135 01136 #undef A 01137 #undef LOAD32 01138 #undef STORE32 01139 #undef MAX32 01140 #undef INIT 01141 #undef NEXT 01142 #undef LAST 01143 01144 #endif /* POLARSSL_ECP_DP_SECP224R1_ENABLED || 01145 POLARSSL_ECP_DP_SECP256R1_ENABLED || 01146 POLARSSL_ECP_DP_SECP384R1_ENABLED */ 01147 01148 #if defined(POLARSSL_ECP_DP_SECP521R1_ENABLED) 01149 /* 01150 * Here we have an actual Mersenne prime, so things are more straightforward. 01151 * However, chunks are aligned on a 'weird' boundary (521 bits). 01152 */ 01153 01154 /* Size of p521 in terms of t_uint */ 01155 #define P521_WIDTH ( 521 / 8 / sizeof( t_uint ) + 1 ) 01156 01157 /* Bits to keep in the most significant t_uint */ 01158 #if defined(POLARSSL_HAVE_INT8) 01159 #define P521_MASK 0x01 01160 #else 01161 #define P521_MASK 0x01FF 01162 #endif 01163 01164 /* 01165 * Fast quasi-reduction modulo p521 (FIPS 186-3 D.2.5) 01166 * Write N as A1 + 2^521 A0, return A0 + A1 01167 */ 01168 static int ecp_mod_p521( mpi *N ) 01169 { 01170 int ret; 01171 size_t i; 01172 mpi M; 01173 t_uint Mp[P521_WIDTH + 1]; 01174 /* Worst case for the size of M is when t_uint is 16 bits: 01175 * we need to hold bits 513 to 1056, which is 34 limbs, that is 01176 * P521_WIDTH + 1. Otherwise P521_WIDTH is enough. */ 01177 01178 if( N->n < P521_WIDTH ) 01179 return( 0 ); 01180 01181 /* M = A1 */ 01182 M.s = 1; 01183 M.n = N->n - ( P521_WIDTH - 1 ); 01184 if( M.n > P521_WIDTH + 1 ) 01185 M.n = P521_WIDTH + 1; 01186 M.p = Mp; 01187 memcpy( Mp, N->p + P521_WIDTH - 1, M.n * sizeof( t_uint ) ); 01188 MPI_CHK( mpi_shift_r( &M, 521 % ( 8 * sizeof( t_uint ) ) ) ); 01189 01190 /* N = A0 */ 01191 N->p [P521_WIDTH - 1] &= P521_MASK; 01192 for( i = P521_WIDTH; i < N->n ; i++ ) 01193 N->p [i] = 0; 01194 01195 /* N = A0 + A1 */ 01196 MPI_CHK( mpi_add_abs( N, N, &M ) ); 01197 01198 cleanup: 01199 return( ret ); 01200 } 01201 01202 #undef P521_WIDTH 01203 #undef P521_MASK 01204 #endif /* POLARSSL_ECP_DP_SECP521R1_ENABLED */ 01205 01206 #endif /* POLARSSL_ECP_NIST_OPTIM */ 01207 01208 #if defined(POLARSSL_ECP_DP_M255_ENABLED) 01209 01210 /* Size of p255 in terms of t_uint */ 01211 #define P255_WIDTH ( 255 / 8 / sizeof( t_uint ) + 1 ) 01212 01213 /* 01214 * Fast quasi-reduction modulo p255 = 2^255 - 19 01215 * Write N as A0 + 2^255 A1, return A0 + 19 * A1 01216 */ 01217 static int ecp_mod_p255( mpi *N ) 01218 { 01219 int ret; 01220 size_t i; 01221 mpi M; 01222 t_uint Mp[P255_WIDTH + 2]; 01223 01224 if( N->n < P255_WIDTH ) 01225 return( 0 ); 01226 01227 /* M = A1 */ 01228 M.s = 1; 01229 M.n = N->n - ( P255_WIDTH - 1 ); 01230 if( M.n > P255_WIDTH + 1 ) 01231 M.n = P255_WIDTH + 1; 01232 M.p = Mp; 01233 memset( Mp, 0, sizeof Mp ); 01234 memcpy( Mp, N->p + P255_WIDTH - 1, M.n * sizeof( t_uint ) ); 01235 MPI_CHK( mpi_shift_r( &M, 255 % ( 8 * sizeof( t_uint ) ) ) ); 01236 M.n ++; /* Make room for multiplication by 19 */ 01237 01238 /* N = A0 */ 01239 MPI_CHK( mpi_set_bit( N, 255, 0 ) ); 01240 for( i = P255_WIDTH; i < N->n ; i++ ) 01241 N->p [i] = 0; 01242 01243 /* N = A0 + 19 * A1 */ 01244 MPI_CHK( mpi_mul_int( &M, &M, 19 ) ); 01245 MPI_CHK( mpi_add_abs( N, N, &M ) ); 01246 01247 cleanup: 01248 return( ret ); 01249 } 01250 #endif /* POLARSSL_ECP_DP_M255_ENABLED */ 01251 01252 #if defined(POLARSSL_ECP_DP_SECP192K1_ENABLED) || \ 01253 defined(POLARSSL_ECP_DP_SECP224K1_ENABLED) || \ 01254 defined(POLARSSL_ECP_DP_SECP256K1_ENABLED) 01255 /* 01256 * Fast quasi-reduction modulo P = 2^s - R, 01257 * with R about 33 bits, used by the Koblitz curves. 01258 * 01259 * Write N as A0 + 2^224 A1, return A0 + R * A1. 01260 * Actually do two passes, since R is big. 01261 */ 01262 #define P_KOBLITZ_MAX ( 256 / 8 / sizeof( t_uint ) ) // Max limbs in P 01263 #define P_KOBLITZ_R ( 8 / sizeof( t_uint ) ) // Limbs in R 01264 static inline int ecp_mod_koblitz( mpi *N, t_uint *Rp, size_t p_limbs, 01265 size_t adjust, size_t shift, t_uint mask ) 01266 { 01267 int ret; 01268 size_t i; 01269 mpi M, R; 01270 t_uint Mp[P_KOBLITZ_MAX + P_KOBLITZ_R]; 01271 01272 if( N->n < p_limbs ) 01273 return( 0 ); 01274 01275 /* Init R */ 01276 R.s = 1; 01277 R.p = Rp; 01278 R.n = P_KOBLITZ_R; 01279 01280 /* Common setup for M */ 01281 M.s = 1; 01282 M.p = Mp; 01283 01284 /* M = A1 */ 01285 M.n = N->n - ( p_limbs - adjust ); 01286 if( M.n > p_limbs + adjust ) 01287 M.n = p_limbs + adjust; 01288 memset( Mp, 0, sizeof Mp ); 01289 memcpy( Mp, N->p + p_limbs - adjust, M.n * sizeof( t_uint ) ); 01290 if( shift != 0 ) 01291 MPI_CHK( mpi_shift_r( &M, shift ) ); 01292 M.n += R.n - adjust; /* Make room for multiplication by R */ 01293 01294 /* N = A0 */ 01295 if( mask != 0 ) 01296 N->p [p_limbs - 1] &= mask; 01297 for( i = p_limbs; i < N->n ; i++ ) 01298 N->p [i] = 0; 01299 01300 /* N = A0 + R * A1 */ 01301 MPI_CHK( mpi_mul_mpi( &M, &M, &R ) ); 01302 MPI_CHK( mpi_add_abs( N, N, &M ) ); 01303 01304 /* Second pass */ 01305 01306 /* M = A1 */ 01307 M.n = N->n - ( p_limbs - adjust ); 01308 if( M.n > p_limbs + adjust ) 01309 M.n = p_limbs + adjust; 01310 memset( Mp, 0, sizeof Mp ); 01311 memcpy( Mp, N->p + p_limbs - adjust, M.n * sizeof( t_uint ) ); 01312 if( shift != 0 ) 01313 MPI_CHK( mpi_shift_r( &M, shift ) ); 01314 M.n += R.n - adjust; /* Make room for multiplication by R */ 01315 01316 /* N = A0 */ 01317 if( mask != 0 ) 01318 N->p [p_limbs - 1] &= mask; 01319 for( i = p_limbs; i < N->n ; i++ ) 01320 N->p [i] = 0; 01321 01322 /* N = A0 + R * A1 */ 01323 MPI_CHK( mpi_mul_mpi( &M, &M, &R ) ); 01324 MPI_CHK( mpi_add_abs( N, N, &M ) ); 01325 01326 cleanup: 01327 return( ret ); 01328 } 01329 #endif /* POLARSSL_ECP_DP_SECP192K1_ENABLED) || 01330 POLARSSL_ECP_DP_SECP224K1_ENABLED) || 01331 POLARSSL_ECP_DP_SECP256K1_ENABLED) */ 01332 01333 #if defined(POLARSSL_ECP_DP_SECP192K1_ENABLED) 01334 /* 01335 * Fast quasi-reduction modulo p192k1 = 2^192 - R, 01336 * with R = 2^32 + 2^12 + 2^8 + 2^7 + 2^6 + 2^3 + 1 = 0x0100001119 01337 */ 01338 static int ecp_mod_p192k1( mpi *N ) 01339 { 01340 static t_uint Rp[] = { 01341 BYTES_TO_T_UINT_8( 0xC9, 0x11, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) }; 01342 01343 return( ecp_mod_koblitz( N, Rp, 192 / 8 / sizeof( t_uint ), 0, 0, 0 ) ); 01344 } 01345 #endif /* POLARSSL_ECP_DP_SECP192K1_ENABLED */ 01346 01347 #if defined(POLARSSL_ECP_DP_SECP224K1_ENABLED) 01348 /* 01349 * Fast quasi-reduction modulo p224k1 = 2^224 - R, 01350 * with R = 2^32 + 2^12 + 2^11 + 2^9 + 2^7 + 2^4 + 2 + 1 = 0x0100001A93 01351 */ 01352 static int ecp_mod_p224k1( mpi *N ) 01353 { 01354 static t_uint Rp[] = { 01355 BYTES_TO_T_UINT_8( 0x93, 0x1A, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) }; 01356 01357 #if defined(POLARSSL_HAVE_INT64) 01358 return( ecp_mod_koblitz( N, Rp, 4, 1, 32, 0xFFFFFFFF ) ); 01359 #else 01360 return( ecp_mod_koblitz( N, Rp, 224 / 8 / sizeof( t_uint ), 0, 0, 0 ) ); 01361 #endif 01362 } 01363 01364 #endif /* POLARSSL_ECP_DP_SECP224K1_ENABLED */ 01365 01366 #if defined(POLARSSL_ECP_DP_SECP256K1_ENABLED) 01367 /* 01368 * Fast quasi-reduction modulo p256k1 = 2^256 - R, 01369 * with R = 2^32 + 2^9 + 2^8 + 2^7 + 2^6 + 2^4 + 1 = 0x01000003D1 01370 */ 01371 static int ecp_mod_p256k1( mpi *N ) 01372 { 01373 static t_uint Rp[] = { 01374 BYTES_TO_T_UINT_8( 0xD1, 0x03, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) }; 01375 return( ecp_mod_koblitz( N, Rp, 256 / 8 / sizeof( t_uint ), 0, 0, 0 ) ); 01376 } 01377 #endif /* POLARSSL_ECP_DP_SECP256K1_ENABLED */ 01378 01379 #endif /* POLARSSL_ECP_C */ 01380
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