ecp_curves.c 41 KB
Newer Older
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
/*
 *  Elliptic curves over GF(p): curve-specific data and functions
 *
 *  Copyright (C) 2006-2013, Brainspark B.V.
 *
 *  This file is part of PolarSSL (http://www.polarssl.org)
 *  Lead Maintainer: Paul Bakker <polarssl_maintainer at polarssl.org>
 *
 *  All rights reserved.
 *
 *  This program is free software; you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation; either version 2 of the License, or
 *  (at your option) any later version.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public License along
 *  with this program; if not, write to the Free Software Foundation, Inc.,
 *  51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
 */

#include "polarssl/config.h"

#if defined(POLARSSL_ECP_C)

#include "polarssl/ecp.h"

32 33 34 35 36 37 38 39
#if defined(_MSC_VER) && !defined(inline)
#define inline _inline
#else
#if defined(__ARMCC_VERSION) && !defined(inline)
#define inline __inline
#endif /* __ARMCC_VERSION */
#endif /*_MSC_VER */

40 41 42 43
/*
 * Conversion macros for embedded constants:
 * build lists of t_uint's from lists of unsigned char's grouped by 8
 */
44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84
#if defined(POLARSSL_HAVE_INT8)

#define BYTES_TO_T_UINT( a, b, c, d, e, f, g, h ) \
    a, b, c, d, e, f, g, h

#elif defined(POLARSSL_HAVE_INT16)

#define TWO_BYTES_TO_T_UINT( a, b )     \
    ( (t_uint) a << 0 ) |               \
    ( (t_uint) b << 8 )
#define BYTES_TO_T_UINT( a, b, c, d, e, f, g, h )   \
    TWO_BYTES_TO_T_UINT( a, b ),                    \
    TWO_BYTES_TO_T_UINT( c, d ),                    \
    TWO_BYTES_TO_T_UINT( e, f ),                    \
    TWO_BYTES_TO_T_UINT( g, h )

#elif defined(POLARSSL_HAVE_INT32)

#define FOUR_BYTES_TO_T_UINT( a, b, c, d )  \
    ( (t_uint) a <<  0 ) |                  \
    ( (t_uint) b <<  8 ) |                  \
    ( (t_uint) c << 16 ) |                  \
    ( (t_uint) d << 24 )
#define BYTES_TO_T_UINT( a, b, c, d, e, f, g, h )   \
    FOUR_BYTES_TO_T_UINT( a, b, c, d )              \
    FOUR_BYTES_TO_T_UINT( e, f, g, h )

#else /* 64-bits */

#define BYTES_TO_T_UINT( a, b, c, d, e, f, g, h )   \
    ( (t_uint) a <<  0 ) |                          \
    ( (t_uint) b <<  8 ) |                          \
    ( (t_uint) c << 16 ) |                          \
    ( (t_uint) d << 24 ) |                          \
    ( (t_uint) e << 32 ) |                          \
    ( (t_uint) f << 40 ) |                          \
    ( (t_uint) g << 48 ) |                          \
    ( (t_uint) h << 56 )

#endif /* bits in t_uint */

Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
85 86 87
/*
 * Domain parameters for secp192r1
 */
88
#if defined(POLARSSL_ECP_DP_SECP192R1_ENABLED)
89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113
static t_uint secp192r1_p[] = {
    BYTES_TO_T_UINT( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
};
static t_uint secp192r1_b[] = {
    BYTES_TO_T_UINT( 0xB1, 0xB9, 0x46, 0xC1, 0xEC, 0xDE, 0xB8, 0xFE ),
    BYTES_TO_T_UINT( 0x49, 0x30, 0x24, 0x72, 0xAB, 0xE9, 0xA7, 0x0F ),
    BYTES_TO_T_UINT( 0xE7, 0x80, 0x9C, 0xE5, 0x19, 0x05, 0x21, 0x64 ),
};
static t_uint secp192r1_gx[] = {
    BYTES_TO_T_UINT( 0x12, 0x10, 0xFF, 0x82, 0xFD, 0x0A, 0xFF, 0xF4 ),
    BYTES_TO_T_UINT( 0x00, 0x88, 0xA1, 0x43, 0xEB, 0x20, 0xBF, 0x7C ),
    BYTES_TO_T_UINT( 0xF6, 0x90, 0x30, 0xB0, 0x0E, 0xA8, 0x8D, 0x18 ),
};
static t_uint secp192r1_gy[] = {
    BYTES_TO_T_UINT( 0x11, 0x48, 0x79, 0x1E, 0xA1, 0x77, 0xF9, 0x73 ),
    BYTES_TO_T_UINT( 0xD5, 0xCD, 0x24, 0x6B, 0xED, 0x11, 0x10, 0x63 ),
    BYTES_TO_T_UINT( 0x78, 0xDA, 0xC8, 0xFF, 0x95, 0x2B, 0x19, 0x07 ),
};
static t_uint secp192r1_n[] = {
    BYTES_TO_T_UINT( 0x31, 0x28, 0xD2, 0xB4, 0xB1, 0xC9, 0x6B, 0x14 ),
    BYTES_TO_T_UINT( 0x36, 0xF8, 0xDE, 0x99, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
};
114
#endif /* POLARSSL_ECP_DP_SECP192R1_ENABLED */
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
115 116 117 118

/*
 * Domain parameters for secp224r1
 */
119
#if defined(POLARSSL_ECP_DP_SECP224R1_ENABLED)
120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149
static t_uint secp224r1_p[] = {
    BYTES_TO_T_UINT( 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ),
    BYTES_TO_T_UINT( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ),
};
static t_uint secp224r1_b[] = {
    BYTES_TO_T_UINT( 0xB4, 0xFF, 0x55, 0x23, 0x43, 0x39, 0x0B, 0x27 ),
    BYTES_TO_T_UINT( 0xBA, 0xD8, 0xBF, 0xD7, 0xB7, 0xB0, 0x44, 0x50 ),
    BYTES_TO_T_UINT( 0x56, 0x32, 0x41, 0xF5, 0xAB, 0xB3, 0x04, 0x0C ),
    BYTES_TO_T_UINT( 0x85, 0x0A, 0x05, 0xB4, 0x00, 0x00, 0x00, 0x00 ),
};
static t_uint secp224r1_gx[] = {
    BYTES_TO_T_UINT( 0x21, 0x1D, 0x5C, 0x11, 0xD6, 0x80, 0x32, 0x34 ),
    BYTES_TO_T_UINT( 0x22, 0x11, 0xC2, 0x56, 0xD3, 0xC1, 0x03, 0x4A ),
    BYTES_TO_T_UINT( 0xB9, 0x90, 0x13, 0x32, 0x7F, 0xBF, 0xB4, 0x6B ),
    BYTES_TO_T_UINT( 0xBD, 0x0C, 0x0E, 0xB7, 0x00, 0x00, 0x00, 0x00 ),
};
static t_uint secp224r1_gy[] = {
    BYTES_TO_T_UINT( 0x34, 0x7E, 0x00, 0x85, 0x99, 0x81, 0xD5, 0x44 ),
    BYTES_TO_T_UINT( 0x64, 0x47, 0x07, 0x5A, 0xA0, 0x75, 0x43, 0xCD ),
    BYTES_TO_T_UINT( 0xE6, 0xDF, 0x22, 0x4C, 0xFB, 0x23, 0xF7, 0xB5 ),
    BYTES_TO_T_UINT( 0x88, 0x63, 0x37, 0xBD, 0x00, 0x00, 0x00, 0x00 ),
};
static t_uint secp224r1_n[] = {
    BYTES_TO_T_UINT( 0x3D, 0x2A, 0x5C, 0x5C, 0x45, 0x29, 0xDD, 0x13 ),
    BYTES_TO_T_UINT( 0x3E, 0xF0, 0xB8, 0xE0, 0xA2, 0x16, 0xFF, 0xFF ),
    BYTES_TO_T_UINT( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ),
};
150
#endif /* POLARSSL_ECP_DP_SECP224R1_ENABLED */
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
151 152 153 154

/*
 * Domain parameters for secp256r1
 */
155
#if defined(POLARSSL_ECP_DP_SECP256R1_ENABLED)
156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185
static t_uint secp256r1_p[] = {
    BYTES_TO_T_UINT( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ),
    BYTES_TO_T_UINT( 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ),
    BYTES_TO_T_UINT( 0x01, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ),
};
static t_uint secp256r1_b[] = {
    BYTES_TO_T_UINT( 0x4B, 0x60, 0xD2, 0x27, 0x3E, 0x3C, 0xCE, 0x3B ),
    BYTES_TO_T_UINT( 0xF6, 0xB0, 0x53, 0xCC, 0xB0, 0x06, 0x1D, 0x65 ),
    BYTES_TO_T_UINT( 0xBC, 0x86, 0x98, 0x76, 0x55, 0xBD, 0xEB, 0xB3 ),
    BYTES_TO_T_UINT( 0xE7, 0x93, 0x3A, 0xAA, 0xD8, 0x35, 0xC6, 0x5A ),
};
static t_uint secp256r1_gx[] = {
    BYTES_TO_T_UINT( 0x96, 0xC2, 0x98, 0xD8, 0x45, 0x39, 0xA1, 0xF4 ),
    BYTES_TO_T_UINT( 0xA0, 0x33, 0xEB, 0x2D, 0x81, 0x7D, 0x03, 0x77 ),
    BYTES_TO_T_UINT( 0xF2, 0x40, 0xA4, 0x63, 0xE5, 0xE6, 0xBC, 0xF8 ),
    BYTES_TO_T_UINT( 0x47, 0x42, 0x2C, 0xE1, 0xF2, 0xD1, 0x17, 0x6B ),
};
static t_uint secp256r1_gy[] = {
    BYTES_TO_T_UINT( 0xF5, 0x51, 0xBF, 0x37, 0x68, 0x40, 0xB6, 0xCB ),
    BYTES_TO_T_UINT( 0xCE, 0x5E, 0x31, 0x6B, 0x57, 0x33, 0xCE, 0x2B ),
    BYTES_TO_T_UINT( 0x16, 0x9E, 0x0F, 0x7C, 0x4A, 0xEB, 0xE7, 0x8E ),
    BYTES_TO_T_UINT( 0x9B, 0x7F, 0x1A, 0xFE, 0xE2, 0x42, 0xE3, 0x4F ),
};
static t_uint secp256r1_n[] = {
    BYTES_TO_T_UINT( 0x51, 0x25, 0x63, 0xFC, 0xC2, 0xCA, 0xB9, 0xF3 ),
    BYTES_TO_T_UINT( 0x84, 0x9E, 0x17, 0xA7, 0xAD, 0xFA, 0xE6, 0xBC ),
    BYTES_TO_T_UINT( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ),
};
186
#endif /* POLARSSL_ECP_DP_SECP256R1_ENABLED */
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
187 188 189 190

/*
 * Domain parameters for secp384r1
 */
191
#if defined(POLARSSL_ECP_DP_SECP384R1_ENABLED)
192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231
static t_uint secp384r1_p[] = {
    BYTES_TO_T_UINT( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ),
    BYTES_TO_T_UINT( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
};
static t_uint secp384r1_b[] = {
    BYTES_TO_T_UINT( 0xEF, 0x2A, 0xEC, 0xD3, 0xED, 0xC8, 0x85, 0x2A ),
    BYTES_TO_T_UINT( 0x9D, 0xD1, 0x2E, 0x8A, 0x8D, 0x39, 0x56, 0xC6 ),
    BYTES_TO_T_UINT( 0x5A, 0x87, 0x13, 0x50, 0x8F, 0x08, 0x14, 0x03 ),
    BYTES_TO_T_UINT( 0x12, 0x41, 0x81, 0xFE, 0x6E, 0x9C, 0x1D, 0x18 ),
    BYTES_TO_T_UINT( 0x19, 0x2D, 0xF8, 0xE3, 0x6B, 0x05, 0x8E, 0x98 ),
    BYTES_TO_T_UINT( 0xE4, 0xE7, 0x3E, 0xE2, 0xA7, 0x2F, 0x31, 0xB3 ),
};
static t_uint secp384r1_gx[] = {
    BYTES_TO_T_UINT( 0xB7, 0x0A, 0x76, 0x72, 0x38, 0x5E, 0x54, 0x3A ),
    BYTES_TO_T_UINT( 0x6C, 0x29, 0x55, 0xBF, 0x5D, 0xF2, 0x02, 0x55 ),
    BYTES_TO_T_UINT( 0x38, 0x2A, 0x54, 0x82, 0xE0, 0x41, 0xF7, 0x59 ),
    BYTES_TO_T_UINT( 0x98, 0x9B, 0xA7, 0x8B, 0x62, 0x3B, 0x1D, 0x6E ),
    BYTES_TO_T_UINT( 0x74, 0xAD, 0x20, 0xF3, 0x1E, 0xC7, 0xB1, 0x8E ),
    BYTES_TO_T_UINT( 0x37, 0x05, 0x8B, 0xBE, 0x22, 0xCA, 0x87, 0xAA ),
};
static t_uint secp384r1_gy[] = {
    BYTES_TO_T_UINT( 0x5F, 0x0E, 0xEA, 0x90, 0x7C, 0x1D, 0x43, 0x7A ),
    BYTES_TO_T_UINT( 0x9D, 0x81, 0x7E, 0x1D, 0xCE, 0xB1, 0x60, 0x0A ),
    BYTES_TO_T_UINT( 0xC0, 0xB8, 0xF0, 0xB5, 0x13, 0x31, 0xDA, 0xE9 ),
    BYTES_TO_T_UINT( 0x7C, 0x14, 0x9A, 0x28, 0xBD, 0x1D, 0xF4, 0xF8 ),
    BYTES_TO_T_UINT( 0x29, 0xDC, 0x92, 0x92, 0xBF, 0x98, 0x9E, 0x5D ),
    BYTES_TO_T_UINT( 0x6F, 0x2C, 0x26, 0x96, 0x4A, 0xDE, 0x17, 0x36 ),
};
static t_uint secp384r1_n[] = {
    BYTES_TO_T_UINT( 0x73, 0x29, 0xC5, 0xCC, 0x6A, 0x19, 0xEC, 0xEC ),
    BYTES_TO_T_UINT( 0x7A, 0xA7, 0xB0, 0x48, 0xB2, 0x0D, 0x1A, 0x58 ),
    BYTES_TO_T_UINT( 0xDF, 0x2D, 0x37, 0xF4, 0x81, 0x4D, 0x63, 0xC7 ),
    BYTES_TO_T_UINT( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
};
232
#endif /* POLARSSL_ECP_DP_SECP384R1_ENABLED */
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
233 234 235 236

/*
 * Domain parameters for secp521r1
 */
237
#if defined(POLARSSL_ECP_DP_SECP521R1_ENABLED)
238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292
static t_uint secp521r1_p[] = {
    BYTES_TO_T_UINT( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT( 0xFF, 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ),
};
static t_uint secp521r1_b[] = {
    BYTES_TO_T_UINT( 0x00, 0x3F, 0x50, 0x6B, 0xD4, 0x1F, 0x45, 0xEF ),
    BYTES_TO_T_UINT( 0xF1, 0x34, 0x2C, 0x3D, 0x88, 0xDF, 0x73, 0x35 ),
    BYTES_TO_T_UINT( 0x07, 0xBF, 0xB1, 0x3B, 0xBD, 0xC0, 0x52, 0x16 ),
    BYTES_TO_T_UINT( 0x7B, 0x93, 0x7E, 0xEC, 0x51, 0x39, 0x19, 0x56 ),
    BYTES_TO_T_UINT( 0xE1, 0x09, 0xF1, 0x8E, 0x91, 0x89, 0xB4, 0xB8 ),
    BYTES_TO_T_UINT( 0xF3, 0x15, 0xB3, 0x99, 0x5B, 0x72, 0xDA, 0xA2 ),
    BYTES_TO_T_UINT( 0xEE, 0x40, 0x85, 0xB6, 0xA0, 0x21, 0x9A, 0x92 ),
    BYTES_TO_T_UINT( 0x1F, 0x9A, 0x1C, 0x8E, 0x61, 0xB9, 0x3E, 0x95 ),
    BYTES_TO_T_UINT( 0x51, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ),
};
static t_uint secp521r1_gx[] = {
    BYTES_TO_T_UINT( 0x66, 0xBD, 0xE5, 0xC2, 0x31, 0x7E, 0x7E, 0xF9 ),
    BYTES_TO_T_UINT( 0x9B, 0x42, 0x6A, 0x85, 0xC1, 0xB3, 0x48, 0x33 ),
    BYTES_TO_T_UINT( 0xDE, 0xA8, 0xFF, 0xA2, 0x27, 0xC1, 0x1D, 0xFE ),
    BYTES_TO_T_UINT( 0x28, 0x59, 0xE7, 0xEF, 0x77, 0x5E, 0x4B, 0xA1 ),
    BYTES_TO_T_UINT( 0xBA, 0x3D, 0x4D, 0x6B, 0x60, 0xAF, 0x28, 0xF8 ),
    BYTES_TO_T_UINT( 0x21, 0xB5, 0x3F, 0x05, 0x39, 0x81, 0x64, 0x9C ),
    BYTES_TO_T_UINT( 0x42, 0xB4, 0x95, 0x23, 0x66, 0xCB, 0x3E, 0x9E ),
    BYTES_TO_T_UINT( 0xCD, 0xE9, 0x04, 0x04, 0xB7, 0x06, 0x8E, 0x85 ),
    BYTES_TO_T_UINT( 0xC6, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ),
};
static t_uint secp521r1_gy[] = {
    BYTES_TO_T_UINT( 0x50, 0x66, 0xD1, 0x9F, 0x76, 0x94, 0xBE, 0x88 ),
    BYTES_TO_T_UINT( 0x40, 0xC2, 0x72, 0xA2, 0x86, 0x70, 0x3C, 0x35 ),
    BYTES_TO_T_UINT( 0x61, 0x07, 0xAD, 0x3F, 0x01, 0xB9, 0x50, 0xC5 ),
    BYTES_TO_T_UINT( 0x40, 0x26, 0xF4, 0x5E, 0x99, 0x72, 0xEE, 0x97 ),
    BYTES_TO_T_UINT( 0x2C, 0x66, 0x3E, 0x27, 0x17, 0xBD, 0xAF, 0x17 ),
    BYTES_TO_T_UINT( 0x68, 0x44, 0x9B, 0x57, 0x49, 0x44, 0xF5, 0x98 ),
    BYTES_TO_T_UINT( 0xD9, 0x1B, 0x7D, 0x2C, 0xB4, 0x5F, 0x8A, 0x5C ),
    BYTES_TO_T_UINT( 0x04, 0xC0, 0x3B, 0x9A, 0x78, 0x6A, 0x29, 0x39 ),
    BYTES_TO_T_UINT( 0x18, 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ),
};
static t_uint secp521r1_n[] = {
    BYTES_TO_T_UINT( 0x09, 0x64, 0x38, 0x91, 0x1E, 0xB7, 0x6F, 0xBB ),
    BYTES_TO_T_UINT( 0xAE, 0x47, 0x9C, 0x89, 0xB8, 0xC9, 0xB5, 0x3B ),
    BYTES_TO_T_UINT( 0xD0, 0xA5, 0x09, 0xF7, 0x48, 0x01, 0xCC, 0x7F ),
    BYTES_TO_T_UINT( 0x6B, 0x96, 0x2F, 0xBF, 0x83, 0x87, 0x86, 0x51 ),
    BYTES_TO_T_UINT( 0xFA, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT( 0xFF, 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ),
};
293
#endif /* POLARSSL_ECP_DP_SECP521R1_ENABLED */
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
294 295 296 297

/*
 * Domain parameters for brainpoolP256r1 (RFC 5639 3.4)
 */
298
#if defined(POLARSSL_ECP_DP_BP256R1_ENABLED)
299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334
static t_uint brainpoolP256r1_p[] = {
    BYTES_TO_T_UINT( 0x77, 0x53, 0x6E, 0x1F, 0x1D, 0x48, 0x13, 0x20 ),
    BYTES_TO_T_UINT( 0x28, 0x20, 0x26, 0xD5, 0x23, 0xF6, 0x3B, 0x6E ),
    BYTES_TO_T_UINT( 0x72, 0x8D, 0x83, 0x9D, 0x90, 0x0A, 0x66, 0x3E ),
    BYTES_TO_T_UINT( 0xBC, 0xA9, 0xEE, 0xA1, 0xDB, 0x57, 0xFB, 0xA9 ),
};
static t_uint brainpoolP256r1_a[] = {
    BYTES_TO_T_UINT( 0xD9, 0xB5, 0x30, 0xF3, 0x44, 0x4B, 0x4A, 0xE9 ),
    BYTES_TO_T_UINT( 0x6C, 0x5C, 0xDC, 0x26, 0xC1, 0x55, 0x80, 0xFB ),
    BYTES_TO_T_UINT( 0xE7, 0xFF, 0x7A, 0x41, 0x30, 0x75, 0xF6, 0xEE ),
    BYTES_TO_T_UINT( 0x57, 0x30, 0x2C, 0xFC, 0x75, 0x09, 0x5A, 0x7D ),
};
static t_uint brainpoolP256r1_b[] = {
    BYTES_TO_T_UINT( 0xB6, 0x07, 0x8C, 0xFF, 0x18, 0xDC, 0xCC, 0x6B ),
    BYTES_TO_T_UINT( 0xCE, 0xE1, 0xF7, 0x5C, 0x29, 0x16, 0x84, 0x95 ),
    BYTES_TO_T_UINT( 0xBF, 0x7C, 0xD7, 0xBB, 0xD9, 0xB5, 0x30, 0xF3 ),
    BYTES_TO_T_UINT( 0x44, 0x4B, 0x4A, 0xE9, 0x6C, 0x5C, 0xDC, 0x26 ),
};
static t_uint brainpoolP256r1_gx[] = {
    BYTES_TO_T_UINT( 0x62, 0x32, 0xCE, 0x9A, 0xBD, 0x53, 0x44, 0x3A ),
    BYTES_TO_T_UINT( 0xC2, 0x23, 0xBD, 0xE3, 0xE1, 0x27, 0xDE, 0xB9 ),
    BYTES_TO_T_UINT( 0xAF, 0xB7, 0x81, 0xFC, 0x2F, 0x48, 0x4B, 0x2C ),
    BYTES_TO_T_UINT( 0xCB, 0x57, 0x7E, 0xCB, 0xB9, 0xAE, 0xD2, 0x8B ),
};
static t_uint brainpoolP256r1_gy[] = {
    BYTES_TO_T_UINT( 0x97, 0x69, 0x04, 0x2F, 0xC7, 0x54, 0x1D, 0x5C ),
    BYTES_TO_T_UINT( 0x54, 0x8E, 0xED, 0x2D, 0x13, 0x45, 0x77, 0xC2 ),
    BYTES_TO_T_UINT( 0xC9, 0x1D, 0x61, 0x14, 0x1A, 0x46, 0xF8, 0x97 ),
    BYTES_TO_T_UINT( 0xFD, 0xC4, 0xDA, 0xC3, 0x35, 0xF8, 0x7E, 0x54 ),
};
static t_uint brainpoolP256r1_n[] = {
    BYTES_TO_T_UINT( 0xA7, 0x56, 0x48, 0x97, 0x82, 0x0E, 0x1E, 0x90 ),
    BYTES_TO_T_UINT( 0xF7, 0xA6, 0x61, 0xB5, 0xA3, 0x7A, 0x39, 0x8C ),
    BYTES_TO_T_UINT( 0x71, 0x8D, 0x83, 0x9D, 0x90, 0x0A, 0x66, 0x3E ),
    BYTES_TO_T_UINT( 0xBC, 0xA9, 0xEE, 0xA1, 0xDB, 0x57, 0xFB, 0xA9 ),
};
335
#endif /* POLARSSL_ECP_DP_BP256R1_ENABLED */
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
336 337 338 339

/*
 * Domain parameters for brainpoolP384r1 (RFC 5639 3.6)
 */
340
#if defined(POLARSSL_ECP_DP_BP384R1_ENABLED)
341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388
static t_uint brainpoolP384r1_p[] = {
    BYTES_TO_T_UINT( 0x53, 0xEC, 0x07, 0x31, 0x13, 0x00, 0x47, 0x87 ),
    BYTES_TO_T_UINT( 0x71, 0x1A, 0x1D, 0x90, 0x29, 0xA7, 0xD3, 0xAC ),
    BYTES_TO_T_UINT( 0x23, 0x11, 0xB7, 0x7F, 0x19, 0xDA, 0xB1, 0x12 ),
    BYTES_TO_T_UINT( 0xB4, 0x56, 0x54, 0xED, 0x09, 0x71, 0x2F, 0x15 ),
    BYTES_TO_T_UINT( 0xDF, 0x41, 0xE6, 0x50, 0x7E, 0x6F, 0x5D, 0x0F ),
    BYTES_TO_T_UINT( 0x28, 0x6D, 0x38, 0xA3, 0x82, 0x1E, 0xB9, 0x8C ),
};
static t_uint brainpoolP384r1_a[] = {
    BYTES_TO_T_UINT( 0x26, 0x28, 0xCE, 0x22, 0xDD, 0xC7, 0xA8, 0x04 ),
    BYTES_TO_T_UINT( 0xEB, 0xD4, 0x3A, 0x50, 0x4A, 0x81, 0xA5, 0x8A ),
    BYTES_TO_T_UINT( 0x0F, 0xF9, 0x91, 0xBA, 0xEF, 0x65, 0x91, 0x13 ),
    BYTES_TO_T_UINT( 0x87, 0x27, 0xB2, 0x4F, 0x8E, 0xA2, 0xBE, 0xC2 ),
    BYTES_TO_T_UINT( 0xA0, 0xAF, 0x05, 0xCE, 0x0A, 0x08, 0x72, 0x3C ),
    BYTES_TO_T_UINT( 0x0C, 0x15, 0x8C, 0x3D, 0xC6, 0x82, 0xC3, 0x7B ),
};
static t_uint brainpoolP384r1_b[] = {
    BYTES_TO_T_UINT( 0x11, 0x4C, 0x50, 0xFA, 0x96, 0x86, 0xB7, 0x3A ),
    BYTES_TO_T_UINT( 0x94, 0xC9, 0xDB, 0x95, 0x02, 0x39, 0xB4, 0x7C ),
    BYTES_TO_T_UINT( 0xD5, 0x62, 0xEB, 0x3E, 0xA5, 0x0E, 0x88, 0x2E ),
    BYTES_TO_T_UINT( 0xA6, 0xD2, 0xDC, 0x07, 0xE1, 0x7D, 0xB7, 0x2F ),
    BYTES_TO_T_UINT( 0x7C, 0x44, 0xF0, 0x16, 0x54, 0xB5, 0x39, 0x8B ),
    BYTES_TO_T_UINT( 0x26, 0x28, 0xCE, 0x22, 0xDD, 0xC7, 0xA8, 0x04 ),
};
static t_uint brainpoolP384r1_gx[] = {
    BYTES_TO_T_UINT( 0x1E, 0xAF, 0xD4, 0x47, 0xE2, 0xB2, 0x87, 0xEF ),
    BYTES_TO_T_UINT( 0xAA, 0x46, 0xD6, 0x36, 0x34, 0xE0, 0x26, 0xE8 ),
    BYTES_TO_T_UINT( 0xE8, 0x10, 0xBD, 0x0C, 0xFE, 0xCA, 0x7F, 0xDB ),
    BYTES_TO_T_UINT( 0xE3, 0x4F, 0xF1, 0x7E, 0xE7, 0xA3, 0x47, 0x88 ),
    BYTES_TO_T_UINT( 0x6B, 0x3F, 0xC1, 0xB7, 0x81, 0x3A, 0xA6, 0xA2 ),
    BYTES_TO_T_UINT( 0xFF, 0x45, 0xCF, 0x68, 0xF0, 0x64, 0x1C, 0x1D ),
};
static t_uint brainpoolP384r1_gy[] = {
    BYTES_TO_T_UINT( 0x15, 0x53, 0x3C, 0x26, 0x41, 0x03, 0x82, 0x42 ),
    BYTES_TO_T_UINT( 0x11, 0x81, 0x91, 0x77, 0x21, 0x46, 0x46, 0x0E ),
    BYTES_TO_T_UINT( 0x28, 0x29, 0x91, 0xF9, 0x4F, 0x05, 0x9C, 0xE1 ),
    BYTES_TO_T_UINT( 0x64, 0x58, 0xEC, 0xFE, 0x29, 0x0B, 0xB7, 0x62 ),
    BYTES_TO_T_UINT( 0x52, 0xD5, 0xCF, 0x95, 0x8E, 0xEB, 0xB1, 0x5C ),
    BYTES_TO_T_UINT( 0xA4, 0xC2, 0xF9, 0x20, 0x75, 0x1D, 0xBE, 0x8A ),
};
static t_uint brainpoolP384r1_n[] = {
    BYTES_TO_T_UINT( 0x65, 0x65, 0x04, 0xE9, 0x02, 0x32, 0x88, 0x3B ),
    BYTES_TO_T_UINT( 0x10, 0xC3, 0x7F, 0x6B, 0xAF, 0xB6, 0x3A, 0xCF ),
    BYTES_TO_T_UINT( 0xA7, 0x25, 0x04, 0xAC, 0x6C, 0x6E, 0x16, 0x1F ),
    BYTES_TO_T_UINT( 0xB3, 0x56, 0x54, 0xED, 0x09, 0x71, 0x2F, 0x15 ),
    BYTES_TO_T_UINT( 0xDF, 0x41, 0xE6, 0x50, 0x7E, 0x6F, 0x5D, 0x0F ),
    BYTES_TO_T_UINT( 0x28, 0x6D, 0x38, 0xA3, 0x82, 0x1E, 0xB9, 0x8C ),
};
389
#endif /* POLARSSL_ECP_DP_BP384R1_ENABLED */
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
390 391 392 393

/*
 * Domain parameters for brainpoolP512r1 (RFC 5639 3.7)
 */
394
#if defined(POLARSSL_ECP_DP_BP512R1_ENABLED)
395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454
static t_uint brainpoolP512r1_p[] = {
    BYTES_TO_T_UINT( 0xF3, 0x48, 0x3A, 0x58, 0x56, 0x60, 0xAA, 0x28 ),
    BYTES_TO_T_UINT( 0x85, 0xC6, 0x82, 0x2D, 0x2F, 0xFF, 0x81, 0x28 ),
    BYTES_TO_T_UINT( 0xE6, 0x80, 0xA3, 0xE6, 0x2A, 0xA1, 0xCD, 0xAE ),
    BYTES_TO_T_UINT( 0x42, 0x68, 0xC6, 0x9B, 0x00, 0x9B, 0x4D, 0x7D ),
    BYTES_TO_T_UINT( 0x71, 0x08, 0x33, 0x70, 0xCA, 0x9C, 0x63, 0xD6 ),
    BYTES_TO_T_UINT( 0x0E, 0xD2, 0xC9, 0xB3, 0xB3, 0x8D, 0x30, 0xCB ),
    BYTES_TO_T_UINT( 0x07, 0xFC, 0xC9, 0x33, 0xAE, 0xE6, 0xD4, 0x3F ),
    BYTES_TO_T_UINT( 0x8B, 0xC4, 0xE9, 0xDB, 0xB8, 0x9D, 0xDD, 0xAA ),
};
static t_uint brainpoolP512r1_a[] = {
    BYTES_TO_T_UINT( 0xCA, 0x94, 0xFC, 0x77, 0x4D, 0xAC, 0xC1, 0xE7 ),
    BYTES_TO_T_UINT( 0xB9, 0xC7, 0xF2, 0x2B, 0xA7, 0x17, 0x11, 0x7F ),
    BYTES_TO_T_UINT( 0xB5, 0xC8, 0x9A, 0x8B, 0xC9, 0xF1, 0x2E, 0x0A ),
    BYTES_TO_T_UINT( 0xA1, 0x3A, 0x25, 0xA8, 0x5A, 0x5D, 0xED, 0x2D ),
    BYTES_TO_T_UINT( 0xBC, 0x63, 0x98, 0xEA, 0xCA, 0x41, 0x34, 0xA8 ),
    BYTES_TO_T_UINT( 0x10, 0x16, 0xF9, 0x3D, 0x8D, 0xDD, 0xCB, 0x94 ),
    BYTES_TO_T_UINT( 0xC5, 0x4C, 0x23, 0xAC, 0x45, 0x71, 0x32, 0xE2 ),
    BYTES_TO_T_UINT( 0x89, 0x3B, 0x60, 0x8B, 0x31, 0xA3, 0x30, 0x78 ),
};
static t_uint brainpoolP512r1_b[] = {
    BYTES_TO_T_UINT( 0x23, 0xF7, 0x16, 0x80, 0x63, 0xBD, 0x09, 0x28 ),
    BYTES_TO_T_UINT( 0xDD, 0xE5, 0xBA, 0x5E, 0xB7, 0x50, 0x40, 0x98 ),
    BYTES_TO_T_UINT( 0x67, 0x3E, 0x08, 0xDC, 0xCA, 0x94, 0xFC, 0x77 ),
    BYTES_TO_T_UINT( 0x4D, 0xAC, 0xC1, 0xE7, 0xB9, 0xC7, 0xF2, 0x2B ),
    BYTES_TO_T_UINT( 0xA7, 0x17, 0x11, 0x7F, 0xB5, 0xC8, 0x9A, 0x8B ),
    BYTES_TO_T_UINT( 0xC9, 0xF1, 0x2E, 0x0A, 0xA1, 0x3A, 0x25, 0xA8 ),
    BYTES_TO_T_UINT( 0x5A, 0x5D, 0xED, 0x2D, 0xBC, 0x63, 0x98, 0xEA ),
    BYTES_TO_T_UINT( 0xCA, 0x41, 0x34, 0xA8, 0x10, 0x16, 0xF9, 0x3D ),
};
static t_uint brainpoolP512r1_gx[] = {
    BYTES_TO_T_UINT( 0x22, 0xF8, 0xB9, 0xBC, 0x09, 0x22, 0x35, 0x8B ),
    BYTES_TO_T_UINT( 0x68, 0x5E, 0x6A, 0x40, 0x47, 0x50, 0x6D, 0x7C ),
    BYTES_TO_T_UINT( 0x5F, 0x7D, 0xB9, 0x93, 0x7B, 0x68, 0xD1, 0x50 ),
    BYTES_TO_T_UINT( 0x8D, 0xD4, 0xD0, 0xE2, 0x78, 0x1F, 0x3B, 0xFF ),
    BYTES_TO_T_UINT( 0x8E, 0x09, 0xD0, 0xF4, 0xEE, 0x62, 0x3B, 0xB4 ),
    BYTES_TO_T_UINT( 0xC1, 0x16, 0xD9, 0xB5, 0x70, 0x9F, 0xED, 0x85 ),
    BYTES_TO_T_UINT( 0x93, 0x6A, 0x4C, 0x9C, 0x2E, 0x32, 0x21, 0x5A ),
    BYTES_TO_T_UINT( 0x64, 0xD9, 0x2E, 0xD8, 0xBD, 0xE4, 0xAE, 0x81 ),
};
static t_uint brainpoolP512r1_gy[] = {
    BYTES_TO_T_UINT( 0x92, 0x08, 0xD8, 0x3A, 0x0F, 0x1E, 0xCD, 0x78 ),
    BYTES_TO_T_UINT( 0x06, 0x54, 0xF0, 0xA8, 0x2F, 0x2B, 0xCA, 0xD1 ),
    BYTES_TO_T_UINT( 0xAE, 0x63, 0x27, 0x8A, 0xD8, 0x4B, 0xCA, 0x5B ),
    BYTES_TO_T_UINT( 0x5E, 0x48, 0x5F, 0x4A, 0x49, 0xDE, 0xDC, 0xB2 ),
    BYTES_TO_T_UINT( 0x11, 0x81, 0x1F, 0x88, 0x5B, 0xC5, 0x00, 0xA0 ),
    BYTES_TO_T_UINT( 0x1A, 0x7B, 0xA5, 0x24, 0x00, 0xF7, 0x09, 0xF2 ),
    BYTES_TO_T_UINT( 0xFD, 0x22, 0x78, 0xCF, 0xA9, 0xBF, 0xEA, 0xC0 ),
    BYTES_TO_T_UINT( 0xEC, 0x32, 0x63, 0x56, 0x5D, 0x38, 0xDE, 0x7D ),
};
static t_uint brainpoolP512r1_n[] = {
    BYTES_TO_T_UINT( 0x69, 0x00, 0xA9, 0x9C, 0x82, 0x96, 0x87, 0xB5 ),
    BYTES_TO_T_UINT( 0xDD, 0xDA, 0x5D, 0x08, 0x81, 0xD3, 0xB1, 0x1D ),
    BYTES_TO_T_UINT( 0x47, 0x10, 0xAC, 0x7F, 0x19, 0x61, 0x86, 0x41 ),
    BYTES_TO_T_UINT( 0x19, 0x26, 0xA9, 0x4C, 0x41, 0x5C, 0x3E, 0x55 ),
    BYTES_TO_T_UINT( 0x70, 0x08, 0x33, 0x70, 0xCA, 0x9C, 0x63, 0xD6 ),
    BYTES_TO_T_UINT( 0x0E, 0xD2, 0xC9, 0xB3, 0xB3, 0x8D, 0x30, 0xCB ),
    BYTES_TO_T_UINT( 0x07, 0xFC, 0xC9, 0x33, 0xAE, 0xE6, 0xD4, 0x3F ),
    BYTES_TO_T_UINT( 0x8B, 0xC4, 0xE9, 0xDB, 0xB8, 0x9D, 0xDD, 0xAA ),
};
455
#endif /* POLARSSL_ECP_DP_BP512R1_ENABLED */
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
456 457

/*
458 459
 * Create an MPI from embedded constants
 * (assumes len is an exact multiple of sizeof t_uint)
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
460
 */
461 462 463 464 465 466 467
static inline void ecp_mpi_load( mpi *X, const t_uint *p, size_t len )
{
    X->s = 1;
    X->n = len / sizeof( t_uint );
    X->p = (t_uint *) p;
}

468 469 470 471 472 473 474 475 476 477 478
/*
 * Set an MPI to static value 1
 */
static inline void ecp_mpi_set1( mpi *X )
{
    static t_uint one[] = { 1 };
    X->s = 1;
    X->n = 1;
    X->p = one;
}

479 480 481 482 483 484 485 486 487 488
/*
 * Make group available from embedded constants
 */
static int ecp_group_load( ecp_group *grp,
                           const t_uint *p,  size_t plen,
                           const t_uint *a,  size_t alen,
                           const t_uint *b,  size_t blen,
                           const t_uint *gx, size_t gxlen,
                           const t_uint *gy, size_t gylen,
                           const t_uint *n,  size_t nlen)
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
489
{
490
    ecp_mpi_load( &grp->P, p, plen );
491
    if( a != NULL )
492 493 494
        ecp_mpi_load( &grp->A, a, alen );
    ecp_mpi_load( &grp->B, b, blen );
    ecp_mpi_load( &grp->N, n, nlen );
495

496 497
    ecp_mpi_load( &grp->G.X, gx, gxlen );
    ecp_mpi_load( &grp->G.Y, gy, gylen );
498
    ecp_mpi_set1( &grp->G.Z );
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
499 500 501 502

    grp->pbits = mpi_msb( &grp->P );
    grp->nbits = mpi_msb( &grp->N );

503 504
    grp->h = 1;

505
    return( 0 );
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
506 507 508 509
}

#if defined(POLARSSL_ECP_NIST_OPTIM)
/* Forward declarations */
510
#if defined(POLARSSL_ECP_DP_SECP192R1_ENABLED)
511
static int ecp_mod_p192( mpi * );
512 513
#endif
#if defined(POLARSSL_ECP_DP_SECP224R1_ENABLED)
514
static int ecp_mod_p224( mpi * );
515 516
#endif
#if defined(POLARSSL_ECP_DP_SECP256R1_ENABLED)
517
static int ecp_mod_p256( mpi * );
518 519
#endif
#if defined(POLARSSL_ECP_DP_SECP384R1_ENABLED)
520
static int ecp_mod_p384( mpi * );
521 522
#endif
#if defined(POLARSSL_ECP_DP_SECP521R1_ENABLED)
523
static int ecp_mod_p521( mpi * );
524 525 526 527
#endif
#if defined(POLARSSL_ECP_DP_M255_ENABLED)
static int ecp_mod_p255( mpi * );
#endif
528 529 530 531

#define NIST_MODP( P )      grp->modp = ecp_mod_ ## P;
#else
#define NIST_MODP( P )
532
#endif /* POLARSSL_ECP_NIST_OPTIM */
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
533

534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549
#define LOAD_GROUP_A( G )   ecp_group_load( grp,            \
                            G ## _p,  sizeof( G ## _p  ),   \
                            G ## _a,  sizeof( G ## _a  ),   \
                            G ## _b,  sizeof( G ## _b  ),   \
                            G ## _gx, sizeof( G ## _gx ),   \
                            G ## _gy, sizeof( G ## _gy ),   \
                            G ## _n,  sizeof( G ## _n  ) )

#define LOAD_GROUP( G )     ecp_group_load( grp,            \
                            G ## _p,  sizeof( G ## _p  ),   \
                            NULL,     0,                    \
                            G ## _b,  sizeof( G ## _b  ),   \
                            G ## _gx, sizeof( G ## _gx ),   \
                            G ## _gy, sizeof( G ## _gy ),   \
                            G ## _n,  sizeof( G ## _n  ) )

550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565
/*
 * Specialized function for creating the Curve25519 group
 */
static int ecp_use_curve25519( ecp_group *grp )
{
    int ret;

    /* Actually ( A + 2 ) / 4 */
    MPI_CHK( mpi_read_string( &grp->A, 16, "01DB42" ) );

    /* P = 2^255 - 19 */
    MPI_CHK( mpi_lset( &grp->P, 1 ) );
    MPI_CHK( mpi_shift_l( &grp->P, 255 ) );
    MPI_CHK( mpi_sub_int( &grp->P, &grp->P, 19 ) );
    grp->pbits = mpi_msb( &grp->P );

566 567 568 569 570 571
    /* Y intentionaly not set, since we use x/z coordinates.
     * This is used as a marker to identify Montgomery curves! */
    MPI_CHK( mpi_lset( &grp->G.X, 9 ) );
    MPI_CHK( mpi_lset( &grp->G.Z, 1 ) );
    mpi_free( &grp->G.Y );

572 573 574 575 576 577 578 579 580 581
    /* Actually, the required msb for private keys */
    grp->nbits = 254;

cleanup:
    if( ret != 0 )
        ecp_group_free( grp );

    return( ret );
}

Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
582 583 584 585 586
/*
 * Set a group using well-known domain parameters
 */
int ecp_use_known_dp( ecp_group *grp, ecp_group_id id )
{
587 588
    ecp_group_free( grp );

Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
589 590 591 592 593 594
    grp->id = id;

    switch( id )
    {
#if defined(POLARSSL_ECP_DP_SECP192R1_ENABLED)
        case POLARSSL_ECP_DP_SECP192R1:
595
            NIST_MODP( p192 );
596
            return( LOAD_GROUP( secp192r1 ) );
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
597 598 599 600
#endif /* POLARSSL_ECP_DP_SECP192R1_ENABLED */

#if defined(POLARSSL_ECP_DP_SECP224R1_ENABLED)
        case POLARSSL_ECP_DP_SECP224R1:
601
            NIST_MODP( p224 );
602
            return( LOAD_GROUP( secp224r1 ) );
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
603 604 605 606
#endif /* POLARSSL_ECP_DP_SECP224R1_ENABLED */

#if defined(POLARSSL_ECP_DP_SECP256R1_ENABLED)
        case POLARSSL_ECP_DP_SECP256R1:
607
            NIST_MODP( p256 );
608
            return( LOAD_GROUP( secp256r1 ) );
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
609 610 611 612
#endif /* POLARSSL_ECP_DP_SECP256R1_ENABLED */

#if defined(POLARSSL_ECP_DP_SECP384R1_ENABLED)
        case POLARSSL_ECP_DP_SECP384R1:
613
            NIST_MODP( p384 );
614
            return( LOAD_GROUP( secp384r1 ) );
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
615 616 617 618
#endif /* POLARSSL_ECP_DP_SECP384R1_ENABLED */

#if defined(POLARSSL_ECP_DP_SECP521R1_ENABLED)
        case POLARSSL_ECP_DP_SECP521R1:
619
            NIST_MODP( p521 );
620
            return( LOAD_GROUP( secp521r1 ) );
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
621 622 623 624
#endif /* POLARSSL_ECP_DP_SECP521R1_ENABLED */

#if defined(POLARSSL_ECP_DP_BP256R1_ENABLED)
        case POLARSSL_ECP_DP_BP256R1:
625
            return( LOAD_GROUP_A( brainpoolP256r1 ) );
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
626 627 628 629
#endif /* POLARSSL_ECP_DP_BP256R1_ENABLED */

#if defined(POLARSSL_ECP_DP_BP384R1_ENABLED)
        case POLARSSL_ECP_DP_BP384R1:
630
            return( LOAD_GROUP_A( brainpoolP384r1 ) );
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
631 632 633 634
#endif /* POLARSSL_ECP_DP_BP384R1_ENABLED */

#if defined(POLARSSL_ECP_DP_BP512R1_ENABLED)
        case POLARSSL_ECP_DP_BP512R1:
635
            return( LOAD_GROUP_A( brainpoolP512r1 ) );
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
636 637
#endif /* POLARSSL_ECP_DP_BP512R1_ENABLED */

638 639
#if defined(POLARSSL_ECP_DP_M255_ENABLED)
        case POLARSSL_ECP_DP_M255:
640
            grp->modp = ecp_mod_p255;
641 642 643
            return( ecp_use_curve25519( grp ) );
#endif /* POLARSSL_ECP_DP_M255_ENABLED */

Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706
        default:
            ecp_group_free( grp );
            return( POLARSSL_ERR_ECP_FEATURE_UNAVAILABLE );
    }
}

#if defined(POLARSSL_ECP_NIST_OPTIM)
/*
 * Fast reduction modulo the primes used by the NIST curves.
 *
 * These functions are critical for speed, but not needed for correct
 * operations. So, we make the choice to heavily rely on the internals of our
 * bignum library, which creates a tight coupling between these functions and
 * our MPI implementation.  However, the coupling between the ECP module and
 * MPI remains loose, since these functions can be deactivated at will.
 */

#if defined(POLARSSL_ECP_DP_SECP192R1_ENABLED)
/*
 * Compared to the way things are presented in FIPS 186-3 D.2,
 * we proceed in columns, from right (least significant chunk) to left,
 * adding chunks to N in place, and keeping a carry for the next chunk.
 * This avoids moving things around in memory, and uselessly adding zeros,
 * compared to the more straightforward, line-oriented approach.
 *
 * For this prime we need to handle data in chunks of 64 bits.
 * Since this is always a multiple of our basic t_uint, we can
 * use a t_uint * to designate such a chunk, and small loops to handle it.
 */

/* Add 64-bit chunks (dst += src) and update carry */
static inline void add64( t_uint *dst, t_uint *src, t_uint *carry )
{
    unsigned char i;
    t_uint c = 0;
    for( i = 0; i < 8 / sizeof( t_uint ); i++, dst++, src++ )
    {
        *dst += c;      c  = ( *dst < c );
        *dst += *src;   c += ( *dst < *src );
    }
    *carry += c;
}

/* Add carry to a 64-bit chunk and update carry */
static inline void carry64( t_uint *dst, t_uint *carry )
{
    unsigned char i;
    for( i = 0; i < 8 / sizeof( t_uint ); i++, dst++ )
    {
        *dst += *carry;
        *carry  = ( *dst < *carry );
    }
}

#define WIDTH       8 / sizeof( t_uint )
#define A( i )      N->p + i * WIDTH
#define ADD( i )    add64( p, A( i ), &c )
#define NEXT        p += WIDTH; carry64( p, &c )
#define LAST        p += WIDTH; *p = c; while( ++p < end ) *p = 0

/*
 * Fast quasi-reduction modulo p192 (FIPS 186-3 D.2.1)
 */
707
static int ecp_mod_p192( mpi *N )
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877
{
    int ret;
    t_uint c = 0;
    t_uint *p, *end;

    /* Make sure we have enough blocks so that A(5) is legal */
    MPI_CHK( mpi_grow( N, 6 * WIDTH ) );

    p = N->p;
    end = p + N->n;

    ADD( 3 ); ADD( 5 );             NEXT; // A0 += A3 + A5
    ADD( 3 ); ADD( 4 ); ADD( 5 );   NEXT; // A1 += A3 + A4 + A5
    ADD( 4 ); ADD( 5 );             LAST; // A2 += A4 + A5

cleanup:
    return( ret );
}

#undef WIDTH
#undef A
#undef ADD
#undef NEXT
#undef LAST
#endif /* POLARSSL_ECP_DP_SECP192R1_ENABLED */

#if defined(POLARSSL_ECP_DP_SECP224R1_ENABLED) ||   \
    defined(POLARSSL_ECP_DP_SECP256R1_ENABLED) ||   \
    defined(POLARSSL_ECP_DP_SECP384R1_ENABLED)
/*
 * The reader is advised to first understand ecp_mod_p192() since the same
 * general structure is used here, but with additional complications:
 * (1) chunks of 32 bits, and (2) subtractions.
 */

/*
 * For these primes, we need to handle data in chunks of 32 bits.
 * This makes it more complicated if we use 64 bits limbs in MPI,
 * which prevents us from using a uniform access method as for p192.
 *
 * So, we define a mini abstraction layer to access 32 bit chunks,
 * load them in 'cur' for work, and store them back from 'cur' when done.
 *
 * While at it, also define the size of N in terms of 32-bit chunks.
 */
#define LOAD32      cur = A( i );

#if defined(POLARSSL_HAVE_INT8)     /* 8 bit */

#define MAX32       N->n / 4
#define A( j )      (uint32_t)( N->p[4*j+0]       ) |  \
                              ( N->p[4*j+1] << 8  ) |  \
                              ( N->p[4*j+2] << 16 ) |  \
                              ( N->p[4*j+3] << 24 )
#define STORE32     N->p[4*i+0] = (t_uint)( cur       );   \
                    N->p[4*i+1] = (t_uint)( cur >> 8  );   \
                    N->p[4*i+2] = (t_uint)( cur >> 16 );   \
                    N->p[4*i+3] = (t_uint)( cur >> 24 );

#elif defined(POLARSSL_HAVE_INT16)  /* 16 bit */

#define MAX32       N->n / 2
#define A( j )      (uint32_t)( N->p[2*j] ) | ( N->p[2*j+1] << 16 )
#define STORE32     N->p[2*i+0] = (t_uint)( cur       );  \
                    N->p[2*i+1] = (t_uint)( cur >> 16 );

#elif defined(POLARSSL_HAVE_INT32)  /* 32 bit */

#define MAX32       N->n
#define A( j )      N->p[j]
#define STORE32     N->p[i] = cur;

#else                               /* 64-bit */

#define MAX32       N->n * 2
#define A( j ) j % 2 ? (uint32_t)( N->p[j/2] >> 32 ) : (uint32_t)( N->p[j/2] )
#define STORE32                                   \
    if( i % 2 ) {                                 \
        N->p[i/2] &= 0x00000000FFFFFFFF;          \
        N->p[i/2] |= ((t_uint) cur) << 32;        \
    } else {                                      \
        N->p[i/2] &= 0xFFFFFFFF00000000;          \
        N->p[i/2] |= (t_uint) cur;                \
    }

#endif /* sizeof( t_uint ) */

/*
 * Helpers for addition and subtraction of chunks, with signed carry.
 */
static inline void add32( uint32_t *dst, uint32_t src, signed char *carry )
{
    *dst += src;
    *carry += ( *dst < src );
}

static inline void sub32( uint32_t *dst, uint32_t src, signed char *carry )
{
    *carry -= ( *dst < src );
    *dst -= src;
}

#define ADD( j )    add32( &cur, A( j ), &c );
#define SUB( j )    sub32( &cur, A( j ), &c );

/*
 * Helpers for the main 'loop'
 * (see fix_negative for the motivation of C)
 */
#define INIT( b )                                           \
    int ret;                                                \
    signed char c = 0, cc;                                  \
    uint32_t cur;                                           \
    size_t i = 0, bits = b;                                 \
    mpi C;                                                  \
    t_uint Cp[ b / 8 / sizeof( t_uint) + 1 ];               \
                                                            \
    C.s = 1;                                                \
    C.n = b / 8 / sizeof( t_uint) + 1;                      \
    C.p = Cp;                                               \
    memset( Cp, 0, C.n * sizeof( t_uint ) );                \
                                                            \
    MPI_CHK( mpi_grow( N, b * 2 / 8 / sizeof( t_uint ) ) ); \
    LOAD32;

#define NEXT                    \
    STORE32; i++; LOAD32;       \
    cc = c; c = 0;              \
    if( cc < 0 )                \
        sub32( &cur, -cc, &c ); \
    else                        \
        add32( &cur, cc, &c );  \

#define LAST                                    \
    STORE32; i++;                               \
    cur = c > 0 ? c : 0; STORE32;               \
    cur = 0; while( ++i < MAX32 ) { STORE32; }  \
    if( c < 0 ) fix_negative( N, c, &C, bits );

/*
 * If the result is negative, we get it in the form
 * c * 2^(bits + 32) + N, with c negative and N positive shorter than 'bits'
 */
static inline int fix_negative( mpi *N, signed char c, mpi *C, size_t bits )
{
    int ret;

    /* C = - c * 2^(bits + 32) */
#if !defined(POLARSSL_HAVE_INT64)
    ((void) bits);
#else
    if( bits == 224 )
        C->p[ C->n - 1 ] = ((t_uint) -c) << 32;
    else
#endif
        C->p[ C->n - 1 ] = (t_uint) -c;

    /* N = - ( C - N ) */
    MPI_CHK( mpi_sub_abs( N, C, N ) );
    N->s = -1;

cleanup:

    return( ret );
}

#if defined(POLARSSL_ECP_DP_SECP224R1_ENABLED)
/*
 * Fast quasi-reduction modulo p224 (FIPS 186-3 D.2.2)
 */
878
static int ecp_mod_p224( mpi *N )
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898
{
    INIT( 224 );

    SUB(  7 ); SUB( 11 );               NEXT; // A0 += -A7 - A11
    SUB(  8 ); SUB( 12 );               NEXT; // A1 += -A8 - A12
    SUB(  9 ); SUB( 13 );               NEXT; // A2 += -A9 - A13
    SUB( 10 ); ADD(  7 ); ADD( 11 );    NEXT; // A3 += -A10 + A7 + A11
    SUB( 11 ); ADD(  8 ); ADD( 12 );    NEXT; // A4 += -A11 + A8 + A12
    SUB( 12 ); ADD(  9 ); ADD( 13 );    NEXT; // A5 += -A12 + A9 + A13
    SUB( 13 ); ADD( 10 );               LAST; // A6 += -A13 + A10

cleanup:
    return( ret );
}
#endif /* POLARSSL_ECP_DP_SECP224R1_ENABLED */

#if defined(POLARSSL_ECP_DP_SECP256R1_ENABLED)
/*
 * Fast quasi-reduction modulo p256 (FIPS 186-3 D.2.3)
 */
899
static int ecp_mod_p256( mpi *N )
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935
{
    INIT( 256 );

    ADD(  8 ); ADD(  9 );
    SUB( 11 ); SUB( 12 ); SUB( 13 ); SUB( 14 );             NEXT; // A0

    ADD(  9 ); ADD( 10 );
    SUB( 12 ); SUB( 13 ); SUB( 14 ); SUB( 15 );             NEXT; // A1

    ADD( 10 ); ADD( 11 );
    SUB( 13 ); SUB( 14 ); SUB( 15 );                        NEXT; // A2

    ADD( 11 ); ADD( 11 ); ADD( 12 ); ADD( 12 ); ADD( 13 );
    SUB( 15 ); SUB(  8 ); SUB(  9 );                        NEXT; // A3

    ADD( 12 ); ADD( 12 ); ADD( 13 ); ADD( 13 ); ADD( 14 );
    SUB(  9 ); SUB( 10 );                                   NEXT; // A4

    ADD( 13 ); ADD( 13 ); ADD( 14 ); ADD( 14 ); ADD( 15 );
    SUB( 10 ); SUB( 11 );                                   NEXT; // A5

    ADD( 14 ); ADD( 14 ); ADD( 15 ); ADD( 15 ); ADD( 14 ); ADD( 13 );
    SUB(  8 ); SUB(  9 );                                   NEXT; // A6

    ADD( 15 ); ADD( 15 ); ADD( 15 ); ADD( 8 );
    SUB( 10 ); SUB( 11 ); SUB( 12 ); SUB( 13 );             LAST; // A7

cleanup:
    return( ret );
}
#endif /* POLARSSL_ECP_DP_SECP256R1_ENABLED */

#if defined(POLARSSL_ECP_DP_SECP384R1_ENABLED)
/*
 * Fast quasi-reduction modulo p384 (FIPS 186-3 D.2.4)
 */
936
static int ecp_mod_p384( mpi *N )
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012
{
    INIT( 384 );

    ADD( 12 ); ADD( 21 ); ADD( 20 );
    SUB( 23 );                                              NEXT; // A0

    ADD( 13 ); ADD( 22 ); ADD( 23 );
    SUB( 12 ); SUB( 20 );                                   NEXT; // A2

    ADD( 14 ); ADD( 23 );
    SUB( 13 ); SUB( 21 );                                   NEXT; // A2

    ADD( 15 ); ADD( 12 ); ADD( 20 ); ADD( 21 );
    SUB( 14 ); SUB( 22 ); SUB( 23 );                        NEXT; // A3

    ADD( 21 ); ADD( 21 ); ADD( 16 ); ADD( 13 ); ADD( 12 ); ADD( 20 ); ADD( 22 );
    SUB( 15 ); SUB( 23 ); SUB( 23 );                        NEXT; // A4

    ADD( 22 ); ADD( 22 ); ADD( 17 ); ADD( 14 ); ADD( 13 ); ADD( 21 ); ADD( 23 );
    SUB( 16 );                                              NEXT; // A5

    ADD( 23 ); ADD( 23 ); ADD( 18 ); ADD( 15 ); ADD( 14 ); ADD( 22 );
    SUB( 17 );                                              NEXT; // A6

    ADD( 19 ); ADD( 16 ); ADD( 15 ); ADD( 23 );
    SUB( 18 );                                              NEXT; // A7

    ADD( 20 ); ADD( 17 ); ADD( 16 );
    SUB( 19 );                                              NEXT; // A8

    ADD( 21 ); ADD( 18 ); ADD( 17 );
    SUB( 20 );                                              NEXT; // A9

    ADD( 22 ); ADD( 19 ); ADD( 18 );
    SUB( 21 );                                              NEXT; // A10

    ADD( 23 ); ADD( 20 ); ADD( 19 );
    SUB( 22 );                                              LAST; // A11

cleanup:
    return( ret );
}
#endif /* POLARSSL_ECP_DP_SECP384R1_ENABLED */

#undef A
#undef LOAD32
#undef STORE32
#undef MAX32
#undef INIT
#undef NEXT
#undef LAST

#endif /* POLARSSL_ECP_DP_SECP224R1_ENABLED ||
          POLARSSL_ECP_DP_SECP256R1_ENABLED ||
          POLARSSL_ECP_DP_SECP384R1_ENABLED */

#if defined(POLARSSL_ECP_DP_SECP521R1_ENABLED)
/*
 * Here we have an actual Mersenne prime, so things are more straightforward.
 * However, chunks are aligned on a 'weird' boundary (521 bits).
 */

/* Size of p521 in terms of t_uint */
#define P521_WIDTH      ( 521 / 8 / sizeof( t_uint ) + 1 )

/* Bits to keep in the most significant t_uint */
#if defined(POLARSSL_HAVE_INT8)
#define P521_MASK       0x01
#else
#define P521_MASK       0x01FF
#endif

/*
 * Fast quasi-reduction modulo p521 (FIPS 186-3 D.2.5)
 * Write N as A1 + 2^521 A0, return A0 + A1
 */
1013
static int ecp_mod_p521( mpi *N )
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052
{
    int ret;
    size_t i;
    mpi M;
    t_uint Mp[P521_WIDTH + 1];
    /* Worst case for the size of M is when t_uint is 16 bits:
     * we need to hold bits 513 to 1056, which is 34 limbs, that is
     * P521_WIDTH + 1. Otherwise P521_WIDTH is enough. */

    if( N->n < P521_WIDTH )
        return( 0 );

    /* M = A1 */
    M.s = 1;
    M.n = N->n - ( P521_WIDTH - 1 );
    if( M.n > P521_WIDTH + 1 )
        M.n = P521_WIDTH + 1;
    M.p = Mp;
    memcpy( Mp, N->p + P521_WIDTH - 1, M.n * sizeof( t_uint ) );
    MPI_CHK( mpi_shift_r( &M, 521 % ( 8 * sizeof( t_uint ) ) ) );

    /* N = A0 */
    N->p[P521_WIDTH - 1] &= P521_MASK;
    for( i = P521_WIDTH; i < N->n; i++ )
        N->p[i] = 0;

    /* N = A0 + A1 */
    MPI_CHK( mpi_add_abs( N, N, &M ) );

cleanup:
    return( ret );
}

#undef P521_WIDTH
#undef P521_MASK
#endif /* POLARSSL_ECP_DP_SECP521R1_ENABLED */

#endif /* POLARSSL_ECP_NIST_OPTIM */

1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096
#if defined(POLARSSL_ECP_DP_M255_ENABLED)

/* Size of p255 in terms of t_uint */
#define P255_WIDTH      ( 255 / 8 / sizeof( t_uint ) + 1 )

/*
 * Fast quasi-reduction modulo p255 = 2^255 - 19
 * Write N as A1 + 2^255 A1, return A0 + 19 * A1
 */
static int ecp_mod_p255( mpi *N )
{
    int ret;
    size_t i;
    mpi M;
    t_uint Mp[P255_WIDTH + 2];

    if( N->n < P255_WIDTH )
        return( 0 );

    /* M = A1 */
    M.s = 1;
    M.n = N->n - ( P255_WIDTH - 1 );
    if( M.n > P255_WIDTH + 1 )
        M.n = P255_WIDTH + 1;
    M.p = Mp;
    memset( Mp, 0, sizeof Mp );
    memcpy( Mp, N->p + P255_WIDTH - 1, M.n * sizeof( t_uint ) );
    MPI_CHK( mpi_shift_r( &M, 255 % ( 8 * sizeof( t_uint ) ) ) );
    M.n++; /* Make room for multiplication by 19 */

    /* N = A0 */
    mpi_set_bit( N, 255, 0 );
    for( i = P255_WIDTH; i < N->n; i++ )
        N->p[i] = 0;

    /* N = A0 + 19 * A1 */
    MPI_CHK( mpi_mul_int( &M, &M, 19 ) );
    MPI_CHK( mpi_add_abs( N, N, &M ) );

cleanup:
    return( ret );
}
#endif /* POLARSSL_ECP_DP_M255_ENABLED */

Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
1097
#endif