ecp_curves.c 43.7 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
/*
 * Conversion macros for embedded constants:
42
 * build lists of t_uint's from lists of unsigned char's grouped by 8, 4 or 2
43
 */
44 45
#if defined(POLARSSL_HAVE_INT8)

Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
46
#define BYTES_TO_T_UINT_8( a, b, c, d, e, f, g, h ) \
47 48
    a, b, c, d, e, f, g, h

49 50 51 52 53 54
#define BYTES_TO_T_UINT_4( a, b, c, d )             \
    a, b, c, d

#define BYTES_TO_T_UINT_2( a, b )                   \
    a, b

55 56
#elif defined(POLARSSL_HAVE_INT16)

Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
57 58
#define BYTES_TO_T_UINT_2( a, b )                   \
    ( (t_uint) a << 0 ) |                           \
59
    ( (t_uint) b << 8 )
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
60

61 62 63 64
#define BYTES_TO_T_UINT_4( a, b, c, d )             \
    BYTES_TO_T_UINT_2( a, b ),                      \
    BYTES_TO_T_UINT_2( c, d )

Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
65 66 67 68 69
#define BYTES_TO_T_UINT_8( a, b, c, d, e, f, g, h ) \
    BYTES_TO_T_UINT_2( a, b ),                      \
    BYTES_TO_T_UINT_2( c, d ),                      \
    BYTES_TO_T_UINT_2( e, f ),                      \
    BYTES_TO_T_UINT_2( g, h )
70 71 72

#elif defined(POLARSSL_HAVE_INT32)

Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
73 74 75 76
#define BYTES_TO_T_UINT_4( a, b, c, d )             \
    ( (t_uint) a <<  0 ) |                          \
    ( (t_uint) b <<  8 ) |                          \
    ( (t_uint) c << 16 ) |                          \
77
    ( (t_uint) d << 24 )
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
78

79 80 81
#define BYTES_TO_T_UINT_2( a, b )                   \
    BYTES_TO_T_UINT_4( a, b, 0, 0 )

Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
82
#define BYTES_TO_T_UINT_8( a, b, c, d, e, f, g, h ) \
83
    BYTES_TO_T_UINT_4( a, b, c, d ),                \
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
84
    BYTES_TO_T_UINT_4( e, f, g, h )
85 86 87

#else /* 64-bits */

Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
88
#define BYTES_TO_T_UINT_8( a, b, c, d, e, f, g, h ) \
89 90 91 92 93 94 95 96 97
    ( (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 )

98 99 100 101 102 103
#define BYTES_TO_T_UINT_4( a, b, c, d )             \
    BYTES_TO_T_UINT_8( a, b, c, d, 0, 0, 0, 0 )

#define BYTES_TO_T_UINT_2( a, b )                   \
    BYTES_TO_T_UINT_8( a, b, 0, 0, 0, 0, 0, 0 )

104 105
#endif /* bits in t_uint */

106 107 108 109 110
/*
 * Note: the constants are in little-endian order
 * to be directly usable in MPIs
 */

Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
111 112 113
/*
 * Domain parameters for secp192r1
 */
114
#if defined(POLARSSL_ECP_DP_SECP192R1_ENABLED)
115
static t_uint secp192r1_p[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
116 117 118
    BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
119 120
};
static t_uint secp192r1_b[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
121 122 123
    BYTES_TO_T_UINT_8( 0xB1, 0xB9, 0x46, 0xC1, 0xEC, 0xDE, 0xB8, 0xFE ),
    BYTES_TO_T_UINT_8( 0x49, 0x30, 0x24, 0x72, 0xAB, 0xE9, 0xA7, 0x0F ),
    BYTES_TO_T_UINT_8( 0xE7, 0x80, 0x9C, 0xE5, 0x19, 0x05, 0x21, 0x64 ),
124 125
};
static t_uint secp192r1_gx[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
126 127 128
    BYTES_TO_T_UINT_8( 0x12, 0x10, 0xFF, 0x82, 0xFD, 0x0A, 0xFF, 0xF4 ),
    BYTES_TO_T_UINT_8( 0x00, 0x88, 0xA1, 0x43, 0xEB, 0x20, 0xBF, 0x7C ),
    BYTES_TO_T_UINT_8( 0xF6, 0x90, 0x30, 0xB0, 0x0E, 0xA8, 0x8D, 0x18 ),
129 130
};
static t_uint secp192r1_gy[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
131 132 133
    BYTES_TO_T_UINT_8( 0x11, 0x48, 0x79, 0x1E, 0xA1, 0x77, 0xF9, 0x73 ),
    BYTES_TO_T_UINT_8( 0xD5, 0xCD, 0x24, 0x6B, 0xED, 0x11, 0x10, 0x63 ),
    BYTES_TO_T_UINT_8( 0x78, 0xDA, 0xC8, 0xFF, 0x95, 0x2B, 0x19, 0x07 ),
134 135
};
static t_uint secp192r1_n[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
136 137 138
    BYTES_TO_T_UINT_8( 0x31, 0x28, 0xD2, 0xB4, 0xB1, 0xC9, 0x6B, 0x14 ),
    BYTES_TO_T_UINT_8( 0x36, 0xF8, 0xDE, 0x99, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
139
};
140
#endif /* POLARSSL_ECP_DP_SECP192R1_ENABLED */
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
141 142 143 144

/*
 * Domain parameters for secp224r1
 */
145
#if defined(POLARSSL_ECP_DP_SECP224R1_ENABLED)
146
static t_uint secp224r1_p[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
147 148 149 150
    BYTES_TO_T_UINT_8( 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ),
    BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ),
151 152
};
static t_uint secp224r1_b[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
153 154 155
    BYTES_TO_T_UINT_8( 0xB4, 0xFF, 0x55, 0x23, 0x43, 0x39, 0x0B, 0x27 ),
    BYTES_TO_T_UINT_8( 0xBA, 0xD8, 0xBF, 0xD7, 0xB7, 0xB0, 0x44, 0x50 ),
    BYTES_TO_T_UINT_8( 0x56, 0x32, 0x41, 0xF5, 0xAB, 0xB3, 0x04, 0x0C ),
156
    BYTES_TO_T_UINT_4( 0x85, 0x0A, 0x05, 0xB4 ),
157 158
};
static t_uint secp224r1_gx[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
159 160 161
    BYTES_TO_T_UINT_8( 0x21, 0x1D, 0x5C, 0x11, 0xD6, 0x80, 0x32, 0x34 ),
    BYTES_TO_T_UINT_8( 0x22, 0x11, 0xC2, 0x56, 0xD3, 0xC1, 0x03, 0x4A ),
    BYTES_TO_T_UINT_8( 0xB9, 0x90, 0x13, 0x32, 0x7F, 0xBF, 0xB4, 0x6B ),
162
    BYTES_TO_T_UINT_4( 0xBD, 0x0C, 0x0E, 0xB7 ),
163 164
};
static t_uint secp224r1_gy[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
165 166 167
    BYTES_TO_T_UINT_8( 0x34, 0x7E, 0x00, 0x85, 0x99, 0x81, 0xD5, 0x44 ),
    BYTES_TO_T_UINT_8( 0x64, 0x47, 0x07, 0x5A, 0xA0, 0x75, 0x43, 0xCD ),
    BYTES_TO_T_UINT_8( 0xE6, 0xDF, 0x22, 0x4C, 0xFB, 0x23, 0xF7, 0xB5 ),
168
    BYTES_TO_T_UINT_4( 0x88, 0x63, 0x37, 0xBD ),
169 170
};
static t_uint secp224r1_n[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
171 172 173
    BYTES_TO_T_UINT_8( 0x3D, 0x2A, 0x5C, 0x5C, 0x45, 0x29, 0xDD, 0x13 ),
    BYTES_TO_T_UINT_8( 0x3E, 0xF0, 0xB8, 0xE0, 0xA2, 0x16, 0xFF, 0xFF ),
    BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
174
    BYTES_TO_T_UINT_4( 0xFF, 0xFF, 0xFF, 0xFF ),
175
};
176
#endif /* POLARSSL_ECP_DP_SECP224R1_ENABLED */
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
177 178 179 180

/*
 * Domain parameters for secp256r1
 */
181
#if defined(POLARSSL_ECP_DP_SECP256R1_ENABLED)
182
static t_uint secp256r1_p[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
183 184 185 186
    BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ),
    BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ),
    BYTES_TO_T_UINT_8( 0x01, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ),
187 188
};
static t_uint secp256r1_b[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
189 190 191 192
    BYTES_TO_T_UINT_8( 0x4B, 0x60, 0xD2, 0x27, 0x3E, 0x3C, 0xCE, 0x3B ),
    BYTES_TO_T_UINT_8( 0xF6, 0xB0, 0x53, 0xCC, 0xB0, 0x06, 0x1D, 0x65 ),
    BYTES_TO_T_UINT_8( 0xBC, 0x86, 0x98, 0x76, 0x55, 0xBD, 0xEB, 0xB3 ),
    BYTES_TO_T_UINT_8( 0xE7, 0x93, 0x3A, 0xAA, 0xD8, 0x35, 0xC6, 0x5A ),
193 194
};
static t_uint secp256r1_gx[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
195 196 197 198
    BYTES_TO_T_UINT_8( 0x96, 0xC2, 0x98, 0xD8, 0x45, 0x39, 0xA1, 0xF4 ),
    BYTES_TO_T_UINT_8( 0xA0, 0x33, 0xEB, 0x2D, 0x81, 0x7D, 0x03, 0x77 ),
    BYTES_TO_T_UINT_8( 0xF2, 0x40, 0xA4, 0x63, 0xE5, 0xE6, 0xBC, 0xF8 ),
    BYTES_TO_T_UINT_8( 0x47, 0x42, 0x2C, 0xE1, 0xF2, 0xD1, 0x17, 0x6B ),
199 200
};
static t_uint secp256r1_gy[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
201 202 203 204
    BYTES_TO_T_UINT_8( 0xF5, 0x51, 0xBF, 0x37, 0x68, 0x40, 0xB6, 0xCB ),
    BYTES_TO_T_UINT_8( 0xCE, 0x5E, 0x31, 0x6B, 0x57, 0x33, 0xCE, 0x2B ),
    BYTES_TO_T_UINT_8( 0x16, 0x9E, 0x0F, 0x7C, 0x4A, 0xEB, 0xE7, 0x8E ),
    BYTES_TO_T_UINT_8( 0x9B, 0x7F, 0x1A, 0xFE, 0xE2, 0x42, 0xE3, 0x4F ),
205 206
};
static t_uint secp256r1_n[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
207 208 209 210
    BYTES_TO_T_UINT_8( 0x51, 0x25, 0x63, 0xFC, 0xC2, 0xCA, 0xB9, 0xF3 ),
    BYTES_TO_T_UINT_8( 0x84, 0x9E, 0x17, 0xA7, 0xAD, 0xFA, 0xE6, 0xBC ),
    BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ),
211
};
212
#endif /* POLARSSL_ECP_DP_SECP256R1_ENABLED */
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
213 214 215 216

/*
 * Domain parameters for secp384r1
 */
217
#if defined(POLARSSL_ECP_DP_SECP384R1_ENABLED)
218
static t_uint secp384r1_p[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
219 220 221 222 223 224
    BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ),
    BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
225 226
};
static t_uint secp384r1_b[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
227 228 229 230 231 232
    BYTES_TO_T_UINT_8( 0xEF, 0x2A, 0xEC, 0xD3, 0xED, 0xC8, 0x85, 0x2A ),
    BYTES_TO_T_UINT_8( 0x9D, 0xD1, 0x2E, 0x8A, 0x8D, 0x39, 0x56, 0xC6 ),
    BYTES_TO_T_UINT_8( 0x5A, 0x87, 0x13, 0x50, 0x8F, 0x08, 0x14, 0x03 ),
    BYTES_TO_T_UINT_8( 0x12, 0x41, 0x81, 0xFE, 0x6E, 0x9C, 0x1D, 0x18 ),
    BYTES_TO_T_UINT_8( 0x19, 0x2D, 0xF8, 0xE3, 0x6B, 0x05, 0x8E, 0x98 ),
    BYTES_TO_T_UINT_8( 0xE4, 0xE7, 0x3E, 0xE2, 0xA7, 0x2F, 0x31, 0xB3 ),
233 234
};
static t_uint secp384r1_gx[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
235 236 237 238 239 240
    BYTES_TO_T_UINT_8( 0xB7, 0x0A, 0x76, 0x72, 0x38, 0x5E, 0x54, 0x3A ),
    BYTES_TO_T_UINT_8( 0x6C, 0x29, 0x55, 0xBF, 0x5D, 0xF2, 0x02, 0x55 ),
    BYTES_TO_T_UINT_8( 0x38, 0x2A, 0x54, 0x82, 0xE0, 0x41, 0xF7, 0x59 ),
    BYTES_TO_T_UINT_8( 0x98, 0x9B, 0xA7, 0x8B, 0x62, 0x3B, 0x1D, 0x6E ),
    BYTES_TO_T_UINT_8( 0x74, 0xAD, 0x20, 0xF3, 0x1E, 0xC7, 0xB1, 0x8E ),
    BYTES_TO_T_UINT_8( 0x37, 0x05, 0x8B, 0xBE, 0x22, 0xCA, 0x87, 0xAA ),
241 242
};
static t_uint secp384r1_gy[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
243 244 245 246 247 248
    BYTES_TO_T_UINT_8( 0x5F, 0x0E, 0xEA, 0x90, 0x7C, 0x1D, 0x43, 0x7A ),
    BYTES_TO_T_UINT_8( 0x9D, 0x81, 0x7E, 0x1D, 0xCE, 0xB1, 0x60, 0x0A ),
    BYTES_TO_T_UINT_8( 0xC0, 0xB8, 0xF0, 0xB5, 0x13, 0x31, 0xDA, 0xE9 ),
    BYTES_TO_T_UINT_8( 0x7C, 0x14, 0x9A, 0x28, 0xBD, 0x1D, 0xF4, 0xF8 ),
    BYTES_TO_T_UINT_8( 0x29, 0xDC, 0x92, 0x92, 0xBF, 0x98, 0x9E, 0x5D ),
    BYTES_TO_T_UINT_8( 0x6F, 0x2C, 0x26, 0x96, 0x4A, 0xDE, 0x17, 0x36 ),
249 250
};
static t_uint secp384r1_n[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
251 252 253 254 255 256
    BYTES_TO_T_UINT_8( 0x73, 0x29, 0xC5, 0xCC, 0x6A, 0x19, 0xEC, 0xEC ),
    BYTES_TO_T_UINT_8( 0x7A, 0xA7, 0xB0, 0x48, 0xB2, 0x0D, 0x1A, 0x58 ),
    BYTES_TO_T_UINT_8( 0xDF, 0x2D, 0x37, 0xF4, 0x81, 0x4D, 0x63, 0xC7 ),
    BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
257
};
258
#endif /* POLARSSL_ECP_DP_SECP384R1_ENABLED */
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
259 260 261 262

/*
 * Domain parameters for secp521r1
 */
263
#if defined(POLARSSL_ECP_DP_SECP521R1_ENABLED)
264
static t_uint secp521r1_p[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
265 266 267 268 269 270 271 272
    BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
273
    BYTES_TO_T_UINT_2( 0xFF, 0x01 ),
274 275
};
static t_uint secp521r1_b[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
276 277 278 279 280 281 282 283
    BYTES_TO_T_UINT_8( 0x00, 0x3F, 0x50, 0x6B, 0xD4, 0x1F, 0x45, 0xEF ),
    BYTES_TO_T_UINT_8( 0xF1, 0x34, 0x2C, 0x3D, 0x88, 0xDF, 0x73, 0x35 ),
    BYTES_TO_T_UINT_8( 0x07, 0xBF, 0xB1, 0x3B, 0xBD, 0xC0, 0x52, 0x16 ),
    BYTES_TO_T_UINT_8( 0x7B, 0x93, 0x7E, 0xEC, 0x51, 0x39, 0x19, 0x56 ),
    BYTES_TO_T_UINT_8( 0xE1, 0x09, 0xF1, 0x8E, 0x91, 0x89, 0xB4, 0xB8 ),
    BYTES_TO_T_UINT_8( 0xF3, 0x15, 0xB3, 0x99, 0x5B, 0x72, 0xDA, 0xA2 ),
    BYTES_TO_T_UINT_8( 0xEE, 0x40, 0x85, 0xB6, 0xA0, 0x21, 0x9A, 0x92 ),
    BYTES_TO_T_UINT_8( 0x1F, 0x9A, 0x1C, 0x8E, 0x61, 0xB9, 0x3E, 0x95 ),
284
    BYTES_TO_T_UINT_2( 0x51, 0x00 ),
285 286
};
static t_uint secp521r1_gx[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
287 288 289 290 291 292 293 294
    BYTES_TO_T_UINT_8( 0x66, 0xBD, 0xE5, 0xC2, 0x31, 0x7E, 0x7E, 0xF9 ),
    BYTES_TO_T_UINT_8( 0x9B, 0x42, 0x6A, 0x85, 0xC1, 0xB3, 0x48, 0x33 ),
    BYTES_TO_T_UINT_8( 0xDE, 0xA8, 0xFF, 0xA2, 0x27, 0xC1, 0x1D, 0xFE ),
    BYTES_TO_T_UINT_8( 0x28, 0x59, 0xE7, 0xEF, 0x77, 0x5E, 0x4B, 0xA1 ),
    BYTES_TO_T_UINT_8( 0xBA, 0x3D, 0x4D, 0x6B, 0x60, 0xAF, 0x28, 0xF8 ),
    BYTES_TO_T_UINT_8( 0x21, 0xB5, 0x3F, 0x05, 0x39, 0x81, 0x64, 0x9C ),
    BYTES_TO_T_UINT_8( 0x42, 0xB4, 0x95, 0x23, 0x66, 0xCB, 0x3E, 0x9E ),
    BYTES_TO_T_UINT_8( 0xCD, 0xE9, 0x04, 0x04, 0xB7, 0x06, 0x8E, 0x85 ),
295
    BYTES_TO_T_UINT_2( 0xC6, 0x00 ),
296 297
};
static t_uint secp521r1_gy[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
298 299 300 301 302 303 304 305
    BYTES_TO_T_UINT_8( 0x50, 0x66, 0xD1, 0x9F, 0x76, 0x94, 0xBE, 0x88 ),
    BYTES_TO_T_UINT_8( 0x40, 0xC2, 0x72, 0xA2, 0x86, 0x70, 0x3C, 0x35 ),
    BYTES_TO_T_UINT_8( 0x61, 0x07, 0xAD, 0x3F, 0x01, 0xB9, 0x50, 0xC5 ),
    BYTES_TO_T_UINT_8( 0x40, 0x26, 0xF4, 0x5E, 0x99, 0x72, 0xEE, 0x97 ),
    BYTES_TO_T_UINT_8( 0x2C, 0x66, 0x3E, 0x27, 0x17, 0xBD, 0xAF, 0x17 ),
    BYTES_TO_T_UINT_8( 0x68, 0x44, 0x9B, 0x57, 0x49, 0x44, 0xF5, 0x98 ),
    BYTES_TO_T_UINT_8( 0xD9, 0x1B, 0x7D, 0x2C, 0xB4, 0x5F, 0x8A, 0x5C ),
    BYTES_TO_T_UINT_8( 0x04, 0xC0, 0x3B, 0x9A, 0x78, 0x6A, 0x29, 0x39 ),
306
    BYTES_TO_T_UINT_2( 0x18, 0x01 ),
307 308
};
static t_uint secp521r1_n[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
309 310 311 312 313 314 315 316
    BYTES_TO_T_UINT_8( 0x09, 0x64, 0x38, 0x91, 0x1E, 0xB7, 0x6F, 0xBB ),
    BYTES_TO_T_UINT_8( 0xAE, 0x47, 0x9C, 0x89, 0xB8, 0xC9, 0xB5, 0x3B ),
    BYTES_TO_T_UINT_8( 0xD0, 0xA5, 0x09, 0xF7, 0x48, 0x01, 0xCC, 0x7F ),
    BYTES_TO_T_UINT_8( 0x6B, 0x96, 0x2F, 0xBF, 0x83, 0x87, 0x86, 0x51 ),
    BYTES_TO_T_UINT_8( 0xFA, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
317
    BYTES_TO_T_UINT_2( 0xFF, 0x01 ),
318
};
319
#endif /* POLARSSL_ECP_DP_SECP521R1_ENABLED */
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
320

321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353
#if defined(POLARSSL_ECP_DP_SECP256K1_ENABLED)
static t_uint secp256k1_p[] = {
    BYTES_TO_T_UINT_8( 0x2F, 0xFC, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
};
static t_uint secp256k1_a[] = {
    BYTES_TO_T_UINT_2( 0x00, 0x00 ),
};
static t_uint secp256k1_b[] = {
    BYTES_TO_T_UINT_2( 0x07, 0x00 ),
};
static t_uint secp256k1_gx[] = {
    BYTES_TO_T_UINT_8( 0x98, 0x17, 0xF8, 0x16, 0x5B, 0x81, 0xF2, 0x59 ),
    BYTES_TO_T_UINT_8( 0xD9, 0x28, 0xCE, 0x2D, 0xDB, 0xFC, 0x9B, 0x02 ),
    BYTES_TO_T_UINT_8( 0x07, 0x0B, 0x87, 0xCE, 0x95, 0x62, 0xA0, 0x55 ),
    BYTES_TO_T_UINT_8( 0xAC, 0xBB, 0xDC, 0xF9, 0x7E, 0x66, 0xBE, 0x79 ),
};
static t_uint secp256k1_gy[] = {
    BYTES_TO_T_UINT_8( 0xB8, 0xD4, 0x10, 0xFB, 0x8F, 0xD0, 0x47, 0x9C ),
    BYTES_TO_T_UINT_8( 0x19, 0x54, 0x85, 0xA6, 0x48, 0xB4, 0x17, 0xFD ),
    BYTES_TO_T_UINT_8( 0xA8, 0x08, 0x11, 0x0E, 0xFC, 0xFB, 0xA4, 0x5D ),
    BYTES_TO_T_UINT_8( 0x65, 0xC4, 0xA3, 0x26, 0x77, 0xDA, 0x3A, 0x48 ),
};
static t_uint secp256k1_n[] = {
    BYTES_TO_T_UINT_8( 0x41, 0x41, 0x36, 0xD0, 0x8C, 0x5E, 0xD2, 0xBF ),
    BYTES_TO_T_UINT_8( 0x3B, 0xA0, 0x48, 0xAF, 0xE6, 0xDC, 0xAE, 0xBA ),
    BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
    BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
};
#endif /* POLARSSL_ECP_DP_SECP256K1_ENABLED */

Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
354 355 356
/*
 * Domain parameters for brainpoolP256r1 (RFC 5639 3.4)
 */
357
#if defined(POLARSSL_ECP_DP_BP256R1_ENABLED)
358
static t_uint brainpoolP256r1_p[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
359 360 361 362
    BYTES_TO_T_UINT_8( 0x77, 0x53, 0x6E, 0x1F, 0x1D, 0x48, 0x13, 0x20 ),
    BYTES_TO_T_UINT_8( 0x28, 0x20, 0x26, 0xD5, 0x23, 0xF6, 0x3B, 0x6E ),
    BYTES_TO_T_UINT_8( 0x72, 0x8D, 0x83, 0x9D, 0x90, 0x0A, 0x66, 0x3E ),
    BYTES_TO_T_UINT_8( 0xBC, 0xA9, 0xEE, 0xA1, 0xDB, 0x57, 0xFB, 0xA9 ),
363 364
};
static t_uint brainpoolP256r1_a[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
365 366 367 368
    BYTES_TO_T_UINT_8( 0xD9, 0xB5, 0x30, 0xF3, 0x44, 0x4B, 0x4A, 0xE9 ),
    BYTES_TO_T_UINT_8( 0x6C, 0x5C, 0xDC, 0x26, 0xC1, 0x55, 0x80, 0xFB ),
    BYTES_TO_T_UINT_8( 0xE7, 0xFF, 0x7A, 0x41, 0x30, 0x75, 0xF6, 0xEE ),
    BYTES_TO_T_UINT_8( 0x57, 0x30, 0x2C, 0xFC, 0x75, 0x09, 0x5A, 0x7D ),
369 370
};
static t_uint brainpoolP256r1_b[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
371 372 373 374
    BYTES_TO_T_UINT_8( 0xB6, 0x07, 0x8C, 0xFF, 0x18, 0xDC, 0xCC, 0x6B ),
    BYTES_TO_T_UINT_8( 0xCE, 0xE1, 0xF7, 0x5C, 0x29, 0x16, 0x84, 0x95 ),
    BYTES_TO_T_UINT_8( 0xBF, 0x7C, 0xD7, 0xBB, 0xD9, 0xB5, 0x30, 0xF3 ),
    BYTES_TO_T_UINT_8( 0x44, 0x4B, 0x4A, 0xE9, 0x6C, 0x5C, 0xDC, 0x26 ),
375 376
};
static t_uint brainpoolP256r1_gx[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
377 378 379 380
    BYTES_TO_T_UINT_8( 0x62, 0x32, 0xCE, 0x9A, 0xBD, 0x53, 0x44, 0x3A ),
    BYTES_TO_T_UINT_8( 0xC2, 0x23, 0xBD, 0xE3, 0xE1, 0x27, 0xDE, 0xB9 ),
    BYTES_TO_T_UINT_8( 0xAF, 0xB7, 0x81, 0xFC, 0x2F, 0x48, 0x4B, 0x2C ),
    BYTES_TO_T_UINT_8( 0xCB, 0x57, 0x7E, 0xCB, 0xB9, 0xAE, 0xD2, 0x8B ),
381 382
};
static t_uint brainpoolP256r1_gy[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
383 384 385 386
    BYTES_TO_T_UINT_8( 0x97, 0x69, 0x04, 0x2F, 0xC7, 0x54, 0x1D, 0x5C ),
    BYTES_TO_T_UINT_8( 0x54, 0x8E, 0xED, 0x2D, 0x13, 0x45, 0x77, 0xC2 ),
    BYTES_TO_T_UINT_8( 0xC9, 0x1D, 0x61, 0x14, 0x1A, 0x46, 0xF8, 0x97 ),
    BYTES_TO_T_UINT_8( 0xFD, 0xC4, 0xDA, 0xC3, 0x35, 0xF8, 0x7E, 0x54 ),
387 388
};
static t_uint brainpoolP256r1_n[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
389 390 391 392
    BYTES_TO_T_UINT_8( 0xA7, 0x56, 0x48, 0x97, 0x82, 0x0E, 0x1E, 0x90 ),
    BYTES_TO_T_UINT_8( 0xF7, 0xA6, 0x61, 0xB5, 0xA3, 0x7A, 0x39, 0x8C ),
    BYTES_TO_T_UINT_8( 0x71, 0x8D, 0x83, 0x9D, 0x90, 0x0A, 0x66, 0x3E ),
    BYTES_TO_T_UINT_8( 0xBC, 0xA9, 0xEE, 0xA1, 0xDB, 0x57, 0xFB, 0xA9 ),
393
};
394
#endif /* POLARSSL_ECP_DP_BP256R1_ENABLED */
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
395 396 397 398

/*
 * Domain parameters for brainpoolP384r1 (RFC 5639 3.6)
 */
399
#if defined(POLARSSL_ECP_DP_BP384R1_ENABLED)
400
static t_uint brainpoolP384r1_p[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
401 402 403 404 405 406
    BYTES_TO_T_UINT_8( 0x53, 0xEC, 0x07, 0x31, 0x13, 0x00, 0x47, 0x87 ),
    BYTES_TO_T_UINT_8( 0x71, 0x1A, 0x1D, 0x90, 0x29, 0xA7, 0xD3, 0xAC ),
    BYTES_TO_T_UINT_8( 0x23, 0x11, 0xB7, 0x7F, 0x19, 0xDA, 0xB1, 0x12 ),
    BYTES_TO_T_UINT_8( 0xB4, 0x56, 0x54, 0xED, 0x09, 0x71, 0x2F, 0x15 ),
    BYTES_TO_T_UINT_8( 0xDF, 0x41, 0xE6, 0x50, 0x7E, 0x6F, 0x5D, 0x0F ),
    BYTES_TO_T_UINT_8( 0x28, 0x6D, 0x38, 0xA3, 0x82, 0x1E, 0xB9, 0x8C ),
407 408
};
static t_uint brainpoolP384r1_a[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
409 410 411 412 413 414
    BYTES_TO_T_UINT_8( 0x26, 0x28, 0xCE, 0x22, 0xDD, 0xC7, 0xA8, 0x04 ),
    BYTES_TO_T_UINT_8( 0xEB, 0xD4, 0x3A, 0x50, 0x4A, 0x81, 0xA5, 0x8A ),
    BYTES_TO_T_UINT_8( 0x0F, 0xF9, 0x91, 0xBA, 0xEF, 0x65, 0x91, 0x13 ),
    BYTES_TO_T_UINT_8( 0x87, 0x27, 0xB2, 0x4F, 0x8E, 0xA2, 0xBE, 0xC2 ),
    BYTES_TO_T_UINT_8( 0xA0, 0xAF, 0x05, 0xCE, 0x0A, 0x08, 0x72, 0x3C ),
    BYTES_TO_T_UINT_8( 0x0C, 0x15, 0x8C, 0x3D, 0xC6, 0x82, 0xC3, 0x7B ),
415 416
};
static t_uint brainpoolP384r1_b[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
417 418 419 420 421 422
    BYTES_TO_T_UINT_8( 0x11, 0x4C, 0x50, 0xFA, 0x96, 0x86, 0xB7, 0x3A ),
    BYTES_TO_T_UINT_8( 0x94, 0xC9, 0xDB, 0x95, 0x02, 0x39, 0xB4, 0x7C ),
    BYTES_TO_T_UINT_8( 0xD5, 0x62, 0xEB, 0x3E, 0xA5, 0x0E, 0x88, 0x2E ),
    BYTES_TO_T_UINT_8( 0xA6, 0xD2, 0xDC, 0x07, 0xE1, 0x7D, 0xB7, 0x2F ),
    BYTES_TO_T_UINT_8( 0x7C, 0x44, 0xF0, 0x16, 0x54, 0xB5, 0x39, 0x8B ),
    BYTES_TO_T_UINT_8( 0x26, 0x28, 0xCE, 0x22, 0xDD, 0xC7, 0xA8, 0x04 ),
423 424
};
static t_uint brainpoolP384r1_gx[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
425 426 427 428 429 430
    BYTES_TO_T_UINT_8( 0x1E, 0xAF, 0xD4, 0x47, 0xE2, 0xB2, 0x87, 0xEF ),
    BYTES_TO_T_UINT_8( 0xAA, 0x46, 0xD6, 0x36, 0x34, 0xE0, 0x26, 0xE8 ),
    BYTES_TO_T_UINT_8( 0xE8, 0x10, 0xBD, 0x0C, 0xFE, 0xCA, 0x7F, 0xDB ),
    BYTES_TO_T_UINT_8( 0xE3, 0x4F, 0xF1, 0x7E, 0xE7, 0xA3, 0x47, 0x88 ),
    BYTES_TO_T_UINT_8( 0x6B, 0x3F, 0xC1, 0xB7, 0x81, 0x3A, 0xA6, 0xA2 ),
    BYTES_TO_T_UINT_8( 0xFF, 0x45, 0xCF, 0x68, 0xF0, 0x64, 0x1C, 0x1D ),
431 432
};
static t_uint brainpoolP384r1_gy[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
433 434 435 436 437 438
    BYTES_TO_T_UINT_8( 0x15, 0x53, 0x3C, 0x26, 0x41, 0x03, 0x82, 0x42 ),
    BYTES_TO_T_UINT_8( 0x11, 0x81, 0x91, 0x77, 0x21, 0x46, 0x46, 0x0E ),
    BYTES_TO_T_UINT_8( 0x28, 0x29, 0x91, 0xF9, 0x4F, 0x05, 0x9C, 0xE1 ),
    BYTES_TO_T_UINT_8( 0x64, 0x58, 0xEC, 0xFE, 0x29, 0x0B, 0xB7, 0x62 ),
    BYTES_TO_T_UINT_8( 0x52, 0xD5, 0xCF, 0x95, 0x8E, 0xEB, 0xB1, 0x5C ),
    BYTES_TO_T_UINT_8( 0xA4, 0xC2, 0xF9, 0x20, 0x75, 0x1D, 0xBE, 0x8A ),
439 440
};
static t_uint brainpoolP384r1_n[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
441 442 443 444 445 446
    BYTES_TO_T_UINT_8( 0x65, 0x65, 0x04, 0xE9, 0x02, 0x32, 0x88, 0x3B ),
    BYTES_TO_T_UINT_8( 0x10, 0xC3, 0x7F, 0x6B, 0xAF, 0xB6, 0x3A, 0xCF ),
    BYTES_TO_T_UINT_8( 0xA7, 0x25, 0x04, 0xAC, 0x6C, 0x6E, 0x16, 0x1F ),
    BYTES_TO_T_UINT_8( 0xB3, 0x56, 0x54, 0xED, 0x09, 0x71, 0x2F, 0x15 ),
    BYTES_TO_T_UINT_8( 0xDF, 0x41, 0xE6, 0x50, 0x7E, 0x6F, 0x5D, 0x0F ),
    BYTES_TO_T_UINT_8( 0x28, 0x6D, 0x38, 0xA3, 0x82, 0x1E, 0xB9, 0x8C ),
447
};
448
#endif /* POLARSSL_ECP_DP_BP384R1_ENABLED */
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
449 450 451 452

/*
 * Domain parameters for brainpoolP512r1 (RFC 5639 3.7)
 */
453
#if defined(POLARSSL_ECP_DP_BP512R1_ENABLED)
454
static t_uint brainpoolP512r1_p[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
455 456 457 458 459 460 461 462
    BYTES_TO_T_UINT_8( 0xF3, 0x48, 0x3A, 0x58, 0x56, 0x60, 0xAA, 0x28 ),
    BYTES_TO_T_UINT_8( 0x85, 0xC6, 0x82, 0x2D, 0x2F, 0xFF, 0x81, 0x28 ),
    BYTES_TO_T_UINT_8( 0xE6, 0x80, 0xA3, 0xE6, 0x2A, 0xA1, 0xCD, 0xAE ),
    BYTES_TO_T_UINT_8( 0x42, 0x68, 0xC6, 0x9B, 0x00, 0x9B, 0x4D, 0x7D ),
    BYTES_TO_T_UINT_8( 0x71, 0x08, 0x33, 0x70, 0xCA, 0x9C, 0x63, 0xD6 ),
    BYTES_TO_T_UINT_8( 0x0E, 0xD2, 0xC9, 0xB3, 0xB3, 0x8D, 0x30, 0xCB ),
    BYTES_TO_T_UINT_8( 0x07, 0xFC, 0xC9, 0x33, 0xAE, 0xE6, 0xD4, 0x3F ),
    BYTES_TO_T_UINT_8( 0x8B, 0xC4, 0xE9, 0xDB, 0xB8, 0x9D, 0xDD, 0xAA ),
463 464
};
static t_uint brainpoolP512r1_a[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
465 466 467 468 469 470 471 472
    BYTES_TO_T_UINT_8( 0xCA, 0x94, 0xFC, 0x77, 0x4D, 0xAC, 0xC1, 0xE7 ),
    BYTES_TO_T_UINT_8( 0xB9, 0xC7, 0xF2, 0x2B, 0xA7, 0x17, 0x11, 0x7F ),
    BYTES_TO_T_UINT_8( 0xB5, 0xC8, 0x9A, 0x8B, 0xC9, 0xF1, 0x2E, 0x0A ),
    BYTES_TO_T_UINT_8( 0xA1, 0x3A, 0x25, 0xA8, 0x5A, 0x5D, 0xED, 0x2D ),
    BYTES_TO_T_UINT_8( 0xBC, 0x63, 0x98, 0xEA, 0xCA, 0x41, 0x34, 0xA8 ),
    BYTES_TO_T_UINT_8( 0x10, 0x16, 0xF9, 0x3D, 0x8D, 0xDD, 0xCB, 0x94 ),
    BYTES_TO_T_UINT_8( 0xC5, 0x4C, 0x23, 0xAC, 0x45, 0x71, 0x32, 0xE2 ),
    BYTES_TO_T_UINT_8( 0x89, 0x3B, 0x60, 0x8B, 0x31, 0xA3, 0x30, 0x78 ),
473 474
};
static t_uint brainpoolP512r1_b[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
475 476 477 478 479 480 481 482
    BYTES_TO_T_UINT_8( 0x23, 0xF7, 0x16, 0x80, 0x63, 0xBD, 0x09, 0x28 ),
    BYTES_TO_T_UINT_8( 0xDD, 0xE5, 0xBA, 0x5E, 0xB7, 0x50, 0x40, 0x98 ),
    BYTES_TO_T_UINT_8( 0x67, 0x3E, 0x08, 0xDC, 0xCA, 0x94, 0xFC, 0x77 ),
    BYTES_TO_T_UINT_8( 0x4D, 0xAC, 0xC1, 0xE7, 0xB9, 0xC7, 0xF2, 0x2B ),
    BYTES_TO_T_UINT_8( 0xA7, 0x17, 0x11, 0x7F, 0xB5, 0xC8, 0x9A, 0x8B ),
    BYTES_TO_T_UINT_8( 0xC9, 0xF1, 0x2E, 0x0A, 0xA1, 0x3A, 0x25, 0xA8 ),
    BYTES_TO_T_UINT_8( 0x5A, 0x5D, 0xED, 0x2D, 0xBC, 0x63, 0x98, 0xEA ),
    BYTES_TO_T_UINT_8( 0xCA, 0x41, 0x34, 0xA8, 0x10, 0x16, 0xF9, 0x3D ),
483 484
};
static t_uint brainpoolP512r1_gx[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
485 486 487 488 489 490 491 492
    BYTES_TO_T_UINT_8( 0x22, 0xF8, 0xB9, 0xBC, 0x09, 0x22, 0x35, 0x8B ),
    BYTES_TO_T_UINT_8( 0x68, 0x5E, 0x6A, 0x40, 0x47, 0x50, 0x6D, 0x7C ),
    BYTES_TO_T_UINT_8( 0x5F, 0x7D, 0xB9, 0x93, 0x7B, 0x68, 0xD1, 0x50 ),
    BYTES_TO_T_UINT_8( 0x8D, 0xD4, 0xD0, 0xE2, 0x78, 0x1F, 0x3B, 0xFF ),
    BYTES_TO_T_UINT_8( 0x8E, 0x09, 0xD0, 0xF4, 0xEE, 0x62, 0x3B, 0xB4 ),
    BYTES_TO_T_UINT_8( 0xC1, 0x16, 0xD9, 0xB5, 0x70, 0x9F, 0xED, 0x85 ),
    BYTES_TO_T_UINT_8( 0x93, 0x6A, 0x4C, 0x9C, 0x2E, 0x32, 0x21, 0x5A ),
    BYTES_TO_T_UINT_8( 0x64, 0xD9, 0x2E, 0xD8, 0xBD, 0xE4, 0xAE, 0x81 ),
493 494
};
static t_uint brainpoolP512r1_gy[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
495 496 497 498 499 500 501 502
    BYTES_TO_T_UINT_8( 0x92, 0x08, 0xD8, 0x3A, 0x0F, 0x1E, 0xCD, 0x78 ),
    BYTES_TO_T_UINT_8( 0x06, 0x54, 0xF0, 0xA8, 0x2F, 0x2B, 0xCA, 0xD1 ),
    BYTES_TO_T_UINT_8( 0xAE, 0x63, 0x27, 0x8A, 0xD8, 0x4B, 0xCA, 0x5B ),
    BYTES_TO_T_UINT_8( 0x5E, 0x48, 0x5F, 0x4A, 0x49, 0xDE, 0xDC, 0xB2 ),
    BYTES_TO_T_UINT_8( 0x11, 0x81, 0x1F, 0x88, 0x5B, 0xC5, 0x00, 0xA0 ),
    BYTES_TO_T_UINT_8( 0x1A, 0x7B, 0xA5, 0x24, 0x00, 0xF7, 0x09, 0xF2 ),
    BYTES_TO_T_UINT_8( 0xFD, 0x22, 0x78, 0xCF, 0xA9, 0xBF, 0xEA, 0xC0 ),
    BYTES_TO_T_UINT_8( 0xEC, 0x32, 0x63, 0x56, 0x5D, 0x38, 0xDE, 0x7D ),
503 504
};
static t_uint brainpoolP512r1_n[] = {
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
505 506 507 508 509 510 511 512
    BYTES_TO_T_UINT_8( 0x69, 0x00, 0xA9, 0x9C, 0x82, 0x96, 0x87, 0xB5 ),
    BYTES_TO_T_UINT_8( 0xDD, 0xDA, 0x5D, 0x08, 0x81, 0xD3, 0xB1, 0x1D ),
    BYTES_TO_T_UINT_8( 0x47, 0x10, 0xAC, 0x7F, 0x19, 0x61, 0x86, 0x41 ),
    BYTES_TO_T_UINT_8( 0x19, 0x26, 0xA9, 0x4C, 0x41, 0x5C, 0x3E, 0x55 ),
    BYTES_TO_T_UINT_8( 0x70, 0x08, 0x33, 0x70, 0xCA, 0x9C, 0x63, 0xD6 ),
    BYTES_TO_T_UINT_8( 0x0E, 0xD2, 0xC9, 0xB3, 0xB3, 0x8D, 0x30, 0xCB ),
    BYTES_TO_T_UINT_8( 0x07, 0xFC, 0xC9, 0x33, 0xAE, 0xE6, 0xD4, 0x3F ),
    BYTES_TO_T_UINT_8( 0x8B, 0xC4, 0xE9, 0xDB, 0xB8, 0x9D, 0xDD, 0xAA ),
513
};
514
#endif /* POLARSSL_ECP_DP_BP512R1_ENABLED */
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
515 516

/*
517 518
 * 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
519
 */
520 521 522 523 524 525 526
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;
}

527 528 529 530 531 532 533 534 535 536 537
/*
 * 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;
}

538 539 540 541 542 543 544 545 546 547
/*
 * 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
548
{
549
    ecp_mpi_load( &grp->P, p, plen );
550
    if( a != NULL )
551 552 553
        ecp_mpi_load( &grp->A, a, alen );
    ecp_mpi_load( &grp->B, b, blen );
    ecp_mpi_load( &grp->N, n, nlen );
554

555 556
    ecp_mpi_load( &grp->G.X, gx, gxlen );
    ecp_mpi_load( &grp->G.Y, gy, gylen );
557
    ecp_mpi_set1( &grp->G.Z );
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
558 559 560 561

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

562 563
    grp->h = 1;

564
    return( 0 );
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
565 566 567 568
}

#if defined(POLARSSL_ECP_NIST_OPTIM)
/* Forward declarations */
569
#if defined(POLARSSL_ECP_DP_SECP192R1_ENABLED)
570
static int ecp_mod_p192( mpi * );
571 572
#endif
#if defined(POLARSSL_ECP_DP_SECP224R1_ENABLED)
573
static int ecp_mod_p224( mpi * );
574 575
#endif
#if defined(POLARSSL_ECP_DP_SECP256R1_ENABLED)
576
static int ecp_mod_p256( mpi * );
577 578
#endif
#if defined(POLARSSL_ECP_DP_SECP384R1_ENABLED)
579
static int ecp_mod_p384( mpi * );
580 581
#endif
#if defined(POLARSSL_ECP_DP_SECP521R1_ENABLED)
582
static int ecp_mod_p521( mpi * );
583 584 585 586
#endif
#if defined(POLARSSL_ECP_DP_M255_ENABLED)
static int ecp_mod_p255( mpi * );
#endif
587 588 589 590

#define NIST_MODP( P )      grp->modp = ecp_mod_ ## P;
#else
#define NIST_MODP( P )
591
#endif /* POLARSSL_ECP_NIST_OPTIM */
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
592

593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608
#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  ) )

609
#if defined(POLARSSL_ECP_DP_M255_ENABLED)
610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625
/*
 * 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 );

626 627 628 629 630 631
    /* 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 );

632 633 634 635 636 637 638 639 640
    /* Actually, the required msb for private keys */
    grp->nbits = 254;

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

    return( ret );
}
641
#endif /* POLARSSL_ECP_DP_M255_ENABLED */
642

Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
643 644 645 646 647
/*
 * Set a group using well-known domain parameters
 */
int ecp_use_known_dp( ecp_group *grp, ecp_group_id id )
{
648 649
    ecp_group_free( grp );

Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
650 651 652 653 654 655
    grp->id = id;

    switch( id )
    {
#if defined(POLARSSL_ECP_DP_SECP192R1_ENABLED)
        case POLARSSL_ECP_DP_SECP192R1:
656
            NIST_MODP( p192 );
657
            return( LOAD_GROUP( secp192r1 ) );
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
658 659 660 661
#endif /* POLARSSL_ECP_DP_SECP192R1_ENABLED */

#if defined(POLARSSL_ECP_DP_SECP224R1_ENABLED)
        case POLARSSL_ECP_DP_SECP224R1:
662
            NIST_MODP( p224 );
663
            return( LOAD_GROUP( secp224r1 ) );
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
664 665 666 667
#endif /* POLARSSL_ECP_DP_SECP224R1_ENABLED */

#if defined(POLARSSL_ECP_DP_SECP256R1_ENABLED)
        case POLARSSL_ECP_DP_SECP256R1:
668
            NIST_MODP( p256 );
669
            return( LOAD_GROUP( secp256r1 ) );
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
670 671 672 673
#endif /* POLARSSL_ECP_DP_SECP256R1_ENABLED */

#if defined(POLARSSL_ECP_DP_SECP384R1_ENABLED)
        case POLARSSL_ECP_DP_SECP384R1:
674
            NIST_MODP( p384 );
675
            return( LOAD_GROUP( secp384r1 ) );
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
676 677 678 679
#endif /* POLARSSL_ECP_DP_SECP384R1_ENABLED */

#if defined(POLARSSL_ECP_DP_SECP521R1_ENABLED)
        case POLARSSL_ECP_DP_SECP521R1:
680
            NIST_MODP( p521 );
681
            return( LOAD_GROUP( secp521r1 ) );
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
682 683
#endif /* POLARSSL_ECP_DP_SECP521R1_ENABLED */

684 685 686 687 688
#if defined(POLARSSL_ECP_DP_SECP256K1_ENABLED)
        case POLARSSL_ECP_DP_SECP256K1:
            return( LOAD_GROUP_A( secp256k1 ) );
#endif /* POLARSSL_ECP_DP_SECP256K1_ENABLED */

Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
689 690
#if defined(POLARSSL_ECP_DP_BP256R1_ENABLED)
        case POLARSSL_ECP_DP_BP256R1:
691
            return( LOAD_GROUP_A( brainpoolP256r1 ) );
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
692 693 694 695
#endif /* POLARSSL_ECP_DP_BP256R1_ENABLED */

#if defined(POLARSSL_ECP_DP_BP384R1_ENABLED)
        case POLARSSL_ECP_DP_BP384R1:
696
            return( LOAD_GROUP_A( brainpoolP384r1 ) );
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
697 698 699 700
#endif /* POLARSSL_ECP_DP_BP384R1_ENABLED */

#if defined(POLARSSL_ECP_DP_BP512R1_ENABLED)
        case POLARSSL_ECP_DP_BP512R1:
701
            return( LOAD_GROUP_A( brainpoolP512r1 ) );
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
702 703
#endif /* POLARSSL_ECP_DP_BP512R1_ENABLED */

704 705
#if defined(POLARSSL_ECP_DP_M255_ENABLED)
        case POLARSSL_ECP_DP_M255:
706
            grp->modp = ecp_mod_p255;
707 708 709
            return( ecp_use_curve25519( grp ) );
#endif /* POLARSSL_ECP_DP_M255_ENABLED */

Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
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
        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)
 */
773
static int ecp_mod_p192( mpi *N )
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943
{
    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)
 */
944
static int ecp_mod_p224( mpi *N )
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964
{
    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)
 */
965
static int ecp_mod_p256( mpi *N )
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
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
{
    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)
 */
1002
static int ecp_mod_p384( mpi *N )
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 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 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
{
    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
 */
1079
static int ecp_mod_p521( mpi *N )
Manuel Pégourié-Gonnard's avatar
Manuel Pégourié-Gonnard committed
1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118
{
    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 */

1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162
#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
1163
#endif