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move from polarssl to mbedtls (#708)
[proxmark3-svn] / common / mbedtls / ecp_curves.c
CommitLineData
700d8687
OM		 1/*
2 * Elliptic curves over GF(p): curve-specific data and functions
3 *
4 * Copyright (C) 2006-2015, ARM Limited, All Rights Reserved
5 * SPDX-License-Identifier: GPL-2.0
6 *
7 * This program is free software; you can redistribute it and/or modify
8 * it under the terms of the GNU General Public License as published by
9 * the Free Software Foundation; either version 2 of the License, or
10 * (at your option) any later version.
11 *
12 * This program is distributed in the hope that it will be useful,
13 * but WITHOUT ANY WARRANTY; without even the implied warranty of
14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
15 * GNU General Public License for more details.
16 *
17 * You should have received a copy of the GNU General Public License along
18 * with this program; if not, write to the Free Software Foundation, Inc.,
19 * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
20 *
21 * This file is part of mbed TLS (https://tls.mbed.org)
22 */
23
24#if !defined(MBEDTLS_CONFIG_FILE)
25#include "mbedtls/config.h"
26#else
27#include MBEDTLS_CONFIG_FILE
28#endif
29
30#if defined(MBEDTLS_ECP_C)
31
32#include "mbedtls/ecp.h"
33
34#include <string.h>
35
36#if !defined(MBEDTLS_ECP_ALT)
37
38#if ( defined(__ARMCC_VERSION) || defined(_MSC_VER) ) && \
39 !defined(inline) && !defined(__cplusplus)
40#define inline __inline
41#endif
42
43/*
44 * Conversion macros for embedded constants:
45 * build lists of mbedtls_mpi_uint's from lists of unsigned char's grouped by 8, 4 or 2
46 */
47#if defined(MBEDTLS_HAVE_INT32)
48
49#define BYTES_TO_T_UINT_4( a, b, c, d ) \
50 ( (mbedtls_mpi_uint) a << 0 ) | \
51 ( (mbedtls_mpi_uint) b << 8 ) | \
52 ( (mbedtls_mpi_uint) c << 16 ) | \
53 ( (mbedtls_mpi_uint) d << 24 )
54
55#define BYTES_TO_T_UINT_2( a, b ) \
56 BYTES_TO_T_UINT_4( a, b, 0, 0 )
57
58#define BYTES_TO_T_UINT_8( a, b, c, d, e, f, g, h ) \
59 BYTES_TO_T_UINT_4( a, b, c, d ), \
60 BYTES_TO_T_UINT_4( e, f, g, h )
61
62#else /* 64-bits */
63
64#define BYTES_TO_T_UINT_8( a, b, c, d, e, f, g, h ) \
65 ( (mbedtls_mpi_uint) a << 0 ) | \
66 ( (mbedtls_mpi_uint) b << 8 ) | \
67 ( (mbedtls_mpi_uint) c << 16 ) | \
68 ( (mbedtls_mpi_uint) d << 24 ) | \
69 ( (mbedtls_mpi_uint) e << 32 ) | \
70 ( (mbedtls_mpi_uint) f << 40 ) | \
71 ( (mbedtls_mpi_uint) g << 48 ) | \
72 ( (mbedtls_mpi_uint) h << 56 )
73
74#define BYTES_TO_T_UINT_4( a, b, c, d ) \
75 BYTES_TO_T_UINT_8( a, b, c, d, 0, 0, 0, 0 )
76
77#define BYTES_TO_T_UINT_2( a, b ) \
78 BYTES_TO_T_UINT_8( a, b, 0, 0, 0, 0, 0, 0 )
79
80#endif /* bits in mbedtls_mpi_uint */
81
82/*
83 * Note: the constants are in little-endian order
84 * to be directly usable in MPIs
85 */
86
87/*
88 * Domain parameters for secp192r1
89 */
90#if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
91static const mbedtls_mpi_uint secp192r1_p[] = {
92 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
93 BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
94 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
95};
96static const mbedtls_mpi_uint secp192r1_b[] = {
97 BYTES_TO_T_UINT_8( 0xB1, 0xB9, 0x46, 0xC1, 0xEC, 0xDE, 0xB8, 0xFE ),
98 BYTES_TO_T_UINT_8( 0x49, 0x30, 0x24, 0x72, 0xAB, 0xE9, 0xA7, 0x0F ),
99 BYTES_TO_T_UINT_8( 0xE7, 0x80, 0x9C, 0xE5, 0x19, 0x05, 0x21, 0x64 ),
100};
101static const mbedtls_mpi_uint secp192r1_gx[] = {
102 BYTES_TO_T_UINT_8( 0x12, 0x10, 0xFF, 0x82, 0xFD, 0x0A, 0xFF, 0xF4 ),
103 BYTES_TO_T_UINT_8( 0x00, 0x88, 0xA1, 0x43, 0xEB, 0x20, 0xBF, 0x7C ),
104 BYTES_TO_T_UINT_8( 0xF6, 0x90, 0x30, 0xB0, 0x0E, 0xA8, 0x8D, 0x18 ),
105};
106static const mbedtls_mpi_uint secp192r1_gy[] = {
107 BYTES_TO_T_UINT_8( 0x11, 0x48, 0x79, 0x1E, 0xA1, 0x77, 0xF9, 0x73 ),
108 BYTES_TO_T_UINT_8( 0xD5, 0xCD, 0x24, 0x6B, 0xED, 0x11, 0x10, 0x63 ),
109 BYTES_TO_T_UINT_8( 0x78, 0xDA, 0xC8, 0xFF, 0x95, 0x2B, 0x19, 0x07 ),
110};
111static const mbedtls_mpi_uint secp192r1_n[] = {
112 BYTES_TO_T_UINT_8( 0x31, 0x28, 0xD2, 0xB4, 0xB1, 0xC9, 0x6B, 0x14 ),
113 BYTES_TO_T_UINT_8( 0x36, 0xF8, 0xDE, 0x99, 0xFF, 0xFF, 0xFF, 0xFF ),
114 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
115};
116#endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */
117
118/*
119 * Domain parameters for secp224r1
120 */
121#if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
122static const mbedtls_mpi_uint secp224r1_p[] = {
123 BYTES_TO_T_UINT_8( 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ),
124 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ),
125 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
126 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ),
127};
128static const mbedtls_mpi_uint secp224r1_b[] = {
129 BYTES_TO_T_UINT_8( 0xB4, 0xFF, 0x55, 0x23, 0x43, 0x39, 0x0B, 0x27 ),
130 BYTES_TO_T_UINT_8( 0xBA, 0xD8, 0xBF, 0xD7, 0xB7, 0xB0, 0x44, 0x50 ),
131 BYTES_TO_T_UINT_8( 0x56, 0x32, 0x41, 0xF5, 0xAB, 0xB3, 0x04, 0x0C ),
132 BYTES_TO_T_UINT_4( 0x85, 0x0A, 0x05, 0xB4 ),
133};
134static const mbedtls_mpi_uint secp224r1_gx[] = {
135 BYTES_TO_T_UINT_8( 0x21, 0x1D, 0x5C, 0x11, 0xD6, 0x80, 0x32, 0x34 ),
136 BYTES_TO_T_UINT_8( 0x22, 0x11, 0xC2, 0x56, 0xD3, 0xC1, 0x03, 0x4A ),
137 BYTES_TO_T_UINT_8( 0xB9, 0x90, 0x13, 0x32, 0x7F, 0xBF, 0xB4, 0x6B ),
138 BYTES_TO_T_UINT_4( 0xBD, 0x0C, 0x0E, 0xB7 ),
139};
140static const mbedtls_mpi_uint secp224r1_gy[] = {
141 BYTES_TO_T_UINT_8( 0x34, 0x7E, 0x00, 0x85, 0x99, 0x81, 0xD5, 0x44 ),
142 BYTES_TO_T_UINT_8( 0x64, 0x47, 0x07, 0x5A, 0xA0, 0x75, 0x43, 0xCD ),
143 BYTES_TO_T_UINT_8( 0xE6, 0xDF, 0x22, 0x4C, 0xFB, 0x23, 0xF7, 0xB5 ),
144 BYTES_TO_T_UINT_4( 0x88, 0x63, 0x37, 0xBD ),
145};
146static const mbedtls_mpi_uint secp224r1_n[] = {
147 BYTES_TO_T_UINT_8( 0x3D, 0x2A, 0x5C, 0x5C, 0x45, 0x29, 0xDD, 0x13 ),
148 BYTES_TO_T_UINT_8( 0x3E, 0xF0, 0xB8, 0xE0, 0xA2, 0x16, 0xFF, 0xFF ),
149 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
150 BYTES_TO_T_UINT_4( 0xFF, 0xFF, 0xFF, 0xFF ),
151};
152#endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */
153
154/*
155 * Domain parameters for secp256r1
156 */
157#if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
158static const mbedtls_mpi_uint secp256r1_p[] = {
159 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
160 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ),
161 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ),
162 BYTES_TO_T_UINT_8( 0x01, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ),
163};
164static const mbedtls_mpi_uint secp256r1_b[] = {
165 BYTES_TO_T_UINT_8( 0x4B, 0x60, 0xD2, 0x27, 0x3E, 0x3C, 0xCE, 0x3B ),
166 BYTES_TO_T_UINT_8( 0xF6, 0xB0, 0x53, 0xCC, 0xB0, 0x06, 0x1D, 0x65 ),
167 BYTES_TO_T_UINT_8( 0xBC, 0x86, 0x98, 0x76, 0x55, 0xBD, 0xEB, 0xB3 ),
168 BYTES_TO_T_UINT_8( 0xE7, 0x93, 0x3A, 0xAA, 0xD8, 0x35, 0xC6, 0x5A ),
169};
170static const mbedtls_mpi_uint secp256r1_gx[] = {
171 BYTES_TO_T_UINT_8( 0x96, 0xC2, 0x98, 0xD8, 0x45, 0x39, 0xA1, 0xF4 ),
172 BYTES_TO_T_UINT_8( 0xA0, 0x33, 0xEB, 0x2D, 0x81, 0x7D, 0x03, 0x77 ),
173 BYTES_TO_T_UINT_8( 0xF2, 0x40, 0xA4, 0x63, 0xE5, 0xE6, 0xBC, 0xF8 ),
174 BYTES_TO_T_UINT_8( 0x47, 0x42, 0x2C, 0xE1, 0xF2, 0xD1, 0x17, 0x6B ),
175};
176static const mbedtls_mpi_uint secp256r1_gy[] = {
177 BYTES_TO_T_UINT_8( 0xF5, 0x51, 0xBF, 0x37, 0x68, 0x40, 0xB6, 0xCB ),
178 BYTES_TO_T_UINT_8( 0xCE, 0x5E, 0x31, 0x6B, 0x57, 0x33, 0xCE, 0x2B ),
179 BYTES_TO_T_UINT_8( 0x16, 0x9E, 0x0F, 0x7C, 0x4A, 0xEB, 0xE7, 0x8E ),
180 BYTES_TO_T_UINT_8( 0x9B, 0x7F, 0x1A, 0xFE, 0xE2, 0x42, 0xE3, 0x4F ),
181};
182static const mbedtls_mpi_uint secp256r1_n[] = {
183 BYTES_TO_T_UINT_8( 0x51, 0x25, 0x63, 0xFC, 0xC2, 0xCA, 0xB9, 0xF3 ),
184 BYTES_TO_T_UINT_8( 0x84, 0x9E, 0x17, 0xA7, 0xAD, 0xFA, 0xE6, 0xBC ),
185 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
186 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ),
187};
188#endif /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */
189
190/*
191 * Domain parameters for secp384r1
192 */
193#if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
194static const mbedtls_mpi_uint secp384r1_p[] = {
195 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ),
196 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ),
197 BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
198 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
199 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
200 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
201};
202static const mbedtls_mpi_uint secp384r1_b[] = {
203 BYTES_TO_T_UINT_8( 0xEF, 0x2A, 0xEC, 0xD3, 0xED, 0xC8, 0x85, 0x2A ),
204 BYTES_TO_T_UINT_8( 0x9D, 0xD1, 0x2E, 0x8A, 0x8D, 0x39, 0x56, 0xC6 ),
205 BYTES_TO_T_UINT_8( 0x5A, 0x87, 0x13, 0x50, 0x8F, 0x08, 0x14, 0x03 ),
206 BYTES_TO_T_UINT_8( 0x12, 0x41, 0x81, 0xFE, 0x6E, 0x9C, 0x1D, 0x18 ),
207 BYTES_TO_T_UINT_8( 0x19, 0x2D, 0xF8, 0xE3, 0x6B, 0x05, 0x8E, 0x98 ),
208 BYTES_TO_T_UINT_8( 0xE4, 0xE7, 0x3E, 0xE2, 0xA7, 0x2F, 0x31, 0xB3 ),
209};
210static const mbedtls_mpi_uint secp384r1_gx[] = {
211 BYTES_TO_T_UINT_8( 0xB7, 0x0A, 0x76, 0x72, 0x38, 0x5E, 0x54, 0x3A ),
212 BYTES_TO_T_UINT_8( 0x6C, 0x29, 0x55, 0xBF, 0x5D, 0xF2, 0x02, 0x55 ),
213 BYTES_TO_T_UINT_8( 0x38, 0x2A, 0x54, 0x82, 0xE0, 0x41, 0xF7, 0x59 ),
214 BYTES_TO_T_UINT_8( 0x98, 0x9B, 0xA7, 0x8B, 0x62, 0x3B, 0x1D, 0x6E ),
215 BYTES_TO_T_UINT_8( 0x74, 0xAD, 0x20, 0xF3, 0x1E, 0xC7, 0xB1, 0x8E ),
216 BYTES_TO_T_UINT_8( 0x37, 0x05, 0x8B, 0xBE, 0x22, 0xCA, 0x87, 0xAA ),
217};
218static const mbedtls_mpi_uint secp384r1_gy[] = {
219 BYTES_TO_T_UINT_8( 0x5F, 0x0E, 0xEA, 0x90, 0x7C, 0x1D, 0x43, 0x7A ),
220 BYTES_TO_T_UINT_8( 0x9D, 0x81, 0x7E, 0x1D, 0xCE, 0xB1, 0x60, 0x0A ),
221 BYTES_TO_T_UINT_8( 0xC0, 0xB8, 0xF0, 0xB5, 0x13, 0x31, 0xDA, 0xE9 ),
222 BYTES_TO_T_UINT_8( 0x7C, 0x14, 0x9A, 0x28, 0xBD, 0x1D, 0xF4, 0xF8 ),
223 BYTES_TO_T_UINT_8( 0x29, 0xDC, 0x92, 0x92, 0xBF, 0x98, 0x9E, 0x5D ),
224 BYTES_TO_T_UINT_8( 0x6F, 0x2C, 0x26, 0x96, 0x4A, 0xDE, 0x17, 0x36 ),
225};
226static const mbedtls_mpi_uint secp384r1_n[] = {
227 BYTES_TO_T_UINT_8( 0x73, 0x29, 0xC5, 0xCC, 0x6A, 0x19, 0xEC, 0xEC ),
228 BYTES_TO_T_UINT_8( 0x7A, 0xA7, 0xB0, 0x48, 0xB2, 0x0D, 0x1A, 0x58 ),
229 BYTES_TO_T_UINT_8( 0xDF, 0x2D, 0x37, 0xF4, 0x81, 0x4D, 0x63, 0xC7 ),
230 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
231 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
232 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
233};
234#endif /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */
235
236/*
237 * Domain parameters for secp521r1
238 */
239#if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
240static const mbedtls_mpi_uint secp521r1_p[] = {
241 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
242 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
243 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
244 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
245 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
246 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
247 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
248 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
249 BYTES_TO_T_UINT_2( 0xFF, 0x01 ),
250};
251static const mbedtls_mpi_uint secp521r1_b[] = {
252 BYTES_TO_T_UINT_8( 0x00, 0x3F, 0x50, 0x6B, 0xD4, 0x1F, 0x45, 0xEF ),
253 BYTES_TO_T_UINT_8( 0xF1, 0x34, 0x2C, 0x3D, 0x88, 0xDF, 0x73, 0x35 ),
254 BYTES_TO_T_UINT_8( 0x07, 0xBF, 0xB1, 0x3B, 0xBD, 0xC0, 0x52, 0x16 ),
255 BYTES_TO_T_UINT_8( 0x7B, 0x93, 0x7E, 0xEC, 0x51, 0x39, 0x19, 0x56 ),
256 BYTES_TO_T_UINT_8( 0xE1, 0x09, 0xF1, 0x8E, 0x91, 0x89, 0xB4, 0xB8 ),
257 BYTES_TO_T_UINT_8( 0xF3, 0x15, 0xB3, 0x99, 0x5B, 0x72, 0xDA, 0xA2 ),
258 BYTES_TO_T_UINT_8( 0xEE, 0x40, 0x85, 0xB6, 0xA0, 0x21, 0x9A, 0x92 ),
259 BYTES_TO_T_UINT_8( 0x1F, 0x9A, 0x1C, 0x8E, 0x61, 0xB9, 0x3E, 0x95 ),
260 BYTES_TO_T_UINT_2( 0x51, 0x00 ),
261};
262static const mbedtls_mpi_uint secp521r1_gx[] = {
263 BYTES_TO_T_UINT_8( 0x66, 0xBD, 0xE5, 0xC2, 0x31, 0x7E, 0x7E, 0xF9 ),
264 BYTES_TO_T_UINT_8( 0x9B, 0x42, 0x6A, 0x85, 0xC1, 0xB3, 0x48, 0x33 ),
265 BYTES_TO_T_UINT_8( 0xDE, 0xA8, 0xFF, 0xA2, 0x27, 0xC1, 0x1D, 0xFE ),
266 BYTES_TO_T_UINT_8( 0x28, 0x59, 0xE7, 0xEF, 0x77, 0x5E, 0x4B, 0xA1 ),
267 BYTES_TO_T_UINT_8( 0xBA, 0x3D, 0x4D, 0x6B, 0x60, 0xAF, 0x28, 0xF8 ),
268 BYTES_TO_T_UINT_8( 0x21, 0xB5, 0x3F, 0x05, 0x39, 0x81, 0x64, 0x9C ),
269 BYTES_TO_T_UINT_8( 0x42, 0xB4, 0x95, 0x23, 0x66, 0xCB, 0x3E, 0x9E ),
270 BYTES_TO_T_UINT_8( 0xCD, 0xE9, 0x04, 0x04, 0xB7, 0x06, 0x8E, 0x85 ),
271 BYTES_TO_T_UINT_2( 0xC6, 0x00 ),
272};
273static const mbedtls_mpi_uint secp521r1_gy[] = {
274 BYTES_TO_T_UINT_8( 0x50, 0x66, 0xD1, 0x9F, 0x76, 0x94, 0xBE, 0x88 ),
275 BYTES_TO_T_UINT_8( 0x40, 0xC2, 0x72, 0xA2, 0x86, 0x70, 0x3C, 0x35 ),
276 BYTES_TO_T_UINT_8( 0x61, 0x07, 0xAD, 0x3F, 0x01, 0xB9, 0x50, 0xC5 ),
277 BYTES_TO_T_UINT_8( 0x40, 0x26, 0xF4, 0x5E, 0x99, 0x72, 0xEE, 0x97 ),
278 BYTES_TO_T_UINT_8( 0x2C, 0x66, 0x3E, 0x27, 0x17, 0xBD, 0xAF, 0x17 ),
279 BYTES_TO_T_UINT_8( 0x68, 0x44, 0x9B, 0x57, 0x49, 0x44, 0xF5, 0x98 ),
280 BYTES_TO_T_UINT_8( 0xD9, 0x1B, 0x7D, 0x2C, 0xB4, 0x5F, 0x8A, 0x5C ),
281 BYTES_TO_T_UINT_8( 0x04, 0xC0, 0x3B, 0x9A, 0x78, 0x6A, 0x29, 0x39 ),
282 BYTES_TO_T_UINT_2( 0x18, 0x01 ),
283};
284static const mbedtls_mpi_uint secp521r1_n[] = {
285 BYTES_TO_T_UINT_8( 0x09, 0x64, 0x38, 0x91, 0x1E, 0xB7, 0x6F, 0xBB ),
286 BYTES_TO_T_UINT_8( 0xAE, 0x47, 0x9C, 0x89, 0xB8, 0xC9, 0xB5, 0x3B ),
287 BYTES_TO_T_UINT_8( 0xD0, 0xA5, 0x09, 0xF7, 0x48, 0x01, 0xCC, 0x7F ),
288 BYTES_TO_T_UINT_8( 0x6B, 0x96, 0x2F, 0xBF, 0x83, 0x87, 0x86, 0x51 ),
289 BYTES_TO_T_UINT_8( 0xFA, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
290 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
291 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
292 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
293 BYTES_TO_T_UINT_2( 0xFF, 0x01 ),
294};
295#endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */
296
297#if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
298static const mbedtls_mpi_uint secp192k1_p[] = {
299 BYTES_TO_T_UINT_8( 0x37, 0xEE, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ),
300 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
301 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
302};
303static const mbedtls_mpi_uint secp192k1_a[] = {
304 BYTES_TO_T_UINT_2( 0x00, 0x00 ),
305};
306static const mbedtls_mpi_uint secp192k1_b[] = {
307 BYTES_TO_T_UINT_2( 0x03, 0x00 ),
308};
309static const mbedtls_mpi_uint secp192k1_gx[] = {
310 BYTES_TO_T_UINT_8( 0x7D, 0x6C, 0xE0, 0xEA, 0xB1, 0xD1, 0xA5, 0x1D ),
311 BYTES_TO_T_UINT_8( 0x34, 0xF4, 0xB7, 0x80, 0x02, 0x7D, 0xB0, 0x26 ),
312 BYTES_TO_T_UINT_8( 0xAE, 0xE9, 0x57, 0xC0, 0x0E, 0xF1, 0x4F, 0xDB ),
313};
314static const mbedtls_mpi_uint secp192k1_gy[] = {
315 BYTES_TO_T_UINT_8( 0x9D, 0x2F, 0x5E, 0xD9, 0x88, 0xAA, 0x82, 0x40 ),
316 BYTES_TO_T_UINT_8( 0x34, 0x86, 0xBE, 0x15, 0xD0, 0x63, 0x41, 0x84 ),
317 BYTES_TO_T_UINT_8( 0xA7, 0x28, 0x56, 0x9C, 0x6D, 0x2F, 0x2F, 0x9B ),
318};
319static const mbedtls_mpi_uint secp192k1_n[] = {
320 BYTES_TO_T_UINT_8( 0x8D, 0xFD, 0xDE, 0x74, 0x6A, 0x46, 0x69, 0x0F ),
321 BYTES_TO_T_UINT_8( 0x17, 0xFC, 0xF2, 0x26, 0xFE, 0xFF, 0xFF, 0xFF ),
322 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
323};
324#endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */
325
326#if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
327static const mbedtls_mpi_uint secp224k1_p[] = {
328 BYTES_TO_T_UINT_8( 0x6D, 0xE5, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ),
329 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
330 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
331 BYTES_TO_T_UINT_4( 0xFF, 0xFF, 0xFF, 0xFF ),
332};
333static const mbedtls_mpi_uint secp224k1_a[] = {
334 BYTES_TO_T_UINT_2( 0x00, 0x00 ),
335};
336static const mbedtls_mpi_uint secp224k1_b[] = {
337 BYTES_TO_T_UINT_2( 0x05, 0x00 ),
338};
339static const mbedtls_mpi_uint secp224k1_gx[] = {
340 BYTES_TO_T_UINT_8( 0x5C, 0xA4, 0xB7, 0xB6, 0x0E, 0x65, 0x7E, 0x0F ),
341 BYTES_TO_T_UINT_8( 0xA9, 0x75, 0x70, 0xE4, 0xE9, 0x67, 0xA4, 0x69 ),
342 BYTES_TO_T_UINT_8( 0xA1, 0x28, 0xFC, 0x30, 0xDF, 0x99, 0xF0, 0x4D ),
343 BYTES_TO_T_UINT_4( 0x33, 0x5B, 0x45, 0xA1 ),
344};
345static const mbedtls_mpi_uint secp224k1_gy[] = {
346 BYTES_TO_T_UINT_8( 0xA5, 0x61, 0x6D, 0x55, 0xDB, 0x4B, 0xCA, 0xE2 ),
347 BYTES_TO_T_UINT_8( 0x59, 0xBD, 0xB0, 0xC0, 0xF7, 0x19, 0xE3, 0xF7 ),
348 BYTES_TO_T_UINT_8( 0xD6, 0xFB, 0xCA, 0x82, 0x42, 0x34, 0xBA, 0x7F ),
349 BYTES_TO_T_UINT_4( 0xED, 0x9F, 0x08, 0x7E ),
350};
351static const mbedtls_mpi_uint secp224k1_n[] = {
352 BYTES_TO_T_UINT_8( 0xF7, 0xB1, 0x9F, 0x76, 0x71, 0xA9, 0xF0, 0xCA ),
353 BYTES_TO_T_UINT_8( 0x84, 0x61, 0xEC, 0xD2, 0xE8, 0xDC, 0x01, 0x00 ),
354 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ),
355 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ),
356};
357#endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */
358
359#if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
360static const mbedtls_mpi_uint secp256k1_p[] = {
361 BYTES_TO_T_UINT_8( 0x2F, 0xFC, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ),
362 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
363 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
364 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
365};
366static const mbedtls_mpi_uint secp256k1_a[] = {
367 BYTES_TO_T_UINT_2( 0x00, 0x00 ),
368};
369static const mbedtls_mpi_uint secp256k1_b[] = {
370 BYTES_TO_T_UINT_2( 0x07, 0x00 ),
371};
372static const mbedtls_mpi_uint secp256k1_gx[] = {
373 BYTES_TO_T_UINT_8( 0x98, 0x17, 0xF8, 0x16, 0x5B, 0x81, 0xF2, 0x59 ),
374 BYTES_TO_T_UINT_8( 0xD9, 0x28, 0xCE, 0x2D, 0xDB, 0xFC, 0x9B, 0x02 ),
375 BYTES_TO_T_UINT_8( 0x07, 0x0B, 0x87, 0xCE, 0x95, 0x62, 0xA0, 0x55 ),
376 BYTES_TO_T_UINT_8( 0xAC, 0xBB, 0xDC, 0xF9, 0x7E, 0x66, 0xBE, 0x79 ),
377};
378static const mbedtls_mpi_uint secp256k1_gy[] = {
379 BYTES_TO_T_UINT_8( 0xB8, 0xD4, 0x10, 0xFB, 0x8F, 0xD0, 0x47, 0x9C ),
380 BYTES_TO_T_UINT_8( 0x19, 0x54, 0x85, 0xA6, 0x48, 0xB4, 0x17, 0xFD ),
381 BYTES_TO_T_UINT_8( 0xA8, 0x08, 0x11, 0x0E, 0xFC, 0xFB, 0xA4, 0x5D ),
382 BYTES_TO_T_UINT_8( 0x65, 0xC4, 0xA3, 0x26, 0x77, 0xDA, 0x3A, 0x48 ),
383};
384static const mbedtls_mpi_uint secp256k1_n[] = {
385 BYTES_TO_T_UINT_8( 0x41, 0x41, 0x36, 0xD0, 0x8C, 0x5E, 0xD2, 0xBF ),
386 BYTES_TO_T_UINT_8( 0x3B, 0xA0, 0x48, 0xAF, 0xE6, 0xDC, 0xAE, 0xBA ),
387 BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
388 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
389};
390#endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */
391
392/*
393 * Domain parameters for brainpoolP256r1 (RFC 5639 3.4)
394 */
395#if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED)
396static const mbedtls_mpi_uint brainpoolP256r1_p[] = {
397 BYTES_TO_T_UINT_8( 0x77, 0x53, 0x6E, 0x1F, 0x1D, 0x48, 0x13, 0x20 ),
398 BYTES_TO_T_UINT_8( 0x28, 0x20, 0x26, 0xD5, 0x23, 0xF6, 0x3B, 0x6E ),
399 BYTES_TO_T_UINT_8( 0x72, 0x8D, 0x83, 0x9D, 0x90, 0x0A, 0x66, 0x3E ),
400 BYTES_TO_T_UINT_8( 0xBC, 0xA9, 0xEE, 0xA1, 0xDB, 0x57, 0xFB, 0xA9 ),
401};
402static const mbedtls_mpi_uint brainpoolP256r1_a[] = {
403 BYTES_TO_T_UINT_8( 0xD9, 0xB5, 0x30, 0xF3, 0x44, 0x4B, 0x4A, 0xE9 ),
404 BYTES_TO_T_UINT_8( 0x6C, 0x5C, 0xDC, 0x26, 0xC1, 0x55, 0x80, 0xFB ),
405 BYTES_TO_T_UINT_8( 0xE7, 0xFF, 0x7A, 0x41, 0x30, 0x75, 0xF6, 0xEE ),
406 BYTES_TO_T_UINT_8( 0x57, 0x30, 0x2C, 0xFC, 0x75, 0x09, 0x5A, 0x7D ),
407};
408static const mbedtls_mpi_uint brainpoolP256r1_b[] = {
409 BYTES_TO_T_UINT_8( 0xB6, 0x07, 0x8C, 0xFF, 0x18, 0xDC, 0xCC, 0x6B ),
410 BYTES_TO_T_UINT_8( 0xCE, 0xE1, 0xF7, 0x5C, 0x29, 0x16, 0x84, 0x95 ),
411 BYTES_TO_T_UINT_8( 0xBF, 0x7C, 0xD7, 0xBB, 0xD9, 0xB5, 0x30, 0xF3 ),
412 BYTES_TO_T_UINT_8( 0x44, 0x4B, 0x4A, 0xE9, 0x6C, 0x5C, 0xDC, 0x26 ),
413};
414static const mbedtls_mpi_uint brainpoolP256r1_gx[] = {
415 BYTES_TO_T_UINT_8( 0x62, 0x32, 0xCE, 0x9A, 0xBD, 0x53, 0x44, 0x3A ),
416 BYTES_TO_T_UINT_8( 0xC2, 0x23, 0xBD, 0xE3, 0xE1, 0x27, 0xDE, 0xB9 ),
417 BYTES_TO_T_UINT_8( 0xAF, 0xB7, 0x81, 0xFC, 0x2F, 0x48, 0x4B, 0x2C ),
418 BYTES_TO_T_UINT_8( 0xCB, 0x57, 0x7E, 0xCB, 0xB9, 0xAE, 0xD2, 0x8B ),
419};
420static const mbedtls_mpi_uint brainpoolP256r1_gy[] = {
421 BYTES_TO_T_UINT_8( 0x97, 0x69, 0x04, 0x2F, 0xC7, 0x54, 0x1D, 0x5C ),
422 BYTES_TO_T_UINT_8( 0x54, 0x8E, 0xED, 0x2D, 0x13, 0x45, 0x77, 0xC2 ),
423 BYTES_TO_T_UINT_8( 0xC9, 0x1D, 0x61, 0x14, 0x1A, 0x46, 0xF8, 0x97 ),
424 BYTES_TO_T_UINT_8( 0xFD, 0xC4, 0xDA, 0xC3, 0x35, 0xF8, 0x7E, 0x54 ),
425};
426static const mbedtls_mpi_uint brainpoolP256r1_n[] = {
427 BYTES_TO_T_UINT_8( 0xA7, 0x56, 0x48, 0x97, 0x82, 0x0E, 0x1E, 0x90 ),
428 BYTES_TO_T_UINT_8( 0xF7, 0xA6, 0x61, 0xB5, 0xA3, 0x7A, 0x39, 0x8C ),
429 BYTES_TO_T_UINT_8( 0x71, 0x8D, 0x83, 0x9D, 0x90, 0x0A, 0x66, 0x3E ),
430 BYTES_TO_T_UINT_8( 0xBC, 0xA9, 0xEE, 0xA1, 0xDB, 0x57, 0xFB, 0xA9 ),
431};
432#endif /* MBEDTLS_ECP_DP_BP256R1_ENABLED */
433
434/*
435 * Domain parameters for brainpoolP384r1 (RFC 5639 3.6)
436 */
437#if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED)
438static const mbedtls_mpi_uint brainpoolP384r1_p[] = {
439 BYTES_TO_T_UINT_8( 0x53, 0xEC, 0x07, 0x31, 0x13, 0x00, 0x47, 0x87 ),
440 BYTES_TO_T_UINT_8( 0x71, 0x1A, 0x1D, 0x90, 0x29, 0xA7, 0xD3, 0xAC ),
441 BYTES_TO_T_UINT_8( 0x23, 0x11, 0xB7, 0x7F, 0x19, 0xDA, 0xB1, 0x12 ),
442 BYTES_TO_T_UINT_8( 0xB4, 0x56, 0x54, 0xED, 0x09, 0x71, 0x2F, 0x15 ),
443 BYTES_TO_T_UINT_8( 0xDF, 0x41, 0xE6, 0x50, 0x7E, 0x6F, 0x5D, 0x0F ),
444 BYTES_TO_T_UINT_8( 0x28, 0x6D, 0x38, 0xA3, 0x82, 0x1E, 0xB9, 0x8C ),
445};
446static const mbedtls_mpi_uint brainpoolP384r1_a[] = {
447 BYTES_TO_T_UINT_8( 0x26, 0x28, 0xCE, 0x22, 0xDD, 0xC7, 0xA8, 0x04 ),
448 BYTES_TO_T_UINT_8( 0xEB, 0xD4, 0x3A, 0x50, 0x4A, 0x81, 0xA5, 0x8A ),
449 BYTES_TO_T_UINT_8( 0x0F, 0xF9, 0x91, 0xBA, 0xEF, 0x65, 0x91, 0x13 ),
450 BYTES_TO_T_UINT_8( 0x87, 0x27, 0xB2, 0x4F, 0x8E, 0xA2, 0xBE, 0xC2 ),
451 BYTES_TO_T_UINT_8( 0xA0, 0xAF, 0x05, 0xCE, 0x0A, 0x08, 0x72, 0x3C ),
452 BYTES_TO_T_UINT_8( 0x0C, 0x15, 0x8C, 0x3D, 0xC6, 0x82, 0xC3, 0x7B ),
453};
454static const mbedtls_mpi_uint brainpoolP384r1_b[] = {
455 BYTES_TO_T_UINT_8( 0x11, 0x4C, 0x50, 0xFA, 0x96, 0x86, 0xB7, 0x3A ),
456 BYTES_TO_T_UINT_8( 0x94, 0xC9, 0xDB, 0x95, 0x02, 0x39, 0xB4, 0x7C ),
457 BYTES_TO_T_UINT_8( 0xD5, 0x62, 0xEB, 0x3E, 0xA5, 0x0E, 0x88, 0x2E ),
458 BYTES_TO_T_UINT_8( 0xA6, 0xD2, 0xDC, 0x07, 0xE1, 0x7D, 0xB7, 0x2F ),
459 BYTES_TO_T_UINT_8( 0x7C, 0x44, 0xF0, 0x16, 0x54, 0xB5, 0x39, 0x8B ),
460 BYTES_TO_T_UINT_8( 0x26, 0x28, 0xCE, 0x22, 0xDD, 0xC7, 0xA8, 0x04 ),
461};
462static const mbedtls_mpi_uint brainpoolP384r1_gx[] = {
463 BYTES_TO_T_UINT_8( 0x1E, 0xAF, 0xD4, 0x47, 0xE2, 0xB2, 0x87, 0xEF ),
464 BYTES_TO_T_UINT_8( 0xAA, 0x46, 0xD6, 0x36, 0x34, 0xE0, 0x26, 0xE8 ),
465 BYTES_TO_T_UINT_8( 0xE8, 0x10, 0xBD, 0x0C, 0xFE, 0xCA, 0x7F, 0xDB ),
466 BYTES_TO_T_UINT_8( 0xE3, 0x4F, 0xF1, 0x7E, 0xE7, 0xA3, 0x47, 0x88 ),
467 BYTES_TO_T_UINT_8( 0x6B, 0x3F, 0xC1, 0xB7, 0x81, 0x3A, 0xA6, 0xA2 ),
468 BYTES_TO_T_UINT_8( 0xFF, 0x45, 0xCF, 0x68, 0xF0, 0x64, 0x1C, 0x1D ),
469};
470static const mbedtls_mpi_uint brainpoolP384r1_gy[] = {
471 BYTES_TO_T_UINT_8( 0x15, 0x53, 0x3C, 0x26, 0x41, 0x03, 0x82, 0x42 ),
472 BYTES_TO_T_UINT_8( 0x11, 0x81, 0x91, 0x77, 0x21, 0x46, 0x46, 0x0E ),
473 BYTES_TO_T_UINT_8( 0x28, 0x29, 0x91, 0xF9, 0x4F, 0x05, 0x9C, 0xE1 ),
474 BYTES_TO_T_UINT_8( 0x64, 0x58, 0xEC, 0xFE, 0x29, 0x0B, 0xB7, 0x62 ),
475 BYTES_TO_T_UINT_8( 0x52, 0xD5, 0xCF, 0x95, 0x8E, 0xEB, 0xB1, 0x5C ),
476 BYTES_TO_T_UINT_8( 0xA4, 0xC2, 0xF9, 0x20, 0x75, 0x1D, 0xBE, 0x8A ),
477};
478static const mbedtls_mpi_uint brainpoolP384r1_n[] = {
479 BYTES_TO_T_UINT_8( 0x65, 0x65, 0x04, 0xE9, 0x02, 0x32, 0x88, 0x3B ),
480 BYTES_TO_T_UINT_8( 0x10, 0xC3, 0x7F, 0x6B, 0xAF, 0xB6, 0x3A, 0xCF ),
481 BYTES_TO_T_UINT_8( 0xA7, 0x25, 0x04, 0xAC, 0x6C, 0x6E, 0x16, 0x1F ),
482 BYTES_TO_T_UINT_8( 0xB3, 0x56, 0x54, 0xED, 0x09, 0x71, 0x2F, 0x15 ),
483 BYTES_TO_T_UINT_8( 0xDF, 0x41, 0xE6, 0x50, 0x7E, 0x6F, 0x5D, 0x0F ),
484 BYTES_TO_T_UINT_8( 0x28, 0x6D, 0x38, 0xA3, 0x82, 0x1E, 0xB9, 0x8C ),
485};
486#endif /* MBEDTLS_ECP_DP_BP384R1_ENABLED */
487
488/*
489 * Domain parameters for brainpoolP512r1 (RFC 5639 3.7)
490 */
491#if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED)
492static const mbedtls_mpi_uint brainpoolP512r1_p[] = {
493 BYTES_TO_T_UINT_8( 0xF3, 0x48, 0x3A, 0x58, 0x56, 0x60, 0xAA, 0x28 ),
494 BYTES_TO_T_UINT_8( 0x85, 0xC6, 0x82, 0x2D, 0x2F, 0xFF, 0x81, 0x28 ),
495 BYTES_TO_T_UINT_8( 0xE6, 0x80, 0xA3, 0xE6, 0x2A, 0xA1, 0xCD, 0xAE ),
496 BYTES_TO_T_UINT_8( 0x42, 0x68, 0xC6, 0x9B, 0x00, 0x9B, 0x4D, 0x7D ),
497 BYTES_TO_T_UINT_8( 0x71, 0x08, 0x33, 0x70, 0xCA, 0x9C, 0x63, 0xD6 ),
498 BYTES_TO_T_UINT_8( 0x0E, 0xD2, 0xC9, 0xB3, 0xB3, 0x8D, 0x30, 0xCB ),
499 BYTES_TO_T_UINT_8( 0x07, 0xFC, 0xC9, 0x33, 0xAE, 0xE6, 0xD4, 0x3F ),
500 BYTES_TO_T_UINT_8( 0x8B, 0xC4, 0xE9, 0xDB, 0xB8, 0x9D, 0xDD, 0xAA ),
501};
502static const mbedtls_mpi_uint brainpoolP512r1_a[] = {
503 BYTES_TO_T_UINT_8( 0xCA, 0x94, 0xFC, 0x77, 0x4D, 0xAC, 0xC1, 0xE7 ),
504 BYTES_TO_T_UINT_8( 0xB9, 0xC7, 0xF2, 0x2B, 0xA7, 0x17, 0x11, 0x7F ),
505 BYTES_TO_T_UINT_8( 0xB5, 0xC8, 0x9A, 0x8B, 0xC9, 0xF1, 0x2E, 0x0A ),
506 BYTES_TO_T_UINT_8( 0xA1, 0x3A, 0x25, 0xA8, 0x5A, 0x5D, 0xED, 0x2D ),
507 BYTES_TO_T_UINT_8( 0xBC, 0x63, 0x98, 0xEA, 0xCA, 0x41, 0x34, 0xA8 ),
508 BYTES_TO_T_UINT_8( 0x10, 0x16, 0xF9, 0x3D, 0x8D, 0xDD, 0xCB, 0x94 ),
509 BYTES_TO_T_UINT_8( 0xC5, 0x4C, 0x23, 0xAC, 0x45, 0x71, 0x32, 0xE2 ),
510 BYTES_TO_T_UINT_8( 0x89, 0x3B, 0x60, 0x8B, 0x31, 0xA3, 0x30, 0x78 ),
511};
512static const mbedtls_mpi_uint brainpoolP512r1_b[] = {
513 BYTES_TO_T_UINT_8( 0x23, 0xF7, 0x16, 0x80, 0x63, 0xBD, 0x09, 0x28 ),
514 BYTES_TO_T_UINT_8( 0xDD, 0xE5, 0xBA, 0x5E, 0xB7, 0x50, 0x40, 0x98 ),
515 BYTES_TO_T_UINT_8( 0x67, 0x3E, 0x08, 0xDC, 0xCA, 0x94, 0xFC, 0x77 ),
516 BYTES_TO_T_UINT_8( 0x4D, 0xAC, 0xC1, 0xE7, 0xB9, 0xC7, 0xF2, 0x2B ),
517 BYTES_TO_T_UINT_8( 0xA7, 0x17, 0x11, 0x7F, 0xB5, 0xC8, 0x9A, 0x8B ),
518 BYTES_TO_T_UINT_8( 0xC9, 0xF1, 0x2E, 0x0A, 0xA1, 0x3A, 0x25, 0xA8 ),
519 BYTES_TO_T_UINT_8( 0x5A, 0x5D, 0xED, 0x2D, 0xBC, 0x63, 0x98, 0xEA ),
520 BYTES_TO_T_UINT_8( 0xCA, 0x41, 0x34, 0xA8, 0x10, 0x16, 0xF9, 0x3D ),
521};
522static const mbedtls_mpi_uint brainpoolP512r1_gx[] = {
523 BYTES_TO_T_UINT_8( 0x22, 0xF8, 0xB9, 0xBC, 0x09, 0x22, 0x35, 0x8B ),
524 BYTES_TO_T_UINT_8( 0x68, 0x5E, 0x6A, 0x40, 0x47, 0x50, 0x6D, 0x7C ),
525 BYTES_TO_T_UINT_8( 0x5F, 0x7D, 0xB9, 0x93, 0x7B, 0x68, 0xD1, 0x50 ),
526 BYTES_TO_T_UINT_8( 0x8D, 0xD4, 0xD0, 0xE2, 0x78, 0x1F, 0x3B, 0xFF ),
527 BYTES_TO_T_UINT_8( 0x8E, 0x09, 0xD0, 0xF4, 0xEE, 0x62, 0x3B, 0xB4 ),
528 BYTES_TO_T_UINT_8( 0xC1, 0x16, 0xD9, 0xB5, 0x70, 0x9F, 0xED, 0x85 ),
529 BYTES_TO_T_UINT_8( 0x93, 0x6A, 0x4C, 0x9C, 0x2E, 0x32, 0x21, 0x5A ),
530 BYTES_TO_T_UINT_8( 0x64, 0xD9, 0x2E, 0xD8, 0xBD, 0xE4, 0xAE, 0x81 ),
531};
532static const mbedtls_mpi_uint brainpoolP512r1_gy[] = {
533 BYTES_TO_T_UINT_8( 0x92, 0x08, 0xD8, 0x3A, 0x0F, 0x1E, 0xCD, 0x78 ),
534 BYTES_TO_T_UINT_8( 0x06, 0x54, 0xF0, 0xA8, 0x2F, 0x2B, 0xCA, 0xD1 ),
535 BYTES_TO_T_UINT_8( 0xAE, 0x63, 0x27, 0x8A, 0xD8, 0x4B, 0xCA, 0x5B ),
536 BYTES_TO_T_UINT_8( 0x5E, 0x48, 0x5F, 0x4A, 0x49, 0xDE, 0xDC, 0xB2 ),
537 BYTES_TO_T_UINT_8( 0x11, 0x81, 0x1F, 0x88, 0x5B, 0xC5, 0x00, 0xA0 ),
538 BYTES_TO_T_UINT_8( 0x1A, 0x7B, 0xA5, 0x24, 0x00, 0xF7, 0x09, 0xF2 ),
539 BYTES_TO_T_UINT_8( 0xFD, 0x22, 0x78, 0xCF, 0xA9, 0xBF, 0xEA, 0xC0 ),
540 BYTES_TO_T_UINT_8( 0xEC, 0x32, 0x63, 0x56, 0x5D, 0x38, 0xDE, 0x7D ),
541};
542static const mbedtls_mpi_uint brainpoolP512r1_n[] = {
543 BYTES_TO_T_UINT_8( 0x69, 0x00, 0xA9, 0x9C, 0x82, 0x96, 0x87, 0xB5 ),
544 BYTES_TO_T_UINT_8( 0xDD, 0xDA, 0x5D, 0x08, 0x81, 0xD3, 0xB1, 0x1D ),
545 BYTES_TO_T_UINT_8( 0x47, 0x10, 0xAC, 0x7F, 0x19, 0x61, 0x86, 0x41 ),
546 BYTES_TO_T_UINT_8( 0x19, 0x26, 0xA9, 0x4C, 0x41, 0x5C, 0x3E, 0x55 ),
547 BYTES_TO_T_UINT_8( 0x70, 0x08, 0x33, 0x70, 0xCA, 0x9C, 0x63, 0xD6 ),
548 BYTES_TO_T_UINT_8( 0x0E, 0xD2, 0xC9, 0xB3, 0xB3, 0x8D, 0x30, 0xCB ),
549 BYTES_TO_T_UINT_8( 0x07, 0xFC, 0xC9, 0x33, 0xAE, 0xE6, 0xD4, 0x3F ),
550 BYTES_TO_T_UINT_8( 0x8B, 0xC4, 0xE9, 0xDB, 0xB8, 0x9D, 0xDD, 0xAA ),
551};
552#endif /* MBEDTLS_ECP_DP_BP512R1_ENABLED */
553
554/*
555 * Create an MPI from embedded constants
556 * (assumes len is an exact multiple of sizeof mbedtls_mpi_uint)
557 */
558static inline void ecp_mpi_load( mbedtls_mpi *X, const mbedtls_mpi_uint *p, size_t len )
559{
560 X->s = 1;
561 X->n = len / sizeof( mbedtls_mpi_uint );
562 X->p = (mbedtls_mpi_uint *) p;
563}
564
565/*
566 * Set an MPI to static value 1
567 */
568static inline void ecp_mpi_set1( mbedtls_mpi *X )
569{
570 static mbedtls_mpi_uint one[] = { 1 };
571 X->s = 1;
572 X->n = 1;
573 X->p = one;
574}
575
576/*
577 * Make group available from embedded constants
578 */
579static int ecp_group_load( mbedtls_ecp_group *grp,
580 const mbedtls_mpi_uint *p, size_t plen,
581 const mbedtls_mpi_uint *a, size_t alen,
582 const mbedtls_mpi_uint *b, size_t blen,
583 const mbedtls_mpi_uint *gx, size_t gxlen,
584 const mbedtls_mpi_uint *gy, size_t gylen,
585 const mbedtls_mpi_uint *n, size_t nlen)
586{
587 ecp_mpi_load( &grp->P, p, plen );
588 if( a != NULL )
589 ecp_mpi_load( &grp->A, a, alen );
590 ecp_mpi_load( &grp->B, b, blen );
591 ecp_mpi_load( &grp->N, n, nlen );
592
593 ecp_mpi_load( &grp->G.X, gx, gxlen );
594 ecp_mpi_load( &grp->G.Y, gy, gylen );
595 ecp_mpi_set1( &grp->G.Z );
596
597 grp->pbits = mbedtls_mpi_bitlen( &grp->P );
598 grp->nbits = mbedtls_mpi_bitlen( &grp->N );
599
600 grp->h = 1;
601
602 return( 0 );
603}
604
605#if defined(MBEDTLS_ECP_NIST_OPTIM)
606/* Forward declarations */
607#if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
608static int ecp_mod_p192( mbedtls_mpi * );
609#endif
610#if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
611static int ecp_mod_p224( mbedtls_mpi * );
612#endif
613#if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
614static int ecp_mod_p256( mbedtls_mpi * );
615#endif
616#if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
617static int ecp_mod_p384( mbedtls_mpi * );
618#endif
619#if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
620static int ecp_mod_p521( mbedtls_mpi * );
621#endif
622
623#define NIST_MODP( P ) grp->modp = ecp_mod_ ## P;
624#else
625#define NIST_MODP( P )
626#endif /* MBEDTLS_ECP_NIST_OPTIM */
627
628/* Additional forward declarations */
629#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
630static int ecp_mod_p255( mbedtls_mpi * );
631#endif
632#if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
633static int ecp_mod_p448( mbedtls_mpi * );
634#endif
635#if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
636static int ecp_mod_p192k1( mbedtls_mpi * );
637#endif
638#if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
639static int ecp_mod_p224k1( mbedtls_mpi * );
640#endif
641#if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
642static int ecp_mod_p256k1( mbedtls_mpi * );
643#endif
644
645#define LOAD_GROUP_A( G ) ecp_group_load( grp, \
646 G ## _p, sizeof( G ## _p ), \
647 G ## _a, sizeof( G ## _a ), \
648 G ## _b, sizeof( G ## _b ), \
649 G ## _gx, sizeof( G ## _gx ), \
650 G ## _gy, sizeof( G ## _gy ), \
651 G ## _n, sizeof( G ## _n ) )
652
653#define LOAD_GROUP( G ) ecp_group_load( grp, \
654 G ## _p, sizeof( G ## _p ), \
655 NULL, 0, \
656 G ## _b, sizeof( G ## _b ), \
657 G ## _gx, sizeof( G ## _gx ), \
658 G ## _gy, sizeof( G ## _gy ), \
659 G ## _n, sizeof( G ## _n ) )
660
661#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
662/*
663 * Specialized function for creating the Curve25519 group
664 */
665static int ecp_use_curve25519( mbedtls_ecp_group *grp )
666{
667 int ret;
668
669 /* Actually ( A + 2 ) / 4 */
670 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &grp->A, 16, "01DB42" ) );
671
672 /* P = 2^255 - 19 */
673 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->P, 1 ) );
674 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &grp->P, 255 ) );
675 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &grp->P, &grp->P, 19 ) );
676 grp->pbits = mbedtls_mpi_bitlen( &grp->P );
677
678 /* N = 2^252 + 27742317777372353535851937790883648493 */
679 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &grp->N, 16,
680 "14DEF9DEA2F79CD65812631A5CF5D3ED" ) );
681 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &grp->N, 252, 1 ) );
682
683 /* Y intentionally not set, since we use x/z coordinates.
684 * This is used as a marker to identify Montgomery curves! */
685 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.X, 9 ) );
686 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.Z, 1 ) );
687 mbedtls_mpi_free( &grp->G.Y );
688
689 /* Actually, the required msb for private keys */
690 grp->nbits = 254;
691
692cleanup:
693 if( ret != 0 )
694 mbedtls_ecp_group_free( grp );
695
696 return( ret );
697}
698#endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */
699
700#if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
701/*
702 * Specialized function for creating the Curve448 group
703 */
704static int ecp_use_curve448( mbedtls_ecp_group *grp )
705{
706 mbedtls_mpi Ns;
707 int ret;
708
709 mbedtls_mpi_init( &Ns );
710
711 /* Actually ( A + 2 ) / 4 */
712 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &grp->A, 16, "98AA" ) );
713
714 /* P = 2^448 - 2^224 - 1 */
715 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->P, 1 ) );
716 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &grp->P, 224 ) );
717 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &grp->P, &grp->P, 1 ) );
718 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &grp->P, 224 ) );
719 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &grp->P, &grp->P, 1 ) );
720 grp->pbits = mbedtls_mpi_bitlen( &grp->P );
721
722 /* Y intentionally not set, since we use x/z coordinates.
723 * This is used as a marker to identify Montgomery curves! */
724 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.X, 5 ) );
725 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.Z, 1 ) );
726 mbedtls_mpi_free( &grp->G.Y );
727
728 /* N = 2^446 - 13818066809895115352007386748515426880336692474882178609894547503885 */
729 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &grp->N, 446, 1 ) );
730 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &Ns, 16,
731 "8335DC163BB124B65129C96FDE933D8D723A70AADC873D6D54A7BB0D" ) );
732 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &grp->N, &grp->N, &Ns ) );
733
734 /* Actually, the required msb for private keys */
735 grp->nbits = 447;
736
737cleanup:
738 mbedtls_mpi_free( &Ns );
739 if( ret != 0 )
740 mbedtls_ecp_group_free( grp );
741
742 return( ret );
743}
744#endif /* MBEDTLS_ECP_DP_CURVE448_ENABLED */
745
746/*
747 * Set a group using well-known domain parameters
748 */
749int mbedtls_ecp_group_load( mbedtls_ecp_group *grp, mbedtls_ecp_group_id id )
750{
751 mbedtls_ecp_group_free( grp );
752
753 grp->id = id;
754
755 switch( id )
756 {
757#if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
758 case MBEDTLS_ECP_DP_SECP192R1:
759 NIST_MODP( p192 );
760 return( LOAD_GROUP( secp192r1 ) );
761#endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */
762
763#if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
764 case MBEDTLS_ECP_DP_SECP224R1:
765 NIST_MODP( p224 );
766 return( LOAD_GROUP( secp224r1 ) );
767#endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */
768
769#if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
770 case MBEDTLS_ECP_DP_SECP256R1:
771 NIST_MODP( p256 );
772 return( LOAD_GROUP( secp256r1 ) );
773#endif /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */
774
775#if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
776 case MBEDTLS_ECP_DP_SECP384R1:
777 NIST_MODP( p384 );
778 return( LOAD_GROUP( secp384r1 ) );
779#endif /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */
780
781#if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
782 case MBEDTLS_ECP_DP_SECP521R1:
783 NIST_MODP( p521 );
784 return( LOAD_GROUP( secp521r1 ) );
785#endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */
786
787#if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
788 case MBEDTLS_ECP_DP_SECP192K1:
789 grp->modp = ecp_mod_p192k1;
790 return( LOAD_GROUP_A( secp192k1 ) );
791#endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */
792
793#if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
794 case MBEDTLS_ECP_DP_SECP224K1:
795 grp->modp = ecp_mod_p224k1;
796 return( LOAD_GROUP_A( secp224k1 ) );
797#endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */
798
799#if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
800 case MBEDTLS_ECP_DP_SECP256K1:
801 grp->modp = ecp_mod_p256k1;
802 return( LOAD_GROUP_A( secp256k1 ) );
803#endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */
804
805#if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED)
806 case MBEDTLS_ECP_DP_BP256R1:
807 return( LOAD_GROUP_A( brainpoolP256r1 ) );
808#endif /* MBEDTLS_ECP_DP_BP256R1_ENABLED */
809
810#if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED)
811 case MBEDTLS_ECP_DP_BP384R1:
812 return( LOAD_GROUP_A( brainpoolP384r1 ) );
813#endif /* MBEDTLS_ECP_DP_BP384R1_ENABLED */
814
815#if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED)
816 case MBEDTLS_ECP_DP_BP512R1:
817 return( LOAD_GROUP_A( brainpoolP512r1 ) );
818#endif /* MBEDTLS_ECP_DP_BP512R1_ENABLED */
819
820#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
821 case MBEDTLS_ECP_DP_CURVE25519:
822 grp->modp = ecp_mod_p255;
823 return( ecp_use_curve25519( grp ) );
824#endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */
825
826#if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
827 case MBEDTLS_ECP_DP_CURVE448:
828 grp->modp = ecp_mod_p448;
829 return( ecp_use_curve448( grp ) );
830#endif /* MBEDTLS_ECP_DP_CURVE448_ENABLED */
831
832 default:
833 mbedtls_ecp_group_free( grp );
834 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
835 }
836}
837
838#if defined(MBEDTLS_ECP_NIST_OPTIM)
839/*
840 * Fast reduction modulo the primes used by the NIST curves.
841 *
842 * These functions are critical for speed, but not needed for correct
843 * operations. So, we make the choice to heavily rely on the internals of our
844 * bignum library, which creates a tight coupling between these functions and
845 * our MPI implementation. However, the coupling between the ECP module and
846 * MPI remains loose, since these functions can be deactivated at will.
847 */
848
849#if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
850/*
851 * Compared to the way things are presented in FIPS 186-3 D.2,
852 * we proceed in columns, from right (least significant chunk) to left,
853 * adding chunks to N in place, and keeping a carry for the next chunk.
854 * This avoids moving things around in memory, and uselessly adding zeros,
855 * compared to the more straightforward, line-oriented approach.
856 *
857 * For this prime we need to handle data in chunks of 64 bits.
858 * Since this is always a multiple of our basic mbedtls_mpi_uint, we can
859 * use a mbedtls_mpi_uint * to designate such a chunk, and small loops to handle it.
860 */
861
862/* Add 64-bit chunks (dst += src) and update carry */
863static inline void add64( mbedtls_mpi_uint *dst, mbedtls_mpi_uint *src, mbedtls_mpi_uint *carry )
864{
865 unsigned char i;
866 mbedtls_mpi_uint c = 0;
867 for( i = 0; i < 8 / sizeof( mbedtls_mpi_uint ); i++, dst++, src++ )
868 {
869 *dst += c; c = ( *dst < c );
870 *dst += *src; c += ( *dst < *src );
871 }
872 *carry += c;
873}
874
875/* Add carry to a 64-bit chunk and update carry */
876static inline void carry64( mbedtls_mpi_uint *dst, mbedtls_mpi_uint *carry )
877{
878 unsigned char i;
879 for( i = 0; i < 8 / sizeof( mbedtls_mpi_uint ); i++, dst++ )
880 {
881 *dst += *carry;
882 *carry = ( *dst < *carry );
883 }
884}
885
886#define WIDTH 8 / sizeof( mbedtls_mpi_uint )
887#define A( i ) N->p + i * WIDTH
888#define ADD( i ) add64( p, A( i ), &c )
889#define NEXT p += WIDTH; carry64( p, &c )
890#define LAST p += WIDTH; *p = c; while( ++p < end ) *p = 0
891
892/*
893 * Fast quasi-reduction modulo p192 (FIPS 186-3 D.2.1)
894 */
895static int ecp_mod_p192( mbedtls_mpi *N )
896{
897 int ret;
898 mbedtls_mpi_uint c = 0;
899 mbedtls_mpi_uint *p, *end;
900
901 /* Make sure we have enough blocks so that A(5) is legal */
902 MBEDTLS_MPI_CHK( mbedtls_mpi_grow( N, 6 * WIDTH ) );
903
904 p = N->p;
905 end = p + N->n;
906
907 ADD( 3 ); ADD( 5 ); NEXT; // A0 += A3 + A5
908 ADD( 3 ); ADD( 4 ); ADD( 5 ); NEXT; // A1 += A3 + A4 + A5
909 ADD( 4 ); ADD( 5 ); LAST; // A2 += A4 + A5
910
911cleanup:
912 return( ret );
913}
914
915#undef WIDTH
916#undef A
917#undef ADD
918#undef NEXT
919#undef LAST
920#endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */
921
922#if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) || \
923 defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) || \
924 defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
925/*
926 * The reader is advised to first understand ecp_mod_p192() since the same
927 * general structure is used here, but with additional complications:
928 * (1) chunks of 32 bits, and (2) subtractions.
929 */
930
931/*
932 * For these primes, we need to handle data in chunks of 32 bits.
933 * This makes it more complicated if we use 64 bits limbs in MPI,
934 * which prevents us from using a uniform access method as for p192.
935 *
936 * So, we define a mini abstraction layer to access 32 bit chunks,
937 * load them in 'cur' for work, and store them back from 'cur' when done.
938 *
939 * While at it, also define the size of N in terms of 32-bit chunks.
940 */
941#define LOAD32 cur = A( i );
942
943#if defined(MBEDTLS_HAVE_INT32) /* 32 bit */
944
945#define MAX32 N->n
946#define A( j ) N->p[j]
947#define STORE32 N->p[i] = cur;
948
949#else /* 64-bit */
950
951#define MAX32 N->n * 2
952#define A( j ) j % 2 ? (uint32_t)( N->p[j/2] >> 32 ) : (uint32_t)( N->p[j/2] )
953#define STORE32 \
954 if( i % 2 ) { \
955 N->p[i/2] &= 0x00000000FFFFFFFF; \
956 N->p[i/2] |= ((mbedtls_mpi_uint) cur) << 32; \
957 } else { \
958 N->p[i/2] &= 0xFFFFFFFF00000000; \
959 N->p[i/2] |= (mbedtls_mpi_uint) cur; \
960 }
961
962#endif /* sizeof( mbedtls_mpi_uint ) */
963
964/*
965 * Helpers for addition and subtraction of chunks, with signed carry.
966 */
967static inline void add32( uint32_t *dst, uint32_t src, signed char *carry )
968{
969 *dst += src;
970 *carry += ( *dst < src );
971}
972
973static inline void sub32( uint32_t *dst, uint32_t src, signed char *carry )
974{
975 *carry -= ( *dst < src );
976 *dst -= src;
977}
978
979#define ADD( j ) add32( &cur, A( j ), &c );
980#define SUB( j ) sub32( &cur, A( j ), &c );
981
982/*
983 * Helpers for the main 'loop'
984 * (see fix_negative for the motivation of C)
985 */
986#define INIT( b ) \
987 int ret; \
988 signed char c = 0, cc; \
989 uint32_t cur; \
990 size_t i = 0, bits = b; \
991 mbedtls_mpi C; \
992 mbedtls_mpi_uint Cp[ b / 8 / sizeof( mbedtls_mpi_uint) + 1 ]; \
993 \
994 C.s = 1; \
995 C.n = b / 8 / sizeof( mbedtls_mpi_uint) + 1; \
996 C.p = Cp; \
997 memset( Cp, 0, C.n * sizeof( mbedtls_mpi_uint ) ); \
998 \
999 MBEDTLS_MPI_CHK( mbedtls_mpi_grow( N, b * 2 / 8 / sizeof( mbedtls_mpi_uint ) ) ); \
1000 LOAD32;
1001
1002#define NEXT \
1003 STORE32; i++; LOAD32; \
1004 cc = c; c = 0; \
1005 if( cc < 0 ) \
1006 sub32( &cur, -cc, &c ); \
1007 else \
1008 add32( &cur, cc, &c ); \
1009
1010#define LAST \
1011 STORE32; i++; \
1012 cur = c > 0 ? c : 0; STORE32; \
1013 cur = 0; while( ++i < MAX32 ) { STORE32; } \
1014 if( c < 0 ) fix_negative( N, c, &C, bits );
1015
1016/*
1017 * If the result is negative, we get it in the form
1018 * c * 2^(bits + 32) + N, with c negative and N positive shorter than 'bits'
1019 */
1020static inline int fix_negative( mbedtls_mpi *N, signed char c, mbedtls_mpi *C, size_t bits )
1021{
1022 int ret;
1023
1024 /* C = - c * 2^(bits + 32) */
1025#if !defined(MBEDTLS_HAVE_INT64)
1026 ((void) bits);
1027#else
1028 if( bits == 224 )
1029 C->p[ C->n - 1 ] = ((mbedtls_mpi_uint) -c) << 32;
1030 else
1031#endif
1032 C->p[ C->n - 1 ] = (mbedtls_mpi_uint) -c;
1033
1034 /* N = - ( C - N ) */
1035 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( N, C, N ) );
1036 N->s = -1;
1037
1038cleanup:
1039
1040 return( ret );
1041}
1042
1043#if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
1044/*
1045 * Fast quasi-reduction modulo p224 (FIPS 186-3 D.2.2)
1046 */
1047static int ecp_mod_p224( mbedtls_mpi *N )
1048{
1049 INIT( 224 );
1050
1051 SUB( 7 ); SUB( 11 ); NEXT; // A0 += -A7 - A11
1052 SUB( 8 ); SUB( 12 ); NEXT; // A1 += -A8 - A12
1053 SUB( 9 ); SUB( 13 ); NEXT; // A2 += -A9 - A13
1054 SUB( 10 ); ADD( 7 ); ADD( 11 ); NEXT; // A3 += -A10 + A7 + A11
1055 SUB( 11 ); ADD( 8 ); ADD( 12 ); NEXT; // A4 += -A11 + A8 + A12
1056 SUB( 12 ); ADD( 9 ); ADD( 13 ); NEXT; // A5 += -A12 + A9 + A13
1057 SUB( 13 ); ADD( 10 ); LAST; // A6 += -A13 + A10
1058
1059cleanup:
1060 return( ret );
1061}
1062#endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */
1063
1064#if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
1065/*
1066 * Fast quasi-reduction modulo p256 (FIPS 186-3 D.2.3)
1067 */
1068static int ecp_mod_p256( mbedtls_mpi *N )
1069{
1070 INIT( 256 );
1071
1072 ADD( 8 ); ADD( 9 );
1073 SUB( 11 ); SUB( 12 ); SUB( 13 ); SUB( 14 ); NEXT; // A0
1074
1075 ADD( 9 ); ADD( 10 );
1076 SUB( 12 ); SUB( 13 ); SUB( 14 ); SUB( 15 ); NEXT; // A1
1077
1078 ADD( 10 ); ADD( 11 );
1079 SUB( 13 ); SUB( 14 ); SUB( 15 ); NEXT; // A2
1080
1081 ADD( 11 ); ADD( 11 ); ADD( 12 ); ADD( 12 ); ADD( 13 );
1082 SUB( 15 ); SUB( 8 ); SUB( 9 ); NEXT; // A3
1083
1084 ADD( 12 ); ADD( 12 ); ADD( 13 ); ADD( 13 ); ADD( 14 );
1085 SUB( 9 ); SUB( 10 ); NEXT; // A4
1086
1087 ADD( 13 ); ADD( 13 ); ADD( 14 ); ADD( 14 ); ADD( 15 );
1088 SUB( 10 ); SUB( 11 ); NEXT; // A5
1089
1090 ADD( 14 ); ADD( 14 ); ADD( 15 ); ADD( 15 ); ADD( 14 ); ADD( 13 );
1091 SUB( 8 ); SUB( 9 ); NEXT; // A6
1092
1093 ADD( 15 ); ADD( 15 ); ADD( 15 ); ADD( 8 );
1094 SUB( 10 ); SUB( 11 ); SUB( 12 ); SUB( 13 ); LAST; // A7
1095
1096cleanup:
1097 return( ret );
1098}
1099#endif /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */
1100
1101#if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
1102/*
1103 * Fast quasi-reduction modulo p384 (FIPS 186-3 D.2.4)
1104 */
1105static int ecp_mod_p384( mbedtls_mpi *N )
1106{
1107 INIT( 384 );
1108
1109 ADD( 12 ); ADD( 21 ); ADD( 20 );
1110 SUB( 23 ); NEXT; // A0
1111
1112 ADD( 13 ); ADD( 22 ); ADD( 23 );
1113 SUB( 12 ); SUB( 20 ); NEXT; // A2
1114
1115 ADD( 14 ); ADD( 23 );
1116 SUB( 13 ); SUB( 21 ); NEXT; // A2
1117
1118 ADD( 15 ); ADD( 12 ); ADD( 20 ); ADD( 21 );
1119 SUB( 14 ); SUB( 22 ); SUB( 23 ); NEXT; // A3
1120
1121 ADD( 21 ); ADD( 21 ); ADD( 16 ); ADD( 13 ); ADD( 12 ); ADD( 20 ); ADD( 22 );
1122 SUB( 15 ); SUB( 23 ); SUB( 23 ); NEXT; // A4
1123
1124 ADD( 22 ); ADD( 22 ); ADD( 17 ); ADD( 14 ); ADD( 13 ); ADD( 21 ); ADD( 23 );
1125 SUB( 16 ); NEXT; // A5
1126
1127 ADD( 23 ); ADD( 23 ); ADD( 18 ); ADD( 15 ); ADD( 14 ); ADD( 22 );
1128 SUB( 17 ); NEXT; // A6
1129
1130 ADD( 19 ); ADD( 16 ); ADD( 15 ); ADD( 23 );
1131 SUB( 18 ); NEXT; // A7
1132
1133 ADD( 20 ); ADD( 17 ); ADD( 16 );
1134 SUB( 19 ); NEXT; // A8
1135
1136 ADD( 21 ); ADD( 18 ); ADD( 17 );
1137 SUB( 20 ); NEXT; // A9
1138
1139 ADD( 22 ); ADD( 19 ); ADD( 18 );
1140 SUB( 21 ); NEXT; // A10
1141
1142 ADD( 23 ); ADD( 20 ); ADD( 19 );
1143 SUB( 22 ); LAST; // A11
1144
1145cleanup:
1146 return( ret );
1147}
1148#endif /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */
1149
1150#undef A
1151#undef LOAD32
1152#undef STORE32
1153#undef MAX32
1154#undef INIT
1155#undef NEXT
1156#undef LAST
1157
1158#endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED ||
1159 MBEDTLS_ECP_DP_SECP256R1_ENABLED ||
1160 MBEDTLS_ECP_DP_SECP384R1_ENABLED */
1161
1162#if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
1163/*
1164 * Here we have an actual Mersenne prime, so things are more straightforward.
1165 * However, chunks are aligned on a 'weird' boundary (521 bits).
1166 */
1167
1168/* Size of p521 in terms of mbedtls_mpi_uint */
1169#define P521_WIDTH ( 521 / 8 / sizeof( mbedtls_mpi_uint ) + 1 )
1170
1171/* Bits to keep in the most significant mbedtls_mpi_uint */
1172#define P521_MASK 0x01FF
1173
1174/*
1175 * Fast quasi-reduction modulo p521 (FIPS 186-3 D.2.5)
1176 * Write N as A1 + 2^521 A0, return A0 + A1
1177 */
1178static int ecp_mod_p521( mbedtls_mpi *N )
1179{
1180 int ret;
1181 size_t i;
1182 mbedtls_mpi M;
1183 mbedtls_mpi_uint Mp[P521_WIDTH + 1];
1184 /* Worst case for the size of M is when mbedtls_mpi_uint is 16 bits:
1185 * we need to hold bits 513 to 1056, which is 34 limbs, that is
1186 * P521_WIDTH + 1. Otherwise P521_WIDTH is enough. */
1187
1188 if( N->n < P521_WIDTH )
1189 return( 0 );
1190
1191 /* M = A1 */
1192 M.s = 1;
1193 M.n = N->n - ( P521_WIDTH - 1 );
1194 if( M.n > P521_WIDTH + 1 )
1195 M.n = P521_WIDTH + 1;
1196 M.p = Mp;
1197 memcpy( Mp, N->p + P521_WIDTH - 1, M.n * sizeof( mbedtls_mpi_uint ) );
1198 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, 521 % ( 8 * sizeof( mbedtls_mpi_uint ) ) ) );
1199
1200 /* N = A0 */
1201 N->p[P521_WIDTH - 1] &= P521_MASK;
1202 for( i = P521_WIDTH; i < N->n; i++ )
1203 N->p[i] = 0;
1204
1205 /* N = A0 + A1 */
1206 MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) );
1207
1208cleanup:
1209 return( ret );
1210}
1211
1212#undef P521_WIDTH
1213#undef P521_MASK
1214#endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */
1215
1216#endif /* MBEDTLS_ECP_NIST_OPTIM */
1217
1218#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
1219
1220/* Size of p255 in terms of mbedtls_mpi_uint */
1221#define P255_WIDTH ( 255 / 8 / sizeof( mbedtls_mpi_uint ) + 1 )
1222
1223/*
1224 * Fast quasi-reduction modulo p255 = 2^255 - 19
1225 * Write N as A0 + 2^255 A1, return A0 + 19 * A1
1226 */
1227static int ecp_mod_p255( mbedtls_mpi *N )
1228{
1229 int ret;
1230 size_t i;
1231 mbedtls_mpi M;
1232 mbedtls_mpi_uint Mp[P255_WIDTH + 2];
1233
1234 if( N->n < P255_WIDTH )
1235 return( 0 );
1236
1237 /* M = A1 */
1238 M.s = 1;
1239 M.n = N->n - ( P255_WIDTH - 1 );
1240 if( M.n > P255_WIDTH + 1 )
1241 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1242 M.p = Mp;
1243 memset( Mp, 0, sizeof Mp );
1244 memcpy( Mp, N->p + P255_WIDTH - 1, M.n * sizeof( mbedtls_mpi_uint ) );
1245 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, 255 % ( 8 * sizeof( mbedtls_mpi_uint ) ) ) );
1246 M.n++; /* Make room for multiplication by 19 */
1247
1248 /* N = A0 */
1249 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( N, 255, 0 ) );
1250 for( i = P255_WIDTH; i < N->n; i++ )
1251 N->p[i] = 0;
1252
1253 /* N = A0 + 19 * A1 */
1254 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &M, 19 ) );
1255 MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) );
1256
1257cleanup:
1258 return( ret );
1259}
1260#endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */
1261
1262#if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
1263
1264/* Size of p448 in terms of mbedtls_mpi_uint */
1265#define P448_WIDTH ( 448 / 8 / sizeof( mbedtls_mpi_uint ) )
1266
1267/* Number of limbs fully occupied by 2^224 (max), and limbs used by it (min) */
1268#define DIV_ROUND_UP( X, Y ) ( ( ( X ) + ( Y ) - 1 ) / ( Y ) )
1269#define P224_WIDTH_MIN ( 28 / sizeof( mbedtls_mpi_uint ) )
1270#define P224_WIDTH_MAX DIV_ROUND_UP( 28, sizeof( mbedtls_mpi_uint ) )
1271#define P224_UNUSED_BITS ( ( P224_WIDTH_MAX * sizeof( mbedtls_mpi_uint ) * 8 ) - 224 )
1272
1273/*
1274 * Fast quasi-reduction modulo p448 = 2^448 - 2^224 - 1
1275 * Write N as A0 + 2^448 A1 and A1 as B0 + 2^224 B1, and return
1276 * A0 + A1 + B1 + (B0 + B1) * 2^224. This is different to the reference
1277 * implementation of Curve448, which uses its own special 56-bit limbs rather
1278 * than a generic bignum library. We could squeeze some extra speed out on
1279 * 32-bit machines by splitting N up into 32-bit limbs and doing the
1280 * arithmetic using the limbs directly as we do for the NIST primes above,
1281 * but for 64-bit targets it should use half the number of operations if we do
1282 * the reduction with 224-bit limbs, since mpi_add_mpi will then use 64-bit adds.
1283 */
1284static int ecp_mod_p448( mbedtls_mpi *N )
1285{
1286 int ret;
1287 size_t i;
1288 mbedtls_mpi M, Q;
1289 mbedtls_mpi_uint Mp[P448_WIDTH + 1], Qp[P448_WIDTH];
1290
1291 if( N->n <= P448_WIDTH )
1292 return( 0 );
1293
1294 /* M = A1 */
1295 M.s = 1;
1296 M.n = N->n - ( P448_WIDTH );
1297 if( M.n > P448_WIDTH )
1298 /* Shouldn't be called with N larger than 2^896! */
1299 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1300 M.p = Mp;
1301 memset( Mp, 0, sizeof( Mp ) );
1302 memcpy( Mp, N->p + P448_WIDTH, M.n * sizeof( mbedtls_mpi_uint ) );
1303
1304 /* N = A0 */
1305 for( i = P448_WIDTH; i < N->n; i++ )
1306 N->p[i] = 0;
1307
1308 /* N += A1 */
1309 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &M ) );
1310
1311 /* Q = B1, N += B1 */
1312 Q = M;
1313 Q.p = Qp;
1314 memcpy( Qp, Mp, sizeof( Qp ) );
1315 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &Q, 224 ) );
1316 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &Q ) );
1317
1318 /* M = (B0 + B1) * 2^224, N += M */
1319 if( sizeof( mbedtls_mpi_uint ) > 4 )
1320 Mp[P224_WIDTH_MIN] &= ( (mbedtls_mpi_uint)-1 ) >> ( P224_UNUSED_BITS );
1321 for( i = P224_WIDTH_MAX; i < M.n; ++i )
1322 Mp[i] = 0;
1323 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &M, &M, &Q ) );
1324 M.n = P448_WIDTH + 1; /* Make room for shifted carry bit from the addition */
1325 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &M, 224 ) );
1326 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &M ) );
1327
1328cleanup:
1329 return( ret );
1330}
1331#endif /* MBEDTLS_ECP_DP_CURVE448_ENABLED */
1332
1333#if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) || \
1334 defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) || \
1335 defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
1336/*
1337 * Fast quasi-reduction modulo P = 2^s - R,
1338 * with R about 33 bits, used by the Koblitz curves.
1339 *
1340 * Write N as A0 + 2^224 A1, return A0 + R * A1.
1341 * Actually do two passes, since R is big.
1342 */
1343#define P_KOBLITZ_MAX ( 256 / 8 / sizeof( mbedtls_mpi_uint ) ) // Max limbs in P
1344#define P_KOBLITZ_R ( 8 / sizeof( mbedtls_mpi_uint ) ) // Limbs in R
1345static inline int ecp_mod_koblitz( mbedtls_mpi *N, mbedtls_mpi_uint *Rp, size_t p_limbs,
1346 size_t adjust, size_t shift, mbedtls_mpi_uint mask )
1347{
1348 int ret;
1349 size_t i;
1350 mbedtls_mpi M, R;
1351 mbedtls_mpi_uint Mp[P_KOBLITZ_MAX + P_KOBLITZ_R + 1];
1352
1353 if( N->n < p_limbs )
1354 return( 0 );
1355
1356 /* Init R */
1357 R.s = 1;
1358 R.p = Rp;
1359 R.n = P_KOBLITZ_R;
1360
1361 /* Common setup for M */
1362 M.s = 1;
1363 M.p = Mp;
1364
1365 /* M = A1 */
1366 M.n = N->n - ( p_limbs - adjust );
1367 if( M.n > p_limbs + adjust )
1368 M.n = p_limbs + adjust;
1369 memset( Mp, 0, sizeof Mp );
1370 memcpy( Mp, N->p + p_limbs - adjust, M.n * sizeof( mbedtls_mpi_uint ) );
1371 if( shift != 0 )
1372 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, shift ) );
1373 M.n += R.n; /* Make room for multiplication by R */
1374
1375 /* N = A0 */
1376 if( mask != 0 )
1377 N->p[p_limbs - 1] &= mask;
1378 for( i = p_limbs; i < N->n; i++ )
1379 N->p[i] = 0;
1380
1381 /* N = A0 + R * A1 */
1382 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &M, &M, &R ) );
1383 MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) );
1384
1385 /* Second pass */
1386
1387 /* M = A1 */
1388 M.n = N->n - ( p_limbs - adjust );
1389 if( M.n > p_limbs + adjust )
1390 M.n = p_limbs + adjust;
1391 memset( Mp, 0, sizeof Mp );
1392 memcpy( Mp, N->p + p_limbs - adjust, M.n * sizeof( mbedtls_mpi_uint ) );
1393 if( shift != 0 )
1394 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, shift ) );
1395 M.n += R.n; /* Make room for multiplication by R */
1396
1397 /* N = A0 */
1398 if( mask != 0 )
1399 N->p[p_limbs - 1] &= mask;
1400 for( i = p_limbs; i < N->n; i++ )
1401 N->p[i] = 0;
1402
1403 /* N = A0 + R * A1 */
1404 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &M, &M, &R ) );
1405 MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) );
1406
1407cleanup:
1408 return( ret );
1409}
1410#endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED) ||
1411 MBEDTLS_ECP_DP_SECP224K1_ENABLED) ||
1412 MBEDTLS_ECP_DP_SECP256K1_ENABLED) */
1413
1414#if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
1415/*
1416 * Fast quasi-reduction modulo p192k1 = 2^192 - R,
1417 * with R = 2^32 + 2^12 + 2^8 + 2^7 + 2^6 + 2^3 + 1 = 0x0100001119
1418 */
1419static int ecp_mod_p192k1( mbedtls_mpi *N )
1420{
1421 static mbedtls_mpi_uint Rp[] = {
1422 BYTES_TO_T_UINT_8( 0xC9, 0x11, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) };
1423
1424 return( ecp_mod_koblitz( N, Rp, 192 / 8 / sizeof( mbedtls_mpi_uint ), 0, 0, 0 ) );
1425}
1426#endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */
1427
1428#if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
1429/*
1430 * Fast quasi-reduction modulo p224k1 = 2^224 - R,
1431 * with R = 2^32 + 2^12 + 2^11 + 2^9 + 2^7 + 2^4 + 2 + 1 = 0x0100001A93
1432 */
1433static int ecp_mod_p224k1( mbedtls_mpi *N )
1434{
1435 static mbedtls_mpi_uint Rp[] = {
1436 BYTES_TO_T_UINT_8( 0x93, 0x1A, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) };
1437
1438#if defined(MBEDTLS_HAVE_INT64)
1439 return( ecp_mod_koblitz( N, Rp, 4, 1, 32, 0xFFFFFFFF ) );
1440#else
1441 return( ecp_mod_koblitz( N, Rp, 224 / 8 / sizeof( mbedtls_mpi_uint ), 0, 0, 0 ) );
1442#endif
1443}
1444
1445#endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */
1446
1447#if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
1448/*
1449 * Fast quasi-reduction modulo p256k1 = 2^256 - R,
1450 * with R = 2^32 + 2^9 + 2^8 + 2^7 + 2^6 + 2^4 + 1 = 0x01000003D1
1451 */
1452static int ecp_mod_p256k1( mbedtls_mpi *N )
1453{
1454 static mbedtls_mpi_uint Rp[] = {
1455 BYTES_TO_T_UINT_8( 0xD1, 0x03, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) };
1456 return( ecp_mod_koblitz( N, Rp, 256 / 8 / sizeof( mbedtls_mpi_uint ), 0, 0, 0 ) );
1457}
1458#endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */
1459
1460#endif /* !MBEDTLS_ECP_ALT */
1461
1462#endif /* MBEDTLS_ECP_C */
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