1 /*
2 * Elliptic curves over GF(p): curve-specific data and functions
3 *
4 * Copyright The Mbed TLS Contributors
5 * SPDX-License-Identifier: Apache-2.0 OR GPL-2.0-or-later
6 *
7 * This file is provided under the Apache License 2.0, or the
8 * GNU General Public License v2.0 or later.
9 *
10 * **********
11 * Apache License 2.0:
12 *
13 * Licensed under the Apache License, Version 2.0 (the "License"); you may
14 * not use this file except in compliance with the License.
15 * You may obtain a copy of the License at
16 *
17 * http://www.apache.org/licenses/LICENSE-2.0
18 *
19 * Unless required by applicable law or agreed to in writing, software
20 * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
21 * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
22 * See the License for the specific language governing permissions and
23 * limitations under the License.
24 *
25 * **********
26 *
27 * **********
28 * GNU General Public License v2.0 or later:
29 *
30 * This program is free software; you can redistribute it and/or modify
31 * it under the terms of the GNU General Public License as published by
32 * the Free Software Foundation; either version 2 of the License, or
33 * (at your option) any later version.
34 *
35 * This program is distributed in the hope that it will be useful,
36 * but WITHOUT ANY WARRANTY; without even the implied warranty of
37 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
38 * GNU General Public License for more details.
39 *
40 * You should have received a copy of the GNU General Public License along
41 * with this program; if not, write to the Free Software Foundation, Inc.,
42 * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
43 *
44 * **********
45 */
46
47 #if !defined(MBEDTLS_CONFIG_FILE)
48 #include "mbedtls/config.h"
49 #else
50 #include MBEDTLS_CONFIG_FILE
51 #endif
52
53 #if defined(MBEDTLS_ECP_C)
54
55 #include "mbedtls/ecp.h"
56 #include "mbedtls/platform_util.h"
57
58 #include <string.h>
59
60 #if !defined(MBEDTLS_ECP_ALT)
61
62 /* Parameter validation macros based on platform_util.h */
63 #define ECP_VALIDATE_RET( cond ) \
64 MBEDTLS_INTERNAL_VALIDATE_RET( cond, MBEDTLS_ERR_ECP_BAD_INPUT_DATA )
65 #define ECP_VALIDATE( cond ) \
66 MBEDTLS_INTERNAL_VALIDATE( cond )
67
68 #if ( defined(__ARMCC_VERSION) || defined(_MSC_VER) ) && \
69 !defined(inline) && !defined(__cplusplus)
70 #define inline __inline
71 #endif
72
73 /*
74 * Conversion macros for embedded constants:
75 * build lists of mbedtls_mpi_uint's from lists of unsigned char's grouped by 8, 4 or 2
76 */
77 #if defined(MBEDTLS_HAVE_INT32)
78
79 #define BYTES_TO_T_UINT_4( a, b, c, d ) \
80 ( (mbedtls_mpi_uint) (a) << 0 ) | \
81 ( (mbedtls_mpi_uint) (b) << 8 ) | \
82 ( (mbedtls_mpi_uint) (c) << 16 ) | \
83 ( (mbedtls_mpi_uint) (d) << 24 )
84
85 #define BYTES_TO_T_UINT_2( a, b ) \
86 BYTES_TO_T_UINT_4( a, b, 0, 0 )
87
88 #define BYTES_TO_T_UINT_8( a, b, c, d, e, f, g, h ) \
89 BYTES_TO_T_UINT_4( a, b, c, d ), \
90 BYTES_TO_T_UINT_4( e, f, g, h )
91
92 #else /* 64-bits */
93
94 #define BYTES_TO_T_UINT_8( a, b, c, d, e, f, g, h ) \
95 ( (mbedtls_mpi_uint) (a) << 0 ) | \
96 ( (mbedtls_mpi_uint) (b) << 8 ) | \
97 ( (mbedtls_mpi_uint) (c) << 16 ) | \
98 ( (mbedtls_mpi_uint) (d) << 24 ) | \
99 ( (mbedtls_mpi_uint) (e) << 32 ) | \
100 ( (mbedtls_mpi_uint) (f) << 40 ) | \
101 ( (mbedtls_mpi_uint) (g) << 48 ) | \
102 ( (mbedtls_mpi_uint) (h) << 56 )
103
104 #define BYTES_TO_T_UINT_4( a, b, c, d ) \
105 BYTES_TO_T_UINT_8( a, b, c, d, 0, 0, 0, 0 )
106
107 #define BYTES_TO_T_UINT_2( a, b ) \
108 BYTES_TO_T_UINT_8( a, b, 0, 0, 0, 0, 0, 0 )
109
110 #endif /* bits in mbedtls_mpi_uint */
111
112 /*
113 * Note: the constants are in little-endian order
114 * to be directly usable in MPIs
115 */
116
117 /*
118 * Domain parameters for secp192r1
119 */
120 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
121 static const mbedtls_mpi_uint secp192r1_p[] = {
122 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
123 BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
124 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
125 };
126 static const mbedtls_mpi_uint secp192r1_b[] = {
127 BYTES_TO_T_UINT_8( 0xB1, 0xB9, 0x46, 0xC1, 0xEC, 0xDE, 0xB8, 0xFE ),
128 BYTES_TO_T_UINT_8( 0x49, 0x30, 0x24, 0x72, 0xAB, 0xE9, 0xA7, 0x0F ),
129 BYTES_TO_T_UINT_8( 0xE7, 0x80, 0x9C, 0xE5, 0x19, 0x05, 0x21, 0x64 ),
130 };
131 static const mbedtls_mpi_uint secp192r1_gx[] = {
132 BYTES_TO_T_UINT_8( 0x12, 0x10, 0xFF, 0x82, 0xFD, 0x0A, 0xFF, 0xF4 ),
133 BYTES_TO_T_UINT_8( 0x00, 0x88, 0xA1, 0x43, 0xEB, 0x20, 0xBF, 0x7C ),
134 BYTES_TO_T_UINT_8( 0xF6, 0x90, 0x30, 0xB0, 0x0E, 0xA8, 0x8D, 0x18 ),
135 };
136 static const mbedtls_mpi_uint secp192r1_gy[] = {
137 BYTES_TO_T_UINT_8( 0x11, 0x48, 0x79, 0x1E, 0xA1, 0x77, 0xF9, 0x73 ),
138 BYTES_TO_T_UINT_8( 0xD5, 0xCD, 0x24, 0x6B, 0xED, 0x11, 0x10, 0x63 ),
139 BYTES_TO_T_UINT_8( 0x78, 0xDA, 0xC8, 0xFF, 0x95, 0x2B, 0x19, 0x07 ),
140 };
141 static const mbedtls_mpi_uint secp192r1_n[] = {
142 BYTES_TO_T_UINT_8( 0x31, 0x28, 0xD2, 0xB4, 0xB1, 0xC9, 0x6B, 0x14 ),
143 BYTES_TO_T_UINT_8( 0x36, 0xF8, 0xDE, 0x99, 0xFF, 0xFF, 0xFF, 0xFF ),
144 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
145 };
146 #endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */
147
148 /*
149 * Domain parameters for secp224r1
150 */
151 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
152 static const mbedtls_mpi_uint secp224r1_p[] = {
153 BYTES_TO_T_UINT_8( 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ),
154 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ),
155 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
156 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ),
157 };
158 static const mbedtls_mpi_uint secp224r1_b[] = {
159 BYTES_TO_T_UINT_8( 0xB4, 0xFF, 0x55, 0x23, 0x43, 0x39, 0x0B, 0x27 ),
160 BYTES_TO_T_UINT_8( 0xBA, 0xD8, 0xBF, 0xD7, 0xB7, 0xB0, 0x44, 0x50 ),
161 BYTES_TO_T_UINT_8( 0x56, 0x32, 0x41, 0xF5, 0xAB, 0xB3, 0x04, 0x0C ),
162 BYTES_TO_T_UINT_4( 0x85, 0x0A, 0x05, 0xB4 ),
163 };
164 static const mbedtls_mpi_uint secp224r1_gx[] = {
165 BYTES_TO_T_UINT_8( 0x21, 0x1D, 0x5C, 0x11, 0xD6, 0x80, 0x32, 0x34 ),
166 BYTES_TO_T_UINT_8( 0x22, 0x11, 0xC2, 0x56, 0xD3, 0xC1, 0x03, 0x4A ),
167 BYTES_TO_T_UINT_8( 0xB9, 0x90, 0x13, 0x32, 0x7F, 0xBF, 0xB4, 0x6B ),
168 BYTES_TO_T_UINT_4( 0xBD, 0x0C, 0x0E, 0xB7 ),
169 };
170 static const mbedtls_mpi_uint secp224r1_gy[] = {
171 BYTES_TO_T_UINT_8( 0x34, 0x7E, 0x00, 0x85, 0x99, 0x81, 0xD5, 0x44 ),
172 BYTES_TO_T_UINT_8( 0x64, 0x47, 0x07, 0x5A, 0xA0, 0x75, 0x43, 0xCD ),
173 BYTES_TO_T_UINT_8( 0xE6, 0xDF, 0x22, 0x4C, 0xFB, 0x23, 0xF7, 0xB5 ),
174 BYTES_TO_T_UINT_4( 0x88, 0x63, 0x37, 0xBD ),
175 };
176 static const mbedtls_mpi_uint secp224r1_n[] = {
177 BYTES_TO_T_UINT_8( 0x3D, 0x2A, 0x5C, 0x5C, 0x45, 0x29, 0xDD, 0x13 ),
178 BYTES_TO_T_UINT_8( 0x3E, 0xF0, 0xB8, 0xE0, 0xA2, 0x16, 0xFF, 0xFF ),
179 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
180 BYTES_TO_T_UINT_4( 0xFF, 0xFF, 0xFF, 0xFF ),
181 };
182 #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */
183
184 /*
185 * Domain parameters for secp256r1
186 */
187 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
188 static const mbedtls_mpi_uint secp256r1_p[] = {
189 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
190 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ),
191 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ),
192 BYTES_TO_T_UINT_8( 0x01, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ),
193 };
194 static const mbedtls_mpi_uint secp256r1_b[] = {
195 BYTES_TO_T_UINT_8( 0x4B, 0x60, 0xD2, 0x27, 0x3E, 0x3C, 0xCE, 0x3B ),
196 BYTES_TO_T_UINT_8( 0xF6, 0xB0, 0x53, 0xCC, 0xB0, 0x06, 0x1D, 0x65 ),
197 BYTES_TO_T_UINT_8( 0xBC, 0x86, 0x98, 0x76, 0x55, 0xBD, 0xEB, 0xB3 ),
198 BYTES_TO_T_UINT_8( 0xE7, 0x93, 0x3A, 0xAA, 0xD8, 0x35, 0xC6, 0x5A ),
199 };
200 static const mbedtls_mpi_uint secp256r1_gx[] = {
201 BYTES_TO_T_UINT_8( 0x96, 0xC2, 0x98, 0xD8, 0x45, 0x39, 0xA1, 0xF4 ),
202 BYTES_TO_T_UINT_8( 0xA0, 0x33, 0xEB, 0x2D, 0x81, 0x7D, 0x03, 0x77 ),
203 BYTES_TO_T_UINT_8( 0xF2, 0x40, 0xA4, 0x63, 0xE5, 0xE6, 0xBC, 0xF8 ),
204 BYTES_TO_T_UINT_8( 0x47, 0x42, 0x2C, 0xE1, 0xF2, 0xD1, 0x17, 0x6B ),
205 };
206 static const mbedtls_mpi_uint secp256r1_gy[] = {
207 BYTES_TO_T_UINT_8( 0xF5, 0x51, 0xBF, 0x37, 0x68, 0x40, 0xB6, 0xCB ),
208 BYTES_TO_T_UINT_8( 0xCE, 0x5E, 0x31, 0x6B, 0x57, 0x33, 0xCE, 0x2B ),
209 BYTES_TO_T_UINT_8( 0x16, 0x9E, 0x0F, 0x7C, 0x4A, 0xEB, 0xE7, 0x8E ),
210 BYTES_TO_T_UINT_8( 0x9B, 0x7F, 0x1A, 0xFE, 0xE2, 0x42, 0xE3, 0x4F ),
211 };
212 static const mbedtls_mpi_uint secp256r1_n[] = {
213 BYTES_TO_T_UINT_8( 0x51, 0x25, 0x63, 0xFC, 0xC2, 0xCA, 0xB9, 0xF3 ),
214 BYTES_TO_T_UINT_8( 0x84, 0x9E, 0x17, 0xA7, 0xAD, 0xFA, 0xE6, 0xBC ),
215 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
216 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ),
217 };
218 #endif /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */
219
220 /*
221 * Domain parameters for secp384r1
222 */
223 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
224 static const mbedtls_mpi_uint secp384r1_p[] = {
225 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ),
226 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ),
227 BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
228 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
229 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
230 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
231 };
232 static const mbedtls_mpi_uint secp384r1_b[] = {
233 BYTES_TO_T_UINT_8( 0xEF, 0x2A, 0xEC, 0xD3, 0xED, 0xC8, 0x85, 0x2A ),
234 BYTES_TO_T_UINT_8( 0x9D, 0xD1, 0x2E, 0x8A, 0x8D, 0x39, 0x56, 0xC6 ),
235 BYTES_TO_T_UINT_8( 0x5A, 0x87, 0x13, 0x50, 0x8F, 0x08, 0x14, 0x03 ),
236 BYTES_TO_T_UINT_8( 0x12, 0x41, 0x81, 0xFE, 0x6E, 0x9C, 0x1D, 0x18 ),
237 BYTES_TO_T_UINT_8( 0x19, 0x2D, 0xF8, 0xE3, 0x6B, 0x05, 0x8E, 0x98 ),
238 BYTES_TO_T_UINT_8( 0xE4, 0xE7, 0x3E, 0xE2, 0xA7, 0x2F, 0x31, 0xB3 ),
239 };
240 static const mbedtls_mpi_uint secp384r1_gx[] = {
241 BYTES_TO_T_UINT_8( 0xB7, 0x0A, 0x76, 0x72, 0x38, 0x5E, 0x54, 0x3A ),
242 BYTES_TO_T_UINT_8( 0x6C, 0x29, 0x55, 0xBF, 0x5D, 0xF2, 0x02, 0x55 ),
243 BYTES_TO_T_UINT_8( 0x38, 0x2A, 0x54, 0x82, 0xE0, 0x41, 0xF7, 0x59 ),
244 BYTES_TO_T_UINT_8( 0x98, 0x9B, 0xA7, 0x8B, 0x62, 0x3B, 0x1D, 0x6E ),
245 BYTES_TO_T_UINT_8( 0x74, 0xAD, 0x20, 0xF3, 0x1E, 0xC7, 0xB1, 0x8E ),
246 BYTES_TO_T_UINT_8( 0x37, 0x05, 0x8B, 0xBE, 0x22, 0xCA, 0x87, 0xAA ),
247 };
248 static const mbedtls_mpi_uint secp384r1_gy[] = {
249 BYTES_TO_T_UINT_8( 0x5F, 0x0E, 0xEA, 0x90, 0x7C, 0x1D, 0x43, 0x7A ),
250 BYTES_TO_T_UINT_8( 0x9D, 0x81, 0x7E, 0x1D, 0xCE, 0xB1, 0x60, 0x0A ),
251 BYTES_TO_T_UINT_8( 0xC0, 0xB8, 0xF0, 0xB5, 0x13, 0x31, 0xDA, 0xE9 ),
252 BYTES_TO_T_UINT_8( 0x7C, 0x14, 0x9A, 0x28, 0xBD, 0x1D, 0xF4, 0xF8 ),
253 BYTES_TO_T_UINT_8( 0x29, 0xDC, 0x92, 0x92, 0xBF, 0x98, 0x9E, 0x5D ),
254 BYTES_TO_T_UINT_8( 0x6F, 0x2C, 0x26, 0x96, 0x4A, 0xDE, 0x17, 0x36 ),
255 };
256 static const mbedtls_mpi_uint secp384r1_n[] = {
257 BYTES_TO_T_UINT_8( 0x73, 0x29, 0xC5, 0xCC, 0x6A, 0x19, 0xEC, 0xEC ),
258 BYTES_TO_T_UINT_8( 0x7A, 0xA7, 0xB0, 0x48, 0xB2, 0x0D, 0x1A, 0x58 ),
259 BYTES_TO_T_UINT_8( 0xDF, 0x2D, 0x37, 0xF4, 0x81, 0x4D, 0x63, 0xC7 ),
260 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
261 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
262 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
263 };
264 #endif /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */
265
266 /*
267 * Domain parameters for secp521r1
268 */
269 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
270 static const mbedtls_mpi_uint secp521r1_p[] = {
271 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
272 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
273 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
274 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
275 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
276 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
277 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
278 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
279 BYTES_TO_T_UINT_2( 0xFF, 0x01 ),
280 };
281 static const mbedtls_mpi_uint secp521r1_b[] = {
282 BYTES_TO_T_UINT_8( 0x00, 0x3F, 0x50, 0x6B, 0xD4, 0x1F, 0x45, 0xEF ),
283 BYTES_TO_T_UINT_8( 0xF1, 0x34, 0x2C, 0x3D, 0x88, 0xDF, 0x73, 0x35 ),
284 BYTES_TO_T_UINT_8( 0x07, 0xBF, 0xB1, 0x3B, 0xBD, 0xC0, 0x52, 0x16 ),
285 BYTES_TO_T_UINT_8( 0x7B, 0x93, 0x7E, 0xEC, 0x51, 0x39, 0x19, 0x56 ),
286 BYTES_TO_T_UINT_8( 0xE1, 0x09, 0xF1, 0x8E, 0x91, 0x89, 0xB4, 0xB8 ),
287 BYTES_TO_T_UINT_8( 0xF3, 0x15, 0xB3, 0x99, 0x5B, 0x72, 0xDA, 0xA2 ),
288 BYTES_TO_T_UINT_8( 0xEE, 0x40, 0x85, 0xB6, 0xA0, 0x21, 0x9A, 0x92 ),
289 BYTES_TO_T_UINT_8( 0x1F, 0x9A, 0x1C, 0x8E, 0x61, 0xB9, 0x3E, 0x95 ),
290 BYTES_TO_T_UINT_2( 0x51, 0x00 ),
291 };
292 static const mbedtls_mpi_uint secp521r1_gx[] = {
293 BYTES_TO_T_UINT_8( 0x66, 0xBD, 0xE5, 0xC2, 0x31, 0x7E, 0x7E, 0xF9 ),
294 BYTES_TO_T_UINT_8( 0x9B, 0x42, 0x6A, 0x85, 0xC1, 0xB3, 0x48, 0x33 ),
295 BYTES_TO_T_UINT_8( 0xDE, 0xA8, 0xFF, 0xA2, 0x27, 0xC1, 0x1D, 0xFE ),
296 BYTES_TO_T_UINT_8( 0x28, 0x59, 0xE7, 0xEF, 0x77, 0x5E, 0x4B, 0xA1 ),
297 BYTES_TO_T_UINT_8( 0xBA, 0x3D, 0x4D, 0x6B, 0x60, 0xAF, 0x28, 0xF8 ),
298 BYTES_TO_T_UINT_8( 0x21, 0xB5, 0x3F, 0x05, 0x39, 0x81, 0x64, 0x9C ),
299 BYTES_TO_T_UINT_8( 0x42, 0xB4, 0x95, 0x23, 0x66, 0xCB, 0x3E, 0x9E ),
300 BYTES_TO_T_UINT_8( 0xCD, 0xE9, 0x04, 0x04, 0xB7, 0x06, 0x8E, 0x85 ),
301 BYTES_TO_T_UINT_2( 0xC6, 0x00 ),
302 };
303 static const mbedtls_mpi_uint secp521r1_gy[] = {
304 BYTES_TO_T_UINT_8( 0x50, 0x66, 0xD1, 0x9F, 0x76, 0x94, 0xBE, 0x88 ),
305 BYTES_TO_T_UINT_8( 0x40, 0xC2, 0x72, 0xA2, 0x86, 0x70, 0x3C, 0x35 ),
306 BYTES_TO_T_UINT_8( 0x61, 0x07, 0xAD, 0x3F, 0x01, 0xB9, 0x50, 0xC5 ),
307 BYTES_TO_T_UINT_8( 0x40, 0x26, 0xF4, 0x5E, 0x99, 0x72, 0xEE, 0x97 ),
308 BYTES_TO_T_UINT_8( 0x2C, 0x66, 0x3E, 0x27, 0x17, 0xBD, 0xAF, 0x17 ),
309 BYTES_TO_T_UINT_8( 0x68, 0x44, 0x9B, 0x57, 0x49, 0x44, 0xF5, 0x98 ),
310 BYTES_TO_T_UINT_8( 0xD9, 0x1B, 0x7D, 0x2C, 0xB4, 0x5F, 0x8A, 0x5C ),
311 BYTES_TO_T_UINT_8( 0x04, 0xC0, 0x3B, 0x9A, 0x78, 0x6A, 0x29, 0x39 ),
312 BYTES_TO_T_UINT_2( 0x18, 0x01 ),
313 };
314 static const mbedtls_mpi_uint secp521r1_n[] = {
315 BYTES_TO_T_UINT_8( 0x09, 0x64, 0x38, 0x91, 0x1E, 0xB7, 0x6F, 0xBB ),
316 BYTES_TO_T_UINT_8( 0xAE, 0x47, 0x9C, 0x89, 0xB8, 0xC9, 0xB5, 0x3B ),
317 BYTES_TO_T_UINT_8( 0xD0, 0xA5, 0x09, 0xF7, 0x48, 0x01, 0xCC, 0x7F ),
318 BYTES_TO_T_UINT_8( 0x6B, 0x96, 0x2F, 0xBF, 0x83, 0x87, 0x86, 0x51 ),
319 BYTES_TO_T_UINT_8( 0xFA, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
320 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
321 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
322 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
323 BYTES_TO_T_UINT_2( 0xFF, 0x01 ),
324 };
325 #endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */
326
327 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
328 static const mbedtls_mpi_uint secp192k1_p[] = {
329 BYTES_TO_T_UINT_8( 0x37, 0xEE, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ),
330 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
331 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
332 };
333 static const mbedtls_mpi_uint secp192k1_a[] = {
334 BYTES_TO_T_UINT_2( 0x00, 0x00 ),
335 };
336 static const mbedtls_mpi_uint secp192k1_b[] = {
337 BYTES_TO_T_UINT_2( 0x03, 0x00 ),
338 };
339 static const mbedtls_mpi_uint secp192k1_gx[] = {
340 BYTES_TO_T_UINT_8( 0x7D, 0x6C, 0xE0, 0xEA, 0xB1, 0xD1, 0xA5, 0x1D ),
341 BYTES_TO_T_UINT_8( 0x34, 0xF4, 0xB7, 0x80, 0x02, 0x7D, 0xB0, 0x26 ),
342 BYTES_TO_T_UINT_8( 0xAE, 0xE9, 0x57, 0xC0, 0x0E, 0xF1, 0x4F, 0xDB ),
343 };
344 static const mbedtls_mpi_uint secp192k1_gy[] = {
345 BYTES_TO_T_UINT_8( 0x9D, 0x2F, 0x5E, 0xD9, 0x88, 0xAA, 0x82, 0x40 ),
346 BYTES_TO_T_UINT_8( 0x34, 0x86, 0xBE, 0x15, 0xD0, 0x63, 0x41, 0x84 ),
347 BYTES_TO_T_UINT_8( 0xA7, 0x28, 0x56, 0x9C, 0x6D, 0x2F, 0x2F, 0x9B ),
348 };
349 static const mbedtls_mpi_uint secp192k1_n[] = {
350 BYTES_TO_T_UINT_8( 0x8D, 0xFD, 0xDE, 0x74, 0x6A, 0x46, 0x69, 0x0F ),
351 BYTES_TO_T_UINT_8( 0x17, 0xFC, 0xF2, 0x26, 0xFE, 0xFF, 0xFF, 0xFF ),
352 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
353 };
354 #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */
355
356 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
357 static const mbedtls_mpi_uint secp224k1_p[] = {
358 BYTES_TO_T_UINT_8( 0x6D, 0xE5, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ),
359 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
360 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
361 BYTES_TO_T_UINT_4( 0xFF, 0xFF, 0xFF, 0xFF ),
362 };
363 static const mbedtls_mpi_uint secp224k1_a[] = {
364 BYTES_TO_T_UINT_2( 0x00, 0x00 ),
365 };
366 static const mbedtls_mpi_uint secp224k1_b[] = {
367 BYTES_TO_T_UINT_2( 0x05, 0x00 ),
368 };
369 static const mbedtls_mpi_uint secp224k1_gx[] = {
370 BYTES_TO_T_UINT_8( 0x5C, 0xA4, 0xB7, 0xB6, 0x0E, 0x65, 0x7E, 0x0F ),
371 BYTES_TO_T_UINT_8( 0xA9, 0x75, 0x70, 0xE4, 0xE9, 0x67, 0xA4, 0x69 ),
372 BYTES_TO_T_UINT_8( 0xA1, 0x28, 0xFC, 0x30, 0xDF, 0x99, 0xF0, 0x4D ),
373 BYTES_TO_T_UINT_4( 0x33, 0x5B, 0x45, 0xA1 ),
374 };
375 static const mbedtls_mpi_uint secp224k1_gy[] = {
376 BYTES_TO_T_UINT_8( 0xA5, 0x61, 0x6D, 0x55, 0xDB, 0x4B, 0xCA, 0xE2 ),
377 BYTES_TO_T_UINT_8( 0x59, 0xBD, 0xB0, 0xC0, 0xF7, 0x19, 0xE3, 0xF7 ),
378 BYTES_TO_T_UINT_8( 0xD6, 0xFB, 0xCA, 0x82, 0x42, 0x34, 0xBA, 0x7F ),
379 BYTES_TO_T_UINT_4( 0xED, 0x9F, 0x08, 0x7E ),
380 };
381 static const mbedtls_mpi_uint secp224k1_n[] = {
382 BYTES_TO_T_UINT_8( 0xF7, 0xB1, 0x9F, 0x76, 0x71, 0xA9, 0xF0, 0xCA ),
383 BYTES_TO_T_UINT_8( 0x84, 0x61, 0xEC, 0xD2, 0xE8, 0xDC, 0x01, 0x00 ),
384 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ),
385 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ),
386 };
387 #endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */
388
389 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
390 static const mbedtls_mpi_uint secp256k1_p[] = {
391 BYTES_TO_T_UINT_8( 0x2F, 0xFC, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ),
392 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
393 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
394 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
395 };
396 static const mbedtls_mpi_uint secp256k1_a[] = {
397 BYTES_TO_T_UINT_2( 0x00, 0x00 ),
398 };
399 static const mbedtls_mpi_uint secp256k1_b[] = {
400 BYTES_TO_T_UINT_2( 0x07, 0x00 ),
401 };
402 static const mbedtls_mpi_uint secp256k1_gx[] = {
403 BYTES_TO_T_UINT_8( 0x98, 0x17, 0xF8, 0x16, 0x5B, 0x81, 0xF2, 0x59 ),
404 BYTES_TO_T_UINT_8( 0xD9, 0x28, 0xCE, 0x2D, 0xDB, 0xFC, 0x9B, 0x02 ),
405 BYTES_TO_T_UINT_8( 0x07, 0x0B, 0x87, 0xCE, 0x95, 0x62, 0xA0, 0x55 ),
406 BYTES_TO_T_UINT_8( 0xAC, 0xBB, 0xDC, 0xF9, 0x7E, 0x66, 0xBE, 0x79 ),
407 };
408 static const mbedtls_mpi_uint secp256k1_gy[] = {
409 BYTES_TO_T_UINT_8( 0xB8, 0xD4, 0x10, 0xFB, 0x8F, 0xD0, 0x47, 0x9C ),
410 BYTES_TO_T_UINT_8( 0x19, 0x54, 0x85, 0xA6, 0x48, 0xB4, 0x17, 0xFD ),
411 BYTES_TO_T_UINT_8( 0xA8, 0x08, 0x11, 0x0E, 0xFC, 0xFB, 0xA4, 0x5D ),
412 BYTES_TO_T_UINT_8( 0x65, 0xC4, 0xA3, 0x26, 0x77, 0xDA, 0x3A, 0x48 ),
413 };
414 static const mbedtls_mpi_uint secp256k1_n[] = {
415 BYTES_TO_T_UINT_8( 0x41, 0x41, 0x36, 0xD0, 0x8C, 0x5E, 0xD2, 0xBF ),
416 BYTES_TO_T_UINT_8( 0x3B, 0xA0, 0x48, 0xAF, 0xE6, 0xDC, 0xAE, 0xBA ),
417 BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
418 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
419 };
420 #endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */
421
422 /*
423 * Domain parameters for brainpoolP256r1 (RFC 5639 3.4)
424 */
425 #if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED)
426 static const mbedtls_mpi_uint brainpoolP256r1_p[] = {
427 BYTES_TO_T_UINT_8( 0x77, 0x53, 0x6E, 0x1F, 0x1D, 0x48, 0x13, 0x20 ),
428 BYTES_TO_T_UINT_8( 0x28, 0x20, 0x26, 0xD5, 0x23, 0xF6, 0x3B, 0x6E ),
429 BYTES_TO_T_UINT_8( 0x72, 0x8D, 0x83, 0x9D, 0x90, 0x0A, 0x66, 0x3E ),
430 BYTES_TO_T_UINT_8( 0xBC, 0xA9, 0xEE, 0xA1, 0xDB, 0x57, 0xFB, 0xA9 ),
431 };
432 static const mbedtls_mpi_uint brainpoolP256r1_a[] = {
433 BYTES_TO_T_UINT_8( 0xD9, 0xB5, 0x30, 0xF3, 0x44, 0x4B, 0x4A, 0xE9 ),
434 BYTES_TO_T_UINT_8( 0x6C, 0x5C, 0xDC, 0x26, 0xC1, 0x55, 0x80, 0xFB ),
435 BYTES_TO_T_UINT_8( 0xE7, 0xFF, 0x7A, 0x41, 0x30, 0x75, 0xF6, 0xEE ),
436 BYTES_TO_T_UINT_8( 0x57, 0x30, 0x2C, 0xFC, 0x75, 0x09, 0x5A, 0x7D ),
437 };
438 static const mbedtls_mpi_uint brainpoolP256r1_b[] = {
439 BYTES_TO_T_UINT_8( 0xB6, 0x07, 0x8C, 0xFF, 0x18, 0xDC, 0xCC, 0x6B ),
440 BYTES_TO_T_UINT_8( 0xCE, 0xE1, 0xF7, 0x5C, 0x29, 0x16, 0x84, 0x95 ),
441 BYTES_TO_T_UINT_8( 0xBF, 0x7C, 0xD7, 0xBB, 0xD9, 0xB5, 0x30, 0xF3 ),
442 BYTES_TO_T_UINT_8( 0x44, 0x4B, 0x4A, 0xE9, 0x6C, 0x5C, 0xDC, 0x26 ),
443 };
444 static const mbedtls_mpi_uint brainpoolP256r1_gx[] = {
445 BYTES_TO_T_UINT_8( 0x62, 0x32, 0xCE, 0x9A, 0xBD, 0x53, 0x44, 0x3A ),
446 BYTES_TO_T_UINT_8( 0xC2, 0x23, 0xBD, 0xE3, 0xE1, 0x27, 0xDE, 0xB9 ),
447 BYTES_TO_T_UINT_8( 0xAF, 0xB7, 0x81, 0xFC, 0x2F, 0x48, 0x4B, 0x2C ),
448 BYTES_TO_T_UINT_8( 0xCB, 0x57, 0x7E, 0xCB, 0xB9, 0xAE, 0xD2, 0x8B ),
449 };
450 static const mbedtls_mpi_uint brainpoolP256r1_gy[] = {
451 BYTES_TO_T_UINT_8( 0x97, 0x69, 0x04, 0x2F, 0xC7, 0x54, 0x1D, 0x5C ),
452 BYTES_TO_T_UINT_8( 0x54, 0x8E, 0xED, 0x2D, 0x13, 0x45, 0x77, 0xC2 ),
453 BYTES_TO_T_UINT_8( 0xC9, 0x1D, 0x61, 0x14, 0x1A, 0x46, 0xF8, 0x97 ),
454 BYTES_TO_T_UINT_8( 0xFD, 0xC4, 0xDA, 0xC3, 0x35, 0xF8, 0x7E, 0x54 ),
455 };
456 static const mbedtls_mpi_uint brainpoolP256r1_n[] = {
457 BYTES_TO_T_UINT_8( 0xA7, 0x56, 0x48, 0x97, 0x82, 0x0E, 0x1E, 0x90 ),
458 BYTES_TO_T_UINT_8( 0xF7, 0xA6, 0x61, 0xB5, 0xA3, 0x7A, 0x39, 0x8C ),
459 BYTES_TO_T_UINT_8( 0x71, 0x8D, 0x83, 0x9D, 0x90, 0x0A, 0x66, 0x3E ),
460 BYTES_TO_T_UINT_8( 0xBC, 0xA9, 0xEE, 0xA1, 0xDB, 0x57, 0xFB, 0xA9 ),
461 };
462 #endif /* MBEDTLS_ECP_DP_BP256R1_ENABLED */
463
464 /*
465 * Domain parameters for brainpoolP384r1 (RFC 5639 3.6)
466 */
467 #if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED)
468 static const mbedtls_mpi_uint brainpoolP384r1_p[] = {
469 BYTES_TO_T_UINT_8( 0x53, 0xEC, 0x07, 0x31, 0x13, 0x00, 0x47, 0x87 ),
470 BYTES_TO_T_UINT_8( 0x71, 0x1A, 0x1D, 0x90, 0x29, 0xA7, 0xD3, 0xAC ),
471 BYTES_TO_T_UINT_8( 0x23, 0x11, 0xB7, 0x7F, 0x19, 0xDA, 0xB1, 0x12 ),
472 BYTES_TO_T_UINT_8( 0xB4, 0x56, 0x54, 0xED, 0x09, 0x71, 0x2F, 0x15 ),
473 BYTES_TO_T_UINT_8( 0xDF, 0x41, 0xE6, 0x50, 0x7E, 0x6F, 0x5D, 0x0F ),
474 BYTES_TO_T_UINT_8( 0x28, 0x6D, 0x38, 0xA3, 0x82, 0x1E, 0xB9, 0x8C ),
475 };
476 static const mbedtls_mpi_uint brainpoolP384r1_a[] = {
477 BYTES_TO_T_UINT_8( 0x26, 0x28, 0xCE, 0x22, 0xDD, 0xC7, 0xA8, 0x04 ),
478 BYTES_TO_T_UINT_8( 0xEB, 0xD4, 0x3A, 0x50, 0x4A, 0x81, 0xA5, 0x8A ),
479 BYTES_TO_T_UINT_8( 0x0F, 0xF9, 0x91, 0xBA, 0xEF, 0x65, 0x91, 0x13 ),
480 BYTES_TO_T_UINT_8( 0x87, 0x27, 0xB2, 0x4F, 0x8E, 0xA2, 0xBE, 0xC2 ),
481 BYTES_TO_T_UINT_8( 0xA0, 0xAF, 0x05, 0xCE, 0x0A, 0x08, 0x72, 0x3C ),
482 BYTES_TO_T_UINT_8( 0x0C, 0x15, 0x8C, 0x3D, 0xC6, 0x82, 0xC3, 0x7B ),
483 };
484 static const mbedtls_mpi_uint brainpoolP384r1_b[] = {
485 BYTES_TO_T_UINT_8( 0x11, 0x4C, 0x50, 0xFA, 0x96, 0x86, 0xB7, 0x3A ),
486 BYTES_TO_T_UINT_8( 0x94, 0xC9, 0xDB, 0x95, 0x02, 0x39, 0xB4, 0x7C ),
487 BYTES_TO_T_UINT_8( 0xD5, 0x62, 0xEB, 0x3E, 0xA5, 0x0E, 0x88, 0x2E ),
488 BYTES_TO_T_UINT_8( 0xA6, 0xD2, 0xDC, 0x07, 0xE1, 0x7D, 0xB7, 0x2F ),
489 BYTES_TO_T_UINT_8( 0x7C, 0x44, 0xF0, 0x16, 0x54, 0xB5, 0x39, 0x8B ),
490 BYTES_TO_T_UINT_8( 0x26, 0x28, 0xCE, 0x22, 0xDD, 0xC7, 0xA8, 0x04 ),
491 };
492 static const mbedtls_mpi_uint brainpoolP384r1_gx[] = {
493 BYTES_TO_T_UINT_8( 0x1E, 0xAF, 0xD4, 0x47, 0xE2, 0xB2, 0x87, 0xEF ),
494 BYTES_TO_T_UINT_8( 0xAA, 0x46, 0xD6, 0x36, 0x34, 0xE0, 0x26, 0xE8 ),
495 BYTES_TO_T_UINT_8( 0xE8, 0x10, 0xBD, 0x0C, 0xFE, 0xCA, 0x7F, 0xDB ),
496 BYTES_TO_T_UINT_8( 0xE3, 0x4F, 0xF1, 0x7E, 0xE7, 0xA3, 0x47, 0x88 ),
497 BYTES_TO_T_UINT_8( 0x6B, 0x3F, 0xC1, 0xB7, 0x81, 0x3A, 0xA6, 0xA2 ),
498 BYTES_TO_T_UINT_8( 0xFF, 0x45, 0xCF, 0x68, 0xF0, 0x64, 0x1C, 0x1D ),
499 };
500 static const mbedtls_mpi_uint brainpoolP384r1_gy[] = {
501 BYTES_TO_T_UINT_8( 0x15, 0x53, 0x3C, 0x26, 0x41, 0x03, 0x82, 0x42 ),
502 BYTES_TO_T_UINT_8( 0x11, 0x81, 0x91, 0x77, 0x21, 0x46, 0x46, 0x0E ),
503 BYTES_TO_T_UINT_8( 0x28, 0x29, 0x91, 0xF9, 0x4F, 0x05, 0x9C, 0xE1 ),
504 BYTES_TO_T_UINT_8( 0x64, 0x58, 0xEC, 0xFE, 0x29, 0x0B, 0xB7, 0x62 ),
505 BYTES_TO_T_UINT_8( 0x52, 0xD5, 0xCF, 0x95, 0x8E, 0xEB, 0xB1, 0x5C ),
506 BYTES_TO_T_UINT_8( 0xA4, 0xC2, 0xF9, 0x20, 0x75, 0x1D, 0xBE, 0x8A ),
507 };
508 static const mbedtls_mpi_uint brainpoolP384r1_n[] = {
509 BYTES_TO_T_UINT_8( 0x65, 0x65, 0x04, 0xE9, 0x02, 0x32, 0x88, 0x3B ),
510 BYTES_TO_T_UINT_8( 0x10, 0xC3, 0x7F, 0x6B, 0xAF, 0xB6, 0x3A, 0xCF ),
511 BYTES_TO_T_UINT_8( 0xA7, 0x25, 0x04, 0xAC, 0x6C, 0x6E, 0x16, 0x1F ),
512 BYTES_TO_T_UINT_8( 0xB3, 0x56, 0x54, 0xED, 0x09, 0x71, 0x2F, 0x15 ),
513 BYTES_TO_T_UINT_8( 0xDF, 0x41, 0xE6, 0x50, 0x7E, 0x6F, 0x5D, 0x0F ),
514 BYTES_TO_T_UINT_8( 0x28, 0x6D, 0x38, 0xA3, 0x82, 0x1E, 0xB9, 0x8C ),
515 };
516 #endif /* MBEDTLS_ECP_DP_BP384R1_ENABLED */
517
518 /*
519 * Domain parameters for brainpoolP512r1 (RFC 5639 3.7)
520 */
521 #if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED)
522 static const mbedtls_mpi_uint brainpoolP512r1_p[] = {
523 BYTES_TO_T_UINT_8( 0xF3, 0x48, 0x3A, 0x58, 0x56, 0x60, 0xAA, 0x28 ),
524 BYTES_TO_T_UINT_8( 0x85, 0xC6, 0x82, 0x2D, 0x2F, 0xFF, 0x81, 0x28 ),
525 BYTES_TO_T_UINT_8( 0xE6, 0x80, 0xA3, 0xE6, 0x2A, 0xA1, 0xCD, 0xAE ),
526 BYTES_TO_T_UINT_8( 0x42, 0x68, 0xC6, 0x9B, 0x00, 0x9B, 0x4D, 0x7D ),
527 BYTES_TO_T_UINT_8( 0x71, 0x08, 0x33, 0x70, 0xCA, 0x9C, 0x63, 0xD6 ),
528 BYTES_TO_T_UINT_8( 0x0E, 0xD2, 0xC9, 0xB3, 0xB3, 0x8D, 0x30, 0xCB ),
529 BYTES_TO_T_UINT_8( 0x07, 0xFC, 0xC9, 0x33, 0xAE, 0xE6, 0xD4, 0x3F ),
530 BYTES_TO_T_UINT_8( 0x8B, 0xC4, 0xE9, 0xDB, 0xB8, 0x9D, 0xDD, 0xAA ),
531 };
532 static const mbedtls_mpi_uint brainpoolP512r1_a[] = {
533 BYTES_TO_T_UINT_8( 0xCA, 0x94, 0xFC, 0x77, 0x4D, 0xAC, 0xC1, 0xE7 ),
534 BYTES_TO_T_UINT_8( 0xB9, 0xC7, 0xF2, 0x2B, 0xA7, 0x17, 0x11, 0x7F ),
535 BYTES_TO_T_UINT_8( 0xB5, 0xC8, 0x9A, 0x8B, 0xC9, 0xF1, 0x2E, 0x0A ),
536 BYTES_TO_T_UINT_8( 0xA1, 0x3A, 0x25, 0xA8, 0x5A, 0x5D, 0xED, 0x2D ),
537 BYTES_TO_T_UINT_8( 0xBC, 0x63, 0x98, 0xEA, 0xCA, 0x41, 0x34, 0xA8 ),
538 BYTES_TO_T_UINT_8( 0x10, 0x16, 0xF9, 0x3D, 0x8D, 0xDD, 0xCB, 0x94 ),
539 BYTES_TO_T_UINT_8( 0xC5, 0x4C, 0x23, 0xAC, 0x45, 0x71, 0x32, 0xE2 ),
540 BYTES_TO_T_UINT_8( 0x89, 0x3B, 0x60, 0x8B, 0x31, 0xA3, 0x30, 0x78 ),
541 };
542 static const mbedtls_mpi_uint brainpoolP512r1_b[] = {
543 BYTES_TO_T_UINT_8( 0x23, 0xF7, 0x16, 0x80, 0x63, 0xBD, 0x09, 0x28 ),
544 BYTES_TO_T_UINT_8( 0xDD, 0xE5, 0xBA, 0x5E, 0xB7, 0x50, 0x40, 0x98 ),
545 BYTES_TO_T_UINT_8( 0x67, 0x3E, 0x08, 0xDC, 0xCA, 0x94, 0xFC, 0x77 ),
546 BYTES_TO_T_UINT_8( 0x4D, 0xAC, 0xC1, 0xE7, 0xB9, 0xC7, 0xF2, 0x2B ),
547 BYTES_TO_T_UINT_8( 0xA7, 0x17, 0x11, 0x7F, 0xB5, 0xC8, 0x9A, 0x8B ),
548 BYTES_TO_T_UINT_8( 0xC9, 0xF1, 0x2E, 0x0A, 0xA1, 0x3A, 0x25, 0xA8 ),
549 BYTES_TO_T_UINT_8( 0x5A, 0x5D, 0xED, 0x2D, 0xBC, 0x63, 0x98, 0xEA ),
550 BYTES_TO_T_UINT_8( 0xCA, 0x41, 0x34, 0xA8, 0x10, 0x16, 0xF9, 0x3D ),
551 };
552 static const mbedtls_mpi_uint brainpoolP512r1_gx[] = {
553 BYTES_TO_T_UINT_8( 0x22, 0xF8, 0xB9, 0xBC, 0x09, 0x22, 0x35, 0x8B ),
554 BYTES_TO_T_UINT_8( 0x68, 0x5E, 0x6A, 0x40, 0x47, 0x50, 0x6D, 0x7C ),
555 BYTES_TO_T_UINT_8( 0x5F, 0x7D, 0xB9, 0x93, 0x7B, 0x68, 0xD1, 0x50 ),
556 BYTES_TO_T_UINT_8( 0x8D, 0xD4, 0xD0, 0xE2, 0x78, 0x1F, 0x3B, 0xFF ),
557 BYTES_TO_T_UINT_8( 0x8E, 0x09, 0xD0, 0xF4, 0xEE, 0x62, 0x3B, 0xB4 ),
558 BYTES_TO_T_UINT_8( 0xC1, 0x16, 0xD9, 0xB5, 0x70, 0x9F, 0xED, 0x85 ),
559 BYTES_TO_T_UINT_8( 0x93, 0x6A, 0x4C, 0x9C, 0x2E, 0x32, 0x21, 0x5A ),
560 BYTES_TO_T_UINT_8( 0x64, 0xD9, 0x2E, 0xD8, 0xBD, 0xE4, 0xAE, 0x81 ),
561 };
562 static const mbedtls_mpi_uint brainpoolP512r1_gy[] = {
563 BYTES_TO_T_UINT_8( 0x92, 0x08, 0xD8, 0x3A, 0x0F, 0x1E, 0xCD, 0x78 ),
564 BYTES_TO_T_UINT_8( 0x06, 0x54, 0xF0, 0xA8, 0x2F, 0x2B, 0xCA, 0xD1 ),
565 BYTES_TO_T_UINT_8( 0xAE, 0x63, 0x27, 0x8A, 0xD8, 0x4B, 0xCA, 0x5B ),
566 BYTES_TO_T_UINT_8( 0x5E, 0x48, 0x5F, 0x4A, 0x49, 0xDE, 0xDC, 0xB2 ),
567 BYTES_TO_T_UINT_8( 0x11, 0x81, 0x1F, 0x88, 0x5B, 0xC5, 0x00, 0xA0 ),
568 BYTES_TO_T_UINT_8( 0x1A, 0x7B, 0xA5, 0x24, 0x00, 0xF7, 0x09, 0xF2 ),
569 BYTES_TO_T_UINT_8( 0xFD, 0x22, 0x78, 0xCF, 0xA9, 0xBF, 0xEA, 0xC0 ),
570 BYTES_TO_T_UINT_8( 0xEC, 0x32, 0x63, 0x56, 0x5D, 0x38, 0xDE, 0x7D ),
571 };
572 static const mbedtls_mpi_uint brainpoolP512r1_n[] = {
573 BYTES_TO_T_UINT_8( 0x69, 0x00, 0xA9, 0x9C, 0x82, 0x96, 0x87, 0xB5 ),
574 BYTES_TO_T_UINT_8( 0xDD, 0xDA, 0x5D, 0x08, 0x81, 0xD3, 0xB1, 0x1D ),
575 BYTES_TO_T_UINT_8( 0x47, 0x10, 0xAC, 0x7F, 0x19, 0x61, 0x86, 0x41 ),
576 BYTES_TO_T_UINT_8( 0x19, 0x26, 0xA9, 0x4C, 0x41, 0x5C, 0x3E, 0x55 ),
577 BYTES_TO_T_UINT_8( 0x70, 0x08, 0x33, 0x70, 0xCA, 0x9C, 0x63, 0xD6 ),
578 BYTES_TO_T_UINT_8( 0x0E, 0xD2, 0xC9, 0xB3, 0xB3, 0x8D, 0x30, 0xCB ),
579 BYTES_TO_T_UINT_8( 0x07, 0xFC, 0xC9, 0x33, 0xAE, 0xE6, 0xD4, 0x3F ),
580 BYTES_TO_T_UINT_8( 0x8B, 0xC4, 0xE9, 0xDB, 0xB8, 0x9D, 0xDD, 0xAA ),
581 };
582 #endif /* MBEDTLS_ECP_DP_BP512R1_ENABLED */
583
584 /*
585 * Create an MPI from embedded constants
586 * (assumes len is an exact multiple of sizeof mbedtls_mpi_uint)
587 */
ecp_mpi_load(mbedtls_mpi * X,const mbedtls_mpi_uint * p,size_t len)588 static inline void ecp_mpi_load( mbedtls_mpi *X, const mbedtls_mpi_uint *p, size_t len )
589 {
590 X->s = 1;
591 X->n = len / sizeof( mbedtls_mpi_uint );
592 X->p = (mbedtls_mpi_uint *) p;
593 }
594
595 /*
596 * Set an MPI to static value 1
597 */
ecp_mpi_set1(mbedtls_mpi * X)598 static inline void ecp_mpi_set1( mbedtls_mpi *X )
599 {
600 static mbedtls_mpi_uint one[] = { 1 };
601 X->s = 1;
602 X->n = 1;
603 X->p = one;
604 }
605
606 /*
607 * Make group available from embedded constants
608 */
ecp_group_load(mbedtls_ecp_group * grp,const mbedtls_mpi_uint * p,size_t plen,const mbedtls_mpi_uint * a,size_t alen,const mbedtls_mpi_uint * b,size_t blen,const mbedtls_mpi_uint * gx,size_t gxlen,const mbedtls_mpi_uint * gy,size_t gylen,const mbedtls_mpi_uint * n,size_t nlen)609 static int ecp_group_load( mbedtls_ecp_group *grp,
610 const mbedtls_mpi_uint *p, size_t plen,
611 const mbedtls_mpi_uint *a, size_t alen,
612 const mbedtls_mpi_uint *b, size_t blen,
613 const mbedtls_mpi_uint *gx, size_t gxlen,
614 const mbedtls_mpi_uint *gy, size_t gylen,
615 const mbedtls_mpi_uint *n, size_t nlen)
616 {
617 ecp_mpi_load( &grp->P, p, plen );
618 if( a != NULL )
619 ecp_mpi_load( &grp->A, a, alen );
620 ecp_mpi_load( &grp->B, b, blen );
621 ecp_mpi_load( &grp->N, n, nlen );
622
623 ecp_mpi_load( &grp->G.X, gx, gxlen );
624 ecp_mpi_load( &grp->G.Y, gy, gylen );
625 ecp_mpi_set1( &grp->G.Z );
626
627 grp->pbits = mbedtls_mpi_bitlen( &grp->P );
628 grp->nbits = mbedtls_mpi_bitlen( &grp->N );
629
630 grp->h = 1;
631
632 return( 0 );
633 }
634
635 #if defined(MBEDTLS_ECP_NIST_OPTIM)
636 /* Forward declarations */
637 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
638 static int ecp_mod_p192( mbedtls_mpi * );
639 #endif
640 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
641 static int ecp_mod_p224( mbedtls_mpi * );
642 #endif
643 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
644 static int ecp_mod_p256( mbedtls_mpi * );
645 #endif
646 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
647 static int ecp_mod_p384( mbedtls_mpi * );
648 #endif
649 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
650 static int ecp_mod_p521( mbedtls_mpi * );
651 #endif
652
653 #define NIST_MODP( P ) grp->modp = ecp_mod_ ## P;
654 #else
655 #define NIST_MODP( P )
656 #endif /* MBEDTLS_ECP_NIST_OPTIM */
657
658 /* Additional forward declarations */
659 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
660 static int ecp_mod_p255( mbedtls_mpi * );
661 #endif
662 #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
663 static int ecp_mod_p448( mbedtls_mpi * );
664 #endif
665 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
666 static int ecp_mod_p192k1( mbedtls_mpi * );
667 #endif
668 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
669 static int ecp_mod_p224k1( mbedtls_mpi * );
670 #endif
671 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
672 static int ecp_mod_p256k1( mbedtls_mpi * );
673 #endif
674
675 #define LOAD_GROUP_A( G ) ecp_group_load( grp, \
676 G ## _p, sizeof( G ## _p ), \
677 G ## _a, sizeof( G ## _a ), \
678 G ## _b, sizeof( G ## _b ), \
679 G ## _gx, sizeof( G ## _gx ), \
680 G ## _gy, sizeof( G ## _gy ), \
681 G ## _n, sizeof( G ## _n ) )
682
683 #define LOAD_GROUP( G ) ecp_group_load( grp, \
684 G ## _p, sizeof( G ## _p ), \
685 NULL, 0, \
686 G ## _b, sizeof( G ## _b ), \
687 G ## _gx, sizeof( G ## _gx ), \
688 G ## _gy, sizeof( G ## _gy ), \
689 G ## _n, sizeof( G ## _n ) )
690
691 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
692 /*
693 * Specialized function for creating the Curve25519 group
694 */
ecp_use_curve25519(mbedtls_ecp_group * grp)695 static int ecp_use_curve25519( mbedtls_ecp_group *grp )
696 {
697 int ret;
698
699 /* Actually ( A + 2 ) / 4 */
700 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &grp->A, 16, "01DB42" ) );
701
702 /* P = 2^255 - 19 */
703 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->P, 1 ) );
704 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &grp->P, 255 ) );
705 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &grp->P, &grp->P, 19 ) );
706 grp->pbits = mbedtls_mpi_bitlen( &grp->P );
707
708 /* N = 2^252 + 27742317777372353535851937790883648493 */
709 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &grp->N, 16,
710 "14DEF9DEA2F79CD65812631A5CF5D3ED" ) );
711 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &grp->N, 252, 1 ) );
712
713 /* Y intentionally not set, since we use x/z coordinates.
714 * This is used as a marker to identify Montgomery curves! */
715 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.X, 9 ) );
716 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.Z, 1 ) );
717 mbedtls_mpi_free( &grp->G.Y );
718
719 /* Actually, the required msb for private keys */
720 grp->nbits = 254;
721
722 cleanup:
723 if( ret != 0 )
724 mbedtls_ecp_group_free( grp );
725
726 return( ret );
727 }
728 #endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */
729
730 #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
731 /*
732 * Specialized function for creating the Curve448 group
733 */
ecp_use_curve448(mbedtls_ecp_group * grp)734 static int ecp_use_curve448( mbedtls_ecp_group *grp )
735 {
736 mbedtls_mpi Ns;
737 int ret;
738
739 mbedtls_mpi_init( &Ns );
740
741 /* Actually ( A + 2 ) / 4 */
742 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &grp->A, 16, "98AA" ) );
743
744 /* P = 2^448 - 2^224 - 1 */
745 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->P, 1 ) );
746 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &grp->P, 224 ) );
747 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &grp->P, &grp->P, 1 ) );
748 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &grp->P, 224 ) );
749 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &grp->P, &grp->P, 1 ) );
750 grp->pbits = mbedtls_mpi_bitlen( &grp->P );
751
752 /* Y intentionally not set, since we use x/z coordinates.
753 * This is used as a marker to identify Montgomery curves! */
754 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.X, 5 ) );
755 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.Z, 1 ) );
756 mbedtls_mpi_free( &grp->G.Y );
757
758 /* N = 2^446 - 13818066809895115352007386748515426880336692474882178609894547503885 */
759 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &grp->N, 446, 1 ) );
760 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &Ns, 16,
761 "8335DC163BB124B65129C96FDE933D8D723A70AADC873D6D54A7BB0D" ) );
762 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &grp->N, &grp->N, &Ns ) );
763
764 /* Actually, the required msb for private keys */
765 grp->nbits = 447;
766
767 cleanup:
768 mbedtls_mpi_free( &Ns );
769 if( ret != 0 )
770 mbedtls_ecp_group_free( grp );
771
772 return( ret );
773 }
774 #endif /* MBEDTLS_ECP_DP_CURVE448_ENABLED */
775
776 /*
777 * Set a group using well-known domain parameters
778 */
mbedtls_ecp_group_load(mbedtls_ecp_group * grp,mbedtls_ecp_group_id id)779 int mbedtls_ecp_group_load( mbedtls_ecp_group *grp, mbedtls_ecp_group_id id )
780 {
781 ECP_VALIDATE_RET( grp != NULL );
782 mbedtls_ecp_group_free( grp );
783
784 grp->id = id;
785
786 switch( id )
787 {
788 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
789 case MBEDTLS_ECP_DP_SECP192R1:
790 NIST_MODP( p192 );
791 return( LOAD_GROUP( secp192r1 ) );
792 #endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */
793
794 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
795 case MBEDTLS_ECP_DP_SECP224R1:
796 NIST_MODP( p224 );
797 return( LOAD_GROUP( secp224r1 ) );
798 #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */
799
800 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
801 case MBEDTLS_ECP_DP_SECP256R1:
802 NIST_MODP( p256 );
803 return( LOAD_GROUP( secp256r1 ) );
804 #endif /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */
805
806 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
807 case MBEDTLS_ECP_DP_SECP384R1:
808 NIST_MODP( p384 );
809 return( LOAD_GROUP( secp384r1 ) );
810 #endif /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */
811
812 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
813 case MBEDTLS_ECP_DP_SECP521R1:
814 NIST_MODP( p521 );
815 return( LOAD_GROUP( secp521r1 ) );
816 #endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */
817
818 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
819 case MBEDTLS_ECP_DP_SECP192K1:
820 grp->modp = ecp_mod_p192k1;
821 return( LOAD_GROUP_A( secp192k1 ) );
822 #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */
823
824 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
825 case MBEDTLS_ECP_DP_SECP224K1:
826 grp->modp = ecp_mod_p224k1;
827 return( LOAD_GROUP_A( secp224k1 ) );
828 #endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */
829
830 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
831 case MBEDTLS_ECP_DP_SECP256K1:
832 grp->modp = ecp_mod_p256k1;
833 return( LOAD_GROUP_A( secp256k1 ) );
834 #endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */
835
836 #if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED)
837 case MBEDTLS_ECP_DP_BP256R1:
838 return( LOAD_GROUP_A( brainpoolP256r1 ) );
839 #endif /* MBEDTLS_ECP_DP_BP256R1_ENABLED */
840
841 #if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED)
842 case MBEDTLS_ECP_DP_BP384R1:
843 return( LOAD_GROUP_A( brainpoolP384r1 ) );
844 #endif /* MBEDTLS_ECP_DP_BP384R1_ENABLED */
845
846 #if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED)
847 case MBEDTLS_ECP_DP_BP512R1:
848 return( LOAD_GROUP_A( brainpoolP512r1 ) );
849 #endif /* MBEDTLS_ECP_DP_BP512R1_ENABLED */
850
851 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
852 case MBEDTLS_ECP_DP_CURVE25519:
853 grp->modp = ecp_mod_p255;
854 return( ecp_use_curve25519( grp ) );
855 #endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */
856
857 #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
858 case MBEDTLS_ECP_DP_CURVE448:
859 grp->modp = ecp_mod_p448;
860 return( ecp_use_curve448( grp ) );
861 #endif /* MBEDTLS_ECP_DP_CURVE448_ENABLED */
862
863 default:
864 mbedtls_ecp_group_free( grp );
865 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
866 }
867 }
868
869 #if defined(MBEDTLS_ECP_NIST_OPTIM)
870 /*
871 * Fast reduction modulo the primes used by the NIST curves.
872 *
873 * These functions are critical for speed, but not needed for correct
874 * operations. So, we make the choice to heavily rely on the internals of our
875 * bignum library, which creates a tight coupling between these functions and
876 * our MPI implementation. However, the coupling between the ECP module and
877 * MPI remains loose, since these functions can be deactivated at will.
878 */
879
880 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
881 /*
882 * Compared to the way things are presented in FIPS 186-3 D.2,
883 * we proceed in columns, from right (least significant chunk) to left,
884 * adding chunks to N in place, and keeping a carry for the next chunk.
885 * This avoids moving things around in memory, and uselessly adding zeros,
886 * compared to the more straightforward, line-oriented approach.
887 *
888 * For this prime we need to handle data in chunks of 64 bits.
889 * Since this is always a multiple of our basic mbedtls_mpi_uint, we can
890 * use a mbedtls_mpi_uint * to designate such a chunk, and small loops to handle it.
891 */
892
893 /* Add 64-bit chunks (dst += src) and update carry */
add64(mbedtls_mpi_uint * dst,mbedtls_mpi_uint * src,mbedtls_mpi_uint * carry)894 static inline void add64( mbedtls_mpi_uint *dst, mbedtls_mpi_uint *src, mbedtls_mpi_uint *carry )
895 {
896 unsigned char i;
897 mbedtls_mpi_uint c = 0;
898 for( i = 0; i < 8 / sizeof( mbedtls_mpi_uint ); i++, dst++, src++ )
899 {
900 *dst += c; c = ( *dst < c );
901 *dst += *src; c += ( *dst < *src );
902 }
903 *carry += c;
904 }
905
906 /* Add carry to a 64-bit chunk and update carry */
carry64(mbedtls_mpi_uint * dst,mbedtls_mpi_uint * carry)907 static inline void carry64( mbedtls_mpi_uint *dst, mbedtls_mpi_uint *carry )
908 {
909 unsigned char i;
910 for( i = 0; i < 8 / sizeof( mbedtls_mpi_uint ); i++, dst++ )
911 {
912 *dst += *carry;
913 *carry = ( *dst < *carry );
914 }
915 }
916
917 #define WIDTH 8 / sizeof( mbedtls_mpi_uint )
918 #define A( i ) N->p + (i) * WIDTH
919 #define ADD( i ) add64( p, A( i ), &c )
920 #define NEXT p += WIDTH; carry64( p, &c )
921 #define LAST p += WIDTH; *p = c; while( ++p < end ) *p = 0
922
923 /*
924 * Fast quasi-reduction modulo p192 (FIPS 186-3 D.2.1)
925 */
ecp_mod_p192(mbedtls_mpi * N)926 static int ecp_mod_p192( mbedtls_mpi *N )
927 {
928 int ret;
929 mbedtls_mpi_uint c = 0;
930 mbedtls_mpi_uint *p, *end;
931
932 /* Make sure we have enough blocks so that A(5) is legal */
933 MBEDTLS_MPI_CHK( mbedtls_mpi_grow( N, 6 * WIDTH ) );
934
935 p = N->p;
936 end = p + N->n;
937
938 ADD( 3 ); ADD( 5 ); NEXT; // A0 += A3 + A5
939 ADD( 3 ); ADD( 4 ); ADD( 5 ); NEXT; // A1 += A3 + A4 + A5
940 ADD( 4 ); ADD( 5 ); LAST; // A2 += A4 + A5
941
942 cleanup:
943 return( ret );
944 }
945
946 #undef WIDTH
947 #undef A
948 #undef ADD
949 #undef NEXT
950 #undef LAST
951 #endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */
952
953 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) || \
954 defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) || \
955 defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
956 /*
957 * The reader is advised to first understand ecp_mod_p192() since the same
958 * general structure is used here, but with additional complications:
959 * (1) chunks of 32 bits, and (2) subtractions.
960 */
961
962 /*
963 * For these primes, we need to handle data in chunks of 32 bits.
964 * This makes it more complicated if we use 64 bits limbs in MPI,
965 * which prevents us from using a uniform access method as for p192.
966 *
967 * So, we define a mini abstraction layer to access 32 bit chunks,
968 * load them in 'cur' for work, and store them back from 'cur' when done.
969 *
970 * While at it, also define the size of N in terms of 32-bit chunks.
971 */
972 #define LOAD32 cur = A( i );
973
974 #if defined(MBEDTLS_HAVE_INT32) /* 32 bit */
975
976 #define MAX32 N->n
977 #define A( j ) N->p[j]
978 #define STORE32 N->p[i] = cur;
979
980 #else /* 64-bit */
981
982 #define MAX32 N->n * 2
983 #define A( j ) (j) % 2 ? (uint32_t)( N->p[(j)/2] >> 32 ) : \
984 (uint32_t)( N->p[(j)/2] )
985 #define STORE32 \
986 if( i % 2 ) { \
987 N->p[i/2] &= 0x00000000FFFFFFFF; \
988 N->p[i/2] |= ((mbedtls_mpi_uint) cur) << 32; \
989 } else { \
990 N->p[i/2] &= 0xFFFFFFFF00000000; \
991 N->p[i/2] |= (mbedtls_mpi_uint) cur; \
992 }
993
994 #endif /* sizeof( mbedtls_mpi_uint ) */
995
996 /*
997 * Helpers for addition and subtraction of chunks, with signed carry.
998 */
add32(uint32_t * dst,uint32_t src,signed char * carry)999 static inline void add32( uint32_t *dst, uint32_t src, signed char *carry )
1000 {
1001 *dst += src;
1002 *carry += ( *dst < src );
1003 }
1004
sub32(uint32_t * dst,uint32_t src,signed char * carry)1005 static inline void sub32( uint32_t *dst, uint32_t src, signed char *carry )
1006 {
1007 *carry -= ( *dst < src );
1008 *dst -= src;
1009 }
1010
1011 #define ADD( j ) add32( &cur, A( j ), &c );
1012 #define SUB( j ) sub32( &cur, A( j ), &c );
1013
1014 /*
1015 * Helpers for the main 'loop'
1016 * (see fix_negative for the motivation of C)
1017 */
1018 #define INIT( b ) \
1019 int ret; \
1020 signed char c = 0, cc; \
1021 uint32_t cur; \
1022 size_t i = 0, bits = (b); \
1023 mbedtls_mpi C; \
1024 mbedtls_mpi_uint Cp[ (b) / 8 / sizeof( mbedtls_mpi_uint) + 1 ]; \
1025 \
1026 C.s = 1; \
1027 C.n = (b) / 8 / sizeof( mbedtls_mpi_uint) + 1; \
1028 C.p = Cp; \
1029 memset( Cp, 0, C.n * sizeof( mbedtls_mpi_uint ) ); \
1030 \
1031 MBEDTLS_MPI_CHK( mbedtls_mpi_grow( N, (b) * 2 / 8 / \
1032 sizeof( mbedtls_mpi_uint ) ) ); \
1033 LOAD32;
1034
1035 #define NEXT \
1036 STORE32; i++; LOAD32; \
1037 cc = c; c = 0; \
1038 if( cc < 0 ) \
1039 sub32( &cur, -cc, &c ); \
1040 else \
1041 add32( &cur, cc, &c ); \
1042
1043 #define LAST \
1044 STORE32; i++; \
1045 cur = c > 0 ? c : 0; STORE32; \
1046 cur = 0; while( ++i < MAX32 ) { STORE32; } \
1047 if( c < 0 ) MBEDTLS_MPI_CHK( fix_negative( N, c, &C, bits ) );
1048
1049 /*
1050 * If the result is negative, we get it in the form
1051 * c * 2^(bits + 32) + N, with c negative and N positive shorter than 'bits'
1052 */
fix_negative(mbedtls_mpi * N,signed char c,mbedtls_mpi * C,size_t bits)1053 static inline int fix_negative( mbedtls_mpi *N, signed char c, mbedtls_mpi *C, size_t bits )
1054 {
1055 int ret;
1056
1057 /* C = - c * 2^(bits + 32) */
1058 #if !defined(MBEDTLS_HAVE_INT64)
1059 ((void) bits);
1060 #else
1061 if( bits == 224 )
1062 C->p[ C->n - 1 ] = ((mbedtls_mpi_uint) -c) << 32;
1063 else
1064 #endif
1065 C->p[ C->n - 1 ] = (mbedtls_mpi_uint) -c;
1066
1067 /* N = - ( C - N ) */
1068 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( N, C, N ) );
1069 N->s = -1;
1070
1071 cleanup:
1072
1073 return( ret );
1074 }
1075
1076 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
1077 /*
1078 * Fast quasi-reduction modulo p224 (FIPS 186-3 D.2.2)
1079 */
ecp_mod_p224(mbedtls_mpi * N)1080 static int ecp_mod_p224( mbedtls_mpi *N )
1081 {
1082 INIT( 224 );
1083
1084 SUB( 7 ); SUB( 11 ); NEXT; // A0 += -A7 - A11
1085 SUB( 8 ); SUB( 12 ); NEXT; // A1 += -A8 - A12
1086 SUB( 9 ); SUB( 13 ); NEXT; // A2 += -A9 - A13
1087 SUB( 10 ); ADD( 7 ); ADD( 11 ); NEXT; // A3 += -A10 + A7 + A11
1088 SUB( 11 ); ADD( 8 ); ADD( 12 ); NEXT; // A4 += -A11 + A8 + A12
1089 SUB( 12 ); ADD( 9 ); ADD( 13 ); NEXT; // A5 += -A12 + A9 + A13
1090 SUB( 13 ); ADD( 10 ); LAST; // A6 += -A13 + A10
1091
1092 cleanup:
1093 return( ret );
1094 }
1095 #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */
1096
1097 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
1098 /*
1099 * Fast quasi-reduction modulo p256 (FIPS 186-3 D.2.3)
1100 */
ecp_mod_p256(mbedtls_mpi * N)1101 static int ecp_mod_p256( mbedtls_mpi *N )
1102 {
1103 INIT( 256 );
1104
1105 ADD( 8 ); ADD( 9 );
1106 SUB( 11 ); SUB( 12 ); SUB( 13 ); SUB( 14 ); NEXT; // A0
1107
1108 ADD( 9 ); ADD( 10 );
1109 SUB( 12 ); SUB( 13 ); SUB( 14 ); SUB( 15 ); NEXT; // A1
1110
1111 ADD( 10 ); ADD( 11 );
1112 SUB( 13 ); SUB( 14 ); SUB( 15 ); NEXT; // A2
1113
1114 ADD( 11 ); ADD( 11 ); ADD( 12 ); ADD( 12 ); ADD( 13 );
1115 SUB( 15 ); SUB( 8 ); SUB( 9 ); NEXT; // A3
1116
1117 ADD( 12 ); ADD( 12 ); ADD( 13 ); ADD( 13 ); ADD( 14 );
1118 SUB( 9 ); SUB( 10 ); NEXT; // A4
1119
1120 ADD( 13 ); ADD( 13 ); ADD( 14 ); ADD( 14 ); ADD( 15 );
1121 SUB( 10 ); SUB( 11 ); NEXT; // A5
1122
1123 ADD( 14 ); ADD( 14 ); ADD( 15 ); ADD( 15 ); ADD( 14 ); ADD( 13 );
1124 SUB( 8 ); SUB( 9 ); NEXT; // A6
1125
1126 ADD( 15 ); ADD( 15 ); ADD( 15 ); ADD( 8 );
1127 SUB( 10 ); SUB( 11 ); SUB( 12 ); SUB( 13 ); LAST; // A7
1128
1129 cleanup:
1130 return( ret );
1131 }
1132 #endif /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */
1133
1134 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
1135 /*
1136 * Fast quasi-reduction modulo p384 (FIPS 186-3 D.2.4)
1137 */
ecp_mod_p384(mbedtls_mpi * N)1138 static int ecp_mod_p384( mbedtls_mpi *N )
1139 {
1140 INIT( 384 );
1141
1142 ADD( 12 ); ADD( 21 ); ADD( 20 );
1143 SUB( 23 ); NEXT; // A0
1144
1145 ADD( 13 ); ADD( 22 ); ADD( 23 );
1146 SUB( 12 ); SUB( 20 ); NEXT; // A2
1147
1148 ADD( 14 ); ADD( 23 );
1149 SUB( 13 ); SUB( 21 ); NEXT; // A2
1150
1151 ADD( 15 ); ADD( 12 ); ADD( 20 ); ADD( 21 );
1152 SUB( 14 ); SUB( 22 ); SUB( 23 ); NEXT; // A3
1153
1154 ADD( 21 ); ADD( 21 ); ADD( 16 ); ADD( 13 ); ADD( 12 ); ADD( 20 ); ADD( 22 );
1155 SUB( 15 ); SUB( 23 ); SUB( 23 ); NEXT; // A4
1156
1157 ADD( 22 ); ADD( 22 ); ADD( 17 ); ADD( 14 ); ADD( 13 ); ADD( 21 ); ADD( 23 );
1158 SUB( 16 ); NEXT; // A5
1159
1160 ADD( 23 ); ADD( 23 ); ADD( 18 ); ADD( 15 ); ADD( 14 ); ADD( 22 );
1161 SUB( 17 ); NEXT; // A6
1162
1163 ADD( 19 ); ADD( 16 ); ADD( 15 ); ADD( 23 );
1164 SUB( 18 ); NEXT; // A7
1165
1166 ADD( 20 ); ADD( 17 ); ADD( 16 );
1167 SUB( 19 ); NEXT; // A8
1168
1169 ADD( 21 ); ADD( 18 ); ADD( 17 );
1170 SUB( 20 ); NEXT; // A9
1171
1172 ADD( 22 ); ADD( 19 ); ADD( 18 );
1173 SUB( 21 ); NEXT; // A10
1174
1175 ADD( 23 ); ADD( 20 ); ADD( 19 );
1176 SUB( 22 ); LAST; // A11
1177
1178 cleanup:
1179 return( ret );
1180 }
1181 #endif /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */
1182
1183 #undef A
1184 #undef LOAD32
1185 #undef STORE32
1186 #undef MAX32
1187 #undef INIT
1188 #undef NEXT
1189 #undef LAST
1190
1191 #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED ||
1192 MBEDTLS_ECP_DP_SECP256R1_ENABLED ||
1193 MBEDTLS_ECP_DP_SECP384R1_ENABLED */
1194
1195 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
1196 /*
1197 * Here we have an actual Mersenne prime, so things are more straightforward.
1198 * However, chunks are aligned on a 'weird' boundary (521 bits).
1199 */
1200
1201 /* Size of p521 in terms of mbedtls_mpi_uint */
1202 #define P521_WIDTH ( 521 / 8 / sizeof( mbedtls_mpi_uint ) + 1 )
1203
1204 /* Bits to keep in the most significant mbedtls_mpi_uint */
1205 #define P521_MASK 0x01FF
1206
1207 /*
1208 * Fast quasi-reduction modulo p521 (FIPS 186-3 D.2.5)
1209 * Write N as A1 + 2^521 A0, return A0 + A1
1210 */
ecp_mod_p521(mbedtls_mpi * N)1211 static int ecp_mod_p521( mbedtls_mpi *N )
1212 {
1213 int ret;
1214 size_t i;
1215 mbedtls_mpi M;
1216 mbedtls_mpi_uint Mp[P521_WIDTH + 1];
1217 /* Worst case for the size of M is when mbedtls_mpi_uint is 16 bits:
1218 * we need to hold bits 513 to 1056, which is 34 limbs, that is
1219 * P521_WIDTH + 1. Otherwise P521_WIDTH is enough. */
1220
1221 if( N->n < P521_WIDTH )
1222 return( 0 );
1223
1224 /* M = A1 */
1225 M.s = 1;
1226 M.n = N->n - ( P521_WIDTH - 1 );
1227 if( M.n > P521_WIDTH + 1 )
1228 M.n = P521_WIDTH + 1;
1229 M.p = Mp;
1230 memcpy( Mp, N->p + P521_WIDTH - 1, M.n * sizeof( mbedtls_mpi_uint ) );
1231 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, 521 % ( 8 * sizeof( mbedtls_mpi_uint ) ) ) );
1232
1233 /* N = A0 */
1234 N->p[P521_WIDTH - 1] &= P521_MASK;
1235 for( i = P521_WIDTH; i < N->n; i++ )
1236 N->p[i] = 0;
1237
1238 /* N = A0 + A1 */
1239 MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) );
1240
1241 cleanup:
1242 return( ret );
1243 }
1244
1245 #undef P521_WIDTH
1246 #undef P521_MASK
1247 #endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */
1248
1249 #endif /* MBEDTLS_ECP_NIST_OPTIM */
1250
1251 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
1252
1253 /* Size of p255 in terms of mbedtls_mpi_uint */
1254 #define P255_WIDTH ( 255 / 8 / sizeof( mbedtls_mpi_uint ) + 1 )
1255
1256 /*
1257 * Fast quasi-reduction modulo p255 = 2^255 - 19
1258 * Write N as A0 + 2^255 A1, return A0 + 19 * A1
1259 */
ecp_mod_p255(mbedtls_mpi * N)1260 static int ecp_mod_p255( mbedtls_mpi *N )
1261 {
1262 int ret;
1263 size_t i;
1264 mbedtls_mpi M;
1265 mbedtls_mpi_uint Mp[P255_WIDTH + 2];
1266
1267 if( N->n < P255_WIDTH )
1268 return( 0 );
1269
1270 /* M = A1 */
1271 M.s = 1;
1272 M.n = N->n - ( P255_WIDTH - 1 );
1273 if( M.n > P255_WIDTH + 1 )
1274 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1275 M.p = Mp;
1276 memset( Mp, 0, sizeof Mp );
1277 memcpy( Mp, N->p + P255_WIDTH - 1, M.n * sizeof( mbedtls_mpi_uint ) );
1278 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, 255 % ( 8 * sizeof( mbedtls_mpi_uint ) ) ) );
1279 M.n++; /* Make room for multiplication by 19 */
1280
1281 /* N = A0 */
1282 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( N, 255, 0 ) );
1283 for( i = P255_WIDTH; i < N->n; i++ )
1284 N->p[i] = 0;
1285
1286 /* N = A0 + 19 * A1 */
1287 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &M, 19 ) );
1288 MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) );
1289
1290 cleanup:
1291 return( ret );
1292 }
1293 #endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */
1294
1295 #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
1296
1297 /* Size of p448 in terms of mbedtls_mpi_uint */
1298 #define P448_WIDTH ( 448 / 8 / sizeof( mbedtls_mpi_uint ) )
1299
1300 /* Number of limbs fully occupied by 2^224 (max), and limbs used by it (min) */
1301 #define DIV_ROUND_UP( X, Y ) ( ( ( X ) + ( Y ) - 1 ) / ( Y ) )
1302 #define P224_WIDTH_MIN ( 28 / sizeof( mbedtls_mpi_uint ) )
1303 #define P224_WIDTH_MAX DIV_ROUND_UP( 28, sizeof( mbedtls_mpi_uint ) )
1304 #define P224_UNUSED_BITS ( ( P224_WIDTH_MAX * sizeof( mbedtls_mpi_uint ) * 8 ) - 224 )
1305
1306 /*
1307 * Fast quasi-reduction modulo p448 = 2^448 - 2^224 - 1
1308 * Write N as A0 + 2^448 A1 and A1 as B0 + 2^224 B1, and return
1309 * A0 + A1 + B1 + (B0 + B1) * 2^224. This is different to the reference
1310 * implementation of Curve448, which uses its own special 56-bit limbs rather
1311 * than a generic bignum library. We could squeeze some extra speed out on
1312 * 32-bit machines by splitting N up into 32-bit limbs and doing the
1313 * arithmetic using the limbs directly as we do for the NIST primes above,
1314 * but for 64-bit targets it should use half the number of operations if we do
1315 * the reduction with 224-bit limbs, since mpi_add_mpi will then use 64-bit adds.
1316 */
ecp_mod_p448(mbedtls_mpi * N)1317 static int ecp_mod_p448( mbedtls_mpi *N )
1318 {
1319 int ret;
1320 size_t i;
1321 mbedtls_mpi M, Q;
1322 mbedtls_mpi_uint Mp[P448_WIDTH + 1], Qp[P448_WIDTH];
1323
1324 if( N->n <= P448_WIDTH )
1325 return( 0 );
1326
1327 /* M = A1 */
1328 M.s = 1;
1329 M.n = N->n - ( P448_WIDTH );
1330 if( M.n > P448_WIDTH )
1331 /* Shouldn't be called with N larger than 2^896! */
1332 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1333 M.p = Mp;
1334 memset( Mp, 0, sizeof( Mp ) );
1335 memcpy( Mp, N->p + P448_WIDTH, M.n * sizeof( mbedtls_mpi_uint ) );
1336
1337 /* N = A0 */
1338 for( i = P448_WIDTH; i < N->n; i++ )
1339 N->p[i] = 0;
1340
1341 /* N += A1 */
1342 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &M ) );
1343
1344 /* Q = B1, N += B1 */
1345 Q = M;
1346 Q.p = Qp;
1347 memcpy( Qp, Mp, sizeof( Qp ) );
1348 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &Q, 224 ) );
1349 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &Q ) );
1350
1351 /* M = (B0 + B1) * 2^224, N += M */
1352 if( sizeof( mbedtls_mpi_uint ) > 4 )
1353 Mp[P224_WIDTH_MIN] &= ( (mbedtls_mpi_uint)-1 ) >> ( P224_UNUSED_BITS );
1354 for( i = P224_WIDTH_MAX; i < M.n; ++i )
1355 Mp[i] = 0;
1356 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &M, &M, &Q ) );
1357 M.n = P448_WIDTH + 1; /* Make room for shifted carry bit from the addition */
1358 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &M, 224 ) );
1359 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &M ) );
1360
1361 cleanup:
1362 return( ret );
1363 }
1364 #endif /* MBEDTLS_ECP_DP_CURVE448_ENABLED */
1365
1366 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) || \
1367 defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) || \
1368 defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
1369 /*
1370 * Fast quasi-reduction modulo P = 2^s - R,
1371 * with R about 33 bits, used by the Koblitz curves.
1372 *
1373 * Write N as A0 + 2^224 A1, return A0 + R * A1.
1374 * Actually do two passes, since R is big.
1375 */
1376 #define P_KOBLITZ_MAX ( 256 / 8 / sizeof( mbedtls_mpi_uint ) ) // Max limbs in P
1377 #define P_KOBLITZ_R ( 8 / sizeof( mbedtls_mpi_uint ) ) // Limbs in R
ecp_mod_koblitz(mbedtls_mpi * N,mbedtls_mpi_uint * Rp,size_t p_limbs,size_t adjust,size_t shift,mbedtls_mpi_uint mask)1378 static inline int ecp_mod_koblitz( mbedtls_mpi *N, mbedtls_mpi_uint *Rp, size_t p_limbs,
1379 size_t adjust, size_t shift, mbedtls_mpi_uint mask )
1380 {
1381 int ret;
1382 size_t i;
1383 mbedtls_mpi M, R;
1384 mbedtls_mpi_uint Mp[P_KOBLITZ_MAX + P_KOBLITZ_R + 1];
1385
1386 if( N->n < p_limbs )
1387 return( 0 );
1388
1389 /* Init R */
1390 R.s = 1;
1391 R.p = Rp;
1392 R.n = P_KOBLITZ_R;
1393
1394 /* Common setup for M */
1395 M.s = 1;
1396 M.p = Mp;
1397
1398 /* M = A1 */
1399 M.n = N->n - ( p_limbs - adjust );
1400 if( M.n > p_limbs + adjust )
1401 M.n = p_limbs + adjust;
1402 memset( Mp, 0, sizeof Mp );
1403 memcpy( Mp, N->p + p_limbs - adjust, M.n * sizeof( mbedtls_mpi_uint ) );
1404 if( shift != 0 )
1405 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, shift ) );
1406 M.n += R.n; /* Make room for multiplication by R */
1407
1408 /* N = A0 */
1409 if( mask != 0 )
1410 N->p[p_limbs - 1] &= mask;
1411 for( i = p_limbs; i < N->n; i++ )
1412 N->p[i] = 0;
1413
1414 /* N = A0 + R * A1 */
1415 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &M, &M, &R ) );
1416 MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) );
1417
1418 /* Second pass */
1419
1420 /* M = A1 */
1421 M.n = N->n - ( p_limbs - adjust );
1422 if( M.n > p_limbs + adjust )
1423 M.n = p_limbs + adjust;
1424 memset( Mp, 0, sizeof Mp );
1425 memcpy( Mp, N->p + p_limbs - adjust, M.n * sizeof( mbedtls_mpi_uint ) );
1426 if( shift != 0 )
1427 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, shift ) );
1428 M.n += R.n; /* Make room for multiplication by R */
1429
1430 /* N = A0 */
1431 if( mask != 0 )
1432 N->p[p_limbs - 1] &= mask;
1433 for( i = p_limbs; i < N->n; i++ )
1434 N->p[i] = 0;
1435
1436 /* N = A0 + R * A1 */
1437 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &M, &M, &R ) );
1438 MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) );
1439
1440 cleanup:
1441 return( ret );
1442 }
1443 #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED) ||
1444 MBEDTLS_ECP_DP_SECP224K1_ENABLED) ||
1445 MBEDTLS_ECP_DP_SECP256K1_ENABLED) */
1446
1447 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
1448 /*
1449 * Fast quasi-reduction modulo p192k1 = 2^192 - R,
1450 * with R = 2^32 + 2^12 + 2^8 + 2^7 + 2^6 + 2^3 + 1 = 0x0100001119
1451 */
ecp_mod_p192k1(mbedtls_mpi * N)1452 static int ecp_mod_p192k1( mbedtls_mpi *N )
1453 {
1454 static mbedtls_mpi_uint Rp[] = {
1455 BYTES_TO_T_UINT_8( 0xC9, 0x11, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) };
1456
1457 return( ecp_mod_koblitz( N, Rp, 192 / 8 / sizeof( mbedtls_mpi_uint ), 0, 0, 0 ) );
1458 }
1459 #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */
1460
1461 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
1462 /*
1463 * Fast quasi-reduction modulo p224k1 = 2^224 - R,
1464 * with R = 2^32 + 2^12 + 2^11 + 2^9 + 2^7 + 2^4 + 2 + 1 = 0x0100001A93
1465 */
ecp_mod_p224k1(mbedtls_mpi * N)1466 static int ecp_mod_p224k1( mbedtls_mpi *N )
1467 {
1468 static mbedtls_mpi_uint Rp[] = {
1469 BYTES_TO_T_UINT_8( 0x93, 0x1A, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) };
1470
1471 #if defined(MBEDTLS_HAVE_INT64)
1472 return( ecp_mod_koblitz( N, Rp, 4, 1, 32, 0xFFFFFFFF ) );
1473 #else
1474 return( ecp_mod_koblitz( N, Rp, 224 / 8 / sizeof( mbedtls_mpi_uint ), 0, 0, 0 ) );
1475 #endif
1476 }
1477
1478 #endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */
1479
1480 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
1481 /*
1482 * Fast quasi-reduction modulo p256k1 = 2^256 - R,
1483 * with R = 2^32 + 2^9 + 2^8 + 2^7 + 2^6 + 2^4 + 1 = 0x01000003D1
1484 */
ecp_mod_p256k1(mbedtls_mpi * N)1485 static int ecp_mod_p256k1( mbedtls_mpi *N )
1486 {
1487 static mbedtls_mpi_uint Rp[] = {
1488 BYTES_TO_T_UINT_8( 0xD1, 0x03, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) };
1489 return( ecp_mod_koblitz( N, Rp, 256 / 8 / sizeof( mbedtls_mpi_uint ), 0, 0, 0 ) );
1490 }
1491 #endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */
1492
1493 #endif /* !MBEDTLS_ECP_ALT */
1494
1495 #endif /* MBEDTLS_ECP_C */
1496