1 /*
2 * Elliptic curves over GF(p): curve-specific data and functions
3 *
4 * Copyright (C) 2006-2022, ARM Limited, All Rights Reserved
5 * Copyright (C) 2019, STMicroelectronics, All Rights Reserved
6 * SPDX-License-Identifier: Apache-2.0
7 *
8 * Licensed under the Apache License, Version 2.0 (the "License"); you may
9 * not use this file except in compliance with the License.
10 * You may obtain a copy of the License at
11 *
12 * http://www.apache.org/licenses/LICENSE-2.0
13 *
14 * Unless required by applicable law or agreed to in writing, software
15 * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
16 * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
17 * See the License for the specific language governing permissions and
18 * limitations under the License.
19 *
20 * This file implements STMicroelectronics EC group load
21 * with HW services based on mbed TLS API
22 */
23
24 #include "mbedtls/build_info.h"
25
26 #if defined(MBEDTLS_ECP_C)
27
28 #include "mbedtls/ecp.h"
29 #include "mbedtls/platform_util.h"
30 #include "mbedtls/error.h"
31
32 #include <string.h>
33
34 #if defined(MBEDTLS_ECP_ALT)
35
36 #if defined(MBEDTLS_ECP_NIST_OPTIM)
37 #error "MBEDTLS_ECP_NIST_OPTIM defined, but it cannot coexist with ST alternative ECP implementation"
38 #endif
39
40 /* Parameter validation macros - mbedtls/platform_util.h has deprecated them */
41 #define ECP_VALIDATE_RET( cond ) do { } while(0)
42 #define ECP_VALIDATE( cond ) do { } while(0)
43
44 #if ( defined(__ARMCC_VERSION) || defined(_MSC_VER) ) \
45 && !defined(inline) && !defined(__cplusplus)
46 #define inline __inline
47 #endif
48
49 /*
50 * Conversion macros for embedded constants:
51 * build lists of mbedtls_mpi_uint's from lists of unsigned char's grouped by 8, 4 or 2
52 */
53 #if defined(MBEDTLS_HAVE_INT32)
54
55 #define BYTES_TO_T_UINT_4( a, b, c, d ) \
56 ( (mbedtls_mpi_uint) (a) << 0 ) | \
57 ( (mbedtls_mpi_uint) (b) << 8 ) | \
58 ( (mbedtls_mpi_uint) (c) << 16 ) | \
59 ( (mbedtls_mpi_uint) (d) << 24 )
60
61 #define BYTES_TO_T_UINT_2( a, b ) \
62 BYTES_TO_T_UINT_4( a, b, 0, 0 )
63
64 #define BYTES_TO_T_UINT_8( a, b, c, d, e, f, g, h ) \
65 BYTES_TO_T_UINT_4( a, b, c, d ), \
66 BYTES_TO_T_UINT_4( e, f, g, h )
67
68 #else /* 64-bits */
69
70 #define BYTES_TO_T_UINT_8( a, b, c, d, e, f, g, h ) \
71 ( (mbedtls_mpi_uint) (a) << 0 ) | \
72 ( (mbedtls_mpi_uint) (b) << 8 ) | \
73 ( (mbedtls_mpi_uint) (c) << 16 ) | \
74 ( (mbedtls_mpi_uint) (d) << 24 ) | \
75 ( (mbedtls_mpi_uint) (e) << 32 ) | \
76 ( (mbedtls_mpi_uint) (f) << 40 ) | \
77 ( (mbedtls_mpi_uint) (g) << 48 ) | \
78 ( (mbedtls_mpi_uint) (h) << 56 )
79
80 #define BYTES_TO_T_UINT_4( a, b, c, d ) \
81 BYTES_TO_T_UINT_8( a, b, c, d, 0, 0, 0, 0 )
82
83 #define BYTES_TO_T_UINT_2( a, b ) \
84 BYTES_TO_T_UINT_8( a, b, 0, 0, 0, 0, 0, 0 )
85
86 #endif /* bits in mbedtls_mpi_uint */
87
88 /*
89 * Note: the constants are in little-endian order
90 * to be directly usable in MPIs
91 */
92
93 /*
94 * Domain parameters for secp192r1
95 */
96 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
97 static const mbedtls_mpi_uint secp192r1_p[] = {
98 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
99 BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
100 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
101 };
102 static const mbedtls_mpi_uint secp192r1_b[] = {
103 BYTES_TO_T_UINT_8( 0xB1, 0xB9, 0x46, 0xC1, 0xEC, 0xDE, 0xB8, 0xFE ),
104 BYTES_TO_T_UINT_8( 0x49, 0x30, 0x24, 0x72, 0xAB, 0xE9, 0xA7, 0x0F ),
105 BYTES_TO_T_UINT_8( 0xE7, 0x80, 0x9C, 0xE5, 0x19, 0x05, 0x21, 0x64 ),
106 };
107 static const mbedtls_mpi_uint secp192r1_gx[] = {
108 BYTES_TO_T_UINT_8( 0x12, 0x10, 0xFF, 0x82, 0xFD, 0x0A, 0xFF, 0xF4 ),
109 BYTES_TO_T_UINT_8( 0x00, 0x88, 0xA1, 0x43, 0xEB, 0x20, 0xBF, 0x7C ),
110 BYTES_TO_T_UINT_8( 0xF6, 0x90, 0x30, 0xB0, 0x0E, 0xA8, 0x8D, 0x18 ),
111 };
112 static const mbedtls_mpi_uint secp192r1_gy[] = {
113 BYTES_TO_T_UINT_8( 0x11, 0x48, 0x79, 0x1E, 0xA1, 0x77, 0xF9, 0x73 ),
114 BYTES_TO_T_UINT_8( 0xD5, 0xCD, 0x24, 0x6B, 0xED, 0x11, 0x10, 0x63 ),
115 BYTES_TO_T_UINT_8( 0x78, 0xDA, 0xC8, 0xFF, 0x95, 0x2B, 0x19, 0x07 ),
116 };
117 static const mbedtls_mpi_uint secp192r1_n[] = {
118 BYTES_TO_T_UINT_8( 0x31, 0x28, 0xD2, 0xB4, 0xB1, 0xC9, 0x6B, 0x14 ),
119 BYTES_TO_T_UINT_8( 0x36, 0xF8, 0xDE, 0x99, 0xFF, 0xFF, 0xFF, 0xFF ),
120 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
121 };
122 #endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */
123
124 /*
125 * Domain parameters for secp224r1
126 */
127 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
128 static const mbedtls_mpi_uint secp224r1_p[] = {
129 BYTES_TO_T_UINT_8( 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ),
130 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ),
131 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
132 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ),
133 };
134 static const mbedtls_mpi_uint secp224r1_b[] = {
135 BYTES_TO_T_UINT_8( 0xB4, 0xFF, 0x55, 0x23, 0x43, 0x39, 0x0B, 0x27 ),
136 BYTES_TO_T_UINT_8( 0xBA, 0xD8, 0xBF, 0xD7, 0xB7, 0xB0, 0x44, 0x50 ),
137 BYTES_TO_T_UINT_8( 0x56, 0x32, 0x41, 0xF5, 0xAB, 0xB3, 0x04, 0x0C ),
138 BYTES_TO_T_UINT_4( 0x85, 0x0A, 0x05, 0xB4 ),
139 };
140 static const mbedtls_mpi_uint secp224r1_gx[] = {
141 BYTES_TO_T_UINT_8( 0x21, 0x1D, 0x5C, 0x11, 0xD6, 0x80, 0x32, 0x34 ),
142 BYTES_TO_T_UINT_8( 0x22, 0x11, 0xC2, 0x56, 0xD3, 0xC1, 0x03, 0x4A ),
143 BYTES_TO_T_UINT_8( 0xB9, 0x90, 0x13, 0x32, 0x7F, 0xBF, 0xB4, 0x6B ),
144 BYTES_TO_T_UINT_4( 0xBD, 0x0C, 0x0E, 0xB7 ),
145 };
146 static const mbedtls_mpi_uint secp224r1_gy[] = {
147 BYTES_TO_T_UINT_8( 0x34, 0x7E, 0x00, 0x85, 0x99, 0x81, 0xD5, 0x44 ),
148 BYTES_TO_T_UINT_8( 0x64, 0x47, 0x07, 0x5A, 0xA0, 0x75, 0x43, 0xCD ),
149 BYTES_TO_T_UINT_8( 0xE6, 0xDF, 0x22, 0x4C, 0xFB, 0x23, 0xF7, 0xB5 ),
150 BYTES_TO_T_UINT_4( 0x88, 0x63, 0x37, 0xBD ),
151 };
152 static const mbedtls_mpi_uint secp224r1_n[] = {
153 BYTES_TO_T_UINT_8( 0x3D, 0x2A, 0x5C, 0x5C, 0x45, 0x29, 0xDD, 0x13 ),
154 BYTES_TO_T_UINT_8( 0x3E, 0xF0, 0xB8, 0xE0, 0xA2, 0x16, 0xFF, 0xFF ),
155 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
156 BYTES_TO_T_UINT_4( 0xFF, 0xFF, 0xFF, 0xFF ),
157 };
158 #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */
159
160 /*
161 * Domain parameters for secp256r1
162 */
163 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
164 static const mbedtls_mpi_uint secp256r1_p[] = {
165 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
166 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ),
167 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ),
168 BYTES_TO_T_UINT_8( 0x01, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ),
169 };
170 static const mbedtls_mpi_uint secp256r1_b[] = {
171 BYTES_TO_T_UINT_8( 0x4B, 0x60, 0xD2, 0x27, 0x3E, 0x3C, 0xCE, 0x3B ),
172 BYTES_TO_T_UINT_8( 0xF6, 0xB0, 0x53, 0xCC, 0xB0, 0x06, 0x1D, 0x65 ),
173 BYTES_TO_T_UINT_8( 0xBC, 0x86, 0x98, 0x76, 0x55, 0xBD, 0xEB, 0xB3 ),
174 BYTES_TO_T_UINT_8( 0xE7, 0x93, 0x3A, 0xAA, 0xD8, 0x35, 0xC6, 0x5A ),
175 };
176 static const mbedtls_mpi_uint secp256r1_gx[] = {
177 BYTES_TO_T_UINT_8( 0x96, 0xC2, 0x98, 0xD8, 0x45, 0x39, 0xA1, 0xF4 ),
178 BYTES_TO_T_UINT_8( 0xA0, 0x33, 0xEB, 0x2D, 0x81, 0x7D, 0x03, 0x77 ),
179 BYTES_TO_T_UINT_8( 0xF2, 0x40, 0xA4, 0x63, 0xE5, 0xE6, 0xBC, 0xF8 ),
180 BYTES_TO_T_UINT_8( 0x47, 0x42, 0x2C, 0xE1, 0xF2, 0xD1, 0x17, 0x6B ),
181 };
182 static const mbedtls_mpi_uint secp256r1_gy[] = {
183 BYTES_TO_T_UINT_8( 0xF5, 0x51, 0xBF, 0x37, 0x68, 0x40, 0xB6, 0xCB ),
184 BYTES_TO_T_UINT_8( 0xCE, 0x5E, 0x31, 0x6B, 0x57, 0x33, 0xCE, 0x2B ),
185 BYTES_TO_T_UINT_8( 0x16, 0x9E, 0x0F, 0x7C, 0x4A, 0xEB, 0xE7, 0x8E ),
186 BYTES_TO_T_UINT_8( 0x9B, 0x7F, 0x1A, 0xFE, 0xE2, 0x42, 0xE3, 0x4F ),
187 };
188 static const mbedtls_mpi_uint secp256r1_n[] = {
189 BYTES_TO_T_UINT_8( 0x51, 0x25, 0x63, 0xFC, 0xC2, 0xCA, 0xB9, 0xF3 ),
190 BYTES_TO_T_UINT_8( 0x84, 0x9E, 0x17, 0xA7, 0xAD, 0xFA, 0xE6, 0xBC ),
191 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
192 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ),
193 };
194 #endif /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */
195
196 /*
197 * Domain parameters for secp384r1
198 */
199 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
200 static const mbedtls_mpi_uint secp384r1_p[] = {
201 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ),
202 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ),
203 BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
204 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
205 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
206 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
207 };
208 static const mbedtls_mpi_uint secp384r1_b[] = {
209 BYTES_TO_T_UINT_8( 0xEF, 0x2A, 0xEC, 0xD3, 0xED, 0xC8, 0x85, 0x2A ),
210 BYTES_TO_T_UINT_8( 0x9D, 0xD1, 0x2E, 0x8A, 0x8D, 0x39, 0x56, 0xC6 ),
211 BYTES_TO_T_UINT_8( 0x5A, 0x87, 0x13, 0x50, 0x8F, 0x08, 0x14, 0x03 ),
212 BYTES_TO_T_UINT_8( 0x12, 0x41, 0x81, 0xFE, 0x6E, 0x9C, 0x1D, 0x18 ),
213 BYTES_TO_T_UINT_8( 0x19, 0x2D, 0xF8, 0xE3, 0x6B, 0x05, 0x8E, 0x98 ),
214 BYTES_TO_T_UINT_8( 0xE4, 0xE7, 0x3E, 0xE2, 0xA7, 0x2F, 0x31, 0xB3 ),
215 };
216 static const mbedtls_mpi_uint secp384r1_gx[] = {
217 BYTES_TO_T_UINT_8( 0xB7, 0x0A, 0x76, 0x72, 0x38, 0x5E, 0x54, 0x3A ),
218 BYTES_TO_T_UINT_8( 0x6C, 0x29, 0x55, 0xBF, 0x5D, 0xF2, 0x02, 0x55 ),
219 BYTES_TO_T_UINT_8( 0x38, 0x2A, 0x54, 0x82, 0xE0, 0x41, 0xF7, 0x59 ),
220 BYTES_TO_T_UINT_8( 0x98, 0x9B, 0xA7, 0x8B, 0x62, 0x3B, 0x1D, 0x6E ),
221 BYTES_TO_T_UINT_8( 0x74, 0xAD, 0x20, 0xF3, 0x1E, 0xC7, 0xB1, 0x8E ),
222 BYTES_TO_T_UINT_8( 0x37, 0x05, 0x8B, 0xBE, 0x22, 0xCA, 0x87, 0xAA ),
223 };
224 static const mbedtls_mpi_uint secp384r1_gy[] = {
225 BYTES_TO_T_UINT_8( 0x5F, 0x0E, 0xEA, 0x90, 0x7C, 0x1D, 0x43, 0x7A ),
226 BYTES_TO_T_UINT_8( 0x9D, 0x81, 0x7E, 0x1D, 0xCE, 0xB1, 0x60, 0x0A ),
227 BYTES_TO_T_UINT_8( 0xC0, 0xB8, 0xF0, 0xB5, 0x13, 0x31, 0xDA, 0xE9 ),
228 BYTES_TO_T_UINT_8( 0x7C, 0x14, 0x9A, 0x28, 0xBD, 0x1D, 0xF4, 0xF8 ),
229 BYTES_TO_T_UINT_8( 0x29, 0xDC, 0x92, 0x92, 0xBF, 0x98, 0x9E, 0x5D ),
230 BYTES_TO_T_UINT_8( 0x6F, 0x2C, 0x26, 0x96, 0x4A, 0xDE, 0x17, 0x36 ),
231 };
232 static const mbedtls_mpi_uint secp384r1_n[] = {
233 BYTES_TO_T_UINT_8( 0x73, 0x29, 0xC5, 0xCC, 0x6A, 0x19, 0xEC, 0xEC ),
234 BYTES_TO_T_UINT_8( 0x7A, 0xA7, 0xB0, 0x48, 0xB2, 0x0D, 0x1A, 0x58 ),
235 BYTES_TO_T_UINT_8( 0xDF, 0x2D, 0x37, 0xF4, 0x81, 0x4D, 0x63, 0xC7 ),
236 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
237 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
238 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
239 };
240 #endif /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */
241
242 /*
243 * Domain parameters for secp521r1
244 */
245 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
246 static const mbedtls_mpi_uint secp521r1_p[] = {
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_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
250 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
251 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
252 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
253 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
254 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
255 BYTES_TO_T_UINT_2( 0xFF, 0x01 ),
256 };
257 static const mbedtls_mpi_uint secp521r1_b[] = {
258 BYTES_TO_T_UINT_8( 0x00, 0x3F, 0x50, 0x6B, 0xD4, 0x1F, 0x45, 0xEF ),
259 BYTES_TO_T_UINT_8( 0xF1, 0x34, 0x2C, 0x3D, 0x88, 0xDF, 0x73, 0x35 ),
260 BYTES_TO_T_UINT_8( 0x07, 0xBF, 0xB1, 0x3B, 0xBD, 0xC0, 0x52, 0x16 ),
261 BYTES_TO_T_UINT_8( 0x7B, 0x93, 0x7E, 0xEC, 0x51, 0x39, 0x19, 0x56 ),
262 BYTES_TO_T_UINT_8( 0xE1, 0x09, 0xF1, 0x8E, 0x91, 0x89, 0xB4, 0xB8 ),
263 BYTES_TO_T_UINT_8( 0xF3, 0x15, 0xB3, 0x99, 0x5B, 0x72, 0xDA, 0xA2 ),
264 BYTES_TO_T_UINT_8( 0xEE, 0x40, 0x85, 0xB6, 0xA0, 0x21, 0x9A, 0x92 ),
265 BYTES_TO_T_UINT_8( 0x1F, 0x9A, 0x1C, 0x8E, 0x61, 0xB9, 0x3E, 0x95 ),
266 BYTES_TO_T_UINT_2( 0x51, 0x00 ),
267 };
268 static const mbedtls_mpi_uint secp521r1_gx[] = {
269 BYTES_TO_T_UINT_8( 0x66, 0xBD, 0xE5, 0xC2, 0x31, 0x7E, 0x7E, 0xF9 ),
270 BYTES_TO_T_UINT_8( 0x9B, 0x42, 0x6A, 0x85, 0xC1, 0xB3, 0x48, 0x33 ),
271 BYTES_TO_T_UINT_8( 0xDE, 0xA8, 0xFF, 0xA2, 0x27, 0xC1, 0x1D, 0xFE ),
272 BYTES_TO_T_UINT_8( 0x28, 0x59, 0xE7, 0xEF, 0x77, 0x5E, 0x4B, 0xA1 ),
273 BYTES_TO_T_UINT_8( 0xBA, 0x3D, 0x4D, 0x6B, 0x60, 0xAF, 0x28, 0xF8 ),
274 BYTES_TO_T_UINT_8( 0x21, 0xB5, 0x3F, 0x05, 0x39, 0x81, 0x64, 0x9C ),
275 BYTES_TO_T_UINT_8( 0x42, 0xB4, 0x95, 0x23, 0x66, 0xCB, 0x3E, 0x9E ),
276 BYTES_TO_T_UINT_8( 0xCD, 0xE9, 0x04, 0x04, 0xB7, 0x06, 0x8E, 0x85 ),
277 BYTES_TO_T_UINT_2( 0xC6, 0x00 ),
278 };
279 static const mbedtls_mpi_uint secp521r1_gy[] = {
280 BYTES_TO_T_UINT_8( 0x50, 0x66, 0xD1, 0x9F, 0x76, 0x94, 0xBE, 0x88 ),
281 BYTES_TO_T_UINT_8( 0x40, 0xC2, 0x72, 0xA2, 0x86, 0x70, 0x3C, 0x35 ),
282 BYTES_TO_T_UINT_8( 0x61, 0x07, 0xAD, 0x3F, 0x01, 0xB9, 0x50, 0xC5 ),
283 BYTES_TO_T_UINT_8( 0x40, 0x26, 0xF4, 0x5E, 0x99, 0x72, 0xEE, 0x97 ),
284 BYTES_TO_T_UINT_8( 0x2C, 0x66, 0x3E, 0x27, 0x17, 0xBD, 0xAF, 0x17 ),
285 BYTES_TO_T_UINT_8( 0x68, 0x44, 0x9B, 0x57, 0x49, 0x44, 0xF5, 0x98 ),
286 BYTES_TO_T_UINT_8( 0xD9, 0x1B, 0x7D, 0x2C, 0xB4, 0x5F, 0x8A, 0x5C ),
287 BYTES_TO_T_UINT_8( 0x04, 0xC0, 0x3B, 0x9A, 0x78, 0x6A, 0x29, 0x39 ),
288 BYTES_TO_T_UINT_2( 0x18, 0x01 ),
289 };
290 static const mbedtls_mpi_uint secp521r1_n[] = {
291 BYTES_TO_T_UINT_8( 0x09, 0x64, 0x38, 0x91, 0x1E, 0xB7, 0x6F, 0xBB ),
292 BYTES_TO_T_UINT_8( 0xAE, 0x47, 0x9C, 0x89, 0xB8, 0xC9, 0xB5, 0x3B ),
293 BYTES_TO_T_UINT_8( 0xD0, 0xA5, 0x09, 0xF7, 0x48, 0x01, 0xCC, 0x7F ),
294 BYTES_TO_T_UINT_8( 0x6B, 0x96, 0x2F, 0xBF, 0x83, 0x87, 0x86, 0x51 ),
295 BYTES_TO_T_UINT_8( 0xFA, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
296 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
297 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
298 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
299 BYTES_TO_T_UINT_2( 0xFF, 0x01 ),
300 };
301 #endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */
302
303 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
304 static const mbedtls_mpi_uint secp192k1_p[] = {
305 BYTES_TO_T_UINT_8( 0x37, 0xEE, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ),
306 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
307 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
308 };
309 static const mbedtls_mpi_uint secp192k1_a[] = {
310 BYTES_TO_T_UINT_2( 0x00, 0x00 ),
311 };
312 static const mbedtls_mpi_uint secp192k1_b[] = {
313 BYTES_TO_T_UINT_2( 0x03, 0x00 ),
314 };
315 static const mbedtls_mpi_uint secp192k1_gx[] = {
316 BYTES_TO_T_UINT_8( 0x7D, 0x6C, 0xE0, 0xEA, 0xB1, 0xD1, 0xA5, 0x1D ),
317 BYTES_TO_T_UINT_8( 0x34, 0xF4, 0xB7, 0x80, 0x02, 0x7D, 0xB0, 0x26 ),
318 BYTES_TO_T_UINT_8( 0xAE, 0xE9, 0x57, 0xC0, 0x0E, 0xF1, 0x4F, 0xDB ),
319 };
320 static const mbedtls_mpi_uint secp192k1_gy[] = {
321 BYTES_TO_T_UINT_8( 0x9D, 0x2F, 0x5E, 0xD9, 0x88, 0xAA, 0x82, 0x40 ),
322 BYTES_TO_T_UINT_8( 0x34, 0x86, 0xBE, 0x15, 0xD0, 0x63, 0x41, 0x84 ),
323 BYTES_TO_T_UINT_8( 0xA7, 0x28, 0x56, 0x9C, 0x6D, 0x2F, 0x2F, 0x9B ),
324 };
325 static const mbedtls_mpi_uint secp192k1_n[] = {
326 BYTES_TO_T_UINT_8( 0x8D, 0xFD, 0xDE, 0x74, 0x6A, 0x46, 0x69, 0x0F ),
327 BYTES_TO_T_UINT_8( 0x17, 0xFC, 0xF2, 0x26, 0xFE, 0xFF, 0xFF, 0xFF ),
328 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
329 };
330 #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */
331
332 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
333 static const mbedtls_mpi_uint secp224k1_p[] = {
334 BYTES_TO_T_UINT_8( 0x6D, 0xE5, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ),
335 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
336 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
337 BYTES_TO_T_UINT_4( 0xFF, 0xFF, 0xFF, 0xFF ),
338 };
339 static const mbedtls_mpi_uint secp224k1_a[] = {
340 BYTES_TO_T_UINT_2( 0x00, 0x00 ),
341 };
342 static const mbedtls_mpi_uint secp224k1_b[] = {
343 BYTES_TO_T_UINT_2( 0x05, 0x00 ),
344 };
345 static const mbedtls_mpi_uint secp224k1_gx[] = {
346 BYTES_TO_T_UINT_8( 0x5C, 0xA4, 0xB7, 0xB6, 0x0E, 0x65, 0x7E, 0x0F ),
347 BYTES_TO_T_UINT_8( 0xA9, 0x75, 0x70, 0xE4, 0xE9, 0x67, 0xA4, 0x69 ),
348 BYTES_TO_T_UINT_8( 0xA1, 0x28, 0xFC, 0x30, 0xDF, 0x99, 0xF0, 0x4D ),
349 BYTES_TO_T_UINT_4( 0x33, 0x5B, 0x45, 0xA1 ),
350 };
351 static const mbedtls_mpi_uint secp224k1_gy[] = {
352 BYTES_TO_T_UINT_8( 0xA5, 0x61, 0x6D, 0x55, 0xDB, 0x4B, 0xCA, 0xE2 ),
353 BYTES_TO_T_UINT_8( 0x59, 0xBD, 0xB0, 0xC0, 0xF7, 0x19, 0xE3, 0xF7 ),
354 BYTES_TO_T_UINT_8( 0xD6, 0xFB, 0xCA, 0x82, 0x42, 0x34, 0xBA, 0x7F ),
355 BYTES_TO_T_UINT_4( 0xED, 0x9F, 0x08, 0x7E ),
356 };
357 static const mbedtls_mpi_uint secp224k1_n[] = {
358 BYTES_TO_T_UINT_8( 0xF7, 0xB1, 0x9F, 0x76, 0x71, 0xA9, 0xF0, 0xCA ),
359 BYTES_TO_T_UINT_8( 0x84, 0x61, 0xEC, 0xD2, 0xE8, 0xDC, 0x01, 0x00 ),
360 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ),
361 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ),
362 };
363 #endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */
364
365 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
366 static const mbedtls_mpi_uint secp256k1_p[] = {
367 BYTES_TO_T_UINT_8( 0x2F, 0xFC, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ),
368 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
369 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
370 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
371 };
372 static const mbedtls_mpi_uint secp256k1_a[] = {
373 BYTES_TO_T_UINT_2( 0x00, 0x00 ),
374 };
375 static const mbedtls_mpi_uint secp256k1_b[] = {
376 BYTES_TO_T_UINT_2( 0x07, 0x00 ),
377 };
378 static const mbedtls_mpi_uint secp256k1_gx[] = {
379 BYTES_TO_T_UINT_8( 0x98, 0x17, 0xF8, 0x16, 0x5B, 0x81, 0xF2, 0x59 ),
380 BYTES_TO_T_UINT_8( 0xD9, 0x28, 0xCE, 0x2D, 0xDB, 0xFC, 0x9B, 0x02 ),
381 BYTES_TO_T_UINT_8( 0x07, 0x0B, 0x87, 0xCE, 0x95, 0x62, 0xA0, 0x55 ),
382 BYTES_TO_T_UINT_8( 0xAC, 0xBB, 0xDC, 0xF9, 0x7E, 0x66, 0xBE, 0x79 ),
383 };
384 static const mbedtls_mpi_uint secp256k1_gy[] = {
385 BYTES_TO_T_UINT_8( 0xB8, 0xD4, 0x10, 0xFB, 0x8F, 0xD0, 0x47, 0x9C ),
386 BYTES_TO_T_UINT_8( 0x19, 0x54, 0x85, 0xA6, 0x48, 0xB4, 0x17, 0xFD ),
387 BYTES_TO_T_UINT_8( 0xA8, 0x08, 0x11, 0x0E, 0xFC, 0xFB, 0xA4, 0x5D ),
388 BYTES_TO_T_UINT_8( 0x65, 0xC4, 0xA3, 0x26, 0x77, 0xDA, 0x3A, 0x48 ),
389 };
390 static const mbedtls_mpi_uint secp256k1_n[] = {
391 BYTES_TO_T_UINT_8( 0x41, 0x41, 0x36, 0xD0, 0x8C, 0x5E, 0xD2, 0xBF ),
392 BYTES_TO_T_UINT_8( 0x3B, 0xA0, 0x48, 0xAF, 0xE6, 0xDC, 0xAE, 0xBA ),
393 BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
394 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
395 };
396 #endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */
397
398 /*
399 * Domain parameters for brainpoolP256r1 (RFC 5639 3.4)
400 */
401 #if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED)
402 static const mbedtls_mpi_uint brainpoolP256r1_p[] = {
403 BYTES_TO_T_UINT_8( 0x77, 0x53, 0x6E, 0x1F, 0x1D, 0x48, 0x13, 0x20 ),
404 BYTES_TO_T_UINT_8( 0x28, 0x20, 0x26, 0xD5, 0x23, 0xF6, 0x3B, 0x6E ),
405 BYTES_TO_T_UINT_8( 0x72, 0x8D, 0x83, 0x9D, 0x90, 0x0A, 0x66, 0x3E ),
406 BYTES_TO_T_UINT_8( 0xBC, 0xA9, 0xEE, 0xA1, 0xDB, 0x57, 0xFB, 0xA9 ),
407 };
408 static const mbedtls_mpi_uint brainpoolP256r1_a[] = {
409 BYTES_TO_T_UINT_8( 0xD9, 0xB5, 0x30, 0xF3, 0x44, 0x4B, 0x4A, 0xE9 ),
410 BYTES_TO_T_UINT_8( 0x6C, 0x5C, 0xDC, 0x26, 0xC1, 0x55, 0x80, 0xFB ),
411 BYTES_TO_T_UINT_8( 0xE7, 0xFF, 0x7A, 0x41, 0x30, 0x75, 0xF6, 0xEE ),
412 BYTES_TO_T_UINT_8( 0x57, 0x30, 0x2C, 0xFC, 0x75, 0x09, 0x5A, 0x7D ),
413 };
414 static const mbedtls_mpi_uint brainpoolP256r1_b[] = {
415 BYTES_TO_T_UINT_8( 0xB6, 0x07, 0x8C, 0xFF, 0x18, 0xDC, 0xCC, 0x6B ),
416 BYTES_TO_T_UINT_8( 0xCE, 0xE1, 0xF7, 0x5C, 0x29, 0x16, 0x84, 0x95 ),
417 BYTES_TO_T_UINT_8( 0xBF, 0x7C, 0xD7, 0xBB, 0xD9, 0xB5, 0x30, 0xF3 ),
418 BYTES_TO_T_UINT_8( 0x44, 0x4B, 0x4A, 0xE9, 0x6C, 0x5C, 0xDC, 0x26 ),
419 };
420 static const mbedtls_mpi_uint brainpoolP256r1_gx[] = {
421 BYTES_TO_T_UINT_8( 0x62, 0x32, 0xCE, 0x9A, 0xBD, 0x53, 0x44, 0x3A ),
422 BYTES_TO_T_UINT_8( 0xC2, 0x23, 0xBD, 0xE3, 0xE1, 0x27, 0xDE, 0xB9 ),
423 BYTES_TO_T_UINT_8( 0xAF, 0xB7, 0x81, 0xFC, 0x2F, 0x48, 0x4B, 0x2C ),
424 BYTES_TO_T_UINT_8( 0xCB, 0x57, 0x7E, 0xCB, 0xB9, 0xAE, 0xD2, 0x8B ),
425 };
426 static const mbedtls_mpi_uint brainpoolP256r1_gy[] = {
427 BYTES_TO_T_UINT_8( 0x97, 0x69, 0x04, 0x2F, 0xC7, 0x54, 0x1D, 0x5C ),
428 BYTES_TO_T_UINT_8( 0x54, 0x8E, 0xED, 0x2D, 0x13, 0x45, 0x77, 0xC2 ),
429 BYTES_TO_T_UINT_8( 0xC9, 0x1D, 0x61, 0x14, 0x1A, 0x46, 0xF8, 0x97 ),
430 BYTES_TO_T_UINT_8( 0xFD, 0xC4, 0xDA, 0xC3, 0x35, 0xF8, 0x7E, 0x54 ),
431 };
432 static const mbedtls_mpi_uint brainpoolP256r1_n[] = {
433 BYTES_TO_T_UINT_8( 0xA7, 0x56, 0x48, 0x97, 0x82, 0x0E, 0x1E, 0x90 ),
434 BYTES_TO_T_UINT_8( 0xF7, 0xA6, 0x61, 0xB5, 0xA3, 0x7A, 0x39, 0x8C ),
435 BYTES_TO_T_UINT_8( 0x71, 0x8D, 0x83, 0x9D, 0x90, 0x0A, 0x66, 0x3E ),
436 BYTES_TO_T_UINT_8( 0xBC, 0xA9, 0xEE, 0xA1, 0xDB, 0x57, 0xFB, 0xA9 ),
437 };
438 #endif /* MBEDTLS_ECP_DP_BP256R1_ENABLED */
439
440 /*
441 * Domain parameters for brainpoolP384r1 (RFC 5639 3.6)
442 */
443 #if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED)
444 static const mbedtls_mpi_uint brainpoolP384r1_p[] = {
445 BYTES_TO_T_UINT_8( 0x53, 0xEC, 0x07, 0x31, 0x13, 0x00, 0x47, 0x87 ),
446 BYTES_TO_T_UINT_8( 0x71, 0x1A, 0x1D, 0x90, 0x29, 0xA7, 0xD3, 0xAC ),
447 BYTES_TO_T_UINT_8( 0x23, 0x11, 0xB7, 0x7F, 0x19, 0xDA, 0xB1, 0x12 ),
448 BYTES_TO_T_UINT_8( 0xB4, 0x56, 0x54, 0xED, 0x09, 0x71, 0x2F, 0x15 ),
449 BYTES_TO_T_UINT_8( 0xDF, 0x41, 0xE6, 0x50, 0x7E, 0x6F, 0x5D, 0x0F ),
450 BYTES_TO_T_UINT_8( 0x28, 0x6D, 0x38, 0xA3, 0x82, 0x1E, 0xB9, 0x8C ),
451 };
452 static const mbedtls_mpi_uint brainpoolP384r1_a[] = {
453 BYTES_TO_T_UINT_8( 0x26, 0x28, 0xCE, 0x22, 0xDD, 0xC7, 0xA8, 0x04 ),
454 BYTES_TO_T_UINT_8( 0xEB, 0xD4, 0x3A, 0x50, 0x4A, 0x81, 0xA5, 0x8A ),
455 BYTES_TO_T_UINT_8( 0x0F, 0xF9, 0x91, 0xBA, 0xEF, 0x65, 0x91, 0x13 ),
456 BYTES_TO_T_UINT_8( 0x87, 0x27, 0xB2, 0x4F, 0x8E, 0xA2, 0xBE, 0xC2 ),
457 BYTES_TO_T_UINT_8( 0xA0, 0xAF, 0x05, 0xCE, 0x0A, 0x08, 0x72, 0x3C ),
458 BYTES_TO_T_UINT_8( 0x0C, 0x15, 0x8C, 0x3D, 0xC6, 0x82, 0xC3, 0x7B ),
459 };
460 static const mbedtls_mpi_uint brainpoolP384r1_b[] = {
461 BYTES_TO_T_UINT_8( 0x11, 0x4C, 0x50, 0xFA, 0x96, 0x86, 0xB7, 0x3A ),
462 BYTES_TO_T_UINT_8( 0x94, 0xC9, 0xDB, 0x95, 0x02, 0x39, 0xB4, 0x7C ),
463 BYTES_TO_T_UINT_8( 0xD5, 0x62, 0xEB, 0x3E, 0xA5, 0x0E, 0x88, 0x2E ),
464 BYTES_TO_T_UINT_8( 0xA6, 0xD2, 0xDC, 0x07, 0xE1, 0x7D, 0xB7, 0x2F ),
465 BYTES_TO_T_UINT_8( 0x7C, 0x44, 0xF0, 0x16, 0x54, 0xB5, 0x39, 0x8B ),
466 BYTES_TO_T_UINT_8( 0x26, 0x28, 0xCE, 0x22, 0xDD, 0xC7, 0xA8, 0x04 ),
467 };
468 static const mbedtls_mpi_uint brainpoolP384r1_gx[] = {
469 BYTES_TO_T_UINT_8( 0x1E, 0xAF, 0xD4, 0x47, 0xE2, 0xB2, 0x87, 0xEF ),
470 BYTES_TO_T_UINT_8( 0xAA, 0x46, 0xD6, 0x36, 0x34, 0xE0, 0x26, 0xE8 ),
471 BYTES_TO_T_UINT_8( 0xE8, 0x10, 0xBD, 0x0C, 0xFE, 0xCA, 0x7F, 0xDB ),
472 BYTES_TO_T_UINT_8( 0xE3, 0x4F, 0xF1, 0x7E, 0xE7, 0xA3, 0x47, 0x88 ),
473 BYTES_TO_T_UINT_8( 0x6B, 0x3F, 0xC1, 0xB7, 0x81, 0x3A, 0xA6, 0xA2 ),
474 BYTES_TO_T_UINT_8( 0xFF, 0x45, 0xCF, 0x68, 0xF0, 0x64, 0x1C, 0x1D ),
475 };
476 static const mbedtls_mpi_uint brainpoolP384r1_gy[] = {
477 BYTES_TO_T_UINT_8( 0x15, 0x53, 0x3C, 0x26, 0x41, 0x03, 0x82, 0x42 ),
478 BYTES_TO_T_UINT_8( 0x11, 0x81, 0x91, 0x77, 0x21, 0x46, 0x46, 0x0E ),
479 BYTES_TO_T_UINT_8( 0x28, 0x29, 0x91, 0xF9, 0x4F, 0x05, 0x9C, 0xE1 ),
480 BYTES_TO_T_UINT_8( 0x64, 0x58, 0xEC, 0xFE, 0x29, 0x0B, 0xB7, 0x62 ),
481 BYTES_TO_T_UINT_8( 0x52, 0xD5, 0xCF, 0x95, 0x8E, 0xEB, 0xB1, 0x5C ),
482 BYTES_TO_T_UINT_8( 0xA4, 0xC2, 0xF9, 0x20, 0x75, 0x1D, 0xBE, 0x8A ),
483 };
484 static const mbedtls_mpi_uint brainpoolP384r1_n[] = {
485 BYTES_TO_T_UINT_8( 0x65, 0x65, 0x04, 0xE9, 0x02, 0x32, 0x88, 0x3B ),
486 BYTES_TO_T_UINT_8( 0x10, 0xC3, 0x7F, 0x6B, 0xAF, 0xB6, 0x3A, 0xCF ),
487 BYTES_TO_T_UINT_8( 0xA7, 0x25, 0x04, 0xAC, 0x6C, 0x6E, 0x16, 0x1F ),
488 BYTES_TO_T_UINT_8( 0xB3, 0x56, 0x54, 0xED, 0x09, 0x71, 0x2F, 0x15 ),
489 BYTES_TO_T_UINT_8( 0xDF, 0x41, 0xE6, 0x50, 0x7E, 0x6F, 0x5D, 0x0F ),
490 BYTES_TO_T_UINT_8( 0x28, 0x6D, 0x38, 0xA3, 0x82, 0x1E, 0xB9, 0x8C ),
491 };
492 #endif /* MBEDTLS_ECP_DP_BP384R1_ENABLED */
493
494 /*
495 * Domain parameters for brainpoolP512r1 (RFC 5639 3.7)
496 */
497 #if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED)
498 static const mbedtls_mpi_uint brainpoolP512r1_p[] = {
499 BYTES_TO_T_UINT_8( 0xF3, 0x48, 0x3A, 0x58, 0x56, 0x60, 0xAA, 0x28 ),
500 BYTES_TO_T_UINT_8( 0x85, 0xC6, 0x82, 0x2D, 0x2F, 0xFF, 0x81, 0x28 ),
501 BYTES_TO_T_UINT_8( 0xE6, 0x80, 0xA3, 0xE6, 0x2A, 0xA1, 0xCD, 0xAE ),
502 BYTES_TO_T_UINT_8( 0x42, 0x68, 0xC6, 0x9B, 0x00, 0x9B, 0x4D, 0x7D ),
503 BYTES_TO_T_UINT_8( 0x71, 0x08, 0x33, 0x70, 0xCA, 0x9C, 0x63, 0xD6 ),
504 BYTES_TO_T_UINT_8( 0x0E, 0xD2, 0xC9, 0xB3, 0xB3, 0x8D, 0x30, 0xCB ),
505 BYTES_TO_T_UINT_8( 0x07, 0xFC, 0xC9, 0x33, 0xAE, 0xE6, 0xD4, 0x3F ),
506 BYTES_TO_T_UINT_8( 0x8B, 0xC4, 0xE9, 0xDB, 0xB8, 0x9D, 0xDD, 0xAA ),
507 };
508 static const mbedtls_mpi_uint brainpoolP512r1_a[] = {
509 BYTES_TO_T_UINT_8( 0xCA, 0x94, 0xFC, 0x77, 0x4D, 0xAC, 0xC1, 0xE7 ),
510 BYTES_TO_T_UINT_8( 0xB9, 0xC7, 0xF2, 0x2B, 0xA7, 0x17, 0x11, 0x7F ),
511 BYTES_TO_T_UINT_8( 0xB5, 0xC8, 0x9A, 0x8B, 0xC9, 0xF1, 0x2E, 0x0A ),
512 BYTES_TO_T_UINT_8( 0xA1, 0x3A, 0x25, 0xA8, 0x5A, 0x5D, 0xED, 0x2D ),
513 BYTES_TO_T_UINT_8( 0xBC, 0x63, 0x98, 0xEA, 0xCA, 0x41, 0x34, 0xA8 ),
514 BYTES_TO_T_UINT_8( 0x10, 0x16, 0xF9, 0x3D, 0x8D, 0xDD, 0xCB, 0x94 ),
515 BYTES_TO_T_UINT_8( 0xC5, 0x4C, 0x23, 0xAC, 0x45, 0x71, 0x32, 0xE2 ),
516 BYTES_TO_T_UINT_8( 0x89, 0x3B, 0x60, 0x8B, 0x31, 0xA3, 0x30, 0x78 ),
517 };
518 static const mbedtls_mpi_uint brainpoolP512r1_b[] = {
519 BYTES_TO_T_UINT_8( 0x23, 0xF7, 0x16, 0x80, 0x63, 0xBD, 0x09, 0x28 ),
520 BYTES_TO_T_UINT_8( 0xDD, 0xE5, 0xBA, 0x5E, 0xB7, 0x50, 0x40, 0x98 ),
521 BYTES_TO_T_UINT_8( 0x67, 0x3E, 0x08, 0xDC, 0xCA, 0x94, 0xFC, 0x77 ),
522 BYTES_TO_T_UINT_8( 0x4D, 0xAC, 0xC1, 0xE7, 0xB9, 0xC7, 0xF2, 0x2B ),
523 BYTES_TO_T_UINT_8( 0xA7, 0x17, 0x11, 0x7F, 0xB5, 0xC8, 0x9A, 0x8B ),
524 BYTES_TO_T_UINT_8( 0xC9, 0xF1, 0x2E, 0x0A, 0xA1, 0x3A, 0x25, 0xA8 ),
525 BYTES_TO_T_UINT_8( 0x5A, 0x5D, 0xED, 0x2D, 0xBC, 0x63, 0x98, 0xEA ),
526 BYTES_TO_T_UINT_8( 0xCA, 0x41, 0x34, 0xA8, 0x10, 0x16, 0xF9, 0x3D ),
527 };
528 static const mbedtls_mpi_uint brainpoolP512r1_gx[] = {
529 BYTES_TO_T_UINT_8( 0x22, 0xF8, 0xB9, 0xBC, 0x09, 0x22, 0x35, 0x8B ),
530 BYTES_TO_T_UINT_8( 0x68, 0x5E, 0x6A, 0x40, 0x47, 0x50, 0x6D, 0x7C ),
531 BYTES_TO_T_UINT_8( 0x5F, 0x7D, 0xB9, 0x93, 0x7B, 0x68, 0xD1, 0x50 ),
532 BYTES_TO_T_UINT_8( 0x8D, 0xD4, 0xD0, 0xE2, 0x78, 0x1F, 0x3B, 0xFF ),
533 BYTES_TO_T_UINT_8( 0x8E, 0x09, 0xD0, 0xF4, 0xEE, 0x62, 0x3B, 0xB4 ),
534 BYTES_TO_T_UINT_8( 0xC1, 0x16, 0xD9, 0xB5, 0x70, 0x9F, 0xED, 0x85 ),
535 BYTES_TO_T_UINT_8( 0x93, 0x6A, 0x4C, 0x9C, 0x2E, 0x32, 0x21, 0x5A ),
536 BYTES_TO_T_UINT_8( 0x64, 0xD9, 0x2E, 0xD8, 0xBD, 0xE4, 0xAE, 0x81 ),
537 };
538 static const mbedtls_mpi_uint brainpoolP512r1_gy[] = {
539 BYTES_TO_T_UINT_8( 0x92, 0x08, 0xD8, 0x3A, 0x0F, 0x1E, 0xCD, 0x78 ),
540 BYTES_TO_T_UINT_8( 0x06, 0x54, 0xF0, 0xA8, 0x2F, 0x2B, 0xCA, 0xD1 ),
541 BYTES_TO_T_UINT_8( 0xAE, 0x63, 0x27, 0x8A, 0xD8, 0x4B, 0xCA, 0x5B ),
542 BYTES_TO_T_UINT_8( 0x5E, 0x48, 0x5F, 0x4A, 0x49, 0xDE, 0xDC, 0xB2 ),
543 BYTES_TO_T_UINT_8( 0x11, 0x81, 0x1F, 0x88, 0x5B, 0xC5, 0x00, 0xA0 ),
544 BYTES_TO_T_UINT_8( 0x1A, 0x7B, 0xA5, 0x24, 0x00, 0xF7, 0x09, 0xF2 ),
545 BYTES_TO_T_UINT_8( 0xFD, 0x22, 0x78, 0xCF, 0xA9, 0xBF, 0xEA, 0xC0 ),
546 BYTES_TO_T_UINT_8( 0xEC, 0x32, 0x63, 0x56, 0x5D, 0x38, 0xDE, 0x7D ),
547 };
548 static const mbedtls_mpi_uint brainpoolP512r1_n[] = {
549 BYTES_TO_T_UINT_8( 0x69, 0x00, 0xA9, 0x9C, 0x82, 0x96, 0x87, 0xB5 ),
550 BYTES_TO_T_UINT_8( 0xDD, 0xDA, 0x5D, 0x08, 0x81, 0xD3, 0xB1, 0x1D ),
551 BYTES_TO_T_UINT_8( 0x47, 0x10, 0xAC, 0x7F, 0x19, 0x61, 0x86, 0x41 ),
552 BYTES_TO_T_UINT_8( 0x19, 0x26, 0xA9, 0x4C, 0x41, 0x5C, 0x3E, 0x55 ),
553 BYTES_TO_T_UINT_8( 0x70, 0x08, 0x33, 0x70, 0xCA, 0x9C, 0x63, 0xD6 ),
554 BYTES_TO_T_UINT_8( 0x0E, 0xD2, 0xC9, 0xB3, 0xB3, 0x8D, 0x30, 0xCB ),
555 BYTES_TO_T_UINT_8( 0x07, 0xFC, 0xC9, 0x33, 0xAE, 0xE6, 0xD4, 0x3F ),
556 BYTES_TO_T_UINT_8( 0x8B, 0xC4, 0xE9, 0xDB, 0xB8, 0x9D, 0xDD, 0xAA ),
557 };
558 #endif /* MBEDTLS_ECP_DP_BP512R1_ENABLED */
559
560 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) \
561 || defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) \
562 || defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) \
563 || defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) \
564 || defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) \
565 || defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) \
566 || defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) \
567 || defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) \
568 || defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) \
569 || defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) \
570 || defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
571 /* For these curves, we build the group parameters dynamically. */
572 #define ECP_LOAD_GROUP
573 #endif
574
575 #if defined(ECP_LOAD_GROUP)
576 /*
577 * Create an MPI from embedded constants
578 * (assumes len is an exact multiple of sizeof mbedtls_mpi_uint)
579 */
ecp_mpi_load(mbedtls_mpi * X,const mbedtls_mpi_uint * p,size_t len)580 static inline void ecp_mpi_load( mbedtls_mpi *X, const mbedtls_mpi_uint *p, size_t len )
581 {
582 X->MBEDTLS_PRIVATE(s) = 1;
583 X->MBEDTLS_PRIVATE(n) = len / sizeof( mbedtls_mpi_uint );
584 X->MBEDTLS_PRIVATE(p) = (mbedtls_mpi_uint *) p;
585 }
586
587 /*
588 * Set an MPI to static value 1
589 */
ecp_mpi_set1(mbedtls_mpi * X)590 static inline void ecp_mpi_set1( mbedtls_mpi *X )
591 {
592 static mbedtls_mpi_uint one[] = { 1 };
593 X->MBEDTLS_PRIVATE(s) = 1;
594 X->MBEDTLS_PRIVATE(n) = 1;
595 X->MBEDTLS_PRIVATE(p) = one;
596 }
597
598 /*
599 * Make group available from embedded constants
600 *
601 * STMicroelectronics edition
602 *
603 */
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)604 static int ecp_group_load( mbedtls_ecp_group *grp,
605 const mbedtls_mpi_uint *p, size_t plen,
606 const mbedtls_mpi_uint *a, size_t alen,
607 const mbedtls_mpi_uint *b, size_t blen,
608 const mbedtls_mpi_uint *gx, size_t gxlen,
609 const mbedtls_mpi_uint *gy, size_t gylen,
610 const mbedtls_mpi_uint *n, size_t nlen)
611 {
612 int ret = 0;
613
614 ecp_mpi_load( &grp->P, p, plen );
615 if( a != NULL )
616 ecp_mpi_load( &grp->A, a, alen );
617 ecp_mpi_load( &grp->B, b, blen );
618 ecp_mpi_load( &grp->N, n, nlen );
619
620 ecp_mpi_load( &grp->G.MBEDTLS_PRIVATE(X), gx, gxlen );
621 ecp_mpi_load( &grp->G.MBEDTLS_PRIVATE(Y), gy, gylen );
622 ecp_mpi_set1( &grp->G.MBEDTLS_PRIVATE(Z) );
623
624 grp->pbits = mbedtls_mpi_bitlen( &grp->P );
625 grp->nbits = mbedtls_mpi_bitlen( &grp->N );
626
627 grp->h = 1;
628
629 /* ST coefs group load:
630 ST coef tables are big endian, whereas mpi coef tables are little endian
631 */
632 grp->st_modulus_size = mbedtls_mpi_size( &grp->P );
633 grp->st_order_size = mbedtls_mpi_size( &grp->N );
634
635 grp->st_p = mbedtls_calloc(grp->st_modulus_size, sizeof( uint8_t ));
636 MBEDTLS_MPI_CHK((grp->st_p == NULL) ? MBEDTLS_ERR_ECP_ALLOC_FAILED : 0);
637 mbedtls_mpi_write_binary(&grp->P, grp->st_p, grp->st_modulus_size);
638
639 grp->st_a_abs = mbedtls_calloc(grp->st_modulus_size, sizeof( uint8_t ));
640 MBEDTLS_MPI_CHK((grp->st_a_abs == NULL) ? MBEDTLS_ERR_ECP_ALLOC_FAILED : 0);
641
642 if (grp->A.MBEDTLS_PRIVATE(p) == NULL)
643 {
644 /* NIST prime curves: A coef = -3 */
645 mbedtls_platform_zeroize(grp->st_a_abs, grp->st_modulus_size);
646 grp->st_a_abs[grp->st_modulus_size - 1] = 3U;
647 /* For HW, sign is 1 for negative value and 0 for positive value */
648 grp->st_a_sign = 1U;
649 }
650 else
651 {
652 /* Other curves: A coef is positive */
653 mbedtls_mpi_write_binary(&grp->A, grp->st_a_abs, grp->st_modulus_size);
654 grp->st_a_sign = 0;
655 }
656
657 grp->st_b = mbedtls_calloc(grp->st_modulus_size, sizeof( uint8_t ));
658 MBEDTLS_MPI_CHK((grp->st_b == NULL) ? MBEDTLS_ERR_ECP_ALLOC_FAILED : 0);
659 mbedtls_mpi_write_binary(&grp->B, grp->st_b, grp->st_modulus_size);
660
661 grp->st_gx = mbedtls_calloc(grp->st_modulus_size, sizeof( uint8_t ));
662 MBEDTLS_MPI_CHK((grp->st_gx == NULL) ? MBEDTLS_ERR_ECP_ALLOC_FAILED : 0);
663 mbedtls_mpi_write_binary(&grp->G.MBEDTLS_PRIVATE(X), grp->st_gx, grp->st_modulus_size);
664
665 grp->st_gy = mbedtls_calloc(grp->st_modulus_size, sizeof( uint8_t ));
666 MBEDTLS_MPI_CHK((grp->st_gy == NULL) ? MBEDTLS_ERR_ECP_ALLOC_FAILED : 0);
667 mbedtls_mpi_write_binary(&grp->G.MBEDTLS_PRIVATE(Y), grp->st_gy, grp->st_modulus_size);
668
669 grp->st_n = mbedtls_calloc(grp->st_order_size, sizeof( uint8_t ));
670 MBEDTLS_MPI_CHK((grp->st_n == NULL) ? MBEDTLS_ERR_ECP_ALLOC_FAILED : 0);
671 mbedtls_mpi_write_binary(&grp->N, grp->st_n, grp->st_order_size);
672
673 cleanup:
674 if( ret != 0 )
675 mbedtls_ecp_group_free( grp );
676
677 return( ret );
678 }
679 #endif /* ECP_LOAD_GROUP */
680
681 #if defined(MBEDTLS_ECP_NIST_OPTIM)
682 /* Forward declarations */
683 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
684 static int ecp_mod_p192( mbedtls_mpi * );
685 #endif
686 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
687 static int ecp_mod_p224( mbedtls_mpi * );
688 #endif
689 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
690 static int ecp_mod_p256( mbedtls_mpi * );
691 #endif
692 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
693 static int ecp_mod_p384( mbedtls_mpi * );
694 #endif
695 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
696 static int ecp_mod_p521( mbedtls_mpi * );
697 #endif
698
699 #define NIST_MODP( P ) grp->modp = ecp_mod_ ## P;
700 #else
701 #define NIST_MODP( P )
702 #endif /* MBEDTLS_ECP_NIST_OPTIM */
703
704 /* Additional forward declarations */
705 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
706 static int ecp_mod_p255( mbedtls_mpi * );
707 #endif
708 #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
709 static int ecp_mod_p448( mbedtls_mpi * );
710 #endif
711 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
712 static int ecp_mod_p192k1( mbedtls_mpi * );
713 #endif
714 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
715 static int ecp_mod_p224k1( mbedtls_mpi * );
716 #endif
717 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
718 static int ecp_mod_p256k1( mbedtls_mpi * );
719 #endif
720
721 #if defined(ECP_LOAD_GROUP)
722 #define LOAD_GROUP_A( G ) ecp_group_load( grp, \
723 G ## _p, sizeof( G ## _p ), \
724 G ## _a, sizeof( G ## _a ), \
725 G ## _b, sizeof( G ## _b ), \
726 G ## _gx, sizeof( G ## _gx ), \
727 G ## _gy, sizeof( G ## _gy ), \
728 G ## _n, sizeof( G ## _n ) )
729
730 #define LOAD_GROUP( G ) ecp_group_load( grp, \
731 G ## _p, sizeof( G ## _p ), \
732 NULL, 0, \
733 G ## _b, sizeof( G ## _b ), \
734 G ## _gx, sizeof( G ## _gx ), \
735 G ## _gy, sizeof( G ## _gy ), \
736 G ## _n, sizeof( G ## _n ) )
737 #endif /* ECP_LOAD_GROUP */
738
739 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
740 /*
741 * Specialized function for creating the Curve25519 group
742 */
ecp_use_curve25519(mbedtls_ecp_group * grp)743 static int ecp_use_curve25519( mbedtls_ecp_group *grp )
744 {
745 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
746
747 /* Actually ( A + 2 ) / 4 */
748 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &grp->A, 16, "01DB42" ) );
749
750 /* P = 2^255 - 19 */
751 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->P, 1 ) );
752 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &grp->P, 255 ) );
753 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &grp->P, &grp->P, 19 ) );
754 grp->pbits = mbedtls_mpi_bitlen( &grp->P );
755
756 /* N = 2^252 + 27742317777372353535851937790883648493 */
757 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &grp->N, 16,
758 "14DEF9DEA2F79CD65812631A5CF5D3ED" ) );
759 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &grp->N, 252, 1 ) );
760
761 /* Y intentionally not set, since we use x/z coordinates.
762 * This is used as a marker to identify Montgomery curves! */
763 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.MBEDTLS_PRIVATE(X), 9 ) );
764 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.MBEDTLS_PRIVATE(Z), 1 ) );
765 mbedtls_mpi_free( &grp->G.MBEDTLS_PRIVATE(Y) );
766
767 /* Actually, the required msb for private keys */
768 grp->nbits = 254;
769
770 cleanup:
771 if( ret != 0 )
772 mbedtls_ecp_group_free( grp );
773
774 return( ret );
775 }
776 #endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */
777
778 #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
779 /*
780 * Specialized function for creating the Curve448 group
781 */
ecp_use_curve448(mbedtls_ecp_group * grp)782 static int ecp_use_curve448( mbedtls_ecp_group *grp )
783 {
784 mbedtls_mpi Ns;
785 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
786
787 mbedtls_mpi_init( &Ns );
788
789 /* Actually ( A + 2 ) / 4 */
790 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &grp->A, 16, "98AA" ) );
791
792 /* P = 2^448 - 2^224 - 1 */
793 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->P, 1 ) );
794 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &grp->P, 224 ) );
795 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &grp->P, &grp->P, 1 ) );
796 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &grp->P, 224 ) );
797 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &grp->P, &grp->P, 1 ) );
798 grp->pbits = mbedtls_mpi_bitlen( &grp->P );
799
800 /* Y intentionally not set, since we use x/z coordinates.
801 * This is used as a marker to identify Montgomery curves! */
802 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.MBEDTLS_PRIVATE(X), 5 ) );
803 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.MBEDTLS_PRIVATE(Z), 1 ) );
804 mbedtls_mpi_free( &grp->G.MBEDTLS_PRIVATE(Y) );
805
806 /* N = 2^446 - 13818066809895115352007386748515426880336692474882178609894547503885 */
807 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &grp->N, 446, 1 ) );
808 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &Ns, 16,
809 "8335DC163BB124B65129C96FDE933D8D723A70AADC873D6D54A7BB0D" ) );
810 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &grp->N, &grp->N, &Ns ) );
811
812 /* Actually, the required msb for private keys */
813 grp->nbits = 447;
814
815 cleanup:
816 mbedtls_mpi_free( &Ns );
817 if( ret != 0 )
818 mbedtls_ecp_group_free( grp );
819
820 return( ret );
821 }
822 #endif /* MBEDTLS_ECP_DP_CURVE448_ENABLED */
823
824 /*
825 * Set a group using well-known domain parameters
826 */
mbedtls_ecp_group_load(mbedtls_ecp_group * grp,mbedtls_ecp_group_id id)827 int mbedtls_ecp_group_load( mbedtls_ecp_group *grp, mbedtls_ecp_group_id id )
828 {
829 ECP_VALIDATE_RET( grp != NULL );
830 mbedtls_ecp_group_free( grp );
831
832 grp->id = id;
833
834 switch( id )
835 {
836 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
837 case MBEDTLS_ECP_DP_SECP192R1:
838 NIST_MODP( p192 );
839 return( LOAD_GROUP( secp192r1 ) );
840 #endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */
841
842 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
843 case MBEDTLS_ECP_DP_SECP224R1:
844 NIST_MODP( p224 );
845 return( LOAD_GROUP( secp224r1 ) );
846 #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */
847
848 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
849 case MBEDTLS_ECP_DP_SECP256R1:
850 NIST_MODP( p256 );
851 return( LOAD_GROUP( secp256r1 ) );
852 #endif /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */
853
854 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
855 case MBEDTLS_ECP_DP_SECP384R1:
856 NIST_MODP( p384 );
857 return( LOAD_GROUP( secp384r1 ) );
858 #endif /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */
859
860 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
861 case MBEDTLS_ECP_DP_SECP521R1:
862 NIST_MODP( p521 );
863 return( LOAD_GROUP( secp521r1 ) );
864 #endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */
865
866 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
867 case MBEDTLS_ECP_DP_SECP192K1:
868 grp->modp = ecp_mod_p192k1;
869 return( LOAD_GROUP_A( secp192k1 ) );
870 #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */
871
872 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
873 case MBEDTLS_ECP_DP_SECP224K1:
874 grp->modp = ecp_mod_p224k1;
875 return( LOAD_GROUP_A( secp224k1 ) );
876 #endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */
877
878 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
879 case MBEDTLS_ECP_DP_SECP256K1:
880 grp->modp = ecp_mod_p256k1;
881 return( LOAD_GROUP_A( secp256k1 ) );
882 #endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */
883
884 #if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED)
885 case MBEDTLS_ECP_DP_BP256R1:
886 return( LOAD_GROUP_A( brainpoolP256r1 ) );
887 #endif /* MBEDTLS_ECP_DP_BP256R1_ENABLED */
888
889 #if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED)
890 case MBEDTLS_ECP_DP_BP384R1:
891 return( LOAD_GROUP_A( brainpoolP384r1 ) );
892 #endif /* MBEDTLS_ECP_DP_BP384R1_ENABLED */
893
894 #if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED)
895 case MBEDTLS_ECP_DP_BP512R1:
896 return( LOAD_GROUP_A( brainpoolP512r1 ) );
897 #endif /* MBEDTLS_ECP_DP_BP512R1_ENABLED */
898
899 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
900 case MBEDTLS_ECP_DP_CURVE25519:
901 grp->modp = ecp_mod_p255;
902 return( ecp_use_curve25519( grp ) );
903 #endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */
904
905 #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
906 case MBEDTLS_ECP_DP_CURVE448:
907 grp->modp = ecp_mod_p448;
908 return( ecp_use_curve448( grp ) );
909 #endif /* MBEDTLS_ECP_DP_CURVE448_ENABLED */
910
911 default:
912 mbedtls_ecp_group_free( grp );
913 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
914 }
915 }
916
917 #if defined(MBEDTLS_ECP_NIST_OPTIM)
918 /*
919 * Fast reduction modulo the primes used by the NIST curves.
920 *
921 * These functions are critical for speed, but not needed for correct
922 * operations. So, we make the choice to heavily rely on the internals of our
923 * bignum library, which creates a tight coupling between these functions and
924 * our MPI implementation. However, the coupling between the ECP module and
925 * MPI remains loose, since these functions can be deactivated at will.
926 */
927
928 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
929 /*
930 * Compared to the way things are presented in FIPS 186-3 D.2,
931 * we proceed in columns, from right (least significant chunk) to left,
932 * adding chunks to N in place, and keeping a carry for the next chunk.
933 * This avoids moving things around in memory, and uselessly adding zeros,
934 * compared to the more straightforward, line-oriented approach.
935 *
936 * For this prime we need to handle data in chunks of 64 bits.
937 * Since this is always a multiple of our basic mbedtls_mpi_uint, we can
938 * use a mbedtls_mpi_uint * to designate such a chunk, and small loops to handle it.
939 */
940
941 /* Add 64-bit chunks (dst += src) and update carry */
add64(mbedtls_mpi_uint * dst,mbedtls_mpi_uint * src,mbedtls_mpi_uint * carry)942 static inline void add64( mbedtls_mpi_uint *dst, mbedtls_mpi_uint *src, mbedtls_mpi_uint *carry )
943 {
944 unsigned char i;
945 mbedtls_mpi_uint c = 0;
946 for( i = 0; i < 8 / sizeof( mbedtls_mpi_uint ); i++, dst++, src++ )
947 {
948 *dst += c; c = ( *dst < c );
949 *dst += *src; c += ( *dst < *src );
950 }
951 *carry += c;
952 }
953
954 /* Add carry to a 64-bit chunk and update carry */
carry64(mbedtls_mpi_uint * dst,mbedtls_mpi_uint * carry)955 static inline void carry64( mbedtls_mpi_uint *dst, mbedtls_mpi_uint *carry )
956 {
957 unsigned char i;
958 for( i = 0; i < 8 / sizeof( mbedtls_mpi_uint ); i++, dst++ )
959 {
960 *dst += *carry;
961 *carry = ( *dst < *carry );
962 }
963 }
964
965 #define WIDTH 8 / sizeof( mbedtls_mpi_uint )
966 #define A( i ) N->MBEDTLS_PRIVATE(p) + (i) * WIDTH
967 #define ADD( i ) add64( p, A( i ), &c )
968 #define NEXT p += WIDTH; carry64( p, &c )
969 #define LAST p += WIDTH; *p = c; while( ++p < end ) *p = 0
970
971 /*
972 * Fast quasi-reduction modulo p192 (FIPS 186-3 D.2.1)
973 */
ecp_mod_p192(mbedtls_mpi * N)974 static int ecp_mod_p192( mbedtls_mpi *N )
975 {
976 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
977 mbedtls_mpi_uint c = 0;
978 mbedtls_mpi_uint *p, *end;
979
980 /* Make sure we have enough blocks so that A(5) is legal */
981 MBEDTLS_MPI_CHK( mbedtls_mpi_grow( N, 6 * WIDTH ) );
982
983 p = N->MBEDTLS_PRIVATE(p);
984 end = p + N->MBEDTLS_PRIVATE(n);
985
986 ADD( 3 ); ADD( 5 ); NEXT; // A0 += A3 + A5
987 ADD( 3 ); ADD( 4 ); ADD( 5 ); NEXT; // A1 += A3 + A4 + A5
988 ADD( 4 ); ADD( 5 ); LAST; // A2 += A4 + A5
989
990 cleanup:
991 return( ret );
992 }
993
994 #undef WIDTH
995 #undef A
996 #undef ADD
997 #undef NEXT
998 #undef LAST
999 #endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */
1000
1001 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) \
1002 || defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) \
1003 || defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
1004 /*
1005 * The reader is advised to first understand ecp_mod_p192() since the same
1006 * general structure is used here, but with additional complications:
1007 * (1) chunks of 32 bits, and (2) subtractions.
1008 */
1009
1010 /*
1011 * For these primes, we need to handle data in chunks of 32 bits.
1012 * This makes it more complicated if we use 64 bits limbs in MPI,
1013 * which prevents us from using a uniform access method as for p192.
1014 *
1015 * So, we define a mini abstraction layer to access 32 bit chunks,
1016 * load them in 'cur' for work, and store them back from 'cur' when done.
1017 *
1018 * While at it, also define the size of N in terms of 32-bit chunks.
1019 */
1020 #define LOAD32 cur = A( i );
1021
1022 #if defined(MBEDTLS_HAVE_INT32)
1023 /* 32 bit */
1024
1025 #define MAX32 N->MBEDTLS_PRIVATE(n)
1026 #define A( j ) N->MBEDTLS_PRIVATE(p)[j]
1027 #define STORE32 N->MBEDTLS_PRIVATE(p)[i] = cur;
1028
1029 #else /* 64-bit */
1030
1031 #define MAX32 N->MBEDTLS_PRIVATE(n) * 2
1032 #define A( j ) (j) % 2 ? (uint32_t)( N->MBEDTLS_PRIVATE(p)[(j)/2] >> 32 ) : \
1033 (uint32_t)( N->MBEDTLS_PRIVATE(p)[(j)/2] )
1034 #define STORE32 \
1035 if( i % 2 ) { \
1036 N->MBEDTLS_PRIVATE(p)[i/2] &= 0x00000000FFFFFFFF; \
1037 N->MBEDTLS_PRIVATE(p)[i/2] |= ((mbedtls_mpi_uint) cur) << 32; \
1038 } else { \
1039 N->MBEDTLS_PRIVATE(p)[i/2] &= 0xFFFFFFFF00000000; \
1040 N->MBEDTLS_PRIVATE(p)[i/2] |= (mbedtls_mpi_uint) cur; \
1041 }
1042
1043 #endif /* sizeof( mbedtls_mpi_uint ) */
1044
1045 /*
1046 * Helpers for addition and subtraction of chunks, with signed carry.
1047 */
add32(uint32_t * dst,uint32_t src,signed char * carry)1048 static inline void add32( uint32_t *dst, uint32_t src, signed char *carry )
1049 {
1050 *dst += src;
1051 *carry += ( *dst < src );
1052 }
1053
sub32(uint32_t * dst,uint32_t src,signed char * carry)1054 static inline void sub32( uint32_t *dst, uint32_t src, signed char *carry )
1055 {
1056 *carry -= ( *dst < src );
1057 *dst -= src;
1058 }
1059
1060 #define ADD( j ) add32( &cur, A( j ), &c );
1061 #define SUB( j ) sub32( &cur, A( j ), &c );
1062
1063 /*
1064 * Helpers for the main 'loop'
1065 * (see fix_negative for the motivation of C)
1066 */
1067 #define INIT( b ) \
1068 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; \
1069 signed char c = 0, cc; \
1070 uint32_t cur; \
1071 size_t i = 0, bits = (b); \
1072 mbedtls_mpi C; \
1073 mbedtls_mpi_uint Cp[ (b) / 8 / sizeof( mbedtls_mpi_uint) + 1 ]; \
1074 \
1075 C.MBEDTLS_PRIVATE(s) = 1; \
1076 C.MBEDTLS_PRIVATE(n) = (b) / 8 / sizeof( mbedtls_mpi_uint) + 1; \
1077 C.MBEDTLS_PRIVATE(p) = Cp; \
1078 memset( Cp, 0, C.MBEDTLS_PRIVATE(n) * sizeof( mbedtls_mpi_uint ) ); \
1079 \
1080 MBEDTLS_MPI_CHK( mbedtls_mpi_grow( N, (b) * 2 / 8 / \
1081 sizeof( mbedtls_mpi_uint ) ) ); \
1082 LOAD32;
1083
1084 #define NEXT \
1085 STORE32; i++; LOAD32; \
1086 cc = c; c = 0; \
1087 if( cc < 0 ) \
1088 sub32( &cur, -cc, &c ); \
1089 else \
1090 add32( &cur, cc, &c ); \
1091
1092 #define LAST \
1093 STORE32; i++; \
1094 cur = c > 0 ? c : 0; STORE32; \
1095 cur = 0; while( ++i < MAX32 ) { STORE32; } \
1096 if( c < 0 ) fix_negative( N, c, &C, bits );
1097
1098 /*
1099 * If the result is negative, we get it in the form
1100 * c * 2^(bits + 32) + N, with c negative and N positive shorter than 'bits'
1101 */
fix_negative(mbedtls_mpi * N,signed char c,mbedtls_mpi * C,size_t bits)1102 static inline int fix_negative( mbedtls_mpi *N, signed char c, mbedtls_mpi *C, size_t bits )
1103 {
1104 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1105
1106 /* C = - c * 2^(bits + 32) */
1107 #if !defined(MBEDTLS_HAVE_INT64)
1108 ((void) bits);
1109 #else
1110 if( bits == 224 )
1111 C->MBEDTLS_PRIVATE(p)[ C->MBEDTLS_PRIVATE(n) - 1 ] = ((mbedtls_mpi_uint) -c) << 32;
1112 else
1113 #endif
1114 C->MBEDTLS_PRIVATE(p)[ C->MBEDTLS_PRIVATE(n) - 1 ] = (mbedtls_mpi_uint) -c;
1115
1116 /* N = - ( C - N ) */
1117 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( N, C, N ) );
1118 N->MBEDTLS_PRIVATE(s) = -1;
1119
1120 cleanup:
1121
1122 return( ret );
1123 }
1124
1125 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
1126 /*
1127 * Fast quasi-reduction modulo p224 (FIPS 186-3 D.2.2)
1128 */
ecp_mod_p224(mbedtls_mpi * N)1129 static int ecp_mod_p224( mbedtls_mpi *N )
1130 {
1131 INIT( 224 );
1132
1133 SUB( 7 ); SUB( 11 ); NEXT; // A0 += -A7 - A11
1134 SUB( 8 ); SUB( 12 ); NEXT; // A1 += -A8 - A12
1135 SUB( 9 ); SUB( 13 ); NEXT; // A2 += -A9 - A13
1136 SUB( 10 ); ADD( 7 ); ADD( 11 ); NEXT; // A3 += -A10 + A7 + A11
1137 SUB( 11 ); ADD( 8 ); ADD( 12 ); NEXT; // A4 += -A11 + A8 + A12
1138 SUB( 12 ); ADD( 9 ); ADD( 13 ); NEXT; // A5 += -A12 + A9 + A13
1139 SUB( 13 ); ADD( 10 ); LAST; // A6 += -A13 + A10
1140
1141 cleanup:
1142 return( ret );
1143 }
1144 #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */
1145
1146 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
1147 /*
1148 * Fast quasi-reduction modulo p256 (FIPS 186-3 D.2.3)
1149 */
ecp_mod_p256(mbedtls_mpi * N)1150 static int ecp_mod_p256( mbedtls_mpi *N )
1151 {
1152 INIT( 256 );
1153
1154 ADD( 8 ); ADD( 9 );
1155 SUB( 11 ); SUB( 12 ); SUB( 13 ); SUB( 14 ); NEXT; // A0
1156
1157 ADD( 9 ); ADD( 10 );
1158 SUB( 12 ); SUB( 13 ); SUB( 14 ); SUB( 15 ); NEXT; // A1
1159
1160 ADD( 10 ); ADD( 11 );
1161 SUB( 13 ); SUB( 14 ); SUB( 15 ); NEXT; // A2
1162
1163 ADD( 11 ); ADD( 11 ); ADD( 12 ); ADD( 12 ); ADD( 13 );
1164 SUB( 15 ); SUB( 8 ); SUB( 9 ); NEXT; // A3
1165
1166 ADD( 12 ); ADD( 12 ); ADD( 13 ); ADD( 13 ); ADD( 14 );
1167 SUB( 9 ); SUB( 10 ); NEXT; // A4
1168
1169 ADD( 13 ); ADD( 13 ); ADD( 14 ); ADD( 14 ); ADD( 15 );
1170 SUB( 10 ); SUB( 11 ); NEXT; // A5
1171
1172 ADD( 14 ); ADD( 14 ); ADD( 15 ); ADD( 15 ); ADD( 14 ); ADD( 13 );
1173 SUB( 8 ); SUB( 9 ); NEXT; // A6
1174
1175 ADD( 15 ); ADD( 15 ); ADD( 15 ); ADD( 8 );
1176 SUB( 10 ); SUB( 11 ); SUB( 12 ); SUB( 13 ); LAST; // A7
1177
1178 cleanup:
1179 return( ret );
1180 }
1181 #endif /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */
1182
1183 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
1184 /*
1185 * Fast quasi-reduction modulo p384 (FIPS 186-3 D.2.4)
1186 */
ecp_mod_p384(mbedtls_mpi * N)1187 static int ecp_mod_p384( mbedtls_mpi *N )
1188 {
1189 INIT( 384 );
1190
1191 ADD( 12 ); ADD( 21 ); ADD( 20 );
1192 SUB( 23 ); NEXT; // A0
1193
1194 ADD( 13 ); ADD( 22 ); ADD( 23 );
1195 SUB( 12 ); SUB( 20 ); NEXT; // A2
1196
1197 ADD( 14 ); ADD( 23 );
1198 SUB( 13 ); SUB( 21 ); NEXT; // A2
1199
1200 ADD( 15 ); ADD( 12 ); ADD( 20 ); ADD( 21 );
1201 SUB( 14 ); SUB( 22 ); SUB( 23 ); NEXT; // A3
1202
1203 ADD( 21 ); ADD( 21 ); ADD( 16 ); ADD( 13 ); ADD( 12 ); ADD( 20 ); ADD( 22 );
1204 SUB( 15 ); SUB( 23 ); SUB( 23 ); NEXT; // A4
1205
1206 ADD( 22 ); ADD( 22 ); ADD( 17 ); ADD( 14 ); ADD( 13 ); ADD( 21 ); ADD( 23 );
1207 SUB( 16 ); NEXT; // A5
1208
1209 ADD( 23 ); ADD( 23 ); ADD( 18 ); ADD( 15 ); ADD( 14 ); ADD( 22 );
1210 SUB( 17 ); NEXT; // A6
1211
1212 ADD( 19 ); ADD( 16 ); ADD( 15 ); ADD( 23 );
1213 SUB( 18 ); NEXT; // A7
1214
1215 ADD( 20 ); ADD( 17 ); ADD( 16 );
1216 SUB( 19 ); NEXT; // A8
1217
1218 ADD( 21 ); ADD( 18 ); ADD( 17 );
1219 SUB( 20 ); NEXT; // A9
1220
1221 ADD( 22 ); ADD( 19 ); ADD( 18 );
1222 SUB( 21 ); NEXT; // A10
1223
1224 ADD( 23 ); ADD( 20 ); ADD( 19 );
1225 SUB( 22 ); LAST; // A11
1226
1227 cleanup:
1228 return( ret );
1229 }
1230 #endif /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */
1231
1232 #undef A
1233 #undef LOAD32
1234 #undef STORE32
1235 #undef MAX32
1236 #undef INIT
1237 #undef NEXT
1238 #undef LAST
1239
1240 #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED ||
1241 MBEDTLS_ECP_DP_SECP256R1_ENABLED ||
1242 MBEDTLS_ECP_DP_SECP384R1_ENABLED */
1243
1244 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
1245 /*
1246 * Here we have an actual Mersenne prime, so things are more straightforward.
1247 * However, chunks are aligned on a 'weird' boundary (521 bits).
1248 */
1249
1250 /* Size of p521 in terms of mbedtls_mpi_uint */
1251 #define P521_WIDTH ( 521 / 8 / sizeof( mbedtls_mpi_uint ) + 1 )
1252
1253 /* Bits to keep in the most significant mbedtls_mpi_uint */
1254 #define P521_MASK 0x01FF
1255
1256 /*
1257 * Fast quasi-reduction modulo p521 (FIPS 186-3 D.2.5)
1258 * Write N as A1 + 2^521 A0, return A0 + A1
1259 */
ecp_mod_p521(mbedtls_mpi * N)1260 static int ecp_mod_p521( mbedtls_mpi *N )
1261 {
1262 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1263 size_t i;
1264 mbedtls_mpi M;
1265 mbedtls_mpi_uint Mp[P521_WIDTH + 1];
1266 /* Worst case for the size of M is when mbedtls_mpi_uint is 16 bits:
1267 * we need to hold bits 513 to 1056, which is 34 limbs, that is
1268 * P521_WIDTH + 1. Otherwise P521_WIDTH is enough. */
1269
1270 if( N->MBEDTLS_PRIVATE(n) < P521_WIDTH )
1271 return( 0 );
1272
1273 /* M = A1 */
1274 M.MBEDTLS_PRIVATE(s) = 1;
1275 M.MBEDTLS_PRIVATE(n) = N->MBEDTLS_PRIVATE(n) - ( P521_WIDTH - 1 );
1276 if( M.MBEDTLS_PRIVATE(n) > P521_WIDTH + 1 )
1277 M.MBEDTLS_PRIVATE(n) = P521_WIDTH + 1;
1278 M.MBEDTLS_PRIVATE(p) = Mp;
1279 memcpy( Mp, N->MBEDTLS_PRIVATE(p) + P521_WIDTH - 1, M.MBEDTLS_PRIVATE(n) * sizeof( mbedtls_mpi_uint ) );
1280 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, 521 % ( 8 * sizeof( mbedtls_mpi_uint ) ) ) );
1281
1282 /* N = A0 */
1283 N->MBEDTLS_PRIVATE(p)[P521_WIDTH - 1] &= P521_MASK;
1284 for( i = P521_WIDTH; i < N->MBEDTLS_PRIVATE(n); i++ )
1285 N->MBEDTLS_PRIVATE(p)[i] = 0;
1286
1287 /* N = A0 + A1 */
1288 MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) );
1289
1290 cleanup:
1291 return( ret );
1292 }
1293
1294 #undef P521_WIDTH
1295 #undef P521_MASK
1296 #endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */
1297
1298 #endif /* MBEDTLS_ECP_NIST_OPTIM */
1299
1300 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
1301
1302 /* Size of p255 in terms of mbedtls_mpi_uint */
1303 #define P255_WIDTH ( 255 / 8 / sizeof( mbedtls_mpi_uint ) + 1 )
1304
1305 /*
1306 * Fast quasi-reduction modulo p255 = 2^255 - 19
1307 * Write N as A0 + 2^255 A1, return A0 + 19 * A1
1308 */
ecp_mod_p255(mbedtls_mpi * N)1309 static int ecp_mod_p255( mbedtls_mpi *N )
1310 {
1311 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1312 size_t i;
1313 mbedtls_mpi M;
1314 mbedtls_mpi_uint Mp[P255_WIDTH + 2];
1315
1316 if( N->MBEDTLS_PRIVATE(n) < P255_WIDTH )
1317 return( 0 );
1318
1319 /* M = A1 */
1320 M.MBEDTLS_PRIVATE(s) = 1;
1321 M.MBEDTLS_PRIVATE(n) = N->MBEDTLS_PRIVATE(n) - ( P255_WIDTH - 1 );
1322 if( M.MBEDTLS_PRIVATE(n) > P255_WIDTH + 1 )
1323 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1324 M.MBEDTLS_PRIVATE(p) = Mp;
1325 memset( Mp, 0, sizeof Mp );
1326 memcpy( Mp, N->MBEDTLS_PRIVATE(p) + P255_WIDTH - 1, M.MBEDTLS_PRIVATE(n) * sizeof( mbedtls_mpi_uint ) );
1327 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, 255 % ( 8 * sizeof( mbedtls_mpi_uint ) ) ) );
1328 M.MBEDTLS_PRIVATE(n)++; /* Make room for multiplication by 19 */
1329
1330 /* N = A0 */
1331 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( N, 255, 0 ) );
1332 for( i = P255_WIDTH; i < N->MBEDTLS_PRIVATE(n); i++ )
1333 N->MBEDTLS_PRIVATE(p)[i] = 0;
1334
1335 /* N = A0 + 19 * A1 */
1336 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &M, 19 ) );
1337 MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) );
1338
1339 cleanup:
1340 return( ret );
1341 }
1342 #endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */
1343
1344 #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
1345
1346 /* Size of p448 in terms of mbedtls_mpi_uint */
1347 #define P448_WIDTH ( 448 / 8 / sizeof( mbedtls_mpi_uint ) )
1348
1349 /* Number of limbs fully occupied by 2^224 (max), and limbs used by it (min) */
1350 #define DIV_ROUND_UP( X, Y ) ( ( ( X ) + ( Y ) - 1 ) / ( Y ) )
1351 #define P224_WIDTH_MIN ( 28 / sizeof( mbedtls_mpi_uint ) )
1352 #define P224_WIDTH_MAX DIV_ROUND_UP( 28, sizeof( mbedtls_mpi_uint ) )
1353 #define P224_UNUSED_BITS ( ( P224_WIDTH_MAX * sizeof( mbedtls_mpi_uint ) * 8 ) - 224 )
1354
1355 /*
1356 * Fast quasi-reduction modulo p448 = 2^448 - 2^224 - 1
1357 * Write N as A0 + 2^448 A1 and A1 as B0 + 2^224 B1, and return
1358 * A0 + A1 + B1 + (B0 + B1) * 2^224. This is different to the reference
1359 * implementation of Curve448, which uses its own special 56-bit limbs rather
1360 * than a generic bignum library. We could squeeze some extra speed out on
1361 * 32-bit machines by splitting N up into 32-bit limbs and doing the
1362 * arithmetic using the limbs directly as we do for the NIST primes above,
1363 * but for 64-bit targets it should use half the number of operations if we do
1364 * the reduction with 224-bit limbs, since mpi_add_mpi will then use 64-bit adds.
1365 */
ecp_mod_p448(mbedtls_mpi * N)1366 static int ecp_mod_p448( mbedtls_mpi *N )
1367 {
1368 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1369 size_t i;
1370 mbedtls_mpi M, Q;
1371 mbedtls_mpi_uint Mp[P448_WIDTH + 1], Qp[P448_WIDTH];
1372
1373 if( N->MBEDTLS_PRIVATE(n) <= P448_WIDTH )
1374 return( 0 );
1375
1376 /* M = A1 */
1377 M.MBEDTLS_PRIVATE(s) = 1;
1378 M.MBEDTLS_PRIVATE(n) = N->MBEDTLS_PRIVATE(n) - ( P448_WIDTH );
1379 if( M.MBEDTLS_PRIVATE(n) > P448_WIDTH )
1380 /* Shouldn't be called with N larger than 2^896! */
1381 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1382 M.MBEDTLS_PRIVATE(p) = Mp;
1383 memset( Mp, 0, sizeof( Mp ) );
1384 memcpy( Mp, N->MBEDTLS_PRIVATE(p) + P448_WIDTH, M.MBEDTLS_PRIVATE(n) * sizeof( mbedtls_mpi_uint ) );
1385
1386 /* N = A0 */
1387 for( i = P448_WIDTH; i < N->MBEDTLS_PRIVATE(n); i++ )
1388 N->MBEDTLS_PRIVATE(p)[i] = 0;
1389
1390 /* N += A1 */
1391 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &M ) );
1392
1393 /* Q = B1, N += B1 */
1394 Q = M;
1395 Q.MBEDTLS_PRIVATE(p) = Qp;
1396 memcpy( Qp, Mp, sizeof( Qp ) );
1397 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &Q, 224 ) );
1398 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &Q ) );
1399
1400 /* M = (B0 + B1) * 2^224, N += M */
1401 if( sizeof( mbedtls_mpi_uint ) > 4 )
1402 Mp[P224_WIDTH_MIN] &= ( (mbedtls_mpi_uint)-1 ) >> ( P224_UNUSED_BITS );
1403 for( i = P224_WIDTH_MAX; i < M.MBEDTLS_PRIVATE(n); ++i )
1404 Mp[i] = 0;
1405 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &M, &M, &Q ) );
1406 M.MBEDTLS_PRIVATE(n) = P448_WIDTH + 1; /* Make room for shifted carry bit from the addition */
1407 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &M, 224 ) );
1408 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &M ) );
1409
1410 cleanup:
1411 return( ret );
1412 }
1413 #endif /* MBEDTLS_ECP_DP_CURVE448_ENABLED */
1414
1415 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) \
1416 || defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) \
1417 || defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
1418 /*
1419 * Fast quasi-reduction modulo P = 2^s - R,
1420 * with R about 33 bits, used by the Koblitz curves.
1421 *
1422 * Write N as A0 + 2^224 A1, return A0 + R * A1.
1423 * Actually do two passes, since R is big.
1424 */
1425 #define P_KOBLITZ_MAX ( 256 / 8 / sizeof( mbedtls_mpi_uint ) ) // Max limbs in P
1426 #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)1427 static inline int ecp_mod_koblitz( mbedtls_mpi *N, mbedtls_mpi_uint *Rp, size_t p_limbs,
1428 size_t adjust, size_t shift, mbedtls_mpi_uint mask )
1429 {
1430 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1431 size_t i;
1432 mbedtls_mpi M, R;
1433 mbedtls_mpi_uint Mp[P_KOBLITZ_MAX + P_KOBLITZ_R + 1];
1434
1435 if( N->MBEDTLS_PRIVATE(n) < p_limbs )
1436 return( 0 );
1437
1438 /* Init R */
1439 R.MBEDTLS_PRIVATE(s) = 1;
1440 R.MBEDTLS_PRIVATE(p) = Rp;
1441 R.MBEDTLS_PRIVATE(n) = P_KOBLITZ_R;
1442
1443 /* Common setup for M */
1444 M.MBEDTLS_PRIVATE(s) = 1;
1445 M.MBEDTLS_PRIVATE(p) = Mp;
1446
1447 /* M = A1 */
1448 M.MBEDTLS_PRIVATE(n) = N->MBEDTLS_PRIVATE(n) - ( p_limbs - adjust );
1449 if( M.MBEDTLS_PRIVATE(n) > p_limbs + adjust )
1450 M.MBEDTLS_PRIVATE(n) = p_limbs + adjust;
1451 memset( Mp, 0, sizeof Mp );
1452 memcpy( Mp, N->MBEDTLS_PRIVATE(p) + p_limbs - adjust, M.MBEDTLS_PRIVATE(n) * sizeof( mbedtls_mpi_uint ) );
1453 if( shift != 0 )
1454 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, shift ) );
1455 M.MBEDTLS_PRIVATE(n) += R.MBEDTLS_PRIVATE(n); /* Make room for multiplication by R */
1456
1457 /* N = A0 */
1458 if( mask != 0 )
1459 N->MBEDTLS_PRIVATE(p)[p_limbs - 1] &= mask;
1460 for( i = p_limbs; i < N->MBEDTLS_PRIVATE(n); i++ )
1461 N->MBEDTLS_PRIVATE(p)[i] = 0;
1462
1463 /* N = A0 + R * A1 */
1464 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &M, &M, &R ) );
1465 MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) );
1466
1467 /* Second pass */
1468
1469 /* M = A1 */
1470 M.MBEDTLS_PRIVATE(n) = N->MBEDTLS_PRIVATE(n) - ( p_limbs - adjust );
1471 if( M.MBEDTLS_PRIVATE(n) > p_limbs + adjust )
1472 M.MBEDTLS_PRIVATE(n) = p_limbs + adjust;
1473 memset( Mp, 0, sizeof Mp );
1474 memcpy( Mp, N->MBEDTLS_PRIVATE(p) + p_limbs - adjust, M.MBEDTLS_PRIVATE(n) * sizeof( mbedtls_mpi_uint ) );
1475 if( shift != 0 )
1476 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, shift ) );
1477 M.MBEDTLS_PRIVATE(n) += R.MBEDTLS_PRIVATE(n); /* Make room for multiplication by R */
1478
1479 /* N = A0 */
1480 if( mask != 0 )
1481 N->MBEDTLS_PRIVATE(p)[p_limbs - 1] &= mask;
1482 for( i = p_limbs; i < N->MBEDTLS_PRIVATE(n); i++ )
1483 N->MBEDTLS_PRIVATE(p)[i] = 0;
1484
1485 /* N = A0 + R * A1 */
1486 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &M, &M, &R ) );
1487 MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) );
1488
1489 cleanup:
1490 return( ret );
1491 }
1492 #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED) ||
1493 MBEDTLS_ECP_DP_SECP224K1_ENABLED) ||
1494 MBEDTLS_ECP_DP_SECP256K1_ENABLED) */
1495
1496 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
1497 /*
1498 * Fast quasi-reduction modulo p192k1 = 2^192 - R,
1499 * with R = 2^32 + 2^12 + 2^8 + 2^7 + 2^6 + 2^3 + 1 = 0x0100001119
1500 */
ecp_mod_p192k1(mbedtls_mpi * N)1501 static int ecp_mod_p192k1( mbedtls_mpi *N )
1502 {
1503 static mbedtls_mpi_uint Rp[] = {
1504 BYTES_TO_T_UINT_8( 0xC9, 0x11, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) };
1505
1506 return( ecp_mod_koblitz( N, Rp, 192 / 8 / sizeof( mbedtls_mpi_uint ), 0, 0, 0 ) );
1507 }
1508 #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */
1509
1510 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
1511 /*
1512 * Fast quasi-reduction modulo p224k1 = 2^224 - R,
1513 * with R = 2^32 + 2^12 + 2^11 + 2^9 + 2^7 + 2^4 + 2 + 1 = 0x0100001A93
1514 */
ecp_mod_p224k1(mbedtls_mpi * N)1515 static int ecp_mod_p224k1( mbedtls_mpi *N )
1516 {
1517 static mbedtls_mpi_uint Rp[] = {
1518 BYTES_TO_T_UINT_8( 0x93, 0x1A, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) };
1519
1520 #if defined(MBEDTLS_HAVE_INT64)
1521 return( ecp_mod_koblitz( N, Rp, 4, 1, 32, 0xFFFFFFFF ) );
1522 #else
1523 return( ecp_mod_koblitz( N, Rp, 224 / 8 / sizeof( mbedtls_mpi_uint ), 0, 0, 0 ) );
1524 #endif
1525 }
1526
1527 #endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */
1528
1529 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
1530 /*
1531 * Fast quasi-reduction modulo p256k1 = 2^256 - R,
1532 * with R = 2^32 + 2^9 + 2^8 + 2^7 + 2^6 + 2^4 + 1 = 0x01000003D1
1533 */
ecp_mod_p256k1(mbedtls_mpi * N)1534 static int ecp_mod_p256k1( mbedtls_mpi *N )
1535 {
1536 static mbedtls_mpi_uint Rp[] = {
1537 BYTES_TO_T_UINT_8( 0xD1, 0x03, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) };
1538 return( ecp_mod_koblitz( N, Rp, 256 / 8 / sizeof( mbedtls_mpi_uint ), 0, 0, 0 ) );
1539 }
1540 #endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */
1541
1542 #endif /* !MBEDTLS_ECP_ALT */
1543
1544 #endif /* MBEDTLS_ECP_C */
1545
