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