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