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68323c5823aa6b1c372236ab1585b5dce93a18f2
[reactos.git] / reactos / dll / 3rdparty / mbedtls / ecp_curves.c
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
22 #if !defined(MBEDTLS_CONFIG_FILE)
23 #include "mbedtls/config.h"
24 #else
25 #include MBEDTLS_CONFIG_FILE
26 #endif
27
28 #if defined(MBEDTLS_ECP_C)
29
30 #include "mbedtls/ecp.h"
31
32 #include <string.h>
33
34 #if ( defined(__ARMCC_VERSION) || defined(_MSC_VER) ) && !defined(inline)
35 #define inline __inline
36 #endif
37
38 /*
39 * Conversion macros for embedded constants:
40 * build lists of mbedtls_mpi_uint's from lists of unsigned char's grouped by 8, 4 or 2
41 */
42 #if defined(MBEDTLS_HAVE_INT32)
43
44 #define BYTES_TO_T_UINT_4( a, b, c, d ) \
45 ( (mbedtls_mpi_uint) a << 0 ) | \
46 ( (mbedtls_mpi_uint) b << 8 ) | \
47 ( (mbedtls_mpi_uint) c << 16 ) | \
48 ( (mbedtls_mpi_uint) d << 24 )
49
50 #define BYTES_TO_T_UINT_2( a, b ) \
51 BYTES_TO_T_UINT_4( a, b, 0, 0 )
52
53 #define BYTES_TO_T_UINT_8( a, b, c, d, e, f, g, h ) \
54 BYTES_TO_T_UINT_4( a, b, c, d ), \
55 BYTES_TO_T_UINT_4( e, f, g, h )
56
57 #else /* 64-bits */
58
59 #define BYTES_TO_T_UINT_8( a, b, c, d, e, f, g, h ) \
60 ( (mbedtls_mpi_uint) a << 0 ) | \
61 ( (mbedtls_mpi_uint) b << 8 ) | \
62 ( (mbedtls_mpi_uint) c << 16 ) | \
63 ( (mbedtls_mpi_uint) d << 24 ) | \
64 ( (mbedtls_mpi_uint) e << 32 ) | \
65 ( (mbedtls_mpi_uint) f << 40 ) | \
66 ( (mbedtls_mpi_uint) g << 48 ) | \
67 ( (mbedtls_mpi_uint) h << 56 )
68
69 #define BYTES_TO_T_UINT_4( a, b, c, d ) \
70 BYTES_TO_T_UINT_8( a, b, c, d, 0, 0, 0, 0 )
71
72 #define BYTES_TO_T_UINT_2( a, b ) \
73 BYTES_TO_T_UINT_8( a, b, 0, 0, 0, 0, 0, 0 )
74
75 #endif /* bits in mbedtls_mpi_uint */
76
77 /*
78 * Note: the constants are in little-endian order
79 * to be directly usable in MPIs
80 */
81
82 /*
83 * Domain parameters for secp192r1
84 */
85 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
86 static const mbedtls_mpi_uint secp192r1_p[] = {
87 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
88 BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
89 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
90 };
91 static const mbedtls_mpi_uint secp192r1_b[] = {
92 BYTES_TO_T_UINT_8( 0xB1, 0xB9, 0x46, 0xC1, 0xEC, 0xDE, 0xB8, 0xFE ),
93 BYTES_TO_T_UINT_8( 0x49, 0x30, 0x24, 0x72, 0xAB, 0xE9, 0xA7, 0x0F ),
94 BYTES_TO_T_UINT_8( 0xE7, 0x80, 0x9C, 0xE5, 0x19, 0x05, 0x21, 0x64 ),
95 };
96 static const mbedtls_mpi_uint secp192r1_gx[] = {
97 BYTES_TO_T_UINT_8( 0x12, 0x10, 0xFF, 0x82, 0xFD, 0x0A, 0xFF, 0xF4 ),
98 BYTES_TO_T_UINT_8( 0x00, 0x88, 0xA1, 0x43, 0xEB, 0x20, 0xBF, 0x7C ),
99 BYTES_TO_T_UINT_8( 0xF6, 0x90, 0x30, 0xB0, 0x0E, 0xA8, 0x8D, 0x18 ),
100 };
101 static const mbedtls_mpi_uint secp192r1_gy[] = {
102 BYTES_TO_T_UINT_8( 0x11, 0x48, 0x79, 0x1E, 0xA1, 0x77, 0xF9, 0x73 ),
103 BYTES_TO_T_UINT_8( 0xD5, 0xCD, 0x24, 0x6B, 0xED, 0x11, 0x10, 0x63 ),
104 BYTES_TO_T_UINT_8( 0x78, 0xDA, 0xC8, 0xFF, 0x95, 0x2B, 0x19, 0x07 ),
105 };
106 static const mbedtls_mpi_uint secp192r1_n[] = {
107 BYTES_TO_T_UINT_8( 0x31, 0x28, 0xD2, 0xB4, 0xB1, 0xC9, 0x6B, 0x14 ),
108 BYTES_TO_T_UINT_8( 0x36, 0xF8, 0xDE, 0x99, 0xFF, 0xFF, 0xFF, 0xFF ),
109 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
110 };
111 #endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */
112
113 /*
114 * Domain parameters for secp224r1
115 */
116 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
117 static const mbedtls_mpi_uint secp224r1_p[] = {
118 BYTES_TO_T_UINT_8( 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ),
119 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ),
120 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
121 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ),
122 };
123 static const mbedtls_mpi_uint secp224r1_b[] = {
124 BYTES_TO_T_UINT_8( 0xB4, 0xFF, 0x55, 0x23, 0x43, 0x39, 0x0B, 0x27 ),
125 BYTES_TO_T_UINT_8( 0xBA, 0xD8, 0xBF, 0xD7, 0xB7, 0xB0, 0x44, 0x50 ),
126 BYTES_TO_T_UINT_8( 0x56, 0x32, 0x41, 0xF5, 0xAB, 0xB3, 0x04, 0x0C ),
127 BYTES_TO_T_UINT_4( 0x85, 0x0A, 0x05, 0xB4 ),
128 };
129 static const mbedtls_mpi_uint secp224r1_gx[] = {
130 BYTES_TO_T_UINT_8( 0x21, 0x1D, 0x5C, 0x11, 0xD6, 0x80, 0x32, 0x34 ),
131 BYTES_TO_T_UINT_8( 0x22, 0x11, 0xC2, 0x56, 0xD3, 0xC1, 0x03, 0x4A ),
132 BYTES_TO_T_UINT_8( 0xB9, 0x90, 0x13, 0x32, 0x7F, 0xBF, 0xB4, 0x6B ),
133 BYTES_TO_T_UINT_4( 0xBD, 0x0C, 0x0E, 0xB7 ),
134 };
135 static const mbedtls_mpi_uint secp224r1_gy[] = {
136 BYTES_TO_T_UINT_8( 0x34, 0x7E, 0x00, 0x85, 0x99, 0x81, 0xD5, 0x44 ),
137 BYTES_TO_T_UINT_8( 0x64, 0x47, 0x07, 0x5A, 0xA0, 0x75, 0x43, 0xCD ),
138 BYTES_TO_T_UINT_8( 0xE6, 0xDF, 0x22, 0x4C, 0xFB, 0x23, 0xF7, 0xB5 ),
139 BYTES_TO_T_UINT_4( 0x88, 0x63, 0x37, 0xBD ),
140 };
141 static const mbedtls_mpi_uint secp224r1_n[] = {
142 BYTES_TO_T_UINT_8( 0x3D, 0x2A, 0x5C, 0x5C, 0x45, 0x29, 0xDD, 0x13 ),
143 BYTES_TO_T_UINT_8( 0x3E, 0xF0, 0xB8, 0xE0, 0xA2, 0x16, 0xFF, 0xFF ),
144 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
145 BYTES_TO_T_UINT_4( 0xFF, 0xFF, 0xFF, 0xFF ),
146 };
147 #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */
148
149 /*
150 * Domain parameters for secp256r1
151 */
152 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
153 static const mbedtls_mpi_uint secp256r1_p[] = {
154 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
155 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ),
156 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ),
157 BYTES_TO_T_UINT_8( 0x01, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ),
158 };
159 static const mbedtls_mpi_uint secp256r1_b[] = {
160 BYTES_TO_T_UINT_8( 0x4B, 0x60, 0xD2, 0x27, 0x3E, 0x3C, 0xCE, 0x3B ),
161 BYTES_TO_T_UINT_8( 0xF6, 0xB0, 0x53, 0xCC, 0xB0, 0x06, 0x1D, 0x65 ),
162 BYTES_TO_T_UINT_8( 0xBC, 0x86, 0x98, 0x76, 0x55, 0xBD, 0xEB, 0xB3 ),
163 BYTES_TO_T_UINT_8( 0xE7, 0x93, 0x3A, 0xAA, 0xD8, 0x35, 0xC6, 0x5A ),
164 };
165 static const mbedtls_mpi_uint secp256r1_gx[] = {
166 BYTES_TO_T_UINT_8( 0x96, 0xC2, 0x98, 0xD8, 0x45, 0x39, 0xA1, 0xF4 ),
167 BYTES_TO_T_UINT_8( 0xA0, 0x33, 0xEB, 0x2D, 0x81, 0x7D, 0x03, 0x77 ),
168 BYTES_TO_T_UINT_8( 0xF2, 0x40, 0xA4, 0x63, 0xE5, 0xE6, 0xBC, 0xF8 ),
169 BYTES_TO_T_UINT_8( 0x47, 0x42, 0x2C, 0xE1, 0xF2, 0xD1, 0x17, 0x6B ),
170 };
171 static const mbedtls_mpi_uint secp256r1_gy[] = {
172 BYTES_TO_T_UINT_8( 0xF5, 0x51, 0xBF, 0x37, 0x68, 0x40, 0xB6, 0xCB ),
173 BYTES_TO_T_UINT_8( 0xCE, 0x5E, 0x31, 0x6B, 0x57, 0x33, 0xCE, 0x2B ),
174 BYTES_TO_T_UINT_8( 0x16, 0x9E, 0x0F, 0x7C, 0x4A, 0xEB, 0xE7, 0x8E ),
175 BYTES_TO_T_UINT_8( 0x9B, 0x7F, 0x1A, 0xFE, 0xE2, 0x42, 0xE3, 0x4F ),
176 };
177 static const mbedtls_mpi_uint secp256r1_n[] = {
178 BYTES_TO_T_UINT_8( 0x51, 0x25, 0x63, 0xFC, 0xC2, 0xCA, 0xB9, 0xF3 ),
179 BYTES_TO_T_UINT_8( 0x84, 0x9E, 0x17, 0xA7, 0xAD, 0xFA, 0xE6, 0xBC ),
180 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
181 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ),
182 };
183 #endif /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */
184
185 /*
186 * Domain parameters for secp384r1
187 */
188 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
189 static const mbedtls_mpi_uint secp384r1_p[] = {
190 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ),
191 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ),
192 BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
193 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
194 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
195 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
196 };
197 static const mbedtls_mpi_uint secp384r1_b[] = {
198 BYTES_TO_T_UINT_8( 0xEF, 0x2A, 0xEC, 0xD3, 0xED, 0xC8, 0x85, 0x2A ),
199 BYTES_TO_T_UINT_8( 0x9D, 0xD1, 0x2E, 0x8A, 0x8D, 0x39, 0x56, 0xC6 ),
200 BYTES_TO_T_UINT_8( 0x5A, 0x87, 0x13, 0x50, 0x8F, 0x08, 0x14, 0x03 ),
201 BYTES_TO_T_UINT_8( 0x12, 0x41, 0x81, 0xFE, 0x6E, 0x9C, 0x1D, 0x18 ),
202 BYTES_TO_T_UINT_8( 0x19, 0x2D, 0xF8, 0xE3, 0x6B, 0x05, 0x8E, 0x98 ),
203 BYTES_TO_T_UINT_8( 0xE4, 0xE7, 0x3E, 0xE2, 0xA7, 0x2F, 0x31, 0xB3 ),
204 };
205 static const mbedtls_mpi_uint secp384r1_gx[] = {
206 BYTES_TO_T_UINT_8( 0xB7, 0x0A, 0x76, 0x72, 0x38, 0x5E, 0x54, 0x3A ),
207 BYTES_TO_T_UINT_8( 0x6C, 0x29, 0x55, 0xBF, 0x5D, 0xF2, 0x02, 0x55 ),
208 BYTES_TO_T_UINT_8( 0x38, 0x2A, 0x54, 0x82, 0xE0, 0x41, 0xF7, 0x59 ),
209 BYTES_TO_T_UINT_8( 0x98, 0x9B, 0xA7, 0x8B, 0x62, 0x3B, 0x1D, 0x6E ),
210 BYTES_TO_T_UINT_8( 0x74, 0xAD, 0x20, 0xF3, 0x1E, 0xC7, 0xB1, 0x8E ),
211 BYTES_TO_T_UINT_8( 0x37, 0x05, 0x8B, 0xBE, 0x22, 0xCA, 0x87, 0xAA ),
212 };
213 static const mbedtls_mpi_uint secp384r1_gy[] = {
214 BYTES_TO_T_UINT_8( 0x5F, 0x0E, 0xEA, 0x90, 0x7C, 0x1D, 0x43, 0x7A ),
215 BYTES_TO_T_UINT_8( 0x9D, 0x81, 0x7E, 0x1D, 0xCE, 0xB1, 0x60, 0x0A ),
216 BYTES_TO_T_UINT_8( 0xC0, 0xB8, 0xF0, 0xB5, 0x13, 0x31, 0xDA, 0xE9 ),
217 BYTES_TO_T_UINT_8( 0x7C, 0x14, 0x9A, 0x28, 0xBD, 0x1D, 0xF4, 0xF8 ),
218 BYTES_TO_T_UINT_8( 0x29, 0xDC, 0x92, 0x92, 0xBF, 0x98, 0x9E, 0x5D ),
219 BYTES_TO_T_UINT_8( 0x6F, 0x2C, 0x26, 0x96, 0x4A, 0xDE, 0x17, 0x36 ),
220 };
221 static const mbedtls_mpi_uint secp384r1_n[] = {
222 BYTES_TO_T_UINT_8( 0x73, 0x29, 0xC5, 0xCC, 0x6A, 0x19, 0xEC, 0xEC ),
223 BYTES_TO_T_UINT_8( 0x7A, 0xA7, 0xB0, 0x48, 0xB2, 0x0D, 0x1A, 0x58 ),
224 BYTES_TO_T_UINT_8( 0xDF, 0x2D, 0x37, 0xF4, 0x81, 0x4D, 0x63, 0xC7 ),
225 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
226 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
227 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
228 };
229 #endif /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */
230
231 /*
232 * Domain parameters for secp521r1
233 */
234 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
235 static const mbedtls_mpi_uint secp521r1_p[] = {
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_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
240 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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_2( 0xFF, 0x01 ),
245 };
246 static const mbedtls_mpi_uint secp521r1_b[] = {
247 BYTES_TO_T_UINT_8( 0x00, 0x3F, 0x50, 0x6B, 0xD4, 0x1F, 0x45, 0xEF ),
248 BYTES_TO_T_UINT_8( 0xF1, 0x34, 0x2C, 0x3D, 0x88, 0xDF, 0x73, 0x35 ),
249 BYTES_TO_T_UINT_8( 0x07, 0xBF, 0xB1, 0x3B, 0xBD, 0xC0, 0x52, 0x16 ),
250 BYTES_TO_T_UINT_8( 0x7B, 0x93, 0x7E, 0xEC, 0x51, 0x39, 0x19, 0x56 ),
251 BYTES_TO_T_UINT_8( 0xE1, 0x09, 0xF1, 0x8E, 0x91, 0x89, 0xB4, 0xB8 ),
252 BYTES_TO_T_UINT_8( 0xF3, 0x15, 0xB3, 0x99, 0x5B, 0x72, 0xDA, 0xA2 ),
253 BYTES_TO_T_UINT_8( 0xEE, 0x40, 0x85, 0xB6, 0xA0, 0x21, 0x9A, 0x92 ),
254 BYTES_TO_T_UINT_8( 0x1F, 0x9A, 0x1C, 0x8E, 0x61, 0xB9, 0x3E, 0x95 ),
255 BYTES_TO_T_UINT_2( 0x51, 0x00 ),
256 };
257 static const mbedtls_mpi_uint secp521r1_gx[] = {
258 BYTES_TO_T_UINT_8( 0x66, 0xBD, 0xE5, 0xC2, 0x31, 0x7E, 0x7E, 0xF9 ),
259 BYTES_TO_T_UINT_8( 0x9B, 0x42, 0x6A, 0x85, 0xC1, 0xB3, 0x48, 0x33 ),
260 BYTES_TO_T_UINT_8( 0xDE, 0xA8, 0xFF, 0xA2, 0x27, 0xC1, 0x1D, 0xFE ),
261 BYTES_TO_T_UINT_8( 0x28, 0x59, 0xE7, 0xEF, 0x77, 0x5E, 0x4B, 0xA1 ),
262 BYTES_TO_T_UINT_8( 0xBA, 0x3D, 0x4D, 0x6B, 0x60, 0xAF, 0x28, 0xF8 ),
263 BYTES_TO_T_UINT_8( 0x21, 0xB5, 0x3F, 0x05, 0x39, 0x81, 0x64, 0x9C ),
264 BYTES_TO_T_UINT_8( 0x42, 0xB4, 0x95, 0x23, 0x66, 0xCB, 0x3E, 0x9E ),
265 BYTES_TO_T_UINT_8( 0xCD, 0xE9, 0x04, 0x04, 0xB7, 0x06, 0x8E, 0x85 ),
266 BYTES_TO_T_UINT_2( 0xC6, 0x00 ),
267 };
268 static const mbedtls_mpi_uint secp521r1_gy[] = {
269 BYTES_TO_T_UINT_8( 0x50, 0x66, 0xD1, 0x9F, 0x76, 0x94, 0xBE, 0x88 ),
270 BYTES_TO_T_UINT_8( 0x40, 0xC2, 0x72, 0xA2, 0x86, 0x70, 0x3C, 0x35 ),
271 BYTES_TO_T_UINT_8( 0x61, 0x07, 0xAD, 0x3F, 0x01, 0xB9, 0x50, 0xC5 ),
272 BYTES_TO_T_UINT_8( 0x40, 0x26, 0xF4, 0x5E, 0x99, 0x72, 0xEE, 0x97 ),
273 BYTES_TO_T_UINT_8( 0x2C, 0x66, 0x3E, 0x27, 0x17, 0xBD, 0xAF, 0x17 ),
274 BYTES_TO_T_UINT_8( 0x68, 0x44, 0x9B, 0x57, 0x49, 0x44, 0xF5, 0x98 ),
275 BYTES_TO_T_UINT_8( 0xD9, 0x1B, 0x7D, 0x2C, 0xB4, 0x5F, 0x8A, 0x5C ),
276 BYTES_TO_T_UINT_8( 0x04, 0xC0, 0x3B, 0x9A, 0x78, 0x6A, 0x29, 0x39 ),
277 BYTES_TO_T_UINT_2( 0x18, 0x01 ),
278 };
279 static const mbedtls_mpi_uint secp521r1_n[] = {
280 BYTES_TO_T_UINT_8( 0x09, 0x64, 0x38, 0x91, 0x1E, 0xB7, 0x6F, 0xBB ),
281 BYTES_TO_T_UINT_8( 0xAE, 0x47, 0x9C, 0x89, 0xB8, 0xC9, 0xB5, 0x3B ),
282 BYTES_TO_T_UINT_8( 0xD0, 0xA5, 0x09, 0xF7, 0x48, 0x01, 0xCC, 0x7F ),
283 BYTES_TO_T_UINT_8( 0x6B, 0x96, 0x2F, 0xBF, 0x83, 0x87, 0x86, 0x51 ),
284 BYTES_TO_T_UINT_8( 0xFA, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
285 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
286 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
287 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
288 BYTES_TO_T_UINT_2( 0xFF, 0x01 ),
289 };
290 #endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */
291
292 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
293 static const mbedtls_mpi_uint secp192k1_p[] = {
294 BYTES_TO_T_UINT_8( 0x37, 0xEE, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ),
295 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
296 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
297 };
298 static const mbedtls_mpi_uint secp192k1_a[] = {
299 BYTES_TO_T_UINT_2( 0x00, 0x00 ),
300 };
301 static const mbedtls_mpi_uint secp192k1_b[] = {
302 BYTES_TO_T_UINT_2( 0x03, 0x00 ),
303 };
304 static const mbedtls_mpi_uint secp192k1_gx[] = {
305 BYTES_TO_T_UINT_8( 0x7D, 0x6C, 0xE0, 0xEA, 0xB1, 0xD1, 0xA5, 0x1D ),
306 BYTES_TO_T_UINT_8( 0x34, 0xF4, 0xB7, 0x80, 0x02, 0x7D, 0xB0, 0x26 ),
307 BYTES_TO_T_UINT_8( 0xAE, 0xE9, 0x57, 0xC0, 0x0E, 0xF1, 0x4F, 0xDB ),
308 };
309 static const mbedtls_mpi_uint secp192k1_gy[] = {
310 BYTES_TO_T_UINT_8( 0x9D, 0x2F, 0x5E, 0xD9, 0x88, 0xAA, 0x82, 0x40 ),
311 BYTES_TO_T_UINT_8( 0x34, 0x86, 0xBE, 0x15, 0xD0, 0x63, 0x41, 0x84 ),
312 BYTES_TO_T_UINT_8( 0xA7, 0x28, 0x56, 0x9C, 0x6D, 0x2F, 0x2F, 0x9B ),
313 };
314 static const mbedtls_mpi_uint secp192k1_n[] = {
315 BYTES_TO_T_UINT_8( 0x8D, 0xFD, 0xDE, 0x74, 0x6A, 0x46, 0x69, 0x0F ),
316 BYTES_TO_T_UINT_8( 0x17, 0xFC, 0xF2, 0x26, 0xFE, 0xFF, 0xFF, 0xFF ),
317 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
318 };
319 #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */
320
321 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
322 static const mbedtls_mpi_uint secp224k1_p[] = {
323 BYTES_TO_T_UINT_8( 0x6D, 0xE5, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ),
324 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
325 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
326 BYTES_TO_T_UINT_4( 0xFF, 0xFF, 0xFF, 0xFF ),
327 };
328 static const mbedtls_mpi_uint secp224k1_a[] = {
329 BYTES_TO_T_UINT_2( 0x00, 0x00 ),
330 };
331 static const mbedtls_mpi_uint secp224k1_b[] = {
332 BYTES_TO_T_UINT_2( 0x05, 0x00 ),
333 };
334 static const mbedtls_mpi_uint secp224k1_gx[] = {
335 BYTES_TO_T_UINT_8( 0x5C, 0xA4, 0xB7, 0xB6, 0x0E, 0x65, 0x7E, 0x0F ),
336 BYTES_TO_T_UINT_8( 0xA9, 0x75, 0x70, 0xE4, 0xE9, 0x67, 0xA4, 0x69 ),
337 BYTES_TO_T_UINT_8( 0xA1, 0x28, 0xFC, 0x30, 0xDF, 0x99, 0xF0, 0x4D ),
338 BYTES_TO_T_UINT_4( 0x33, 0x5B, 0x45, 0xA1 ),
339 };
340 static const mbedtls_mpi_uint secp224k1_gy[] = {
341 BYTES_TO_T_UINT_8( 0xA5, 0x61, 0x6D, 0x55, 0xDB, 0x4B, 0xCA, 0xE2 ),
342 BYTES_TO_T_UINT_8( 0x59, 0xBD, 0xB0, 0xC0, 0xF7, 0x19, 0xE3, 0xF7 ),
343 BYTES_TO_T_UINT_8( 0xD6, 0xFB, 0xCA, 0x82, 0x42, 0x34, 0xBA, 0x7F ),
344 BYTES_TO_T_UINT_4( 0xED, 0x9F, 0x08, 0x7E ),
345 };
346 static const mbedtls_mpi_uint secp224k1_n[] = {
347 BYTES_TO_T_UINT_8( 0xF7, 0xB1, 0x9F, 0x76, 0x71, 0xA9, 0xF0, 0xCA ),
348 BYTES_TO_T_UINT_8( 0x84, 0x61, 0xEC, 0xD2, 0xE8, 0xDC, 0x01, 0x00 ),
349 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ),
350 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ),
351 };
352 #endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */
353
354 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
355 static const mbedtls_mpi_uint secp256k1_p[] = {
356 BYTES_TO_T_UINT_8( 0x2F, 0xFC, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ),
357 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
358 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
359 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
360 };
361 static const mbedtls_mpi_uint secp256k1_a[] = {
362 BYTES_TO_T_UINT_2( 0x00, 0x00 ),
363 };
364 static const mbedtls_mpi_uint secp256k1_b[] = {
365 BYTES_TO_T_UINT_2( 0x07, 0x00 ),
366 };
367 static const mbedtls_mpi_uint secp256k1_gx[] = {
368 BYTES_TO_T_UINT_8( 0x98, 0x17, 0xF8, 0x16, 0x5B, 0x81, 0xF2, 0x59 ),
369 BYTES_TO_T_UINT_8( 0xD9, 0x28, 0xCE, 0x2D, 0xDB, 0xFC, 0x9B, 0x02 ),
370 BYTES_TO_T_UINT_8( 0x07, 0x0B, 0x87, 0xCE, 0x95, 0x62, 0xA0, 0x55 ),
371 BYTES_TO_T_UINT_8( 0xAC, 0xBB, 0xDC, 0xF9, 0x7E, 0x66, 0xBE, 0x79 ),
372 };
373 static const mbedtls_mpi_uint secp256k1_gy[] = {
374 BYTES_TO_T_UINT_8( 0xB8, 0xD4, 0x10, 0xFB, 0x8F, 0xD0, 0x47, 0x9C ),
375 BYTES_TO_T_UINT_8( 0x19, 0x54, 0x85, 0xA6, 0x48, 0xB4, 0x17, 0xFD ),
376 BYTES_TO_T_UINT_8( 0xA8, 0x08, 0x11, 0x0E, 0xFC, 0xFB, 0xA4, 0x5D ),
377 BYTES_TO_T_UINT_8( 0x65, 0xC4, 0xA3, 0x26, 0x77, 0xDA, 0x3A, 0x48 ),
378 };
379 static const mbedtls_mpi_uint secp256k1_n[] = {
380 BYTES_TO_T_UINT_8( 0x41, 0x41, 0x36, 0xD0, 0x8C, 0x5E, 0xD2, 0xBF ),
381 BYTES_TO_T_UINT_8( 0x3B, 0xA0, 0x48, 0xAF, 0xE6, 0xDC, 0xAE, 0xBA ),
382 BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
383 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
384 };
385 #endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */
386
387 /*
388 * Domain parameters for brainpoolP256r1 (RFC 5639 3.4)
389 */
390 #if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED)
391 static const mbedtls_mpi_uint brainpoolP256r1_p[] = {
392 BYTES_TO_T_UINT_8( 0x77, 0x53, 0x6E, 0x1F, 0x1D, 0x48, 0x13, 0x20 ),
393 BYTES_TO_T_UINT_8( 0x28, 0x20, 0x26, 0xD5, 0x23, 0xF6, 0x3B, 0x6E ),
394 BYTES_TO_T_UINT_8( 0x72, 0x8D, 0x83, 0x9D, 0x90, 0x0A, 0x66, 0x3E ),
395 BYTES_TO_T_UINT_8( 0xBC, 0xA9, 0xEE, 0xA1, 0xDB, 0x57, 0xFB, 0xA9 ),
396 };
397 static const mbedtls_mpi_uint brainpoolP256r1_a[] = {
398 BYTES_TO_T_UINT_8( 0xD9, 0xB5, 0x30, 0xF3, 0x44, 0x4B, 0x4A, 0xE9 ),
399 BYTES_TO_T_UINT_8( 0x6C, 0x5C, 0xDC, 0x26, 0xC1, 0x55, 0x80, 0xFB ),
400 BYTES_TO_T_UINT_8( 0xE7, 0xFF, 0x7A, 0x41, 0x30, 0x75, 0xF6, 0xEE ),
401 BYTES_TO_T_UINT_8( 0x57, 0x30, 0x2C, 0xFC, 0x75, 0x09, 0x5A, 0x7D ),
402 };
403 static const mbedtls_mpi_uint brainpoolP256r1_b[] = {
404 BYTES_TO_T_UINT_8( 0xB6, 0x07, 0x8C, 0xFF, 0x18, 0xDC, 0xCC, 0x6B ),
405 BYTES_TO_T_UINT_8( 0xCE, 0xE1, 0xF7, 0x5C, 0x29, 0x16, 0x84, 0x95 ),
406 BYTES_TO_T_UINT_8( 0xBF, 0x7C, 0xD7, 0xBB, 0xD9, 0xB5, 0x30, 0xF3 ),
407 BYTES_TO_T_UINT_8( 0x44, 0x4B, 0x4A, 0xE9, 0x6C, 0x5C, 0xDC, 0x26 ),
408 };
409 static const mbedtls_mpi_uint brainpoolP256r1_gx[] = {
410 BYTES_TO_T_UINT_8( 0x62, 0x32, 0xCE, 0x9A, 0xBD, 0x53, 0x44, 0x3A ),
411 BYTES_TO_T_UINT_8( 0xC2, 0x23, 0xBD, 0xE3, 0xE1, 0x27, 0xDE, 0xB9 ),
412 BYTES_TO_T_UINT_8( 0xAF, 0xB7, 0x81, 0xFC, 0x2F, 0x48, 0x4B, 0x2C ),
413 BYTES_TO_T_UINT_8( 0xCB, 0x57, 0x7E, 0xCB, 0xB9, 0xAE, 0xD2, 0x8B ),
414 };
415 static const mbedtls_mpi_uint brainpoolP256r1_gy[] = {
416 BYTES_TO_T_UINT_8( 0x97, 0x69, 0x04, 0x2F, 0xC7, 0x54, 0x1D, 0x5C ),
417 BYTES_TO_T_UINT_8( 0x54, 0x8E, 0xED, 0x2D, 0x13, 0x45, 0x77, 0xC2 ),
418 BYTES_TO_T_UINT_8( 0xC9, 0x1D, 0x61, 0x14, 0x1A, 0x46, 0xF8, 0x97 ),
419 BYTES_TO_T_UINT_8( 0xFD, 0xC4, 0xDA, 0xC3, 0x35, 0xF8, 0x7E, 0x54 ),
420 };
421 static const mbedtls_mpi_uint brainpoolP256r1_n[] = {
422 BYTES_TO_T_UINT_8( 0xA7, 0x56, 0x48, 0x97, 0x82, 0x0E, 0x1E, 0x90 ),
423 BYTES_TO_T_UINT_8( 0xF7, 0xA6, 0x61, 0xB5, 0xA3, 0x7A, 0x39, 0x8C ),
424 BYTES_TO_T_UINT_8( 0x71, 0x8D, 0x83, 0x9D, 0x90, 0x0A, 0x66, 0x3E ),
425 BYTES_TO_T_UINT_8( 0xBC, 0xA9, 0xEE, 0xA1, 0xDB, 0x57, 0xFB, 0xA9 ),
426 };
427 #endif /* MBEDTLS_ECP_DP_BP256R1_ENABLED */
428
429 /*
430 * Domain parameters for brainpoolP384r1 (RFC 5639 3.6)
431 */
432 #if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED)
433 static const mbedtls_mpi_uint brainpoolP384r1_p[] = {
434 BYTES_TO_T_UINT_8( 0x53, 0xEC, 0x07, 0x31, 0x13, 0x00, 0x47, 0x87 ),
435 BYTES_TO_T_UINT_8( 0x71, 0x1A, 0x1D, 0x90, 0x29, 0xA7, 0xD3, 0xAC ),
436 BYTES_TO_T_UINT_8( 0x23, 0x11, 0xB7, 0x7F, 0x19, 0xDA, 0xB1, 0x12 ),
437 BYTES_TO_T_UINT_8( 0xB4, 0x56, 0x54, 0xED, 0x09, 0x71, 0x2F, 0x15 ),
438 BYTES_TO_T_UINT_8( 0xDF, 0x41, 0xE6, 0x50, 0x7E, 0x6F, 0x5D, 0x0F ),
439 BYTES_TO_T_UINT_8( 0x28, 0x6D, 0x38, 0xA3, 0x82, 0x1E, 0xB9, 0x8C ),
440 };
441 static const mbedtls_mpi_uint brainpoolP384r1_a[] = {
442 BYTES_TO_T_UINT_8( 0x26, 0x28, 0xCE, 0x22, 0xDD, 0xC7, 0xA8, 0x04 ),
443 BYTES_TO_T_UINT_8( 0xEB, 0xD4, 0x3A, 0x50, 0x4A, 0x81, 0xA5, 0x8A ),
444 BYTES_TO_T_UINT_8( 0x0F, 0xF9, 0x91, 0xBA, 0xEF, 0x65, 0x91, 0x13 ),
445 BYTES_TO_T_UINT_8( 0x87, 0x27, 0xB2, 0x4F, 0x8E, 0xA2, 0xBE, 0xC2 ),
446 BYTES_TO_T_UINT_8( 0xA0, 0xAF, 0x05, 0xCE, 0x0A, 0x08, 0x72, 0x3C ),
447 BYTES_TO_T_UINT_8( 0x0C, 0x15, 0x8C, 0x3D, 0xC6, 0x82, 0xC3, 0x7B ),
448 };
449 static const mbedtls_mpi_uint brainpoolP384r1_b[] = {
450 BYTES_TO_T_UINT_8( 0x11, 0x4C, 0x50, 0xFA, 0x96, 0x86, 0xB7, 0x3A ),
451 BYTES_TO_T_UINT_8( 0x94, 0xC9, 0xDB, 0x95, 0x02, 0x39, 0xB4, 0x7C ),
452 BYTES_TO_T_UINT_8( 0xD5, 0x62, 0xEB, 0x3E, 0xA5, 0x0E, 0x88, 0x2E ),
453 BYTES_TO_T_UINT_8( 0xA6, 0xD2, 0xDC, 0x07, 0xE1, 0x7D, 0xB7, 0x2F ),
454 BYTES_TO_T_UINT_8( 0x7C, 0x44, 0xF0, 0x16, 0x54, 0xB5, 0x39, 0x8B ),
455 BYTES_TO_T_UINT_8( 0x26, 0x28, 0xCE, 0x22, 0xDD, 0xC7, 0xA8, 0x04 ),
456 };
457 static const mbedtls_mpi_uint brainpoolP384r1_gx[] = {
458 BYTES_TO_T_UINT_8( 0x1E, 0xAF, 0xD4, 0x47, 0xE2, 0xB2, 0x87, 0xEF ),
459 BYTES_TO_T_UINT_8( 0xAA, 0x46, 0xD6, 0x36, 0x34, 0xE0, 0x26, 0xE8 ),
460 BYTES_TO_T_UINT_8( 0xE8, 0x10, 0xBD, 0x0C, 0xFE, 0xCA, 0x7F, 0xDB ),
461 BYTES_TO_T_UINT_8( 0xE3, 0x4F, 0xF1, 0x7E, 0xE7, 0xA3, 0x47, 0x88 ),
462 BYTES_TO_T_UINT_8( 0x6B, 0x3F, 0xC1, 0xB7, 0x81, 0x3A, 0xA6, 0xA2 ),
463 BYTES_TO_T_UINT_8( 0xFF, 0x45, 0xCF, 0x68, 0xF0, 0x64, 0x1C, 0x1D ),
464 };
465 static const mbedtls_mpi_uint brainpoolP384r1_gy[] = {
466 BYTES_TO_T_UINT_8( 0x15, 0x53, 0x3C, 0x26, 0x41, 0x03, 0x82, 0x42 ),
467 BYTES_TO_T_UINT_8( 0x11, 0x81, 0x91, 0x77, 0x21, 0x46, 0x46, 0x0E ),
468 BYTES_TO_T_UINT_8( 0x28, 0x29, 0x91, 0xF9, 0x4F, 0x05, 0x9C, 0xE1 ),
469 BYTES_TO_T_UINT_8( 0x64, 0x58, 0xEC, 0xFE, 0x29, 0x0B, 0xB7, 0x62 ),
470 BYTES_TO_T_UINT_8( 0x52, 0xD5, 0xCF, 0x95, 0x8E, 0xEB, 0xB1, 0x5C ),
471 BYTES_TO_T_UINT_8( 0xA4, 0xC2, 0xF9, 0x20, 0x75, 0x1D, 0xBE, 0x8A ),
472 };
473 static const mbedtls_mpi_uint brainpoolP384r1_n[] = {
474 BYTES_TO_T_UINT_8( 0x65, 0x65, 0x04, 0xE9, 0x02, 0x32, 0x88, 0x3B ),
475 BYTES_TO_T_UINT_8( 0x10, 0xC3, 0x7F, 0x6B, 0xAF, 0xB6, 0x3A, 0xCF ),
476 BYTES_TO_T_UINT_8( 0xA7, 0x25, 0x04, 0xAC, 0x6C, 0x6E, 0x16, 0x1F ),
477 BYTES_TO_T_UINT_8( 0xB3, 0x56, 0x54, 0xED, 0x09, 0x71, 0x2F, 0x15 ),
478 BYTES_TO_T_UINT_8( 0xDF, 0x41, 0xE6, 0x50, 0x7E, 0x6F, 0x5D, 0x0F ),
479 BYTES_TO_T_UINT_8( 0x28, 0x6D, 0x38, 0xA3, 0x82, 0x1E, 0xB9, 0x8C ),
480 };
481 #endif /* MBEDTLS_ECP_DP_BP384R1_ENABLED */
482
483 /*
484 * Domain parameters for brainpoolP512r1 (RFC 5639 3.7)
485 */
486 #if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED)
487 static const mbedtls_mpi_uint brainpoolP512r1_p[] = {
488 BYTES_TO_T_UINT_8( 0xF3, 0x48, 0x3A, 0x58, 0x56, 0x60, 0xAA, 0x28 ),
489 BYTES_TO_T_UINT_8( 0x85, 0xC6, 0x82, 0x2D, 0x2F, 0xFF, 0x81, 0x28 ),
490 BYTES_TO_T_UINT_8( 0xE6, 0x80, 0xA3, 0xE6, 0x2A, 0xA1, 0xCD, 0xAE ),
491 BYTES_TO_T_UINT_8( 0x42, 0x68, 0xC6, 0x9B, 0x00, 0x9B, 0x4D, 0x7D ),
492 BYTES_TO_T_UINT_8( 0x71, 0x08, 0x33, 0x70, 0xCA, 0x9C, 0x63, 0xD6 ),
493 BYTES_TO_T_UINT_8( 0x0E, 0xD2, 0xC9, 0xB3, 0xB3, 0x8D, 0x30, 0xCB ),
494 BYTES_TO_T_UINT_8( 0x07, 0xFC, 0xC9, 0x33, 0xAE, 0xE6, 0xD4, 0x3F ),
495 BYTES_TO_T_UINT_8( 0x8B, 0xC4, 0xE9, 0xDB, 0xB8, 0x9D, 0xDD, 0xAA ),
496 };
497 static const mbedtls_mpi_uint brainpoolP512r1_a[] = {
498 BYTES_TO_T_UINT_8( 0xCA, 0x94, 0xFC, 0x77, 0x4D, 0xAC, 0xC1, 0xE7 ),
499 BYTES_TO_T_UINT_8( 0xB9, 0xC7, 0xF2, 0x2B, 0xA7, 0x17, 0x11, 0x7F ),
500 BYTES_TO_T_UINT_8( 0xB5, 0xC8, 0x9A, 0x8B, 0xC9, 0xF1, 0x2E, 0x0A ),
501 BYTES_TO_T_UINT_8( 0xA1, 0x3A, 0x25, 0xA8, 0x5A, 0x5D, 0xED, 0x2D ),
502 BYTES_TO_T_UINT_8( 0xBC, 0x63, 0x98, 0xEA, 0xCA, 0x41, 0x34, 0xA8 ),
503 BYTES_TO_T_UINT_8( 0x10, 0x16, 0xF9, 0x3D, 0x8D, 0xDD, 0xCB, 0x94 ),
504 BYTES_TO_T_UINT_8( 0xC5, 0x4C, 0x23, 0xAC, 0x45, 0x71, 0x32, 0xE2 ),
505 BYTES_TO_T_UINT_8( 0x89, 0x3B, 0x60, 0x8B, 0x31, 0xA3, 0x30, 0x78 ),
506 };
507 static const mbedtls_mpi_uint brainpoolP512r1_b[] = {
508 BYTES_TO_T_UINT_8( 0x23, 0xF7, 0x16, 0x80, 0x63, 0xBD, 0x09, 0x28 ),
509 BYTES_TO_T_UINT_8( 0xDD, 0xE5, 0xBA, 0x5E, 0xB7, 0x50, 0x40, 0x98 ),
510 BYTES_TO_T_UINT_8( 0x67, 0x3E, 0x08, 0xDC, 0xCA, 0x94, 0xFC, 0x77 ),
511 BYTES_TO_T_UINT_8( 0x4D, 0xAC, 0xC1, 0xE7, 0xB9, 0xC7, 0xF2, 0x2B ),
512 BYTES_TO_T_UINT_8( 0xA7, 0x17, 0x11, 0x7F, 0xB5, 0xC8, 0x9A, 0x8B ),
513 BYTES_TO_T_UINT_8( 0xC9, 0xF1, 0x2E, 0x0A, 0xA1, 0x3A, 0x25, 0xA8 ),
514 BYTES_TO_T_UINT_8( 0x5A, 0x5D, 0xED, 0x2D, 0xBC, 0x63, 0x98, 0xEA ),
515 BYTES_TO_T_UINT_8( 0xCA, 0x41, 0x34, 0xA8, 0x10, 0x16, 0xF9, 0x3D ),
516 };
517 static const mbedtls_mpi_uint brainpoolP512r1_gx[] = {
518 BYTES_TO_T_UINT_8( 0x22, 0xF8, 0xB9, 0xBC, 0x09, 0x22, 0x35, 0x8B ),
519 BYTES_TO_T_UINT_8( 0x68, 0x5E, 0x6A, 0x40, 0x47, 0x50, 0x6D, 0x7C ),
520 BYTES_TO_T_UINT_8( 0x5F, 0x7D, 0xB9, 0x93, 0x7B, 0x68, 0xD1, 0x50 ),
521 BYTES_TO_T_UINT_8( 0x8D, 0xD4, 0xD0, 0xE2, 0x78, 0x1F, 0x3B, 0xFF ),
522 BYTES_TO_T_UINT_8( 0x8E, 0x09, 0xD0, 0xF4, 0xEE, 0x62, 0x3B, 0xB4 ),
523 BYTES_TO_T_UINT_8( 0xC1, 0x16, 0xD9, 0xB5, 0x70, 0x9F, 0xED, 0x85 ),
524 BYTES_TO_T_UINT_8( 0x93, 0x6A, 0x4C, 0x9C, 0x2E, 0x32, 0x21, 0x5A ),
525 BYTES_TO_T_UINT_8( 0x64, 0xD9, 0x2E, 0xD8, 0xBD, 0xE4, 0xAE, 0x81 ),
526 };
527 static const mbedtls_mpi_uint brainpoolP512r1_gy[] = {
528 BYTES_TO_T_UINT_8( 0x92, 0x08, 0xD8, 0x3A, 0x0F, 0x1E, 0xCD, 0x78 ),
529 BYTES_TO_T_UINT_8( 0x06, 0x54, 0xF0, 0xA8, 0x2F, 0x2B, 0xCA, 0xD1 ),
530 BYTES_TO_T_UINT_8( 0xAE, 0x63, 0x27, 0x8A, 0xD8, 0x4B, 0xCA, 0x5B ),
531 BYTES_TO_T_UINT_8( 0x5E, 0x48, 0x5F, 0x4A, 0x49, 0xDE, 0xDC, 0xB2 ),
532 BYTES_TO_T_UINT_8( 0x11, 0x81, 0x1F, 0x88, 0x5B, 0xC5, 0x00, 0xA0 ),
533 BYTES_TO_T_UINT_8( 0x1A, 0x7B, 0xA5, 0x24, 0x00, 0xF7, 0x09, 0xF2 ),
534 BYTES_TO_T_UINT_8( 0xFD, 0x22, 0x78, 0xCF, 0xA9, 0xBF, 0xEA, 0xC0 ),
535 BYTES_TO_T_UINT_8( 0xEC, 0x32, 0x63, 0x56, 0x5D, 0x38, 0xDE, 0x7D ),
536 };
537 static const mbedtls_mpi_uint brainpoolP512r1_n[] = {
538 BYTES_TO_T_UINT_8( 0x69, 0x00, 0xA9, 0x9C, 0x82, 0x96, 0x87, 0xB5 ),
539 BYTES_TO_T_UINT_8( 0xDD, 0xDA, 0x5D, 0x08, 0x81, 0xD3, 0xB1, 0x1D ),
540 BYTES_TO_T_UINT_8( 0x47, 0x10, 0xAC, 0x7F, 0x19, 0x61, 0x86, 0x41 ),
541 BYTES_TO_T_UINT_8( 0x19, 0x26, 0xA9, 0x4C, 0x41, 0x5C, 0x3E, 0x55 ),
542 BYTES_TO_T_UINT_8( 0x70, 0x08, 0x33, 0x70, 0xCA, 0x9C, 0x63, 0xD6 ),
543 BYTES_TO_T_UINT_8( 0x0E, 0xD2, 0xC9, 0xB3, 0xB3, 0x8D, 0x30, 0xCB ),
544 BYTES_TO_T_UINT_8( 0x07, 0xFC, 0xC9, 0x33, 0xAE, 0xE6, 0xD4, 0x3F ),
545 BYTES_TO_T_UINT_8( 0x8B, 0xC4, 0xE9, 0xDB, 0xB8, 0x9D, 0xDD, 0xAA ),
546 };
547 #endif /* MBEDTLS_ECP_DP_BP512R1_ENABLED */
548
549 /*
550 * Create an MPI from embedded constants
551 * (assumes len is an exact multiple of sizeof mbedtls_mpi_uint)
552 */
553 static inline void ecp_mpi_load( mbedtls_mpi *X, const mbedtls_mpi_uint *p, size_t len )
554 {
555 X->s = 1;
556 X->n = len / sizeof( mbedtls_mpi_uint );
557 X->p = (mbedtls_mpi_uint *) p;
558 }
559
560 /*
561 * Set an MPI to static value 1
562 */
563 static inline void ecp_mpi_set1( mbedtls_mpi *X )
564 {
565 static mbedtls_mpi_uint one[] = { 1 };
566 X->s = 1;
567 X->n = 1;
568 X->p = one;
569 }
570
571 /*
572 * Make group available from embedded constants
573 */
574 static int ecp_group_load( mbedtls_ecp_group *grp,
575 const mbedtls_mpi_uint *p, size_t plen,
576 const mbedtls_mpi_uint *a, size_t alen,
577 const mbedtls_mpi_uint *b, size_t blen,
578 const mbedtls_mpi_uint *gx, size_t gxlen,
579 const mbedtls_mpi_uint *gy, size_t gylen,
580 const mbedtls_mpi_uint *n, size_t nlen)
581 {
582 ecp_mpi_load( &grp->P, p, plen );
583 if( a != NULL )
584 ecp_mpi_load( &grp->A, a, alen );
585 ecp_mpi_load( &grp->B, b, blen );
586 ecp_mpi_load( &grp->N, n, nlen );
587
588 ecp_mpi_load( &grp->G.X, gx, gxlen );
589 ecp_mpi_load( &grp->G.Y, gy, gylen );
590 ecp_mpi_set1( &grp->G.Z );
591
592 grp->pbits = mbedtls_mpi_bitlen( &grp->P );
593 grp->nbits = mbedtls_mpi_bitlen( &grp->N );
594
595 grp->h = 1;
596
597 return( 0 );
598 }
599
600 #if defined(MBEDTLS_ECP_NIST_OPTIM)
601 /* Forward declarations */
602 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
603 static int ecp_mod_p192( mbedtls_mpi * );
604 #endif
605 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
606 static int ecp_mod_p224( mbedtls_mpi * );
607 #endif
608 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
609 static int ecp_mod_p256( mbedtls_mpi * );
610 #endif
611 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
612 static int ecp_mod_p384( mbedtls_mpi * );
613 #endif
614 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
615 static int ecp_mod_p521( mbedtls_mpi * );
616 #endif
617
618 #define NIST_MODP( P ) grp->modp = ecp_mod_ ## P;
619 #else
620 #define NIST_MODP( P )
621 #endif /* MBEDTLS_ECP_NIST_OPTIM */
622
623 /* Additional forward declarations */
624 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
625 static int ecp_mod_p255( mbedtls_mpi * );
626 #endif
627 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
628 static int ecp_mod_p192k1( mbedtls_mpi * );
629 #endif
630 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
631 static int ecp_mod_p224k1( mbedtls_mpi * );
632 #endif
633 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
634 static int ecp_mod_p256k1( mbedtls_mpi * );
635 #endif
636
637 #define LOAD_GROUP_A( G ) ecp_group_load( grp, \
638 G ## _p, sizeof( G ## _p ), \
639 G ## _a, sizeof( G ## _a ), \
640 G ## _b, sizeof( G ## _b ), \
641 G ## _gx, sizeof( G ## _gx ), \
642 G ## _gy, sizeof( G ## _gy ), \
643 G ## _n, sizeof( G ## _n ) )
644
645 #define LOAD_GROUP( G ) ecp_group_load( grp, \
646 G ## _p, sizeof( G ## _p ), \
647 NULL, 0, \
648 G ## _b, sizeof( G ## _b ), \
649 G ## _gx, sizeof( G ## _gx ), \
650 G ## _gy, sizeof( G ## _gy ), \
651 G ## _n, sizeof( G ## _n ) )
652
653 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
654 /*
655 * Specialized function for creating the Curve25519 group
656 */
657 static int ecp_use_curve25519( mbedtls_ecp_group *grp )
658 {
659 int ret;
660
661 /* Actually ( A + 2 ) / 4 */
662 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &grp->A, 16, "01DB42" ) );
663
664 /* P = 2^255 - 19 */
665 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->P, 1 ) );
666 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &grp->P, 255 ) );
667 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &grp->P, &grp->P, 19 ) );
668 grp->pbits = mbedtls_mpi_bitlen( &grp->P );
669
670 /* Y intentionaly not set, since we use x/z coordinates.
671 * This is used as a marker to identify Montgomery curves! */
672 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.X, 9 ) );
673 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.Z, 1 ) );
674 mbedtls_mpi_free( &grp->G.Y );
675
676 /* Actually, the required msb for private keys */
677 grp->nbits = 254;
678
679 cleanup:
680 if( ret != 0 )
681 mbedtls_ecp_group_free( grp );
682
683 return( ret );
684 }
685 #endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */
686
687 /*
688 * Set a group using well-known domain parameters
689 */
690 int mbedtls_ecp_group_load( mbedtls_ecp_group *grp, mbedtls_ecp_group_id id )
691 {
692 mbedtls_ecp_group_free( grp );
693
694 grp->id = id;
695
696 switch( id )
697 {
698 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
699 case MBEDTLS_ECP_DP_SECP192R1:
700 NIST_MODP( p192 );
701 return( LOAD_GROUP( secp192r1 ) );
702 #endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */
703
704 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
705 case MBEDTLS_ECP_DP_SECP224R1:
706 NIST_MODP( p224 );
707 return( LOAD_GROUP( secp224r1 ) );
708 #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */
709
710 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
711 case MBEDTLS_ECP_DP_SECP256R1:
712 NIST_MODP( p256 );
713 return( LOAD_GROUP( secp256r1 ) );
714 #endif /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */
715
716 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
717 case MBEDTLS_ECP_DP_SECP384R1:
718 NIST_MODP( p384 );
719 return( LOAD_GROUP( secp384r1 ) );
720 #endif /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */
721
722 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
723 case MBEDTLS_ECP_DP_SECP521R1:
724 NIST_MODP( p521 );
725 return( LOAD_GROUP( secp521r1 ) );
726 #endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */
727
728 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
729 case MBEDTLS_ECP_DP_SECP192K1:
730 grp->modp = ecp_mod_p192k1;
731 return( LOAD_GROUP_A( secp192k1 ) );
732 #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */
733
734 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
735 case MBEDTLS_ECP_DP_SECP224K1:
736 grp->modp = ecp_mod_p224k1;
737 return( LOAD_GROUP_A( secp224k1 ) );
738 #endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */
739
740 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
741 case MBEDTLS_ECP_DP_SECP256K1:
742 grp->modp = ecp_mod_p256k1;
743 return( LOAD_GROUP_A( secp256k1 ) );
744 #endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */
745
746 #if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED)
747 case MBEDTLS_ECP_DP_BP256R1:
748 return( LOAD_GROUP_A( brainpoolP256r1 ) );
749 #endif /* MBEDTLS_ECP_DP_BP256R1_ENABLED */
750
751 #if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED)
752 case MBEDTLS_ECP_DP_BP384R1:
753 return( LOAD_GROUP_A( brainpoolP384r1 ) );
754 #endif /* MBEDTLS_ECP_DP_BP384R1_ENABLED */
755
756 #if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED)
757 case MBEDTLS_ECP_DP_BP512R1:
758 return( LOAD_GROUP_A( brainpoolP512r1 ) );
759 #endif /* MBEDTLS_ECP_DP_BP512R1_ENABLED */
760
761 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
762 case MBEDTLS_ECP_DP_CURVE25519:
763 grp->modp = ecp_mod_p255;
764 return( ecp_use_curve25519( grp ) );
765 #endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */
766
767 default:
768 mbedtls_ecp_group_free( grp );
769 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
770 }
771 }
772
773 #if defined(MBEDTLS_ECP_NIST_OPTIM)
774 /*
775 * Fast reduction modulo the primes used by the NIST curves.
776 *
777 * These functions are critical for speed, but not needed for correct
778 * operations. So, we make the choice to heavily rely on the internals of our
779 * bignum library, which creates a tight coupling between these functions and
780 * our MPI implementation. However, the coupling between the ECP module and
781 * MPI remains loose, since these functions can be deactivated at will.
782 */
783
784 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
785 /*
786 * Compared to the way things are presented in FIPS 186-3 D.2,
787 * we proceed in columns, from right (least significant chunk) to left,
788 * adding chunks to N in place, and keeping a carry for the next chunk.
789 * This avoids moving things around in memory, and uselessly adding zeros,
790 * compared to the more straightforward, line-oriented approach.
791 *
792 * For this prime we need to handle data in chunks of 64 bits.
793 * Since this is always a multiple of our basic mbedtls_mpi_uint, we can
794 * use a mbedtls_mpi_uint * to designate such a chunk, and small loops to handle it.
795 */
796
797 /* Add 64-bit chunks (dst += src) and update carry */
798 static inline void add64( mbedtls_mpi_uint *dst, mbedtls_mpi_uint *src, mbedtls_mpi_uint *carry )
799 {
800 unsigned char i;
801 mbedtls_mpi_uint c = 0;
802 for( i = 0; i < 8 / sizeof( mbedtls_mpi_uint ); i++, dst++, src++ )
803 {
804 *dst += c; c = ( *dst < c );
805 *dst += *src; c += ( *dst < *src );
806 }
807 *carry += c;
808 }
809
810 /* Add carry to a 64-bit chunk and update carry */
811 static inline void carry64( mbedtls_mpi_uint *dst, mbedtls_mpi_uint *carry )
812 {
813 unsigned char i;
814 for( i = 0; i < 8 / sizeof( mbedtls_mpi_uint ); i++, dst++ )
815 {
816 *dst += *carry;
817 *carry = ( *dst < *carry );
818 }
819 }
820
821 #define WIDTH 8 / sizeof( mbedtls_mpi_uint )
822 #define A( i ) N->p + i * WIDTH
823 #define ADD( i ) add64( p, A( i ), &c )
824 #define NEXT p += WIDTH; carry64( p, &c )
825 #define LAST p += WIDTH; *p = c; while( ++p < end ) *p = 0
826
827 /*
828 * Fast quasi-reduction modulo p192 (FIPS 186-3 D.2.1)
829 */
830 static int ecp_mod_p192( mbedtls_mpi *N )
831 {
832 int ret;
833 mbedtls_mpi_uint c = 0;
834 mbedtls_mpi_uint *p, *end;
835
836 /* Make sure we have enough blocks so that A(5) is legal */
837 MBEDTLS_MPI_CHK( mbedtls_mpi_grow( N, 6 * WIDTH ) );
838
839 p = N->p;
840 end = p + N->n;
841
842 ADD( 3 ); ADD( 5 ); NEXT; // A0 += A3 + A5
843 ADD( 3 ); ADD( 4 ); ADD( 5 ); NEXT; // A1 += A3 + A4 + A5
844 ADD( 4 ); ADD( 5 ); LAST; // A2 += A4 + A5
845
846 cleanup:
847 return( ret );
848 }
849
850 #undef WIDTH
851 #undef A
852 #undef ADD
853 #undef NEXT
854 #undef LAST
855 #endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */
856
857 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) || \
858 defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) || \
859 defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
860 /*
861 * The reader is advised to first understand ecp_mod_p192() since the same
862 * general structure is used here, but with additional complications:
863 * (1) chunks of 32 bits, and (2) subtractions.
864 */
865
866 /*
867 * For these primes, we need to handle data in chunks of 32 bits.
868 * This makes it more complicated if we use 64 bits limbs in MPI,
869 * which prevents us from using a uniform access method as for p192.
870 *
871 * So, we define a mini abstraction layer to access 32 bit chunks,
872 * load them in 'cur' for work, and store them back from 'cur' when done.
873 *
874 * While at it, also define the size of N in terms of 32-bit chunks.
875 */
876 #define LOAD32 cur = A( i );
877
878 #if defined(MBEDTLS_HAVE_INT32) /* 32 bit */
879
880 #define MAX32 N->n
881 #define A( j ) N->p[j]
882 #define STORE32 N->p[i] = cur;
883
884 #else /* 64-bit */
885
886 #define MAX32 N->n * 2
887 #define A( j ) j % 2 ? (uint32_t)( N->p[j/2] >> 32 ) : (uint32_t)( N->p[j/2] )
888 #define STORE32 \
889 if( i % 2 ) { \
890 N->p[i/2] &= 0x00000000FFFFFFFF; \
891 N->p[i/2] |= ((mbedtls_mpi_uint) cur) << 32; \
892 } else { \
893 N->p[i/2] &= 0xFFFFFFFF00000000; \
894 N->p[i/2] |= (mbedtls_mpi_uint) cur; \
895 }
896
897 #endif /* sizeof( mbedtls_mpi_uint ) */
898
899 /*
900 * Helpers for addition and subtraction of chunks, with signed carry.
901 */
902 static inline void add32( uint32_t *dst, uint32_t src, signed char *carry )
903 {
904 *dst += src;
905 *carry += ( *dst < src );
906 }
907
908 static inline void sub32( uint32_t *dst, uint32_t src, signed char *carry )
909 {
910 *carry -= ( *dst < src );
911 *dst -= src;
912 }
913
914 #define ADD( j ) add32( &cur, A( j ), &c );
915 #define SUB( j ) sub32( &cur, A( j ), &c );
916
917 /*
918 * Helpers for the main 'loop'
919 * (see fix_negative for the motivation of C)
920 */
921 #define INIT( b ) \
922 int ret; \
923 signed char c = 0, cc; \
924 uint32_t cur; \
925 size_t i = 0, bits = b; \
926 mbedtls_mpi C; \
927 mbedtls_mpi_uint Cp[ b / 8 / sizeof( mbedtls_mpi_uint) + 1 ]; \
928 \
929 C.s = 1; \
930 C.n = b / 8 / sizeof( mbedtls_mpi_uint) + 1; \
931 C.p = Cp; \
932 memset( Cp, 0, C.n * sizeof( mbedtls_mpi_uint ) ); \
933 \
934 MBEDTLS_MPI_CHK( mbedtls_mpi_grow( N, b * 2 / 8 / sizeof( mbedtls_mpi_uint ) ) ); \
935 LOAD32;
936
937 #define NEXT \
938 STORE32; i++; LOAD32; \
939 cc = c; c = 0; \
940 if( cc < 0 ) \
941 sub32( &cur, -cc, &c ); \
942 else \
943 add32( &cur, cc, &c ); \
944
945 #define LAST \
946 STORE32; i++; \
947 cur = c > 0 ? c : 0; STORE32; \
948 cur = 0; while( ++i < MAX32 ) { STORE32; } \
949 if( c < 0 ) fix_negative( N, c, &C, bits );
950
951 /*
952 * If the result is negative, we get it in the form
953 * c * 2^(bits + 32) + N, with c negative and N positive shorter than 'bits'
954 */
955 static inline int fix_negative( mbedtls_mpi *N, signed char c, mbedtls_mpi *C, size_t bits )
956 {
957 int ret;
958
959 /* C = - c * 2^(bits + 32) */
960 #if !defined(MBEDTLS_HAVE_INT64)
961 ((void) bits);
962 #else
963 if( bits == 224 )
964 C->p[ C->n - 1 ] = ((mbedtls_mpi_uint) -c) << 32;
965 else
966 #endif
967 C->p[ C->n - 1 ] = (mbedtls_mpi_uint) -c;
968
969 /* N = - ( C - N ) */
970 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( N, C, N ) );
971 N->s = -1;
972
973 cleanup:
974
975 return( ret );
976 }
977
978 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
979 /*
980 * Fast quasi-reduction modulo p224 (FIPS 186-3 D.2.2)
981 */
982 static int ecp_mod_p224( mbedtls_mpi *N )
983 {
984 INIT( 224 );
985
986 SUB( 7 ); SUB( 11 ); NEXT; // A0 += -A7 - A11
987 SUB( 8 ); SUB( 12 ); NEXT; // A1 += -A8 - A12
988 SUB( 9 ); SUB( 13 ); NEXT; // A2 += -A9 - A13
989 SUB( 10 ); ADD( 7 ); ADD( 11 ); NEXT; // A3 += -A10 + A7 + A11
990 SUB( 11 ); ADD( 8 ); ADD( 12 ); NEXT; // A4 += -A11 + A8 + A12
991 SUB( 12 ); ADD( 9 ); ADD( 13 ); NEXT; // A5 += -A12 + A9 + A13
992 SUB( 13 ); ADD( 10 ); LAST; // A6 += -A13 + A10
993
994 cleanup:
995 return( ret );
996 }
997 #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */
998
999 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
1000 /*
1001 * Fast quasi-reduction modulo p256 (FIPS 186-3 D.2.3)
1002 */
1003 static int ecp_mod_p256( mbedtls_mpi *N )
1004 {
1005 INIT( 256 );
1006
1007 ADD( 8 ); ADD( 9 );
1008 SUB( 11 ); SUB( 12 ); SUB( 13 ); SUB( 14 ); NEXT; // A0
1009
1010 ADD( 9 ); ADD( 10 );
1011 SUB( 12 ); SUB( 13 ); SUB( 14 ); SUB( 15 ); NEXT; // A1
1012
1013 ADD( 10 ); ADD( 11 );
1014 SUB( 13 ); SUB( 14 ); SUB( 15 ); NEXT; // A2
1015
1016 ADD( 11 ); ADD( 11 ); ADD( 12 ); ADD( 12 ); ADD( 13 );
1017 SUB( 15 ); SUB( 8 ); SUB( 9 ); NEXT; // A3
1018
1019 ADD( 12 ); ADD( 12 ); ADD( 13 ); ADD( 13 ); ADD( 14 );
1020 SUB( 9 ); SUB( 10 ); NEXT; // A4
1021
1022 ADD( 13 ); ADD( 13 ); ADD( 14 ); ADD( 14 ); ADD( 15 );
1023 SUB( 10 ); SUB( 11 ); NEXT; // A5
1024
1025 ADD( 14 ); ADD( 14 ); ADD( 15 ); ADD( 15 ); ADD( 14 ); ADD( 13 );
1026 SUB( 8 ); SUB( 9 ); NEXT; // A6
1027
1028 ADD( 15 ); ADD( 15 ); ADD( 15 ); ADD( 8 );
1029 SUB( 10 ); SUB( 11 ); SUB( 12 ); SUB( 13 ); LAST; // A7
1030
1031 cleanup:
1032 return( ret );
1033 }
1034 #endif /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */
1035
1036 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
1037 /*
1038 * Fast quasi-reduction modulo p384 (FIPS 186-3 D.2.4)
1039 */
1040 static int ecp_mod_p384( mbedtls_mpi *N )
1041 {
1042 INIT( 384 );
1043
1044 ADD( 12 ); ADD( 21 ); ADD( 20 );
1045 SUB( 23 ); NEXT; // A0
1046
1047 ADD( 13 ); ADD( 22 ); ADD( 23 );
1048 SUB( 12 ); SUB( 20 ); NEXT; // A2
1049
1050 ADD( 14 ); ADD( 23 );
1051 SUB( 13 ); SUB( 21 ); NEXT; // A2
1052
1053 ADD( 15 ); ADD( 12 ); ADD( 20 ); ADD( 21 );
1054 SUB( 14 ); SUB( 22 ); SUB( 23 ); NEXT; // A3
1055
1056 ADD( 21 ); ADD( 21 ); ADD( 16 ); ADD( 13 ); ADD( 12 ); ADD( 20 ); ADD( 22 );
1057 SUB( 15 ); SUB( 23 ); SUB( 23 ); NEXT; // A4
1058
1059 ADD( 22 ); ADD( 22 ); ADD( 17 ); ADD( 14 ); ADD( 13 ); ADD( 21 ); ADD( 23 );
1060 SUB( 16 ); NEXT; // A5
1061
1062 ADD( 23 ); ADD( 23 ); ADD( 18 ); ADD( 15 ); ADD( 14 ); ADD( 22 );
1063 SUB( 17 ); NEXT; // A6
1064
1065 ADD( 19 ); ADD( 16 ); ADD( 15 ); ADD( 23 );
1066 SUB( 18 ); NEXT; // A7
1067
1068 ADD( 20 ); ADD( 17 ); ADD( 16 );
1069 SUB( 19 ); NEXT; // A8
1070
1071 ADD( 21 ); ADD( 18 ); ADD( 17 );
1072 SUB( 20 ); NEXT; // A9
1073
1074 ADD( 22 ); ADD( 19 ); ADD( 18 );
1075 SUB( 21 ); NEXT; // A10
1076
1077 ADD( 23 ); ADD( 20 ); ADD( 19 );
1078 SUB( 22 ); LAST; // A11
1079
1080 cleanup:
1081 return( ret );
1082 }
1083 #endif /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */
1084
1085 #undef A
1086 #undef LOAD32
1087 #undef STORE32
1088 #undef MAX32
1089 #undef INIT
1090 #undef NEXT
1091 #undef LAST
1092
1093 #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED ||
1094 MBEDTLS_ECP_DP_SECP256R1_ENABLED ||
1095 MBEDTLS_ECP_DP_SECP384R1_ENABLED */
1096
1097 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
1098 /*
1099 * Here we have an actual Mersenne prime, so things are more straightforward.
1100 * However, chunks are aligned on a 'weird' boundary (521 bits).
1101 */
1102
1103 /* Size of p521 in terms of mbedtls_mpi_uint */
1104 #define P521_WIDTH ( 521 / 8 / sizeof( mbedtls_mpi_uint ) + 1 )
1105
1106 /* Bits to keep in the most significant mbedtls_mpi_uint */
1107 #define P521_MASK 0x01FF
1108
1109 /*
1110 * Fast quasi-reduction modulo p521 (FIPS 186-3 D.2.5)
1111 * Write N as A1 + 2^521 A0, return A0 + A1
1112 */
1113 static int ecp_mod_p521( mbedtls_mpi *N )
1114 {
1115 int ret;
1116 size_t i;
1117 mbedtls_mpi M;
1118 mbedtls_mpi_uint Mp[P521_WIDTH + 1];
1119 /* Worst case for the size of M is when mbedtls_mpi_uint is 16 bits:
1120 * we need to hold bits 513 to 1056, which is 34 limbs, that is
1121 * P521_WIDTH + 1. Otherwise P521_WIDTH is enough. */
1122
1123 if( N->n < P521_WIDTH )
1124 return( 0 );
1125
1126 /* M = A1 */
1127 M.s = 1;
1128 M.n = N->n - ( P521_WIDTH - 1 );
1129 if( M.n > P521_WIDTH + 1 )
1130 M.n = P521_WIDTH + 1;
1131 M.p = Mp;
1132 memcpy( Mp, N->p + P521_WIDTH - 1, M.n * sizeof( mbedtls_mpi_uint ) );
1133 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, 521 % ( 8 * sizeof( mbedtls_mpi_uint ) ) ) );
1134
1135 /* N = A0 */
1136 N->p[P521_WIDTH - 1] &= P521_MASK;
1137 for( i = P521_WIDTH; i < N->n; i++ )
1138 N->p[i] = 0;
1139
1140 /* N = A0 + A1 */
1141 MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) );
1142
1143 cleanup:
1144 return( ret );
1145 }
1146
1147 #undef P521_WIDTH
1148 #undef P521_MASK
1149 #endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */
1150
1151 #endif /* MBEDTLS_ECP_NIST_OPTIM */
1152
1153 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
1154
1155 /* Size of p255 in terms of mbedtls_mpi_uint */
1156 #define P255_WIDTH ( 255 / 8 / sizeof( mbedtls_mpi_uint ) + 1 )
1157
1158 /*
1159 * Fast quasi-reduction modulo p255 = 2^255 - 19
1160 * Write N as A0 + 2^255 A1, return A0 + 19 * A1
1161 */
1162 static int ecp_mod_p255( mbedtls_mpi *N )
1163 {
1164 int ret;
1165 size_t i;
1166 mbedtls_mpi M;
1167 mbedtls_mpi_uint Mp[P255_WIDTH + 2];
1168
1169 if( N->n < P255_WIDTH )
1170 return( 0 );
1171
1172 /* M = A1 */
1173 M.s = 1;
1174 M.n = N->n - ( P255_WIDTH - 1 );
1175 if( M.n > P255_WIDTH + 1 )
1176 M.n = P255_WIDTH + 1;
1177 M.p = Mp;
1178 memset( Mp, 0, sizeof Mp );
1179 memcpy( Mp, N->p + P255_WIDTH - 1, M.n * sizeof( mbedtls_mpi_uint ) );
1180 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, 255 % ( 8 * sizeof( mbedtls_mpi_uint ) ) ) );
1181 M.n++; /* Make room for multiplication by 19 */
1182
1183 /* N = A0 */
1184 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( N, 255, 0 ) );
1185 for( i = P255_WIDTH; i < N->n; i++ )
1186 N->p[i] = 0;
1187
1188 /* N = A0 + 19 * A1 */
1189 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &M, 19 ) );
1190 MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) );
1191
1192 cleanup:
1193 return( ret );
1194 }
1195 #endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */
1196
1197 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) || \
1198 defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) || \
1199 defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
1200 /*
1201 * Fast quasi-reduction modulo P = 2^s - R,
1202 * with R about 33 bits, used by the Koblitz curves.
1203 *
1204 * Write N as A0 + 2^224 A1, return A0 + R * A1.
1205 * Actually do two passes, since R is big.
1206 */
1207 #define P_KOBLITZ_MAX ( 256 / 8 / sizeof( mbedtls_mpi_uint ) ) // Max limbs in P
1208 #define P_KOBLITZ_R ( 8 / sizeof( mbedtls_mpi_uint ) ) // Limbs in R
1209 static inline int ecp_mod_koblitz( mbedtls_mpi *N, mbedtls_mpi_uint *Rp, size_t p_limbs,
1210 size_t adjust, size_t shift, mbedtls_mpi_uint mask )
1211 {
1212 int ret;
1213 size_t i;
1214 mbedtls_mpi M, R;
1215 mbedtls_mpi_uint Mp[P_KOBLITZ_MAX + P_KOBLITZ_R];
1216
1217 if( N->n < p_limbs )
1218 return( 0 );
1219
1220 /* Init R */
1221 R.s = 1;
1222 R.p = Rp;
1223 R.n = P_KOBLITZ_R;
1224
1225 /* Common setup for M */
1226 M.s = 1;
1227 M.p = Mp;
1228
1229 /* M = A1 */
1230 M.n = N->n - ( p_limbs - adjust );
1231 if( M.n > p_limbs + adjust )
1232 M.n = p_limbs + adjust;
1233 memset( Mp, 0, sizeof Mp );
1234 memcpy( Mp, N->p + p_limbs - adjust, M.n * sizeof( mbedtls_mpi_uint ) );
1235 if( shift != 0 )
1236 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, shift ) );
1237 M.n += R.n - adjust; /* Make room for multiplication by R */
1238
1239 /* N = A0 */
1240 if( mask != 0 )
1241 N->p[p_limbs - 1] &= mask;
1242 for( i = p_limbs; i < N->n; i++ )
1243 N->p[i] = 0;
1244
1245 /* N = A0 + R * A1 */
1246 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &M, &M, &R ) );
1247 MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) );
1248
1249 /* Second pass */
1250
1251 /* M = A1 */
1252 M.n = N->n - ( p_limbs - adjust );
1253 if( M.n > p_limbs + adjust )
1254 M.n = p_limbs + adjust;
1255 memset( Mp, 0, sizeof Mp );
1256 memcpy( Mp, N->p + p_limbs - adjust, M.n * sizeof( mbedtls_mpi_uint ) );
1257 if( shift != 0 )
1258 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, shift ) );
1259 M.n += R.n - adjust; /* Make room for multiplication by R */
1260
1261 /* N = A0 */
1262 if( mask != 0 )
1263 N->p[p_limbs - 1] &= mask;
1264 for( i = p_limbs; i < N->n; i++ )
1265 N->p[i] = 0;
1266
1267 /* N = A0 + R * A1 */
1268 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &M, &M, &R ) );
1269 MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) );
1270
1271 cleanup:
1272 return( ret );
1273 }
1274 #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED) ||
1275 MBEDTLS_ECP_DP_SECP224K1_ENABLED) ||
1276 MBEDTLS_ECP_DP_SECP256K1_ENABLED) */
1277
1278 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
1279 /*
1280 * Fast quasi-reduction modulo p192k1 = 2^192 - R,
1281 * with R = 2^32 + 2^12 + 2^8 + 2^7 + 2^6 + 2^3 + 1 = 0x0100001119
1282 */
1283 static int ecp_mod_p192k1( mbedtls_mpi *N )
1284 {
1285 static mbedtls_mpi_uint Rp[] = {
1286 BYTES_TO_T_UINT_8( 0xC9, 0x11, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) };
1287
1288 return( ecp_mod_koblitz( N, Rp, 192 / 8 / sizeof( mbedtls_mpi_uint ), 0, 0, 0 ) );
1289 }
1290 #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */
1291
1292 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
1293 /*
1294 * Fast quasi-reduction modulo p224k1 = 2^224 - R,
1295 * with R = 2^32 + 2^12 + 2^11 + 2^9 + 2^7 + 2^4 + 2 + 1 = 0x0100001A93
1296 */
1297 static int ecp_mod_p224k1( mbedtls_mpi *N )
1298 {
1299 static mbedtls_mpi_uint Rp[] = {
1300 BYTES_TO_T_UINT_8( 0x93, 0x1A, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) };
1301
1302 #if defined(MBEDTLS_HAVE_INT64)
1303 return( ecp_mod_koblitz( N, Rp, 4, 1, 32, 0xFFFFFFFF ) );
1304 #else
1305 return( ecp_mod_koblitz( N, Rp, 224 / 8 / sizeof( mbedtls_mpi_uint ), 0, 0, 0 ) );
1306 #endif
1307 }
1308
1309 #endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */
1310
1311 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
1312 /*
1313 * Fast quasi-reduction modulo p256k1 = 2^256 - R,
1314 * with R = 2^32 + 2^9 + 2^8 + 2^7 + 2^6 + 2^4 + 1 = 0x01000003D1
1315 */
1316 static int ecp_mod_p256k1( mbedtls_mpi *N )
1317 {
1318 static mbedtls_mpi_uint Rp[] = {
1319 BYTES_TO_T_UINT_8( 0xD1, 0x03, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) };
1320 return( ecp_mod_koblitz( N, Rp, 256 / 8 / sizeof( mbedtls_mpi_uint ), 0, 0, 0 ) );
1321 }
1322 #endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */
1323
1324 #endif /* MBEDTLS_ECP_C */
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