source: azure_iot_hub_mbedtls/trunk/mbedtls-2.16.1/library/ecp_curves.c@ 398

Last change on this file since 398 was 398, checked in by coas-nagasima, 5 years ago

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