2 * Elliptic curves over GF(p): curve-specific data and functions
4 * Copyright (C) 2006-2015, ARM Limited, All Rights Reserved
5 * SPDX-License-Identifier: Apache-2.0
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
11 * http://www.apache.org/licenses/LICENSE-2.0
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.
19 * This file is part of mbed TLS (https://tls.mbed.org)
22 #if !defined(MBEDTLS_CONFIG_FILE)
23 #include "mbedtls/config.h"
25 #include MBEDTLS_CONFIG_FILE
28 #if defined(MBEDTLS_ECP_C)
30 #include "mbedtls/ecp.h"
34 #if ( defined(__ARMCC_VERSION) || defined(_MSC_VER) ) && \
35 !defined(inline) && !defined(__cplusplus)
36 #define inline __inline
40 * Conversion macros for embedded constants:
41 * build lists of mbedtls_mpi_uint's from lists of unsigned char's grouped by 8, 4 or 2
43 #if defined(MBEDTLS_HAVE_INT32)
45 #define BYTES_TO_T_UINT_4( a, b, c, d ) \
46 ( (mbedtls_mpi_uint) a << 0 ) | \
47 ( (mbedtls_mpi_uint) b << 8 ) | \
48 ( (mbedtls_mpi_uint) c << 16 ) | \
49 ( (mbedtls_mpi_uint) d << 24 )
51 #define BYTES_TO_T_UINT_2( a, b ) \
52 BYTES_TO_T_UINT_4( a, b, 0, 0 )
54 #define BYTES_TO_T_UINT_8( a, b, c, d, e, f, g, h ) \
55 BYTES_TO_T_UINT_4( a, b, c, d ), \
56 BYTES_TO_T_UINT_4( e, f, g, h )
60 #define BYTES_TO_T_UINT_8( a, b, c, d, e, f, g, h ) \
61 ( (mbedtls_mpi_uint) a << 0 ) | \
62 ( (mbedtls_mpi_uint) b << 8 ) | \
63 ( (mbedtls_mpi_uint) c << 16 ) | \
64 ( (mbedtls_mpi_uint) d << 24 ) | \
65 ( (mbedtls_mpi_uint) e << 32 ) | \
66 ( (mbedtls_mpi_uint) f << 40 ) | \
67 ( (mbedtls_mpi_uint) g << 48 ) | \
68 ( (mbedtls_mpi_uint) h << 56 )
70 #define BYTES_TO_T_UINT_4( a, b, c, d ) \
71 BYTES_TO_T_UINT_8( a, b, c, d, 0, 0, 0, 0 )
73 #define BYTES_TO_T_UINT_2( a, b ) \
74 BYTES_TO_T_UINT_8( a, b, 0, 0, 0, 0, 0, 0 )
76 #endif /* bits in mbedtls_mpi_uint */
79 * Note: the constants are in little-endian order
80 * to be directly usable in MPIs
84 * Domain parameters for secp192r1
86 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
87 static const mbedtls_mpi_uint secp192r1_p
[] = {
88 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
89 BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
90 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
92 static const mbedtls_mpi_uint secp192r1_b
[] = {
93 BYTES_TO_T_UINT_8( 0xB1, 0xB9, 0x46, 0xC1, 0xEC, 0xDE, 0xB8, 0xFE ),
94 BYTES_TO_T_UINT_8( 0x49, 0x30, 0x24, 0x72, 0xAB, 0xE9, 0xA7, 0x0F ),
95 BYTES_TO_T_UINT_8( 0xE7, 0x80, 0x9C, 0xE5, 0x19, 0x05, 0x21, 0x64 ),
97 static const mbedtls_mpi_uint secp192r1_gx
[] = {
98 BYTES_TO_T_UINT_8( 0x12, 0x10, 0xFF, 0x82, 0xFD, 0x0A, 0xFF, 0xF4 ),
99 BYTES_TO_T_UINT_8( 0x00, 0x88, 0xA1, 0x43, 0xEB, 0x20, 0xBF, 0x7C ),
100 BYTES_TO_T_UINT_8( 0xF6, 0x90, 0x30, 0xB0, 0x0E, 0xA8, 0x8D, 0x18 ),
102 static const mbedtls_mpi_uint secp192r1_gy
[] = {
103 BYTES_TO_T_UINT_8( 0x11, 0x48, 0x79, 0x1E, 0xA1, 0x77, 0xF9, 0x73 ),
104 BYTES_TO_T_UINT_8( 0xD5, 0xCD, 0x24, 0x6B, 0xED, 0x11, 0x10, 0x63 ),
105 BYTES_TO_T_UINT_8( 0x78, 0xDA, 0xC8, 0xFF, 0x95, 0x2B, 0x19, 0x07 ),
107 static const mbedtls_mpi_uint secp192r1_n
[] = {
108 BYTES_TO_T_UINT_8( 0x31, 0x28, 0xD2, 0xB4, 0xB1, 0xC9, 0x6B, 0x14 ),
109 BYTES_TO_T_UINT_8( 0x36, 0xF8, 0xDE, 0x99, 0xFF, 0xFF, 0xFF, 0xFF ),
110 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
112 #endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */
115 * Domain parameters for secp224r1
117 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
118 static const mbedtls_mpi_uint secp224r1_p
[] = {
119 BYTES_TO_T_UINT_8( 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ),
120 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ),
121 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
122 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ),
124 static const mbedtls_mpi_uint secp224r1_b
[] = {
125 BYTES_TO_T_UINT_8( 0xB4, 0xFF, 0x55, 0x23, 0x43, 0x39, 0x0B, 0x27 ),
126 BYTES_TO_T_UINT_8( 0xBA, 0xD8, 0xBF, 0xD7, 0xB7, 0xB0, 0x44, 0x50 ),
127 BYTES_TO_T_UINT_8( 0x56, 0x32, 0x41, 0xF5, 0xAB, 0xB3, 0x04, 0x0C ),
128 BYTES_TO_T_UINT_4( 0x85, 0x0A, 0x05, 0xB4 ),
130 static const mbedtls_mpi_uint secp224r1_gx
[] = {
131 BYTES_TO_T_UINT_8( 0x21, 0x1D, 0x5C, 0x11, 0xD6, 0x80, 0x32, 0x34 ),
132 BYTES_TO_T_UINT_8( 0x22, 0x11, 0xC2, 0x56, 0xD3, 0xC1, 0x03, 0x4A ),
133 BYTES_TO_T_UINT_8( 0xB9, 0x90, 0x13, 0x32, 0x7F, 0xBF, 0xB4, 0x6B ),
134 BYTES_TO_T_UINT_4( 0xBD, 0x0C, 0x0E, 0xB7 ),
136 static const mbedtls_mpi_uint secp224r1_gy
[] = {
137 BYTES_TO_T_UINT_8( 0x34, 0x7E, 0x00, 0x85, 0x99, 0x81, 0xD5, 0x44 ),
138 BYTES_TO_T_UINT_8( 0x64, 0x47, 0x07, 0x5A, 0xA0, 0x75, 0x43, 0xCD ),
139 BYTES_TO_T_UINT_8( 0xE6, 0xDF, 0x22, 0x4C, 0xFB, 0x23, 0xF7, 0xB5 ),
140 BYTES_TO_T_UINT_4( 0x88, 0x63, 0x37, 0xBD ),
142 static const mbedtls_mpi_uint secp224r1_n
[] = {
143 BYTES_TO_T_UINT_8( 0x3D, 0x2A, 0x5C, 0x5C, 0x45, 0x29, 0xDD, 0x13 ),
144 BYTES_TO_T_UINT_8( 0x3E, 0xF0, 0xB8, 0xE0, 0xA2, 0x16, 0xFF, 0xFF ),
145 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
146 BYTES_TO_T_UINT_4( 0xFF, 0xFF, 0xFF, 0xFF ),
148 #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */
151 * Domain parameters for secp256r1
153 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
154 static const mbedtls_mpi_uint secp256r1_p
[] = {
155 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
156 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ),
157 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ),
158 BYTES_TO_T_UINT_8( 0x01, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ),
160 static const mbedtls_mpi_uint secp256r1_b
[] = {
161 BYTES_TO_T_UINT_8( 0x4B, 0x60, 0xD2, 0x27, 0x3E, 0x3C, 0xCE, 0x3B ),
162 BYTES_TO_T_UINT_8( 0xF6, 0xB0, 0x53, 0xCC, 0xB0, 0x06, 0x1D, 0x65 ),
163 BYTES_TO_T_UINT_8( 0xBC, 0x86, 0x98, 0x76, 0x55, 0xBD, 0xEB, 0xB3 ),
164 BYTES_TO_T_UINT_8( 0xE7, 0x93, 0x3A, 0xAA, 0xD8, 0x35, 0xC6, 0x5A ),
166 static const mbedtls_mpi_uint secp256r1_gx
[] = {
167 BYTES_TO_T_UINT_8( 0x96, 0xC2, 0x98, 0xD8, 0x45, 0x39, 0xA1, 0xF4 ),
168 BYTES_TO_T_UINT_8( 0xA0, 0x33, 0xEB, 0x2D, 0x81, 0x7D, 0x03, 0x77 ),
169 BYTES_TO_T_UINT_8( 0xF2, 0x40, 0xA4, 0x63, 0xE5, 0xE6, 0xBC, 0xF8 ),
170 BYTES_TO_T_UINT_8( 0x47, 0x42, 0x2C, 0xE1, 0xF2, 0xD1, 0x17, 0x6B ),
172 static const mbedtls_mpi_uint secp256r1_gy
[] = {
173 BYTES_TO_T_UINT_8( 0xF5, 0x51, 0xBF, 0x37, 0x68, 0x40, 0xB6, 0xCB ),
174 BYTES_TO_T_UINT_8( 0xCE, 0x5E, 0x31, 0x6B, 0x57, 0x33, 0xCE, 0x2B ),
175 BYTES_TO_T_UINT_8( 0x16, 0x9E, 0x0F, 0x7C, 0x4A, 0xEB, 0xE7, 0x8E ),
176 BYTES_TO_T_UINT_8( 0x9B, 0x7F, 0x1A, 0xFE, 0xE2, 0x42, 0xE3, 0x4F ),
178 static const mbedtls_mpi_uint secp256r1_n
[] = {
179 BYTES_TO_T_UINT_8( 0x51, 0x25, 0x63, 0xFC, 0xC2, 0xCA, 0xB9, 0xF3 ),
180 BYTES_TO_T_UINT_8( 0x84, 0x9E, 0x17, 0xA7, 0xAD, 0xFA, 0xE6, 0xBC ),
181 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
182 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ),
184 #endif /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */
187 * Domain parameters for secp384r1
189 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
190 static const mbedtls_mpi_uint secp384r1_p
[] = {
191 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ),
192 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ),
193 BYTES_TO_T_UINT_8( 0xFE, 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 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
198 static const mbedtls_mpi_uint secp384r1_b
[] = {
199 BYTES_TO_T_UINT_8( 0xEF, 0x2A, 0xEC, 0xD3, 0xED, 0xC8, 0x85, 0x2A ),
200 BYTES_TO_T_UINT_8( 0x9D, 0xD1, 0x2E, 0x8A, 0x8D, 0x39, 0x56, 0xC6 ),
201 BYTES_TO_T_UINT_8( 0x5A, 0x87, 0x13, 0x50, 0x8F, 0x08, 0x14, 0x03 ),
202 BYTES_TO_T_UINT_8( 0x12, 0x41, 0x81, 0xFE, 0x6E, 0x9C, 0x1D, 0x18 ),
203 BYTES_TO_T_UINT_8( 0x19, 0x2D, 0xF8, 0xE3, 0x6B, 0x05, 0x8E, 0x98 ),
204 BYTES_TO_T_UINT_8( 0xE4, 0xE7, 0x3E, 0xE2, 0xA7, 0x2F, 0x31, 0xB3 ),
206 static const mbedtls_mpi_uint secp384r1_gx
[] = {
207 BYTES_TO_T_UINT_8( 0xB7, 0x0A, 0x76, 0x72, 0x38, 0x5E, 0x54, 0x3A ),
208 BYTES_TO_T_UINT_8( 0x6C, 0x29, 0x55, 0xBF, 0x5D, 0xF2, 0x02, 0x55 ),
209 BYTES_TO_T_UINT_8( 0x38, 0x2A, 0x54, 0x82, 0xE0, 0x41, 0xF7, 0x59 ),
210 BYTES_TO_T_UINT_8( 0x98, 0x9B, 0xA7, 0x8B, 0x62, 0x3B, 0x1D, 0x6E ),
211 BYTES_TO_T_UINT_8( 0x74, 0xAD, 0x20, 0xF3, 0x1E, 0xC7, 0xB1, 0x8E ),
212 BYTES_TO_T_UINT_8( 0x37, 0x05, 0x8B, 0xBE, 0x22, 0xCA, 0x87, 0xAA ),
214 static const mbedtls_mpi_uint secp384r1_gy
[] = {
215 BYTES_TO_T_UINT_8( 0x5F, 0x0E, 0xEA, 0x90, 0x7C, 0x1D, 0x43, 0x7A ),
216 BYTES_TO_T_UINT_8( 0x9D, 0x81, 0x7E, 0x1D, 0xCE, 0xB1, 0x60, 0x0A ),
217 BYTES_TO_T_UINT_8( 0xC0, 0xB8, 0xF0, 0xB5, 0x13, 0x31, 0xDA, 0xE9 ),
218 BYTES_TO_T_UINT_8( 0x7C, 0x14, 0x9A, 0x28, 0xBD, 0x1D, 0xF4, 0xF8 ),
219 BYTES_TO_T_UINT_8( 0x29, 0xDC, 0x92, 0x92, 0xBF, 0x98, 0x9E, 0x5D ),
220 BYTES_TO_T_UINT_8( 0x6F, 0x2C, 0x26, 0x96, 0x4A, 0xDE, 0x17, 0x36 ),
222 static const mbedtls_mpi_uint secp384r1_n
[] = {
223 BYTES_TO_T_UINT_8( 0x73, 0x29, 0xC5, 0xCC, 0x6A, 0x19, 0xEC, 0xEC ),
224 BYTES_TO_T_UINT_8( 0x7A, 0xA7, 0xB0, 0x48, 0xB2, 0x0D, 0x1A, 0x58 ),
225 BYTES_TO_T_UINT_8( 0xDF, 0x2D, 0x37, 0xF4, 0x81, 0x4D, 0x63, 0xC7 ),
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 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
230 #endif /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */
233 * Domain parameters for secp521r1
235 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
236 static const mbedtls_mpi_uint secp521r1_p
[] = {
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_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
245 BYTES_TO_T_UINT_2( 0xFF, 0x01 ),
247 static const mbedtls_mpi_uint secp521r1_b
[] = {
248 BYTES_TO_T_UINT_8( 0x00, 0x3F, 0x50, 0x6B, 0xD4, 0x1F, 0x45, 0xEF ),
249 BYTES_TO_T_UINT_8( 0xF1, 0x34, 0x2C, 0x3D, 0x88, 0xDF, 0x73, 0x35 ),
250 BYTES_TO_T_UINT_8( 0x07, 0xBF, 0xB1, 0x3B, 0xBD, 0xC0, 0x52, 0x16 ),
251 BYTES_TO_T_UINT_8( 0x7B, 0x93, 0x7E, 0xEC, 0x51, 0x39, 0x19, 0x56 ),
252 BYTES_TO_T_UINT_8( 0xE1, 0x09, 0xF1, 0x8E, 0x91, 0x89, 0xB4, 0xB8 ),
253 BYTES_TO_T_UINT_8( 0xF3, 0x15, 0xB3, 0x99, 0x5B, 0x72, 0xDA, 0xA2 ),
254 BYTES_TO_T_UINT_8( 0xEE, 0x40, 0x85, 0xB6, 0xA0, 0x21, 0x9A, 0x92 ),
255 BYTES_TO_T_UINT_8( 0x1F, 0x9A, 0x1C, 0x8E, 0x61, 0xB9, 0x3E, 0x95 ),
256 BYTES_TO_T_UINT_2( 0x51, 0x00 ),
258 static const mbedtls_mpi_uint secp521r1_gx
[] = {
259 BYTES_TO_T_UINT_8( 0x66, 0xBD, 0xE5, 0xC2, 0x31, 0x7E, 0x7E, 0xF9 ),
260 BYTES_TO_T_UINT_8( 0x9B, 0x42, 0x6A, 0x85, 0xC1, 0xB3, 0x48, 0x33 ),
261 BYTES_TO_T_UINT_8( 0xDE, 0xA8, 0xFF, 0xA2, 0x27, 0xC1, 0x1D, 0xFE ),
262 BYTES_TO_T_UINT_8( 0x28, 0x59, 0xE7, 0xEF, 0x77, 0x5E, 0x4B, 0xA1 ),
263 BYTES_TO_T_UINT_8( 0xBA, 0x3D, 0x4D, 0x6B, 0x60, 0xAF, 0x28, 0xF8 ),
264 BYTES_TO_T_UINT_8( 0x21, 0xB5, 0x3F, 0x05, 0x39, 0x81, 0x64, 0x9C ),
265 BYTES_TO_T_UINT_8( 0x42, 0xB4, 0x95, 0x23, 0x66, 0xCB, 0x3E, 0x9E ),
266 BYTES_TO_T_UINT_8( 0xCD, 0xE9, 0x04, 0x04, 0xB7, 0x06, 0x8E, 0x85 ),
267 BYTES_TO_T_UINT_2( 0xC6, 0x00 ),
269 static const mbedtls_mpi_uint secp521r1_gy
[] = {
270 BYTES_TO_T_UINT_8( 0x50, 0x66, 0xD1, 0x9F, 0x76, 0x94, 0xBE, 0x88 ),
271 BYTES_TO_T_UINT_8( 0x40, 0xC2, 0x72, 0xA2, 0x86, 0x70, 0x3C, 0x35 ),
272 BYTES_TO_T_UINT_8( 0x61, 0x07, 0xAD, 0x3F, 0x01, 0xB9, 0x50, 0xC5 ),
273 BYTES_TO_T_UINT_8( 0x40, 0x26, 0xF4, 0x5E, 0x99, 0x72, 0xEE, 0x97 ),
274 BYTES_TO_T_UINT_8( 0x2C, 0x66, 0x3E, 0x27, 0x17, 0xBD, 0xAF, 0x17 ),
275 BYTES_TO_T_UINT_8( 0x68, 0x44, 0x9B, 0x57, 0x49, 0x44, 0xF5, 0x98 ),
276 BYTES_TO_T_UINT_8( 0xD9, 0x1B, 0x7D, 0x2C, 0xB4, 0x5F, 0x8A, 0x5C ),
277 BYTES_TO_T_UINT_8( 0x04, 0xC0, 0x3B, 0x9A, 0x78, 0x6A, 0x29, 0x39 ),
278 BYTES_TO_T_UINT_2( 0x18, 0x01 ),
280 static const mbedtls_mpi_uint secp521r1_n
[] = {
281 BYTES_TO_T_UINT_8( 0x09, 0x64, 0x38, 0x91, 0x1E, 0xB7, 0x6F, 0xBB ),
282 BYTES_TO_T_UINT_8( 0xAE, 0x47, 0x9C, 0x89, 0xB8, 0xC9, 0xB5, 0x3B ),
283 BYTES_TO_T_UINT_8( 0xD0, 0xA5, 0x09, 0xF7, 0x48, 0x01, 0xCC, 0x7F ),
284 BYTES_TO_T_UINT_8( 0x6B, 0x96, 0x2F, 0xBF, 0x83, 0x87, 0x86, 0x51 ),
285 BYTES_TO_T_UINT_8( 0xFA, 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_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
289 BYTES_TO_T_UINT_2( 0xFF, 0x01 ),
291 #endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */
293 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
294 static const mbedtls_mpi_uint secp192k1_p
[] = {
295 BYTES_TO_T_UINT_8( 0x37, 0xEE, 0xFF, 0xFF, 0xFE, 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 ),
299 static const mbedtls_mpi_uint secp192k1_a
[] = {
300 BYTES_TO_T_UINT_2( 0x00, 0x00 ),
302 static const mbedtls_mpi_uint secp192k1_b
[] = {
303 BYTES_TO_T_UINT_2( 0x03, 0x00 ),
305 static const mbedtls_mpi_uint secp192k1_gx
[] = {
306 BYTES_TO_T_UINT_8( 0x7D, 0x6C, 0xE0, 0xEA, 0xB1, 0xD1, 0xA5, 0x1D ),
307 BYTES_TO_T_UINT_8( 0x34, 0xF4, 0xB7, 0x80, 0x02, 0x7D, 0xB0, 0x26 ),
308 BYTES_TO_T_UINT_8( 0xAE, 0xE9, 0x57, 0xC0, 0x0E, 0xF1, 0x4F, 0xDB ),
310 static const mbedtls_mpi_uint secp192k1_gy
[] = {
311 BYTES_TO_T_UINT_8( 0x9D, 0x2F, 0x5E, 0xD9, 0x88, 0xAA, 0x82, 0x40 ),
312 BYTES_TO_T_UINT_8( 0x34, 0x86, 0xBE, 0x15, 0xD0, 0x63, 0x41, 0x84 ),
313 BYTES_TO_T_UINT_8( 0xA7, 0x28, 0x56, 0x9C, 0x6D, 0x2F, 0x2F, 0x9B ),
315 static const mbedtls_mpi_uint secp192k1_n
[] = {
316 BYTES_TO_T_UINT_8( 0x8D, 0xFD, 0xDE, 0x74, 0x6A, 0x46, 0x69, 0x0F ),
317 BYTES_TO_T_UINT_8( 0x17, 0xFC, 0xF2, 0x26, 0xFE, 0xFF, 0xFF, 0xFF ),
318 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
320 #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */
322 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
323 static const mbedtls_mpi_uint secp224k1_p
[] = {
324 BYTES_TO_T_UINT_8( 0x6D, 0xE5, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ),
325 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
326 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
327 BYTES_TO_T_UINT_4( 0xFF, 0xFF, 0xFF, 0xFF ),
329 static const mbedtls_mpi_uint secp224k1_a
[] = {
330 BYTES_TO_T_UINT_2( 0x00, 0x00 ),
332 static const mbedtls_mpi_uint secp224k1_b
[] = {
333 BYTES_TO_T_UINT_2( 0x05, 0x00 ),
335 static const mbedtls_mpi_uint secp224k1_gx
[] = {
336 BYTES_TO_T_UINT_8( 0x5C, 0xA4, 0xB7, 0xB6, 0x0E, 0x65, 0x7E, 0x0F ),
337 BYTES_TO_T_UINT_8( 0xA9, 0x75, 0x70, 0xE4, 0xE9, 0x67, 0xA4, 0x69 ),
338 BYTES_TO_T_UINT_8( 0xA1, 0x28, 0xFC, 0x30, 0xDF, 0x99, 0xF0, 0x4D ),
339 BYTES_TO_T_UINT_4( 0x33, 0x5B, 0x45, 0xA1 ),
341 static const mbedtls_mpi_uint secp224k1_gy
[] = {
342 BYTES_TO_T_UINT_8( 0xA5, 0x61, 0x6D, 0x55, 0xDB, 0x4B, 0xCA, 0xE2 ),
343 BYTES_TO_T_UINT_8( 0x59, 0xBD, 0xB0, 0xC0, 0xF7, 0x19, 0xE3, 0xF7 ),
344 BYTES_TO_T_UINT_8( 0xD6, 0xFB, 0xCA, 0x82, 0x42, 0x34, 0xBA, 0x7F ),
345 BYTES_TO_T_UINT_4( 0xED, 0x9F, 0x08, 0x7E ),
347 static const mbedtls_mpi_uint secp224k1_n
[] = {
348 BYTES_TO_T_UINT_8( 0xF7, 0xB1, 0x9F, 0x76, 0x71, 0xA9, 0xF0, 0xCA ),
349 BYTES_TO_T_UINT_8( 0x84, 0x61, 0xEC, 0xD2, 0xE8, 0xDC, 0x01, 0x00 ),
350 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ),
351 BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ),
353 #endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */
355 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
356 static const mbedtls_mpi_uint secp256k1_p
[] = {
357 BYTES_TO_T_UINT_8( 0x2F, 0xFC, 0xFF, 0xFF, 0xFE, 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 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
362 static const mbedtls_mpi_uint secp256k1_a
[] = {
363 BYTES_TO_T_UINT_2( 0x00, 0x00 ),
365 static const mbedtls_mpi_uint secp256k1_b
[] = {
366 BYTES_TO_T_UINT_2( 0x07, 0x00 ),
368 static const mbedtls_mpi_uint secp256k1_gx
[] = {
369 BYTES_TO_T_UINT_8( 0x98, 0x17, 0xF8, 0x16, 0x5B, 0x81, 0xF2, 0x59 ),
370 BYTES_TO_T_UINT_8( 0xD9, 0x28, 0xCE, 0x2D, 0xDB, 0xFC, 0x9B, 0x02 ),
371 BYTES_TO_T_UINT_8( 0x07, 0x0B, 0x87, 0xCE, 0x95, 0x62, 0xA0, 0x55 ),
372 BYTES_TO_T_UINT_8( 0xAC, 0xBB, 0xDC, 0xF9, 0x7E, 0x66, 0xBE, 0x79 ),
374 static const mbedtls_mpi_uint secp256k1_gy
[] = {
375 BYTES_TO_T_UINT_8( 0xB8, 0xD4, 0x10, 0xFB, 0x8F, 0xD0, 0x47, 0x9C ),
376 BYTES_TO_T_UINT_8( 0x19, 0x54, 0x85, 0xA6, 0x48, 0xB4, 0x17, 0xFD ),
377 BYTES_TO_T_UINT_8( 0xA8, 0x08, 0x11, 0x0E, 0xFC, 0xFB, 0xA4, 0x5D ),
378 BYTES_TO_T_UINT_8( 0x65, 0xC4, 0xA3, 0x26, 0x77, 0xDA, 0x3A, 0x48 ),
380 static const mbedtls_mpi_uint secp256k1_n
[] = {
381 BYTES_TO_T_UINT_8( 0x41, 0x41, 0x36, 0xD0, 0x8C, 0x5E, 0xD2, 0xBF ),
382 BYTES_TO_T_UINT_8( 0x3B, 0xA0, 0x48, 0xAF, 0xE6, 0xDC, 0xAE, 0xBA ),
383 BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
384 BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
386 #endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */
389 * Domain parameters for brainpoolP256r1 (RFC 5639 3.4)
391 #if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED)
392 static const mbedtls_mpi_uint brainpoolP256r1_p
[] = {
393 BYTES_TO_T_UINT_8( 0x77, 0x53, 0x6E, 0x1F, 0x1D, 0x48, 0x13, 0x20 ),
394 BYTES_TO_T_UINT_8( 0x28, 0x20, 0x26, 0xD5, 0x23, 0xF6, 0x3B, 0x6E ),
395 BYTES_TO_T_UINT_8( 0x72, 0x8D, 0x83, 0x9D, 0x90, 0x0A, 0x66, 0x3E ),
396 BYTES_TO_T_UINT_8( 0xBC, 0xA9, 0xEE, 0xA1, 0xDB, 0x57, 0xFB, 0xA9 ),
398 static const mbedtls_mpi_uint brainpoolP256r1_a
[] = {
399 BYTES_TO_T_UINT_8( 0xD9, 0xB5, 0x30, 0xF3, 0x44, 0x4B, 0x4A, 0xE9 ),
400 BYTES_TO_T_UINT_8( 0x6C, 0x5C, 0xDC, 0x26, 0xC1, 0x55, 0x80, 0xFB ),
401 BYTES_TO_T_UINT_8( 0xE7, 0xFF, 0x7A, 0x41, 0x30, 0x75, 0xF6, 0xEE ),
402 BYTES_TO_T_UINT_8( 0x57, 0x30, 0x2C, 0xFC, 0x75, 0x09, 0x5A, 0x7D ),
404 static const mbedtls_mpi_uint brainpoolP256r1_b
[] = {
405 BYTES_TO_T_UINT_8( 0xB6, 0x07, 0x8C, 0xFF, 0x18, 0xDC, 0xCC, 0x6B ),
406 BYTES_TO_T_UINT_8( 0xCE, 0xE1, 0xF7, 0x5C, 0x29, 0x16, 0x84, 0x95 ),
407 BYTES_TO_T_UINT_8( 0xBF, 0x7C, 0xD7, 0xBB, 0xD9, 0xB5, 0x30, 0xF3 ),
408 BYTES_TO_T_UINT_8( 0x44, 0x4B, 0x4A, 0xE9, 0x6C, 0x5C, 0xDC, 0x26 ),
410 static const mbedtls_mpi_uint brainpoolP256r1_gx
[] = {
411 BYTES_TO_T_UINT_8( 0x62, 0x32, 0xCE, 0x9A, 0xBD, 0x53, 0x44, 0x3A ),
412 BYTES_TO_T_UINT_8( 0xC2, 0x23, 0xBD, 0xE3, 0xE1, 0x27, 0xDE, 0xB9 ),
413 BYTES_TO_T_UINT_8( 0xAF, 0xB7, 0x81, 0xFC, 0x2F, 0x48, 0x4B, 0x2C ),
414 BYTES_TO_T_UINT_8( 0xCB, 0x57, 0x7E, 0xCB, 0xB9, 0xAE, 0xD2, 0x8B ),
416 static const mbedtls_mpi_uint brainpoolP256r1_gy
[] = {
417 BYTES_TO_T_UINT_8( 0x97, 0x69, 0x04, 0x2F, 0xC7, 0x54, 0x1D, 0x5C ),
418 BYTES_TO_T_UINT_8( 0x54, 0x8E, 0xED, 0x2D, 0x13, 0x45, 0x77, 0xC2 ),
419 BYTES_TO_T_UINT_8( 0xC9, 0x1D, 0x61, 0x14, 0x1A, 0x46, 0xF8, 0x97 ),
420 BYTES_TO_T_UINT_8( 0xFD, 0xC4, 0xDA, 0xC3, 0x35, 0xF8, 0x7E, 0x54 ),
422 static const mbedtls_mpi_uint brainpoolP256r1_n
[] = {
423 BYTES_TO_T_UINT_8( 0xA7, 0x56, 0x48, 0x97, 0x82, 0x0E, 0x1E, 0x90 ),
424 BYTES_TO_T_UINT_8( 0xF7, 0xA6, 0x61, 0xB5, 0xA3, 0x7A, 0x39, 0x8C ),
425 BYTES_TO_T_UINT_8( 0x71, 0x8D, 0x83, 0x9D, 0x90, 0x0A, 0x66, 0x3E ),
426 BYTES_TO_T_UINT_8( 0xBC, 0xA9, 0xEE, 0xA1, 0xDB, 0x57, 0xFB, 0xA9 ),
428 #endif /* MBEDTLS_ECP_DP_BP256R1_ENABLED */
431 * Domain parameters for brainpoolP384r1 (RFC 5639 3.6)
433 #if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED)
434 static const mbedtls_mpi_uint brainpoolP384r1_p
[] = {
435 BYTES_TO_T_UINT_8( 0x53, 0xEC, 0x07, 0x31, 0x13, 0x00, 0x47, 0x87 ),
436 BYTES_TO_T_UINT_8( 0x71, 0x1A, 0x1D, 0x90, 0x29, 0xA7, 0xD3, 0xAC ),
437 BYTES_TO_T_UINT_8( 0x23, 0x11, 0xB7, 0x7F, 0x19, 0xDA, 0xB1, 0x12 ),
438 BYTES_TO_T_UINT_8( 0xB4, 0x56, 0x54, 0xED, 0x09, 0x71, 0x2F, 0x15 ),
439 BYTES_TO_T_UINT_8( 0xDF, 0x41, 0xE6, 0x50, 0x7E, 0x6F, 0x5D, 0x0F ),
440 BYTES_TO_T_UINT_8( 0x28, 0x6D, 0x38, 0xA3, 0x82, 0x1E, 0xB9, 0x8C ),
442 static const mbedtls_mpi_uint brainpoolP384r1_a
[] = {
443 BYTES_TO_T_UINT_8( 0x26, 0x28, 0xCE, 0x22, 0xDD, 0xC7, 0xA8, 0x04 ),
444 BYTES_TO_T_UINT_8( 0xEB, 0xD4, 0x3A, 0x50, 0x4A, 0x81, 0xA5, 0x8A ),
445 BYTES_TO_T_UINT_8( 0x0F, 0xF9, 0x91, 0xBA, 0xEF, 0x65, 0x91, 0x13 ),
446 BYTES_TO_T_UINT_8( 0x87, 0x27, 0xB2, 0x4F, 0x8E, 0xA2, 0xBE, 0xC2 ),
447 BYTES_TO_T_UINT_8( 0xA0, 0xAF, 0x05, 0xCE, 0x0A, 0x08, 0x72, 0x3C ),
448 BYTES_TO_T_UINT_8( 0x0C, 0x15, 0x8C, 0x3D, 0xC6, 0x82, 0xC3, 0x7B ),
450 static const mbedtls_mpi_uint brainpoolP384r1_b
[] = {
451 BYTES_TO_T_UINT_8( 0x11, 0x4C, 0x50, 0xFA, 0x96, 0x86, 0xB7, 0x3A ),
452 BYTES_TO_T_UINT_8( 0x94, 0xC9, 0xDB, 0x95, 0x02, 0x39, 0xB4, 0x7C ),
453 BYTES_TO_T_UINT_8( 0xD5, 0x62, 0xEB, 0x3E, 0xA5, 0x0E, 0x88, 0x2E ),
454 BYTES_TO_T_UINT_8( 0xA6, 0xD2, 0xDC, 0x07, 0xE1, 0x7D, 0xB7, 0x2F ),
455 BYTES_TO_T_UINT_8( 0x7C, 0x44, 0xF0, 0x16, 0x54, 0xB5, 0x39, 0x8B ),
456 BYTES_TO_T_UINT_8( 0x26, 0x28, 0xCE, 0x22, 0xDD, 0xC7, 0xA8, 0x04 ),
458 static const mbedtls_mpi_uint brainpoolP384r1_gx
[] = {
459 BYTES_TO_T_UINT_8( 0x1E, 0xAF, 0xD4, 0x47, 0xE2, 0xB2, 0x87, 0xEF ),
460 BYTES_TO_T_UINT_8( 0xAA, 0x46, 0xD6, 0x36, 0x34, 0xE0, 0x26, 0xE8 ),
461 BYTES_TO_T_UINT_8( 0xE8, 0x10, 0xBD, 0x0C, 0xFE, 0xCA, 0x7F, 0xDB ),
462 BYTES_TO_T_UINT_8( 0xE3, 0x4F, 0xF1, 0x7E, 0xE7, 0xA3, 0x47, 0x88 ),
463 BYTES_TO_T_UINT_8( 0x6B, 0x3F, 0xC1, 0xB7, 0x81, 0x3A, 0xA6, 0xA2 ),
464 BYTES_TO_T_UINT_8( 0xFF, 0x45, 0xCF, 0x68, 0xF0, 0x64, 0x1C, 0x1D ),
466 static const mbedtls_mpi_uint brainpoolP384r1_gy
[] = {
467 BYTES_TO_T_UINT_8( 0x15, 0x53, 0x3C, 0x26, 0x41, 0x03, 0x82, 0x42 ),
468 BYTES_TO_T_UINT_8( 0x11, 0x81, 0x91, 0x77, 0x21, 0x46, 0x46, 0x0E ),
469 BYTES_TO_T_UINT_8( 0x28, 0x29, 0x91, 0xF9, 0x4F, 0x05, 0x9C, 0xE1 ),
470 BYTES_TO_T_UINT_8( 0x64, 0x58, 0xEC, 0xFE, 0x29, 0x0B, 0xB7, 0x62 ),
471 BYTES_TO_T_UINT_8( 0x52, 0xD5, 0xCF, 0x95, 0x8E, 0xEB, 0xB1, 0x5C ),
472 BYTES_TO_T_UINT_8( 0xA4, 0xC2, 0xF9, 0x20, 0x75, 0x1D, 0xBE, 0x8A ),
474 static const mbedtls_mpi_uint brainpoolP384r1_n
[] = {
475 BYTES_TO_T_UINT_8( 0x65, 0x65, 0x04, 0xE9, 0x02, 0x32, 0x88, 0x3B ),
476 BYTES_TO_T_UINT_8( 0x10, 0xC3, 0x7F, 0x6B, 0xAF, 0xB6, 0x3A, 0xCF ),
477 BYTES_TO_T_UINT_8( 0xA7, 0x25, 0x04, 0xAC, 0x6C, 0x6E, 0x16, 0x1F ),
478 BYTES_TO_T_UINT_8( 0xB3, 0x56, 0x54, 0xED, 0x09, 0x71, 0x2F, 0x15 ),
479 BYTES_TO_T_UINT_8( 0xDF, 0x41, 0xE6, 0x50, 0x7E, 0x6F, 0x5D, 0x0F ),
480 BYTES_TO_T_UINT_8( 0x28, 0x6D, 0x38, 0xA3, 0x82, 0x1E, 0xB9, 0x8C ),
482 #endif /* MBEDTLS_ECP_DP_BP384R1_ENABLED */
485 * Domain parameters for brainpoolP512r1 (RFC 5639 3.7)
487 #if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED)
488 static const mbedtls_mpi_uint brainpoolP512r1_p
[] = {
489 BYTES_TO_T_UINT_8( 0xF3, 0x48, 0x3A, 0x58, 0x56, 0x60, 0xAA, 0x28 ),
490 BYTES_TO_T_UINT_8( 0x85, 0xC6, 0x82, 0x2D, 0x2F, 0xFF, 0x81, 0x28 ),
491 BYTES_TO_T_UINT_8( 0xE6, 0x80, 0xA3, 0xE6, 0x2A, 0xA1, 0xCD, 0xAE ),
492 BYTES_TO_T_UINT_8( 0x42, 0x68, 0xC6, 0x9B, 0x00, 0x9B, 0x4D, 0x7D ),
493 BYTES_TO_T_UINT_8( 0x71, 0x08, 0x33, 0x70, 0xCA, 0x9C, 0x63, 0xD6 ),
494 BYTES_TO_T_UINT_8( 0x0E, 0xD2, 0xC9, 0xB3, 0xB3, 0x8D, 0x30, 0xCB ),
495 BYTES_TO_T_UINT_8( 0x07, 0xFC, 0xC9, 0x33, 0xAE, 0xE6, 0xD4, 0x3F ),
496 BYTES_TO_T_UINT_8( 0x8B, 0xC4, 0xE9, 0xDB, 0xB8, 0x9D, 0xDD, 0xAA ),
498 static const mbedtls_mpi_uint brainpoolP512r1_a
[] = {
499 BYTES_TO_T_UINT_8( 0xCA, 0x94, 0xFC, 0x77, 0x4D, 0xAC, 0xC1, 0xE7 ),
500 BYTES_TO_T_UINT_8( 0xB9, 0xC7, 0xF2, 0x2B, 0xA7, 0x17, 0x11, 0x7F ),
501 BYTES_TO_T_UINT_8( 0xB5, 0xC8, 0x9A, 0x8B, 0xC9, 0xF1, 0x2E, 0x0A ),
502 BYTES_TO_T_UINT_8( 0xA1, 0x3A, 0x25, 0xA8, 0x5A, 0x5D, 0xED, 0x2D ),
503 BYTES_TO_T_UINT_8( 0xBC, 0x63, 0x98, 0xEA, 0xCA, 0x41, 0x34, 0xA8 ),
504 BYTES_TO_T_UINT_8( 0x10, 0x16, 0xF9, 0x3D, 0x8D, 0xDD, 0xCB, 0x94 ),
505 BYTES_TO_T_UINT_8( 0xC5, 0x4C, 0x23, 0xAC, 0x45, 0x71, 0x32, 0xE2 ),
506 BYTES_TO_T_UINT_8( 0x89, 0x3B, 0x60, 0x8B, 0x31, 0xA3, 0x30, 0x78 ),
508 static const mbedtls_mpi_uint brainpoolP512r1_b
[] = {
509 BYTES_TO_T_UINT_8( 0x23, 0xF7, 0x16, 0x80, 0x63, 0xBD, 0x09, 0x28 ),
510 BYTES_TO_T_UINT_8( 0xDD, 0xE5, 0xBA, 0x5E, 0xB7, 0x50, 0x40, 0x98 ),
511 BYTES_TO_T_UINT_8( 0x67, 0x3E, 0x08, 0xDC, 0xCA, 0x94, 0xFC, 0x77 ),
512 BYTES_TO_T_UINT_8( 0x4D, 0xAC, 0xC1, 0xE7, 0xB9, 0xC7, 0xF2, 0x2B ),
513 BYTES_TO_T_UINT_8( 0xA7, 0x17, 0x11, 0x7F, 0xB5, 0xC8, 0x9A, 0x8B ),
514 BYTES_TO_T_UINT_8( 0xC9, 0xF1, 0x2E, 0x0A, 0xA1, 0x3A, 0x25, 0xA8 ),
515 BYTES_TO_T_UINT_8( 0x5A, 0x5D, 0xED, 0x2D, 0xBC, 0x63, 0x98, 0xEA ),
516 BYTES_TO_T_UINT_8( 0xCA, 0x41, 0x34, 0xA8, 0x10, 0x16, 0xF9, 0x3D ),
518 static const mbedtls_mpi_uint brainpoolP512r1_gx
[] = {
519 BYTES_TO_T_UINT_8( 0x22, 0xF8, 0xB9, 0xBC, 0x09, 0x22, 0x35, 0x8B ),
520 BYTES_TO_T_UINT_8( 0x68, 0x5E, 0x6A, 0x40, 0x47, 0x50, 0x6D, 0x7C ),
521 BYTES_TO_T_UINT_8( 0x5F, 0x7D, 0xB9, 0x93, 0x7B, 0x68, 0xD1, 0x50 ),
522 BYTES_TO_T_UINT_8( 0x8D, 0xD4, 0xD0, 0xE2, 0x78, 0x1F, 0x3B, 0xFF ),
523 BYTES_TO_T_UINT_8( 0x8E, 0x09, 0xD0, 0xF4, 0xEE, 0x62, 0x3B, 0xB4 ),
524 BYTES_TO_T_UINT_8( 0xC1, 0x16, 0xD9, 0xB5, 0x70, 0x9F, 0xED, 0x85 ),
525 BYTES_TO_T_UINT_8( 0x93, 0x6A, 0x4C, 0x9C, 0x2E, 0x32, 0x21, 0x5A ),
526 BYTES_TO_T_UINT_8( 0x64, 0xD9, 0x2E, 0xD8, 0xBD, 0xE4, 0xAE, 0x81 ),
528 static const mbedtls_mpi_uint brainpoolP512r1_gy
[] = {
529 BYTES_TO_T_UINT_8( 0x92, 0x08, 0xD8, 0x3A, 0x0F, 0x1E, 0xCD, 0x78 ),
530 BYTES_TO_T_UINT_8( 0x06, 0x54, 0xF0, 0xA8, 0x2F, 0x2B, 0xCA, 0xD1 ),
531 BYTES_TO_T_UINT_8( 0xAE, 0x63, 0x27, 0x8A, 0xD8, 0x4B, 0xCA, 0x5B ),
532 BYTES_TO_T_UINT_8( 0x5E, 0x48, 0x5F, 0x4A, 0x49, 0xDE, 0xDC, 0xB2 ),
533 BYTES_TO_T_UINT_8( 0x11, 0x81, 0x1F, 0x88, 0x5B, 0xC5, 0x00, 0xA0 ),
534 BYTES_TO_T_UINT_8( 0x1A, 0x7B, 0xA5, 0x24, 0x00, 0xF7, 0x09, 0xF2 ),
535 BYTES_TO_T_UINT_8( 0xFD, 0x22, 0x78, 0xCF, 0xA9, 0xBF, 0xEA, 0xC0 ),
536 BYTES_TO_T_UINT_8( 0xEC, 0x32, 0x63, 0x56, 0x5D, 0x38, 0xDE, 0x7D ),
538 static const mbedtls_mpi_uint brainpoolP512r1_n
[] = {
539 BYTES_TO_T_UINT_8( 0x69, 0x00, 0xA9, 0x9C, 0x82, 0x96, 0x87, 0xB5 ),
540 BYTES_TO_T_UINT_8( 0xDD, 0xDA, 0x5D, 0x08, 0x81, 0xD3, 0xB1, 0x1D ),
541 BYTES_TO_T_UINT_8( 0x47, 0x10, 0xAC, 0x7F, 0x19, 0x61, 0x86, 0x41 ),
542 BYTES_TO_T_UINT_8( 0x19, 0x26, 0xA9, 0x4C, 0x41, 0x5C, 0x3E, 0x55 ),
543 BYTES_TO_T_UINT_8( 0x70, 0x08, 0x33, 0x70, 0xCA, 0x9C, 0x63, 0xD6 ),
544 BYTES_TO_T_UINT_8( 0x0E, 0xD2, 0xC9, 0xB3, 0xB3, 0x8D, 0x30, 0xCB ),
545 BYTES_TO_T_UINT_8( 0x07, 0xFC, 0xC9, 0x33, 0xAE, 0xE6, 0xD4, 0x3F ),
546 BYTES_TO_T_UINT_8( 0x8B, 0xC4, 0xE9, 0xDB, 0xB8, 0x9D, 0xDD, 0xAA ),
548 #endif /* MBEDTLS_ECP_DP_BP512R1_ENABLED */
551 * Create an MPI from embedded constants
552 * (assumes len is an exact multiple of sizeof mbedtls_mpi_uint)
554 static inline void ecp_mpi_load( mbedtls_mpi
*X
, const mbedtls_mpi_uint
*p
, size_t len
)
557 X
->n
= len
/ sizeof( mbedtls_mpi_uint
);
558 X
->p
= (mbedtls_mpi_uint
*) p
;
562 * Set an MPI to static value 1
564 static inline void ecp_mpi_set1( mbedtls_mpi
*X
)
566 static mbedtls_mpi_uint one
[] = { 1 };
573 * Make group available from embedded constants
575 static int ecp_group_load( mbedtls_ecp_group
*grp
,
576 const mbedtls_mpi_uint
*p
, size_t plen
,
577 const mbedtls_mpi_uint
*a
, size_t alen
,
578 const mbedtls_mpi_uint
*b
, size_t blen
,
579 const mbedtls_mpi_uint
*gx
, size_t gxlen
,
580 const mbedtls_mpi_uint
*gy
, size_t gylen
,
581 const mbedtls_mpi_uint
*n
, size_t nlen
)
583 ecp_mpi_load( &grp
->P
, p
, plen
);
585 ecp_mpi_load( &grp
->A
, a
, alen
);
586 ecp_mpi_load( &grp
->B
, b
, blen
);
587 ecp_mpi_load( &grp
->N
, n
, nlen
);
589 ecp_mpi_load( &grp
->G
.X
, gx
, gxlen
);
590 ecp_mpi_load( &grp
->G
.Y
, gy
, gylen
);
591 ecp_mpi_set1( &grp
->G
.Z
);
593 grp
->pbits
= mbedtls_mpi_bitlen( &grp
->P
);
594 grp
->nbits
= mbedtls_mpi_bitlen( &grp
->N
);
601 #if defined(MBEDTLS_ECP_NIST_OPTIM)
602 /* Forward declarations */
603 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
604 static int ecp_mod_p192( mbedtls_mpi
* );
606 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
607 static int ecp_mod_p224( mbedtls_mpi
* );
609 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
610 static int ecp_mod_p256( mbedtls_mpi
* );
612 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
613 static int ecp_mod_p384( mbedtls_mpi
* );
615 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
616 static int ecp_mod_p521( mbedtls_mpi
* );
619 #define NIST_MODP( P ) grp->modp = ecp_mod_ ## P;
621 #define NIST_MODP( P )
622 #endif /* MBEDTLS_ECP_NIST_OPTIM */
624 /* Additional forward declarations */
625 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
626 static int ecp_mod_p255( mbedtls_mpi
* );
628 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
629 static int ecp_mod_p192k1( mbedtls_mpi
* );
631 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
632 static int ecp_mod_p224k1( mbedtls_mpi
* );
634 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
635 static int ecp_mod_p256k1( mbedtls_mpi
* );
638 #define LOAD_GROUP_A( G ) ecp_group_load( grp, \
639 G ## _p, sizeof( G ## _p ), \
640 G ## _a, sizeof( G ## _a ), \
641 G ## _b, sizeof( G ## _b ), \
642 G ## _gx, sizeof( G ## _gx ), \
643 G ## _gy, sizeof( G ## _gy ), \
644 G ## _n, sizeof( G ## _n ) )
646 #define LOAD_GROUP( G ) ecp_group_load( grp, \
647 G ## _p, sizeof( G ## _p ), \
649 G ## _b, sizeof( G ## _b ), \
650 G ## _gx, sizeof( G ## _gx ), \
651 G ## _gy, sizeof( G ## _gy ), \
652 G ## _n, sizeof( G ## _n ) )
654 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
656 * Specialized function for creating the Curve25519 group
658 static int ecp_use_curve25519( mbedtls_ecp_group
*grp
)
662 /* Actually ( A + 2 ) / 4 */
663 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &grp
->A
, 16, "01DB42" ) );
666 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp
->P
, 1 ) );
667 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &grp
->P
, 255 ) );
668 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &grp
->P
, &grp
->P
, 19 ) );
669 grp
->pbits
= mbedtls_mpi_bitlen( &grp
->P
);
671 /* Y intentionaly not set, since we use x/z coordinates.
672 * This is used as a marker to identify Montgomery curves! */
673 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp
->G
.X
, 9 ) );
674 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp
->G
.Z
, 1 ) );
675 mbedtls_mpi_free( &grp
->G
.Y
);
677 /* Actually, the required msb for private keys */
682 mbedtls_ecp_group_free( grp
);
686 #endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */
689 * Set a group using well-known domain parameters
691 int mbedtls_ecp_group_load( mbedtls_ecp_group
*grp
, mbedtls_ecp_group_id id
)
693 mbedtls_ecp_group_free( grp
);
699 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
700 case MBEDTLS_ECP_DP_SECP192R1
:
702 return( LOAD_GROUP( secp192r1
) );
703 #endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */
705 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
706 case MBEDTLS_ECP_DP_SECP224R1
:
708 return( LOAD_GROUP( secp224r1
) );
709 #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */
711 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
712 case MBEDTLS_ECP_DP_SECP256R1
:
714 return( LOAD_GROUP( secp256r1
) );
715 #endif /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */
717 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
718 case MBEDTLS_ECP_DP_SECP384R1
:
720 return( LOAD_GROUP( secp384r1
) );
721 #endif /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */
723 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
724 case MBEDTLS_ECP_DP_SECP521R1
:
726 return( LOAD_GROUP( secp521r1
) );
727 #endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */
729 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
730 case MBEDTLS_ECP_DP_SECP192K1
:
731 grp
->modp
= ecp_mod_p192k1
;
732 return( LOAD_GROUP_A( secp192k1
) );
733 #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */
735 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
736 case MBEDTLS_ECP_DP_SECP224K1
:
737 grp
->modp
= ecp_mod_p224k1
;
738 return( LOAD_GROUP_A( secp224k1
) );
739 #endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */
741 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
742 case MBEDTLS_ECP_DP_SECP256K1
:
743 grp
->modp
= ecp_mod_p256k1
;
744 return( LOAD_GROUP_A( secp256k1
) );
745 #endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */
747 #if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED)
748 case MBEDTLS_ECP_DP_BP256R1
:
749 return( LOAD_GROUP_A( brainpoolP256r1
) );
750 #endif /* MBEDTLS_ECP_DP_BP256R1_ENABLED */
752 #if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED)
753 case MBEDTLS_ECP_DP_BP384R1
:
754 return( LOAD_GROUP_A( brainpoolP384r1
) );
755 #endif /* MBEDTLS_ECP_DP_BP384R1_ENABLED */
757 #if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED)
758 case MBEDTLS_ECP_DP_BP512R1
:
759 return( LOAD_GROUP_A( brainpoolP512r1
) );
760 #endif /* MBEDTLS_ECP_DP_BP512R1_ENABLED */
762 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
763 case MBEDTLS_ECP_DP_CURVE25519
:
764 grp
->modp
= ecp_mod_p255
;
765 return( ecp_use_curve25519( grp
) );
766 #endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */
769 mbedtls_ecp_group_free( grp
);
770 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE
);
774 #if defined(MBEDTLS_ECP_NIST_OPTIM)
776 * Fast reduction modulo the primes used by the NIST curves.
778 * These functions are critical for speed, but not needed for correct
779 * operations. So, we make the choice to heavily rely on the internals of our
780 * bignum library, which creates a tight coupling between these functions and
781 * our MPI implementation. However, the coupling between the ECP module and
782 * MPI remains loose, since these functions can be deactivated at will.
785 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
787 * Compared to the way things are presented in FIPS 186-3 D.2,
788 * we proceed in columns, from right (least significant chunk) to left,
789 * adding chunks to N in place, and keeping a carry for the next chunk.
790 * This avoids moving things around in memory, and uselessly adding zeros,
791 * compared to the more straightforward, line-oriented approach.
793 * For this prime we need to handle data in chunks of 64 bits.
794 * Since this is always a multiple of our basic mbedtls_mpi_uint, we can
795 * use a mbedtls_mpi_uint * to designate such a chunk, and small loops to handle it.
798 /* Add 64-bit chunks (dst += src) and update carry */
799 static inline void add64( mbedtls_mpi_uint
*dst
, mbedtls_mpi_uint
*src
, mbedtls_mpi_uint
*carry
)
802 mbedtls_mpi_uint c
= 0;
803 for( i
= 0; i
< 8 / sizeof( mbedtls_mpi_uint
); i
++, dst
++, src
++ )
805 *dst
+= c
; c
= ( *dst
< c
);
806 *dst
+= *src
; c
+= ( *dst
< *src
);
811 /* Add carry to a 64-bit chunk and update carry */
812 static inline void carry64( mbedtls_mpi_uint
*dst
, mbedtls_mpi_uint
*carry
)
815 for( i
= 0; i
< 8 / sizeof( mbedtls_mpi_uint
); i
++, dst
++ )
818 *carry
= ( *dst
< *carry
);
822 #define WIDTH 8 / sizeof( mbedtls_mpi_uint )
823 #define A( i ) N->p + i * WIDTH
824 #define ADD( i ) add64( p, A( i ), &c )
825 #define NEXT p += WIDTH; carry64( p, &c )
826 #define LAST p += WIDTH; *p = c; while( ++p < end ) *p = 0
829 * Fast quasi-reduction modulo p192 (FIPS 186-3 D.2.1)
831 static int ecp_mod_p192( mbedtls_mpi
*N
)
834 mbedtls_mpi_uint c
= 0;
835 mbedtls_mpi_uint
*p
, *end
;
837 /* Make sure we have enough blocks so that A(5) is legal */
838 MBEDTLS_MPI_CHK( mbedtls_mpi_grow( N
, 6 * WIDTH
) );
843 ADD( 3 ); ADD( 5 ); NEXT
; // A0 += A3 + A5
844 ADD( 3 ); ADD( 4 ); ADD( 5 ); NEXT
; // A1 += A3 + A4 + A5
845 ADD( 4 ); ADD( 5 ); LAST
; // A2 += A4 + A5
856 #endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */
858 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) || \
859 defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) || \
860 defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
862 * The reader is advised to first understand ecp_mod_p192() since the same
863 * general structure is used here, but with additional complications:
864 * (1) chunks of 32 bits, and (2) subtractions.
868 * For these primes, we need to handle data in chunks of 32 bits.
869 * This makes it more complicated if we use 64 bits limbs in MPI,
870 * which prevents us from using a uniform access method as for p192.
872 * So, we define a mini abstraction layer to access 32 bit chunks,
873 * load them in 'cur' for work, and store them back from 'cur' when done.
875 * While at it, also define the size of N in terms of 32-bit chunks.
877 #define LOAD32 cur = A( i );
879 #if defined(MBEDTLS_HAVE_INT32) /* 32 bit */
882 #define A( j ) N->p[j]
883 #define STORE32 N->p[i] = cur;
887 #define MAX32 N->n * 2
888 #define A( j ) j % 2 ? (uint32_t)( N->p[j/2] >> 32 ) : (uint32_t)( N->p[j/2] )
891 N->p[i/2] &= 0x00000000FFFFFFFF; \
892 N->p[i/2] |= ((mbedtls_mpi_uint) cur) << 32; \
894 N->p[i/2] &= 0xFFFFFFFF00000000; \
895 N->p[i/2] |= (mbedtls_mpi_uint) cur; \
898 #endif /* sizeof( mbedtls_mpi_uint ) */
901 * Helpers for addition and subtraction of chunks, with signed carry.
903 static inline void add32( uint32_t *dst
, uint32_t src
, signed char *carry
)
906 *carry
+= ( *dst
< src
);
909 static inline void sub32( uint32_t *dst
, uint32_t src
, signed char *carry
)
911 *carry
-= ( *dst
< src
);
915 #define ADD( j ) add32( &cur, A( j ), &c );
916 #define SUB( j ) sub32( &cur, A( j ), &c );
919 * Helpers for the main 'loop'
920 * (see fix_negative for the motivation of C)
924 signed char c = 0, cc; \
926 size_t i = 0, bits = b; \
928 mbedtls_mpi_uint Cp[ b / 8 / sizeof( mbedtls_mpi_uint) + 1 ]; \
931 C.n = b / 8 / sizeof( mbedtls_mpi_uint) + 1; \
933 memset( Cp, 0, C.n * sizeof( mbedtls_mpi_uint ) ); \
935 MBEDTLS_MPI_CHK( mbedtls_mpi_grow( N, b * 2 / 8 / sizeof( mbedtls_mpi_uint ) ) ); \
939 STORE32; i++; LOAD32; \
942 sub32( &cur, -cc, &c ); \
944 add32( &cur, cc, &c ); \
948 cur = c > 0 ? c : 0; STORE32; \
949 cur = 0; while( ++i < MAX32 ) { STORE32; } \
950 if( c < 0 ) fix_negative( N, c, &C, bits );
953 * If the result is negative, we get it in the form
954 * c * 2^(bits + 32) + N, with c negative and N positive shorter than 'bits'
956 static inline int fix_negative( mbedtls_mpi
*N
, signed char c
, mbedtls_mpi
*C
, size_t bits
)
960 /* C = - c * 2^(bits + 32) */
961 #if !defined(MBEDTLS_HAVE_INT64)
965 C
->p
[ C
->n
- 1 ] = ((mbedtls_mpi_uint
) -c
) << 32;
968 C
->p
[ C
->n
- 1 ] = (mbedtls_mpi_uint
) -c
;
970 /* N = - ( C - N ) */
971 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( N
, C
, N
) );
979 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
981 * Fast quasi-reduction modulo p224 (FIPS 186-3 D.2.2)
983 static int ecp_mod_p224( mbedtls_mpi
*N
)
987 SUB( 7 ); SUB( 11 ); NEXT
; // A0 += -A7 - A11
988 SUB( 8 ); SUB( 12 ); NEXT
; // A1 += -A8 - A12
989 SUB( 9 ); SUB( 13 ); NEXT
; // A2 += -A9 - A13
990 SUB( 10 ); ADD( 7 ); ADD( 11 ); NEXT
; // A3 += -A10 + A7 + A11
991 SUB( 11 ); ADD( 8 ); ADD( 12 ); NEXT
; // A4 += -A11 + A8 + A12
992 SUB( 12 ); ADD( 9 ); ADD( 13 ); NEXT
; // A5 += -A12 + A9 + A13
993 SUB( 13 ); ADD( 10 ); LAST
; // A6 += -A13 + A10
998 #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */
1000 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
1002 * Fast quasi-reduction modulo p256 (FIPS 186-3 D.2.3)
1004 static int ecp_mod_p256( mbedtls_mpi
*N
)
1009 SUB( 11 ); SUB( 12 ); SUB( 13 ); SUB( 14 ); NEXT
; // A0
1011 ADD( 9 ); ADD( 10 );
1012 SUB( 12 ); SUB( 13 ); SUB( 14 ); SUB( 15 ); NEXT
; // A1
1014 ADD( 10 ); ADD( 11 );
1015 SUB( 13 ); SUB( 14 ); SUB( 15 ); NEXT
; // A2
1017 ADD( 11 ); ADD( 11 ); ADD( 12 ); ADD( 12 ); ADD( 13 );
1018 SUB( 15 ); SUB( 8 ); SUB( 9 ); NEXT
; // A3
1020 ADD( 12 ); ADD( 12 ); ADD( 13 ); ADD( 13 ); ADD( 14 );
1021 SUB( 9 ); SUB( 10 ); NEXT
; // A4
1023 ADD( 13 ); ADD( 13 ); ADD( 14 ); ADD( 14 ); ADD( 15 );
1024 SUB( 10 ); SUB( 11 ); NEXT
; // A5
1026 ADD( 14 ); ADD( 14 ); ADD( 15 ); ADD( 15 ); ADD( 14 ); ADD( 13 );
1027 SUB( 8 ); SUB( 9 ); NEXT
; // A6
1029 ADD( 15 ); ADD( 15 ); ADD( 15 ); ADD( 8 );
1030 SUB( 10 ); SUB( 11 ); SUB( 12 ); SUB( 13 ); LAST
; // A7
1035 #endif /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */
1037 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
1039 * Fast quasi-reduction modulo p384 (FIPS 186-3 D.2.4)
1041 static int ecp_mod_p384( mbedtls_mpi
*N
)
1045 ADD( 12 ); ADD( 21 ); ADD( 20 );
1046 SUB( 23 ); NEXT
; // A0
1048 ADD( 13 ); ADD( 22 ); ADD( 23 );
1049 SUB( 12 ); SUB( 20 ); NEXT
; // A2
1051 ADD( 14 ); ADD( 23 );
1052 SUB( 13 ); SUB( 21 ); NEXT
; // A2
1054 ADD( 15 ); ADD( 12 ); ADD( 20 ); ADD( 21 );
1055 SUB( 14 ); SUB( 22 ); SUB( 23 ); NEXT
; // A3
1057 ADD( 21 ); ADD( 21 ); ADD( 16 ); ADD( 13 ); ADD( 12 ); ADD( 20 ); ADD( 22 );
1058 SUB( 15 ); SUB( 23 ); SUB( 23 ); NEXT
; // A4
1060 ADD( 22 ); ADD( 22 ); ADD( 17 ); ADD( 14 ); ADD( 13 ); ADD( 21 ); ADD( 23 );
1061 SUB( 16 ); NEXT
; // A5
1063 ADD( 23 ); ADD( 23 ); ADD( 18 ); ADD( 15 ); ADD( 14 ); ADD( 22 );
1064 SUB( 17 ); NEXT
; // A6
1066 ADD( 19 ); ADD( 16 ); ADD( 15 ); ADD( 23 );
1067 SUB( 18 ); NEXT
; // A7
1069 ADD( 20 ); ADD( 17 ); ADD( 16 );
1070 SUB( 19 ); NEXT
; // A8
1072 ADD( 21 ); ADD( 18 ); ADD( 17 );
1073 SUB( 20 ); NEXT
; // A9
1075 ADD( 22 ); ADD( 19 ); ADD( 18 );
1076 SUB( 21 ); NEXT
; // A10
1078 ADD( 23 ); ADD( 20 ); ADD( 19 );
1079 SUB( 22 ); LAST
; // A11
1084 #endif /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */
1094 #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED ||
1095 MBEDTLS_ECP_DP_SECP256R1_ENABLED ||
1096 MBEDTLS_ECP_DP_SECP384R1_ENABLED */
1098 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
1100 * Here we have an actual Mersenne prime, so things are more straightforward.
1101 * However, chunks are aligned on a 'weird' boundary (521 bits).
1104 /* Size of p521 in terms of mbedtls_mpi_uint */
1105 #define P521_WIDTH ( 521 / 8 / sizeof( mbedtls_mpi_uint ) + 1 )
1107 /* Bits to keep in the most significant mbedtls_mpi_uint */
1108 #define P521_MASK 0x01FF
1111 * Fast quasi-reduction modulo p521 (FIPS 186-3 D.2.5)
1112 * Write N as A1 + 2^521 A0, return A0 + A1
1114 static int ecp_mod_p521( mbedtls_mpi
*N
)
1119 mbedtls_mpi_uint Mp
[P521_WIDTH
+ 1];
1120 /* Worst case for the size of M is when mbedtls_mpi_uint is 16 bits:
1121 * we need to hold bits 513 to 1056, which is 34 limbs, that is
1122 * P521_WIDTH + 1. Otherwise P521_WIDTH is enough. */
1124 if( N
->n
< P521_WIDTH
)
1129 M
.n
= N
->n
- ( P521_WIDTH
- 1 );
1130 if( M
.n
> P521_WIDTH
+ 1 )
1131 M
.n
= P521_WIDTH
+ 1;
1133 memcpy( Mp
, N
->p
+ P521_WIDTH
- 1, M
.n
* sizeof( mbedtls_mpi_uint
) );
1134 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M
, 521 % ( 8 * sizeof( mbedtls_mpi_uint
) ) ) );
1137 N
->p
[P521_WIDTH
- 1] &= P521_MASK
;
1138 for( i
= P521_WIDTH
; i
< N
->n
; i
++ )
1142 MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N
, N
, &M
) );
1150 #endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */
1152 #endif /* MBEDTLS_ECP_NIST_OPTIM */
1154 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
1156 /* Size of p255 in terms of mbedtls_mpi_uint */
1157 #define P255_WIDTH ( 255 / 8 / sizeof( mbedtls_mpi_uint ) + 1 )
1160 * Fast quasi-reduction modulo p255 = 2^255 - 19
1161 * Write N as A0 + 2^255 A1, return A0 + 19 * A1
1163 static int ecp_mod_p255( mbedtls_mpi
*N
)
1168 mbedtls_mpi_uint Mp
[P255_WIDTH
+ 2];
1170 if( N
->n
< P255_WIDTH
)
1175 M
.n
= N
->n
- ( P255_WIDTH
- 1 );
1176 if( M
.n
> P255_WIDTH
+ 1 )
1177 M
.n
= P255_WIDTH
+ 1;
1179 memset( Mp
, 0, sizeof Mp
);
1180 memcpy( Mp
, N
->p
+ P255_WIDTH
- 1, M
.n
* sizeof( mbedtls_mpi_uint
) );
1181 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M
, 255 % ( 8 * sizeof( mbedtls_mpi_uint
) ) ) );
1182 M
.n
++; /* Make room for multiplication by 19 */
1185 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( N
, 255, 0 ) );
1186 for( i
= P255_WIDTH
; i
< N
->n
; i
++ )
1189 /* N = A0 + 19 * A1 */
1190 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M
, &M
, 19 ) );
1191 MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N
, N
, &M
) );
1196 #endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */
1198 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) || \
1199 defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) || \
1200 defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
1202 * Fast quasi-reduction modulo P = 2^s - R,
1203 * with R about 33 bits, used by the Koblitz curves.
1205 * Write N as A0 + 2^224 A1, return A0 + R * A1.
1206 * Actually do two passes, since R is big.
1208 #define P_KOBLITZ_MAX ( 256 / 8 / sizeof( mbedtls_mpi_uint ) ) // Max limbs in P
1209 #define P_KOBLITZ_R ( 8 / sizeof( mbedtls_mpi_uint ) ) // Limbs in R
1210 static inline int ecp_mod_koblitz( mbedtls_mpi
*N
, mbedtls_mpi_uint
*Rp
, size_t p_limbs
,
1211 size_t adjust
, size_t shift
, mbedtls_mpi_uint mask
)
1216 mbedtls_mpi_uint Mp
[P_KOBLITZ_MAX
+ P_KOBLITZ_R
];
1218 if( N
->n
< p_limbs
)
1226 /* Common setup for M */
1231 M
.n
= N
->n
- ( p_limbs
- adjust
);
1232 if( M
.n
> p_limbs
+ adjust
)
1233 M
.n
= p_limbs
+ adjust
;
1234 memset( Mp
, 0, sizeof Mp
);
1235 memcpy( Mp
, N
->p
+ p_limbs
- adjust
, M
.n
* sizeof( mbedtls_mpi_uint
) );
1237 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M
, shift
) );
1238 M
.n
+= R
.n
- adjust
; /* Make room for multiplication by R */
1242 N
->p
[p_limbs
- 1] &= mask
;
1243 for( i
= p_limbs
; i
< N
->n
; i
++ )
1246 /* N = A0 + R * A1 */
1247 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &M
, &M
, &R
) );
1248 MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N
, N
, &M
) );
1253 M
.n
= N
->n
- ( p_limbs
- adjust
);
1254 if( M
.n
> p_limbs
+ adjust
)
1255 M
.n
= p_limbs
+ adjust
;
1256 memset( Mp
, 0, sizeof Mp
);
1257 memcpy( Mp
, N
->p
+ p_limbs
- adjust
, M
.n
* sizeof( mbedtls_mpi_uint
) );
1259 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M
, shift
) );
1260 M
.n
+= R
.n
- adjust
; /* Make room for multiplication by R */
1264 N
->p
[p_limbs
- 1] &= mask
;
1265 for( i
= p_limbs
; i
< N
->n
; i
++ )
1268 /* N = A0 + R * A1 */
1269 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &M
, &M
, &R
) );
1270 MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N
, N
, &M
) );
1275 #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED) ||
1276 MBEDTLS_ECP_DP_SECP224K1_ENABLED) ||
1277 MBEDTLS_ECP_DP_SECP256K1_ENABLED) */
1279 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
1281 * Fast quasi-reduction modulo p192k1 = 2^192 - R,
1282 * with R = 2^32 + 2^12 + 2^8 + 2^7 + 2^6 + 2^3 + 1 = 0x0100001119
1284 static int ecp_mod_p192k1( mbedtls_mpi
*N
)
1286 static mbedtls_mpi_uint Rp
[] = {
1287 BYTES_TO_T_UINT_8( 0xC9, 0x11, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) };
1289 return( ecp_mod_koblitz( N
, Rp
, 192 / 8 / sizeof( mbedtls_mpi_uint
), 0, 0, 0 ) );
1291 #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */
1293 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
1295 * Fast quasi-reduction modulo p224k1 = 2^224 - R,
1296 * with R = 2^32 + 2^12 + 2^11 + 2^9 + 2^7 + 2^4 + 2 + 1 = 0x0100001A93
1298 static int ecp_mod_p224k1( mbedtls_mpi
*N
)
1300 static mbedtls_mpi_uint Rp
[] = {
1301 BYTES_TO_T_UINT_8( 0x93, 0x1A, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) };
1303 #if defined(MBEDTLS_HAVE_INT64)
1304 return( ecp_mod_koblitz( N
, Rp
, 4, 1, 32, 0xFFFFFFFF ) );
1306 return( ecp_mod_koblitz( N
, Rp
, 224 / 8 / sizeof( mbedtls_mpi_uint
), 0, 0, 0 ) );
1310 #endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */
1312 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
1314 * Fast quasi-reduction modulo p256k1 = 2^256 - R,
1315 * with R = 2^32 + 2^9 + 2^8 + 2^7 + 2^6 + 2^4 + 1 = 0x01000003D1
1317 static int ecp_mod_p256k1( mbedtls_mpi
*N
)
1319 static mbedtls_mpi_uint Rp
[] = {
1320 BYTES_TO_T_UINT_8( 0xD1, 0x03, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) };
1321 return( ecp_mod_koblitz( N
, Rp
, 256 / 8 / sizeof( mbedtls_mpi_uint
), 0, 0, 0 ) );
1323 #endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */
1325 #endif /* MBEDTLS_ECP_C */