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Manuel Pégourié-Gonnard39d2adb2012-10-31 09:26:55 +01001/*
Manuel Pégourié-Gonnard32b04c12013-12-02 15:49:09 +01002 * Elliptic curves over GF(p): generic functions
Manuel Pégourié-Gonnard39d2adb2012-10-31 09:26:55 +01003 *
Manuel Pégourié-Gonnard6fb81872015-07-27 11:11:48 +02004 * Copyright (C) 2006-2015, ARM Limited, All Rights Reserved
Manuel Pégourié-Gonnard37ff1402015-09-04 14:21:07 +02005 * 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.
Manuel Pégourié-Gonnard39d2adb2012-10-31 09:26:55 +010018 *
Manuel Pégourié-Gonnardfe446432015-03-06 13:17:10 +000019 * This file is part of mbed TLS (https://tls.mbed.org)
Manuel Pégourié-Gonnard39d2adb2012-10-31 09:26:55 +010020 */
21
22/*
23 * References:
24 *
Manuel Pégourié-Gonnard883f3132012-11-02 09:40:25 +010025 * SEC1 http://www.secg.org/index.php?action=secg,docs_secg
Manuel Pégourié-Gonnardd070f512012-11-08 17:40:51 +010026 * GECC = Guide to Elliptic Curve Cryptography - Hankerson, Menezes, Vanstone
Manuel Pégourié-Gonnard62aad142012-11-10 00:27:12 +010027 * FIPS 186-3 http://csrc.nist.gov/publications/fips/fips186-3/fips_186-3.pdf
Manuel Pégourié-Gonnard1a967282013-02-09 17:03:58 +010028 * RFC 4492 for the related TLS structures and constants
Nicholas Wilson08f3ef12015-11-10 13:10:01 +000029 * RFC 7748 for the Curve448 and Curve25519 curve definitions
Manuel Pégourié-Gonnard07de4b12013-09-02 16:26:04 +020030 *
Manuel Pégourié-Gonnard07894332015-06-23 00:18:41 +020031 * [Curve25519] http://cr.yp.to/ecdh/curve25519-20060209.pdf
Manuel Pégourié-Gonnardfe0af402013-12-04 18:14:55 +010032 *
Manuel Pégourié-Gonnard998930a2015-04-03 13:48:06 +020033 * [2] CORON, Jean-S'ebastien. Resistance against differential power analysis
Manuel Pégourié-Gonnard07de4b12013-09-02 16:26:04 +020034 * for elliptic curve cryptosystems. In : Cryptographic Hardware and
35 * Embedded Systems. Springer Berlin Heidelberg, 1999. p. 292-302.
36 * <http://link.springer.com/chapter/10.1007/3-540-48059-5_25>
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +010037 *
Manuel Pégourié-Gonnard998930a2015-04-03 13:48:06 +020038 * [3] HEDABOU, Mustapha, PINEL, Pierre, et B'EN'ETEAU, Lucien. A comb method to
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +010039 * render ECC resistant against Side Channel Attacks. IACR Cryptology
40 * ePrint Archive, 2004, vol. 2004, p. 342.
41 * <http://eprint.iacr.org/2004/342.pdf>
Manuel Pégourié-Gonnard39d2adb2012-10-31 09:26:55 +010042 */
43
Gilles Peskinedb09ef62020-06-03 01:43:33 +020044#include "common.h"
Manuel Pégourié-Gonnard39d2adb2012-10-31 09:26:55 +010045
Andrzej Kurekc470b6b2019-01-31 08:20:20 -050046/**
47 * \brief Function level alternative implementation.
48 *
49 * The MBEDTLS_ECP_INTERNAL_ALT macro enables alternative implementations to
50 * replace certain functions in this module. The alternative implementations are
51 * typically hardware accelerators and need to activate the hardware before the
52 * computation starts and deactivate it after it finishes. The
53 * mbedtls_internal_ecp_init() and mbedtls_internal_ecp_free() functions serve
54 * this purpose.
55 *
56 * To preserve the correct functionality the following conditions must hold:
57 *
58 * - The alternative implementation must be activated by
59 * mbedtls_internal_ecp_init() before any of the replaceable functions is
60 * called.
61 * - mbedtls_internal_ecp_free() must \b only be called when the alternative
62 * implementation is activated.
63 * - mbedtls_internal_ecp_init() must \b not be called when the alternative
64 * implementation is activated.
65 * - Public functions must not return while the alternative implementation is
66 * activated.
67 * - Replaceable functions are guarded by \c MBEDTLS_ECP_XXX_ALT macros and
68 * before calling them an \code if( mbedtls_internal_ecp_grp_capable( grp ) )
69 * \endcode ensures that the alternative implementation supports the current
70 * group.
71 */
72#if defined(MBEDTLS_ECP_INTERNAL_ALT)
73#endif
74
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +020075#if defined(MBEDTLS_ECP_C)
Manuel Pégourié-Gonnard39d2adb2012-10-31 09:26:55 +010076
Manuel Pégourié-Gonnard7f809972015-03-09 17:05:11 +000077#include "mbedtls/ecp.h"
Janos Follath430d3372016-11-03 14:25:37 +000078#include "mbedtls/threading.h"
Andres Amaya Garcia1f6301b2018-04-17 09:51:09 -050079#include "mbedtls/platform_util.h"
Janos Follath24eed8d2019-11-22 13:21:35 +000080#include "mbedtls/error.h"
Paul Bakker6e339b52013-07-03 13:37:05 +020081
Rich Evans00ab4702015-02-06 13:43:58 +000082#include <string.h>
83
Janos Follathb0697532016-08-18 12:38:46 +010084#if !defined(MBEDTLS_ECP_ALT)
85
Andrzej Kurekc470b6b2019-01-31 08:20:20 -050086/* Parameter validation macros based on platform_util.h */
87#define ECP_VALIDATE_RET( cond ) \
88 MBEDTLS_INTERNAL_VALIDATE_RET( cond, MBEDTLS_ERR_ECP_BAD_INPUT_DATA )
89#define ECP_VALIDATE( cond ) \
90 MBEDTLS_INTERNAL_VALIDATE( cond )
91
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +020092#if defined(MBEDTLS_PLATFORM_C)
Manuel Pégourié-Gonnard7f809972015-03-09 17:05:11 +000093#include "mbedtls/platform.h"
Paul Bakker6e339b52013-07-03 13:37:05 +020094#else
Rich Evans00ab4702015-02-06 13:43:58 +000095#include <stdlib.h>
Manuel Pégourié-Gonnard981732b2015-02-17 15:46:45 +000096#include <stdio.h>
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +020097#define mbedtls_printf printf
Manuel Pégourié-Gonnard7551cb92015-05-26 16:04:06 +020098#define mbedtls_calloc calloc
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +020099#define mbedtls_free free
Paul Bakker6e339b52013-07-03 13:37:05 +0200100#endif
101
Janos Follath47d28f02016-11-01 13:22:05 +0000102#include "mbedtls/ecp_internal.h"
Janos Follathb0697532016-08-18 12:38:46 +0100103
Manuel Pégourié-Gonnardc52a43c2020-05-22 12:12:36 +0200104#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
Manuel Pégourié-Gonnardd53ef2f2020-06-04 12:32:14 +0200105#if defined(MBEDTLS_HMAC_DRBG_C)
Manuel Pégourié-Gonnardc52a43c2020-05-22 12:12:36 +0200106#include "mbedtls/hmac_drbg.h"
Manuel Pégourié-Gonnardd53ef2f2020-06-04 12:32:14 +0200107#elif defined(MBEDTLS_CTR_DRBG_C)
108#include "mbedtls/ctr_drbg.h"
Manuel Pégourié-Gonnardc52a43c2020-05-22 12:12:36 +0200109#else
110#error "Invalid configuration detected. Include check_config.h to ensure that the configuration is valid."
111#endif
112#endif /* MBEDTLS_ECP_NO_INTERNAL_RNG */
113
Manuel Pégourié-Gonnard0223ab92015-10-05 11:40:01 +0100114#if ( defined(__ARMCC_VERSION) || defined(_MSC_VER) ) && \
115 !defined(inline) && !defined(__cplusplus)
Paul Bakker6a6087e2013-10-28 18:53:08 +0100116#define inline __inline
Manuel Pégourié-Gonnard20af64d2015-07-07 18:33:39 +0200117#endif
Paul Bakker6a6087e2013-10-28 18:53:08 +0100118
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200119#if defined(MBEDTLS_SELF_TEST)
Manuel Pégourié-Gonnardb4a310b2012-11-13 20:57:00 +0100120/*
Manuel Pégourié-Gonnard91814812013-11-21 20:23:55 +0100121 * Counts of point addition and doubling, and field multiplications.
Manuel Pégourié-Gonnard07de4b12013-09-02 16:26:04 +0200122 * Used to test resistance of point multiplication to simple timing attacks.
Manuel Pégourié-Gonnardb4a310b2012-11-13 20:57:00 +0100123 */
Manuel Pégourié-Gonnard43863ee2013-12-01 16:51:27 +0100124static unsigned long add_count, dbl_count, mul_count;
Manuel Pégourié-Gonnardb4a310b2012-11-13 20:57:00 +0100125#endif
126
Manuel Pégourié-Gonnardc52a43c2020-05-22 12:12:36 +0200127#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
128/*
129 * Currently ecp_mul() takes a RNG function as an argument, used for
Manuel Pégourié-Gonnard25705e62020-06-10 09:18:25 +0200130 * side-channel protection, but it can be NULL. The initial reasoning was
Manuel Pégourié-Gonnardc52a43c2020-05-22 12:12:36 +0200131 * that people will pass non-NULL RNG when they care about side-channels, but
132 * unfortunately we have some APIs that call ecp_mul() with a NULL RNG, with
133 * no opportunity for the user to do anything about it.
134 *
135 * The obvious strategies for addressing that include:
136 * - change those APIs so that they take RNG arguments;
137 * - require a global RNG to be available to all crypto modules.
138 *
139 * Unfortunately those would break compatibility. So what we do instead is
140 * have our own internal DRBG instance, seeded from the secret scalar.
141 *
142 * The following is a light-weight abstraction layer for doing that with
Manuel Pégourié-Gonnardd53ef2f2020-06-04 12:32:14 +0200143 * HMAC_DRBG (first choice) or CTR_DRBG.
Manuel Pégourié-Gonnardc52a43c2020-05-22 12:12:36 +0200144 */
145
Manuel Pégourié-Gonnardd53ef2f2020-06-04 12:32:14 +0200146#if defined(MBEDTLS_HMAC_DRBG_C)
147
148/* DRBG context type */
149typedef mbedtls_hmac_drbg_context ecp_drbg_context;
150
151/* DRBG context init */
152static inline void ecp_drbg_init( ecp_drbg_context *ctx )
153{
154 mbedtls_hmac_drbg_init( ctx );
155}
156
157/* DRBG context free */
158static inline void ecp_drbg_free( ecp_drbg_context *ctx )
159{
160 mbedtls_hmac_drbg_free( ctx );
161}
162
163/* DRBG function */
164static inline int ecp_drbg_random( void *p_rng,
165 unsigned char *output, size_t output_len )
166{
167 return( mbedtls_hmac_drbg_random( p_rng, output, output_len ) );
168}
169
170/* DRBG context seeding */
Manuel Pégourié-Gonnard4539a452020-06-18 12:27:56 +0200171static int ecp_drbg_seed( ecp_drbg_context *ctx,
172 const mbedtls_mpi *secret, size_t secret_len )
Manuel Pégourié-Gonnardd53ef2f2020-06-04 12:32:14 +0200173{
Manuel Pégourié-Gonnard4539a452020-06-18 12:27:56 +0200174 int ret;
175 unsigned char secret_bytes[MBEDTLS_ECP_MAX_BYTES];
Manuel Pégourié-Gonnardd53ef2f2020-06-04 12:32:14 +0200176 /* The list starts with strong hashes */
177 const mbedtls_md_type_t md_type = mbedtls_md_list()[0];
178 const mbedtls_md_info_t *md_info = mbedtls_md_info_from_type( md_type );
179
Manuel Pégourié-Gonnard1215c542020-06-19 11:59:49 +0200180 if( secret_len > MBEDTLS_ECP_MAX_BYTES )
181 {
182 ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
183 goto cleanup;
184 }
185
Manuel Pégourié-Gonnard4539a452020-06-18 12:27:56 +0200186 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( secret,
187 secret_bytes, secret_len ) );
188
189 ret = mbedtls_hmac_drbg_seed_buf( ctx, md_info, secret_bytes, secret_len );
190
191cleanup:
192 mbedtls_platform_zeroize( secret_bytes, secret_len );
193
194 return( ret );
Manuel Pégourié-Gonnardd53ef2f2020-06-04 12:32:14 +0200195}
196
197#elif defined(MBEDTLS_CTR_DRBG_C)
198
Manuel Pégourié-Gonnardc52a43c2020-05-22 12:12:36 +0200199/* DRBG context type */
200typedef mbedtls_ctr_drbg_context ecp_drbg_context;
201
202/* DRBG context init */
203static inline void ecp_drbg_init( ecp_drbg_context *ctx )
204{
205 mbedtls_ctr_drbg_init( ctx );
206}
207
208/* DRBG context free */
209static inline void ecp_drbg_free( ecp_drbg_context *ctx )
210{
211 mbedtls_ctr_drbg_free( ctx );
212}
213
214/* DRBG function */
215static inline int ecp_drbg_random( void *p_rng,
216 unsigned char *output, size_t output_len )
217{
218 return( mbedtls_ctr_drbg_random( p_rng, output, output_len ) );
219}
220
221/*
222 * Since CTR_DRBG doesn't have a seed_buf() function the way HMAC_DRBG does,
223 * we need to pass an entropy function when seeding. So we use a dummy
224 * function for that, and pass the actual entropy as customisation string.
225 * (During seeding of CTR_DRBG the entropy input and customisation string are
226 * concatenated before being used to update the secret state.)
227 */
228static int ecp_ctr_drbg_null_entropy(void *ctx, unsigned char *out, size_t len)
229{
230 (void) ctx;
231 memset( out, 0, len );
232 return( 0 );
233}
234
235/* DRBG context seeding */
Manuel Pégourié-Gonnard4539a452020-06-18 12:27:56 +0200236static int ecp_drbg_seed( ecp_drbg_context *ctx,
237 const mbedtls_mpi *secret, size_t secret_len )
Manuel Pégourié-Gonnardc52a43c2020-05-22 12:12:36 +0200238{
Manuel Pégourié-Gonnard4539a452020-06-18 12:27:56 +0200239 int ret;
240 unsigned char secret_bytes[MBEDTLS_ECP_MAX_BYTES];
Manuel Pégourié-Gonnardc52a43c2020-05-22 12:12:36 +0200241
Manuel Pégourié-Gonnard1215c542020-06-19 11:59:49 +0200242 if( secret_len > MBEDTLS_ECP_MAX_BYTES )
243 {
244 ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
245 goto cleanup;
246 }
247
Manuel Pégourié-Gonnard4539a452020-06-18 12:27:56 +0200248 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( secret,
249 secret_bytes, secret_len ) );
250
251 ret = mbedtls_ctr_drbg_seed( ctx, ecp_ctr_drbg_null_entropy, NULL,
252 secret_bytes, secret_len );
253
254cleanup:
255 mbedtls_platform_zeroize( secret_bytes, secret_len );
256
257 return( ret );
Manuel Pégourié-Gonnardc52a43c2020-05-22 12:12:36 +0200258}
259
Manuel Pégourié-Gonnardc52a43c2020-05-22 12:12:36 +0200260#else
261#error "Invalid configuration detected. Include check_config.h to ensure that the configuration is valid."
262#endif /* DRBG modules */
263#endif /* MBEDTLS_ECP_NO_INTERNAL_RNG */
264
Manuel Pégourié-Gonnard4b9c51e2017-04-20 15:50:26 +0200265#if defined(MBEDTLS_ECP_RESTARTABLE)
Manuel Pégourié-Gonnard054433c2017-03-22 11:18:33 +0100266/*
267 * Maximum number of "basic operations" to be done in a row.
Manuel Pégourié-Gonnard7037e222017-08-23 14:30:36 +0200268 *
269 * Default value 0 means that ECC operations will not yield.
270 * Note that regardless of the value of ecp_max_ops, always at
271 * least one step is performed before yielding.
272 *
273 * Setting ecp_max_ops=1 can be suitable for testing purposes
274 * as it will interrupt computation at all possible points.
Manuel Pégourié-Gonnard054433c2017-03-22 11:18:33 +0100275 */
276static unsigned ecp_max_ops = 0;
277
278/*
279 * Set ecp_max_ops
280 */
281void mbedtls_ecp_set_max_ops( unsigned max_ops )
282{
283 ecp_max_ops = max_ops;
284}
Manuel Pégourié-Gonnard510d5ca2017-03-08 11:41:47 +0100285
286/*
Manuel Pégourié-Gonnarda0c5bcc2017-04-21 11:33:57 +0200287 * Check if restart is enabled
288 */
Manuel Pégourié-Gonnardb843b152018-10-16 10:41:31 +0200289int mbedtls_ecp_restart_is_enabled( void )
Manuel Pégourié-Gonnarda0c5bcc2017-04-21 11:33:57 +0200290{
291 return( ecp_max_ops != 0 );
292}
293
294/*
Manuel Pégourié-Gonnard54dd6522017-04-20 13:36:18 +0200295 * Restart sub-context for ecp_mul_comb()
Manuel Pégourié-Gonnard510d5ca2017-03-08 11:41:47 +0100296 */
Manuel Pégourié-Gonnard54dd6522017-04-20 13:36:18 +0200297struct mbedtls_ecp_restart_mul
298{
Manuel Pégourié-Gonnard8962ddb2017-03-14 12:11:21 +0100299 mbedtls_ecp_point R; /* current intermediate result */
Manuel Pégourié-Gonnardc5d844b2017-03-15 13:06:28 +0100300 size_t i; /* current index in various loops, 0 outside */
Manuel Pégourié-Gonnardc9c0aa62017-03-16 14:53:26 +0100301 mbedtls_ecp_point *T; /* table for precomputed points */
302 unsigned char T_size; /* number of points in table T */
Manuel Pégourié-Gonnard4ed1dab2017-08-24 11:02:04 +0200303 enum { /* what were we doing last time we returned? */
304 ecp_rsm_init = 0, /* nothing so far, dummy initial state */
305 ecp_rsm_pre_dbl, /* precompute 2^n multiples */
Manuel Pégourié-Gonnard45fd0162017-03-22 08:24:42 +0100306 ecp_rsm_pre_norm_dbl, /* normalize precomputed 2^n multiples */
307 ecp_rsm_pre_add, /* precompute remaining points by adding */
308 ecp_rsm_pre_norm_add, /* normalize all precomputed points */
Manuel Pégourié-Gonnard4ed1dab2017-08-24 11:02:04 +0200309 ecp_rsm_comb_core, /* ecp_mul_comb_core() */
Manuel Pégourié-Gonnard45fd0162017-03-22 08:24:42 +0100310 ecp_rsm_final_norm, /* do the final normalization */
Manuel Pégourié-Gonnard2fad7ae2017-03-14 13:13:13 +0100311 } state;
Manuel Pégourié-Gonnard53fb66d2020-06-04 09:43:14 +0200312#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
313 ecp_drbg_context drbg_ctx;
314 unsigned char drbg_seeded;
315#endif
Manuel Pégourié-Gonnard77af79a2017-03-14 10:58:00 +0100316};
Manuel Pégourié-Gonnard510d5ca2017-03-08 11:41:47 +0100317
318/*
Manuel Pégourié-Gonnard54dd6522017-04-20 13:36:18 +0200319 * Init restart_mul sub-context
Manuel Pégourié-Gonnard510d5ca2017-03-08 11:41:47 +0100320 */
Manuel Pégourié-Gonnarddb4a8eb2017-08-23 18:18:22 +0200321static void ecp_restart_rsm_init( mbedtls_ecp_restart_mul_ctx *ctx )
Manuel Pégourié-Gonnard77af79a2017-03-14 10:58:00 +0100322{
Manuel Pégourié-Gonnard5bd38b12017-08-23 16:55:59 +0200323 mbedtls_ecp_point_init( &ctx->R );
324 ctx->i = 0;
325 ctx->T = NULL;
326 ctx->T_size = 0;
327 ctx->state = ecp_rsm_init;
Manuel Pégourié-Gonnard53fb66d2020-06-04 09:43:14 +0200328#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
329 ecp_drbg_init( &ctx->drbg_ctx );
330 ctx->drbg_seeded = 0;
331#endif
Manuel Pégourié-Gonnard77af79a2017-03-14 10:58:00 +0100332}
333
334/*
Manuel Pégourié-Gonnard54dd6522017-04-20 13:36:18 +0200335 * Free the components of a restart_mul sub-context
Manuel Pégourié-Gonnard77af79a2017-03-14 10:58:00 +0100336 */
Manuel Pégourié-Gonnarddb4a8eb2017-08-23 18:18:22 +0200337static void ecp_restart_rsm_free( mbedtls_ecp_restart_mul_ctx *ctx )
Manuel Pégourié-Gonnard77af79a2017-03-14 10:58:00 +0100338{
Manuel Pégourié-Gonnardc9c0aa62017-03-16 14:53:26 +0100339 unsigned char i;
340
Manuel Pégourié-Gonnard77af79a2017-03-14 10:58:00 +0100341 if( ctx == NULL )
342 return;
Manuel Pégourié-Gonnard78d564a2017-03-14 11:48:38 +0100343
Manuel Pégourié-Gonnard8962ddb2017-03-14 12:11:21 +0100344 mbedtls_ecp_point_free( &ctx->R );
Manuel Pégourié-Gonnard2fad7ae2017-03-14 13:13:13 +0100345
Manuel Pégourié-Gonnard31f0ef72017-05-17 10:05:58 +0200346 if( ctx->T != NULL )
347 {
Manuel Pégourié-Gonnardc9c0aa62017-03-16 14:53:26 +0100348 for( i = 0; i < ctx->T_size; i++ )
349 mbedtls_ecp_point_free( ctx->T + i );
350 mbedtls_free( ctx->T );
351 }
352
Manuel Pégourié-Gonnard53fb66d2020-06-04 09:43:14 +0200353#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
354 ecp_drbg_free( &ctx->drbg_ctx );
355#endif
356
Manuel Pégourié-Gonnarddb4a8eb2017-08-23 18:18:22 +0200357 ecp_restart_rsm_init( ctx );
Manuel Pégourié-Gonnard77af79a2017-03-14 10:58:00 +0100358}
Manuel Pégourié-Gonnard2fad7ae2017-03-14 13:13:13 +0100359
360/*
Manuel Pégourié-Gonnard54dd6522017-04-20 13:36:18 +0200361 * Restart context for ecp_muladd()
362 */
363struct mbedtls_ecp_restart_muladd
364{
Manuel Pégourié-Gonnard1631d632017-04-20 14:48:56 +0200365 mbedtls_ecp_point mP; /* mP value */
366 mbedtls_ecp_point R; /* R intermediate result */
367 enum { /* what should we do next? */
368 ecp_rsma_mul1 = 0, /* first multiplication */
369 ecp_rsma_mul2, /* second multiplication */
370 ecp_rsma_add, /* addition */
371 ecp_rsma_norm, /* normalization */
372 } state;
Manuel Pégourié-Gonnard54dd6522017-04-20 13:36:18 +0200373};
374
375/*
376 * Init restart_muladd sub-context
377 */
Manuel Pégourié-Gonnarddb4a8eb2017-08-23 18:18:22 +0200378static void ecp_restart_ma_init( mbedtls_ecp_restart_muladd_ctx *ctx )
Manuel Pégourié-Gonnard54dd6522017-04-20 13:36:18 +0200379{
Manuel Pégourié-Gonnard5bd38b12017-08-23 16:55:59 +0200380 mbedtls_ecp_point_init( &ctx->mP );
381 mbedtls_ecp_point_init( &ctx->R );
382 ctx->state = ecp_rsma_mul1;
Manuel Pégourié-Gonnard54dd6522017-04-20 13:36:18 +0200383}
384
385/*
386 * Free the components of a restart_muladd sub-context
387 */
Manuel Pégourié-Gonnarddb4a8eb2017-08-23 18:18:22 +0200388static void ecp_restart_ma_free( mbedtls_ecp_restart_muladd_ctx *ctx )
Manuel Pégourié-Gonnard54dd6522017-04-20 13:36:18 +0200389{
390 if( ctx == NULL )
391 return;
392
Manuel Pégourié-Gonnard1631d632017-04-20 14:48:56 +0200393 mbedtls_ecp_point_free( &ctx->mP );
394 mbedtls_ecp_point_free( &ctx->R );
395
Manuel Pégourié-Gonnarddb4a8eb2017-08-23 18:18:22 +0200396 ecp_restart_ma_init( ctx );
Manuel Pégourié-Gonnard54dd6522017-04-20 13:36:18 +0200397}
398
399/*
Manuel Pégourié-Gonnardb739a712017-04-19 10:11:56 +0200400 * Initialize a restart context
401 */
402void mbedtls_ecp_restart_init( mbedtls_ecp_restart_ctx *ctx )
403{
Andrzej Kurekc470b6b2019-01-31 08:20:20 -0500404 ECP_VALIDATE( ctx != NULL );
Manuel Pégourié-Gonnard5bd38b12017-08-23 16:55:59 +0200405 ctx->ops_done = 0;
406 ctx->depth = 0;
407 ctx->rsm = NULL;
408 ctx->ma = NULL;
Manuel Pégourié-Gonnardb739a712017-04-19 10:11:56 +0200409}
410
411/*
412 * Free the components of a restart context
413 */
414void mbedtls_ecp_restart_free( mbedtls_ecp_restart_ctx *ctx )
415{
416 if( ctx == NULL )
417 return;
418
Manuel Pégourié-Gonnarddb4a8eb2017-08-23 18:18:22 +0200419 ecp_restart_rsm_free( ctx->rsm );
Manuel Pégourié-Gonnardb739a712017-04-19 10:11:56 +0200420 mbedtls_free( ctx->rsm );
Manuel Pégourié-Gonnard1631d632017-04-20 14:48:56 +0200421
Manuel Pégourié-Gonnarddb4a8eb2017-08-23 18:18:22 +0200422 ecp_restart_ma_free( ctx->ma );
Manuel Pégourié-Gonnard1631d632017-04-20 14:48:56 +0200423 mbedtls_free( ctx->ma );
Manuel Pégourié-Gonnard5bd38b12017-08-23 16:55:59 +0200424
425 mbedtls_ecp_restart_init( ctx );
Manuel Pégourié-Gonnardb739a712017-04-19 10:11:56 +0200426}
427
428/*
Manuel Pégourié-Gonnard2fad7ae2017-03-14 13:13:13 +0100429 * Check if we can do the next step
430 */
Manuel Pégourié-Gonnardc7511482017-04-20 16:31:00 +0200431int mbedtls_ecp_check_budget( const mbedtls_ecp_group *grp,
432 mbedtls_ecp_restart_ctx *rs_ctx,
433 unsigned ops )
Manuel Pégourié-Gonnard2fad7ae2017-03-14 13:13:13 +0100434{
Andrzej Kurekc470b6b2019-01-31 08:20:20 -0500435 ECP_VALIDATE_RET( grp != NULL );
436
Manuel Pégourié-Gonnard646393b2017-04-20 10:03:45 +0200437 if( rs_ctx != NULL && ecp_max_ops != 0 )
Manuel Pégourié-Gonnard2fad7ae2017-03-14 13:13:13 +0100438 {
Manuel Pégourié-Gonnarde6854492017-03-20 14:35:19 +0100439 /* scale depending on curve size: the chosen reference is 256-bit,
440 * and multiplication is quadratic. Round to the closest integer. */
441 if( grp->pbits >= 512 )
442 ops *= 4;
443 else if( grp->pbits >= 384 )
444 ops *= 2;
445
Hanno Beckerb10c6602018-10-26 13:50:13 +0100446 /* Avoid infinite loops: always allow first step.
447 * Because of that, however, it's not generally true
448 * that ops_done <= ecp_max_ops, so the check
449 * ops_done > ecp_max_ops below is mandatory. */
450 if( ( rs_ctx->ops_done != 0 ) &&
451 ( rs_ctx->ops_done > ecp_max_ops ||
452 ops > ecp_max_ops - rs_ctx->ops_done ) )
453 {
Manuel Pégourié-Gonnard2fad7ae2017-03-14 13:13:13 +0100454 return( MBEDTLS_ERR_ECP_IN_PROGRESS );
Hanno Beckerb10c6602018-10-26 13:50:13 +0100455 }
Manuel Pégourié-Gonnard2fad7ae2017-03-14 13:13:13 +0100456
Manuel Pégourié-Gonnarde6854492017-03-20 14:35:19 +0100457 /* update running count */
Manuel Pégourié-Gonnard646393b2017-04-20 10:03:45 +0200458 rs_ctx->ops_done += ops;
Manuel Pégourié-Gonnard2fad7ae2017-03-14 13:13:13 +0100459 }
460
461 return( 0 );
462}
463
Manuel Pégourié-Gonnarddb4a8eb2017-08-23 18:18:22 +0200464/* Call this when entering a function that needs its own sub-context */
Manuel Pégourié-Gonnarda58e0112018-10-16 10:42:47 +0200465#define ECP_RS_ENTER( SUB ) do { \
466 /* reset ops count for this call if top-level */ \
467 if( rs_ctx != NULL && rs_ctx->depth++ == 0 ) \
468 rs_ctx->ops_done = 0; \
469 \
470 /* set up our own sub-context if needed */ \
471 if( mbedtls_ecp_restart_is_enabled() && \
472 rs_ctx != NULL && rs_ctx->SUB == NULL ) \
473 { \
474 rs_ctx->SUB = mbedtls_calloc( 1, sizeof( *rs_ctx->SUB ) ); \
475 if( rs_ctx->SUB == NULL ) \
476 return( MBEDTLS_ERR_ECP_ALLOC_FAILED ); \
477 \
478 ecp_restart_## SUB ##_init( rs_ctx->SUB ); \
479 } \
Manuel Pégourié-Gonnarddb4a8eb2017-08-23 18:18:22 +0200480} while( 0 )
481
482/* Call this when leaving a function that needs its own sub-context */
Manuel Pégourié-Gonnarda58e0112018-10-16 10:42:47 +0200483#define ECP_RS_LEAVE( SUB ) do { \
484 /* clear our sub-context when not in progress (done or error) */ \
485 if( rs_ctx != NULL && rs_ctx->SUB != NULL && \
486 ret != MBEDTLS_ERR_ECP_IN_PROGRESS ) \
487 { \
488 ecp_restart_## SUB ##_free( rs_ctx->SUB ); \
489 mbedtls_free( rs_ctx->SUB ); \
490 rs_ctx->SUB = NULL; \
491 } \
492 \
493 if( rs_ctx != NULL ) \
494 rs_ctx->depth--; \
Manuel Pégourié-Gonnarddb4a8eb2017-08-23 18:18:22 +0200495} while( 0 )
496
497#else /* MBEDTLS_ECP_RESTARTABLE */
498
499#define ECP_RS_ENTER( sub ) (void) rs_ctx;
500#define ECP_RS_LEAVE( sub ) (void) rs_ctx;
501
Manuel Pégourié-Gonnard4b9c51e2017-04-20 15:50:26 +0200502#endif /* MBEDTLS_ECP_RESTARTABLE */
Manuel Pégourié-Gonnard054433c2017-03-22 11:18:33 +0100503
Manuel Pégourié-Gonnard7c94d8b2013-12-04 23:15:46 +0100504/*
Manuel Pégourié-Gonnard568c9cf2013-09-16 17:30:04 +0200505 * List of supported curves:
506 * - internal ID
Christoph M. Wintersteigercb310732019-02-15 15:50:38 +0000507 * - TLS NamedCurve ID (RFC 4492 sec. 5.1.1, RFC 7071 sec. 2, RFC 8446 sec. 4.2.7)
Manuel Pégourié-Gonnard568c9cf2013-09-16 17:30:04 +0200508 * - size in bits
Manuel Pégourié-Gonnard8195c1a2013-10-07 19:40:41 +0200509 * - readable name
Gergely Budaie40c4692014-01-22 11:22:20 +0100510 *
Manuel Pégourié-Gonnardac719412014-02-04 14:48:50 +0100511 * Curves are listed in order: largest curves first, and for a given size,
512 * fastest curves first. This provides the default order for the SSL module.
Manuel Pégourié-Gonnard88db5da2015-06-15 14:34:59 +0200513 *
Gilles Peskine1174db52020-02-26 19:52:06 +0100514 * Reminder: update profiles in x509_crt.c when adding a new curves!
Manuel Pégourié-Gonnard568c9cf2013-09-16 17:30:04 +0200515 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200516static const mbedtls_ecp_curve_info ecp_supported_curves[] =
Manuel Pégourié-Gonnard568c9cf2013-09-16 17:30:04 +0200517{
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200518#if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
519 { MBEDTLS_ECP_DP_SECP521R1, 25, 521, "secp521r1" },
Manuel Pégourié-Gonnard568c9cf2013-09-16 17:30:04 +0200520#endif
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200521#if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED)
522 { MBEDTLS_ECP_DP_BP512R1, 28, 512, "brainpoolP512r1" },
Gergely Budaie40c4692014-01-22 11:22:20 +0100523#endif
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200524#if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
525 { MBEDTLS_ECP_DP_SECP384R1, 24, 384, "secp384r1" },
Manuel Pégourié-Gonnard568c9cf2013-09-16 17:30:04 +0200526#endif
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200527#if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED)
528 { MBEDTLS_ECP_DP_BP384R1, 27, 384, "brainpoolP384r1" },
Gergely Budaie40c4692014-01-22 11:22:20 +0100529#endif
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200530#if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
531 { MBEDTLS_ECP_DP_SECP256R1, 23, 256, "secp256r1" },
Manuel Pégourié-Gonnard568c9cf2013-09-16 17:30:04 +0200532#endif
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200533#if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
534 { MBEDTLS_ECP_DP_SECP256K1, 22, 256, "secp256k1" },
Manuel Pégourié-Gonnardac719412014-02-04 14:48:50 +0100535#endif
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200536#if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED)
537 { MBEDTLS_ECP_DP_BP256R1, 26, 256, "brainpoolP256r1" },
Gergely Budaie40c4692014-01-22 11:22:20 +0100538#endif
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200539#if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
540 { MBEDTLS_ECP_DP_SECP224R1, 21, 224, "secp224r1" },
Manuel Pégourié-Gonnard568c9cf2013-09-16 17:30:04 +0200541#endif
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200542#if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
543 { MBEDTLS_ECP_DP_SECP224K1, 20, 224, "secp224k1" },
Manuel Pégourié-Gonnard9bcff392014-01-10 18:26:48 +0100544#endif
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200545#if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
546 { MBEDTLS_ECP_DP_SECP192R1, 19, 192, "secp192r1" },
Manuel Pégourié-Gonnardac719412014-02-04 14:48:50 +0100547#endif
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200548#if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
549 { MBEDTLS_ECP_DP_SECP192K1, 18, 192, "secp192k1" },
Manuel Pégourié-Gonnard9bcff392014-01-10 18:26:48 +0100550#endif
Christoph M. Wintersteiger2c69d102019-02-22 15:05:02 +0000551#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) && defined(MBEDTLS_ECDH_VARIANT_EVEREST_ENABLED)
Christoph M. Wintersteiger86e36c42018-12-06 17:27:31 +0000552 { MBEDTLS_ECP_DP_CURVE25519, 29, 256, "x25519" },
Christoph M. Wintersteigerc9f737b2018-10-25 13:03:05 +0100553#endif
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200554 { MBEDTLS_ECP_DP_NONE, 0, 0, NULL },
Manuel Pégourié-Gonnard568c9cf2013-09-16 17:30:04 +0200555};
Manuel Pégourié-Gonnardac719412014-02-04 14:48:50 +0100556
Manuel Pégourié-Gonnardba782bb2014-07-08 13:31:34 +0200557#define ECP_NB_CURVES sizeof( ecp_supported_curves ) / \
558 sizeof( ecp_supported_curves[0] )
559
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200560static mbedtls_ecp_group_id ecp_supported_grp_id[ECP_NB_CURVES];
Manuel Pégourié-Gonnard568c9cf2013-09-16 17:30:04 +0200561
562/*
Manuel Pégourié-Gonnardda179e42013-09-18 15:31:24 +0200563 * List of supported curves and associated info
564 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200565const mbedtls_ecp_curve_info *mbedtls_ecp_curve_list( void )
Manuel Pégourié-Gonnardda179e42013-09-18 15:31:24 +0200566{
Paul Bakkerd8bb8262014-06-17 14:06:49 +0200567 return( ecp_supported_curves );
Manuel Pégourié-Gonnardda179e42013-09-18 15:31:24 +0200568}
569
570/*
Manuel Pégourié-Gonnardac719412014-02-04 14:48:50 +0100571 * List of supported curves, group ID only
572 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200573const mbedtls_ecp_group_id *mbedtls_ecp_grp_id_list( void )
Manuel Pégourié-Gonnardac719412014-02-04 14:48:50 +0100574{
575 static int init_done = 0;
576
577 if( ! init_done )
578 {
579 size_t i = 0;
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200580 const mbedtls_ecp_curve_info *curve_info;
Manuel Pégourié-Gonnardac719412014-02-04 14:48:50 +0100581
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200582 for( curve_info = mbedtls_ecp_curve_list();
583 curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
Manuel Pégourié-Gonnardac719412014-02-04 14:48:50 +0100584 curve_info++ )
585 {
586 ecp_supported_grp_id[i++] = curve_info->grp_id;
587 }
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200588 ecp_supported_grp_id[i] = MBEDTLS_ECP_DP_NONE;
Manuel Pégourié-Gonnardac719412014-02-04 14:48:50 +0100589
590 init_done = 1;
591 }
592
Paul Bakkerd8bb8262014-06-17 14:06:49 +0200593 return( ecp_supported_grp_id );
Manuel Pégourié-Gonnardac719412014-02-04 14:48:50 +0100594}
595
596/*
597 * Get the curve info for the internal identifier
Manuel Pégourié-Gonnardcae6f3e2013-10-23 20:19:57 +0200598 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200599const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_grp_id( mbedtls_ecp_group_id grp_id )
Manuel Pégourié-Gonnardcae6f3e2013-10-23 20:19:57 +0200600{
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200601 const mbedtls_ecp_curve_info *curve_info;
Manuel Pégourié-Gonnardcae6f3e2013-10-23 20:19:57 +0200602
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200603 for( curve_info = mbedtls_ecp_curve_list();
604 curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
Manuel Pégourié-Gonnardcae6f3e2013-10-23 20:19:57 +0200605 curve_info++ )
606 {
607 if( curve_info->grp_id == grp_id )
608 return( curve_info );
609 }
610
611 return( NULL );
612}
613
614/*
615 * Get the curve info from the TLS identifier
616 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200617const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_tls_id( uint16_t tls_id )
Manuel Pégourié-Gonnardcae6f3e2013-10-23 20:19:57 +0200618{
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200619 const mbedtls_ecp_curve_info *curve_info;
Manuel Pégourié-Gonnardcae6f3e2013-10-23 20:19:57 +0200620
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200621 for( curve_info = mbedtls_ecp_curve_list();
622 curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
Manuel Pégourié-Gonnardcae6f3e2013-10-23 20:19:57 +0200623 curve_info++ )
624 {
625 if( curve_info->tls_id == tls_id )
626 return( curve_info );
627 }
628
629 return( NULL );
630}
631
632/*
Manuel Pégourié-Gonnard0267e3d2013-11-30 15:10:14 +0100633 * Get the curve info from the name
634 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200635const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_name( const char *name )
Manuel Pégourié-Gonnard0267e3d2013-11-30 15:10:14 +0100636{
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200637 const mbedtls_ecp_curve_info *curve_info;
Manuel Pégourié-Gonnard0267e3d2013-11-30 15:10:14 +0100638
Andrzej Kurekc470b6b2019-01-31 08:20:20 -0500639 if( name == NULL )
640 return( NULL );
641
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200642 for( curve_info = mbedtls_ecp_curve_list();
643 curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
Manuel Pégourié-Gonnard0267e3d2013-11-30 15:10:14 +0100644 curve_info++ )
645 {
Manuel Pégourié-Gonnardcb46fd82015-05-28 17:06:07 +0200646 if( strcmp( curve_info->name, name ) == 0 )
Manuel Pégourié-Gonnard0267e3d2013-11-30 15:10:14 +0100647 return( curve_info );
648 }
649
650 return( NULL );
651}
652
653/*
Manuel Pégourié-Gonnard7c94d8b2013-12-04 23:15:46 +0100654 * Get the type of a curve
Manuel Pégourié-Gonnard312d2e82013-12-04 11:08:01 +0100655 */
Janos Follathdf9295b2019-02-26 12:36:52 +0000656mbedtls_ecp_curve_type mbedtls_ecp_get_type( const mbedtls_ecp_group *grp )
Manuel Pégourié-Gonnard312d2e82013-12-04 11:08:01 +0100657{
Manuel Pégourié-Gonnard7c94d8b2013-12-04 23:15:46 +0100658 if( grp->G.X.p == NULL )
Janos Follathdf9295b2019-02-26 12:36:52 +0000659 return( MBEDTLS_ECP_TYPE_NONE );
Manuel Pégourié-Gonnard7c94d8b2013-12-04 23:15:46 +0100660
661 if( grp->G.Y.p == NULL )
Janos Follathdf9295b2019-02-26 12:36:52 +0000662 return( MBEDTLS_ECP_TYPE_MONTGOMERY );
Manuel Pégourié-Gonnard7c94d8b2013-12-04 23:15:46 +0100663 else
Janos Follathdf9295b2019-02-26 12:36:52 +0000664 return( MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS );
Manuel Pégourié-Gonnard312d2e82013-12-04 11:08:01 +0100665}
666
667/*
Manuel Pégourié-Gonnardb505c272012-11-05 17:27:54 +0100668 * Initialize (the components of) a point
Manuel Pégourié-Gonnardae180d02012-11-02 18:14:40 +0100669 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200670void mbedtls_ecp_point_init( mbedtls_ecp_point *pt )
Manuel Pégourié-Gonnardae180d02012-11-02 18:14:40 +0100671{
Andrzej Kurekc470b6b2019-01-31 08:20:20 -0500672 ECP_VALIDATE( pt != NULL );
Manuel Pégourié-Gonnardae180d02012-11-02 18:14:40 +0100673
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200674 mbedtls_mpi_init( &pt->X );
675 mbedtls_mpi_init( &pt->Y );
676 mbedtls_mpi_init( &pt->Z );
Manuel Pégourié-Gonnardb505c272012-11-05 17:27:54 +0100677}
678
679/*
680 * Initialize (the components of) a group
681 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200682void mbedtls_ecp_group_init( mbedtls_ecp_group *grp )
Manuel Pégourié-Gonnardb505c272012-11-05 17:27:54 +0100683{
Andrzej Kurekc470b6b2019-01-31 08:20:20 -0500684 ECP_VALIDATE( grp != NULL );
Manuel Pégourié-Gonnardb505c272012-11-05 17:27:54 +0100685
Manuel Pégourié-Gonnard95e2eca2018-06-20 10:29:47 +0200686 grp->id = MBEDTLS_ECP_DP_NONE;
Manuel Pégourié-Gonnard5bd38b12017-08-23 16:55:59 +0200687 mbedtls_mpi_init( &grp->P );
688 mbedtls_mpi_init( &grp->A );
689 mbedtls_mpi_init( &grp->B );
690 mbedtls_ecp_point_init( &grp->G );
691 mbedtls_mpi_init( &grp->N );
692 grp->pbits = 0;
693 grp->nbits = 0;
694 grp->h = 0;
695 grp->modp = NULL;
696 grp->t_pre = NULL;
697 grp->t_post = NULL;
698 grp->t_data = NULL;
699 grp->T = NULL;
700 grp->T_size = 0;
Manuel Pégourié-Gonnardae180d02012-11-02 18:14:40 +0100701}
702
703/*
Manuel Pégourié-Gonnardb8c6e0e2013-07-01 13:40:52 +0200704 * Initialize (the components of) a key pair
705 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200706void mbedtls_ecp_keypair_init( mbedtls_ecp_keypair *key )
Manuel Pégourié-Gonnardb8c6e0e2013-07-01 13:40:52 +0200707{
Andrzej Kurekc470b6b2019-01-31 08:20:20 -0500708 ECP_VALIDATE( key != NULL );
Manuel Pégourié-Gonnardb8c6e0e2013-07-01 13:40:52 +0200709
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200710 mbedtls_ecp_group_init( &key->grp );
711 mbedtls_mpi_init( &key->d );
712 mbedtls_ecp_point_init( &key->Q );
Manuel Pégourié-Gonnardb8c6e0e2013-07-01 13:40:52 +0200713}
714
715/*
Manuel Pégourié-Gonnard1e8c8ec2012-10-31 19:24:21 +0100716 * Unallocate (the components of) a point
717 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200718void mbedtls_ecp_point_free( mbedtls_ecp_point *pt )
Manuel Pégourié-Gonnard1e8c8ec2012-10-31 19:24:21 +0100719{
720 if( pt == NULL )
721 return;
722
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200723 mbedtls_mpi_free( &( pt->X ) );
724 mbedtls_mpi_free( &( pt->Y ) );
725 mbedtls_mpi_free( &( pt->Z ) );
Manuel Pégourié-Gonnard1e8c8ec2012-10-31 19:24:21 +0100726}
727
728/*
729 * Unallocate (the components of) a group
730 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200731void mbedtls_ecp_group_free( mbedtls_ecp_group *grp )
Manuel Pégourié-Gonnard1e8c8ec2012-10-31 19:24:21 +0100732{
Manuel Pégourié-Gonnard161ef962013-09-17 19:13:10 +0200733 size_t i;
734
Manuel Pégourié-Gonnard1e8c8ec2012-10-31 19:24:21 +0100735 if( grp == NULL )
736 return;
737
Manuel Pégourié-Gonnard1f82b042013-12-06 12:51:50 +0100738 if( grp->h != 1 )
739 {
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200740 mbedtls_mpi_free( &grp->P );
741 mbedtls_mpi_free( &grp->A );
742 mbedtls_mpi_free( &grp->B );
743 mbedtls_ecp_point_free( &grp->G );
744 mbedtls_mpi_free( &grp->N );
Manuel Pégourié-Gonnard1f82b042013-12-06 12:51:50 +0100745 }
Manuel Pégourié-Gonnardc9727702013-09-16 18:56:28 +0200746
Manuel Pégourié-Gonnard161ef962013-09-17 19:13:10 +0200747 if( grp->T != NULL )
748 {
749 for( i = 0; i < grp->T_size; i++ )
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200750 mbedtls_ecp_point_free( &grp->T[i] );
751 mbedtls_free( grp->T );
Manuel Pégourié-Gonnard161ef962013-09-17 19:13:10 +0200752 }
753
Andres Amaya Garcia1f6301b2018-04-17 09:51:09 -0500754 mbedtls_platform_zeroize( grp, sizeof( mbedtls_ecp_group ) );
Manuel Pégourié-Gonnard1e8c8ec2012-10-31 19:24:21 +0100755}
Manuel Pégourié-Gonnard39d2adb2012-10-31 09:26:55 +0100756
Manuel Pégourié-Gonnard883f3132012-11-02 09:40:25 +0100757/*
Manuel Pégourié-Gonnardb8c6e0e2013-07-01 13:40:52 +0200758 * Unallocate (the components of) a key pair
759 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200760void mbedtls_ecp_keypair_free( mbedtls_ecp_keypair *key )
Manuel Pégourié-Gonnardb8c6e0e2013-07-01 13:40:52 +0200761{
Paul Bakker66d5d072014-06-17 16:39:18 +0200762 if( key == NULL )
Manuel Pégourié-Gonnardb8c6e0e2013-07-01 13:40:52 +0200763 return;
764
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200765 mbedtls_ecp_group_free( &key->grp );
766 mbedtls_mpi_free( &key->d );
767 mbedtls_ecp_point_free( &key->Q );
Manuel Pégourié-Gonnardb8c6e0e2013-07-01 13:40:52 +0200768}
769
770/*
Manuel Pégourié-Gonnardcae6f3e2013-10-23 20:19:57 +0200771 * Copy the contents of a point
772 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200773int mbedtls_ecp_copy( mbedtls_ecp_point *P, const mbedtls_ecp_point *Q )
Manuel Pégourié-Gonnardcae6f3e2013-10-23 20:19:57 +0200774{
Janos Follath24eed8d2019-11-22 13:21:35 +0000775 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
Andrzej Kurekc470b6b2019-01-31 08:20:20 -0500776 ECP_VALIDATE_RET( P != NULL );
777 ECP_VALIDATE_RET( Q != NULL );
Manuel Pégourié-Gonnardcae6f3e2013-10-23 20:19:57 +0200778
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200779 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->X, &Q->X ) );
780 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->Y, &Q->Y ) );
781 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->Z, &Q->Z ) );
Manuel Pégourié-Gonnardcae6f3e2013-10-23 20:19:57 +0200782
783cleanup:
784 return( ret );
785}
786
787/*
788 * Copy the contents of a group object
789 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200790int mbedtls_ecp_group_copy( mbedtls_ecp_group *dst, const mbedtls_ecp_group *src )
Manuel Pégourié-Gonnardcae6f3e2013-10-23 20:19:57 +0200791{
Andrzej Kurekc470b6b2019-01-31 08:20:20 -0500792 ECP_VALIDATE_RET( dst != NULL );
793 ECP_VALIDATE_RET( src != NULL );
794
795 return( mbedtls_ecp_group_load( dst, src->id ) );
Manuel Pégourié-Gonnardcae6f3e2013-10-23 20:19:57 +0200796}
797
798/*
Manuel Pégourié-Gonnardae180d02012-11-02 18:14:40 +0100799 * Set point to zero
800 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200801int mbedtls_ecp_set_zero( mbedtls_ecp_point *pt )
Manuel Pégourié-Gonnardae180d02012-11-02 18:14:40 +0100802{
Janos Follath24eed8d2019-11-22 13:21:35 +0000803 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
Andrzej Kurekc470b6b2019-01-31 08:20:20 -0500804 ECP_VALIDATE_RET( pt != NULL );
Manuel Pégourié-Gonnard1c2782c2012-11-19 20:16:28 +0100805
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200806 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->X , 1 ) );
807 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Y , 1 ) );
808 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z , 0 ) );
Manuel Pégourié-Gonnard1c2782c2012-11-19 20:16:28 +0100809
810cleanup:
811 return( ret );
Manuel Pégourié-Gonnardae180d02012-11-02 18:14:40 +0100812}
813
814/*
Manuel Pégourié-Gonnard6545ca72013-01-26 16:05:22 +0100815 * Tell if a point is zero
816 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200817int mbedtls_ecp_is_zero( mbedtls_ecp_point *pt )
Manuel Pégourié-Gonnard6545ca72013-01-26 16:05:22 +0100818{
Andrzej Kurekc470b6b2019-01-31 08:20:20 -0500819 ECP_VALIDATE_RET( pt != NULL );
820
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200821 return( mbedtls_mpi_cmp_int( &pt->Z, 0 ) == 0 );
Manuel Pégourié-Gonnard6545ca72013-01-26 16:05:22 +0100822}
823
824/*
Andrzej Kurekc470b6b2019-01-31 08:20:20 -0500825 * Compare two points lazily
Manuel Pégourié-Gonnard6029a852015-08-11 15:44:41 +0200826 */
827int mbedtls_ecp_point_cmp( const mbedtls_ecp_point *P,
828 const mbedtls_ecp_point *Q )
829{
Andrzej Kurekc470b6b2019-01-31 08:20:20 -0500830 ECP_VALIDATE_RET( P != NULL );
831 ECP_VALIDATE_RET( Q != NULL );
832
Manuel Pégourié-Gonnard6029a852015-08-11 15:44:41 +0200833 if( mbedtls_mpi_cmp_mpi( &P->X, &Q->X ) == 0 &&
834 mbedtls_mpi_cmp_mpi( &P->Y, &Q->Y ) == 0 &&
835 mbedtls_mpi_cmp_mpi( &P->Z, &Q->Z ) == 0 )
836 {
837 return( 0 );
838 }
839
840 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
841}
842
843/*
Manuel Pégourié-Gonnard847395a2012-11-05 13:13:44 +0100844 * Import a non-zero point from ASCII strings
845 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200846int mbedtls_ecp_point_read_string( mbedtls_ecp_point *P, int radix,
Manuel Pégourié-Gonnard847395a2012-11-05 13:13:44 +0100847 const char *x, const char *y )
848{
Janos Follath24eed8d2019-11-22 13:21:35 +0000849 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
Andrzej Kurekc470b6b2019-01-31 08:20:20 -0500850 ECP_VALIDATE_RET( P != NULL );
851 ECP_VALIDATE_RET( x != NULL );
852 ECP_VALIDATE_RET( y != NULL );
Manuel Pégourié-Gonnard847395a2012-11-05 13:13:44 +0100853
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200854 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &P->X, radix, x ) );
855 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &P->Y, radix, y ) );
856 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &P->Z, 1 ) );
Manuel Pégourié-Gonnard847395a2012-11-05 13:13:44 +0100857
858cleanup:
859 return( ret );
860}
861
862/*
Janos Follath7caf8e42019-02-20 12:00:22 +0000863 * Export a point into unsigned binary data (SEC1 2.3.3 and RFC7748)
Manuel Pégourié-Gonnarde19feb52012-11-24 14:10:14 +0100864 */
Andrzej Kurekc470b6b2019-01-31 08:20:20 -0500865int mbedtls_ecp_point_write_binary( const mbedtls_ecp_group *grp,
866 const mbedtls_ecp_point *P,
867 int format, size_t *olen,
868 unsigned char *buf, size_t buflen )
Manuel Pégourié-Gonnarde19feb52012-11-24 14:10:14 +0100869{
Janos Follath28eb06d2019-02-26 10:53:34 +0000870 int ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
Manuel Pégourié-Gonnarde19feb52012-11-24 14:10:14 +0100871 size_t plen;
Andrzej Kurekc470b6b2019-01-31 08:20:20 -0500872 ECP_VALIDATE_RET( grp != NULL );
873 ECP_VALIDATE_RET( P != NULL );
874 ECP_VALIDATE_RET( olen != NULL );
875 ECP_VALIDATE_RET( buf != NULL );
876 ECP_VALIDATE_RET( format == MBEDTLS_ECP_PF_UNCOMPRESSED ||
877 format == MBEDTLS_ECP_PF_COMPRESSED );
Manuel Pégourié-Gonnard37d218a2012-11-24 15:19:55 +0100878
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200879 plen = mbedtls_mpi_size( &grp->P );
Manuel Pégourié-Gonnarde19feb52012-11-24 14:10:14 +0100880
Gilles Peskinee8c04fe2018-09-14 17:44:21 +0200881#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
Gilles Peskine59970052019-02-28 13:12:06 +0100882 (void) format; /* Montgomery curves always use the same point format */
Janos Follathdf9295b2019-02-26 12:36:52 +0000883 if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY )
Manuel Pégourié-Gonnard37d218a2012-11-24 15:19:55 +0100884 {
Janos Follath7caf8e42019-02-20 12:00:22 +0000885 *olen = plen;
Manuel Pégourié-Gonnard37d218a2012-11-24 15:19:55 +0100886 if( buflen < *olen )
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200887 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
Manuel Pégourié-Gonnard37d218a2012-11-24 15:19:55 +0100888
Janos Follath7caf8e42019-02-20 12:00:22 +0000889 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary_le( &P->X, buf, plen ) );
Manuel Pégourié-Gonnard37d218a2012-11-24 15:19:55 +0100890 }
Janos Follath7caf8e42019-02-20 12:00:22 +0000891#endif
Gilles Peskinee8c04fe2018-09-14 17:44:21 +0200892#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
Janos Follathdf9295b2019-02-26 12:36:52 +0000893 if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
Manuel Pégourié-Gonnard37d218a2012-11-24 15:19:55 +0100894 {
Janos Follath7caf8e42019-02-20 12:00:22 +0000895 /*
896 * Common case: P == 0
897 */
898 if( mbedtls_mpi_cmp_int( &P->Z, 0 ) == 0 )
899 {
900 if( buflen < 1 )
901 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
Manuel Pégourié-Gonnard37d218a2012-11-24 15:19:55 +0100902
Janos Follath7caf8e42019-02-20 12:00:22 +0000903 buf[0] = 0x00;
904 *olen = 1;
Manuel Pégourié-Gonnard37d218a2012-11-24 15:19:55 +0100905
Janos Follath7caf8e42019-02-20 12:00:22 +0000906 return( 0 );
907 }
908
909 if( format == MBEDTLS_ECP_PF_UNCOMPRESSED )
910 {
911 *olen = 2 * plen + 1;
912
913 if( buflen < *olen )
914 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
915
916 buf[0] = 0x04;
917 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->X, buf + 1, plen ) );
918 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->Y, buf + 1 + plen, plen ) );
919 }
920 else if( format == MBEDTLS_ECP_PF_COMPRESSED )
921 {
922 *olen = plen + 1;
923
924 if( buflen < *olen )
925 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
926
927 buf[0] = 0x02 + mbedtls_mpi_get_bit( &P->Y, 0 );
928 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->X, buf + 1, plen ) );
929 }
Manuel Pégourié-Gonnard37d218a2012-11-24 15:19:55 +0100930 }
Janos Follath7caf8e42019-02-20 12:00:22 +0000931#endif
Manuel Pégourié-Gonnarde19feb52012-11-24 14:10:14 +0100932
933cleanup:
934 return( ret );
935}
936
937/*
Janos Follath59b813c2019-02-13 10:44:06 +0000938 * Import a point from unsigned binary data (SEC1 2.3.4 and RFC7748)
Manuel Pégourié-Gonnard5e402d82012-11-24 16:19:42 +0100939 */
Andrzej Kurekc470b6b2019-01-31 08:20:20 -0500940int mbedtls_ecp_point_read_binary( const mbedtls_ecp_group *grp,
941 mbedtls_ecp_point *pt,
942 const unsigned char *buf, size_t ilen )
Manuel Pégourié-Gonnard5246ee52014-03-19 16:18:38 +0100943{
Janos Follath28eb06d2019-02-26 10:53:34 +0000944 int ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
Manuel Pégourié-Gonnard5e402d82012-11-24 16:19:42 +0100945 size_t plen;
Andrzej Kurekc470b6b2019-01-31 08:20:20 -0500946 ECP_VALIDATE_RET( grp != NULL );
947 ECP_VALIDATE_RET( pt != NULL );
948 ECP_VALIDATE_RET( buf != NULL );
Manuel Pégourié-Gonnard5e402d82012-11-24 16:19:42 +0100949
Paul Bakker82788fb2014-10-20 13:59:19 +0200950 if( ilen < 1 )
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200951 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
Manuel Pégourié-Gonnard67dbe1e2014-07-08 13:09:24 +0200952
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200953 plen = mbedtls_mpi_size( &grp->P );
Manuel Pégourié-Gonnard5e402d82012-11-24 16:19:42 +0100954
Gilles Peskinee8c04fe2018-09-14 17:44:21 +0200955#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
Janos Follathdf9295b2019-02-26 12:36:52 +0000956 if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY )
Janos Follath59b813c2019-02-13 10:44:06 +0000957 {
958 if( plen != ilen )
959 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
Manuel Pégourié-Gonnard5246ee52014-03-19 16:18:38 +0100960
Janos Follath59b813c2019-02-13 10:44:06 +0000961 MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary_le( &pt->X, buf, plen ) );
962 mbedtls_mpi_free( &pt->Y );
Manuel Pégourié-Gonnard5e402d82012-11-24 16:19:42 +0100963
Janos Follath59b813c2019-02-13 10:44:06 +0000964 if( grp->id == MBEDTLS_ECP_DP_CURVE25519 )
Janos Follathffbd7e82019-02-25 11:35:20 +0000965 /* Set most significant bit to 0 as prescribed in RFC7748 §5 */
Janos Follath59b813c2019-02-13 10:44:06 +0000966 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &pt->X, plen * 8 - 1, 0 ) );
Janos Follath28eb06d2019-02-26 10:53:34 +0000967
968 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) );
Janos Follath59b813c2019-02-13 10:44:06 +0000969 }
970#endif
Gilles Peskinee8c04fe2018-09-14 17:44:21 +0200971#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
Janos Follathdf9295b2019-02-26 12:36:52 +0000972 if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
Janos Follath59b813c2019-02-13 10:44:06 +0000973 {
974 if( buf[0] == 0x00 )
975 {
976 if( ilen == 1 )
977 return( mbedtls_ecp_set_zero( pt ) );
978 else
979 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
980 }
981
982 if( buf[0] != 0x04 )
983 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
984
985 if( ilen != 2 * plen + 1 )
986 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
987
988 MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &pt->X, buf + 1, plen ) );
989 MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &pt->Y,
990 buf + 1 + plen, plen ) );
Janos Follath28eb06d2019-02-26 10:53:34 +0000991 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) );
Janos Follath59b813c2019-02-13 10:44:06 +0000992 }
993#endif
Manuel Pégourié-Gonnard5e402d82012-11-24 16:19:42 +0100994
995cleanup:
996 return( ret );
997}
998
999/*
Manuel Pégourié-Gonnard00794052013-02-09 19:00:07 +01001000 * Import a point from a TLS ECPoint record (RFC 4492)
1001 * struct {
1002 * opaque point <1..2^8-1>;
1003 * } ECPoint;
1004 */
Andrzej Kurekc470b6b2019-01-31 08:20:20 -05001005int mbedtls_ecp_tls_read_point( const mbedtls_ecp_group *grp,
1006 mbedtls_ecp_point *pt,
1007 const unsigned char **buf, size_t buf_len )
Manuel Pégourié-Gonnard00794052013-02-09 19:00:07 +01001008{
1009 unsigned char data_len;
Manuel Pégourié-Gonnard98f51812013-02-10 13:38:29 +01001010 const unsigned char *buf_start;
Andrzej Kurekc470b6b2019-01-31 08:20:20 -05001011 ECP_VALIDATE_RET( grp != NULL );
1012 ECP_VALIDATE_RET( pt != NULL );
1013 ECP_VALIDATE_RET( buf != NULL );
1014 ECP_VALIDATE_RET( *buf != NULL );
Manuel Pégourié-Gonnard00794052013-02-09 19:00:07 +01001015
1016 /*
Manuel Pégourié-Gonnard67dbe1e2014-07-08 13:09:24 +02001017 * We must have at least two bytes (1 for length, at least one for data)
Manuel Pégourié-Gonnard00794052013-02-09 19:00:07 +01001018 */
1019 if( buf_len < 2 )
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001020 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
Manuel Pégourié-Gonnard00794052013-02-09 19:00:07 +01001021
Manuel Pégourié-Gonnard98f51812013-02-10 13:38:29 +01001022 data_len = *(*buf)++;
Manuel Pégourié-Gonnard00794052013-02-09 19:00:07 +01001023 if( data_len < 1 || data_len > buf_len - 1 )
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001024 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
Manuel Pégourié-Gonnard00794052013-02-09 19:00:07 +01001025
Manuel Pégourié-Gonnard98f51812013-02-10 13:38:29 +01001026 /*
1027 * Save buffer start for read_binary and update buf
1028 */
1029 buf_start = *buf;
1030 *buf += data_len;
1031
Andrzej Kurekc470b6b2019-01-31 08:20:20 -05001032 return( mbedtls_ecp_point_read_binary( grp, pt, buf_start, data_len ) );
Manuel Pégourié-Gonnard00794052013-02-09 19:00:07 +01001033}
1034
1035/*
1036 * Export a point as a TLS ECPoint record (RFC 4492)
1037 * struct {
1038 * opaque point <1..2^8-1>;
1039 * } ECPoint;
1040 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001041int mbedtls_ecp_tls_write_point( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt,
Manuel Pégourié-Gonnard420f1eb2013-02-10 12:22:46 +01001042 int format, size_t *olen,
1043 unsigned char *buf, size_t blen )
Manuel Pégourié-Gonnard00794052013-02-09 19:00:07 +01001044{
Janos Follath24eed8d2019-11-22 13:21:35 +00001045 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
Andrzej Kurekc470b6b2019-01-31 08:20:20 -05001046 ECP_VALIDATE_RET( grp != NULL );
1047 ECP_VALIDATE_RET( pt != NULL );
1048 ECP_VALIDATE_RET( olen != NULL );
1049 ECP_VALIDATE_RET( buf != NULL );
1050 ECP_VALIDATE_RET( format == MBEDTLS_ECP_PF_UNCOMPRESSED ||
1051 format == MBEDTLS_ECP_PF_COMPRESSED );
Manuel Pégourié-Gonnard420f1eb2013-02-10 12:22:46 +01001052
Manuel Pégourié-Gonnard00794052013-02-09 19:00:07 +01001053 /*
Manuel Pégourié-Gonnard420f1eb2013-02-10 12:22:46 +01001054 * buffer length must be at least one, for our length byte
Manuel Pégourié-Gonnard00794052013-02-09 19:00:07 +01001055 */
Manuel Pégourié-Gonnard420f1eb2013-02-10 12:22:46 +01001056 if( blen < 1 )
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001057 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
Manuel Pégourié-Gonnard00794052013-02-09 19:00:07 +01001058
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001059 if( ( ret = mbedtls_ecp_point_write_binary( grp, pt, format,
Manuel Pégourié-Gonnard420f1eb2013-02-10 12:22:46 +01001060 olen, buf + 1, blen - 1) ) != 0 )
1061 return( ret );
1062
1063 /*
1064 * write length to the first byte and update total length
1065 */
Paul Bakkerb9cfaa02013-10-11 18:58:55 +02001066 buf[0] = (unsigned char) *olen;
Manuel Pégourié-Gonnard420f1eb2013-02-10 12:22:46 +01001067 ++*olen;
1068
Paul Bakkerd8bb8262014-06-17 14:06:49 +02001069 return( 0 );
Manuel Pégourié-Gonnard00794052013-02-09 19:00:07 +01001070}
1071
1072/*
Manuel Pégourié-Gonnard1a967282013-02-09 17:03:58 +01001073 * Set a group from an ECParameters record (RFC 4492)
1074 */
Andrzej Kurekc470b6b2019-01-31 08:20:20 -05001075int mbedtls_ecp_tls_read_group( mbedtls_ecp_group *grp,
1076 const unsigned char **buf, size_t len )
1077{
Janos Follath24eed8d2019-11-22 13:21:35 +00001078 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
Andrzej Kurekc470b6b2019-01-31 08:20:20 -05001079 mbedtls_ecp_group_id grp_id;
1080 ECP_VALIDATE_RET( grp != NULL );
1081 ECP_VALIDATE_RET( buf != NULL );
1082 ECP_VALIDATE_RET( *buf != NULL );
1083
1084 if( ( ret = mbedtls_ecp_tls_read_group_id( &grp_id, buf, len ) ) != 0 )
1085 return( ret );
1086
1087 return( mbedtls_ecp_group_load( grp, grp_id ) );
1088}
1089
1090/*
1091 * Read a group id from an ECParameters record (RFC 4492) and convert it to
1092 * mbedtls_ecp_group_id.
1093 */
1094int mbedtls_ecp_tls_read_group_id( mbedtls_ecp_group_id *grp,
1095 const unsigned char **buf, size_t len )
Manuel Pégourié-Gonnard1a967282013-02-09 17:03:58 +01001096{
Manuel Pégourié-Gonnardf24b4a72013-09-23 18:14:50 +02001097 uint16_t tls_id;
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001098 const mbedtls_ecp_curve_info *curve_info;
Andrzej Kurekc470b6b2019-01-31 08:20:20 -05001099 ECP_VALIDATE_RET( grp != NULL );
1100 ECP_VALIDATE_RET( buf != NULL );
1101 ECP_VALIDATE_RET( *buf != NULL );
Manuel Pégourié-Gonnard1a967282013-02-09 17:03:58 +01001102
1103 /*
1104 * We expect at least three bytes (see below)
1105 */
1106 if( len < 3 )
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001107 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
Manuel Pégourié-Gonnard1a967282013-02-09 17:03:58 +01001108
1109 /*
1110 * First byte is curve_type; only named_curve is handled
1111 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001112 if( *(*buf)++ != MBEDTLS_ECP_TLS_NAMED_CURVE )
1113 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
Manuel Pégourié-Gonnard1a967282013-02-09 17:03:58 +01001114
1115 /*
Manuel Pégourié-Gonnardb3258872013-02-10 12:06:19 +01001116 * Next two bytes are the namedcurve value
Manuel Pégourié-Gonnard1a967282013-02-09 17:03:58 +01001117 */
Manuel Pégourié-Gonnardf24b4a72013-09-23 18:14:50 +02001118 tls_id = *(*buf)++;
1119 tls_id <<= 8;
1120 tls_id |= *(*buf)++;
1121
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001122 if( ( curve_info = mbedtls_ecp_curve_info_from_tls_id( tls_id ) ) == NULL )
1123 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
Manuel Pégourié-Gonnardf24b4a72013-09-23 18:14:50 +02001124
Andrzej Kurekc470b6b2019-01-31 08:20:20 -05001125 *grp = curve_info->grp_id;
1126
1127 return( 0 );
Manuel Pégourié-Gonnardb3258872013-02-10 12:06:19 +01001128}
1129
1130/*
1131 * Write the ECParameters record corresponding to a group (RFC 4492)
1132 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001133int mbedtls_ecp_tls_write_group( const mbedtls_ecp_group *grp, size_t *olen,
Manuel Pégourié-Gonnardb3258872013-02-10 12:06:19 +01001134 unsigned char *buf, size_t blen )
1135{
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001136 const mbedtls_ecp_curve_info *curve_info;
Andrzej Kurekc470b6b2019-01-31 08:20:20 -05001137 ECP_VALIDATE_RET( grp != NULL );
1138 ECP_VALIDATE_RET( buf != NULL );
1139 ECP_VALIDATE_RET( olen != NULL );
Manuel Pégourié-Gonnardf24b4a72013-09-23 18:14:50 +02001140
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001141 if( ( curve_info = mbedtls_ecp_curve_info_from_grp_id( grp->id ) ) == NULL )
1142 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
Manuel Pégourié-Gonnard70380392013-09-16 16:19:53 +02001143
Manuel Pégourié-Gonnardb3258872013-02-10 12:06:19 +01001144 /*
1145 * We are going to write 3 bytes (see below)
1146 */
1147 *olen = 3;
1148 if( blen < *olen )
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001149 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
Manuel Pégourié-Gonnardb3258872013-02-10 12:06:19 +01001150
1151 /*
1152 * First byte is curve_type, always named_curve
1153 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001154 *buf++ = MBEDTLS_ECP_TLS_NAMED_CURVE;
Manuel Pégourié-Gonnardb3258872013-02-10 12:06:19 +01001155
1156 /*
1157 * Next two bytes are the namedcurve value
1158 */
Manuel Pégourié-Gonnardf24b4a72013-09-23 18:14:50 +02001159 buf[0] = curve_info->tls_id >> 8;
1160 buf[1] = curve_info->tls_id & 0xFF;
Manuel Pégourié-Gonnardb3258872013-02-10 12:06:19 +01001161
Paul Bakkerd8bb8262014-06-17 14:06:49 +02001162 return( 0 );
Manuel Pégourié-Gonnarda5402fe2012-11-07 20:24:05 +01001163}
Manuel Pégourié-Gonnardab38b702012-11-05 17:34:55 +01001164
Manuel Pégourié-Gonnard568c9cf2013-09-16 17:30:04 +02001165/*
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001166 * Wrapper around fast quasi-modp functions, with fall-back to mbedtls_mpi_mod_mpi.
1167 * See the documentation of struct mbedtls_ecp_group.
Manuel Pégourié-Gonnardcae6f3e2013-10-23 20:19:57 +02001168 *
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001169 * This function is in the critial loop for mbedtls_ecp_mul, so pay attention to perf.
Manuel Pégourié-Gonnard568c9cf2013-09-16 17:30:04 +02001170 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001171static int ecp_modp( mbedtls_mpi *N, const mbedtls_ecp_group *grp )
Manuel Pégourié-Gonnard70380392013-09-16 16:19:53 +02001172{
Janos Follath24eed8d2019-11-22 13:21:35 +00001173 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
Manuel Pégourié-Gonnard568c9cf2013-09-16 17:30:04 +02001174
Manuel Pégourié-Gonnardcae6f3e2013-10-23 20:19:57 +02001175 if( grp->modp == NULL )
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001176 return( mbedtls_mpi_mod_mpi( N, N, &grp->P ) );
Manuel Pégourié-Gonnardcae6f3e2013-10-23 20:19:57 +02001177
1178 /* N->s < 0 is a much faster test, which fails only if N is 0 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001179 if( ( N->s < 0 && mbedtls_mpi_cmp_int( N, 0 ) != 0 ) ||
Manuel Pégourié-Gonnardc0696c22015-06-18 16:47:17 +02001180 mbedtls_mpi_bitlen( N ) > 2 * grp->pbits )
Manuel Pégourié-Gonnard70380392013-09-16 16:19:53 +02001181 {
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001182 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
Manuel Pégourié-Gonnard70380392013-09-16 16:19:53 +02001183 }
Manuel Pégourié-Gonnard568c9cf2013-09-16 17:30:04 +02001184
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001185 MBEDTLS_MPI_CHK( grp->modp( N ) );
Manuel Pégourié-Gonnard70380392013-09-16 16:19:53 +02001186
Manuel Pégourié-Gonnardcae6f3e2013-10-23 20:19:57 +02001187 /* N->s < 0 is a much faster test, which fails only if N is 0 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001188 while( N->s < 0 && mbedtls_mpi_cmp_int( N, 0 ) != 0 )
1189 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &grp->P ) );
Manuel Pégourié-Gonnard568c9cf2013-09-16 17:30:04 +02001190
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001191 while( mbedtls_mpi_cmp_mpi( N, &grp->P ) >= 0 )
Manuel Pégourié-Gonnardcae6f3e2013-10-23 20:19:57 +02001192 /* we known P, N and the result are positive */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001193 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( N, N, &grp->P ) );
Manuel Pégourié-Gonnard568c9cf2013-09-16 17:30:04 +02001194
Manuel Pégourié-Gonnardcae6f3e2013-10-23 20:19:57 +02001195cleanup:
1196 return( ret );
Manuel Pégourié-Gonnard70380392013-09-16 16:19:53 +02001197}
Manuel Pégourié-Gonnard568c9cf2013-09-16 17:30:04 +02001198
Manuel Pégourié-Gonnard847395a2012-11-05 13:13:44 +01001199/*
Manuel Pégourié-Gonnard47123252012-11-10 14:44:24 +01001200 * Fast mod-p functions expect their argument to be in the 0..p^2 range.
Manuel Pégourié-Gonnarddada4da2012-11-10 14:23:17 +01001201 *
Manuel Pégourié-Gonnard47123252012-11-10 14:44:24 +01001202 * In order to guarantee that, we need to ensure that operands of
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001203 * mbedtls_mpi_mul_mpi are in the 0..p range. So, after each operation we will
Manuel Pégourié-Gonnarddada4da2012-11-10 14:23:17 +01001204 * bring the result back to this range.
1205 *
Manuel Pégourié-Gonnard47123252012-11-10 14:44:24 +01001206 * The following macros are shortcuts for doing that.
Manuel Pégourié-Gonnarddada4da2012-11-10 14:23:17 +01001207 */
1208
1209/*
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001210 * Reduce a mbedtls_mpi mod p in-place, general case, to use after mbedtls_mpi_mul_mpi
Manuel Pégourié-Gonnard84d1aea2012-11-09 02:09:38 +01001211 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001212#if defined(MBEDTLS_SELF_TEST)
Manuel Pégourié-Gonnard91814812013-11-21 20:23:55 +01001213#define INC_MUL_COUNT mul_count++;
1214#else
1215#define INC_MUL_COUNT
1216#endif
1217
Hanno Becker1eeca412018-10-15 12:01:35 +01001218#define MOD_MUL( N ) \
1219 do \
1220 { \
1221 MBEDTLS_MPI_CHK( ecp_modp( &(N), grp ) ); \
1222 INC_MUL_COUNT \
1223 } while( 0 )
Manuel Pégourié-Gonnard84d1aea2012-11-09 02:09:38 +01001224
Gilles Peskine3b3b34f2019-07-18 21:08:27 +02001225static inline int mbedtls_mpi_mul_mod( const mbedtls_ecp_group *grp,
1226 mbedtls_mpi *X,
1227 const mbedtls_mpi *A,
1228 const mbedtls_mpi *B )
1229{
Janos Follath24eed8d2019-11-22 13:21:35 +00001230 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
Gilles Peskine3b3b34f2019-07-18 21:08:27 +02001231 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( X, A, B ) );
1232 MOD_MUL( *X );
1233cleanup:
1234 return( ret );
1235}
1236
Manuel Pégourié-Gonnard84d1aea2012-11-09 02:09:38 +01001237/*
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001238 * Reduce a mbedtls_mpi mod p in-place, to use after mbedtls_mpi_sub_mpi
Manuel Pégourié-Gonnardc9e387c2013-10-17 17:15:35 +02001239 * N->s < 0 is a very fast test, which fails only if N is 0
Manuel Pégourié-Gonnard84d1aea2012-11-09 02:09:38 +01001240 */
Hanno Becker1eeca412018-10-15 12:01:35 +01001241#define MOD_SUB( N ) \
1242 while( (N).s < 0 && mbedtls_mpi_cmp_int( &(N), 0 ) != 0 ) \
1243 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &(N), &(N), &grp->P ) )
Manuel Pégourié-Gonnard84d1aea2012-11-09 02:09:38 +01001244
Gilles Peskine3b3b34f2019-07-18 21:08:27 +02001245static inline int mbedtls_mpi_sub_mod( const mbedtls_ecp_group *grp,
1246 mbedtls_mpi *X,
1247 const mbedtls_mpi *A,
1248 const mbedtls_mpi *B )
1249{
Janos Follath24eed8d2019-11-22 13:21:35 +00001250 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
Gilles Peskine3b3b34f2019-07-18 21:08:27 +02001251 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( X, A, B ) );
1252 MOD_SUB( *X );
1253cleanup:
1254 return( ret );
1255}
1256
Manuel Pégourié-Gonnard84d1aea2012-11-09 02:09:38 +01001257/*
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001258 * Reduce a mbedtls_mpi mod p in-place, to use after mbedtls_mpi_add_mpi and mbedtls_mpi_mul_int.
Manuel Pégourié-Gonnardc9e387c2013-10-17 17:15:35 +02001259 * We known P, N and the result are positive, so sub_abs is correct, and
1260 * a bit faster.
Manuel Pégourié-Gonnard84d1aea2012-11-09 02:09:38 +01001261 */
Hanno Becker1eeca412018-10-15 12:01:35 +01001262#define MOD_ADD( N ) \
1263 while( mbedtls_mpi_cmp_mpi( &(N), &grp->P ) >= 0 ) \
1264 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( &(N), &(N), &grp->P ) )
Manuel Pégourié-Gonnard84d1aea2012-11-09 02:09:38 +01001265
Gilles Peskine3b3b34f2019-07-18 21:08:27 +02001266static inline int mbedtls_mpi_add_mod( const mbedtls_ecp_group *grp,
1267 mbedtls_mpi *X,
1268 const mbedtls_mpi *A,
1269 const mbedtls_mpi *B )
1270{
Janos Follath24eed8d2019-11-22 13:21:35 +00001271 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
Gilles Peskine3b3b34f2019-07-18 21:08:27 +02001272 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( X, A, B ) );
1273 MOD_ADD( *X );
1274cleanup:
1275 return( ret );
1276}
1277
1278static inline int mbedtls_mpi_shift_l_mod( const mbedtls_ecp_group *grp,
1279 mbedtls_mpi *X,
1280 size_t count )
1281{
Janos Follath24eed8d2019-11-22 13:21:35 +00001282 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
Gilles Peskine3b3b34f2019-07-18 21:08:27 +02001283 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( X, count ) );
1284 MOD_ADD( *X );
1285cleanup:
1286 return( ret );
1287}
1288
Gilles Peskinee8c04fe2018-09-14 17:44:21 +02001289#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
Manuel Pégourié-Gonnard7c94d8b2013-12-04 23:15:46 +01001290/*
1291 * For curves in short Weierstrass form, we do all the internal operations in
1292 * Jacobian coordinates.
1293 *
1294 * For multiplication, we'll use a comb method with coutermeasueres against
1295 * SPA, hence timing attacks.
1296 */
1297
Manuel Pégourié-Gonnard84d1aea2012-11-09 02:09:38 +01001298/*
Manuel Pégourié-Gonnard1c2782c2012-11-19 20:16:28 +01001299 * Normalize jacobian coordinates so that Z == 0 || Z == 1 (GECC 3.2.1)
Manuel Pégourié-Gonnard04a02252013-11-20 22:57:38 +01001300 * Cost: 1N := 1I + 3M + 1S
Manuel Pégourié-Gonnardd070f512012-11-08 17:40:51 +01001301 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001302static int ecp_normalize_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt )
Manuel Pégourié-Gonnardd070f512012-11-08 17:40:51 +01001303{
Janos Follath24eed8d2019-11-22 13:21:35 +00001304 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001305 mbedtls_mpi Zi, ZZi;
Manuel Pégourié-Gonnardd070f512012-11-08 17:40:51 +01001306
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001307 if( mbedtls_mpi_cmp_int( &pt->Z, 0 ) == 0 )
Manuel Pégourié-Gonnardd070f512012-11-08 17:40:51 +01001308 return( 0 );
Manuel Pégourié-Gonnardd070f512012-11-08 17:40:51 +01001309
Janos Follathb0697532016-08-18 12:38:46 +01001310#if defined(MBEDTLS_ECP_NORMALIZE_JAC_ALT)
Manuel Pégourié-Gonnardebac5d32017-08-23 16:23:36 +02001311 if( mbedtls_internal_ecp_grp_capable( grp ) )
1312 return( mbedtls_internal_ecp_normalize_jac( grp, pt ) );
Janos Follath372697b2016-10-28 16:53:11 +01001313#endif /* MBEDTLS_ECP_NORMALIZE_JAC_ALT */
Manuel Pégourié-Gonnardebac5d32017-08-23 16:23:36 +02001314
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001315 mbedtls_mpi_init( &Zi ); mbedtls_mpi_init( &ZZi );
Manuel Pégourié-Gonnardd070f512012-11-08 17:40:51 +01001316
Manuel Pégourié-Gonnard1c2782c2012-11-19 20:16:28 +01001317 /*
1318 * X = X / Z^2 mod p
1319 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001320 MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &Zi, &pt->Z, &grp->P ) );
Gilles Peskine3b3b34f2019-07-18 21:08:27 +02001321 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &ZZi, &Zi, &Zi ) );
1322 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &pt->X, &pt->X, &ZZi ) );
Manuel Pégourié-Gonnardd070f512012-11-08 17:40:51 +01001323
1324 /*
Manuel Pégourié-Gonnard1c2782c2012-11-19 20:16:28 +01001325 * Y = Y / Z^3 mod p
Manuel Pégourié-Gonnardd070f512012-11-08 17:40:51 +01001326 */
Gilles Peskine3b3b34f2019-07-18 21:08:27 +02001327 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &pt->Y, &pt->Y, &ZZi ) );
1328 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &pt->Y, &pt->Y, &Zi ) );
Manuel Pégourié-Gonnardd070f512012-11-08 17:40:51 +01001329
1330 /*
Manuel Pégourié-Gonnard1c2782c2012-11-19 20:16:28 +01001331 * Z = 1
Manuel Pégourié-Gonnardd070f512012-11-08 17:40:51 +01001332 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001333 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) );
Manuel Pégourié-Gonnardd070f512012-11-08 17:40:51 +01001334
1335cleanup:
1336
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001337 mbedtls_mpi_free( &Zi ); mbedtls_mpi_free( &ZZi );
Manuel Pégourié-Gonnardd070f512012-11-08 17:40:51 +01001338
1339 return( ret );
1340}
1341
1342/*
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01001343 * Normalize jacobian coordinates of an array of (pointers to) points,
Manuel Pégourié-Gonnard3680c822012-11-21 18:49:45 +01001344 * using Montgomery's trick to perform only one inversion mod P.
Manuel Pégourié-Gonnardcdd44322012-11-21 16:00:55 +01001345 * (See for example Cohen's "A Course in Computational Algebraic Number
1346 * Theory", Algorithm 10.3.4.)
1347 *
Manuel Pégourié-Gonnard07de4b12013-09-02 16:26:04 +02001348 * Warning: fails (returning an error) if one of the points is zero!
Manuel Pégourié-Gonnard7a949d32013-12-05 10:26:01 +01001349 * This should never happen, see choice of w in ecp_mul_comb().
Manuel Pégourié-Gonnard04a02252013-11-20 22:57:38 +01001350 *
1351 * Cost: 1N(t) := 1I + (6t - 3)M + 1S
Manuel Pégourié-Gonnardcdd44322012-11-21 16:00:55 +01001352 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001353static int ecp_normalize_jac_many( const mbedtls_ecp_group *grp,
Manuel Pégourié-Gonnard92cceb22017-08-23 16:27:29 +02001354 mbedtls_ecp_point *T[], size_t T_size )
Manuel Pégourié-Gonnardcdd44322012-11-21 16:00:55 +01001355{
Janos Follath24eed8d2019-11-22 13:21:35 +00001356 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
Manuel Pégourié-Gonnardcdd44322012-11-21 16:00:55 +01001357 size_t i;
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001358 mbedtls_mpi *c, u, Zi, ZZi;
Manuel Pégourié-Gonnardcdd44322012-11-21 16:00:55 +01001359
Manuel Pégourié-Gonnard92cceb22017-08-23 16:27:29 +02001360 if( T_size < 2 )
Manuel Pégourié-Gonnard3c0b4ea2013-12-02 19:44:41 +01001361 return( ecp_normalize_jac( grp, *T ) );
Manuel Pégourié-Gonnardcdd44322012-11-21 16:00:55 +01001362
Janos Follathb0697532016-08-18 12:38:46 +01001363#if defined(MBEDTLS_ECP_NORMALIZE_JAC_MANY_ALT)
Manuel Pégourié-Gonnardebac5d32017-08-23 16:23:36 +02001364 if( mbedtls_internal_ecp_grp_capable( grp ) )
Manuel Pégourié-Gonnard92cceb22017-08-23 16:27:29 +02001365 return( mbedtls_internal_ecp_normalize_jac_many( grp, T, T_size ) );
Janos Follathb0697532016-08-18 12:38:46 +01001366#endif
1367
Manuel Pégourié-Gonnard92cceb22017-08-23 16:27:29 +02001368 if( ( c = mbedtls_calloc( T_size, sizeof( mbedtls_mpi ) ) ) == NULL )
Manuel Pégourié-Gonnard6a8ca332015-05-28 09:33:39 +02001369 return( MBEDTLS_ERR_ECP_ALLOC_FAILED );
Manuel Pégourié-Gonnardcdd44322012-11-21 16:00:55 +01001370
Manuel Pégourié-Gonnard5bd38b12017-08-23 16:55:59 +02001371 for( i = 0; i < T_size; i++ )
1372 mbedtls_mpi_init( &c[i] );
1373
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001374 mbedtls_mpi_init( &u ); mbedtls_mpi_init( &Zi ); mbedtls_mpi_init( &ZZi );
Manuel Pégourié-Gonnardcdd44322012-11-21 16:00:55 +01001375
1376 /*
1377 * c[i] = Z_0 * ... * Z_i
1378 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001379 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &c[0], &T[0]->Z ) );
Manuel Pégourié-Gonnard92cceb22017-08-23 16:27:29 +02001380 for( i = 1; i < T_size; i++ )
Manuel Pégourié-Gonnardcdd44322012-11-21 16:00:55 +01001381 {
Gilles Peskine3b3b34f2019-07-18 21:08:27 +02001382 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &c[i], &c[i-1], &T[i]->Z ) );
Manuel Pégourié-Gonnardcdd44322012-11-21 16:00:55 +01001383 }
1384
1385 /*
1386 * u = 1 / (Z_0 * ... * Z_n) mod P
1387 */
Manuel Pégourié-Gonnard92cceb22017-08-23 16:27:29 +02001388 MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &u, &c[T_size-1], &grp->P ) );
Manuel Pégourié-Gonnardcdd44322012-11-21 16:00:55 +01001389
Manuel Pégourié-Gonnard92cceb22017-08-23 16:27:29 +02001390 for( i = T_size - 1; ; i-- )
Manuel Pégourié-Gonnardcdd44322012-11-21 16:00:55 +01001391 {
1392 /*
1393 * Zi = 1 / Z_i mod p
1394 * u = 1 / (Z_0 * ... * Z_i) mod P
1395 */
1396 if( i == 0 ) {
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001397 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &Zi, &u ) );
Manuel Pégourié-Gonnardcdd44322012-11-21 16:00:55 +01001398 }
1399 else
1400 {
Gilles Peskine3b3b34f2019-07-18 21:08:27 +02001401 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &Zi, &u, &c[i-1] ) );
1402 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &u, &u, &T[i]->Z ) );
Manuel Pégourié-Gonnardcdd44322012-11-21 16:00:55 +01001403 }
1404
1405 /*
1406 * proceed as in normalize()
1407 */
Gilles Peskine3b3b34f2019-07-18 21:08:27 +02001408 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &ZZi, &Zi, &Zi ) );
1409 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T[i]->X, &T[i]->X, &ZZi ) );
1410 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T[i]->Y, &T[i]->Y, &ZZi ) );
1411 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T[i]->Y, &T[i]->Y, &Zi ) );
Manuel Pégourié-Gonnard1f789b82013-12-30 17:31:56 +01001412
1413 /*
1414 * Post-precessing: reclaim some memory by shrinking coordinates
1415 * - not storing Z (always 1)
1416 * - shrinking other coordinates, but still keeping the same number of
1417 * limbs as P, as otherwise it will too likely be regrown too fast.
1418 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001419 MBEDTLS_MPI_CHK( mbedtls_mpi_shrink( &T[i]->X, grp->P.n ) );
1420 MBEDTLS_MPI_CHK( mbedtls_mpi_shrink( &T[i]->Y, grp->P.n ) );
1421 mbedtls_mpi_free( &T[i]->Z );
Manuel Pégourié-Gonnardcdd44322012-11-21 16:00:55 +01001422
1423 if( i == 0 )
1424 break;
1425 }
1426
1427cleanup:
1428
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001429 mbedtls_mpi_free( &u ); mbedtls_mpi_free( &Zi ); mbedtls_mpi_free( &ZZi );
Manuel Pégourié-Gonnard92cceb22017-08-23 16:27:29 +02001430 for( i = 0; i < T_size; i++ )
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001431 mbedtls_mpi_free( &c[i] );
1432 mbedtls_free( c );
Manuel Pégourié-Gonnardcdd44322012-11-21 16:00:55 +01001433
1434 return( ret );
1435}
1436
Manuel Pégourié-Gonnardcdd44322012-11-21 16:00:55 +01001437/*
Manuel Pégourié-Gonnard01fca5e2013-11-21 17:47:12 +01001438 * Conditional point inversion: Q -> -Q = (Q.X, -Q.Y, Q.Z) without leak.
1439 * "inv" must be 0 (don't invert) or 1 (invert) or the result will be invalid
1440 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001441static int ecp_safe_invert_jac( const mbedtls_ecp_group *grp,
1442 mbedtls_ecp_point *Q,
Manuel Pégourié-Gonnard01fca5e2013-11-21 17:47:12 +01001443 unsigned char inv )
1444{
Janos Follath24eed8d2019-11-22 13:21:35 +00001445 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
Manuel Pégourié-Gonnard01fca5e2013-11-21 17:47:12 +01001446 unsigned char nonzero;
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001447 mbedtls_mpi mQY;
Manuel Pégourié-Gonnard01fca5e2013-11-21 17:47:12 +01001448
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001449 mbedtls_mpi_init( &mQY );
Manuel Pégourié-Gonnard01fca5e2013-11-21 17:47:12 +01001450
1451 /* Use the fact that -Q.Y mod P = P - Q.Y unless Q.Y == 0 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001452 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &mQY, &grp->P, &Q->Y ) );
1453 nonzero = mbedtls_mpi_cmp_int( &Q->Y, 0 ) != 0;
1454 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &Q->Y, &mQY, inv & nonzero ) );
Manuel Pégourié-Gonnard01fca5e2013-11-21 17:47:12 +01001455
1456cleanup:
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001457 mbedtls_mpi_free( &mQY );
Manuel Pégourié-Gonnard01fca5e2013-11-21 17:47:12 +01001458
1459 return( ret );
1460}
1461
1462/*
Manuel Pégourié-Gonnard0cd6f982013-10-10 15:55:39 +02001463 * Point doubling R = 2 P, Jacobian coordinates
Manuel Pégourié-Gonnard0ace4b32013-10-10 12:44:27 +02001464 *
Peter Dettmance661b22015-02-07 14:43:51 +07001465 * Based on http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#doubling-dbl-1998-cmo-2 .
Manuel Pégourié-Gonnard04a02252013-11-20 22:57:38 +01001466 *
Peter Dettmance661b22015-02-07 14:43:51 +07001467 * We follow the variable naming fairly closely. The formula variations that trade a MUL for a SQR
1468 * (plus a few ADDs) aren't useful as our bignum implementation doesn't distinguish squaring.
1469 *
1470 * Standard optimizations are applied when curve parameter A is one of { 0, -3 }.
1471 *
1472 * Cost: 1D := 3M + 4S (A == 0)
1473 * 4M + 4S (A == -3)
1474 * 3M + 6S + 1a otherwise
Manuel Pégourié-Gonnard1c4aa242013-10-09 16:09:46 +02001475 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001476static int ecp_double_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
1477 const mbedtls_ecp_point *P )
Manuel Pégourié-Gonnard1c4aa242013-10-09 16:09:46 +02001478{
Janos Follath24eed8d2019-11-22 13:21:35 +00001479 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
Manuel Pégourié-Gonnard2088ba62015-05-12 10:36:26 +02001480 mbedtls_mpi M, S, T, U;
Manuel Pégourié-Gonnard1c4aa242013-10-09 16:09:46 +02001481
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001482#if defined(MBEDTLS_SELF_TEST)
Manuel Pégourié-Gonnard0cd6f982013-10-10 15:55:39 +02001483 dbl_count++;
1484#endif
1485
Janos Follathb0697532016-08-18 12:38:46 +01001486#if defined(MBEDTLS_ECP_DOUBLE_JAC_ALT)
Manuel Pégourié-Gonnardebac5d32017-08-23 16:23:36 +02001487 if( mbedtls_internal_ecp_grp_capable( grp ) )
1488 return( mbedtls_internal_ecp_double_jac( grp, R, P ) );
Janos Follath372697b2016-10-28 16:53:11 +01001489#endif /* MBEDTLS_ECP_DOUBLE_JAC_ALT */
Janos Follathb0697532016-08-18 12:38:46 +01001490
Manuel Pégourié-Gonnard2088ba62015-05-12 10:36:26 +02001491 mbedtls_mpi_init( &M ); mbedtls_mpi_init( &S ); mbedtls_mpi_init( &T ); mbedtls_mpi_init( &U );
Manuel Pégourié-Gonnard73cc01d2013-12-06 12:41:30 +01001492
1493 /* Special case for A = -3 */
1494 if( grp->A.p == NULL )
1495 {
Peter Dettmance661b22015-02-07 14:43:51 +07001496 /* M = 3(X + Z^2)(X - Z^2) */
Gilles Peskine3b3b34f2019-07-18 21:08:27 +02001497 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S, &P->Z, &P->Z ) );
1498 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &T, &P->X, &S ) );
1499 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &U, &P->X, &S ) );
1500 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S, &T, &U ) );
Manuel Pégourié-Gonnard2088ba62015-05-12 10:36:26 +02001501 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &S, 3 ) ); MOD_ADD( M );
Manuel Pégourié-Gonnard73cc01d2013-12-06 12:41:30 +01001502 }
1503 else
Peter Vaskovica676acf2014-08-06 00:48:39 +02001504 {
Peter Dettmance661b22015-02-07 14:43:51 +07001505 /* M = 3.X^2 */
Gilles Peskine3b3b34f2019-07-18 21:08:27 +02001506 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S, &P->X, &P->X ) );
Manuel Pégourié-Gonnard2088ba62015-05-12 10:36:26 +02001507 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &S, 3 ) ); MOD_ADD( M );
Peter Dettmance661b22015-02-07 14:43:51 +07001508
1509 /* Optimize away for "koblitz" curves with A = 0 */
Manuel Pégourié-Gonnard2088ba62015-05-12 10:36:26 +02001510 if( mbedtls_mpi_cmp_int( &grp->A, 0 ) != 0 )
Peter Dettmance661b22015-02-07 14:43:51 +07001511 {
1512 /* M += A.Z^4 */
Gilles Peskine3b3b34f2019-07-18 21:08:27 +02001513 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S, &P->Z, &P->Z ) );
1514 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T, &S, &S ) );
1515 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S, &T, &grp->A ) );
1516 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &M, &M, &S ) );
Peter Dettmance661b22015-02-07 14:43:51 +07001517 }
Peter Vaskovica676acf2014-08-06 00:48:39 +02001518 }
Manuel Pégourié-Gonnard73cc01d2013-12-06 12:41:30 +01001519
Peter Dettmance661b22015-02-07 14:43:51 +07001520 /* S = 4.X.Y^2 */
Gilles Peskine3b3b34f2019-07-18 21:08:27 +02001521 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T, &P->Y, &P->Y ) );
1522 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l_mod( grp, &T, 1 ) );
1523 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S, &P->X, &T ) );
1524 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l_mod( grp, &S, 1 ) );
Manuel Pégourié-Gonnard1c4aa242013-10-09 16:09:46 +02001525
Peter Dettmance661b22015-02-07 14:43:51 +07001526 /* U = 8.Y^4 */
Gilles Peskine3b3b34f2019-07-18 21:08:27 +02001527 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &U, &T, &T ) );
1528 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l_mod( grp, &U, 1 ) );
Peter Dettmance661b22015-02-07 14:43:51 +07001529
1530 /* T = M^2 - 2.S */
Gilles Peskine3b3b34f2019-07-18 21:08:27 +02001531 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T, &M, &M ) );
1532 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &T, &T, &S ) );
1533 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &T, &T, &S ) );
Peter Dettmance661b22015-02-07 14:43:51 +07001534
1535 /* S = M(S - T) - U */
Gilles Peskine3b3b34f2019-07-18 21:08:27 +02001536 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &S, &S, &T ) );
1537 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S, &S, &M ) );
1538 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &S, &S, &U ) );
Peter Dettmance661b22015-02-07 14:43:51 +07001539
1540 /* U = 2.Y.Z */
Gilles Peskine3b3b34f2019-07-18 21:08:27 +02001541 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &U, &P->Y, &P->Z ) );
1542 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l_mod( grp, &U, 1 ) );
Peter Dettmance661b22015-02-07 14:43:51 +07001543
Manuel Pégourié-Gonnard2088ba62015-05-12 10:36:26 +02001544 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->X, &T ) );
1545 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Y, &S ) );
1546 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Z, &U ) );
Manuel Pégourié-Gonnard1c4aa242013-10-09 16:09:46 +02001547
1548cleanup:
Manuel Pégourié-Gonnard2088ba62015-05-12 10:36:26 +02001549 mbedtls_mpi_free( &M ); mbedtls_mpi_free( &S ); mbedtls_mpi_free( &T ); mbedtls_mpi_free( &U );
Manuel Pégourié-Gonnard1c4aa242013-10-09 16:09:46 +02001550
1551 return( ret );
1552}
1553
1554/*
Manuel Pégourié-Gonnard469a2092013-11-21 18:20:43 +01001555 * Addition: R = P + Q, mixed affine-Jacobian coordinates (GECC 3.22)
Manuel Pégourié-Gonnard9674fd02012-11-19 21:23:27 +01001556 *
1557 * The coordinates of Q must be normalized (= affine),
1558 * but those of P don't need to. R is not normalized.
1559 *
Manuel Pégourié-Gonnardaade42f2013-11-21 19:19:54 +01001560 * Special cases: (1) P or Q is zero, (2) R is zero, (3) P == Q.
Manuel Pégourié-Gonnard7a949d32013-12-05 10:26:01 +01001561 * None of these cases can happen as intermediate step in ecp_mul_comb():
Manuel Pégourié-Gonnardaade42f2013-11-21 19:19:54 +01001562 * - at each step, P, Q and R are multiples of the base point, the factor
1563 * being less than its order, so none of them is zero;
1564 * - Q is an odd multiple of the base point, P an even multiple,
1565 * due to the choice of precomputed points in the modified comb method.
1566 * So branches for these cases do not leak secret information.
1567 *
Manuel Pégourié-Gonnard72c172a2013-12-30 16:04:55 +01001568 * We accept Q->Z being unset (saving memory in tables) as meaning 1.
1569 *
Manuel Pégourié-Gonnard04a02252013-11-20 22:57:38 +01001570 * Cost: 1A := 8M + 3S
Manuel Pégourié-Gonnardae180d02012-11-02 18:14:40 +01001571 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001572static int ecp_add_mixed( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
1573 const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q )
Manuel Pégourié-Gonnardae180d02012-11-02 18:14:40 +01001574{
Janos Follath24eed8d2019-11-22 13:21:35 +00001575 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001576 mbedtls_mpi T1, T2, T3, T4, X, Y, Z;
Manuel Pégourié-Gonnardae180d02012-11-02 18:14:40 +01001577
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001578#if defined(MBEDTLS_SELF_TEST)
Manuel Pégourié-Gonnardb4a310b2012-11-13 20:57:00 +01001579 add_count++;
1580#endif
1581
Janos Follathb0697532016-08-18 12:38:46 +01001582#if defined(MBEDTLS_ECP_ADD_MIXED_ALT)
Manuel Pégourié-Gonnardebac5d32017-08-23 16:23:36 +02001583 if( mbedtls_internal_ecp_grp_capable( grp ) )
1584 return( mbedtls_internal_ecp_add_mixed( grp, R, P, Q ) );
Janos Follath372697b2016-10-28 16:53:11 +01001585#endif /* MBEDTLS_ECP_ADD_MIXED_ALT */
Janos Follathb0697532016-08-18 12:38:46 +01001586
Manuel Pégourié-Gonnardae180d02012-11-02 18:14:40 +01001587 /*
Manuel Pégourié-Gonnardaade42f2013-11-21 19:19:54 +01001588 * Trivial cases: P == 0 or Q == 0 (case 1)
Manuel Pégourié-Gonnardae180d02012-11-02 18:14:40 +01001589 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001590 if( mbedtls_mpi_cmp_int( &P->Z, 0 ) == 0 )
1591 return( mbedtls_ecp_copy( R, Q ) );
Manuel Pégourié-Gonnard469a2092013-11-21 18:20:43 +01001592
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001593 if( Q->Z.p != NULL && mbedtls_mpi_cmp_int( &Q->Z, 0 ) == 0 )
1594 return( mbedtls_ecp_copy( R, P ) );
Manuel Pégourié-Gonnard1c2782c2012-11-19 20:16:28 +01001595
1596 /*
1597 * Make sure Q coordinates are normalized
1598 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001599 if( Q->Z.p != NULL && mbedtls_mpi_cmp_int( &Q->Z, 1 ) != 0 )
1600 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
Manuel Pégourié-Gonnardae180d02012-11-02 18:14:40 +01001601
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001602 mbedtls_mpi_init( &T1 ); mbedtls_mpi_init( &T2 ); mbedtls_mpi_init( &T3 ); mbedtls_mpi_init( &T4 );
1603 mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Y ); mbedtls_mpi_init( &Z );
Manuel Pégourié-Gonnardab38b702012-11-05 17:34:55 +01001604
Gilles Peskine3b3b34f2019-07-18 21:08:27 +02001605 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T1, &P->Z, &P->Z ) );
1606 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T2, &T1, &P->Z ) );
1607 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T1, &T1, &Q->X ) );
1608 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T2, &T2, &Q->Y ) );
1609 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &T1, &T1, &P->X ) );
1610 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &T2, &T2, &P->Y ) );
Manuel Pégourié-Gonnardae180d02012-11-02 18:14:40 +01001611
Manuel Pégourié-Gonnardaade42f2013-11-21 19:19:54 +01001612 /* Special cases (2) and (3) */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001613 if( mbedtls_mpi_cmp_int( &T1, 0 ) == 0 )
Manuel Pégourié-Gonnard7e0adfb2012-11-08 23:21:46 +01001614 {
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001615 if( mbedtls_mpi_cmp_int( &T2, 0 ) == 0 )
Manuel Pégourié-Gonnard7e0adfb2012-11-08 23:21:46 +01001616 {
1617 ret = ecp_double_jac( grp, R, P );
1618 goto cleanup;
1619 }
1620 else
1621 {
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001622 ret = mbedtls_ecp_set_zero( R );
Manuel Pégourié-Gonnard7e0adfb2012-11-08 23:21:46 +01001623 goto cleanup;
1624 }
1625 }
1626
Gilles Peskine3b3b34f2019-07-18 21:08:27 +02001627 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &Z, &P->Z, &T1 ) );
1628 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T3, &T1, &T1 ) );
1629 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T4, &T3, &T1 ) );
1630 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T3, &T3, &P->X ) );
1631 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &T1, &T3 ) );
1632 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l_mod( grp, &T1, 1 ) );
1633 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &X, &T2, &T2 ) );
1634 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &X, &X, &T1 ) );
1635 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &X, &X, &T4 ) );
1636 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &T3, &T3, &X ) );
1637 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T3, &T3, &T2 ) );
1638 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T4, &T4, &P->Y ) );
1639 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &Y, &T3, &T4 ) );
Manuel Pégourié-Gonnard7e0adfb2012-11-08 23:21:46 +01001640
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001641 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->X, &X ) );
1642 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Y, &Y ) );
1643 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Z, &Z ) );
Manuel Pégourié-Gonnardae180d02012-11-02 18:14:40 +01001644
1645cleanup:
1646
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001647 mbedtls_mpi_free( &T1 ); mbedtls_mpi_free( &T2 ); mbedtls_mpi_free( &T3 ); mbedtls_mpi_free( &T4 );
1648 mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Y ); mbedtls_mpi_free( &Z );
Manuel Pégourié-Gonnardae180d02012-11-02 18:14:40 +01001649
1650 return( ret );
1651}
1652
1653/*
Manuel Pégourié-Gonnard07de4b12013-09-02 16:26:04 +02001654 * Randomize jacobian coordinates:
1655 * (X, Y, Z) -> (l^2 X, l^3 Y, l Z) for random l
Manuel Pégourié-Gonnard3c0b4ea2013-12-02 19:44:41 +01001656 * This is sort of the reverse operation of ecp_normalize_jac().
Manuel Pégourié-Gonnard44aab792013-11-21 10:53:59 +01001657 *
1658 * This countermeasure was first suggested in [2].
Manuel Pégourié-Gonnard07de4b12013-09-02 16:26:04 +02001659 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001660static int ecp_randomize_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt,
Manuel Pégourié-Gonnard07de4b12013-09-02 16:26:04 +02001661 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
1662{
Janos Follath24eed8d2019-11-22 13:21:35 +00001663 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001664 mbedtls_mpi l, ll;
Janos Follathb0697532016-08-18 12:38:46 +01001665 size_t p_size;
Manuel Pégourié-Gonnard07de4b12013-09-02 16:26:04 +02001666 int count = 0;
1667
Janos Follathb0697532016-08-18 12:38:46 +01001668#if defined(MBEDTLS_ECP_RANDOMIZE_JAC_ALT)
Manuel Pégourié-Gonnardebac5d32017-08-23 16:23:36 +02001669 if( mbedtls_internal_ecp_grp_capable( grp ) )
1670 return( mbedtls_internal_ecp_randomize_jac( grp, pt, f_rng, p_rng ) );
Janos Follath372697b2016-10-28 16:53:11 +01001671#endif /* MBEDTLS_ECP_RANDOMIZE_JAC_ALT */
Janos Follathb0697532016-08-18 12:38:46 +01001672
1673 p_size = ( grp->pbits + 7 ) / 8;
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001674 mbedtls_mpi_init( &l ); mbedtls_mpi_init( &ll );
Manuel Pégourié-Gonnard07de4b12013-09-02 16:26:04 +02001675
1676 /* Generate l such that 1 < l < p */
1677 do
1678 {
Ron Eldorca6ff582017-01-12 14:50:50 +02001679 MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &l, p_size, f_rng, p_rng ) );
Manuel Pégourié-Gonnard07de4b12013-09-02 16:26:04 +02001680
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001681 while( mbedtls_mpi_cmp_mpi( &l, &grp->P ) >= 0 )
1682 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &l, 1 ) );
Manuel Pégourié-Gonnard07de4b12013-09-02 16:26:04 +02001683
1684 if( count++ > 10 )
Jonas6692a062020-05-08 16:57:18 +09001685 {
1686 ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
1687 goto cleanup;
1688 }
Manuel Pégourié-Gonnard07de4b12013-09-02 16:26:04 +02001689 }
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001690 while( mbedtls_mpi_cmp_int( &l, 1 ) <= 0 );
Manuel Pégourié-Gonnard07de4b12013-09-02 16:26:04 +02001691
1692 /* Z = l * Z */
Gilles Peskine3b3b34f2019-07-18 21:08:27 +02001693 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &pt->Z, &pt->Z, &l ) );
Manuel Pégourié-Gonnard07de4b12013-09-02 16:26:04 +02001694
1695 /* X = l^2 * X */
Gilles Peskine3b3b34f2019-07-18 21:08:27 +02001696 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &ll, &l, &l ) );
1697 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &pt->X, &pt->X, &ll ) );
Manuel Pégourié-Gonnard07de4b12013-09-02 16:26:04 +02001698
1699 /* Y = l^3 * Y */
Gilles Peskine3b3b34f2019-07-18 21:08:27 +02001700 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &ll, &ll, &l ) );
1701 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &pt->Y, &pt->Y, &ll ) );
Manuel Pégourié-Gonnard07de4b12013-09-02 16:26:04 +02001702
1703cleanup:
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001704 mbedtls_mpi_free( &l ); mbedtls_mpi_free( &ll );
Manuel Pégourié-Gonnard07de4b12013-09-02 16:26:04 +02001705
1706 return( ret );
1707}
1708
1709/*
Manuel Pégourié-Gonnardc30200e2013-11-20 18:39:55 +01001710 * Check and define parameters used by the comb method (see below for details)
1711 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001712#if MBEDTLS_ECP_WINDOW_SIZE < 2 || MBEDTLS_ECP_WINDOW_SIZE > 7
1713#error "MBEDTLS_ECP_WINDOW_SIZE out of bounds"
Manuel Pégourié-Gonnardc30200e2013-11-20 18:39:55 +01001714#endif
1715
1716/* d = ceil( n / w ) */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001717#define COMB_MAX_D ( MBEDTLS_ECP_MAX_BITS + 1 ) / 2
Manuel Pégourié-Gonnardc30200e2013-11-20 18:39:55 +01001718
1719/* number of precomputed points */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001720#define COMB_MAX_PRE ( 1 << ( MBEDTLS_ECP_WINDOW_SIZE - 1 ) )
Manuel Pégourié-Gonnardc30200e2013-11-20 18:39:55 +01001721
1722/*
1723 * Compute the representation of m that will be used with our comb method.
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01001724 *
1725 * The basic comb method is described in GECC 3.44 for example. We use a
Manuel Pégourié-Gonnard101a39f2013-11-20 14:47:19 +01001726 * modified version that provides resistance to SPA by avoiding zero
1727 * digits in the representation as in [3]. We modify the method further by
1728 * requiring that all K_i be odd, which has the small cost that our
Manuel Pégourié-Gonnard7037e222017-08-23 14:30:36 +02001729 * representation uses one more K_i, due to carries, but saves on the size of
1730 * the precomputed table.
Manuel Pégourié-Gonnard101a39f2013-11-20 14:47:19 +01001731 *
Manuel Pégourié-Gonnard7037e222017-08-23 14:30:36 +02001732 * Summary of the comb method and its modifications:
1733 *
1734 * - The goal is to compute m*P for some w*d-bit integer m.
1735 *
1736 * - The basic comb method splits m into the w-bit integers
1737 * x[0] .. x[d-1] where x[i] consists of the bits in m whose
1738 * index has residue i modulo d, and computes m * P as
1739 * S[x[0]] + 2 * S[x[1]] + .. + 2^(d-1) S[x[d-1]], where
1740 * S[i_{w-1} .. i_0] := i_{w-1} 2^{(w-1)d} P + ... + i_1 2^d P + i_0 P.
1741 *
1742 * - If it happens that, say, x[i+1]=0 (=> S[x[i+1]]=0), one can replace the sum by
1743 * .. + 2^{i-1} S[x[i-1]] - 2^i S[x[i]] + 2^{i+1} S[x[i]] + 2^{i+2} S[x[i+2]] ..,
1744 * thereby successively converting it into a form where all summands
1745 * are nonzero, at the cost of negative summands. This is the basic idea of [3].
1746 *
1747 * - More generally, even if x[i+1] != 0, we can first transform the sum as
1748 * .. - 2^i S[x[i]] + 2^{i+1} ( S[x[i]] + S[x[i+1]] ) + 2^{i+2} S[x[i+2]] ..,
1749 * and then replace S[x[i]] + S[x[i+1]] = S[x[i] ^ x[i+1]] + 2 S[x[i] & x[i+1]].
1750 * Performing and iterating this procedure for those x[i] that are even
1751 * (keeping track of carry), we can transform the original sum into one of the form
1752 * S[x'[0]] +- 2 S[x'[1]] +- .. +- 2^{d-1} S[x'[d-1]] + 2^d S[x'[d]]
1753 * with all x'[i] odd. It is therefore only necessary to know S at odd indices,
1754 * which is why we are only computing half of it in the first place in
1755 * ecp_precompute_comb and accessing it with index abs(i) / 2 in ecp_select_comb.
1756 *
1757 * - For the sake of compactness, only the seven low-order bits of x[i]
1758 * are used to represent its absolute value (K_i in the paper), and the msb
Manuel Pégourié-Gonnardee68cff2018-10-15 15:27:49 +02001759 * of x[i] encodes the sign (s_i in the paper): it is set if and only if
Manuel Pégourié-Gonnard7037e222017-08-23 14:30:36 +02001760 * if s_i == -1;
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01001761 *
1762 * Calling conventions:
Manuel Pégourié-Gonnard101a39f2013-11-20 14:47:19 +01001763 * - x is an array of size d + 1
Manuel Pégourié-Gonnardc30200e2013-11-20 18:39:55 +01001764 * - w is the size, ie number of teeth, of the comb, and must be between
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001765 * 2 and 7 (in practice, between 2 and MBEDTLS_ECP_WINDOW_SIZE)
Manuel Pégourié-Gonnard101a39f2013-11-20 14:47:19 +01001766 * - m is the MPI, expected to be odd and such that bitlength(m) <= w * d
1767 * (the result will be incorrect if these assumptions are not satisfied)
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01001768 */
Manuel Pégourié-Gonnard62738e92017-03-14 10:00:21 +01001769static void ecp_comb_recode_core( unsigned char x[], size_t d,
1770 unsigned char w, const mbedtls_mpi *m )
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01001771{
1772 size_t i, j;
Manuel Pégourié-Gonnard101a39f2013-11-20 14:47:19 +01001773 unsigned char c, cc, adjust;
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01001774
Manuel Pégourié-Gonnard101a39f2013-11-20 14:47:19 +01001775 memset( x, 0, d+1 );
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01001776
Manuel Pégourié-Gonnardedc1a1f2013-11-21 09:50:00 +01001777 /* First get the classical comb values (except for x_d = 0) */
1778 for( i = 0; i < d; i++ )
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01001779 for( j = 0; j < w; j++ )
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001780 x[i] |= mbedtls_mpi_get_bit( m, i + d * j ) << j;
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01001781
Manuel Pégourié-Gonnardedc1a1f2013-11-21 09:50:00 +01001782 /* Now make sure x_1 .. x_d are odd */
1783 c = 0;
1784 for( i = 1; i <= d; i++ )
1785 {
Manuel Pégourié-Gonnard101a39f2013-11-20 14:47:19 +01001786 /* Add carry and update it */
1787 cc = x[i] & c;
1788 x[i] = x[i] ^ c;
1789 c = cc;
1790
Manuel Pégourié-Gonnardedc1a1f2013-11-21 09:50:00 +01001791 /* Adjust if needed, avoiding branches */
Manuel Pégourié-Gonnard101a39f2013-11-20 14:47:19 +01001792 adjust = 1 - ( x[i] & 0x01 );
1793 c |= x[i] & ( x[i-1] * adjust );
1794 x[i] = x[i] ^ ( x[i-1] * adjust );
1795 x[i-1] |= adjust << 7;
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01001796 }
1797}
1798
1799/*
Manuel Pégourié-Gonnard7037e222017-08-23 14:30:36 +02001800 * Precompute points for the adapted comb method
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01001801 *
Manuel Pégourié-Gonnard7037e222017-08-23 14:30:36 +02001802 * Assumption: T must be able to hold 2^{w - 1} elements.
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01001803 *
Manuel Pégourié-Gonnard7037e222017-08-23 14:30:36 +02001804 * Operation: If i = i_{w-1} ... i_1 is the binary representation of i,
1805 * sets T[i] = i_{w-1} 2^{(w-1)d} P + ... + i_1 2^d P + P.
Manuel Pégourié-Gonnard04a02252013-11-20 22:57:38 +01001806 *
1807 * Cost: d(w-1) D + (2^{w-1} - 1) A + 1 N(w-1) + 1 N(2^{w-1} - 1)
Manuel Pégourié-Gonnard7037e222017-08-23 14:30:36 +02001808 *
1809 * Note: Even comb values (those where P would be omitted from the
1810 * sum defining T[i] above) are not needed in our adaption
Manuel Pégourié-Gonnardee68cff2018-10-15 15:27:49 +02001811 * the comb method. See ecp_comb_recode_core().
Manuel Pégourié-Gonnard7037e222017-08-23 14:30:36 +02001812 *
1813 * This function currently works in four steps:
Manuel Pégourié-Gonnardee68cff2018-10-15 15:27:49 +02001814 * (1) [dbl] Computation of intermediate T[i] for 2-power values of i
Manuel Pégourié-Gonnard4ed1dab2017-08-24 11:02:04 +02001815 * (2) [norm_dbl] Normalization of coordinates of these T[i]
1816 * (3) [add] Computation of all T[i]
1817 * (4) [norm_add] Normalization of all T[i]
Manuel Pégourié-Gonnard7037e222017-08-23 14:30:36 +02001818 *
1819 * Step 1 can be interrupted but not the others; together with the final
1820 * coordinate normalization they are the largest steps done at once, depending
1821 * on the window size. Here are operation counts for P-256:
1822 *
1823 * step (2) (3) (4)
1824 * w = 5 142 165 208
1825 * w = 4 136 77 160
1826 * w = 3 130 33 136
1827 * w = 2 124 11 124
1828 *
1829 * So if ECC operations are blocking for too long even with a low max_ops
1830 * value, it's useful to set MBEDTLS_ECP_WINDOW_SIZE to a lower value in order
1831 * to minimize maximum blocking time.
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01001832 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001833static int ecp_precompute_comb( const mbedtls_ecp_group *grp,
1834 mbedtls_ecp_point T[], const mbedtls_ecp_point *P,
Manuel Pégourié-Gonnard3cade222017-04-20 09:31:00 +02001835 unsigned char w, size_t d,
1836 mbedtls_ecp_restart_ctx *rs_ctx )
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01001837{
Janos Follath24eed8d2019-11-22 13:21:35 +00001838 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
Manuel Pégourié-Gonnardfc3e0be2017-03-20 09:29:31 +01001839 unsigned char i;
Manuel Pégourié-Gonnard213541a2017-03-20 12:50:41 +01001840 size_t j = 0;
Manuel Pégourié-Gonnard92cceb22017-08-23 16:27:29 +02001841 const unsigned char T_size = 1U << ( w - 1 );
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001842 mbedtls_ecp_point *cur, *TT[COMB_MAX_PRE - 1];
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01001843
Manuel Pégourié-Gonnard4b9c51e2017-04-20 15:50:26 +02001844#if defined(MBEDTLS_ECP_RESTARTABLE)
Manuel Pégourié-Gonnard3cade222017-04-20 09:31:00 +02001845 if( rs_ctx != NULL && rs_ctx->rsm != NULL )
Manuel Pégourié-Gonnard085b1df2017-03-16 16:56:04 +01001846 {
Manuel Pégourié-Gonnard4ed1dab2017-08-24 11:02:04 +02001847 if( rs_ctx->rsm->state == ecp_rsm_pre_dbl )
1848 goto dbl;
Manuel Pégourié-Gonnard3cade222017-04-20 09:31:00 +02001849 if( rs_ctx->rsm->state == ecp_rsm_pre_norm_dbl )
Manuel Pégourié-Gonnarde2d7cb32017-03-20 10:24:17 +01001850 goto norm_dbl;
Manuel Pégourié-Gonnard4ed1dab2017-08-24 11:02:04 +02001851 if( rs_ctx->rsm->state == ecp_rsm_pre_add )
1852 goto add;
1853 if( rs_ctx->rsm->state == ecp_rsm_pre_norm_add )
1854 goto norm_add;
Manuel Pégourié-Gonnard085b1df2017-03-16 16:56:04 +01001855 }
Manuel Pégourié-Gonnardee68cff2018-10-15 15:27:49 +02001856#else
1857 (void) rs_ctx;
Manuel Pégourié-Gonnard085b1df2017-03-16 16:56:04 +01001858#endif
1859
Manuel Pégourié-Gonnard4ed1dab2017-08-24 11:02:04 +02001860#if defined(MBEDTLS_ECP_RESTARTABLE)
1861 if( rs_ctx != NULL && rs_ctx->rsm != NULL )
1862 {
1863 rs_ctx->rsm->state = ecp_rsm_pre_dbl;
1864
1865 /* initial state for the loop */
1866 rs_ctx->rsm->i = 0;
1867 }
1868
1869dbl:
1870#endif
Manuel Pégourié-Gonnardee68cff2018-10-15 15:27:49 +02001871 /*
1872 * Set T[0] = P and
1873 * T[2^{l-1}] = 2^{dl} P for l = 1 .. w-1 (this is not the final value)
1874 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001875 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( &T[0], P ) );
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01001876
Manuel Pégourié-Gonnard4b9c51e2017-04-20 15:50:26 +02001877#if defined(MBEDTLS_ECP_RESTARTABLE)
Manuel Pégourié-Gonnard3cade222017-04-20 09:31:00 +02001878 if( rs_ctx != NULL && rs_ctx->rsm != NULL && rs_ctx->rsm->i != 0 )
1879 j = rs_ctx->rsm->i;
Manuel Pégourié-Gonnard213541a2017-03-20 12:50:41 +01001880 else
1881#endif
1882 j = 0;
1883
1884 for( ; j < d * ( w - 1 ); j++ )
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01001885 {
Manuel Pégourié-Gonnardc7511482017-04-20 16:31:00 +02001886 MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_DBL );
Manuel Pégourié-Gonnard213541a2017-03-20 12:50:41 +01001887
Manuel Pégourié-Gonnardae557072017-03-20 12:21:24 +01001888 i = 1U << ( j / d );
Manuel Pégourié-Gonnard101a39f2013-11-20 14:47:19 +01001889 cur = T + i;
Manuel Pégourié-Gonnardae557072017-03-20 12:21:24 +01001890
1891 if( j % d == 0 )
1892 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( cur, T + ( i >> 1 ) ) );
1893
1894 MBEDTLS_MPI_CHK( ecp_double_jac( grp, cur, cur ) );
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01001895 }
1896
Manuel Pégourié-Gonnard4b9c51e2017-04-20 15:50:26 +02001897#if defined(MBEDTLS_ECP_RESTARTABLE)
Manuel Pégourié-Gonnard4ed1dab2017-08-24 11:02:04 +02001898 if( rs_ctx != NULL && rs_ctx->rsm != NULL )
1899 rs_ctx->rsm->state = ecp_rsm_pre_norm_dbl;
1900
Manuel Pégourié-Gonnarde2d7cb32017-03-20 10:24:17 +01001901norm_dbl:
1902#endif
Manuel Pégourié-Gonnardee68cff2018-10-15 15:27:49 +02001903 /*
1904 * Normalize current elements in T. As T has holes,
1905 * use an auxiliary array of pointers to elements in T.
1906 */
Manuel Pégourié-Gonnardfc3e0be2017-03-20 09:29:31 +01001907 j = 0;
Manuel Pégourié-Gonnard92cceb22017-08-23 16:27:29 +02001908 for( i = 1; i < T_size; i <<= 1 )
Manuel Pégourié-Gonnardfc3e0be2017-03-20 09:29:31 +01001909 TT[j++] = T + i;
1910
Manuel Pégourié-Gonnardc7511482017-04-20 16:31:00 +02001911 MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_INV + 6 * j - 2 );
Manuel Pégourié-Gonnarde2d7cb32017-03-20 10:24:17 +01001912
Manuel Pégourié-Gonnardfc3e0be2017-03-20 09:29:31 +01001913 MBEDTLS_MPI_CHK( ecp_normalize_jac_many( grp, TT, j ) );
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01001914
Manuel Pégourié-Gonnard4b9c51e2017-04-20 15:50:26 +02001915#if defined(MBEDTLS_ECP_RESTARTABLE)
Manuel Pégourié-Gonnard4ed1dab2017-08-24 11:02:04 +02001916 if( rs_ctx != NULL && rs_ctx->rsm != NULL )
1917 rs_ctx->rsm->state = ecp_rsm_pre_add;
1918
Manuel Pégourié-Gonnarde2d7cb32017-03-20 10:24:17 +01001919add:
1920#endif
Manuel Pégourié-Gonnardee68cff2018-10-15 15:27:49 +02001921 /*
1922 * Compute the remaining ones using the minimal number of additions
1923 * Be careful to update T[2^l] only after using it!
1924 */
Manuel Pégourié-Gonnard92cceb22017-08-23 16:27:29 +02001925 MBEDTLS_ECP_BUDGET( ( T_size - 1 ) * MBEDTLS_ECP_OPS_ADD );
Manuel Pégourié-Gonnarde2d7cb32017-03-20 10:24:17 +01001926
Manuel Pégourié-Gonnard92cceb22017-08-23 16:27:29 +02001927 for( i = 1; i < T_size; i <<= 1 )
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01001928 {
Manuel Pégourié-Gonnard101a39f2013-11-20 14:47:19 +01001929 j = i;
1930 while( j-- )
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001931 MBEDTLS_MPI_CHK( ecp_add_mixed( grp, &T[i + j], &T[j], &T[i] ) );
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01001932 }
1933
Manuel Pégourié-Gonnard4b9c51e2017-04-20 15:50:26 +02001934#if defined(MBEDTLS_ECP_RESTARTABLE)
Manuel Pégourié-Gonnard4ed1dab2017-08-24 11:02:04 +02001935 if( rs_ctx != NULL && rs_ctx->rsm != NULL )
1936 rs_ctx->rsm->state = ecp_rsm_pre_norm_add;
1937
Manuel Pégourié-Gonnarde2d7cb32017-03-20 10:24:17 +01001938norm_add:
1939#endif
Manuel Pégourié-Gonnardee68cff2018-10-15 15:27:49 +02001940 /*
Manuel Pégourié-Gonnarda966fde2018-10-23 10:41:11 +02001941 * Normalize final elements in T. Even though there are no holes now, we
1942 * still need the auxiliary array for homogeneity with the previous
1943 * call. Also, skip T[0] which is already normalised, being a copy of P.
Manuel Pégourié-Gonnardee68cff2018-10-15 15:27:49 +02001944 */
Manuel Pégourié-Gonnard92cceb22017-08-23 16:27:29 +02001945 for( j = 0; j + 1 < T_size; j++ )
Manuel Pégourié-Gonnardfc3e0be2017-03-20 09:29:31 +01001946 TT[j] = T + j + 1;
1947
Manuel Pégourié-Gonnardc7511482017-04-20 16:31:00 +02001948 MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_INV + 6 * j - 2 );
Manuel Pégourié-Gonnarde2d7cb32017-03-20 10:24:17 +01001949
Manuel Pégourié-Gonnardfc3e0be2017-03-20 09:29:31 +01001950 MBEDTLS_MPI_CHK( ecp_normalize_jac_many( grp, TT, j ) );
Manuel Pégourié-Gonnarde2820122013-11-21 10:08:50 +01001951
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01001952cleanup:
Manuel Pégourié-Gonnard4b9c51e2017-04-20 15:50:26 +02001953#if defined(MBEDTLS_ECP_RESTARTABLE)
Manuel Pégourié-Gonnard3cade222017-04-20 09:31:00 +02001954 if( rs_ctx != NULL && rs_ctx->rsm != NULL &&
1955 ret == MBEDTLS_ERR_ECP_IN_PROGRESS )
Manuel Pégourié-Gonnard213541a2017-03-20 12:50:41 +01001956 {
Manuel Pégourié-Gonnard4ed1dab2017-08-24 11:02:04 +02001957 if( rs_ctx->rsm->state == ecp_rsm_pre_dbl )
Manuel Pégourié-Gonnard3cade222017-04-20 09:31:00 +02001958 rs_ctx->rsm->i = j;
Manuel Pégourié-Gonnard213541a2017-03-20 12:50:41 +01001959 }
1960#endif
Janos Follathb0697532016-08-18 12:38:46 +01001961
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01001962 return( ret );
1963}
1964
1965/*
Manuel Pégourié-Gonnard101a39f2013-11-20 14:47:19 +01001966 * Select precomputed point: R = sign(i) * T[ abs(i) / 2 ]
Manuel Pégourié-Gonnard7037e222017-08-23 14:30:36 +02001967 *
1968 * See ecp_comb_recode_core() for background
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01001969 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001970static int ecp_select_comb( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
Manuel Pégourié-Gonnard92cceb22017-08-23 16:27:29 +02001971 const mbedtls_ecp_point T[], unsigned char T_size,
Manuel Pégourié-Gonnardd7283502013-11-21 20:00:38 +01001972 unsigned char i )
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01001973{
Janos Follath24eed8d2019-11-22 13:21:35 +00001974 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
Manuel Pégourié-Gonnardd7283502013-11-21 20:00:38 +01001975 unsigned char ii, j;
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01001976
Manuel Pégourié-Gonnardd7283502013-11-21 20:00:38 +01001977 /* Ignore the "sign" bit and scale down */
1978 ii = ( i & 0x7Fu ) >> 1;
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01001979
Manuel Pégourié-Gonnardd7283502013-11-21 20:00:38 +01001980 /* Read the whole table to thwart cache-based timing attacks */
Manuel Pégourié-Gonnard92cceb22017-08-23 16:27:29 +02001981 for( j = 0; j < T_size; j++ )
Manuel Pégourié-Gonnardd7283502013-11-21 20:00:38 +01001982 {
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001983 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &R->X, &T[j].X, j == ii ) );
1984 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &R->Y, &T[j].Y, j == ii ) );
Manuel Pégourié-Gonnardd7283502013-11-21 20:00:38 +01001985 }
1986
Manuel Pégourié-Gonnard01fca5e2013-11-21 17:47:12 +01001987 /* Safely invert result if i is "negative" */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02001988 MBEDTLS_MPI_CHK( ecp_safe_invert_jac( grp, R, i >> 7 ) );
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01001989
1990cleanup:
1991 return( ret );
1992}
1993
1994/*
1995 * Core multiplication algorithm for the (modified) comb method.
1996 * This part is actually common with the basic comb method (GECC 3.44)
Manuel Pégourié-Gonnard04a02252013-11-20 22:57:38 +01001997 *
1998 * Cost: d A + d D + 1 R
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01001999 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002000static int ecp_mul_comb_core( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
Manuel Pégourié-Gonnard92cceb22017-08-23 16:27:29 +02002001 const mbedtls_ecp_point T[], unsigned char T_size,
Manuel Pégourié-Gonnard70c14372013-11-20 20:07:26 +01002002 const unsigned char x[], size_t d,
2003 int (*f_rng)(void *, unsigned char *, size_t),
Manuel Pégourié-Gonnard3cade222017-04-20 09:31:00 +02002004 void *p_rng,
2005 mbedtls_ecp_restart_ctx *rs_ctx )
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01002006{
Janos Follath24eed8d2019-11-22 13:21:35 +00002007 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002008 mbedtls_ecp_point Txi;
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01002009 size_t i;
2010
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002011 mbedtls_ecp_point_init( &Txi );
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01002012
Manuel Pégourié-Gonnard4b9c51e2017-04-20 15:50:26 +02002013#if !defined(MBEDTLS_ECP_RESTARTABLE)
Manuel Pégourié-Gonnard3cade222017-04-20 09:31:00 +02002014 (void) rs_ctx;
2015#endif
2016
Manuel Pégourié-Gonnard4b9c51e2017-04-20 15:50:26 +02002017#if defined(MBEDTLS_ECP_RESTARTABLE)
Manuel Pégourié-Gonnard4ed1dab2017-08-24 11:02:04 +02002018 if( rs_ctx != NULL && rs_ctx->rsm != NULL &&
2019 rs_ctx->rsm->state != ecp_rsm_comb_core )
2020 {
2021 rs_ctx->rsm->i = 0;
2022 rs_ctx->rsm->state = ecp_rsm_comb_core;
2023 }
2024
2025 /* new 'if' instead of nested for the sake of the 'else' branch */
Manuel Pégourié-Gonnard3cade222017-04-20 09:31:00 +02002026 if( rs_ctx != NULL && rs_ctx->rsm != NULL && rs_ctx->rsm->i != 0 )
Manuel Pégourié-Gonnardc5d844b2017-03-15 13:06:28 +01002027 {
Manuel Pégourié-Gonnard3cade222017-04-20 09:31:00 +02002028 /* restore current index (R already pointing to rs_ctx->rsm->R) */
2029 i = rs_ctx->rsm->i;
Manuel Pégourié-Gonnardc5d844b2017-03-15 13:06:28 +01002030 }
2031 else
2032#endif
2033 {
2034 /* Start with a non-zero point and randomize its coordinates */
2035 i = d;
Manuel Pégourié-Gonnard92cceb22017-08-23 16:27:29 +02002036 MBEDTLS_MPI_CHK( ecp_select_comb( grp, R, T, T_size, x[i] ) );
Manuel Pégourié-Gonnardc5d844b2017-03-15 13:06:28 +01002037 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->Z, 1 ) );
Manuel Pégourié-Gonnard22b1de32020-06-04 10:43:29 +02002038#if defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
Manuel Pégourié-Gonnardc5d844b2017-03-15 13:06:28 +01002039 if( f_rng != 0 )
Manuel Pégourié-Gonnard22b1de32020-06-04 10:43:29 +02002040#endif
Manuel Pégourié-Gonnardc5d844b2017-03-15 13:06:28 +01002041 MBEDTLS_MPI_CHK( ecp_randomize_jac( grp, R, f_rng, p_rng ) );
2042 }
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01002043
Manuel Pégourié-Gonnard90f31b72018-10-16 10:45:24 +02002044 while( i != 0 )
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01002045 {
Manuel Pégourié-Gonnardc7511482017-04-20 16:31:00 +02002046 MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_DBL + MBEDTLS_ECP_OPS_ADD );
Manuel Pégourié-Gonnard90f31b72018-10-16 10:45:24 +02002047 --i;
2048
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002049 MBEDTLS_MPI_CHK( ecp_double_jac( grp, R, R ) );
Manuel Pégourié-Gonnard92cceb22017-08-23 16:27:29 +02002050 MBEDTLS_MPI_CHK( ecp_select_comb( grp, &Txi, T, T_size, x[i] ) );
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002051 MBEDTLS_MPI_CHK( ecp_add_mixed( grp, R, R, &Txi ) );
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01002052 }
2053
2054cleanup:
Janos Follathb0697532016-08-18 12:38:46 +01002055
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002056 mbedtls_ecp_point_free( &Txi );
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01002057
Manuel Pégourié-Gonnard4b9c51e2017-04-20 15:50:26 +02002058#if defined(MBEDTLS_ECP_RESTARTABLE)
Manuel Pégourié-Gonnard4ed1dab2017-08-24 11:02:04 +02002059 if( rs_ctx != NULL && rs_ctx->rsm != NULL &&
2060 ret == MBEDTLS_ERR_ECP_IN_PROGRESS )
Manuel Pégourié-Gonnardc5d844b2017-03-15 13:06:28 +01002061 {
Manuel Pégourié-Gonnard90f31b72018-10-16 10:45:24 +02002062 rs_ctx->rsm->i = i;
Manuel Pégourié-Gonnard4ed1dab2017-08-24 11:02:04 +02002063 /* no need to save R, already pointing to rs_ctx->rsm->R */
Manuel Pégourié-Gonnardc5d844b2017-03-15 13:06:28 +01002064 }
2065#endif
2066
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01002067 return( ret );
2068}
2069
2070/*
Manuel Pégourié-Gonnard62738e92017-03-14 10:00:21 +01002071 * Recode the scalar to get constant-time comb multiplication
2072 *
2073 * As the actual scalar recoding needs an odd scalar as a starting point,
2074 * this wrapper ensures that by replacing m by N - m if necessary, and
2075 * informs the caller that the result of multiplication will be negated.
Manuel Pégourié-Gonnard7037e222017-08-23 14:30:36 +02002076 *
Manuel Pégourié-Gonnardfd87e352017-08-24 14:21:05 +02002077 * This works because we only support large prime order for Short Weierstrass
2078 * curves, so N is always odd hence either m or N - m is.
2079 *
Manuel Pégourié-Gonnard7037e222017-08-23 14:30:36 +02002080 * See ecp_comb_recode_core() for background.
Manuel Pégourié-Gonnardec5606a2017-03-09 12:46:45 +01002081 */
Manuel Pégourié-Gonnard62738e92017-03-14 10:00:21 +01002082static int ecp_comb_recode_scalar( const mbedtls_ecp_group *grp,
2083 const mbedtls_mpi *m,
2084 unsigned char k[COMB_MAX_D + 1],
2085 size_t d,
2086 unsigned char w,
2087 unsigned char *parity_trick )
Manuel Pégourié-Gonnardec5606a2017-03-09 12:46:45 +01002088{
Janos Follath24eed8d2019-11-22 13:21:35 +00002089 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
Manuel Pégourié-Gonnard62738e92017-03-14 10:00:21 +01002090 mbedtls_mpi M, mm;
Manuel Pégourié-Gonnardec5606a2017-03-09 12:46:45 +01002091
Manuel Pégourié-Gonnard62738e92017-03-14 10:00:21 +01002092 mbedtls_mpi_init( &M );
Manuel Pégourié-Gonnardec5606a2017-03-09 12:46:45 +01002093 mbedtls_mpi_init( &mm );
2094
Manuel Pégourié-Gonnardfd87e352017-08-24 14:21:05 +02002095 /* N is always odd (see above), just make extra sure */
Manuel Pégourié-Gonnardec5606a2017-03-09 12:46:45 +01002096 if( mbedtls_mpi_get_bit( &grp->N, 0 ) != 1 )
2097 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
2098
Manuel Pégourié-Gonnard62738e92017-03-14 10:00:21 +01002099 /* do we need the parity trick? */
2100 *parity_trick = ( mbedtls_mpi_get_bit( m, 0 ) == 0 );
2101
2102 /* execute parity fix in constant time */
2103 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &M, m ) );
Manuel Pégourié-Gonnardec5606a2017-03-09 12:46:45 +01002104 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &mm, &grp->N, m ) );
Manuel Pégourié-Gonnard62738e92017-03-14 10:00:21 +01002105 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &M, &mm, *parity_trick ) );
2106
2107 /* actual scalar recoding */
2108 ecp_comb_recode_core( k, d, w, &M );
Manuel Pégourié-Gonnardec5606a2017-03-09 12:46:45 +01002109
2110cleanup:
2111 mbedtls_mpi_free( &mm );
Manuel Pégourié-Gonnard62738e92017-03-14 10:00:21 +01002112 mbedtls_mpi_free( &M );
Manuel Pégourié-Gonnardec5606a2017-03-09 12:46:45 +01002113
2114 return( ret );
2115}
2116
2117/*
Manuel Pégourié-Gonnard391f4412017-03-13 12:26:21 +01002118 * Perform comb multiplication (for short Weierstrass curves)
2119 * once the auxiliary table has been pre-computed.
Manuel Pégourié-Gonnard62738e92017-03-14 10:00:21 +01002120 *
2121 * Scalar recoding may use a parity trick that makes us compute -m * P,
2122 * if that is the case we'll need to recover m * P at the end.
Manuel Pégourié-Gonnard391f4412017-03-13 12:26:21 +01002123 */
2124static int ecp_mul_comb_after_precomp( const mbedtls_ecp_group *grp,
2125 mbedtls_ecp_point *R,
2126 const mbedtls_mpi *m,
2127 const mbedtls_ecp_point *T,
Manuel Pégourié-Gonnard92cceb22017-08-23 16:27:29 +02002128 unsigned char T_size,
Manuel Pégourié-Gonnard391f4412017-03-13 12:26:21 +01002129 unsigned char w,
2130 size_t d,
2131 int (*f_rng)(void *, unsigned char *, size_t),
Manuel Pégourié-Gonnard3cade222017-04-20 09:31:00 +02002132 void *p_rng,
2133 mbedtls_ecp_restart_ctx *rs_ctx )
Manuel Pégourié-Gonnard391f4412017-03-13 12:26:21 +01002134{
Janos Follath24eed8d2019-11-22 13:21:35 +00002135 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
Manuel Pégourié-Gonnard62738e92017-03-14 10:00:21 +01002136 unsigned char parity_trick;
Manuel Pégourié-Gonnard391f4412017-03-13 12:26:21 +01002137 unsigned char k[COMB_MAX_D + 1];
Manuel Pégourié-Gonnard8962ddb2017-03-14 12:11:21 +01002138 mbedtls_ecp_point *RR = R;
2139
Manuel Pégourié-Gonnard4ed1dab2017-08-24 11:02:04 +02002140#if defined(MBEDTLS_ECP_RESTARTABLE)
2141 if( rs_ctx != NULL && rs_ctx->rsm != NULL )
2142 {
2143 RR = &rs_ctx->rsm->R;
2144
2145 if( rs_ctx->rsm->state == ecp_rsm_final_norm )
2146 goto final_norm;
2147 }
Manuel Pégourié-Gonnard8962ddb2017-03-14 12:11:21 +01002148#endif
Manuel Pégourié-Gonnard391f4412017-03-13 12:26:21 +01002149
Manuel Pégourié-Gonnard4ed1dab2017-08-24 11:02:04 +02002150 MBEDTLS_MPI_CHK( ecp_comb_recode_scalar( grp, m, k, d, w,
2151 &parity_trick ) );
2152 MBEDTLS_MPI_CHK( ecp_mul_comb_core( grp, RR, T, T_size, k, d,
2153 f_rng, p_rng, rs_ctx ) );
2154 MBEDTLS_MPI_CHK( ecp_safe_invert_jac( grp, RR, parity_trick ) );
2155
Manuel Pégourié-Gonnard4b9c51e2017-04-20 15:50:26 +02002156#if defined(MBEDTLS_ECP_RESTARTABLE)
Manuel Pégourié-Gonnard3cade222017-04-20 09:31:00 +02002157 if( rs_ctx != NULL && rs_ctx->rsm != NULL )
Manuel Pégourié-Gonnard4ed1dab2017-08-24 11:02:04 +02002158 rs_ctx->rsm->state = ecp_rsm_final_norm;
Manuel Pégourié-Gonnard3cade222017-04-20 09:31:00 +02002159
Manuel Pégourié-Gonnard4ed1dab2017-08-24 11:02:04 +02002160final_norm:
Manuel Pégourié-Gonnard9b8d34e2020-06-08 09:53:20 +02002161 MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_INV );
Manuel Pégourié-Gonnard2fad7ae2017-03-14 13:13:13 +01002162#endif
Manuel Pégourié-Gonnarda4aa89b2020-03-25 12:41:29 +01002163 /*
2164 * Knowledge of the jacobian coordinates may leak the last few bits of the
2165 * scalar [1], and since our MPI implementation isn't constant-flow,
2166 * inversion (used for coordinate normalization) may leak the full value
2167 * of its input via side-channels [2].
2168 *
2169 * [1] https://eprint.iacr.org/2003/191
2170 * [2] https://eprint.iacr.org/2020/055
2171 *
2172 * Avoid the leak by randomizing coordinates before we normalize them.
2173 */
Manuel Pégourié-Gonnard22b1de32020-06-04 10:43:29 +02002174#if defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
Manuel Pégourié-Gonnarda4aa89b2020-03-25 12:41:29 +01002175 if( f_rng != 0 )
Manuel Pégourié-Gonnard22b1de32020-06-04 10:43:29 +02002176#endif
Manuel Pégourié-Gonnarda4aa89b2020-03-25 12:41:29 +01002177 MBEDTLS_MPI_CHK( ecp_randomize_jac( grp, RR, f_rng, p_rng ) );
2178
Manuel Pégourié-Gonnard8962ddb2017-03-14 12:11:21 +01002179 MBEDTLS_MPI_CHK( ecp_normalize_jac( grp, RR ) );
2180
Manuel Pégourié-Gonnard4b9c51e2017-04-20 15:50:26 +02002181#if defined(MBEDTLS_ECP_RESTARTABLE)
Manuel Pégourié-Gonnard28d16282017-08-23 17:33:27 +02002182 if( rs_ctx != NULL && rs_ctx->rsm != NULL )
2183 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, RR ) );
Manuel Pégourié-Gonnard8962ddb2017-03-14 12:11:21 +01002184#endif
Manuel Pégourié-Gonnard391f4412017-03-13 12:26:21 +01002185
2186cleanup:
Manuel Pégourié-Gonnard391f4412017-03-13 12:26:21 +01002187 return( ret );
2188}
2189
Manuel Pégourié-Gonnard391f4412017-03-13 12:26:21 +01002190/*
Manuel Pégourié-Gonnard4b2336d2017-03-09 13:23:50 +01002191 * Pick window size based on curve size and whether we optimize for base point
2192 */
2193static unsigned char ecp_pick_window_size( const mbedtls_ecp_group *grp,
2194 unsigned char p_eq_g )
2195{
2196 unsigned char w;
2197
2198 /*
2199 * Minimize the number of multiplications, that is minimize
2200 * 10 * d * w + 18 * 2^(w-1) + 11 * d + 7 * w, with d = ceil( nbits / w )
2201 * (see costs of the various parts, with 1S = 1M)
2202 */
2203 w = grp->nbits >= 384 ? 5 : 4;
2204
2205 /*
2206 * If P == G, pre-compute a bit more, since this may be re-used later.
2207 * Just adding one avoids upping the cost of the first mul too much,
2208 * and the memory cost too.
2209 */
2210 if( p_eq_g )
2211 w++;
2212
2213 /*
2214 * Make sure w is within bounds.
2215 * (The last test is useful only for very small curves in the test suite.)
2216 */
k-stachowiak653a4a22019-07-03 14:31:09 +02002217#if( MBEDTLS_ECP_WINDOW_SIZE < 6 )
Manuel Pégourié-Gonnard4b2336d2017-03-09 13:23:50 +01002218 if( w > MBEDTLS_ECP_WINDOW_SIZE )
2219 w = MBEDTLS_ECP_WINDOW_SIZE;
k-stachowiak653a4a22019-07-03 14:31:09 +02002220#endif
Manuel Pégourié-Gonnard4b2336d2017-03-09 13:23:50 +01002221 if( w >= grp->nbits )
2222 w = 2;
2223
2224 return( w );
2225}
2226
2227/*
Manuel Pégourié-Gonnard07bf6f52017-03-16 17:21:38 +01002228 * Multiplication using the comb method - for curves in short Weierstrass form
2229 *
2230 * This function is mainly responsible for administrative work:
2231 * - managing the restart context if enabled
Manuel Pégourié-Gonnard11556e22017-08-24 13:41:19 +02002232 * - managing the table of precomputed points (passed between the below two
Manuel Pégourié-Gonnard07bf6f52017-03-16 17:21:38 +01002233 * functions): allocation, computation, ownership tranfer, freeing.
2234 *
2235 * It delegates the actual arithmetic work to:
2236 * ecp_precompute_comb() and ecp_mul_comb_with_precomp()
2237 *
2238 * See comments on ecp_comb_recode_core() regarding the computation strategy.
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01002239 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002240static int ecp_mul_comb( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
2241 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
Manuel Pégourié-Gonnarda0179b82013-12-04 11:49:20 +01002242 int (*f_rng)(void *, unsigned char *, size_t),
Manuel Pégourié-Gonnard3cade222017-04-20 09:31:00 +02002243 void *p_rng,
2244 mbedtls_ecp_restart_ctx *rs_ctx )
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01002245{
Janos Follath24eed8d2019-11-22 13:21:35 +00002246 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
Manuel Pégourié-Gonnard11556e22017-08-24 13:41:19 +02002247 unsigned char w, p_eq_g, i;
Manuel Pégourié-Gonnardd7283502013-11-21 20:00:38 +01002248 size_t d;
Manuel Pégourié-Gonnardf2a9fcf2020-06-03 12:11:56 +02002249 unsigned char T_size = 0, T_ok = 0;
2250 mbedtls_ecp_point *T = NULL;
2251#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
2252 ecp_drbg_context drbg_ctx;
2253
2254 ecp_drbg_init( &drbg_ctx );
2255#endif
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01002256
Manuel Pégourié-Gonnarddb4a8eb2017-08-23 18:18:22 +02002257 ECP_RS_ENTER( rsm );
Manuel Pégourié-Gonnard510d5ca2017-03-08 11:41:47 +01002258
Manuel Pégourié-Gonnardf2a9fcf2020-06-03 12:11:56 +02002259#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
2260 if( f_rng == NULL )
2261 {
Manuel Pégourié-Gonnard53fb66d2020-06-04 09:43:14 +02002262 /* Adjust pointers */
Manuel Pégourié-Gonnardf2a9fcf2020-06-03 12:11:56 +02002263 f_rng = &ecp_drbg_random;
Manuel Pégourié-Gonnard53fb66d2020-06-04 09:43:14 +02002264#if defined(MBEDTLS_ECP_RESTARTABLE)
2265 if( rs_ctx != NULL && rs_ctx->rsm != NULL )
2266 p_rng = &rs_ctx->rsm->drbg_ctx;
2267 else
2268#endif
2269 p_rng = &drbg_ctx;
2270
2271 /* Initialize internal DRBG if necessary */
2272#if defined(MBEDTLS_ECP_RESTARTABLE)
2273 if( rs_ctx == NULL || rs_ctx->rsm == NULL ||
2274 rs_ctx->rsm->drbg_seeded == 0 )
2275#endif
2276 {
Manuel Pégourié-Gonnard4539a452020-06-18 12:27:56 +02002277 const size_t m_len = ( grp->nbits + 7 ) / 8;
2278 MBEDTLS_MPI_CHK( ecp_drbg_seed( p_rng, m, m_len ) );
Manuel Pégourié-Gonnard53fb66d2020-06-04 09:43:14 +02002279 }
2280#if defined(MBEDTLS_ECP_RESTARTABLE)
2281 if( rs_ctx != NULL && rs_ctx->rsm != NULL )
2282 rs_ctx->rsm->drbg_seeded = 1;
2283#endif
Manuel Pégourié-Gonnardf2a9fcf2020-06-03 12:11:56 +02002284 }
2285#endif /* !MBEDTLS_ECP_NO_INTERNAL_RNG */
2286
Manuel Pégourié-Gonnard22be6352017-03-09 13:02:35 +01002287 /* Is P the base point ? */
2288#if MBEDTLS_ECP_FIXED_POINT_OPTIM == 1
2289 p_eq_g = ( mbedtls_mpi_cmp_mpi( &P->Y, &grp->G.Y ) == 0 &&
2290 mbedtls_mpi_cmp_mpi( &P->X, &grp->G.X ) == 0 );
Manuel Pégourié-Gonnard196d1332017-08-28 13:14:27 +02002291#else
2292 p_eq_g = 0;
Manuel Pégourié-Gonnard22be6352017-03-09 13:02:35 +01002293#endif
2294
Manuel Pégourié-Gonnard391f4412017-03-13 12:26:21 +01002295 /* Pick window size and deduce related sizes */
Manuel Pégourié-Gonnard4b2336d2017-03-09 13:23:50 +01002296 w = ecp_pick_window_size( grp, p_eq_g );
Manuel Pégourié-Gonnard92cceb22017-08-23 16:27:29 +02002297 T_size = 1U << ( w - 1 );
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01002298 d = ( grp->nbits + w - 1 ) / w;
2299
Manuel Pégourié-Gonnard085b1df2017-03-16 16:56:04 +01002300 /* Pre-computed table: do we have it already for the base point? */
2301 if( p_eq_g && grp->T != NULL )
2302 {
Manuel Pégourié-Gonnard7037e222017-08-23 14:30:36 +02002303 /* second pointer to the same table, will be deleted on exit */
Manuel Pégourié-Gonnard085b1df2017-03-16 16:56:04 +01002304 T = grp->T;
2305 T_ok = 1;
2306 }
Manuel Pégourié-Gonnard11556e22017-08-24 13:41:19 +02002307 else
Manuel Pégourié-Gonnard4b9c51e2017-04-20 15:50:26 +02002308#if defined(MBEDTLS_ECP_RESTARTABLE)
Manuel Pégourié-Gonnard085b1df2017-03-16 16:56:04 +01002309 /* Pre-computed table: do we have one in progress? complete? */
Manuel Pégourié-Gonnard11556e22017-08-24 13:41:19 +02002310 if( rs_ctx != NULL && rs_ctx->rsm != NULL && rs_ctx->rsm->T != NULL )
Manuel Pégourié-Gonnardc9c0aa62017-03-16 14:53:26 +01002311 {
Manuel Pégourié-Gonnard45fd0162017-03-22 08:24:42 +01002312 /* transfer ownership of T from rsm to local function */
Manuel Pégourié-Gonnard3cade222017-04-20 09:31:00 +02002313 T = rs_ctx->rsm->T;
2314 rs_ctx->rsm->T = NULL;
2315 rs_ctx->rsm->T_size = 0;
Manuel Pégourié-Gonnard085b1df2017-03-16 16:56:04 +01002316
Manuel Pégourié-Gonnardb25cb602018-10-16 11:48:09 +02002317 /* This effectively jumps to the call to mul_comb_after_precomp() */
Manuel Pégourié-Gonnard11556e22017-08-24 13:41:19 +02002318 T_ok = rs_ctx->rsm->state >= ecp_rsm_comb_core;
Manuel Pégourié-Gonnardc9c0aa62017-03-16 14:53:26 +01002319 }
Manuel Pégourié-Gonnard11556e22017-08-24 13:41:19 +02002320 else
Manuel Pégourié-Gonnardc9c0aa62017-03-16 14:53:26 +01002321#endif
Manuel Pégourié-Gonnard085b1df2017-03-16 16:56:04 +01002322 /* Allocate table if we didn't have any */
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01002323 {
Manuel Pégourié-Gonnard92cceb22017-08-23 16:27:29 +02002324 T = mbedtls_calloc( T_size, sizeof( mbedtls_ecp_point ) );
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01002325 if( T == NULL )
2326 {
Manuel Pégourié-Gonnard6a8ca332015-05-28 09:33:39 +02002327 ret = MBEDTLS_ERR_ECP_ALLOC_FAILED;
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01002328 goto cleanup;
2329 }
Manuel Pégourié-Gonnard5bd38b12017-08-23 16:55:59 +02002330
2331 for( i = 0; i < T_size; i++ )
2332 mbedtls_ecp_point_init( &T[i] );
Manuel Pégourié-Gonnard11556e22017-08-24 13:41:19 +02002333
2334 T_ok = 0;
Manuel Pégourié-Gonnard085b1df2017-03-16 16:56:04 +01002335 }
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01002336
Manuel Pégourié-Gonnard085b1df2017-03-16 16:56:04 +01002337 /* Compute table (or finish computing it) if not done already */
2338 if( !T_ok )
2339 {
Manuel Pégourié-Gonnard3cade222017-04-20 09:31:00 +02002340 MBEDTLS_MPI_CHK( ecp_precompute_comb( grp, T, P, w, d, rs_ctx ) );
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01002341
2342 if( p_eq_g )
2343 {
Manuel Pégourié-Gonnard7037e222017-08-23 14:30:36 +02002344 /* almost transfer ownership of T to the group, but keep a copy of
Manuel Pégourié-Gonnardee68cff2018-10-15 15:27:49 +02002345 * the pointer to use for calling the next function more easily */
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01002346 grp->T = T;
Manuel Pégourié-Gonnard92cceb22017-08-23 16:27:29 +02002347 grp->T_size = T_size;
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01002348 }
2349 }
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01002350
Manuel Pégourié-Gonnard391f4412017-03-13 12:26:21 +01002351 /* Actual comb multiplication using precomputed points */
2352 MBEDTLS_MPI_CHK( ecp_mul_comb_after_precomp( grp, R, m,
Manuel Pégourié-Gonnard92cceb22017-08-23 16:27:29 +02002353 T, T_size, w, d,
Manuel Pégourié-Gonnard3cade222017-04-20 09:31:00 +02002354 f_rng, p_rng, rs_ctx ) );
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01002355
2356cleanup:
2357
Manuel Pégourié-Gonnardf2a9fcf2020-06-03 12:11:56 +02002358#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
2359 ecp_drbg_free( &drbg_ctx );
2360#endif
2361
Manuel Pégourié-Gonnard07bf6f52017-03-16 17:21:38 +01002362 /* does T belong to the group? */
2363 if( T == grp->T )
2364 T = NULL;
2365
2366 /* does T belong to the restart context? */
Manuel Pégourié-Gonnard4b9c51e2017-04-20 15:50:26 +02002367#if defined(MBEDTLS_ECP_RESTARTABLE)
Manuel Pégourié-Gonnard3cade222017-04-20 09:31:00 +02002368 if( rs_ctx != NULL && rs_ctx->rsm != NULL && ret == MBEDTLS_ERR_ECP_IN_PROGRESS && T != NULL )
Manuel Pégourié-Gonnardc9c0aa62017-03-16 14:53:26 +01002369 {
Manuel Pégourié-Gonnard45fd0162017-03-22 08:24:42 +01002370 /* transfer ownership of T from local function to rsm */
Manuel Pégourié-Gonnard92cceb22017-08-23 16:27:29 +02002371 rs_ctx->rsm->T_size = T_size;
Manuel Pégourié-Gonnard3cade222017-04-20 09:31:00 +02002372 rs_ctx->rsm->T = T;
Manuel Pégourié-Gonnardc9c0aa62017-03-16 14:53:26 +01002373 T = NULL;
2374 }
2375#endif
2376
Manuel Pégourié-Gonnard07bf6f52017-03-16 17:21:38 +01002377 /* did T belong to us? then let's destroy it! */
2378 if( T != NULL )
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01002379 {
Manuel Pégourié-Gonnard92cceb22017-08-23 16:27:29 +02002380 for( i = 0; i < T_size; i++ )
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002381 mbedtls_ecp_point_free( &T[i] );
2382 mbedtls_free( T );
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01002383 }
2384
Manuel Pégourié-Gonnard2fad7ae2017-03-14 13:13:13 +01002385 /* don't free R while in progress in case R == P */
Manuel Pégourié-Gonnard4b9c51e2017-04-20 15:50:26 +02002386#if defined(MBEDTLS_ECP_RESTARTABLE)
Manuel Pégourié-Gonnard2fad7ae2017-03-14 13:13:13 +01002387 if( ret != MBEDTLS_ERR_ECP_IN_PROGRESS )
2388#endif
Manuel Pégourié-Gonnard07bf6f52017-03-16 17:21:38 +01002389 /* prevent caller from using invalid value */
Manuel Pégourié-Gonnardaade42f2013-11-21 19:19:54 +01002390 if( ret != 0 )
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002391 mbedtls_ecp_point_free( R );
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01002392
Manuel Pégourié-Gonnarddb4a8eb2017-08-23 18:18:22 +02002393 ECP_RS_LEAVE( rsm );
Manuel Pégourié-Gonnard77af79a2017-03-14 10:58:00 +01002394
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01002395 return( ret );
2396}
2397
Gilles Peskinee8c04fe2018-09-14 17:44:21 +02002398#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
Manuel Pégourié-Gonnard7c94d8b2013-12-04 23:15:46 +01002399
Gilles Peskinee8c04fe2018-09-14 17:44:21 +02002400#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
Manuel Pégourié-Gonnard7c94d8b2013-12-04 23:15:46 +01002401/*
2402 * For Montgomery curves, we do all the internal arithmetic in projective
2403 * coordinates. Import/export of points uses only the x coordinates, which is
2404 * internaly represented as X / Z.
2405 *
2406 * For scalar multiplication, we'll use a Montgomery ladder.
2407 */
2408
Manuel Pégourié-Gonnardd1c1ba92013-11-16 15:50:12 +01002409/*
Manuel Pégourié-Gonnardd9ea82e72013-12-03 12:02:28 +01002410 * Normalize Montgomery x/z coordinates: X = X/Z, Z = 1
2411 * Cost: 1M + 1I
2412 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002413static int ecp_normalize_mxz( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P )
Manuel Pégourié-Gonnardd9ea82e72013-12-03 12:02:28 +01002414{
Janos Follath24eed8d2019-11-22 13:21:35 +00002415 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
Manuel Pégourié-Gonnardd9ea82e72013-12-03 12:02:28 +01002416
Janos Follathb0697532016-08-18 12:38:46 +01002417#if defined(MBEDTLS_ECP_NORMALIZE_MXZ_ALT)
Manuel Pégourié-Gonnardebac5d32017-08-23 16:23:36 +02002418 if( mbedtls_internal_ecp_grp_capable( grp ) )
2419 return( mbedtls_internal_ecp_normalize_mxz( grp, P ) );
Janos Follath372697b2016-10-28 16:53:11 +01002420#endif /* MBEDTLS_ECP_NORMALIZE_MXZ_ALT */
Janos Follathb0697532016-08-18 12:38:46 +01002421
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002422 MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &P->Z, &P->Z, &grp->P ) );
Gilles Peskine3b3b34f2019-07-18 21:08:27 +02002423 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &P->X, &P->X, &P->Z ) );
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002424 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &P->Z, 1 ) );
Manuel Pégourié-Gonnardd9ea82e72013-12-03 12:02:28 +01002425
2426cleanup:
2427 return( ret );
2428}
2429
2430/*
Manuel Pégourié-Gonnard3afa07f2013-12-03 13:28:21 +01002431 * Randomize projective x/z coordinates:
2432 * (X, Z) -> (l X, l Z) for random l
2433 * This is sort of the reverse operation of ecp_normalize_mxz().
2434 *
2435 * This countermeasure was first suggested in [2].
2436 * Cost: 2M
2437 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002438static int ecp_randomize_mxz( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P,
Manuel Pégourié-Gonnard3afa07f2013-12-03 13:28:21 +01002439 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
2440{
Janos Follath24eed8d2019-11-22 13:21:35 +00002441 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002442 mbedtls_mpi l;
Janos Follathb0697532016-08-18 12:38:46 +01002443 size_t p_size;
Manuel Pégourié-Gonnard3afa07f2013-12-03 13:28:21 +01002444 int count = 0;
2445
Janos Follathb0697532016-08-18 12:38:46 +01002446#if defined(MBEDTLS_ECP_RANDOMIZE_MXZ_ALT)
Manuel Pégourié-Gonnardebac5d32017-08-23 16:23:36 +02002447 if( mbedtls_internal_ecp_grp_capable( grp ) )
2448 return( mbedtls_internal_ecp_randomize_mxz( grp, P, f_rng, p_rng );
Janos Follath372697b2016-10-28 16:53:11 +01002449#endif /* MBEDTLS_ECP_RANDOMIZE_MXZ_ALT */
Janos Follathb0697532016-08-18 12:38:46 +01002450
2451 p_size = ( grp->pbits + 7 ) / 8;
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002452 mbedtls_mpi_init( &l );
Manuel Pégourié-Gonnard3afa07f2013-12-03 13:28:21 +01002453
2454 /* Generate l such that 1 < l < p */
2455 do
2456 {
Ron Eldorca6ff582017-01-12 14:50:50 +02002457 MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &l, p_size, f_rng, p_rng ) );
Manuel Pégourié-Gonnard3afa07f2013-12-03 13:28:21 +01002458
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002459 while( mbedtls_mpi_cmp_mpi( &l, &grp->P ) >= 0 )
2460 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &l, 1 ) );
Manuel Pégourié-Gonnard3afa07f2013-12-03 13:28:21 +01002461
2462 if( count++ > 10 )
Jonas6692a062020-05-08 16:57:18 +09002463 {
2464 ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
2465 goto cleanup;
2466 }
Manuel Pégourié-Gonnard3afa07f2013-12-03 13:28:21 +01002467 }
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002468 while( mbedtls_mpi_cmp_int( &l, 1 ) <= 0 );
Manuel Pégourié-Gonnard3afa07f2013-12-03 13:28:21 +01002469
Gilles Peskine3b3b34f2019-07-18 21:08:27 +02002470 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &P->X, &P->X, &l ) );
2471 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &P->Z, &P->Z, &l ) );
Manuel Pégourié-Gonnard3afa07f2013-12-03 13:28:21 +01002472
2473cleanup:
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002474 mbedtls_mpi_free( &l );
Manuel Pégourié-Gonnard3afa07f2013-12-03 13:28:21 +01002475
2476 return( ret );
2477}
2478
2479/*
Manuel Pégourié-Gonnardd9ea82e72013-12-03 12:02:28 +01002480 * Double-and-add: R = 2P, S = P + Q, with d = X(P - Q),
2481 * for Montgomery curves in x/z coordinates.
2482 *
2483 * http://www.hyperelliptic.org/EFD/g1p/auto-code/montgom/xz/ladder/mladd-1987-m.op3
2484 * with
2485 * d = X1
2486 * P = (X2, Z2)
2487 * Q = (X3, Z3)
2488 * R = (X4, Z4)
2489 * S = (X5, Z5)
2490 * and eliminating temporary variables tO, ..., t4.
2491 *
2492 * Cost: 5M + 4S
2493 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002494static int ecp_double_add_mxz( const mbedtls_ecp_group *grp,
2495 mbedtls_ecp_point *R, mbedtls_ecp_point *S,
2496 const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q,
2497 const mbedtls_mpi *d )
Manuel Pégourié-Gonnardd9ea82e72013-12-03 12:02:28 +01002498{
Janos Follath24eed8d2019-11-22 13:21:35 +00002499 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002500 mbedtls_mpi A, AA, B, BB, E, C, D, DA, CB;
Manuel Pégourié-Gonnardd9ea82e72013-12-03 12:02:28 +01002501
Janos Follathb0697532016-08-18 12:38:46 +01002502#if defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT)
Manuel Pégourié-Gonnardebac5d32017-08-23 16:23:36 +02002503 if( mbedtls_internal_ecp_grp_capable( grp ) )
2504 return( mbedtls_internal_ecp_double_add_mxz( grp, R, S, P, Q, d ) );
Janos Follath372697b2016-10-28 16:53:11 +01002505#endif /* MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT */
Janos Follathb0697532016-08-18 12:38:46 +01002506
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002507 mbedtls_mpi_init( &A ); mbedtls_mpi_init( &AA ); mbedtls_mpi_init( &B );
2508 mbedtls_mpi_init( &BB ); mbedtls_mpi_init( &E ); mbedtls_mpi_init( &C );
2509 mbedtls_mpi_init( &D ); mbedtls_mpi_init( &DA ); mbedtls_mpi_init( &CB );
Manuel Pégourié-Gonnardd9ea82e72013-12-03 12:02:28 +01002510
Gilles Peskine3b3b34f2019-07-18 21:08:27 +02002511 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &A, &P->X, &P->Z ) );
2512 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &AA, &A, &A ) );
2513 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &B, &P->X, &P->Z ) );
2514 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &BB, &B, &B ) );
2515 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &E, &AA, &BB ) );
2516 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &C, &Q->X, &Q->Z ) );
2517 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &D, &Q->X, &Q->Z ) );
2518 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &DA, &D, &A ) );
2519 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &CB, &C, &B ) );
Aurelien Jarno66deb382020-04-20 21:36:48 +02002520 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &S->X, &DA, &CB ) );
Gilles Peskine3b3b34f2019-07-18 21:08:27 +02002521 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S->X, &S->X, &S->X ) );
2522 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &S->Z, &DA, &CB ) );
2523 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S->Z, &S->Z, &S->Z ) );
2524 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S->Z, d, &S->Z ) );
2525 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &R->X, &AA, &BB ) );
2526 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &R->Z, &grp->A, &E ) );
2527 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &R->Z, &BB, &R->Z ) );
2528 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &R->Z, &E, &R->Z ) );
Manuel Pégourié-Gonnardd9ea82e72013-12-03 12:02:28 +01002529
2530cleanup:
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002531 mbedtls_mpi_free( &A ); mbedtls_mpi_free( &AA ); mbedtls_mpi_free( &B );
2532 mbedtls_mpi_free( &BB ); mbedtls_mpi_free( &E ); mbedtls_mpi_free( &C );
2533 mbedtls_mpi_free( &D ); mbedtls_mpi_free( &DA ); mbedtls_mpi_free( &CB );
Manuel Pégourié-Gonnardd9ea82e72013-12-03 12:02:28 +01002534
2535 return( ret );
2536}
2537
2538/*
Manuel Pégourié-Gonnarda0179b82013-12-04 11:49:20 +01002539 * Multiplication with Montgomery ladder in x/z coordinates,
2540 * for curves in Montgomery form
Manuel Pégourié-Gonnardd9ea82e72013-12-03 12:02:28 +01002541 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002542static int ecp_mul_mxz( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
2543 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
Manuel Pégourié-Gonnarda0179b82013-12-04 11:49:20 +01002544 int (*f_rng)(void *, unsigned char *, size_t),
2545 void *p_rng )
Manuel Pégourié-Gonnardd9ea82e72013-12-03 12:02:28 +01002546{
Janos Follath24eed8d2019-11-22 13:21:35 +00002547 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
Manuel Pégourié-Gonnardd9ea82e72013-12-03 12:02:28 +01002548 size_t i;
Manuel Pégourié-Gonnardb6f45a62013-12-04 21:54:36 +01002549 unsigned char b;
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002550 mbedtls_ecp_point RP;
2551 mbedtls_mpi PX;
Manuel Pégourié-Gonnardf2a9fcf2020-06-03 12:11:56 +02002552#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
2553 ecp_drbg_context drbg_ctx;
Manuel Pégourié-Gonnardd9ea82e72013-12-03 12:02:28 +01002554
Manuel Pégourié-Gonnardf2a9fcf2020-06-03 12:11:56 +02002555 ecp_drbg_init( &drbg_ctx );
2556#endif
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002557 mbedtls_ecp_point_init( &RP ); mbedtls_mpi_init( &PX );
Manuel Pégourié-Gonnardd9ea82e72013-12-03 12:02:28 +01002558
Manuel Pégourié-Gonnardf2a9fcf2020-06-03 12:11:56 +02002559#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
2560 if( f_rng == NULL )
2561 {
Manuel Pégourié-Gonnard4539a452020-06-18 12:27:56 +02002562 const size_t m_len = ( grp->nbits + 7 ) / 8;
2563 MBEDTLS_MPI_CHK( ecp_drbg_seed( &drbg_ctx, m, m_len ) );
Manuel Pégourié-Gonnardf2a9fcf2020-06-03 12:11:56 +02002564 f_rng = &ecp_drbg_random;
2565 p_rng = &drbg_ctx;
2566 }
2567#endif /* !MBEDTLS_ECP_NO_INTERNAL_RNG */
2568
Manuel Pégourié-Gonnard3afa07f2013-12-03 13:28:21 +01002569 /* Save PX and read from P before writing to R, in case P == R */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002570 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &PX, &P->X ) );
2571 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( &RP, P ) );
Manuel Pégourié-Gonnard357ff652013-12-04 18:39:17 +01002572
2573 /* Set R to zero in modified x/z coordinates */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002574 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->X, 1 ) );
2575 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->Z, 0 ) );
2576 mbedtls_mpi_free( &R->Y );
Manuel Pégourié-Gonnardd9ea82e72013-12-03 12:02:28 +01002577
Manuel Pégourié-Gonnard93f41db2013-12-05 10:48:42 +01002578 /* RP.X might be sligtly larger than P, so reduce it */
2579 MOD_ADD( RP.X );
2580
Manuel Pégourié-Gonnard3afa07f2013-12-03 13:28:21 +01002581 /* Randomize coordinates of the starting point */
Manuel Pégourié-Gonnard22b1de32020-06-04 10:43:29 +02002582#if defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
Manuel Pégourié-Gonnard357ff652013-12-04 18:39:17 +01002583 if( f_rng != NULL )
Manuel Pégourié-Gonnard22b1de32020-06-04 10:43:29 +02002584#endif
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002585 MBEDTLS_MPI_CHK( ecp_randomize_mxz( grp, &RP, f_rng, p_rng ) );
Manuel Pégourié-Gonnardd9ea82e72013-12-03 12:02:28 +01002586
Manuel Pégourié-Gonnardb6f45a62013-12-04 21:54:36 +01002587 /* Loop invariant: R = result so far, RP = R + P */
Manuel Pégourié-Gonnardc0696c22015-06-18 16:47:17 +02002588 i = mbedtls_mpi_bitlen( m ); /* one past the (zero-based) most significant bit */
Manuel Pégourié-Gonnardd9ea82e72013-12-03 12:02:28 +01002589 while( i-- > 0 )
2590 {
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002591 b = mbedtls_mpi_get_bit( m, i );
Manuel Pégourié-Gonnardb6f45a62013-12-04 21:54:36 +01002592 /*
2593 * if (b) R = 2R + P else R = 2R,
2594 * which is:
2595 * if (b) double_add( RP, R, RP, R )
2596 * else double_add( R, RP, R, RP )
2597 * but using safe conditional swaps to avoid leaks
2598 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002599 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->X, &RP.X, b ) );
2600 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->Z, &RP.Z, b ) );
2601 MBEDTLS_MPI_CHK( ecp_double_add_mxz( grp, R, &RP, R, &RP, &PX ) );
2602 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->X, &RP.X, b ) );
2603 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->Z, &RP.Z, b ) );
Manuel Pégourié-Gonnardd9ea82e72013-12-03 12:02:28 +01002604 }
2605
Manuel Pégourié-Gonnarda4aa89b2020-03-25 12:41:29 +01002606 /*
2607 * Knowledge of the projective coordinates may leak the last few bits of the
2608 * scalar [1], and since our MPI implementation isn't constant-flow,
2609 * inversion (used for coordinate normalization) may leak the full value
2610 * of its input via side-channels [2].
2611 *
2612 * [1] https://eprint.iacr.org/2003/191
2613 * [2] https://eprint.iacr.org/2020/055
2614 *
2615 * Avoid the leak by randomizing coordinates before we normalize them.
2616 */
Manuel Pégourié-Gonnard22b1de32020-06-04 10:43:29 +02002617#if defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
Manuel Pégourié-Gonnarda4aa89b2020-03-25 12:41:29 +01002618 if( f_rng != NULL )
Manuel Pégourié-Gonnard22b1de32020-06-04 10:43:29 +02002619#endif
Manuel Pégourié-Gonnarda4aa89b2020-03-25 12:41:29 +01002620 MBEDTLS_MPI_CHK( ecp_randomize_mxz( grp, R, f_rng, p_rng ) );
2621
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002622 MBEDTLS_MPI_CHK( ecp_normalize_mxz( grp, R ) );
Manuel Pégourié-Gonnardd9ea82e72013-12-03 12:02:28 +01002623
2624cleanup:
Manuel Pégourié-Gonnardf2a9fcf2020-06-03 12:11:56 +02002625#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
2626 ecp_drbg_free( &drbg_ctx );
2627#endif
2628
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002629 mbedtls_ecp_point_free( &RP ); mbedtls_mpi_free( &PX );
Manuel Pégourié-Gonnardd9ea82e72013-12-03 12:02:28 +01002630
2631 return( ret );
2632}
2633
Gilles Peskinee8c04fe2018-09-14 17:44:21 +02002634#endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
Manuel Pégourié-Gonnard7c94d8b2013-12-04 23:15:46 +01002635
Manuel Pégourié-Gonnardd9ea82e72013-12-03 12:02:28 +01002636/*
Manuel Pégourié-Gonnard884569c2017-04-20 10:10:59 +02002637 * Restartable multiplication R = m * P
Manuel Pégourié-Gonnarda0179b82013-12-04 11:49:20 +01002638 */
Manuel Pégourié-Gonnard884569c2017-04-20 10:10:59 +02002639int mbedtls_ecp_mul_restartable( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002640 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
Manuel Pégourié-Gonnard884569c2017-04-20 10:10:59 +02002641 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng,
2642 mbedtls_ecp_restart_ctx *rs_ctx )
Manuel Pégourié-Gonnarda0179b82013-12-04 11:49:20 +01002643{
Janos Follathb0697532016-08-18 12:38:46 +01002644 int ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
Janos Follathc44ab972016-11-18 16:38:23 +00002645#if defined(MBEDTLS_ECP_INTERNAL_ALT)
2646 char is_grp_capable = 0;
2647#endif
Andrzej Kurekc470b6b2019-01-31 08:20:20 -05002648 ECP_VALIDATE_RET( grp != NULL );
2649 ECP_VALIDATE_RET( R != NULL );
2650 ECP_VALIDATE_RET( m != NULL );
2651 ECP_VALIDATE_RET( P != NULL );
Manuel Pégourié-Gonnarda0179b82013-12-04 11:49:20 +01002652
Manuel Pégourié-Gonnard4b9c51e2017-04-20 15:50:26 +02002653#if defined(MBEDTLS_ECP_RESTARTABLE)
Manuel Pégourié-Gonnard3a256122017-04-20 11:20:26 +02002654 /* reset ops count for this call if top-level */
2655 if( rs_ctx != NULL && rs_ctx->depth++ == 0 )
2656 rs_ctx->ops_done = 0;
Gilles Peskine59970052019-02-28 13:12:06 +01002657#else
2658 (void) rs_ctx;
Manuel Pégourié-Gonnard3a256122017-04-20 11:20:26 +02002659#endif
Manuel Pégourié-Gonnarda0179b82013-12-04 11:49:20 +01002660
Janos Follathc44ab972016-11-18 16:38:23 +00002661#if defined(MBEDTLS_ECP_INTERNAL_ALT)
Manuel Pégourié-Gonnardebac5d32017-08-23 16:23:36 +02002662 if( ( is_grp_capable = mbedtls_internal_ecp_grp_capable( grp ) ) )
Janos Follathc44ab972016-11-18 16:38:23 +00002663 MBEDTLS_MPI_CHK( mbedtls_internal_ecp_init( grp ) );
Janos Follathc44ab972016-11-18 16:38:23 +00002664#endif /* MBEDTLS_ECP_INTERNAL_ALT */
Manuel Pégourié-Gonnard3a256122017-04-20 11:20:26 +02002665
Manuel Pégourié-Gonnard95aedfe2017-08-24 13:47:04 +02002666#if defined(MBEDTLS_ECP_RESTARTABLE)
Manuel Pégourié-Gonnarda08cd1a2017-04-20 11:29:43 +02002667 /* skip argument check when restarting */
Manuel Pégourié-Gonnard95aedfe2017-08-24 13:47:04 +02002668 if( rs_ctx == NULL || rs_ctx->rsm == NULL )
Manuel Pégourié-Gonnarda08cd1a2017-04-20 11:29:43 +02002669#endif
2670 {
Manuel Pégourié-Gonnard5314f232017-04-21 12:36:59 +02002671 /* check_privkey is free */
2672 MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_CHK );
2673
Manuel Pégourié-Gonnarda08cd1a2017-04-20 11:29:43 +02002674 /* Common sanity checks */
2675 MBEDTLS_MPI_CHK( mbedtls_ecp_check_privkey( grp, m ) );
2676 MBEDTLS_MPI_CHK( mbedtls_ecp_check_pubkey( grp, P ) );
Manuel Pégourié-Gonnarda08cd1a2017-04-20 11:29:43 +02002677 }
Manuel Pégourié-Gonnard3a256122017-04-20 11:20:26 +02002678
2679 ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
Gilles Peskinee8c04fe2018-09-14 17:44:21 +02002680#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
Janos Follathdf9295b2019-02-26 12:36:52 +00002681 if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY )
Manuel Pégourié-Gonnard3a256122017-04-20 11:20:26 +02002682 MBEDTLS_MPI_CHK( ecp_mul_mxz( grp, R, m, P, f_rng, p_rng ) );
Janos Follath430d3372016-11-03 14:25:37 +00002683#endif
Gilles Peskinee8c04fe2018-09-14 17:44:21 +02002684#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
Janos Follathdf9295b2019-02-26 12:36:52 +00002685 if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
Manuel Pégourié-Gonnard3a256122017-04-20 11:20:26 +02002686 MBEDTLS_MPI_CHK( ecp_mul_comb( grp, R, m, P, f_rng, p_rng, rs_ctx ) );
Janos Follath430d3372016-11-03 14:25:37 +00002687#endif
Manuel Pégourié-Gonnard3a256122017-04-20 11:20:26 +02002688
Janos Follath6c8ccd52016-11-29 15:37:09 +00002689cleanup:
Janos Follathb0697532016-08-18 12:38:46 +01002690
Manuel Pégourié-Gonnard3a256122017-04-20 11:20:26 +02002691#if defined(MBEDTLS_ECP_INTERNAL_ALT)
Manuel Pégourié-Gonnardebac5d32017-08-23 16:23:36 +02002692 if( is_grp_capable )
Janos Follathc44ab972016-11-18 16:38:23 +00002693 mbedtls_internal_ecp_free( grp );
Janos Follathc44ab972016-11-18 16:38:23 +00002694#endif /* MBEDTLS_ECP_INTERNAL_ALT */
Manuel Pégourié-Gonnard3a256122017-04-20 11:20:26 +02002695
Manuel Pégourié-Gonnard4b9c51e2017-04-20 15:50:26 +02002696#if defined(MBEDTLS_ECP_RESTARTABLE)
Manuel Pégourié-Gonnard3a256122017-04-20 11:20:26 +02002697 if( rs_ctx != NULL )
2698 rs_ctx->depth--;
2699#endif
2700
Janos Follathb0697532016-08-18 12:38:46 +01002701 return( ret );
Manuel Pégourié-Gonnarda0179b82013-12-04 11:49:20 +01002702}
2703
Manuel Pégourié-Gonnardb739a712017-04-19 10:11:56 +02002704/*
Manuel Pégourié-Gonnard884569c2017-04-20 10:10:59 +02002705 * Multiplication R = m * P
Manuel Pégourié-Gonnardb739a712017-04-19 10:11:56 +02002706 */
Manuel Pégourié-Gonnard884569c2017-04-20 10:10:59 +02002707int mbedtls_ecp_mul( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
Manuel Pégourié-Gonnardb739a712017-04-19 10:11:56 +02002708 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
Manuel Pégourié-Gonnard884569c2017-04-20 10:10:59 +02002709 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
Manuel Pégourié-Gonnardb739a712017-04-19 10:11:56 +02002710{
Andrzej Kurekc470b6b2019-01-31 08:20:20 -05002711 ECP_VALIDATE_RET( grp != NULL );
2712 ECP_VALIDATE_RET( R != NULL );
2713 ECP_VALIDATE_RET( m != NULL );
2714 ECP_VALIDATE_RET( P != NULL );
Manuel Pégourié-Gonnard884569c2017-04-20 10:10:59 +02002715 return( mbedtls_ecp_mul_restartable( grp, R, m, P, f_rng, p_rng, NULL ) );
Manuel Pégourié-Gonnardb739a712017-04-19 10:11:56 +02002716}
Manuel Pégourié-Gonnardb739a712017-04-19 10:11:56 +02002717
Gilles Peskinee8c04fe2018-09-14 17:44:21 +02002718#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
Manuel Pégourié-Gonnarda0179b82013-12-04 11:49:20 +01002719/*
Manuel Pégourié-Gonnardd9622732013-12-05 10:06:06 +01002720 * Check that an affine point is valid as a public key,
2721 * short weierstrass curves (SEC1 3.2.3.1)
Manuel Pégourié-Gonnardc8dc2952013-07-01 14:06:13 +02002722 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002723static int ecp_check_pubkey_sw( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt )
Manuel Pégourié-Gonnardc8dc2952013-07-01 14:06:13 +02002724{
Janos Follath24eed8d2019-11-22 13:21:35 +00002725 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002726 mbedtls_mpi YY, RHS;
Manuel Pégourié-Gonnardc8dc2952013-07-01 14:06:13 +02002727
Manuel Pégourié-Gonnard312d2e82013-12-04 11:08:01 +01002728 /* pt coordinates must be normalized for our checks */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002729 if( mbedtls_mpi_cmp_int( &pt->X, 0 ) < 0 ||
2730 mbedtls_mpi_cmp_int( &pt->Y, 0 ) < 0 ||
2731 mbedtls_mpi_cmp_mpi( &pt->X, &grp->P ) >= 0 ||
2732 mbedtls_mpi_cmp_mpi( &pt->Y, &grp->P ) >= 0 )
2733 return( MBEDTLS_ERR_ECP_INVALID_KEY );
Manuel Pégourié-Gonnardc8dc2952013-07-01 14:06:13 +02002734
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002735 mbedtls_mpi_init( &YY ); mbedtls_mpi_init( &RHS );
Manuel Pégourié-Gonnardc8dc2952013-07-01 14:06:13 +02002736
2737 /*
2738 * YY = Y^2
Manuel Pégourié-Gonnardcd7458a2013-10-08 13:11:30 +02002739 * RHS = X (X^2 + A) + B = X^3 + A X + B
Manuel Pégourié-Gonnardc8dc2952013-07-01 14:06:13 +02002740 */
Gilles Peskine3b3b34f2019-07-18 21:08:27 +02002741 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &YY, &pt->Y, &pt->Y ) );
2742 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &RHS, &pt->X, &pt->X ) );
Manuel Pégourié-Gonnard73cc01d2013-12-06 12:41:30 +01002743
2744 /* Special case for A = -3 */
2745 if( grp->A.p == NULL )
2746 {
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002747 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &RHS, &RHS, 3 ) ); MOD_SUB( RHS );
Manuel Pégourié-Gonnard73cc01d2013-12-06 12:41:30 +01002748 }
2749 else
2750 {
Gilles Peskine3b3b34f2019-07-18 21:08:27 +02002751 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &RHS, &RHS, &grp->A ) );
Manuel Pégourié-Gonnard73cc01d2013-12-06 12:41:30 +01002752 }
2753
Gilles Peskine3b3b34f2019-07-18 21:08:27 +02002754 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &RHS, &RHS, &pt->X ) );
2755 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &RHS, &RHS, &grp->B ) );
Manuel Pégourié-Gonnardc8dc2952013-07-01 14:06:13 +02002756
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002757 if( mbedtls_mpi_cmp_mpi( &YY, &RHS ) != 0 )
2758 ret = MBEDTLS_ERR_ECP_INVALID_KEY;
Manuel Pégourié-Gonnardc8dc2952013-07-01 14:06:13 +02002759
2760cleanup:
2761
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002762 mbedtls_mpi_free( &YY ); mbedtls_mpi_free( &RHS );
Manuel Pégourié-Gonnardc8dc2952013-07-01 14:06:13 +02002763
2764 return( ret );
2765}
Gilles Peskinee8c04fe2018-09-14 17:44:21 +02002766#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
Manuel Pégourié-Gonnardd9622732013-12-05 10:06:06 +01002767
Gilles Peskine9b99a892018-09-14 18:32:19 +02002768#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
Manuel Pégourié-Gonnard56cc88a2015-05-11 18:40:45 +02002769/*
Manuel Pégourié-Gonnardde9f9532015-10-23 15:50:37 +02002770 * R = m * P with shortcuts for m == 1 and m == -1
2771 * NOT constant-time - ONLY for short Weierstrass!
2772 */
2773static int mbedtls_ecp_mul_shortcuts( mbedtls_ecp_group *grp,
2774 mbedtls_ecp_point *R,
2775 const mbedtls_mpi *m,
Manuel Pégourié-Gonnard1631d632017-04-20 14:48:56 +02002776 const mbedtls_ecp_point *P,
2777 mbedtls_ecp_restart_ctx *rs_ctx )
Manuel Pégourié-Gonnardde9f9532015-10-23 15:50:37 +02002778{
Janos Follath24eed8d2019-11-22 13:21:35 +00002779 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
Manuel Pégourié-Gonnardde9f9532015-10-23 15:50:37 +02002780
2781 if( mbedtls_mpi_cmp_int( m, 1 ) == 0 )
2782 {
2783 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, P ) );
2784 }
2785 else if( mbedtls_mpi_cmp_int( m, -1 ) == 0 )
2786 {
2787 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, P ) );
2788 if( mbedtls_mpi_cmp_int( &R->Y, 0 ) != 0 )
2789 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &R->Y, &grp->P, &R->Y ) );
2790 }
2791 else
2792 {
Manuel Pégourié-Gonnard1631d632017-04-20 14:48:56 +02002793 MBEDTLS_MPI_CHK( mbedtls_ecp_mul_restartable( grp, R, m, P,
2794 NULL, NULL, rs_ctx ) );
Manuel Pégourié-Gonnardde9f9532015-10-23 15:50:37 +02002795 }
2796
2797cleanup:
2798 return( ret );
2799}
2800
2801/*
Manuel Pégourié-Gonnard54dd6522017-04-20 13:36:18 +02002802 * Restartable linear combination
Manuel Pégourié-Gonnardde9f9532015-10-23 15:50:37 +02002803 * NOT constant-time
Manuel Pégourié-Gonnard56cc88a2015-05-11 18:40:45 +02002804 */
Manuel Pégourié-Gonnard54dd6522017-04-20 13:36:18 +02002805int mbedtls_ecp_muladd_restartable(
2806 mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
Manuel Pégourié-Gonnard56cc88a2015-05-11 18:40:45 +02002807 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
Manuel Pégourié-Gonnard54dd6522017-04-20 13:36:18 +02002808 const mbedtls_mpi *n, const mbedtls_ecp_point *Q,
2809 mbedtls_ecp_restart_ctx *rs_ctx )
Manuel Pégourié-Gonnard56cc88a2015-05-11 18:40:45 +02002810{
Janos Follath24eed8d2019-11-22 13:21:35 +00002811 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
Manuel Pégourié-Gonnard56cc88a2015-05-11 18:40:45 +02002812 mbedtls_ecp_point mP;
Manuel Pégourié-Gonnard1631d632017-04-20 14:48:56 +02002813 mbedtls_ecp_point *pmP = &mP;
2814 mbedtls_ecp_point *pR = R;
Janos Follathc44ab972016-11-18 16:38:23 +00002815#if defined(MBEDTLS_ECP_INTERNAL_ALT)
2816 char is_grp_capable = 0;
2817#endif
Andrzej Kurekc470b6b2019-01-31 08:20:20 -05002818 ECP_VALIDATE_RET( grp != NULL );
2819 ECP_VALIDATE_RET( R != NULL );
2820 ECP_VALIDATE_RET( m != NULL );
2821 ECP_VALIDATE_RET( P != NULL );
2822 ECP_VALIDATE_RET( n != NULL );
2823 ECP_VALIDATE_RET( Q != NULL );
Manuel Pégourié-Gonnard56cc88a2015-05-11 18:40:45 +02002824
Janos Follathdf9295b2019-02-26 12:36:52 +00002825 if( mbedtls_ecp_get_type( grp ) != MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
Manuel Pégourié-Gonnard56cc88a2015-05-11 18:40:45 +02002826 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
2827
Manuel Pégourié-Gonnard1631d632017-04-20 14:48:56 +02002828 mbedtls_ecp_point_init( &mP );
2829
Manuel Pégourié-Gonnarddb4a8eb2017-08-23 18:18:22 +02002830 ECP_RS_ENTER( ma );
2831
Manuel Pégourié-Gonnard4b9c51e2017-04-20 15:50:26 +02002832#if defined(MBEDTLS_ECP_RESTARTABLE)
Manuel Pégourié-Gonnard1631d632017-04-20 14:48:56 +02002833 if( rs_ctx != NULL && rs_ctx->ma != NULL )
2834 {
2835 /* redirect intermediate results to restart context */
2836 pmP = &rs_ctx->ma->mP;
2837 pR = &rs_ctx->ma->R;
2838
2839 /* jump to next operation */
2840 if( rs_ctx->ma->state == ecp_rsma_mul2 )
2841 goto mul2;
2842 if( rs_ctx->ma->state == ecp_rsma_add )
2843 goto add;
2844 if( rs_ctx->ma->state == ecp_rsma_norm )
2845 goto norm;
2846 }
Manuel Pégourié-Gonnard4b9c51e2017-04-20 15:50:26 +02002847#endif /* MBEDTLS_ECP_RESTARTABLE */
Manuel Pégourié-Gonnard54dd6522017-04-20 13:36:18 +02002848
Manuel Pégourié-Gonnard1631d632017-04-20 14:48:56 +02002849 MBEDTLS_MPI_CHK( mbedtls_ecp_mul_shortcuts( grp, pmP, m, P, rs_ctx ) );
Manuel Pégourié-Gonnard4b9c51e2017-04-20 15:50:26 +02002850#if defined(MBEDTLS_ECP_RESTARTABLE)
Manuel Pégourié-Gonnard1631d632017-04-20 14:48:56 +02002851 if( rs_ctx != NULL && rs_ctx->ma != NULL )
Manuel Pégourié-Gonnardc9efa002017-08-24 10:25:06 +02002852 rs_ctx->ma->state = ecp_rsma_mul2;
Manuel Pégourié-Gonnard56cc88a2015-05-11 18:40:45 +02002853
Manuel Pégourié-Gonnard1631d632017-04-20 14:48:56 +02002854mul2:
2855#endif
2856 MBEDTLS_MPI_CHK( mbedtls_ecp_mul_shortcuts( grp, pR, n, Q, rs_ctx ) );
Andrzej Kurekc470b6b2019-01-31 08:20:20 -05002857
2858#if defined(MBEDTLS_ECP_INTERNAL_ALT)
2859 if( ( is_grp_capable = mbedtls_internal_ecp_grp_capable( grp ) ) )
2860 MBEDTLS_MPI_CHK( mbedtls_internal_ecp_init( grp ) );
2861#endif /* MBEDTLS_ECP_INTERNAL_ALT */
2862
Manuel Pégourié-Gonnard4b9c51e2017-04-20 15:50:26 +02002863#if defined(MBEDTLS_ECP_RESTARTABLE)
Manuel Pégourié-Gonnard1631d632017-04-20 14:48:56 +02002864 if( rs_ctx != NULL && rs_ctx->ma != NULL )
Manuel Pégourié-Gonnardc9efa002017-08-24 10:25:06 +02002865 rs_ctx->ma->state = ecp_rsma_add;
Manuel Pégourié-Gonnard1a7c5ef2015-08-13 10:19:09 +02002866
Manuel Pégourié-Gonnard1631d632017-04-20 14:48:56 +02002867add:
2868#endif
Manuel Pégourié-Gonnardc7511482017-04-20 16:31:00 +02002869 MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_ADD );
Manuel Pégourié-Gonnard1631d632017-04-20 14:48:56 +02002870 MBEDTLS_MPI_CHK( ecp_add_mixed( grp, pR, pmP, pR ) );
Manuel Pégourié-Gonnard4b9c51e2017-04-20 15:50:26 +02002871#if defined(MBEDTLS_ECP_RESTARTABLE)
Manuel Pégourié-Gonnard1631d632017-04-20 14:48:56 +02002872 if( rs_ctx != NULL && rs_ctx->ma != NULL )
Manuel Pégourié-Gonnardc9efa002017-08-24 10:25:06 +02002873 rs_ctx->ma->state = ecp_rsma_norm;
Janos Follath430d3372016-11-03 14:25:37 +00002874
Manuel Pégourié-Gonnard1631d632017-04-20 14:48:56 +02002875norm:
2876#endif
Manuel Pégourié-Gonnardc7511482017-04-20 16:31:00 +02002877 MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_INV );
Manuel Pégourié-Gonnard1631d632017-04-20 14:48:56 +02002878 MBEDTLS_MPI_CHK( ecp_normalize_jac( grp, pR ) );
2879
Manuel Pégourié-Gonnard4b9c51e2017-04-20 15:50:26 +02002880#if defined(MBEDTLS_ECP_RESTARTABLE)
Manuel Pégourié-Gonnard1631d632017-04-20 14:48:56 +02002881 if( rs_ctx != NULL && rs_ctx->ma != NULL )
2882 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, pR ) );
2883#endif
Manuel Pégourié-Gonnard56cc88a2015-05-11 18:40:45 +02002884
2885cleanup:
Janos Follathc44ab972016-11-18 16:38:23 +00002886#if defined(MBEDTLS_ECP_INTERNAL_ALT)
Manuel Pégourié-Gonnardebac5d32017-08-23 16:23:36 +02002887 if( is_grp_capable )
Janos Follathc44ab972016-11-18 16:38:23 +00002888 mbedtls_internal_ecp_free( grp );
Janos Follathc44ab972016-11-18 16:38:23 +00002889#endif /* MBEDTLS_ECP_INTERNAL_ALT */
Manuel Pégourié-Gonnard1631d632017-04-20 14:48:56 +02002890
Manuel Pégourié-Gonnard56cc88a2015-05-11 18:40:45 +02002891 mbedtls_ecp_point_free( &mP );
2892
Manuel Pégourié-Gonnarddb4a8eb2017-08-23 18:18:22 +02002893 ECP_RS_LEAVE( ma );
Manuel Pégourié-Gonnard54dd6522017-04-20 13:36:18 +02002894
Manuel Pégourié-Gonnard56cc88a2015-05-11 18:40:45 +02002895 return( ret );
2896}
2897
Manuel Pégourié-Gonnard54dd6522017-04-20 13:36:18 +02002898/*
2899 * Linear combination
2900 * NOT constant-time
2901 */
2902int mbedtls_ecp_muladd( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
2903 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
2904 const mbedtls_mpi *n, const mbedtls_ecp_point *Q )
2905{
Andrzej Kurekc470b6b2019-01-31 08:20:20 -05002906 ECP_VALIDATE_RET( grp != NULL );
2907 ECP_VALIDATE_RET( R != NULL );
2908 ECP_VALIDATE_RET( m != NULL );
2909 ECP_VALIDATE_RET( P != NULL );
2910 ECP_VALIDATE_RET( n != NULL );
2911 ECP_VALIDATE_RET( Q != NULL );
Manuel Pégourié-Gonnard54dd6522017-04-20 13:36:18 +02002912 return( mbedtls_ecp_muladd_restartable( grp, R, m, P, n, Q, NULL ) );
2913}
Gilles Peskine9b99a892018-09-14 18:32:19 +02002914#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
Manuel Pégourié-Gonnardd9622732013-12-05 10:06:06 +01002915
Gilles Peskinee8c04fe2018-09-14 17:44:21 +02002916#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
Manuel Pégourié-Gonnardd9622732013-12-05 10:06:06 +01002917/*
2918 * Check validity of a public key for Montgomery curves with x-only schemes
2919 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002920static int ecp_check_pubkey_mx( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt )
Manuel Pégourié-Gonnardd9622732013-12-05 10:06:06 +01002921{
Manuel Pégourié-Gonnard07894332015-06-23 00:18:41 +02002922 /* [Curve25519 p. 5] Just check X is the correct number of bytes */
Nicholas Wilson08f3ef12015-11-10 13:10:01 +00002923 /* Allow any public value, if it's too big then we'll just reduce it mod p
2924 * (RFC 7748 sec. 5 para. 3). */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002925 if( mbedtls_mpi_size( &pt->X ) > ( grp->nbits + 7 ) / 8 )
2926 return( MBEDTLS_ERR_ECP_INVALID_KEY );
Manuel Pégourié-Gonnardd9622732013-12-05 10:06:06 +01002927
2928 return( 0 );
2929}
Gilles Peskinee8c04fe2018-09-14 17:44:21 +02002930#endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
Manuel Pégourié-Gonnardd9622732013-12-05 10:06:06 +01002931
2932/*
2933 * Check that a point is valid as a public key
2934 */
Andrzej Kurekc470b6b2019-01-31 08:20:20 -05002935int mbedtls_ecp_check_pubkey( const mbedtls_ecp_group *grp,
2936 const mbedtls_ecp_point *pt )
Manuel Pégourié-Gonnardd9622732013-12-05 10:06:06 +01002937{
Andrzej Kurekc470b6b2019-01-31 08:20:20 -05002938 ECP_VALIDATE_RET( grp != NULL );
2939 ECP_VALIDATE_RET( pt != NULL );
2940
Manuel Pégourié-Gonnardd9622732013-12-05 10:06:06 +01002941 /* Must use affine coordinates */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002942 if( mbedtls_mpi_cmp_int( &pt->Z, 1 ) != 0 )
2943 return( MBEDTLS_ERR_ECP_INVALID_KEY );
Manuel Pégourié-Gonnardd9622732013-12-05 10:06:06 +01002944
Gilles Peskinee8c04fe2018-09-14 17:44:21 +02002945#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
Janos Follathdf9295b2019-02-26 12:36:52 +00002946 if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY )
Manuel Pégourié-Gonnardd9622732013-12-05 10:06:06 +01002947 return( ecp_check_pubkey_mx( grp, pt ) );
2948#endif
Gilles Peskinee8c04fe2018-09-14 17:44:21 +02002949#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
Janos Follathdf9295b2019-02-26 12:36:52 +00002950 if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
Manuel Pégourié-Gonnardd9622732013-12-05 10:06:06 +01002951 return( ecp_check_pubkey_sw( grp, pt ) );
2952#endif
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002953 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
Manuel Pégourié-Gonnardd9622732013-12-05 10:06:06 +01002954}
Manuel Pégourié-Gonnardc8dc2952013-07-01 14:06:13 +02002955
2956/*
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002957 * Check that an mbedtls_mpi is valid as a private key
Manuel Pégourié-Gonnardc8dc2952013-07-01 14:06:13 +02002958 */
Andrzej Kurekc470b6b2019-01-31 08:20:20 -05002959int mbedtls_ecp_check_privkey( const mbedtls_ecp_group *grp,
2960 const mbedtls_mpi *d )
Manuel Pégourié-Gonnardc8dc2952013-07-01 14:06:13 +02002961{
Andrzej Kurekc470b6b2019-01-31 08:20:20 -05002962 ECP_VALIDATE_RET( grp != NULL );
2963 ECP_VALIDATE_RET( d != NULL );
2964
Gilles Peskinee8c04fe2018-09-14 17:44:21 +02002965#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
Janos Follathdf9295b2019-02-26 12:36:52 +00002966 if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY )
Manuel Pégourié-Gonnard312d2e82013-12-04 11:08:01 +01002967 {
Nicholas Wilson08f3ef12015-11-10 13:10:01 +00002968 /* see RFC 7748 sec. 5 para. 5 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002969 if( mbedtls_mpi_get_bit( d, 0 ) != 0 ||
2970 mbedtls_mpi_get_bit( d, 1 ) != 0 ||
Manuel Pégourié-Gonnardc0696c22015-06-18 16:47:17 +02002971 mbedtls_mpi_bitlen( d ) - 1 != grp->nbits ) /* mbedtls_mpi_bitlen is one-based! */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002972 return( MBEDTLS_ERR_ECP_INVALID_KEY );
Nicholas Wilson08f3ef12015-11-10 13:10:01 +00002973
2974 /* see [Curve25519] page 5 */
2975 if( grp->nbits == 254 && mbedtls_mpi_get_bit( d, 2 ) != 0 )
2976 return( MBEDTLS_ERR_ECP_INVALID_KEY );
2977
2978 return( 0 );
Manuel Pégourié-Gonnard312d2e82013-12-04 11:08:01 +01002979 }
Gilles Peskinee8c04fe2018-09-14 17:44:21 +02002980#endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
2981#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
Janos Follathdf9295b2019-02-26 12:36:52 +00002982 if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
Manuel Pégourié-Gonnard312d2e82013-12-04 11:08:01 +01002983 {
2984 /* see SEC1 3.2 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002985 if( mbedtls_mpi_cmp_int( d, 1 ) < 0 ||
2986 mbedtls_mpi_cmp_mpi( d, &grp->N ) >= 0 )
2987 return( MBEDTLS_ERR_ECP_INVALID_KEY );
Manuel Pégourié-Gonnardd9622732013-12-05 10:06:06 +01002988 else
2989 return( 0 );
Manuel Pégourié-Gonnard312d2e82013-12-04 11:08:01 +01002990 }
Gilles Peskinee8c04fe2018-09-14 17:44:21 +02002991#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
Manuel Pégourié-Gonnardc8dc2952013-07-01 14:06:13 +02002992
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02002993 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
Manuel Pégourié-Gonnardc8dc2952013-07-01 14:06:13 +02002994}
2995
2996/*
Manuel Pégourié-Gonnarda7937f92017-04-20 15:37:46 +02002997 * Generate a private key
Manuel Pégourié-Gonnard45a035a2013-01-26 14:42:45 +01002998 */
Manuel Pégourié-Gonnarda7937f92017-04-20 15:37:46 +02002999int mbedtls_ecp_gen_privkey( const mbedtls_ecp_group *grp,
3000 mbedtls_mpi *d,
Manuel Pégourié-Gonnard45a035a2013-01-26 14:42:45 +01003001 int (*f_rng)(void *, unsigned char *, size_t),
3002 void *p_rng )
3003{
Manuel Pégourié-Gonnarda7937f92017-04-20 15:37:46 +02003004 int ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
Andrzej Kurekc470b6b2019-01-31 08:20:20 -05003005 size_t n_size;
3006
3007 ECP_VALIDATE_RET( grp != NULL );
3008 ECP_VALIDATE_RET( d != NULL );
3009 ECP_VALIDATE_RET( f_rng != NULL );
3010
3011 n_size = ( grp->nbits + 7 ) / 8;
Manuel Pégourié-Gonnard45a035a2013-01-26 14:42:45 +01003012
Gilles Peskinee8c04fe2018-09-14 17:44:21 +02003013#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
Janos Follathdf9295b2019-02-26 12:36:52 +00003014 if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY )
Manuel Pégourié-Gonnard45a035a2013-01-26 14:42:45 +01003015 {
Manuel Pégourié-Gonnardfe0af402013-12-04 18:14:55 +01003016 /* [M225] page 5 */
3017 size_t b;
3018
Janos Follath98e28a72016-05-31 14:03:54 +01003019 do {
3020 MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( d, n_size, f_rng, p_rng ) );
3021 } while( mbedtls_mpi_bitlen( d ) == 0);
Manuel Pégourié-Gonnard45a035a2013-01-26 14:42:45 +01003022
Manuel Pégourié-Gonnardfe0af402013-12-04 18:14:55 +01003023 /* Make sure the most significant bit is nbits */
Manuel Pégourié-Gonnardc0696c22015-06-18 16:47:17 +02003024 b = mbedtls_mpi_bitlen( d ) - 1; /* mbedtls_mpi_bitlen is one-based */
Manuel Pégourié-Gonnardfe0af402013-12-04 18:14:55 +01003025 if( b > grp->nbits )
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02003026 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( d, b - grp->nbits ) );
Manuel Pégourié-Gonnardfe0af402013-12-04 18:14:55 +01003027 else
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02003028 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, grp->nbits, 1 ) );
Manuel Pégourié-Gonnard45a035a2013-01-26 14:42:45 +01003029
Nicholas Wilson08f3ef12015-11-10 13:10:01 +00003030 /* Make sure the last two bits are unset for Curve448, three bits for
3031 Curve25519 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02003032 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 0, 0 ) );
3033 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 1, 0 ) );
Nicholas Wilson08f3ef12015-11-10 13:10:01 +00003034 if( grp->nbits == 254 )
3035 {
3036 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 2, 0 ) );
3037 }
Manuel Pégourié-Gonnard45a035a2013-01-26 14:42:45 +01003038 }
Gilles Peskinee8c04fe2018-09-14 17:44:21 +02003039#endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
Manuel Pégourié-Gonnarda7937f92017-04-20 15:37:46 +02003040
Gilles Peskinee8c04fe2018-09-14 17:44:21 +02003041#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
Janos Follathdf9295b2019-02-26 12:36:52 +00003042 if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
Manuel Pégourié-Gonnardfe0af402013-12-04 18:14:55 +01003043 {
3044 /* SEC1 3.2.1: Generate d such that 1 <= n < N */
Manuel Pégourié-Gonnardd9622732013-12-05 10:06:06 +01003045 int count = 0;
Janos Follath0e5532d2019-10-11 14:21:53 +01003046 unsigned cmp = 0;
Manuel Pégourié-Gonnard79f73b92014-01-03 12:35:05 +01003047
3048 /*
3049 * Match the procedure given in RFC 6979 (deterministic ECDSA):
3050 * - use the same byte ordering;
3051 * - keep the leftmost nbits bits of the generated octet string;
3052 * - try until result is in the desired range.
3053 * This also avoids any biais, which is especially important for ECDSA.
3054 */
Manuel Pégourié-Gonnardfe0af402013-12-04 18:14:55 +01003055 do
3056 {
Hanno Becker7c8cb9c2017-10-17 15:19:38 +01003057 MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( d, n_size, f_rng, p_rng ) );
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02003058 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( d, 8 * n_size - grp->nbits ) );
Manuel Pégourié-Gonnardfe0af402013-12-04 18:14:55 +01003059
Manuel Pégourié-Gonnard6e8e34d2014-01-28 19:30:56 +01003060 /*
3061 * Each try has at worst a probability 1/2 of failing (the msb has
3062 * a probability 1/2 of being 0, and then the result will be < N),
3063 * so after 30 tries failure probability is a most 2**(-30).
3064 *
3065 * For most curves, 1 try is enough with overwhelming probability,
3066 * since N starts with a lot of 1s in binary, but some curves
3067 * such as secp224k1 are actually very close to the worst case.
3068 */
Manuel Pégourié-Gonnard67543962017-04-21 13:19:43 +02003069 if( ++count > 30 )
Jonasb2462142020-05-28 20:00:43 +09003070 {
3071 ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
3072 goto cleanup;
3073 }
Janos Follatha779b462019-09-16 14:27:39 +01003074
Janos Follath0e5532d2019-10-11 14:21:53 +01003075 ret = mbedtls_mpi_lt_mpi_ct( d, &grp->N, &cmp );
Janos Follatha779b462019-09-16 14:27:39 +01003076 if( ret != 0 )
3077 {
3078 goto cleanup;
3079 }
Manuel Pégourié-Gonnardfe0af402013-12-04 18:14:55 +01003080 }
Janos Follath0e5532d2019-10-11 14:21:53 +01003081 while( mbedtls_mpi_cmp_int( d, 1 ) < 0 || cmp != 1 );
Manuel Pégourié-Gonnardfe0af402013-12-04 18:14:55 +01003082 }
Gilles Peskinee8c04fe2018-09-14 17:44:21 +02003083#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
Manuel Pégourié-Gonnard45a035a2013-01-26 14:42:45 +01003084
Manuel Pégourié-Gonnardc9573992014-01-03 12:54:00 +01003085cleanup:
Manuel Pégourié-Gonnarda7937f92017-04-20 15:37:46 +02003086 return( ret );
3087}
Manuel Pégourié-Gonnardc9573992014-01-03 12:54:00 +01003088
Manuel Pégourié-Gonnarda7937f92017-04-20 15:37:46 +02003089/*
3090 * Generate a keypair with configurable base point
3091 */
3092int mbedtls_ecp_gen_keypair_base( mbedtls_ecp_group *grp,
3093 const mbedtls_ecp_point *G,
3094 mbedtls_mpi *d, mbedtls_ecp_point *Q,
3095 int (*f_rng)(void *, unsigned char *, size_t),
3096 void *p_rng )
3097{
Janos Follath24eed8d2019-11-22 13:21:35 +00003098 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
Andrzej Kurekc470b6b2019-01-31 08:20:20 -05003099 ECP_VALIDATE_RET( grp != NULL );
3100 ECP_VALIDATE_RET( d != NULL );
3101 ECP_VALIDATE_RET( G != NULL );
3102 ECP_VALIDATE_RET( Q != NULL );
3103 ECP_VALIDATE_RET( f_rng != NULL );
Manuel Pégourié-Gonnarda7937f92017-04-20 15:37:46 +02003104
3105 MBEDTLS_MPI_CHK( mbedtls_ecp_gen_privkey( grp, d, f_rng, p_rng ) );
3106 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( grp, Q, d, G, f_rng, p_rng ) );
3107
3108cleanup:
3109 return( ret );
Manuel Pégourié-Gonnardd9a3f472015-08-11 14:31:03 +02003110}
3111
3112/*
3113 * Generate key pair, wrapper for conventional base point
3114 */
3115int mbedtls_ecp_gen_keypair( mbedtls_ecp_group *grp,
3116 mbedtls_mpi *d, mbedtls_ecp_point *Q,
3117 int (*f_rng)(void *, unsigned char *, size_t),
3118 void *p_rng )
3119{
Andrzej Kurekc470b6b2019-01-31 08:20:20 -05003120 ECP_VALIDATE_RET( grp != NULL );
3121 ECP_VALIDATE_RET( d != NULL );
3122 ECP_VALIDATE_RET( Q != NULL );
3123 ECP_VALIDATE_RET( f_rng != NULL );
3124
Manuel Pégourié-Gonnardd9a3f472015-08-11 14:31:03 +02003125 return( mbedtls_ecp_gen_keypair_base( grp, &grp->G, d, Q, f_rng, p_rng ) );
Manuel Pégourié-Gonnard45a035a2013-01-26 14:42:45 +01003126}
Manuel Pégourié-Gonnardefaa31e2012-11-06 21:34:35 +01003127
Manuel Pégourié-Gonnard104ee1d2013-11-30 14:13:16 +01003128/*
3129 * Generate a keypair, prettier wrapper
3130 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02003131int mbedtls_ecp_gen_key( mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key,
Manuel Pégourié-Gonnard104ee1d2013-11-30 14:13:16 +01003132 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
3133{
Janos Follath24eed8d2019-11-22 13:21:35 +00003134 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
Andrzej Kurekc470b6b2019-01-31 08:20:20 -05003135 ECP_VALIDATE_RET( key != NULL );
3136 ECP_VALIDATE_RET( f_rng != NULL );
Manuel Pégourié-Gonnard104ee1d2013-11-30 14:13:16 +01003137
Manuel Pégourié-Gonnarde3a062b2015-05-11 18:46:47 +02003138 if( ( ret = mbedtls_ecp_group_load( &key->grp, grp_id ) ) != 0 )
Manuel Pégourié-Gonnard104ee1d2013-11-30 14:13:16 +01003139 return( ret );
3140
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02003141 return( mbedtls_ecp_gen_keypair( &key->grp, &key->d, &key->Q, f_rng, p_rng ) );
Manuel Pégourié-Gonnard104ee1d2013-11-30 14:13:16 +01003142}
3143
Janos Follath77800962019-02-25 16:32:08 +00003144#define ECP_CURVE25519_KEY_SIZE 32
Janos Follath171a7ef2019-02-15 16:17:45 +00003145/*
3146 * Read a private key.
3147 */
3148int mbedtls_ecp_read_key( mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key,
3149 const unsigned char *buf, size_t buflen )
3150{
3151 int ret = 0;
3152
Janos Follath28eb06d2019-02-26 10:53:34 +00003153 ECP_VALIDATE_RET( key != NULL );
3154 ECP_VALIDATE_RET( buf != NULL );
3155
Janos Follath171a7ef2019-02-15 16:17:45 +00003156 if( ( ret = mbedtls_ecp_group_load( &key->grp, grp_id ) ) != 0 )
3157 return( ret );
3158
Janos Follath28eb06d2019-02-26 10:53:34 +00003159 ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
3160
Gilles Peskinee8c04fe2018-09-14 17:44:21 +02003161#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
Janos Follathdf9295b2019-02-26 12:36:52 +00003162 if( mbedtls_ecp_get_type( &key->grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY )
Janos Follath171a7ef2019-02-15 16:17:45 +00003163 {
Janos Follath28eb06d2019-02-26 10:53:34 +00003164 /*
3165 * If it is Curve25519 curve then mask the key as mandated by RFC7748
3166 */
3167 if( grp_id == MBEDTLS_ECP_DP_CURVE25519 )
3168 {
3169 if( buflen != ECP_CURVE25519_KEY_SIZE )
3170 return MBEDTLS_ERR_ECP_INVALID_KEY;
Janos Follath171a7ef2019-02-15 16:17:45 +00003171
Janos Follath28eb06d2019-02-26 10:53:34 +00003172 MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary_le( &key->d, buf, buflen ) );
Janos Follath171a7ef2019-02-15 16:17:45 +00003173
Janos Follath28eb06d2019-02-26 10:53:34 +00003174 /* Set the three least significant bits to 0 */
3175 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &key->d, 0, 0 ) );
3176 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &key->d, 1, 0 ) );
3177 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &key->d, 2, 0 ) );
Janos Follath171a7ef2019-02-15 16:17:45 +00003178
Janos Follath28eb06d2019-02-26 10:53:34 +00003179 /* Set the most significant bit to 0 */
3180 MBEDTLS_MPI_CHK(
3181 mbedtls_mpi_set_bit( &key->d,
3182 ECP_CURVE25519_KEY_SIZE * 8 - 1, 0 )
3183 );
Janos Follath171a7ef2019-02-15 16:17:45 +00003184
Janos Follath28eb06d2019-02-26 10:53:34 +00003185 /* Set the second most significant bit to 1 */
3186 MBEDTLS_MPI_CHK(
3187 mbedtls_mpi_set_bit( &key->d,
3188 ECP_CURVE25519_KEY_SIZE * 8 - 2, 1 )
3189 );
3190 }
3191 else
3192 ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
Janos Follath171a7ef2019-02-15 16:17:45 +00003193 }
3194
3195#endif
Gilles Peskinee8c04fe2018-09-14 17:44:21 +02003196#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
Janos Follathdf9295b2019-02-26 12:36:52 +00003197 if( mbedtls_ecp_get_type( &key->grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
Janos Follath171a7ef2019-02-15 16:17:45 +00003198 {
3199 MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &key->d, buf, buflen ) );
3200
3201 MBEDTLS_MPI_CHK( mbedtls_ecp_check_privkey( &key->grp, &key->d ) );
3202 }
3203
3204#endif
3205cleanup:
3206
3207 if( ret != 0 )
3208 mbedtls_mpi_free( &key->d );
3209
3210 return( ret );
3211}
3212
Manuel Pégourié-Gonnard30668d62014-11-06 15:25:32 +01003213/*
Steven Cooremande8593f2020-06-09 19:55:26 +02003214 * Write a private key.
3215 */
Steven Cooreman0024df62020-07-13 10:59:40 +02003216int mbedtls_ecp_write_key( mbedtls_ecp_keypair *key,
Steven Cooremanc9b7f782020-06-11 17:00:36 +02003217 unsigned char *buf, size_t buflen )
Steven Cooremande8593f2020-06-09 19:55:26 +02003218{
Steven Cooreman0024df62020-07-13 10:59:40 +02003219 int ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
Steven Cooremande8593f2020-06-09 19:55:26 +02003220
Steven Cooreman0024df62020-07-13 10:59:40 +02003221 ECP_VALIDATE_RET( key != NULL );
3222 ECP_VALIDATE_RET( buf != NULL );
Steven Cooremande8593f2020-06-09 19:55:26 +02003223
Gilles Peskinee8c04fe2018-09-14 17:44:21 +02003224#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
Steven Cooremande8593f2020-06-09 19:55:26 +02003225 if( mbedtls_ecp_get_type( &key->grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY )
3226 {
Steven Cooreman0024df62020-07-13 10:59:40 +02003227 if( key->grp.id == MBEDTLS_ECP_DP_CURVE25519 )
Steven Cooremande8593f2020-06-09 19:55:26 +02003228 {
3229 if( buflen < ECP_CURVE25519_KEY_SIZE )
3230 return MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL;
3231
3232 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary_le( &key->d, buf, buflen ) );
Steven Cooremande8593f2020-06-09 19:55:26 +02003233 }
3234 else
3235 ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
3236 }
3237
3238#endif
Gilles Peskinee8c04fe2018-09-14 17:44:21 +02003239#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
Steven Cooremande8593f2020-06-09 19:55:26 +02003240 if( mbedtls_ecp_get_type( &key->grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
3241 {
3242 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &key->d, buf, buflen ) );
Steven Cooremande8593f2020-06-09 19:55:26 +02003243 }
3244
3245#endif
3246cleanup:
3247
3248 return( ret );
3249}
3250
3251
3252/*
Manuel Pégourié-Gonnard30668d62014-11-06 15:25:32 +01003253 * Check a public-private key pair
3254 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02003255int mbedtls_ecp_check_pub_priv( const mbedtls_ecp_keypair *pub, const mbedtls_ecp_keypair *prv )
Manuel Pégourié-Gonnard30668d62014-11-06 15:25:32 +01003256{
Janos Follath24eed8d2019-11-22 13:21:35 +00003257 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02003258 mbedtls_ecp_point Q;
3259 mbedtls_ecp_group grp;
Andrzej Kurekc470b6b2019-01-31 08:20:20 -05003260 ECP_VALIDATE_RET( pub != NULL );
3261 ECP_VALIDATE_RET( prv != NULL );
Manuel Pégourié-Gonnard30668d62014-11-06 15:25:32 +01003262
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02003263 if( pub->grp.id == MBEDTLS_ECP_DP_NONE ||
Manuel Pégourié-Gonnard30668d62014-11-06 15:25:32 +01003264 pub->grp.id != prv->grp.id ||
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02003265 mbedtls_mpi_cmp_mpi( &pub->Q.X, &prv->Q.X ) ||
3266 mbedtls_mpi_cmp_mpi( &pub->Q.Y, &prv->Q.Y ) ||
3267 mbedtls_mpi_cmp_mpi( &pub->Q.Z, &prv->Q.Z ) )
Manuel Pégourié-Gonnard30668d62014-11-06 15:25:32 +01003268 {
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02003269 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
Manuel Pégourié-Gonnard30668d62014-11-06 15:25:32 +01003270 }
3271
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02003272 mbedtls_ecp_point_init( &Q );
3273 mbedtls_ecp_group_init( &grp );
Manuel Pégourié-Gonnard30668d62014-11-06 15:25:32 +01003274
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02003275 /* mbedtls_ecp_mul() needs a non-const group... */
3276 mbedtls_ecp_group_copy( &grp, &prv->grp );
Manuel Pégourié-Gonnard30668d62014-11-06 15:25:32 +01003277
3278 /* Also checks d is valid */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02003279 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &Q, &prv->d, &prv->grp.G, NULL, NULL ) );
Manuel Pégourié-Gonnard30668d62014-11-06 15:25:32 +01003280
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02003281 if( mbedtls_mpi_cmp_mpi( &Q.X, &prv->Q.X ) ||
3282 mbedtls_mpi_cmp_mpi( &Q.Y, &prv->Q.Y ) ||
3283 mbedtls_mpi_cmp_mpi( &Q.Z, &prv->Q.Z ) )
Manuel Pégourié-Gonnard30668d62014-11-06 15:25:32 +01003284 {
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02003285 ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
Manuel Pégourié-Gonnard30668d62014-11-06 15:25:32 +01003286 goto cleanup;
3287 }
3288
3289cleanup:
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02003290 mbedtls_ecp_point_free( &Q );
3291 mbedtls_ecp_group_free( &grp );
Manuel Pégourié-Gonnard30668d62014-11-06 15:25:32 +01003292
3293 return( ret );
3294}
3295
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02003296#if defined(MBEDTLS_SELF_TEST)
Manuel Pégourié-Gonnard39d2adb2012-10-31 09:26:55 +01003297
Gilles Peskine6d9c8d72020-07-22 01:26:25 +02003298/* Adjust the exponent to be a valid private point for the specified curve.
3299 * This is sometimes necessary because we use a single set of exponents
3300 * for all curves but the validity of values depends on the curve. */
Gilles Peskinea088c812018-09-17 18:31:15 +02003301static int self_test_adjust_exponent( const mbedtls_ecp_group *grp,
3302 mbedtls_mpi *m )
3303{
3304 int ret = 0;
3305 switch( grp->id )
3306 {
3307 /* If Curve25519 is available, then that's what we use for the
3308 * Montgomery test, so we don't need the adjustment code. */
3309#if ! defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
3310#if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
3311 case MBEDTLS_ECP_DP_CURVE448:
3312 /* Move highest bit from 254 to N-1. Setting bit N-1 is
3313 * necessary to enforce the highest-bit-set constraint. */
3314 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( m, 254, 0 ) );
3315 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( m, grp->nbits, 1 ) );
3316 /* Copy second-highest bit from 253 to N-2. This is not
3317 * necessary but improves the test variety a bit. */
3318 MBEDTLS_MPI_CHK(
3319 mbedtls_mpi_set_bit( m, grp->nbits - 1,
3320 mbedtls_mpi_get_bit( m, 253 ) ) );
3321 break;
3322#endif
3323#endif /* ! defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) */
3324 default:
3325 /* Non-Montgomery curves and Curve25519 need no adjustment. */
3326 (void) grp;
3327 (void) m;
3328 goto cleanup;
3329 }
3330cleanup:
3331 return( ret );
3332}
3333
Gilles Peskine6d9c8d72020-07-22 01:26:25 +02003334/* Calculate R = m.P for each m in exponents. Check that the number of
3335 * basic operations doesn't depend on the value of m. */
Gilles Peskinec95696f2018-09-17 15:59:01 +02003336static int self_test_point( int verbose,
3337 mbedtls_ecp_group *grp,
3338 mbedtls_ecp_point *R,
3339 mbedtls_mpi *m,
Gilles Peskine6d9c8d72020-07-22 01:26:25 +02003340 const mbedtls_ecp_point *P,
Gilles Peskinec95696f2018-09-17 15:59:01 +02003341 const char *const *exponents,
3342 size_t n_exponents )
3343{
3344 int ret = 0;
Gilles Peskine24666792018-09-17 18:29:49 +02003345 size_t i = 0;
Gilles Peskinec95696f2018-09-17 15:59:01 +02003346 unsigned long add_c_prev, dbl_c_prev, mul_c_prev;
3347 add_count = 0;
3348 dbl_count = 0;
3349 mul_count = 0;
Gilles Peskinea088c812018-09-17 18:31:15 +02003350
Gilles Peskinec95696f2018-09-17 15:59:01 +02003351 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( m, 16, exponents[0] ) );
Gilles Peskinea088c812018-09-17 18:31:15 +02003352 MBEDTLS_MPI_CHK( self_test_adjust_exponent( grp, m ) );
Gilles Peskinec95696f2018-09-17 15:59:01 +02003353 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( grp, R, m, P, NULL, NULL ) );
3354
3355 for( i = 1; i < n_exponents; i++ )
3356 {
3357 add_c_prev = add_count;
3358 dbl_c_prev = dbl_count;
3359 mul_c_prev = mul_count;
3360 add_count = 0;
3361 dbl_count = 0;
3362 mul_count = 0;
3363
3364 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( m, 16, exponents[i] ) );
Gilles Peskinea088c812018-09-17 18:31:15 +02003365 MBEDTLS_MPI_CHK( self_test_adjust_exponent( grp, m ) );
Gilles Peskinec95696f2018-09-17 15:59:01 +02003366 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( grp, R, m, P, NULL, NULL ) );
3367
3368 if( add_count != add_c_prev ||
3369 dbl_count != dbl_c_prev ||
3370 mul_count != mul_c_prev )
3371 {
3372 ret = 1;
3373 break;
3374 }
3375 }
3376
3377cleanup:
3378 if( verbose != 0 )
3379 {
3380 if( ret != 0 )
3381 mbedtls_printf( "failed (%u)\n", (unsigned int) i );
3382 else
3383 mbedtls_printf( "passed\n" );
3384 }
3385 return( ret );
3386}
3387
Manuel Pégourié-Gonnardb505c272012-11-05 17:27:54 +01003388/*
Manuel Pégourié-Gonnard39d2adb2012-10-31 09:26:55 +01003389 * Checkup routine
3390 */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02003391int mbedtls_ecp_self_test( int verbose )
Manuel Pégourié-Gonnard39d2adb2012-10-31 09:26:55 +01003392{
Janos Follath24eed8d2019-11-22 13:21:35 +00003393 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02003394 mbedtls_ecp_group grp;
3395 mbedtls_ecp_point R, P;
3396 mbedtls_mpi m;
Gilles Peskine24666792018-09-17 18:29:49 +02003397
3398#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
Gilles Peskined9767a52018-09-14 19:29:47 +02003399 /* Exponents especially adapted for secp192k1, which has the lowest
3400 * order n of all supported curves (secp192r1 is in a slightly larger
3401 * field but the order of its base point is slightly smaller). */
Gilles Peskine24666792018-09-17 18:29:49 +02003402 const char *sw_exponents[] =
Manuel Pégourié-Gonnardb4a310b2012-11-13 20:57:00 +01003403 {
Manuel Pégourié-Gonnardb63f9e92012-11-21 13:00:58 +01003404 "000000000000000000000000000000000000000000000001", /* one */
Gilles Peskined9767a52018-09-14 19:29:47 +02003405 "FFFFFFFFFFFFFFFFFFFFFFFE26F2FC170F69466A74DEFD8C", /* n - 1 */
Manuel Pégourié-Gonnardb63f9e92012-11-21 13:00:58 +01003406 "5EA6F389A38B8BC81E767753B15AA5569E1782E30ABE7D25", /* random */
Manuel Pégourié-Gonnardff27b7c2013-11-21 09:28:03 +01003407 "400000000000000000000000000000000000000000000000", /* one and zeros */
3408 "7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", /* all ones */
3409 "555555555555555555555555555555555555555555555555", /* 101010... */
Manuel Pégourié-Gonnardb4a310b2012-11-13 20:57:00 +01003410 };
Gilles Peskine24666792018-09-17 18:29:49 +02003411#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
3412#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
3413 const char *m_exponents[] =
3414 {
Gilles Peskine6d9c8d72020-07-22 01:26:25 +02003415 /* Valid private values for Curve25519. In a build with Curve448
3416 * but not Curve25519, they will be adjusted in
3417 * self_test_adjust_exponent(). */
Gilles Peskine24666792018-09-17 18:29:49 +02003418 "4000000000000000000000000000000000000000000000000000000000000000",
3419 "5C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C30",
3420 "5715ECCE24583F7A7023C24164390586842E816D7280A49EF6DF4EAE6B280BF8",
3421 "41A2B017516F6D254E1F002BCCBADD54BE30F8CEC737A0E912B4963B6BA74460",
3422 "5555555555555555555555555555555555555555555555555555555555555550",
3423 "7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF8",
3424 };
3425#endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
Manuel Pégourié-Gonnardb4a310b2012-11-13 20:57:00 +01003426
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02003427 mbedtls_ecp_group_init( &grp );
3428 mbedtls_ecp_point_init( &R );
3429 mbedtls_ecp_point_init( &P );
3430 mbedtls_mpi_init( &m );
Manuel Pégourié-Gonnardb4a310b2012-11-13 20:57:00 +01003431
Gilles Peskine24666792018-09-17 18:29:49 +02003432#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
Manuel Pégourié-Gonnardb8012fc2013-10-10 15:40:49 +02003433 /* Use secp192r1 if available, or any available curve */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02003434#if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
Manuel Pégourié-Gonnarde3a062b2015-05-11 18:46:47 +02003435 MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, MBEDTLS_ECP_DP_SECP192R1 ) );
Paul Bakker5dc6b5f2013-06-29 23:26:34 +02003436#else
Manuel Pégourié-Gonnarde3a062b2015-05-11 18:46:47 +02003437 MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, mbedtls_ecp_curve_list()->grp_id ) );
Manuel Pégourié-Gonnardb8012fc2013-10-10 15:40:49 +02003438#endif
Manuel Pégourié-Gonnardb4a310b2012-11-13 20:57:00 +01003439
3440 if( verbose != 0 )
Gilles Peskine24666792018-09-17 18:29:49 +02003441 mbedtls_printf( " ECP SW test #1 (constant op_count, base point G): " );
Manuel Pégourié-Gonnard161ef962013-09-17 19:13:10 +02003442 /* Do a dummy multiplication first to trigger precomputation */
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02003443 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &m, 2 ) );
3444 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &P, &m, &grp.G, NULL, NULL ) );
Gilles Peskinec95696f2018-09-17 15:59:01 +02003445 ret = self_test_point( verbose,
3446 &grp, &R, &m, &grp.G,
Gilles Peskine24666792018-09-17 18:29:49 +02003447 sw_exponents,
3448 sizeof( sw_exponents ) / sizeof( sw_exponents[0] ));
Gilles Peskinec95696f2018-09-17 15:59:01 +02003449 if( ret != 0 )
3450 goto cleanup;
Manuel Pégourié-Gonnardb4a310b2012-11-13 20:57:00 +01003451
Manuel Pégourié-Gonnard161ef962013-09-17 19:13:10 +02003452 if( verbose != 0 )
Gilles Peskine24666792018-09-17 18:29:49 +02003453 mbedtls_printf( " ECP SW test #2 (constant op_count, other point): " );
Manuel Pégourié-Gonnard161ef962013-09-17 19:13:10 +02003454 /* We computed P = 2G last time, use it */
Gilles Peskinec95696f2018-09-17 15:59:01 +02003455 ret = self_test_point( verbose,
3456 &grp, &R, &m, &P,
Gilles Peskine24666792018-09-17 18:29:49 +02003457 sw_exponents,
3458 sizeof( sw_exponents ) / sizeof( sw_exponents[0] ));
3459 if( ret != 0 )
3460 goto cleanup;
3461
3462 mbedtls_ecp_group_free( &grp );
3463 mbedtls_ecp_point_free( &R );
3464#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
3465
3466#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
3467 if( verbose != 0 )
3468 mbedtls_printf( " ECP Montgomery test (constant op_count): " );
3469#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
3470 MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, MBEDTLS_ECP_DP_CURVE25519 ) );
3471#elif defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
3472 MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, MBEDTLS_ECP_DP_CURVE448 ) );
3473#else
3474#error "MBEDTLS_ECP_MONTGOMERY_ENABLED is defined, but no curve is supported for self-test"
3475#endif
3476 ret = self_test_point( verbose,
3477 &grp, &R, &m, &grp.G,
3478 m_exponents,
3479 sizeof( m_exponents ) / sizeof( m_exponents[0] ));
3480 if( ret != 0 )
3481 goto cleanup;
3482#endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
Manuel Pégourié-Gonnard161ef962013-09-17 19:13:10 +02003483
Manuel Pégourié-Gonnardb4a310b2012-11-13 20:57:00 +01003484cleanup:
3485
3486 if( ret < 0 && verbose != 0 )
Kenneth Soerensen518d4352020-04-01 17:22:45 +02003487 mbedtls_printf( "Unexpected error, return code = %08X\n", (unsigned int) ret );
Manuel Pégourié-Gonnardb4a310b2012-11-13 20:57:00 +01003488
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02003489 mbedtls_ecp_group_free( &grp );
3490 mbedtls_ecp_point_free( &R );
3491 mbedtls_ecp_point_free( &P );
3492 mbedtls_mpi_free( &m );
Manuel Pégourié-Gonnardb4a310b2012-11-13 20:57:00 +01003493
3494 if( verbose != 0 )
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02003495 mbedtls_printf( "\n" );
Manuel Pégourié-Gonnardb4a310b2012-11-13 20:57:00 +01003496
3497 return( ret );
Manuel Pégourié-Gonnard39d2adb2012-10-31 09:26:55 +01003498}
3499
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02003500#endif /* MBEDTLS_SELF_TEST */
Manuel Pégourié-Gonnard39d2adb2012-10-31 09:26:55 +01003501
Janos Follathb0697532016-08-18 12:38:46 +01003502#endif /* !MBEDTLS_ECP_ALT */
3503
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +02003504#endif /* MBEDTLS_ECP_C */