1 /*
2 * Elliptic curves over GF(p): generic functions
3 *
4 * Copyright The Mbed TLS Contributors
5 * SPDX-License-Identifier: Apache-2.0
6 *
7 * Licensed under the Apache License, Version 2.0 (the "License"); you may
8 * not use this file except in compliance with the License.
9 * You may obtain a copy of the License at
10 *
11 * http://www.apache.org/licenses/LICENSE-2.0
12 *
13 * Unless required by applicable law or agreed to in writing, software
14 * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
15 * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
16 * See the License for the specific language governing permissions and
17 * limitations under the License.
18 */
19
20 /*
21 * References:
22 *
23 * SEC1 http://www.secg.org/index.php?action=secg,docs_secg
24 * GECC = Guide to Elliptic Curve Cryptography - Hankerson, Menezes, Vanstone
25 * FIPS 186-3 http://csrc.nist.gov/publications/fips/fips186-3/fips_186-3.pdf
26 * RFC 4492 for the related TLS structures and constants
27 * RFC 7748 for the Curve448 and Curve25519 curve definitions
28 *
29 * [Curve25519] http://cr.yp.to/ecdh/curve25519-20060209.pdf
30 *
31 * [2] CORON, Jean-S'ebastien. Resistance against differential power analysis
32 * for elliptic curve cryptosystems. In : Cryptographic Hardware and
33 * Embedded Systems. Springer Berlin Heidelberg, 1999. p. 292-302.
34 * <http://link.springer.com/chapter/10.1007/3-540-48059-5_25>
35 *
36 * [3] HEDABOU, Mustapha, PINEL, Pierre, et B'EN'ETEAU, Lucien. A comb method to
37 * render ECC resistant against Side Channel Attacks. IACR Cryptology
38 * ePrint Archive, 2004, vol. 2004, p. 342.
39 * <http://eprint.iacr.org/2004/342.pdf>
40 */
41
42 #include "common.h"
43
44 /**
45 * \brief Function level alternative implementation.
46 *
47 * The MBEDTLS_ECP_INTERNAL_ALT macro enables alternative implementations to
48 * replace certain functions in this module. The alternative implementations are
49 * typically hardware accelerators and need to activate the hardware before the
50 * computation starts and deactivate it after it finishes. The
51 * mbedtls_internal_ecp_init() and mbedtls_internal_ecp_free() functions serve
52 * this purpose.
53 *
54 * To preserve the correct functionality the following conditions must hold:
55 *
56 * - The alternative implementation must be activated by
57 * mbedtls_internal_ecp_init() before any of the replaceable functions is
58 * called.
59 * - mbedtls_internal_ecp_free() must \b only be called when the alternative
60 * implementation is activated.
61 * - mbedtls_internal_ecp_init() must \b not be called when the alternative
62 * implementation is activated.
63 * - Public functions must not return while the alternative implementation is
64 * activated.
65 * - Replaceable functions are guarded by \c MBEDTLS_ECP_XXX_ALT macros and
66 * before calling them an \code if( mbedtls_internal_ecp_grp_capable( grp ) )
67 * \endcode ensures that the alternative implementation supports the current
68 * group.
69 */
70 #if defined(MBEDTLS_ECP_INTERNAL_ALT)
71 #endif
72
73 #if defined(MBEDTLS_ECP_C)
74
75 #include "mbedtls/ecp.h"
76 #include "mbedtls/threading.h"
77 #include "mbedtls/platform_util.h"
78 #include "mbedtls/error.h"
79
80 #include <string.h>
81
82 #if !defined(MBEDTLS_ECP_ALT)
83
84 /* Parameter validation macros based on platform_util.h */
85 #define ECP_VALIDATE_RET( cond ) \
86 MBEDTLS_INTERNAL_VALIDATE_RET( cond, MBEDTLS_ERR_ECP_BAD_INPUT_DATA )
87 #define ECP_VALIDATE( cond ) \
88 MBEDTLS_INTERNAL_VALIDATE( cond )
89
90 #if defined(MBEDTLS_PLATFORM_C)
91 #include "mbedtls/platform.h"
92 #else
93 #include <stdlib.h>
94 #include <stdio.h>
95 #define mbedtls_printf printf
96 #define mbedtls_calloc calloc
97 #define mbedtls_free free
98 #endif
99
100 #include "mbedtls/ecp_internal.h"
101
102 #if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
103 #if defined(MBEDTLS_HMAC_DRBG_C)
104 #include "mbedtls/hmac_drbg.h"
105 #elif defined(MBEDTLS_CTR_DRBG_C)
106 #include "mbedtls/ctr_drbg.h"
107 #else
108 #error "Invalid configuration detected. Include check_config.h to ensure that the configuration is valid."
109 #endif
110 #endif /* MBEDTLS_ECP_NO_INTERNAL_RNG */
111
112 #if ( defined(__ARMCC_VERSION) || defined(_MSC_VER) ) && \
113 !defined(inline) && !defined(__cplusplus)
114 #define inline __inline
115 #endif
116
117 #if defined(MBEDTLS_SELF_TEST)
118 /*
119 * Counts of point addition and doubling, and field multiplications.
120 * Used to test resistance of point multiplication to simple timing attacks.
121 */
122 static unsigned long add_count, dbl_count, mul_count;
123 #endif
124
125 #if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
126 /*
127 * Currently ecp_mul() takes a RNG function as an argument, used for
128 * side-channel protection, but it can be NULL. The initial reasoning was
129 * that people will pass non-NULL RNG when they care about side-channels, but
130 * unfortunately we have some APIs that call ecp_mul() with a NULL RNG, with
131 * no opportunity for the user to do anything about it.
132 *
133 * The obvious strategies for addressing that include:
134 * - change those APIs so that they take RNG arguments;
135 * - require a global RNG to be available to all crypto modules.
136 *
137 * Unfortunately those would break compatibility. So what we do instead is
138 * have our own internal DRBG instance, seeded from the secret scalar.
139 *
140 * The following is a light-weight abstraction layer for doing that with
141 * HMAC_DRBG (first choice) or CTR_DRBG.
142 */
143
144 #if defined(MBEDTLS_HMAC_DRBG_C)
145
146 /* DRBG context type */
147 typedef mbedtls_hmac_drbg_context ecp_drbg_context;
148
149 /* DRBG context init */
ecp_drbg_init(ecp_drbg_context * ctx)150 static inline void ecp_drbg_init( ecp_drbg_context *ctx )
151 {
152 mbedtls_hmac_drbg_init( ctx );
153 }
154
155 /* DRBG context free */
ecp_drbg_free(ecp_drbg_context * ctx)156 static inline void ecp_drbg_free( ecp_drbg_context *ctx )
157 {
158 mbedtls_hmac_drbg_free( ctx );
159 }
160
161 /* DRBG function */
ecp_drbg_random(void * p_rng,unsigned char * output,size_t output_len)162 static inline int ecp_drbg_random( void *p_rng,
163 unsigned char *output, size_t output_len )
164 {
165 return( mbedtls_hmac_drbg_random( p_rng, output, output_len ) );
166 }
167
168 /* DRBG context seeding */
ecp_drbg_seed(ecp_drbg_context * ctx,const mbedtls_mpi * secret,size_t secret_len)169 static int ecp_drbg_seed( ecp_drbg_context *ctx,
170 const mbedtls_mpi *secret, size_t secret_len )
171 {
172 int ret;
173 unsigned char secret_bytes[MBEDTLS_ECP_MAX_BYTES];
174 /* The list starts with strong hashes */
175 const mbedtls_md_type_t md_type = mbedtls_md_list()[0];
176 const mbedtls_md_info_t *md_info = mbedtls_md_info_from_type( md_type );
177
178 if( secret_len > MBEDTLS_ECP_MAX_BYTES )
179 {
180 ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
181 goto cleanup;
182 }
183
184 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( secret,
185 secret_bytes, secret_len ) );
186
187 ret = mbedtls_hmac_drbg_seed_buf( ctx, md_info, secret_bytes, secret_len );
188
189 cleanup:
190 mbedtls_platform_zeroize( secret_bytes, secret_len );
191
192 return( ret );
193 }
194
195 #elif defined(MBEDTLS_CTR_DRBG_C)
196
197 /* DRBG context type */
198 typedef mbedtls_ctr_drbg_context ecp_drbg_context;
199
200 /* DRBG context init */
ecp_drbg_init(ecp_drbg_context * ctx)201 static inline void ecp_drbg_init( ecp_drbg_context *ctx )
202 {
203 mbedtls_ctr_drbg_init( ctx );
204 }
205
206 /* DRBG context free */
ecp_drbg_free(ecp_drbg_context * ctx)207 static inline void ecp_drbg_free( ecp_drbg_context *ctx )
208 {
209 mbedtls_ctr_drbg_free( ctx );
210 }
211
212 /* DRBG function */
ecp_drbg_random(void * p_rng,unsigned char * output,size_t output_len)213 static inline int ecp_drbg_random( void *p_rng,
214 unsigned char *output, size_t output_len )
215 {
216 return( mbedtls_ctr_drbg_random( p_rng, output, output_len ) );
217 }
218
219 /*
220 * Since CTR_DRBG doesn't have a seed_buf() function the way HMAC_DRBG does,
221 * we need to pass an entropy function when seeding. So we use a dummy
222 * function for that, and pass the actual entropy as customisation string.
223 * (During seeding of CTR_DRBG the entropy input and customisation string are
224 * concatenated before being used to update the secret state.)
225 */
ecp_ctr_drbg_null_entropy(void * ctx,unsigned char * out,size_t len)226 static int ecp_ctr_drbg_null_entropy(void *ctx, unsigned char *out, size_t len)
227 {
228 (void) ctx;
229 memset( out, 0, len );
230 return( 0 );
231 }
232
233 /* DRBG context seeding */
ecp_drbg_seed(ecp_drbg_context * ctx,const mbedtls_mpi * secret,size_t secret_len)234 static int ecp_drbg_seed( ecp_drbg_context *ctx,
235 const mbedtls_mpi *secret, size_t secret_len )
236 {
237 int ret;
238 unsigned char secret_bytes[MBEDTLS_ECP_MAX_BYTES];
239
240 if( secret_len > MBEDTLS_ECP_MAX_BYTES )
241 {
242 ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
243 goto cleanup;
244 }
245
246 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( secret,
247 secret_bytes, secret_len ) );
248
249 ret = mbedtls_ctr_drbg_seed( ctx, ecp_ctr_drbg_null_entropy, NULL,
250 secret_bytes, secret_len );
251
252 cleanup:
253 mbedtls_platform_zeroize( secret_bytes, secret_len );
254
255 return( ret );
256 }
257
258 #else
259 #error "Invalid configuration detected. Include check_config.h to ensure that the configuration is valid."
260 #endif /* DRBG modules */
261 #endif /* MBEDTLS_ECP_NO_INTERNAL_RNG */
262
263 #if defined(MBEDTLS_ECP_RESTARTABLE)
264 /*
265 * Maximum number of "basic operations" to be done in a row.
266 *
267 * Default value 0 means that ECC operations will not yield.
268 * Note that regardless of the value of ecp_max_ops, always at
269 * least one step is performed before yielding.
270 *
271 * Setting ecp_max_ops=1 can be suitable for testing purposes
272 * as it will interrupt computation at all possible points.
273 */
274 static unsigned ecp_max_ops = 0;
275
276 /*
277 * Set ecp_max_ops
278 */
mbedtls_ecp_set_max_ops(unsigned max_ops)279 void mbedtls_ecp_set_max_ops( unsigned max_ops )
280 {
281 ecp_max_ops = max_ops;
282 }
283
284 /*
285 * Check if restart is enabled
286 */
mbedtls_ecp_restart_is_enabled(void)287 int mbedtls_ecp_restart_is_enabled( void )
288 {
289 return( ecp_max_ops != 0 );
290 }
291
292 /*
293 * Restart sub-context for ecp_mul_comb()
294 */
295 struct mbedtls_ecp_restart_mul
296 {
297 mbedtls_ecp_point R; /* current intermediate result */
298 size_t i; /* current index in various loops, 0 outside */
299 mbedtls_ecp_point *T; /* table for precomputed points */
300 unsigned char T_size; /* number of points in table T */
301 enum { /* what were we doing last time we returned? */
302 ecp_rsm_init = 0, /* nothing so far, dummy initial state */
303 ecp_rsm_pre_dbl, /* precompute 2^n multiples */
304 ecp_rsm_pre_norm_dbl, /* normalize precomputed 2^n multiples */
305 ecp_rsm_pre_add, /* precompute remaining points by adding */
306 ecp_rsm_pre_norm_add, /* normalize all precomputed points */
307 ecp_rsm_comb_core, /* ecp_mul_comb_core() */
308 ecp_rsm_final_norm, /* do the final normalization */
309 } state;
310 #if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
311 ecp_drbg_context drbg_ctx;
312 unsigned char drbg_seeded;
313 #endif
314 };
315
316 /*
317 * Init restart_mul sub-context
318 */
ecp_restart_rsm_init(mbedtls_ecp_restart_mul_ctx * ctx)319 static void ecp_restart_rsm_init( mbedtls_ecp_restart_mul_ctx *ctx )
320 {
321 mbedtls_ecp_point_init( &ctx->R );
322 ctx->i = 0;
323 ctx->T = NULL;
324 ctx->T_size = 0;
325 ctx->state = ecp_rsm_init;
326 #if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
327 ecp_drbg_init( &ctx->drbg_ctx );
328 ctx->drbg_seeded = 0;
329 #endif
330 }
331
332 /*
333 * Free the components of a restart_mul sub-context
334 */
ecp_restart_rsm_free(mbedtls_ecp_restart_mul_ctx * ctx)335 static void ecp_restart_rsm_free( mbedtls_ecp_restart_mul_ctx *ctx )
336 {
337 unsigned char i;
338
339 if( ctx == NULL )
340 return;
341
342 mbedtls_ecp_point_free( &ctx->R );
343
344 if( ctx->T != NULL )
345 {
346 for( i = 0; i < ctx->T_size; i++ )
347 mbedtls_ecp_point_free( ctx->T + i );
348 mbedtls_free( ctx->T );
349 }
350
351 #if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
352 ecp_drbg_free( &ctx->drbg_ctx );
353 #endif
354
355 ecp_restart_rsm_init( ctx );
356 }
357
358 /*
359 * Restart context for ecp_muladd()
360 */
361 struct mbedtls_ecp_restart_muladd
362 {
363 mbedtls_ecp_point mP; /* mP value */
364 mbedtls_ecp_point R; /* R intermediate result */
365 enum { /* what should we do next? */
366 ecp_rsma_mul1 = 0, /* first multiplication */
367 ecp_rsma_mul2, /* second multiplication */
368 ecp_rsma_add, /* addition */
369 ecp_rsma_norm, /* normalization */
370 } state;
371 };
372
373 /*
374 * Init restart_muladd sub-context
375 */
ecp_restart_ma_init(mbedtls_ecp_restart_muladd_ctx * ctx)376 static void ecp_restart_ma_init( mbedtls_ecp_restart_muladd_ctx *ctx )
377 {
378 mbedtls_ecp_point_init( &ctx->mP );
379 mbedtls_ecp_point_init( &ctx->R );
380 ctx->state = ecp_rsma_mul1;
381 }
382
383 /*
384 * Free the components of a restart_muladd sub-context
385 */
ecp_restart_ma_free(mbedtls_ecp_restart_muladd_ctx * ctx)386 static void ecp_restart_ma_free( mbedtls_ecp_restart_muladd_ctx *ctx )
387 {
388 if( ctx == NULL )
389 return;
390
391 mbedtls_ecp_point_free( &ctx->mP );
392 mbedtls_ecp_point_free( &ctx->R );
393
394 ecp_restart_ma_init( ctx );
395 }
396
397 /*
398 * Initialize a restart context
399 */
mbedtls_ecp_restart_init(mbedtls_ecp_restart_ctx * ctx)400 void mbedtls_ecp_restart_init( mbedtls_ecp_restart_ctx *ctx )
401 {
402 ECP_VALIDATE( ctx != NULL );
403 ctx->ops_done = 0;
404 ctx->depth = 0;
405 ctx->rsm = NULL;
406 ctx->ma = NULL;
407 }
408
409 /*
410 * Free the components of a restart context
411 */
mbedtls_ecp_restart_free(mbedtls_ecp_restart_ctx * ctx)412 void mbedtls_ecp_restart_free( mbedtls_ecp_restart_ctx *ctx )
413 {
414 if( ctx == NULL )
415 return;
416
417 ecp_restart_rsm_free( ctx->rsm );
418 mbedtls_free( ctx->rsm );
419
420 ecp_restart_ma_free( ctx->ma );
421 mbedtls_free( ctx->ma );
422
423 mbedtls_ecp_restart_init( ctx );
424 }
425
426 /*
427 * Check if we can do the next step
428 */
mbedtls_ecp_check_budget(const mbedtls_ecp_group * grp,mbedtls_ecp_restart_ctx * rs_ctx,unsigned ops)429 int mbedtls_ecp_check_budget( const mbedtls_ecp_group *grp,
430 mbedtls_ecp_restart_ctx *rs_ctx,
431 unsigned ops )
432 {
433 ECP_VALIDATE_RET( grp != NULL );
434
435 if( rs_ctx != NULL && ecp_max_ops != 0 )
436 {
437 /* scale depending on curve size: the chosen reference is 256-bit,
438 * and multiplication is quadratic. Round to the closest integer. */
439 if( grp->pbits >= 512 )
440 ops *= 4;
441 else if( grp->pbits >= 384 )
442 ops *= 2;
443
444 /* Avoid infinite loops: always allow first step.
445 * Because of that, however, it's not generally true
446 * that ops_done <= ecp_max_ops, so the check
447 * ops_done > ecp_max_ops below is mandatory. */
448 if( ( rs_ctx->ops_done != 0 ) &&
449 ( rs_ctx->ops_done > ecp_max_ops ||
450 ops > ecp_max_ops - rs_ctx->ops_done ) )
451 {
452 return( MBEDTLS_ERR_ECP_IN_PROGRESS );
453 }
454
455 /* update running count */
456 rs_ctx->ops_done += ops;
457 }
458
459 return( 0 );
460 }
461
462 /* Call this when entering a function that needs its own sub-context */
463 #define ECP_RS_ENTER( SUB ) do { \
464 /* reset ops count for this call if top-level */ \
465 if( rs_ctx != NULL && rs_ctx->depth++ == 0 ) \
466 rs_ctx->ops_done = 0; \
467 \
468 /* set up our own sub-context if needed */ \
469 if( mbedtls_ecp_restart_is_enabled() && \
470 rs_ctx != NULL && rs_ctx->SUB == NULL ) \
471 { \
472 rs_ctx->SUB = mbedtls_calloc( 1, sizeof( *rs_ctx->SUB ) ); \
473 if( rs_ctx->SUB == NULL ) \
474 return( MBEDTLS_ERR_ECP_ALLOC_FAILED ); \
475 \
476 ecp_restart_## SUB ##_init( rs_ctx->SUB ); \
477 } \
478 } while( 0 )
479
480 /* Call this when leaving a function that needs its own sub-context */
481 #define ECP_RS_LEAVE( SUB ) do { \
482 /* clear our sub-context when not in progress (done or error) */ \
483 if( rs_ctx != NULL && rs_ctx->SUB != NULL && \
484 ret != MBEDTLS_ERR_ECP_IN_PROGRESS ) \
485 { \
486 ecp_restart_## SUB ##_free( rs_ctx->SUB ); \
487 mbedtls_free( rs_ctx->SUB ); \
488 rs_ctx->SUB = NULL; \
489 } \
490 \
491 if( rs_ctx != NULL ) \
492 rs_ctx->depth--; \
493 } while( 0 )
494
495 #else /* MBEDTLS_ECP_RESTARTABLE */
496
497 #define ECP_RS_ENTER( sub ) (void) rs_ctx;
498 #define ECP_RS_LEAVE( sub ) (void) rs_ctx;
499
500 #endif /* MBEDTLS_ECP_RESTARTABLE */
501
502 /*
503 * List of supported curves:
504 * - internal ID
505 * - TLS NamedCurve ID (RFC 4492 sec. 5.1.1, RFC 7071 sec. 2, RFC 8446 sec. 4.2.7)
506 * - size in bits
507 * - readable name
508 *
509 * Curves are listed in order: largest curves first, and for a given size,
510 * fastest curves first. This provides the default order for the SSL module.
511 *
512 * Reminder: update profiles in x509_crt.c when adding a new curves!
513 */
514 static const mbedtls_ecp_curve_info ecp_supported_curves[] =
515 {
516 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
517 { MBEDTLS_ECP_DP_SECP521R1, 25, 521, "secp521r1" },
518 #endif
519 #if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED)
520 { MBEDTLS_ECP_DP_BP512R1, 28, 512, "brainpoolP512r1" },
521 #endif
522 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
523 { MBEDTLS_ECP_DP_SECP384R1, 24, 384, "secp384r1" },
524 #endif
525 #if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED)
526 { MBEDTLS_ECP_DP_BP384R1, 27, 384, "brainpoolP384r1" },
527 #endif
528 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
529 { MBEDTLS_ECP_DP_SECP256R1, 23, 256, "secp256r1" },
530 #endif
531 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
532 { MBEDTLS_ECP_DP_SECP256K1, 22, 256, "secp256k1" },
533 #endif
534 #if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED)
535 { MBEDTLS_ECP_DP_BP256R1, 26, 256, "brainpoolP256r1" },
536 #endif
537 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
538 { MBEDTLS_ECP_DP_SECP224R1, 21, 224, "secp224r1" },
539 #endif
540 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
541 { MBEDTLS_ECP_DP_SECP224K1, 20, 224, "secp224k1" },
542 #endif
543 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
544 { MBEDTLS_ECP_DP_SECP192R1, 19, 192, "secp192r1" },
545 #endif
546 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
547 { MBEDTLS_ECP_DP_SECP192K1, 18, 192, "secp192k1" },
548 #endif
549 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
550 { MBEDTLS_ECP_DP_CURVE25519, 29, 256, "x25519" },
551 #endif
552 #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
553 { MBEDTLS_ECP_DP_CURVE448, 30, 448, "x448" },
554 #endif
555 { MBEDTLS_ECP_DP_NONE, 0, 0, NULL },
556 };
557
558 #define ECP_NB_CURVES sizeof( ecp_supported_curves ) / \
559 sizeof( ecp_supported_curves[0] )
560
561 static mbedtls_ecp_group_id ecp_supported_grp_id[ECP_NB_CURVES];
562
563 /*
564 * List of supported curves and associated info
565 */
mbedtls_ecp_curve_list(void)566 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_list( void )
567 {
568 return( ecp_supported_curves );
569 }
570
571 /*
572 * List of supported curves, group ID only
573 */
mbedtls_ecp_grp_id_list(void)574 const mbedtls_ecp_group_id *mbedtls_ecp_grp_id_list( void )
575 {
576 static int init_done = 0;
577
578 if( ! init_done )
579 {
580 size_t i = 0;
581 const mbedtls_ecp_curve_info *curve_info;
582
583 for( curve_info = mbedtls_ecp_curve_list();
584 curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
585 curve_info++ )
586 {
587 ecp_supported_grp_id[i++] = curve_info->grp_id;
588 }
589 ecp_supported_grp_id[i] = MBEDTLS_ECP_DP_NONE;
590
591 init_done = 1;
592 }
593
594 return( ecp_supported_grp_id );
595 }
596
597 /*
598 * Get the curve info for the internal identifier
599 */
mbedtls_ecp_curve_info_from_grp_id(mbedtls_ecp_group_id grp_id)600 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_grp_id( mbedtls_ecp_group_id grp_id )
601 {
602 const mbedtls_ecp_curve_info *curve_info;
603
604 for( curve_info = mbedtls_ecp_curve_list();
605 curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
606 curve_info++ )
607 {
608 if( curve_info->grp_id == grp_id )
609 return( curve_info );
610 }
611
612 return( NULL );
613 }
614
615 /*
616 * Get the curve info from the TLS identifier
617 */
mbedtls_ecp_curve_info_from_tls_id(uint16_t tls_id)618 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_tls_id( uint16_t tls_id )
619 {
620 const mbedtls_ecp_curve_info *curve_info;
621
622 for( curve_info = mbedtls_ecp_curve_list();
623 curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
624 curve_info++ )
625 {
626 if( curve_info->tls_id == tls_id )
627 return( curve_info );
628 }
629
630 return( NULL );
631 }
632
633 /*
634 * Get the curve info from the name
635 */
mbedtls_ecp_curve_info_from_name(const char * name)636 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_name( const char *name )
637 {
638 const mbedtls_ecp_curve_info *curve_info;
639
640 if( name == NULL )
641 return( NULL );
642
643 for( curve_info = mbedtls_ecp_curve_list();
644 curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
645 curve_info++ )
646 {
647 if( strcmp( curve_info->name, name ) == 0 )
648 return( curve_info );
649 }
650
651 return( NULL );
652 }
653
654 /*
655 * Get the type of a curve
656 */
mbedtls_ecp_get_type(const mbedtls_ecp_group * grp)657 mbedtls_ecp_curve_type mbedtls_ecp_get_type( const mbedtls_ecp_group *grp )
658 {
659 if( grp->G.X.p == NULL )
660 return( MBEDTLS_ECP_TYPE_NONE );
661
662 if( grp->G.Y.p == NULL )
663 return( MBEDTLS_ECP_TYPE_MONTGOMERY );
664 else
665 return( MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS );
666 }
667
668 /*
669 * Initialize (the components of) a point
670 */
mbedtls_ecp_point_init(mbedtls_ecp_point * pt)671 void mbedtls_ecp_point_init( mbedtls_ecp_point *pt )
672 {
673 ECP_VALIDATE( pt != NULL );
674
675 mbedtls_mpi_init( &pt->X );
676 mbedtls_mpi_init( &pt->Y );
677 mbedtls_mpi_init( &pt->Z );
678 }
679
680 /*
681 * Initialize (the components of) a group
682 */
mbedtls_ecp_group_init(mbedtls_ecp_group * grp)683 void mbedtls_ecp_group_init( mbedtls_ecp_group *grp )
684 {
685 ECP_VALIDATE( grp != NULL );
686
687 grp->id = MBEDTLS_ECP_DP_NONE;
688 mbedtls_mpi_init( &grp->P );
689 mbedtls_mpi_init( &grp->A );
690 mbedtls_mpi_init( &grp->B );
691 mbedtls_ecp_point_init( &grp->G );
692 mbedtls_mpi_init( &grp->N );
693 grp->pbits = 0;
694 grp->nbits = 0;
695 grp->h = 0;
696 grp->modp = NULL;
697 grp->t_pre = NULL;
698 grp->t_post = NULL;
699 grp->t_data = NULL;
700 grp->T = NULL;
701 grp->T_size = 0;
702 }
703
704 /*
705 * Initialize (the components of) a key pair
706 */
mbedtls_ecp_keypair_init(mbedtls_ecp_keypair * key)707 void mbedtls_ecp_keypair_init( mbedtls_ecp_keypair *key )
708 {
709 ECP_VALIDATE( key != NULL );
710
711 mbedtls_ecp_group_init( &key->grp );
712 mbedtls_mpi_init( &key->d );
713 mbedtls_ecp_point_init( &key->Q );
714 }
715
716 /*
717 * Unallocate (the components of) a point
718 */
mbedtls_ecp_point_free(mbedtls_ecp_point * pt)719 void mbedtls_ecp_point_free( mbedtls_ecp_point *pt )
720 {
721 if( pt == NULL )
722 return;
723
724 mbedtls_mpi_free( &( pt->X ) );
725 mbedtls_mpi_free( &( pt->Y ) );
726 mbedtls_mpi_free( &( pt->Z ) );
727 }
728
729 /*
730 * Unallocate (the components of) a group
731 */
mbedtls_ecp_group_free(mbedtls_ecp_group * grp)732 void mbedtls_ecp_group_free( mbedtls_ecp_group *grp )
733 {
734 size_t i;
735
736 if( grp == NULL )
737 return;
738
739 if( grp->h != 1 )
740 {
741 mbedtls_mpi_free( &grp->P );
742 mbedtls_mpi_free( &grp->A );
743 mbedtls_mpi_free( &grp->B );
744 mbedtls_ecp_point_free( &grp->G );
745 mbedtls_mpi_free( &grp->N );
746 }
747
748 if( grp->T != NULL )
749 {
750 for( i = 0; i < grp->T_size; i++ )
751 mbedtls_ecp_point_free( &grp->T[i] );
752 mbedtls_free( grp->T );
753 }
754
755 mbedtls_platform_zeroize( grp, sizeof( mbedtls_ecp_group ) );
756 }
757
758 /*
759 * Unallocate (the components of) a key pair
760 */
mbedtls_ecp_keypair_free(mbedtls_ecp_keypair * key)761 void mbedtls_ecp_keypair_free( mbedtls_ecp_keypair *key )
762 {
763 if( key == NULL )
764 return;
765
766 mbedtls_ecp_group_free( &key->grp );
767 mbedtls_mpi_free( &key->d );
768 mbedtls_ecp_point_free( &key->Q );
769 }
770
771 /*
772 * Copy the contents of a point
773 */
mbedtls_ecp_copy(mbedtls_ecp_point * P,const mbedtls_ecp_point * Q)774 int mbedtls_ecp_copy( mbedtls_ecp_point *P, const mbedtls_ecp_point *Q )
775 {
776 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
777 ECP_VALIDATE_RET( P != NULL );
778 ECP_VALIDATE_RET( Q != NULL );
779
780 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->X, &Q->X ) );
781 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->Y, &Q->Y ) );
782 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->Z, &Q->Z ) );
783
784 cleanup:
785 return( ret );
786 }
787
788 /*
789 * Copy the contents of a group object
790 */
mbedtls_ecp_group_copy(mbedtls_ecp_group * dst,const mbedtls_ecp_group * src)791 int mbedtls_ecp_group_copy( mbedtls_ecp_group *dst, const mbedtls_ecp_group *src )
792 {
793 ECP_VALIDATE_RET( dst != NULL );
794 ECP_VALIDATE_RET( src != NULL );
795
796 return( mbedtls_ecp_group_load( dst, src->id ) );
797 }
798
799 /*
800 * Set point to zero
801 */
mbedtls_ecp_set_zero(mbedtls_ecp_point * pt)802 int mbedtls_ecp_set_zero( mbedtls_ecp_point *pt )
803 {
804 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
805 ECP_VALIDATE_RET( pt != NULL );
806
807 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->X , 1 ) );
808 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Y , 1 ) );
809 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z , 0 ) );
810
811 cleanup:
812 return( ret );
813 }
814
815 /*
816 * Tell if a point is zero
817 */
mbedtls_ecp_is_zero(mbedtls_ecp_point * pt)818 int mbedtls_ecp_is_zero( mbedtls_ecp_point *pt )
819 {
820 ECP_VALIDATE_RET( pt != NULL );
821
822 return( mbedtls_mpi_cmp_int( &pt->Z, 0 ) == 0 );
823 }
824
825 /*
826 * Compare two points lazily
827 */
mbedtls_ecp_point_cmp(const mbedtls_ecp_point * P,const mbedtls_ecp_point * Q)828 int mbedtls_ecp_point_cmp( const mbedtls_ecp_point *P,
829 const mbedtls_ecp_point *Q )
830 {
831 ECP_VALIDATE_RET( P != NULL );
832 ECP_VALIDATE_RET( Q != NULL );
833
834 if( mbedtls_mpi_cmp_mpi( &P->X, &Q->X ) == 0 &&
835 mbedtls_mpi_cmp_mpi( &P->Y, &Q->Y ) == 0 &&
836 mbedtls_mpi_cmp_mpi( &P->Z, &Q->Z ) == 0 )
837 {
838 return( 0 );
839 }
840
841 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
842 }
843
844 /*
845 * Import a non-zero point from ASCII strings
846 */
mbedtls_ecp_point_read_string(mbedtls_ecp_point * P,int radix,const char * x,const char * y)847 int mbedtls_ecp_point_read_string( mbedtls_ecp_point *P, int radix,
848 const char *x, const char *y )
849 {
850 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
851 ECP_VALIDATE_RET( P != NULL );
852 ECP_VALIDATE_RET( x != NULL );
853 ECP_VALIDATE_RET( y != NULL );
854
855 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &P->X, radix, x ) );
856 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &P->Y, radix, y ) );
857 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &P->Z, 1 ) );
858
859 cleanup:
860 return( ret );
861 }
862
863 /*
864 * Export a point into unsigned binary data (SEC1 2.3.3 and RFC7748)
865 */
mbedtls_ecp_point_write_binary(const mbedtls_ecp_group * grp,const mbedtls_ecp_point * P,int format,size_t * olen,unsigned char * buf,size_t buflen)866 int mbedtls_ecp_point_write_binary( const mbedtls_ecp_group *grp,
867 const mbedtls_ecp_point *P,
868 int format, size_t *olen,
869 unsigned char *buf, size_t buflen )
870 {
871 int ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
872 size_t plen;
873 ECP_VALIDATE_RET( grp != NULL );
874 ECP_VALIDATE_RET( P != NULL );
875 ECP_VALIDATE_RET( olen != NULL );
876 ECP_VALIDATE_RET( buf != NULL );
877 ECP_VALIDATE_RET( format == MBEDTLS_ECP_PF_UNCOMPRESSED ||
878 format == MBEDTLS_ECP_PF_COMPRESSED );
879
880 plen = mbedtls_mpi_size( &grp->P );
881
882 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
883 (void) format; /* Montgomery curves always use the same point format */
884 if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY )
885 {
886 *olen = plen;
887 if( buflen < *olen )
888 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
889
890 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary_le( &P->X, buf, plen ) );
891 }
892 #endif
893 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
894 if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
895 {
896 /*
897 * Common case: P == 0
898 */
899 if( mbedtls_mpi_cmp_int( &P->Z, 0 ) == 0 )
900 {
901 if( buflen < 1 )
902 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
903
904 buf[0] = 0x00;
905 *olen = 1;
906
907 return( 0 );
908 }
909
910 if( format == MBEDTLS_ECP_PF_UNCOMPRESSED )
911 {
912 *olen = 2 * plen + 1;
913
914 if( buflen < *olen )
915 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
916
917 buf[0] = 0x04;
918 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->X, buf + 1, plen ) );
919 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->Y, buf + 1 + plen, plen ) );
920 }
921 else if( format == MBEDTLS_ECP_PF_COMPRESSED )
922 {
923 *olen = plen + 1;
924
925 if( buflen < *olen )
926 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
927
928 buf[0] = 0x02 + mbedtls_mpi_get_bit( &P->Y, 0 );
929 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->X, buf + 1, plen ) );
930 }
931 }
932 #endif
933
934 cleanup:
935 return( ret );
936 }
937
938 /*
939 * Import a point from unsigned binary data (SEC1 2.3.4 and RFC7748)
940 */
mbedtls_ecp_point_read_binary(const mbedtls_ecp_group * grp,mbedtls_ecp_point * pt,const unsigned char * buf,size_t ilen)941 int mbedtls_ecp_point_read_binary( const mbedtls_ecp_group *grp,
942 mbedtls_ecp_point *pt,
943 const unsigned char *buf, size_t ilen )
944 {
945 int ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
946 size_t plen;
947 ECP_VALIDATE_RET( grp != NULL );
948 ECP_VALIDATE_RET( pt != NULL );
949 ECP_VALIDATE_RET( buf != NULL );
950
951 if( ilen < 1 )
952 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
953
954 plen = mbedtls_mpi_size( &grp->P );
955
956 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
957 if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY )
958 {
959 if( plen != ilen )
960 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
961
962 MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary_le( &pt->X, buf, plen ) );
963 mbedtls_mpi_free( &pt->Y );
964
965 if( grp->id == MBEDTLS_ECP_DP_CURVE25519 )
966 /* Set most significant bit to 0 as prescribed in RFC7748 §5 */
967 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &pt->X, plen * 8 - 1, 0 ) );
968
969 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) );
970 }
971 #endif
972 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
973 if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
974 {
975 if( buf[0] == 0x00 )
976 {
977 if( ilen == 1 )
978 return( mbedtls_ecp_set_zero( pt ) );
979 else
980 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
981 }
982
983 if( buf[0] != 0x04 )
984 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
985
986 if( ilen != 2 * plen + 1 )
987 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
988
989 MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &pt->X, buf + 1, plen ) );
990 MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &pt->Y,
991 buf + 1 + plen, plen ) );
992 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) );
993 }
994 #endif
995
996 cleanup:
997 return( ret );
998 }
999
1000 /*
1001 * Import a point from a TLS ECPoint record (RFC 4492)
1002 * struct {
1003 * opaque point <1..2^8-1>;
1004 * } ECPoint;
1005 */
mbedtls_ecp_tls_read_point(const mbedtls_ecp_group * grp,mbedtls_ecp_point * pt,const unsigned char ** buf,size_t buf_len)1006 int mbedtls_ecp_tls_read_point( const mbedtls_ecp_group *grp,
1007 mbedtls_ecp_point *pt,
1008 const unsigned char **buf, size_t buf_len )
1009 {
1010 unsigned char data_len;
1011 const unsigned char *buf_start;
1012 ECP_VALIDATE_RET( grp != NULL );
1013 ECP_VALIDATE_RET( pt != NULL );
1014 ECP_VALIDATE_RET( buf != NULL );
1015 ECP_VALIDATE_RET( *buf != NULL );
1016
1017 /*
1018 * We must have at least two bytes (1 for length, at least one for data)
1019 */
1020 if( buf_len < 2 )
1021 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1022
1023 data_len = *(*buf)++;
1024 if( data_len < 1 || data_len > buf_len - 1 )
1025 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1026
1027 /*
1028 * Save buffer start for read_binary and update buf
1029 */
1030 buf_start = *buf;
1031 *buf += data_len;
1032
1033 return( mbedtls_ecp_point_read_binary( grp, pt, buf_start, data_len ) );
1034 }
1035
1036 /*
1037 * Export a point as a TLS ECPoint record (RFC 4492)
1038 * struct {
1039 * opaque point <1..2^8-1>;
1040 * } ECPoint;
1041 */
mbedtls_ecp_tls_write_point(const mbedtls_ecp_group * grp,const mbedtls_ecp_point * pt,int format,size_t * olen,unsigned char * buf,size_t blen)1042 int mbedtls_ecp_tls_write_point( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt,
1043 int format, size_t *olen,
1044 unsigned char *buf, size_t blen )
1045 {
1046 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1047 ECP_VALIDATE_RET( grp != NULL );
1048 ECP_VALIDATE_RET( pt != NULL );
1049 ECP_VALIDATE_RET( olen != NULL );
1050 ECP_VALIDATE_RET( buf != NULL );
1051 ECP_VALIDATE_RET( format == MBEDTLS_ECP_PF_UNCOMPRESSED ||
1052 format == MBEDTLS_ECP_PF_COMPRESSED );
1053
1054 /*
1055 * buffer length must be at least one, for our length byte
1056 */
1057 if( blen < 1 )
1058 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1059
1060 if( ( ret = mbedtls_ecp_point_write_binary( grp, pt, format,
1061 olen, buf + 1, blen - 1) ) != 0 )
1062 return( ret );
1063
1064 /*
1065 * write length to the first byte and update total length
1066 */
1067 buf[0] = (unsigned char) *olen;
1068 ++*olen;
1069
1070 return( 0 );
1071 }
1072
1073 /*
1074 * Set a group from an ECParameters record (RFC 4492)
1075 */
mbedtls_ecp_tls_read_group(mbedtls_ecp_group * grp,const unsigned char ** buf,size_t len)1076 int mbedtls_ecp_tls_read_group( mbedtls_ecp_group *grp,
1077 const unsigned char **buf, size_t len )
1078 {
1079 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1080 mbedtls_ecp_group_id grp_id;
1081 ECP_VALIDATE_RET( grp != NULL );
1082 ECP_VALIDATE_RET( buf != NULL );
1083 ECP_VALIDATE_RET( *buf != NULL );
1084
1085 if( ( ret = mbedtls_ecp_tls_read_group_id( &grp_id, buf, len ) ) != 0 )
1086 return( ret );
1087
1088 return( mbedtls_ecp_group_load( grp, grp_id ) );
1089 }
1090
1091 /*
1092 * Read a group id from an ECParameters record (RFC 4492) and convert it to
1093 * mbedtls_ecp_group_id.
1094 */
mbedtls_ecp_tls_read_group_id(mbedtls_ecp_group_id * grp,const unsigned char ** buf,size_t len)1095 int mbedtls_ecp_tls_read_group_id( mbedtls_ecp_group_id *grp,
1096 const unsigned char **buf, size_t len )
1097 {
1098 uint16_t tls_id;
1099 const mbedtls_ecp_curve_info *curve_info;
1100 ECP_VALIDATE_RET( grp != NULL );
1101 ECP_VALIDATE_RET( buf != NULL );
1102 ECP_VALIDATE_RET( *buf != NULL );
1103
1104 /*
1105 * We expect at least three bytes (see below)
1106 */
1107 if( len < 3 )
1108 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1109
1110 /*
1111 * First byte is curve_type; only named_curve is handled
1112 */
1113 if( *(*buf)++ != MBEDTLS_ECP_TLS_NAMED_CURVE )
1114 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1115
1116 /*
1117 * Next two bytes are the namedcurve value
1118 */
1119 tls_id = *(*buf)++;
1120 tls_id <<= 8;
1121 tls_id |= *(*buf)++;
1122
1123 if( ( curve_info = mbedtls_ecp_curve_info_from_tls_id( tls_id ) ) == NULL )
1124 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
1125
1126 *grp = curve_info->grp_id;
1127
1128 return( 0 );
1129 }
1130
1131 /*
1132 * Write the ECParameters record corresponding to a group (RFC 4492)
1133 */
mbedtls_ecp_tls_write_group(const mbedtls_ecp_group * grp,size_t * olen,unsigned char * buf,size_t blen)1134 int mbedtls_ecp_tls_write_group( const mbedtls_ecp_group *grp, size_t *olen,
1135 unsigned char *buf, size_t blen )
1136 {
1137 const mbedtls_ecp_curve_info *curve_info;
1138 ECP_VALIDATE_RET( grp != NULL );
1139 ECP_VALIDATE_RET( buf != NULL );
1140 ECP_VALIDATE_RET( olen != NULL );
1141
1142 if( ( curve_info = mbedtls_ecp_curve_info_from_grp_id( grp->id ) ) == NULL )
1143 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1144
1145 /*
1146 * We are going to write 3 bytes (see below)
1147 */
1148 *olen = 3;
1149 if( blen < *olen )
1150 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
1151
1152 /*
1153 * First byte is curve_type, always named_curve
1154 */
1155 *buf++ = MBEDTLS_ECP_TLS_NAMED_CURVE;
1156
1157 /*
1158 * Next two bytes are the namedcurve value
1159 */
1160 buf[0] = curve_info->tls_id >> 8;
1161 buf[1] = curve_info->tls_id & 0xFF;
1162
1163 return( 0 );
1164 }
1165
1166 /*
1167 * Wrapper around fast quasi-modp functions, with fall-back to mbedtls_mpi_mod_mpi.
1168 * See the documentation of struct mbedtls_ecp_group.
1169 *
1170 * This function is in the critial loop for mbedtls_ecp_mul, so pay attention to perf.
1171 */
ecp_modp(mbedtls_mpi * N,const mbedtls_ecp_group * grp)1172 static int ecp_modp( mbedtls_mpi *N, const mbedtls_ecp_group *grp )
1173 {
1174 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1175
1176 if( grp->modp == NULL )
1177 return( mbedtls_mpi_mod_mpi( N, N, &grp->P ) );
1178
1179 /* N->s < 0 is a much faster test, which fails only if N is 0 */
1180 if( ( N->s < 0 && mbedtls_mpi_cmp_int( N, 0 ) != 0 ) ||
1181 mbedtls_mpi_bitlen( N ) > 2 * grp->pbits )
1182 {
1183 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1184 }
1185
1186 MBEDTLS_MPI_CHK( grp->modp( N ) );
1187
1188 /* N->s < 0 is a much faster test, which fails only if N is 0 */
1189 while( N->s < 0 && mbedtls_mpi_cmp_int( N, 0 ) != 0 )
1190 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &grp->P ) );
1191
1192 while( mbedtls_mpi_cmp_mpi( N, &grp->P ) >= 0 )
1193 /* we known P, N and the result are positive */
1194 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( N, N, &grp->P ) );
1195
1196 cleanup:
1197 return( ret );
1198 }
1199
1200 /*
1201 * Fast mod-p functions expect their argument to be in the 0..p^2 range.
1202 *
1203 * In order to guarantee that, we need to ensure that operands of
1204 * mbedtls_mpi_mul_mpi are in the 0..p range. So, after each operation we will
1205 * bring the result back to this range.
1206 *
1207 * The following macros are shortcuts for doing that.
1208 */
1209
1210 /*
1211 * Reduce a mbedtls_mpi mod p in-place, general case, to use after mbedtls_mpi_mul_mpi
1212 */
1213 #if defined(MBEDTLS_SELF_TEST)
1214 #define INC_MUL_COUNT mul_count++;
1215 #else
1216 #define INC_MUL_COUNT
1217 #endif
1218
1219 #define MOD_MUL( N ) \
1220 do \
1221 { \
1222 MBEDTLS_MPI_CHK( ecp_modp( &(N), grp ) ); \
1223 INC_MUL_COUNT \
1224 } while( 0 )
1225
mbedtls_mpi_mul_mod(const mbedtls_ecp_group * grp,mbedtls_mpi * X,const mbedtls_mpi * A,const mbedtls_mpi * B)1226 static inline int mbedtls_mpi_mul_mod( const mbedtls_ecp_group *grp,
1227 mbedtls_mpi *X,
1228 const mbedtls_mpi *A,
1229 const mbedtls_mpi *B )
1230 {
1231 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1232 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( X, A, B ) );
1233 MOD_MUL( *X );
1234 cleanup:
1235 return( ret );
1236 }
1237
1238 /*
1239 * Reduce a mbedtls_mpi mod p in-place, to use after mbedtls_mpi_sub_mpi
1240 * N->s < 0 is a very fast test, which fails only if N is 0
1241 */
1242 #define MOD_SUB( N ) \
1243 while( (N).s < 0 && mbedtls_mpi_cmp_int( &(N), 0 ) != 0 ) \
1244 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &(N), &(N), &grp->P ) )
1245
1246 #if ( defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) && \
1247 !( defined(MBEDTLS_ECP_NO_FALLBACK) && \
1248 defined(MBEDTLS_ECP_DOUBLE_JAC_ALT) && \
1249 defined(MBEDTLS_ECP_ADD_MIXED_ALT) ) ) || \
1250 ( defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) && \
1251 !( defined(MBEDTLS_ECP_NO_FALLBACK) && \
1252 defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT) ) )
mbedtls_mpi_sub_mod(const mbedtls_ecp_group * grp,mbedtls_mpi * X,const mbedtls_mpi * A,const mbedtls_mpi * B)1253 static inline int mbedtls_mpi_sub_mod( const mbedtls_ecp_group *grp,
1254 mbedtls_mpi *X,
1255 const mbedtls_mpi *A,
1256 const mbedtls_mpi *B )
1257 {
1258 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1259 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( X, A, B ) );
1260 MOD_SUB( *X );
1261 cleanup:
1262 return( ret );
1263 }
1264 #endif /* All functions referencing mbedtls_mpi_sub_mod() are alt-implemented without fallback */
1265
1266 /*
1267 * Reduce a mbedtls_mpi mod p in-place, to use after mbedtls_mpi_add_mpi and mbedtls_mpi_mul_int.
1268 * We known P, N and the result are positive, so sub_abs is correct, and
1269 * a bit faster.
1270 */
1271 #define MOD_ADD( N ) \
1272 while( mbedtls_mpi_cmp_mpi( &(N), &grp->P ) >= 0 ) \
1273 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( &(N), &(N), &grp->P ) )
1274
mbedtls_mpi_add_mod(const mbedtls_ecp_group * grp,mbedtls_mpi * X,const mbedtls_mpi * A,const mbedtls_mpi * B)1275 static inline int mbedtls_mpi_add_mod( const mbedtls_ecp_group *grp,
1276 mbedtls_mpi *X,
1277 const mbedtls_mpi *A,
1278 const mbedtls_mpi *B )
1279 {
1280 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1281 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( X, A, B ) );
1282 MOD_ADD( *X );
1283 cleanup:
1284 return( ret );
1285 }
1286
1287 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) && \
1288 !( defined(MBEDTLS_ECP_NO_FALLBACK) && \
1289 defined(MBEDTLS_ECP_DOUBLE_JAC_ALT) && \
1290 defined(MBEDTLS_ECP_ADD_MIXED_ALT) )
mbedtls_mpi_shift_l_mod(const mbedtls_ecp_group * grp,mbedtls_mpi * X,size_t count)1291 static inline int mbedtls_mpi_shift_l_mod( const mbedtls_ecp_group *grp,
1292 mbedtls_mpi *X,
1293 size_t count )
1294 {
1295 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1296 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( X, count ) );
1297 MOD_ADD( *X );
1298 cleanup:
1299 return( ret );
1300 }
1301 #endif /* All functions referencing mbedtls_mpi_shift_l_mod() are alt-implemented without fallback */
1302
1303 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
1304 /*
1305 * For curves in short Weierstrass form, we do all the internal operations in
1306 * Jacobian coordinates.
1307 *
1308 * For multiplication, we'll use a comb method with coutermeasueres against
1309 * SPA, hence timing attacks.
1310 */
1311
1312 /*
1313 * Normalize jacobian coordinates so that Z == 0 || Z == 1 (GECC 3.2.1)
1314 * Cost: 1N := 1I + 3M + 1S
1315 */
ecp_normalize_jac(const mbedtls_ecp_group * grp,mbedtls_ecp_point * pt)1316 static int ecp_normalize_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt )
1317 {
1318 if( mbedtls_mpi_cmp_int( &pt->Z, 0 ) == 0 )
1319 return( 0 );
1320
1321 #if defined(MBEDTLS_ECP_NORMALIZE_JAC_ALT)
1322 if( mbedtls_internal_ecp_grp_capable( grp ) )
1323 return( mbedtls_internal_ecp_normalize_jac( grp, pt ) );
1324 #endif /* MBEDTLS_ECP_NORMALIZE_JAC_ALT */
1325
1326 #if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_NORMALIZE_JAC_ALT)
1327 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
1328 #else
1329 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1330 mbedtls_mpi Zi, ZZi;
1331 mbedtls_mpi_init( &Zi ); mbedtls_mpi_init( &ZZi );
1332
1333 /*
1334 * X = X / Z^2 mod p
1335 */
1336 MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &Zi, &pt->Z, &grp->P ) );
1337 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &ZZi, &Zi, &Zi ) );
1338 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &pt->X, &pt->X, &ZZi ) );
1339
1340 /*
1341 * Y = Y / Z^3 mod p
1342 */
1343 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &pt->Y, &pt->Y, &ZZi ) );
1344 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &pt->Y, &pt->Y, &Zi ) );
1345
1346 /*
1347 * Z = 1
1348 */
1349 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) );
1350
1351 cleanup:
1352
1353 mbedtls_mpi_free( &Zi ); mbedtls_mpi_free( &ZZi );
1354
1355 return( ret );
1356 #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_NORMALIZE_JAC_ALT) */
1357 }
1358
1359 /*
1360 * Normalize jacobian coordinates of an array of (pointers to) points,
1361 * using Montgomery's trick to perform only one inversion mod P.
1362 * (See for example Cohen's "A Course in Computational Algebraic Number
1363 * Theory", Algorithm 10.3.4.)
1364 *
1365 * Warning: fails (returning an error) if one of the points is zero!
1366 * This should never happen, see choice of w in ecp_mul_comb().
1367 *
1368 * Cost: 1N(t) := 1I + (6t - 3)M + 1S
1369 */
ecp_normalize_jac_many(const mbedtls_ecp_group * grp,mbedtls_ecp_point * T[],size_t T_size)1370 static int ecp_normalize_jac_many( const mbedtls_ecp_group *grp,
1371 mbedtls_ecp_point *T[], size_t T_size )
1372 {
1373 if( T_size < 2 )
1374 return( ecp_normalize_jac( grp, *T ) );
1375
1376 #if defined(MBEDTLS_ECP_NORMALIZE_JAC_MANY_ALT)
1377 if( mbedtls_internal_ecp_grp_capable( grp ) )
1378 return( mbedtls_internal_ecp_normalize_jac_many( grp, T, T_size ) );
1379 #endif
1380
1381 #if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_NORMALIZE_JAC_MANY_ALT)
1382 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
1383 #else
1384 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1385 size_t i;
1386 mbedtls_mpi *c, u, Zi, ZZi;
1387
1388 if( ( c = mbedtls_calloc( T_size, sizeof( mbedtls_mpi ) ) ) == NULL )
1389 return( MBEDTLS_ERR_ECP_ALLOC_FAILED );
1390
1391 for( i = 0; i < T_size; i++ )
1392 mbedtls_mpi_init( &c[i] );
1393
1394 mbedtls_mpi_init( &u ); mbedtls_mpi_init( &Zi ); mbedtls_mpi_init( &ZZi );
1395
1396 /*
1397 * c[i] = Z_0 * ... * Z_i
1398 */
1399 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &c[0], &T[0]->Z ) );
1400 for( i = 1; i < T_size; i++ )
1401 {
1402 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &c[i], &c[i-1], &T[i]->Z ) );
1403 }
1404
1405 /*
1406 * u = 1 / (Z_0 * ... * Z_n) mod P
1407 */
1408 MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &u, &c[T_size-1], &grp->P ) );
1409
1410 for( i = T_size - 1; ; i-- )
1411 {
1412 /*
1413 * Zi = 1 / Z_i mod p
1414 * u = 1 / (Z_0 * ... * Z_i) mod P
1415 */
1416 if( i == 0 ) {
1417 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &Zi, &u ) );
1418 }
1419 else
1420 {
1421 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &Zi, &u, &c[i-1] ) );
1422 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &u, &u, &T[i]->Z ) );
1423 }
1424
1425 /*
1426 * proceed as in normalize()
1427 */
1428 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &ZZi, &Zi, &Zi ) );
1429 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T[i]->X, &T[i]->X, &ZZi ) );
1430 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T[i]->Y, &T[i]->Y, &ZZi ) );
1431 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T[i]->Y, &T[i]->Y, &Zi ) );
1432
1433 /*
1434 * Post-precessing: reclaim some memory by shrinking coordinates
1435 * - not storing Z (always 1)
1436 * - shrinking other coordinates, but still keeping the same number of
1437 * limbs as P, as otherwise it will too likely be regrown too fast.
1438 */
1439 MBEDTLS_MPI_CHK( mbedtls_mpi_shrink( &T[i]->X, grp->P.n ) );
1440 MBEDTLS_MPI_CHK( mbedtls_mpi_shrink( &T[i]->Y, grp->P.n ) );
1441 mbedtls_mpi_free( &T[i]->Z );
1442
1443 if( i == 0 )
1444 break;
1445 }
1446
1447 cleanup:
1448
1449 mbedtls_mpi_free( &u ); mbedtls_mpi_free( &Zi ); mbedtls_mpi_free( &ZZi );
1450 for( i = 0; i < T_size; i++ )
1451 mbedtls_mpi_free( &c[i] );
1452 mbedtls_free( c );
1453
1454 return( ret );
1455 #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_NORMALIZE_JAC_MANY_ALT) */
1456 }
1457
1458 /*
1459 * Conditional point inversion: Q -> -Q = (Q.X, -Q.Y, Q.Z) without leak.
1460 * "inv" must be 0 (don't invert) or 1 (invert) or the result will be invalid
1461 */
ecp_safe_invert_jac(const mbedtls_ecp_group * grp,mbedtls_ecp_point * Q,unsigned char inv)1462 static int ecp_safe_invert_jac( const mbedtls_ecp_group *grp,
1463 mbedtls_ecp_point *Q,
1464 unsigned char inv )
1465 {
1466 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1467 unsigned char nonzero;
1468 mbedtls_mpi mQY;
1469
1470 mbedtls_mpi_init( &mQY );
1471
1472 /* Use the fact that -Q.Y mod P = P - Q.Y unless Q.Y == 0 */
1473 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &mQY, &grp->P, &Q->Y ) );
1474 nonzero = mbedtls_mpi_cmp_int( &Q->Y, 0 ) != 0;
1475 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &Q->Y, &mQY, inv & nonzero ) );
1476
1477 cleanup:
1478 mbedtls_mpi_free( &mQY );
1479
1480 return( ret );
1481 }
1482
1483 /*
1484 * Point doubling R = 2 P, Jacobian coordinates
1485 *
1486 * Based on http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#doubling-dbl-1998-cmo-2 .
1487 *
1488 * We follow the variable naming fairly closely. The formula variations that trade a MUL for a SQR
1489 * (plus a few ADDs) aren't useful as our bignum implementation doesn't distinguish squaring.
1490 *
1491 * Standard optimizations are applied when curve parameter A is one of { 0, -3 }.
1492 *
1493 * Cost: 1D := 3M + 4S (A == 0)
1494 * 4M + 4S (A == -3)
1495 * 3M + 6S + 1a otherwise
1496 */
ecp_double_jac(const mbedtls_ecp_group * grp,mbedtls_ecp_point * R,const mbedtls_ecp_point * P)1497 static int ecp_double_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
1498 const mbedtls_ecp_point *P )
1499 {
1500 #if defined(MBEDTLS_SELF_TEST)
1501 dbl_count++;
1502 #endif
1503
1504 #if defined(MBEDTLS_ECP_DOUBLE_JAC_ALT)
1505 if( mbedtls_internal_ecp_grp_capable( grp ) )
1506 return( mbedtls_internal_ecp_double_jac( grp, R, P ) );
1507 #endif /* MBEDTLS_ECP_DOUBLE_JAC_ALT */
1508
1509 #if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_DOUBLE_JAC_ALT)
1510 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
1511 #else
1512 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1513 mbedtls_mpi M, S, T, U;
1514
1515 mbedtls_mpi_init( &M ); mbedtls_mpi_init( &S ); mbedtls_mpi_init( &T ); mbedtls_mpi_init( &U );
1516
1517 /* Special case for A = -3 */
1518 if( grp->A.p == NULL )
1519 {
1520 /* M = 3(X + Z^2)(X - Z^2) */
1521 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S, &P->Z, &P->Z ) );
1522 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &T, &P->X, &S ) );
1523 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &U, &P->X, &S ) );
1524 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S, &T, &U ) );
1525 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &S, 3 ) ); MOD_ADD( M );
1526 }
1527 else
1528 {
1529 /* M = 3.X^2 */
1530 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S, &P->X, &P->X ) );
1531 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &S, 3 ) ); MOD_ADD( M );
1532
1533 /* Optimize away for "koblitz" curves with A = 0 */
1534 if( mbedtls_mpi_cmp_int( &grp->A, 0 ) != 0 )
1535 {
1536 /* M += A.Z^4 */
1537 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S, &P->Z, &P->Z ) );
1538 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T, &S, &S ) );
1539 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S, &T, &grp->A ) );
1540 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &M, &M, &S ) );
1541 }
1542 }
1543
1544 /* S = 4.X.Y^2 */
1545 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T, &P->Y, &P->Y ) );
1546 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l_mod( grp, &T, 1 ) );
1547 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S, &P->X, &T ) );
1548 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l_mod( grp, &S, 1 ) );
1549
1550 /* U = 8.Y^4 */
1551 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &U, &T, &T ) );
1552 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l_mod( grp, &U, 1 ) );
1553
1554 /* T = M^2 - 2.S */
1555 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T, &M, &M ) );
1556 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &T, &T, &S ) );
1557 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &T, &T, &S ) );
1558
1559 /* S = M(S - T) - U */
1560 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &S, &S, &T ) );
1561 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S, &S, &M ) );
1562 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &S, &S, &U ) );
1563
1564 /* U = 2.Y.Z */
1565 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &U, &P->Y, &P->Z ) );
1566 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l_mod( grp, &U, 1 ) );
1567
1568 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->X, &T ) );
1569 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Y, &S ) );
1570 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Z, &U ) );
1571
1572 cleanup:
1573 mbedtls_mpi_free( &M ); mbedtls_mpi_free( &S ); mbedtls_mpi_free( &T ); mbedtls_mpi_free( &U );
1574
1575 return( ret );
1576 #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_DOUBLE_JAC_ALT) */
1577 }
1578
1579 /*
1580 * Addition: R = P + Q, mixed affine-Jacobian coordinates (GECC 3.22)
1581 *
1582 * The coordinates of Q must be normalized (= affine),
1583 * but those of P don't need to. R is not normalized.
1584 *
1585 * Special cases: (1) P or Q is zero, (2) R is zero, (3) P == Q.
1586 * None of these cases can happen as intermediate step in ecp_mul_comb():
1587 * - at each step, P, Q and R are multiples of the base point, the factor
1588 * being less than its order, so none of them is zero;
1589 * - Q is an odd multiple of the base point, P an even multiple,
1590 * due to the choice of precomputed points in the modified comb method.
1591 * So branches for these cases do not leak secret information.
1592 *
1593 * We accept Q->Z being unset (saving memory in tables) as meaning 1.
1594 *
1595 * Cost: 1A := 8M + 3S
1596 */
ecp_add_mixed(const mbedtls_ecp_group * grp,mbedtls_ecp_point * R,const mbedtls_ecp_point * P,const mbedtls_ecp_point * Q)1597 static int ecp_add_mixed( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
1598 const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q )
1599 {
1600 #if defined(MBEDTLS_SELF_TEST)
1601 add_count++;
1602 #endif
1603
1604 #if defined(MBEDTLS_ECP_ADD_MIXED_ALT)
1605 if( mbedtls_internal_ecp_grp_capable( grp ) )
1606 return( mbedtls_internal_ecp_add_mixed( grp, R, P, Q ) );
1607 #endif /* MBEDTLS_ECP_ADD_MIXED_ALT */
1608
1609 #if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_ADD_MIXED_ALT)
1610 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
1611 #else
1612 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1613 mbedtls_mpi T1, T2, T3, T4, X, Y, Z;
1614
1615 /*
1616 * Trivial cases: P == 0 or Q == 0 (case 1)
1617 */
1618 if( mbedtls_mpi_cmp_int( &P->Z, 0 ) == 0 )
1619 return( mbedtls_ecp_copy( R, Q ) );
1620
1621 if( Q->Z.p != NULL && mbedtls_mpi_cmp_int( &Q->Z, 0 ) == 0 )
1622 return( mbedtls_ecp_copy( R, P ) );
1623
1624 /*
1625 * Make sure Q coordinates are normalized
1626 */
1627 if( Q->Z.p != NULL && mbedtls_mpi_cmp_int( &Q->Z, 1 ) != 0 )
1628 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1629
1630 mbedtls_mpi_init( &T1 ); mbedtls_mpi_init( &T2 ); mbedtls_mpi_init( &T3 ); mbedtls_mpi_init( &T4 );
1631 mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Y ); mbedtls_mpi_init( &Z );
1632
1633 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T1, &P->Z, &P->Z ) );
1634 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T2, &T1, &P->Z ) );
1635 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T1, &T1, &Q->X ) );
1636 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T2, &T2, &Q->Y ) );
1637 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &T1, &T1, &P->X ) );
1638 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &T2, &T2, &P->Y ) );
1639
1640 /* Special cases (2) and (3) */
1641 if( mbedtls_mpi_cmp_int( &T1, 0 ) == 0 )
1642 {
1643 if( mbedtls_mpi_cmp_int( &T2, 0 ) == 0 )
1644 {
1645 ret = ecp_double_jac( grp, R, P );
1646 goto cleanup;
1647 }
1648 else
1649 {
1650 ret = mbedtls_ecp_set_zero( R );
1651 goto cleanup;
1652 }
1653 }
1654
1655 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &Z, &P->Z, &T1 ) );
1656 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T3, &T1, &T1 ) );
1657 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T4, &T3, &T1 ) );
1658 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T3, &T3, &P->X ) );
1659 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &T1, &T3 ) );
1660 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l_mod( grp, &T1, 1 ) );
1661 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &X, &T2, &T2 ) );
1662 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &X, &X, &T1 ) );
1663 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &X, &X, &T4 ) );
1664 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &T3, &T3, &X ) );
1665 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T3, &T3, &T2 ) );
1666 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T4, &T4, &P->Y ) );
1667 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &Y, &T3, &T4 ) );
1668
1669 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->X, &X ) );
1670 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Y, &Y ) );
1671 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Z, &Z ) );
1672
1673 cleanup:
1674
1675 mbedtls_mpi_free( &T1 ); mbedtls_mpi_free( &T2 ); mbedtls_mpi_free( &T3 ); mbedtls_mpi_free( &T4 );
1676 mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Y ); mbedtls_mpi_free( &Z );
1677
1678 return( ret );
1679 #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_ADD_MIXED_ALT) */
1680 }
1681
1682 /*
1683 * Randomize jacobian coordinates:
1684 * (X, Y, Z) -> (l^2 X, l^3 Y, l Z) for random l
1685 * This is sort of the reverse operation of ecp_normalize_jac().
1686 *
1687 * This countermeasure was first suggested in [2].
1688 */
ecp_randomize_jac(const mbedtls_ecp_group * grp,mbedtls_ecp_point * pt,int (* f_rng)(void *,unsigned char *,size_t),void * p_rng)1689 static int ecp_randomize_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt,
1690 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
1691 {
1692 #if defined(MBEDTLS_ECP_RANDOMIZE_JAC_ALT)
1693 if( mbedtls_internal_ecp_grp_capable( grp ) )
1694 return( mbedtls_internal_ecp_randomize_jac( grp, pt, f_rng, p_rng ) );
1695 #endif /* MBEDTLS_ECP_RANDOMIZE_JAC_ALT */
1696
1697 #if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_RANDOMIZE_JAC_ALT)
1698 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
1699 #else
1700 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1701 mbedtls_mpi l, ll;
1702 int count = 0;
1703 size_t p_size = ( grp->pbits + 7 ) / 8;
1704
1705 mbedtls_mpi_init( &l ); mbedtls_mpi_init( &ll );
1706
1707 /* Generate l such that 1 < l < p */
1708 do
1709 {
1710 MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &l, p_size, f_rng, p_rng ) );
1711
1712 while( mbedtls_mpi_cmp_mpi( &l, &grp->P ) >= 0 )
1713 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &l, 1 ) );
1714
1715 if( count++ > 10 )
1716 {
1717 ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
1718 goto cleanup;
1719 }
1720 }
1721 while( mbedtls_mpi_cmp_int( &l, 1 ) <= 0 );
1722
1723 /* Z = l * Z */
1724 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &pt->Z, &pt->Z, &l ) );
1725
1726 /* X = l^2 * X */
1727 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &ll, &l, &l ) );
1728 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &pt->X, &pt->X, &ll ) );
1729
1730 /* Y = l^3 * Y */
1731 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &ll, &ll, &l ) );
1732 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &pt->Y, &pt->Y, &ll ) );
1733
1734 cleanup:
1735 mbedtls_mpi_free( &l ); mbedtls_mpi_free( &ll );
1736
1737 return( ret );
1738 #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_RANDOMIZE_JAC_ALT) */
1739 }
1740
1741 /*
1742 * Check and define parameters used by the comb method (see below for details)
1743 */
1744 #if MBEDTLS_ECP_WINDOW_SIZE < 2 || MBEDTLS_ECP_WINDOW_SIZE > 7
1745 #error "MBEDTLS_ECP_WINDOW_SIZE out of bounds"
1746 #endif
1747
1748 /* d = ceil( n / w ) */
1749 #define COMB_MAX_D ( MBEDTLS_ECP_MAX_BITS + 1 ) / 2
1750
1751 /* number of precomputed points */
1752 #define COMB_MAX_PRE ( 1 << ( MBEDTLS_ECP_WINDOW_SIZE - 1 ) )
1753
1754 /*
1755 * Compute the representation of m that will be used with our comb method.
1756 *
1757 * The basic comb method is described in GECC 3.44 for example. We use a
1758 * modified version that provides resistance to SPA by avoiding zero
1759 * digits in the representation as in [3]. We modify the method further by
1760 * requiring that all K_i be odd, which has the small cost that our
1761 * representation uses one more K_i, due to carries, but saves on the size of
1762 * the precomputed table.
1763 *
1764 * Summary of the comb method and its modifications:
1765 *
1766 * - The goal is to compute m*P for some w*d-bit integer m.
1767 *
1768 * - The basic comb method splits m into the w-bit integers
1769 * x[0] .. x[d-1] where x[i] consists of the bits in m whose
1770 * index has residue i modulo d, and computes m * P as
1771 * S[x[0]] + 2 * S[x[1]] + .. + 2^(d-1) S[x[d-1]], where
1772 * S[i_{w-1} .. i_0] := i_{w-1} 2^{(w-1)d} P + ... + i_1 2^d P + i_0 P.
1773 *
1774 * - If it happens that, say, x[i+1]=0 (=> S[x[i+1]]=0), one can replace the sum by
1775 * .. + 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]] ..,
1776 * thereby successively converting it into a form where all summands
1777 * are nonzero, at the cost of negative summands. This is the basic idea of [3].
1778 *
1779 * - More generally, even if x[i+1] != 0, we can first transform the sum as
1780 * .. - 2^i S[x[i]] + 2^{i+1} ( S[x[i]] + S[x[i+1]] ) + 2^{i+2} S[x[i+2]] ..,
1781 * and then replace S[x[i]] + S[x[i+1]] = S[x[i] ^ x[i+1]] + 2 S[x[i] & x[i+1]].
1782 * Performing and iterating this procedure for those x[i] that are even
1783 * (keeping track of carry), we can transform the original sum into one of the form
1784 * S[x'[0]] +- 2 S[x'[1]] +- .. +- 2^{d-1} S[x'[d-1]] + 2^d S[x'[d]]
1785 * with all x'[i] odd. It is therefore only necessary to know S at odd indices,
1786 * which is why we are only computing half of it in the first place in
1787 * ecp_precompute_comb and accessing it with index abs(i) / 2 in ecp_select_comb.
1788 *
1789 * - For the sake of compactness, only the seven low-order bits of x[i]
1790 * are used to represent its absolute value (K_i in the paper), and the msb
1791 * of x[i] encodes the sign (s_i in the paper): it is set if and only if
1792 * if s_i == -1;
1793 *
1794 * Calling conventions:
1795 * - x is an array of size d + 1
1796 * - w is the size, ie number of teeth, of the comb, and must be between
1797 * 2 and 7 (in practice, between 2 and MBEDTLS_ECP_WINDOW_SIZE)
1798 * - m is the MPI, expected to be odd and such that bitlength(m) <= w * d
1799 * (the result will be incorrect if these assumptions are not satisfied)
1800 */
ecp_comb_recode_core(unsigned char x[],size_t d,unsigned char w,const mbedtls_mpi * m)1801 static void ecp_comb_recode_core( unsigned char x[], size_t d,
1802 unsigned char w, const mbedtls_mpi *m )
1803 {
1804 size_t i, j;
1805 unsigned char c, cc, adjust;
1806
1807 memset( x, 0, d+1 );
1808
1809 /* First get the classical comb values (except for x_d = 0) */
1810 for( i = 0; i < d; i++ )
1811 for( j = 0; j < w; j++ )
1812 x[i] |= mbedtls_mpi_get_bit( m, i + d * j ) << j;
1813
1814 /* Now make sure x_1 .. x_d are odd */
1815 c = 0;
1816 for( i = 1; i <= d; i++ )
1817 {
1818 /* Add carry and update it */
1819 cc = x[i] & c;
1820 x[i] = x[i] ^ c;
1821 c = cc;
1822
1823 /* Adjust if needed, avoiding branches */
1824 adjust = 1 - ( x[i] & 0x01 );
1825 c |= x[i] & ( x[i-1] * adjust );
1826 x[i] = x[i] ^ ( x[i-1] * adjust );
1827 x[i-1] |= adjust << 7;
1828 }
1829 }
1830
1831 /*
1832 * Precompute points for the adapted comb method
1833 *
1834 * Assumption: T must be able to hold 2^{w - 1} elements.
1835 *
1836 * Operation: If i = i_{w-1} ... i_1 is the binary representation of i,
1837 * sets T[i] = i_{w-1} 2^{(w-1)d} P + ... + i_1 2^d P + P.
1838 *
1839 * Cost: d(w-1) D + (2^{w-1} - 1) A + 1 N(w-1) + 1 N(2^{w-1} - 1)
1840 *
1841 * Note: Even comb values (those where P would be omitted from the
1842 * sum defining T[i] above) are not needed in our adaption
1843 * the comb method. See ecp_comb_recode_core().
1844 *
1845 * This function currently works in four steps:
1846 * (1) [dbl] Computation of intermediate T[i] for 2-power values of i
1847 * (2) [norm_dbl] Normalization of coordinates of these T[i]
1848 * (3) [add] Computation of all T[i]
1849 * (4) [norm_add] Normalization of all T[i]
1850 *
1851 * Step 1 can be interrupted but not the others; together with the final
1852 * coordinate normalization they are the largest steps done at once, depending
1853 * on the window size. Here are operation counts for P-256:
1854 *
1855 * step (2) (3) (4)
1856 * w = 5 142 165 208
1857 * w = 4 136 77 160
1858 * w = 3 130 33 136
1859 * w = 2 124 11 124
1860 *
1861 * So if ECC operations are blocking for too long even with a low max_ops
1862 * value, it's useful to set MBEDTLS_ECP_WINDOW_SIZE to a lower value in order
1863 * to minimize maximum blocking time.
1864 */
ecp_precompute_comb(const mbedtls_ecp_group * grp,mbedtls_ecp_point T[],const mbedtls_ecp_point * P,unsigned char w,size_t d,mbedtls_ecp_restart_ctx * rs_ctx)1865 static int ecp_precompute_comb( const mbedtls_ecp_group *grp,
1866 mbedtls_ecp_point T[], const mbedtls_ecp_point *P,
1867 unsigned char w, size_t d,
1868 mbedtls_ecp_restart_ctx *rs_ctx )
1869 {
1870 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1871 unsigned char i;
1872 size_t j = 0;
1873 const unsigned char T_size = 1U << ( w - 1 );
1874 mbedtls_ecp_point *cur, *TT[COMB_MAX_PRE - 1];
1875
1876 #if defined(MBEDTLS_ECP_RESTARTABLE)
1877 if( rs_ctx != NULL && rs_ctx->rsm != NULL )
1878 {
1879 if( rs_ctx->rsm->state == ecp_rsm_pre_dbl )
1880 goto dbl;
1881 if( rs_ctx->rsm->state == ecp_rsm_pre_norm_dbl )
1882 goto norm_dbl;
1883 if( rs_ctx->rsm->state == ecp_rsm_pre_add )
1884 goto add;
1885 if( rs_ctx->rsm->state == ecp_rsm_pre_norm_add )
1886 goto norm_add;
1887 }
1888 #else
1889 (void) rs_ctx;
1890 #endif
1891
1892 #if defined(MBEDTLS_ECP_RESTARTABLE)
1893 if( rs_ctx != NULL && rs_ctx->rsm != NULL )
1894 {
1895 rs_ctx->rsm->state = ecp_rsm_pre_dbl;
1896
1897 /* initial state for the loop */
1898 rs_ctx->rsm->i = 0;
1899 }
1900
1901 dbl:
1902 #endif
1903 /*
1904 * Set T[0] = P and
1905 * T[2^{l-1}] = 2^{dl} P for l = 1 .. w-1 (this is not the final value)
1906 */
1907 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( &T[0], P ) );
1908
1909 #if defined(MBEDTLS_ECP_RESTARTABLE)
1910 if( rs_ctx != NULL && rs_ctx->rsm != NULL && rs_ctx->rsm->i != 0 )
1911 j = rs_ctx->rsm->i;
1912 else
1913 #endif
1914 j = 0;
1915
1916 for( ; j < d * ( w - 1 ); j++ )
1917 {
1918 MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_DBL );
1919
1920 i = 1U << ( j / d );
1921 cur = T + i;
1922
1923 if( j % d == 0 )
1924 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( cur, T + ( i >> 1 ) ) );
1925
1926 MBEDTLS_MPI_CHK( ecp_double_jac( grp, cur, cur ) );
1927 }
1928
1929 #if defined(MBEDTLS_ECP_RESTARTABLE)
1930 if( rs_ctx != NULL && rs_ctx->rsm != NULL )
1931 rs_ctx->rsm->state = ecp_rsm_pre_norm_dbl;
1932
1933 norm_dbl:
1934 #endif
1935 /*
1936 * Normalize current elements in T. As T has holes,
1937 * use an auxiliary array of pointers to elements in T.
1938 */
1939 j = 0;
1940 for( i = 1; i < T_size; i <<= 1 )
1941 TT[j++] = T + i;
1942
1943 MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_INV + 6 * j - 2 );
1944
1945 MBEDTLS_MPI_CHK( ecp_normalize_jac_many( grp, TT, j ) );
1946
1947 #if defined(MBEDTLS_ECP_RESTARTABLE)
1948 if( rs_ctx != NULL && rs_ctx->rsm != NULL )
1949 rs_ctx->rsm->state = ecp_rsm_pre_add;
1950
1951 add:
1952 #endif
1953 /*
1954 * Compute the remaining ones using the minimal number of additions
1955 * Be careful to update T[2^l] only after using it!
1956 */
1957 MBEDTLS_ECP_BUDGET( ( T_size - 1 ) * MBEDTLS_ECP_OPS_ADD );
1958
1959 for( i = 1; i < T_size; i <<= 1 )
1960 {
1961 j = i;
1962 while( j-- )
1963 MBEDTLS_MPI_CHK( ecp_add_mixed( grp, &T[i + j], &T[j], &T[i] ) );
1964 }
1965
1966 #if defined(MBEDTLS_ECP_RESTARTABLE)
1967 if( rs_ctx != NULL && rs_ctx->rsm != NULL )
1968 rs_ctx->rsm->state = ecp_rsm_pre_norm_add;
1969
1970 norm_add:
1971 #endif
1972 /*
1973 * Normalize final elements in T. Even though there are no holes now, we
1974 * still need the auxiliary array for homogeneity with the previous
1975 * call. Also, skip T[0] which is already normalised, being a copy of P.
1976 */
1977 for( j = 0; j + 1 < T_size; j++ )
1978 TT[j] = T + j + 1;
1979
1980 MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_INV + 6 * j - 2 );
1981
1982 MBEDTLS_MPI_CHK( ecp_normalize_jac_many( grp, TT, j ) );
1983
1984 cleanup:
1985 #if defined(MBEDTLS_ECP_RESTARTABLE)
1986 if( rs_ctx != NULL && rs_ctx->rsm != NULL &&
1987 ret == MBEDTLS_ERR_ECP_IN_PROGRESS )
1988 {
1989 if( rs_ctx->rsm->state == ecp_rsm_pre_dbl )
1990 rs_ctx->rsm->i = j;
1991 }
1992 #endif
1993
1994 return( ret );
1995 }
1996
1997 /*
1998 * Select precomputed point: R = sign(i) * T[ abs(i) / 2 ]
1999 *
2000 * See ecp_comb_recode_core() for background
2001 */
ecp_select_comb(const mbedtls_ecp_group * grp,mbedtls_ecp_point * R,const mbedtls_ecp_point T[],unsigned char T_size,unsigned char i)2002 static int ecp_select_comb( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
2003 const mbedtls_ecp_point T[], unsigned char T_size,
2004 unsigned char i )
2005 {
2006 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
2007 unsigned char ii, j;
2008
2009 /* Ignore the "sign" bit and scale down */
2010 ii = ( i & 0x7Fu ) >> 1;
2011
2012 /* Read the whole table to thwart cache-based timing attacks */
2013 for( j = 0; j < T_size; j++ )
2014 {
2015 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &R->X, &T[j].X, j == ii ) );
2016 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &R->Y, &T[j].Y, j == ii ) );
2017 }
2018
2019 /* Safely invert result if i is "negative" */
2020 MBEDTLS_MPI_CHK( ecp_safe_invert_jac( grp, R, i >> 7 ) );
2021
2022 cleanup:
2023 return( ret );
2024 }
2025
2026 /*
2027 * Core multiplication algorithm for the (modified) comb method.
2028 * This part is actually common with the basic comb method (GECC 3.44)
2029 *
2030 * Cost: d A + d D + 1 R
2031 */
ecp_mul_comb_core(const mbedtls_ecp_group * grp,mbedtls_ecp_point * R,const mbedtls_ecp_point T[],unsigned char T_size,const unsigned char x[],size_t d,int (* f_rng)(void *,unsigned char *,size_t),void * p_rng,mbedtls_ecp_restart_ctx * rs_ctx)2032 static int ecp_mul_comb_core( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
2033 const mbedtls_ecp_point T[], unsigned char T_size,
2034 const unsigned char x[], size_t d,
2035 int (*f_rng)(void *, unsigned char *, size_t),
2036 void *p_rng,
2037 mbedtls_ecp_restart_ctx *rs_ctx )
2038 {
2039 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
2040 mbedtls_ecp_point Txi;
2041 size_t i;
2042
2043 mbedtls_ecp_point_init( &Txi );
2044
2045 #if !defined(MBEDTLS_ECP_RESTARTABLE)
2046 (void) rs_ctx;
2047 #endif
2048
2049 #if defined(MBEDTLS_ECP_RESTARTABLE)
2050 if( rs_ctx != NULL && rs_ctx->rsm != NULL &&
2051 rs_ctx->rsm->state != ecp_rsm_comb_core )
2052 {
2053 rs_ctx->rsm->i = 0;
2054 rs_ctx->rsm->state = ecp_rsm_comb_core;
2055 }
2056
2057 /* new 'if' instead of nested for the sake of the 'else' branch */
2058 if( rs_ctx != NULL && rs_ctx->rsm != NULL && rs_ctx->rsm->i != 0 )
2059 {
2060 /* restore current index (R already pointing to rs_ctx->rsm->R) */
2061 i = rs_ctx->rsm->i;
2062 }
2063 else
2064 #endif
2065 {
2066 /* Start with a non-zero point and randomize its coordinates */
2067 i = d;
2068 MBEDTLS_MPI_CHK( ecp_select_comb( grp, R, T, T_size, x[i] ) );
2069 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->Z, 1 ) );
2070 #if defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
2071 if( f_rng != 0 )
2072 #endif
2073 MBEDTLS_MPI_CHK( ecp_randomize_jac( grp, R, f_rng, p_rng ) );
2074 }
2075
2076 while( i != 0 )
2077 {
2078 MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_DBL + MBEDTLS_ECP_OPS_ADD );
2079 --i;
2080
2081 MBEDTLS_MPI_CHK( ecp_double_jac( grp, R, R ) );
2082 MBEDTLS_MPI_CHK( ecp_select_comb( grp, &Txi, T, T_size, x[i] ) );
2083 MBEDTLS_MPI_CHK( ecp_add_mixed( grp, R, R, &Txi ) );
2084 }
2085
2086 cleanup:
2087
2088 mbedtls_ecp_point_free( &Txi );
2089
2090 #if defined(MBEDTLS_ECP_RESTARTABLE)
2091 if( rs_ctx != NULL && rs_ctx->rsm != NULL &&
2092 ret == MBEDTLS_ERR_ECP_IN_PROGRESS )
2093 {
2094 rs_ctx->rsm->i = i;
2095 /* no need to save R, already pointing to rs_ctx->rsm->R */
2096 }
2097 #endif
2098
2099 return( ret );
2100 }
2101
2102 /*
2103 * Recode the scalar to get constant-time comb multiplication
2104 *
2105 * As the actual scalar recoding needs an odd scalar as a starting point,
2106 * this wrapper ensures that by replacing m by N - m if necessary, and
2107 * informs the caller that the result of multiplication will be negated.
2108 *
2109 * This works because we only support large prime order for Short Weierstrass
2110 * curves, so N is always odd hence either m or N - m is.
2111 *
2112 * See ecp_comb_recode_core() for background.
2113 */
ecp_comb_recode_scalar(const mbedtls_ecp_group * grp,const mbedtls_mpi * m,unsigned char k[COMB_MAX_D+1],size_t d,unsigned char w,unsigned char * parity_trick)2114 static int ecp_comb_recode_scalar( const mbedtls_ecp_group *grp,
2115 const mbedtls_mpi *m,
2116 unsigned char k[COMB_MAX_D + 1],
2117 size_t d,
2118 unsigned char w,
2119 unsigned char *parity_trick )
2120 {
2121 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
2122 mbedtls_mpi M, mm;
2123
2124 mbedtls_mpi_init( &M );
2125 mbedtls_mpi_init( &mm );
2126
2127 /* N is always odd (see above), just make extra sure */
2128 if( mbedtls_mpi_get_bit( &grp->N, 0 ) != 1 )
2129 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
2130
2131 /* do we need the parity trick? */
2132 *parity_trick = ( mbedtls_mpi_get_bit( m, 0 ) == 0 );
2133
2134 /* execute parity fix in constant time */
2135 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &M, m ) );
2136 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &mm, &grp->N, m ) );
2137 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &M, &mm, *parity_trick ) );
2138
2139 /* actual scalar recoding */
2140 ecp_comb_recode_core( k, d, w, &M );
2141
2142 cleanup:
2143 mbedtls_mpi_free( &mm );
2144 mbedtls_mpi_free( &M );
2145
2146 return( ret );
2147 }
2148
2149 /*
2150 * Perform comb multiplication (for short Weierstrass curves)
2151 * once the auxiliary table has been pre-computed.
2152 *
2153 * Scalar recoding may use a parity trick that makes us compute -m * P,
2154 * if that is the case we'll need to recover m * P at the end.
2155 */
ecp_mul_comb_after_precomp(const mbedtls_ecp_group * grp,mbedtls_ecp_point * R,const mbedtls_mpi * m,const mbedtls_ecp_point * T,unsigned char T_size,unsigned char w,size_t d,int (* f_rng)(void *,unsigned char *,size_t),void * p_rng,mbedtls_ecp_restart_ctx * rs_ctx)2156 static int ecp_mul_comb_after_precomp( const mbedtls_ecp_group *grp,
2157 mbedtls_ecp_point *R,
2158 const mbedtls_mpi *m,
2159 const mbedtls_ecp_point *T,
2160 unsigned char T_size,
2161 unsigned char w,
2162 size_t d,
2163 int (*f_rng)(void *, unsigned char *, size_t),
2164 void *p_rng,
2165 mbedtls_ecp_restart_ctx *rs_ctx )
2166 {
2167 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
2168 unsigned char parity_trick;
2169 unsigned char k[COMB_MAX_D + 1];
2170 mbedtls_ecp_point *RR = R;
2171
2172 #if defined(MBEDTLS_ECP_RESTARTABLE)
2173 if( rs_ctx != NULL && rs_ctx->rsm != NULL )
2174 {
2175 RR = &rs_ctx->rsm->R;
2176
2177 if( rs_ctx->rsm->state == ecp_rsm_final_norm )
2178 goto final_norm;
2179 }
2180 #endif
2181
2182 MBEDTLS_MPI_CHK( ecp_comb_recode_scalar( grp, m, k, d, w,
2183 &parity_trick ) );
2184 MBEDTLS_MPI_CHK( ecp_mul_comb_core( grp, RR, T, T_size, k, d,
2185 f_rng, p_rng, rs_ctx ) );
2186 MBEDTLS_MPI_CHK( ecp_safe_invert_jac( grp, RR, parity_trick ) );
2187
2188 #if defined(MBEDTLS_ECP_RESTARTABLE)
2189 if( rs_ctx != NULL && rs_ctx->rsm != NULL )
2190 rs_ctx->rsm->state = ecp_rsm_final_norm;
2191
2192 final_norm:
2193 MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_INV );
2194 #endif
2195 /*
2196 * Knowledge of the jacobian coordinates may leak the last few bits of the
2197 * scalar [1], and since our MPI implementation isn't constant-flow,
2198 * inversion (used for coordinate normalization) may leak the full value
2199 * of its input via side-channels [2].
2200 *
2201 * [1] https://eprint.iacr.org/2003/191
2202 * [2] https://eprint.iacr.org/2020/055
2203 *
2204 * Avoid the leak by randomizing coordinates before we normalize them.
2205 */
2206 #if defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
2207 if( f_rng != 0 )
2208 #endif
2209 MBEDTLS_MPI_CHK( ecp_randomize_jac( grp, RR, f_rng, p_rng ) );
2210
2211 MBEDTLS_MPI_CHK( ecp_normalize_jac( grp, RR ) );
2212
2213 #if defined(MBEDTLS_ECP_RESTARTABLE)
2214 if( rs_ctx != NULL && rs_ctx->rsm != NULL )
2215 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, RR ) );
2216 #endif
2217
2218 cleanup:
2219 return( ret );
2220 }
2221
2222 /*
2223 * Pick window size based on curve size and whether we optimize for base point
2224 */
ecp_pick_window_size(const mbedtls_ecp_group * grp,unsigned char p_eq_g)2225 static unsigned char ecp_pick_window_size( const mbedtls_ecp_group *grp,
2226 unsigned char p_eq_g )
2227 {
2228 unsigned char w;
2229
2230 /*
2231 * Minimize the number of multiplications, that is minimize
2232 * 10 * d * w + 18 * 2^(w-1) + 11 * d + 7 * w, with d = ceil( nbits / w )
2233 * (see costs of the various parts, with 1S = 1M)
2234 */
2235 w = grp->nbits >= 384 ? 5 : 4;
2236
2237 /*
2238 * If P == G, pre-compute a bit more, since this may be re-used later.
2239 * Just adding one avoids upping the cost of the first mul too much,
2240 * and the memory cost too.
2241 */
2242 if( p_eq_g )
2243 w++;
2244
2245 /*
2246 * Make sure w is within bounds.
2247 * (The last test is useful only for very small curves in the test suite.)
2248 */
2249 #if( MBEDTLS_ECP_WINDOW_SIZE < 6 )
2250 if( w > MBEDTLS_ECP_WINDOW_SIZE )
2251 w = MBEDTLS_ECP_WINDOW_SIZE;
2252 #endif
2253 if( w >= grp->nbits )
2254 w = 2;
2255
2256 return( w );
2257 }
2258
2259 /*
2260 * Multiplication using the comb method - for curves in short Weierstrass form
2261 *
2262 * This function is mainly responsible for administrative work:
2263 * - managing the restart context if enabled
2264 * - managing the table of precomputed points (passed between the below two
2265 * functions): allocation, computation, ownership tranfer, freeing.
2266 *
2267 * It delegates the actual arithmetic work to:
2268 * ecp_precompute_comb() and ecp_mul_comb_with_precomp()
2269 *
2270 * See comments on ecp_comb_recode_core() regarding the computation strategy.
2271 */
ecp_mul_comb(mbedtls_ecp_group * grp,mbedtls_ecp_point * R,const mbedtls_mpi * m,const mbedtls_ecp_point * P,int (* f_rng)(void *,unsigned char *,size_t),void * p_rng,mbedtls_ecp_restart_ctx * rs_ctx)2272 static int ecp_mul_comb( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
2273 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
2274 int (*f_rng)(void *, unsigned char *, size_t),
2275 void *p_rng,
2276 mbedtls_ecp_restart_ctx *rs_ctx )
2277 {
2278 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
2279 unsigned char w, p_eq_g, i;
2280 size_t d;
2281 unsigned char T_size = 0, T_ok = 0;
2282 mbedtls_ecp_point *T = NULL;
2283 #if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
2284 ecp_drbg_context drbg_ctx;
2285
2286 ecp_drbg_init( &drbg_ctx );
2287 #endif
2288
2289 ECP_RS_ENTER( rsm );
2290
2291 #if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
2292 if( f_rng == NULL )
2293 {
2294 /* Adjust pointers */
2295 f_rng = &ecp_drbg_random;
2296 #if defined(MBEDTLS_ECP_RESTARTABLE)
2297 if( rs_ctx != NULL && rs_ctx->rsm != NULL )
2298 p_rng = &rs_ctx->rsm->drbg_ctx;
2299 else
2300 #endif
2301 p_rng = &drbg_ctx;
2302
2303 /* Initialize internal DRBG if necessary */
2304 #if defined(MBEDTLS_ECP_RESTARTABLE)
2305 if( rs_ctx == NULL || rs_ctx->rsm == NULL ||
2306 rs_ctx->rsm->drbg_seeded == 0 )
2307 #endif
2308 {
2309 const size_t m_len = ( grp->nbits + 7 ) / 8;
2310 MBEDTLS_MPI_CHK( ecp_drbg_seed( p_rng, m, m_len ) );
2311 }
2312 #if defined(MBEDTLS_ECP_RESTARTABLE)
2313 if( rs_ctx != NULL && rs_ctx->rsm != NULL )
2314 rs_ctx->rsm->drbg_seeded = 1;
2315 #endif
2316 }
2317 #endif /* !MBEDTLS_ECP_NO_INTERNAL_RNG */
2318
2319 /* Is P the base point ? */
2320 #if MBEDTLS_ECP_FIXED_POINT_OPTIM == 1
2321 p_eq_g = ( mbedtls_mpi_cmp_mpi( &P->Y, &grp->G.Y ) == 0 &&
2322 mbedtls_mpi_cmp_mpi( &P->X, &grp->G.X ) == 0 );
2323 #else
2324 p_eq_g = 0;
2325 #endif
2326
2327 /* Pick window size and deduce related sizes */
2328 w = ecp_pick_window_size( grp, p_eq_g );
2329 T_size = 1U << ( w - 1 );
2330 d = ( grp->nbits + w - 1 ) / w;
2331
2332 /* Pre-computed table: do we have it already for the base point? */
2333 if( p_eq_g && grp->T != NULL )
2334 {
2335 /* second pointer to the same table, will be deleted on exit */
2336 T = grp->T;
2337 T_ok = 1;
2338 }
2339 else
2340 #if defined(MBEDTLS_ECP_RESTARTABLE)
2341 /* Pre-computed table: do we have one in progress? complete? */
2342 if( rs_ctx != NULL && rs_ctx->rsm != NULL && rs_ctx->rsm->T != NULL )
2343 {
2344 /* transfer ownership of T from rsm to local function */
2345 T = rs_ctx->rsm->T;
2346 rs_ctx->rsm->T = NULL;
2347 rs_ctx->rsm->T_size = 0;
2348
2349 /* This effectively jumps to the call to mul_comb_after_precomp() */
2350 T_ok = rs_ctx->rsm->state >= ecp_rsm_comb_core;
2351 }
2352 else
2353 #endif
2354 /* Allocate table if we didn't have any */
2355 {
2356 T = mbedtls_calloc( T_size, sizeof( mbedtls_ecp_point ) );
2357 if( T == NULL )
2358 {
2359 ret = MBEDTLS_ERR_ECP_ALLOC_FAILED;
2360 goto cleanup;
2361 }
2362
2363 for( i = 0; i < T_size; i++ )
2364 mbedtls_ecp_point_init( &T[i] );
2365
2366 T_ok = 0;
2367 }
2368
2369 /* Compute table (or finish computing it) if not done already */
2370 if( !T_ok )
2371 {
2372 MBEDTLS_MPI_CHK( ecp_precompute_comb( grp, T, P, w, d, rs_ctx ) );
2373
2374 if( p_eq_g )
2375 {
2376 /* almost transfer ownership of T to the group, but keep a copy of
2377 * the pointer to use for calling the next function more easily */
2378 grp->T = T;
2379 grp->T_size = T_size;
2380 }
2381 }
2382
2383 /* Actual comb multiplication using precomputed points */
2384 MBEDTLS_MPI_CHK( ecp_mul_comb_after_precomp( grp, R, m,
2385 T, T_size, w, d,
2386 f_rng, p_rng, rs_ctx ) );
2387
2388 cleanup:
2389
2390 #if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
2391 ecp_drbg_free( &drbg_ctx );
2392 #endif
2393
2394 /* does T belong to the group? */
2395 if( T == grp->T )
2396 T = NULL;
2397
2398 /* does T belong to the restart context? */
2399 #if defined(MBEDTLS_ECP_RESTARTABLE)
2400 if( rs_ctx != NULL && rs_ctx->rsm != NULL && ret == MBEDTLS_ERR_ECP_IN_PROGRESS && T != NULL )
2401 {
2402 /* transfer ownership of T from local function to rsm */
2403 rs_ctx->rsm->T_size = T_size;
2404 rs_ctx->rsm->T = T;
2405 T = NULL;
2406 }
2407 #endif
2408
2409 /* did T belong to us? then let's destroy it! */
2410 if( T != NULL )
2411 {
2412 for( i = 0; i < T_size; i++ )
2413 mbedtls_ecp_point_free( &T[i] );
2414 mbedtls_free( T );
2415 }
2416
2417 /* don't free R while in progress in case R == P */
2418 #if defined(MBEDTLS_ECP_RESTARTABLE)
2419 if( ret != MBEDTLS_ERR_ECP_IN_PROGRESS )
2420 #endif
2421 /* prevent caller from using invalid value */
2422 if( ret != 0 )
2423 mbedtls_ecp_point_free( R );
2424
2425 ECP_RS_LEAVE( rsm );
2426
2427 return( ret );
2428 }
2429
2430 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
2431
2432 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
2433 /*
2434 * For Montgomery curves, we do all the internal arithmetic in projective
2435 * coordinates. Import/export of points uses only the x coordinates, which is
2436 * internaly represented as X / Z.
2437 *
2438 * For scalar multiplication, we'll use a Montgomery ladder.
2439 */
2440
2441 /*
2442 * Normalize Montgomery x/z coordinates: X = X/Z, Z = 1
2443 * Cost: 1M + 1I
2444 */
ecp_normalize_mxz(const mbedtls_ecp_group * grp,mbedtls_ecp_point * P)2445 static int ecp_normalize_mxz( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P )
2446 {
2447 #if defined(MBEDTLS_ECP_NORMALIZE_MXZ_ALT)
2448 if( mbedtls_internal_ecp_grp_capable( grp ) )
2449 return( mbedtls_internal_ecp_normalize_mxz( grp, P ) );
2450 #endif /* MBEDTLS_ECP_NORMALIZE_MXZ_ALT */
2451
2452 #if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_NORMALIZE_MXZ_ALT)
2453 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
2454 #else
2455 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
2456 MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &P->Z, &P->Z, &grp->P ) );
2457 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &P->X, &P->X, &P->Z ) );
2458 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &P->Z, 1 ) );
2459
2460 cleanup:
2461 return( ret );
2462 #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_NORMALIZE_MXZ_ALT) */
2463 }
2464
2465 /*
2466 * Randomize projective x/z coordinates:
2467 * (X, Z) -> (l X, l Z) for random l
2468 * This is sort of the reverse operation of ecp_normalize_mxz().
2469 *
2470 * This countermeasure was first suggested in [2].
2471 * Cost: 2M
2472 */
ecp_randomize_mxz(const mbedtls_ecp_group * grp,mbedtls_ecp_point * P,int (* f_rng)(void *,unsigned char *,size_t),void * p_rng)2473 static int ecp_randomize_mxz( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P,
2474 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
2475 {
2476 #if defined(MBEDTLS_ECP_RANDOMIZE_MXZ_ALT)
2477 if( mbedtls_internal_ecp_grp_capable( grp ) )
2478 return( mbedtls_internal_ecp_randomize_mxz( grp, P, f_rng, p_rng );
2479 #endif /* MBEDTLS_ECP_RANDOMIZE_MXZ_ALT */
2480
2481 #if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_RANDOMIZE_MXZ_ALT)
2482 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
2483 #else
2484 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
2485 mbedtls_mpi l;
2486 int count = 0;
2487 size_t p_size = ( grp->pbits + 7 ) / 8;
2488 mbedtls_mpi_init( &l );
2489
2490 /* Generate l such that 1 < l < p */
2491 do
2492 {
2493 MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &l, p_size, f_rng, p_rng ) );
2494
2495 while( mbedtls_mpi_cmp_mpi( &l, &grp->P ) >= 0 )
2496 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &l, 1 ) );
2497
2498 if( count++ > 10 )
2499 {
2500 ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
2501 goto cleanup;
2502 }
2503 }
2504 while( mbedtls_mpi_cmp_int( &l, 1 ) <= 0 );
2505
2506 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &P->X, &P->X, &l ) );
2507 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &P->Z, &P->Z, &l ) );
2508
2509 cleanup:
2510 mbedtls_mpi_free( &l );
2511
2512 return( ret );
2513 #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_RANDOMIZE_MXZ_ALT) */
2514 }
2515
2516 /*
2517 * Double-and-add: R = 2P, S = P + Q, with d = X(P - Q),
2518 * for Montgomery curves in x/z coordinates.
2519 *
2520 * http://www.hyperelliptic.org/EFD/g1p/auto-code/montgom/xz/ladder/mladd-1987-m.op3
2521 * with
2522 * d = X1
2523 * P = (X2, Z2)
2524 * Q = (X3, Z3)
2525 * R = (X4, Z4)
2526 * S = (X5, Z5)
2527 * and eliminating temporary variables tO, ..., t4.
2528 *
2529 * Cost: 5M + 4S
2530 */
2531 static int ecp_double_add_mxz( const mbedtls_ecp_group *grp,
2532 mbedtls_ecp_point *R, mbedtls_ecp_point *S,
2533 const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q,
2534 const mbedtls_mpi *d )
2535 {
2536 #if defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT)
2537 if( mbedtls_internal_ecp_grp_capable( grp ) )
2538 return( mbedtls_internal_ecp_double_add_mxz( grp, R, S, P, Q, d ) );
2539 #endif /* MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT */
2540
2541 #if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT)
2542 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
2543 #else
2544 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
2545 mbedtls_mpi A, AA, B, BB, E, C, D, DA, CB;
2546
2547 mbedtls_mpi_init( &A ); mbedtls_mpi_init( &AA ); mbedtls_mpi_init( &B );
2548 mbedtls_mpi_init( &BB ); mbedtls_mpi_init( &E ); mbedtls_mpi_init( &C );
2549 mbedtls_mpi_init( &D ); mbedtls_mpi_init( &DA ); mbedtls_mpi_init( &CB );
2550
2551 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &A, &P->X, &P->Z ) );
2552 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &AA, &A, &A ) );
2553 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &B, &P->X, &P->Z ) );
2554 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &BB, &B, &B ) );
2555 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &E, &AA, &BB ) );
2556 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &C, &Q->X, &Q->Z ) );
2557 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &D, &Q->X, &Q->Z ) );
2558 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &DA, &D, &A ) );
2559 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &CB, &C, &B ) );
2560 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &S->X, &DA, &CB ) );
2561 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S->X, &S->X, &S->X ) );
2562 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &S->Z, &DA, &CB ) );
2563 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S->Z, &S->Z, &S->Z ) );
2564 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S->Z, d, &S->Z ) );
2565 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &R->X, &AA, &BB ) );
2566 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &R->Z, &grp->A, &E ) );
2567 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &R->Z, &BB, &R->Z ) );
2568 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &R->Z, &E, &R->Z ) );
2569
2570 cleanup:
2571 mbedtls_mpi_free( &A ); mbedtls_mpi_free( &AA ); mbedtls_mpi_free( &B );
2572 mbedtls_mpi_free( &BB ); mbedtls_mpi_free( &E ); mbedtls_mpi_free( &C );
2573 mbedtls_mpi_free( &D ); mbedtls_mpi_free( &DA ); mbedtls_mpi_free( &CB );
2574
2575 return( ret );
2576 #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT) */
2577 }
2578
2579 /*
2580 * Multiplication with Montgomery ladder in x/z coordinates,
2581 * for curves in Montgomery form
2582 */
2583 static int ecp_mul_mxz( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
2584 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
2585 int (*f_rng)(void *, unsigned char *, size_t),
2586 void *p_rng )
2587 {
2588 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
2589 size_t i;
2590 unsigned char b;
2591 mbedtls_ecp_point RP;
2592 mbedtls_mpi PX;
2593 #if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
2594 ecp_drbg_context drbg_ctx;
2595
2596 ecp_drbg_init( &drbg_ctx );
2597 #endif
2598 mbedtls_ecp_point_init( &RP ); mbedtls_mpi_init( &PX );
2599
2600 #if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
2601 if( f_rng == NULL )
2602 {
2603 const size_t m_len = ( grp->nbits + 7 ) / 8;
2604 MBEDTLS_MPI_CHK( ecp_drbg_seed( &drbg_ctx, m, m_len ) );
2605 f_rng = &ecp_drbg_random;
2606 p_rng = &drbg_ctx;
2607 }
2608 #endif /* !MBEDTLS_ECP_NO_INTERNAL_RNG */
2609
2610 /* Save PX and read from P before writing to R, in case P == R */
2611 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &PX, &P->X ) );
2612 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( &RP, P ) );
2613
2614 /* Set R to zero in modified x/z coordinates */
2615 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->X, 1 ) );
2616 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->Z, 0 ) );
2617 mbedtls_mpi_free( &R->Y );
2618
2619 /* RP.X might be sligtly larger than P, so reduce it */
2620 MOD_ADD( RP.X );
2621
2622 /* Randomize coordinates of the starting point */
2623 #if defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
2624 if( f_rng != NULL )
2625 #endif
2626 MBEDTLS_MPI_CHK( ecp_randomize_mxz( grp, &RP, f_rng, p_rng ) );
2627
2628 /* Loop invariant: R = result so far, RP = R + P */
2629 i = mbedtls_mpi_bitlen( m ); /* one past the (zero-based) most significant bit */
2630 while( i-- > 0 )
2631 {
2632 b = mbedtls_mpi_get_bit( m, i );
2633 /*
2634 * if (b) R = 2R + P else R = 2R,
2635 * which is:
2636 * if (b) double_add( RP, R, RP, R )
2637 * else double_add( R, RP, R, RP )
2638 * but using safe conditional swaps to avoid leaks
2639 */
2640 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->X, &RP.X, b ) );
2641 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->Z, &RP.Z, b ) );
2642 MBEDTLS_MPI_CHK( ecp_double_add_mxz( grp, R, &RP, R, &RP, &PX ) );
2643 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->X, &RP.X, b ) );
2644 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->Z, &RP.Z, b ) );
2645 }
2646
2647 /*
2648 * Knowledge of the projective coordinates may leak the last few bits of the
2649 * scalar [1], and since our MPI implementation isn't constant-flow,
2650 * inversion (used for coordinate normalization) may leak the full value
2651 * of its input via side-channels [2].
2652 *
2653 * [1] https://eprint.iacr.org/2003/191
2654 * [2] https://eprint.iacr.org/2020/055
2655 *
2656 * Avoid the leak by randomizing coordinates before we normalize them.
2657 */
2658 #if defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
2659 if( f_rng != NULL )
2660 #endif
2661 MBEDTLS_MPI_CHK( ecp_randomize_mxz( grp, R, f_rng, p_rng ) );
2662
2663 MBEDTLS_MPI_CHK( ecp_normalize_mxz( grp, R ) );
2664
2665 cleanup:
2666 #if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
2667 ecp_drbg_free( &drbg_ctx );
2668 #endif
2669
2670 mbedtls_ecp_point_free( &RP ); mbedtls_mpi_free( &PX );
2671
2672 return( ret );
2673 }
2674
2675 #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
2676
2677 /*
2678 * Restartable multiplication R = m * P
2679 */
2680 int mbedtls_ecp_mul_restartable( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
2681 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
2682 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng,
2683 mbedtls_ecp_restart_ctx *rs_ctx )
2684 {
2685 int ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
2686 #if defined(MBEDTLS_ECP_INTERNAL_ALT)
2687 char is_grp_capable = 0;
2688 #endif
2689 ECP_VALIDATE_RET( grp != NULL );
2690 ECP_VALIDATE_RET( R != NULL );
2691 ECP_VALIDATE_RET( m != NULL );
2692 ECP_VALIDATE_RET( P != NULL );
2693
2694 #if defined(MBEDTLS_ECP_RESTARTABLE)
2695 /* reset ops count for this call if top-level */
2696 if( rs_ctx != NULL && rs_ctx->depth++ == 0 )
2697 rs_ctx->ops_done = 0;
2698 #else
2699 (void) rs_ctx;
2700 #endif
2701
2702 #if defined(MBEDTLS_ECP_INTERNAL_ALT)
2703 if( ( is_grp_capable = mbedtls_internal_ecp_grp_capable( grp ) ) )
2704 MBEDTLS_MPI_CHK( mbedtls_internal_ecp_init( grp ) );
2705 #endif /* MBEDTLS_ECP_INTERNAL_ALT */
2706
2707 #if defined(MBEDTLS_ECP_RESTARTABLE)
2708 /* skip argument check when restarting */
2709 if( rs_ctx == NULL || rs_ctx->rsm == NULL )
2710 #endif
2711 {
2712 /* check_privkey is free */
2713 MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_CHK );
2714
2715 /* Common sanity checks */
2716 MBEDTLS_MPI_CHK( mbedtls_ecp_check_privkey( grp, m ) );
2717 MBEDTLS_MPI_CHK( mbedtls_ecp_check_pubkey( grp, P ) );
2718 }
2719
2720 ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
2721 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
2722 if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY )
2723 MBEDTLS_MPI_CHK( ecp_mul_mxz( grp, R, m, P, f_rng, p_rng ) );
2724 #endif
2725 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
2726 if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
2727 MBEDTLS_MPI_CHK( ecp_mul_comb( grp, R, m, P, f_rng, p_rng, rs_ctx ) );
2728 #endif
2729
2730 cleanup:
2731
2732 #if defined(MBEDTLS_ECP_INTERNAL_ALT)
2733 if( is_grp_capable )
2734 mbedtls_internal_ecp_free( grp );
2735 #endif /* MBEDTLS_ECP_INTERNAL_ALT */
2736
2737 #if defined(MBEDTLS_ECP_RESTARTABLE)
2738 if( rs_ctx != NULL )
2739 rs_ctx->depth--;
2740 #endif
2741
2742 return( ret );
2743 }
2744
2745 /*
2746 * Multiplication R = m * P
2747 */
2748 int mbedtls_ecp_mul( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
2749 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
2750 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
2751 {
2752 ECP_VALIDATE_RET( grp != NULL );
2753 ECP_VALIDATE_RET( R != NULL );
2754 ECP_VALIDATE_RET( m != NULL );
2755 ECP_VALIDATE_RET( P != NULL );
2756 return( mbedtls_ecp_mul_restartable( grp, R, m, P, f_rng, p_rng, NULL ) );
2757 }
2758
2759 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
2760 /*
2761 * Check that an affine point is valid as a public key,
2762 * short weierstrass curves (SEC1 3.2.3.1)
2763 */
2764 static int ecp_check_pubkey_sw( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt )
2765 {
2766 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
2767 mbedtls_mpi YY, RHS;
2768
2769 /* pt coordinates must be normalized for our checks */
2770 if( mbedtls_mpi_cmp_int( &pt->X, 0 ) < 0 ||
2771 mbedtls_mpi_cmp_int( &pt->Y, 0 ) < 0 ||
2772 mbedtls_mpi_cmp_mpi( &pt->X, &grp->P ) >= 0 ||
2773 mbedtls_mpi_cmp_mpi( &pt->Y, &grp->P ) >= 0 )
2774 return( MBEDTLS_ERR_ECP_INVALID_KEY );
2775
2776 mbedtls_mpi_init( &YY ); mbedtls_mpi_init( &RHS );
2777
2778 /*
2779 * YY = Y^2
2780 * RHS = X (X^2 + A) + B = X^3 + A X + B
2781 */
2782 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &YY, &pt->Y, &pt->Y ) );
2783 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &RHS, &pt->X, &pt->X ) );
2784
2785 /* Special case for A = -3 */
2786 if( grp->A.p == NULL )
2787 {
2788 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &RHS, &RHS, 3 ) ); MOD_SUB( RHS );
2789 }
2790 else
2791 {
2792 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &RHS, &RHS, &grp->A ) );
2793 }
2794
2795 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &RHS, &RHS, &pt->X ) );
2796 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &RHS, &RHS, &grp->B ) );
2797
2798 if( mbedtls_mpi_cmp_mpi( &YY, &RHS ) != 0 )
2799 ret = MBEDTLS_ERR_ECP_INVALID_KEY;
2800
2801 cleanup:
2802
2803 mbedtls_mpi_free( &YY ); mbedtls_mpi_free( &RHS );
2804
2805 return( ret );
2806 }
2807 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
2808
2809 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
2810 /*
2811 * R = m * P with shortcuts for m == 1 and m == -1
2812 * NOT constant-time - ONLY for short Weierstrass!
2813 */
2814 static int mbedtls_ecp_mul_shortcuts( mbedtls_ecp_group *grp,
2815 mbedtls_ecp_point *R,
2816 const mbedtls_mpi *m,
2817 const mbedtls_ecp_point *P,
2818 mbedtls_ecp_restart_ctx *rs_ctx )
2819 {
2820 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
2821
2822 if( mbedtls_mpi_cmp_int( m, 1 ) == 0 )
2823 {
2824 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, P ) );
2825 }
2826 else if( mbedtls_mpi_cmp_int( m, -1 ) == 0 )
2827 {
2828 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, P ) );
2829 if( mbedtls_mpi_cmp_int( &R->Y, 0 ) != 0 )
2830 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &R->Y, &grp->P, &R->Y ) );
2831 }
2832 else
2833 {
2834 MBEDTLS_MPI_CHK( mbedtls_ecp_mul_restartable( grp, R, m, P,
2835 NULL, NULL, rs_ctx ) );
2836 }
2837
2838 cleanup:
2839 return( ret );
2840 }
2841
2842 /*
2843 * Restartable linear combination
2844 * NOT constant-time
2845 */
2846 int mbedtls_ecp_muladd_restartable(
2847 mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
2848 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
2849 const mbedtls_mpi *n, const mbedtls_ecp_point *Q,
2850 mbedtls_ecp_restart_ctx *rs_ctx )
2851 {
2852 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
2853 mbedtls_ecp_point mP;
2854 mbedtls_ecp_point *pmP = &mP;
2855 mbedtls_ecp_point *pR = R;
2856 #if defined(MBEDTLS_ECP_INTERNAL_ALT)
2857 char is_grp_capable = 0;
2858 #endif
2859 ECP_VALIDATE_RET( grp != NULL );
2860 ECP_VALIDATE_RET( R != NULL );
2861 ECP_VALIDATE_RET( m != NULL );
2862 ECP_VALIDATE_RET( P != NULL );
2863 ECP_VALIDATE_RET( n != NULL );
2864 ECP_VALIDATE_RET( Q != NULL );
2865
2866 if( mbedtls_ecp_get_type( grp ) != MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
2867 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
2868
2869 mbedtls_ecp_point_init( &mP );
2870
2871 ECP_RS_ENTER( ma );
2872
2873 #if defined(MBEDTLS_ECP_RESTARTABLE)
2874 if( rs_ctx != NULL && rs_ctx->ma != NULL )
2875 {
2876 /* redirect intermediate results to restart context */
2877 pmP = &rs_ctx->ma->mP;
2878 pR = &rs_ctx->ma->R;
2879
2880 /* jump to next operation */
2881 if( rs_ctx->ma->state == ecp_rsma_mul2 )
2882 goto mul2;
2883 if( rs_ctx->ma->state == ecp_rsma_add )
2884 goto add;
2885 if( rs_ctx->ma->state == ecp_rsma_norm )
2886 goto norm;
2887 }
2888 #endif /* MBEDTLS_ECP_RESTARTABLE */
2889
2890 MBEDTLS_MPI_CHK( mbedtls_ecp_mul_shortcuts( grp, pmP, m, P, rs_ctx ) );
2891 #if defined(MBEDTLS_ECP_RESTARTABLE)
2892 if( rs_ctx != NULL && rs_ctx->ma != NULL )
2893 rs_ctx->ma->state = ecp_rsma_mul2;
2894
2895 mul2:
2896 #endif
2897 MBEDTLS_MPI_CHK( mbedtls_ecp_mul_shortcuts( grp, pR, n, Q, rs_ctx ) );
2898
2899 #if defined(MBEDTLS_ECP_INTERNAL_ALT)
2900 if( ( is_grp_capable = mbedtls_internal_ecp_grp_capable( grp ) ) )
2901 MBEDTLS_MPI_CHK( mbedtls_internal_ecp_init( grp ) );
2902 #endif /* MBEDTLS_ECP_INTERNAL_ALT */
2903
2904 #if defined(MBEDTLS_ECP_RESTARTABLE)
2905 if( rs_ctx != NULL && rs_ctx->ma != NULL )
2906 rs_ctx->ma->state = ecp_rsma_add;
2907
2908 add:
2909 #endif
2910 MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_ADD );
2911 MBEDTLS_MPI_CHK( ecp_add_mixed( grp, pR, pmP, pR ) );
2912 #if defined(MBEDTLS_ECP_RESTARTABLE)
2913 if( rs_ctx != NULL && rs_ctx->ma != NULL )
2914 rs_ctx->ma->state = ecp_rsma_norm;
2915
2916 norm:
2917 #endif
2918 MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_INV );
2919 MBEDTLS_MPI_CHK( ecp_normalize_jac( grp, pR ) );
2920
2921 #if defined(MBEDTLS_ECP_RESTARTABLE)
2922 if( rs_ctx != NULL && rs_ctx->ma != NULL )
2923 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, pR ) );
2924 #endif
2925
2926 cleanup:
2927 #if defined(MBEDTLS_ECP_INTERNAL_ALT)
2928 if( is_grp_capable )
2929 mbedtls_internal_ecp_free( grp );
2930 #endif /* MBEDTLS_ECP_INTERNAL_ALT */
2931
2932 mbedtls_ecp_point_free( &mP );
2933
2934 ECP_RS_LEAVE( ma );
2935
2936 return( ret );
2937 }
2938
2939 /*
2940 * Linear combination
2941 * NOT constant-time
2942 */
2943 int mbedtls_ecp_muladd( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
2944 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
2945 const mbedtls_mpi *n, const mbedtls_ecp_point *Q )
2946 {
2947 ECP_VALIDATE_RET( grp != NULL );
2948 ECP_VALIDATE_RET( R != NULL );
2949 ECP_VALIDATE_RET( m != NULL );
2950 ECP_VALIDATE_RET( P != NULL );
2951 ECP_VALIDATE_RET( n != NULL );
2952 ECP_VALIDATE_RET( Q != NULL );
2953 return( mbedtls_ecp_muladd_restartable( grp, R, m, P, n, Q, NULL ) );
2954 }
2955 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
2956
2957 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
2958 /*
2959 * Check validity of a public key for Montgomery curves with x-only schemes
2960 */
2961 static int ecp_check_pubkey_mx( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt )
2962 {
2963 /* [Curve25519 p. 5] Just check X is the correct number of bytes */
2964 /* Allow any public value, if it's too big then we'll just reduce it mod p
2965 * (RFC 7748 sec. 5 para. 3). */
2966 if( mbedtls_mpi_size( &pt->X ) > ( grp->nbits + 7 ) / 8 )
2967 return( MBEDTLS_ERR_ECP_INVALID_KEY );
2968
2969 return( 0 );
2970 }
2971 #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
2972
2973 /*
2974 * Check that a point is valid as a public key
2975 */
2976 int mbedtls_ecp_check_pubkey( const mbedtls_ecp_group *grp,
2977 const mbedtls_ecp_point *pt )
2978 {
2979 ECP_VALIDATE_RET( grp != NULL );
2980 ECP_VALIDATE_RET( pt != NULL );
2981
2982 /* Must use affine coordinates */
2983 if( mbedtls_mpi_cmp_int( &pt->Z, 1 ) != 0 )
2984 return( MBEDTLS_ERR_ECP_INVALID_KEY );
2985
2986 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
2987 if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY )
2988 return( ecp_check_pubkey_mx( grp, pt ) );
2989 #endif
2990 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
2991 if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
2992 return( ecp_check_pubkey_sw( grp, pt ) );
2993 #endif
2994 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
2995 }
2996
2997 /*
2998 * Check that an mbedtls_mpi is valid as a private key
2999 */
3000 int mbedtls_ecp_check_privkey( const mbedtls_ecp_group *grp,
3001 const mbedtls_mpi *d )
3002 {
3003 ECP_VALIDATE_RET( grp != NULL );
3004 ECP_VALIDATE_RET( d != NULL );
3005
3006 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
3007 if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY )
3008 {
3009 /* see RFC 7748 sec. 5 para. 5 */
3010 if( mbedtls_mpi_get_bit( d, 0 ) != 0 ||
3011 mbedtls_mpi_get_bit( d, 1 ) != 0 ||
3012 mbedtls_mpi_bitlen( d ) - 1 != grp->nbits ) /* mbedtls_mpi_bitlen is one-based! */
3013 return( MBEDTLS_ERR_ECP_INVALID_KEY );
3014
3015 /* see [Curve25519] page 5 */
3016 if( grp->nbits == 254 && mbedtls_mpi_get_bit( d, 2 ) != 0 )
3017 return( MBEDTLS_ERR_ECP_INVALID_KEY );
3018
3019 return( 0 );
3020 }
3021 #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
3022 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
3023 if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
3024 {
3025 /* see SEC1 3.2 */
3026 if( mbedtls_mpi_cmp_int( d, 1 ) < 0 ||
3027 mbedtls_mpi_cmp_mpi( d, &grp->N ) >= 0 )
3028 return( MBEDTLS_ERR_ECP_INVALID_KEY );
3029 else
3030 return( 0 );
3031 }
3032 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
3033
3034 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
3035 }
3036
3037 /*
3038 * Generate a private key
3039 */
3040 int mbedtls_ecp_gen_privkey( const mbedtls_ecp_group *grp,
3041 mbedtls_mpi *d,
3042 int (*f_rng)(void *, unsigned char *, size_t),
3043 void *p_rng )
3044 {
3045 int ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
3046 size_t n_size;
3047
3048 ECP_VALIDATE_RET( grp != NULL );
3049 ECP_VALIDATE_RET( d != NULL );
3050 ECP_VALIDATE_RET( f_rng != NULL );
3051
3052 n_size = ( grp->nbits + 7 ) / 8;
3053
3054 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
3055 if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY )
3056 {
3057 /* [M225] page 5 */
3058 size_t b;
3059
3060 do {
3061 MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( d, n_size, f_rng, p_rng ) );
3062 } while( mbedtls_mpi_bitlen( d ) == 0);
3063
3064 /* Make sure the most significant bit is nbits */
3065 b = mbedtls_mpi_bitlen( d ) - 1; /* mbedtls_mpi_bitlen is one-based */
3066 if( b > grp->nbits )
3067 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( d, b - grp->nbits ) );
3068 else
3069 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, grp->nbits, 1 ) );
3070
3071 /* Make sure the last two bits are unset for Curve448, three bits for
3072 Curve25519 */
3073 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 0, 0 ) );
3074 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 1, 0 ) );
3075 if( grp->nbits == 254 )
3076 {
3077 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 2, 0 ) );
3078 }
3079 }
3080 #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
3081
3082 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
3083 if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
3084 {
3085 /* SEC1 3.2.1: Generate d such that 1 <= n < N */
3086 int count = 0;
3087 unsigned cmp = 0;
3088
3089 /*
3090 * Match the procedure given in RFC 6979 (deterministic ECDSA):
3091 * - use the same byte ordering;
3092 * - keep the leftmost nbits bits of the generated octet string;
3093 * - try until result is in the desired range.
3094 * This also avoids any biais, which is especially important for ECDSA.
3095 */
3096 do
3097 {
3098 MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( d, n_size, f_rng, p_rng ) );
3099 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( d, 8 * n_size - grp->nbits ) );
3100
3101 /*
3102 * Each try has at worst a probability 1/2 of failing (the msb has
3103 * a probability 1/2 of being 0, and then the result will be < N),
3104 * so after 30 tries failure probability is a most 2**(-30).
3105 *
3106 * For most curves, 1 try is enough with overwhelming probability,
3107 * since N starts with a lot of 1s in binary, but some curves
3108 * such as secp224k1 are actually very close to the worst case.
3109 */
3110 if( ++count > 30 )
3111 {
3112 ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
3113 goto cleanup;
3114 }
3115
3116 ret = mbedtls_mpi_lt_mpi_ct( d, &grp->N, &cmp );
3117 if( ret != 0 )
3118 {
3119 goto cleanup;
3120 }
3121 }
3122 while( mbedtls_mpi_cmp_int( d, 1 ) < 0 || cmp != 1 );
3123 }
3124 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
3125
3126 cleanup:
3127 return( ret );
3128 }
3129
3130 /*
3131 * Generate a keypair with configurable base point
3132 */
3133 int mbedtls_ecp_gen_keypair_base( mbedtls_ecp_group *grp,
3134 const mbedtls_ecp_point *G,
3135 mbedtls_mpi *d, mbedtls_ecp_point *Q,
3136 int (*f_rng)(void *, unsigned char *, size_t),
3137 void *p_rng )
3138 {
3139 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
3140 ECP_VALIDATE_RET( grp != NULL );
3141 ECP_VALIDATE_RET( d != NULL );
3142 ECP_VALIDATE_RET( G != NULL );
3143 ECP_VALIDATE_RET( Q != NULL );
3144 ECP_VALIDATE_RET( f_rng != NULL );
3145
3146 MBEDTLS_MPI_CHK( mbedtls_ecp_gen_privkey( grp, d, f_rng, p_rng ) );
3147 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( grp, Q, d, G, f_rng, p_rng ) );
3148
3149 cleanup:
3150 return( ret );
3151 }
3152
3153 /*
3154 * Generate key pair, wrapper for conventional base point
3155 */
3156 int mbedtls_ecp_gen_keypair( mbedtls_ecp_group *grp,
3157 mbedtls_mpi *d, mbedtls_ecp_point *Q,
3158 int (*f_rng)(void *, unsigned char *, size_t),
3159 void *p_rng )
3160 {
3161 ECP_VALIDATE_RET( grp != NULL );
3162 ECP_VALIDATE_RET( d != NULL );
3163 ECP_VALIDATE_RET( Q != NULL );
3164 ECP_VALIDATE_RET( f_rng != NULL );
3165
3166 return( mbedtls_ecp_gen_keypair_base( grp, &grp->G, d, Q, f_rng, p_rng ) );
3167 }
3168
3169 /*
3170 * Generate a keypair, prettier wrapper
3171 */
3172 int mbedtls_ecp_gen_key( mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key,
3173 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
3174 {
3175 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
3176 ECP_VALIDATE_RET( key != NULL );
3177 ECP_VALIDATE_RET( f_rng != NULL );
3178
3179 if( ( ret = mbedtls_ecp_group_load( &key->grp, grp_id ) ) != 0 )
3180 return( ret );
3181
3182 return( mbedtls_ecp_gen_keypair( &key->grp, &key->d, &key->Q, f_rng, p_rng ) );
3183 }
3184
3185 #define ECP_CURVE25519_KEY_SIZE 32
3186 /*
3187 * Read a private key.
3188 */
3189 int mbedtls_ecp_read_key( mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key,
3190 const unsigned char *buf, size_t buflen )
3191 {
3192 int ret = 0;
3193
3194 ECP_VALIDATE_RET( key != NULL );
3195 ECP_VALIDATE_RET( buf != NULL );
3196
3197 if( ( ret = mbedtls_ecp_group_load( &key->grp, grp_id ) ) != 0 )
3198 return( ret );
3199
3200 ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
3201
3202 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
3203 if( mbedtls_ecp_get_type( &key->grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY )
3204 {
3205 /*
3206 * If it is Curve25519 curve then mask the key as mandated by RFC7748
3207 */
3208 if( grp_id == MBEDTLS_ECP_DP_CURVE25519 )
3209 {
3210 if( buflen != ECP_CURVE25519_KEY_SIZE )
3211 return MBEDTLS_ERR_ECP_INVALID_KEY;
3212
3213 MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary_le( &key->d, buf, buflen ) );
3214
3215 /* Set the three least significant bits to 0 */
3216 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &key->d, 0, 0 ) );
3217 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &key->d, 1, 0 ) );
3218 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &key->d, 2, 0 ) );
3219
3220 /* Set the most significant bit to 0 */
3221 MBEDTLS_MPI_CHK(
3222 mbedtls_mpi_set_bit( &key->d,
3223 ECP_CURVE25519_KEY_SIZE * 8 - 1, 0 )
3224 );
3225
3226 /* Set the second most significant bit to 1 */
3227 MBEDTLS_MPI_CHK(
3228 mbedtls_mpi_set_bit( &key->d,
3229 ECP_CURVE25519_KEY_SIZE * 8 - 2, 1 )
3230 );
3231 }
3232 else
3233 ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
3234 }
3235
3236 #endif
3237 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
3238 if( mbedtls_ecp_get_type( &key->grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
3239 {
3240 MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &key->d, buf, buflen ) );
3241
3242 MBEDTLS_MPI_CHK( mbedtls_ecp_check_privkey( &key->grp, &key->d ) );
3243 }
3244
3245 #endif
3246 cleanup:
3247
3248 if( ret != 0 )
3249 mbedtls_mpi_free( &key->d );
3250
3251 return( ret );
3252 }
3253
3254 /*
3255 * Write a private key.
3256 */
3257 int mbedtls_ecp_write_key( mbedtls_ecp_keypair *key,
3258 unsigned char *buf, size_t buflen )
3259 {
3260 int ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
3261
3262 ECP_VALIDATE_RET( key != NULL );
3263 ECP_VALIDATE_RET( buf != NULL );
3264
3265 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
3266 if( mbedtls_ecp_get_type( &key->grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY )
3267 {
3268 if( key->grp.id == MBEDTLS_ECP_DP_CURVE25519 )
3269 {
3270 if( buflen < ECP_CURVE25519_KEY_SIZE )
3271 return MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL;
3272
3273 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary_le( &key->d, buf, buflen ) );
3274 }
3275 else
3276 ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
3277 }
3278
3279 #endif
3280 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
3281 if( mbedtls_ecp_get_type( &key->grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
3282 {
3283 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &key->d, buf, buflen ) );
3284 }
3285
3286 #endif
3287 cleanup:
3288
3289 return( ret );
3290 }
3291
3292
3293 /*
3294 * Check a public-private key pair
3295 */
3296 int mbedtls_ecp_check_pub_priv( const mbedtls_ecp_keypair *pub, const mbedtls_ecp_keypair *prv )
3297 {
3298 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
3299 mbedtls_ecp_point Q;
3300 mbedtls_ecp_group grp;
3301 ECP_VALIDATE_RET( pub != NULL );
3302 ECP_VALIDATE_RET( prv != NULL );
3303
3304 if( pub->grp.id == MBEDTLS_ECP_DP_NONE ||
3305 pub->grp.id != prv->grp.id ||
3306 mbedtls_mpi_cmp_mpi( &pub->Q.X, &prv->Q.X ) ||
3307 mbedtls_mpi_cmp_mpi( &pub->Q.Y, &prv->Q.Y ) ||
3308 mbedtls_mpi_cmp_mpi( &pub->Q.Z, &prv->Q.Z ) )
3309 {
3310 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
3311 }
3312
3313 mbedtls_ecp_point_init( &Q );
3314 mbedtls_ecp_group_init( &grp );
3315
3316 /* mbedtls_ecp_mul() needs a non-const group... */
3317 mbedtls_ecp_group_copy( &grp, &prv->grp );
3318
3319 /* Also checks d is valid */
3320 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &Q, &prv->d, &prv->grp.G, NULL, NULL ) );
3321
3322 if( mbedtls_mpi_cmp_mpi( &Q.X, &prv->Q.X ) ||
3323 mbedtls_mpi_cmp_mpi( &Q.Y, &prv->Q.Y ) ||
3324 mbedtls_mpi_cmp_mpi( &Q.Z, &prv->Q.Z ) )
3325 {
3326 ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
3327 goto cleanup;
3328 }
3329
3330 cleanup:
3331 mbedtls_ecp_point_free( &Q );
3332 mbedtls_ecp_group_free( &grp );
3333
3334 return( ret );
3335 }
3336
3337 #if defined(MBEDTLS_SELF_TEST)
3338
3339 /* Adjust the exponent to be a valid private point for the specified curve.
3340 * This is sometimes necessary because we use a single set of exponents
3341 * for all curves but the validity of values depends on the curve. */
3342 static int self_test_adjust_exponent( const mbedtls_ecp_group *grp,
3343 mbedtls_mpi *m )
3344 {
3345 int ret = 0;
3346 switch( grp->id )
3347 {
3348 /* If Curve25519 is available, then that's what we use for the
3349 * Montgomery test, so we don't need the adjustment code. */
3350 #if ! defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
3351 #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
3352 case MBEDTLS_ECP_DP_CURVE448:
3353 /* Move highest bit from 254 to N-1. Setting bit N-1 is
3354 * necessary to enforce the highest-bit-set constraint. */
3355 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( m, 254, 0 ) );
3356 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( m, grp->nbits, 1 ) );
3357 /* Copy second-highest bit from 253 to N-2. This is not
3358 * necessary but improves the test variety a bit. */
3359 MBEDTLS_MPI_CHK(
3360 mbedtls_mpi_set_bit( m, grp->nbits - 1,
3361 mbedtls_mpi_get_bit( m, 253 ) ) );
3362 break;
3363 #endif
3364 #endif /* ! defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) */
3365 default:
3366 /* Non-Montgomery curves and Curve25519 need no adjustment. */
3367 (void) grp;
3368 (void) m;
3369 goto cleanup;
3370 }
3371 cleanup:
3372 return( ret );
3373 }
3374
3375 /* Calculate R = m.P for each m in exponents. Check that the number of
3376 * basic operations doesn't depend on the value of m. */
3377 static int self_test_point( int verbose,
3378 mbedtls_ecp_group *grp,
3379 mbedtls_ecp_point *R,
3380 mbedtls_mpi *m,
3381 const mbedtls_ecp_point *P,
3382 const char *const *exponents,
3383 size_t n_exponents )
3384 {
3385 int ret = 0;
3386 size_t i = 0;
3387 unsigned long add_c_prev, dbl_c_prev, mul_c_prev;
3388 add_count = 0;
3389 dbl_count = 0;
3390 mul_count = 0;
3391
3392 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( m, 16, exponents[0] ) );
3393 MBEDTLS_MPI_CHK( self_test_adjust_exponent( grp, m ) );
3394 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( grp, R, m, P, NULL, NULL ) );
3395
3396 for( i = 1; i < n_exponents; i++ )
3397 {
3398 add_c_prev = add_count;
3399 dbl_c_prev = dbl_count;
3400 mul_c_prev = mul_count;
3401 add_count = 0;
3402 dbl_count = 0;
3403 mul_count = 0;
3404
3405 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( m, 16, exponents[i] ) );
3406 MBEDTLS_MPI_CHK( self_test_adjust_exponent( grp, m ) );
3407 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( grp, R, m, P, NULL, NULL ) );
3408
3409 if( add_count != add_c_prev ||
3410 dbl_count != dbl_c_prev ||
3411 mul_count != mul_c_prev )
3412 {
3413 ret = 1;
3414 break;
3415 }
3416 }
3417
3418 cleanup:
3419 if( verbose != 0 )
3420 {
3421 if( ret != 0 )
3422 mbedtls_printf( "failed (%u)\n", (unsigned int) i );
3423 else
3424 mbedtls_printf( "passed\n" );
3425 }
3426 return( ret );
3427 }
3428
3429 /*
3430 * Checkup routine
3431 */
3432 int mbedtls_ecp_self_test( int verbose )
3433 {
3434 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
3435 mbedtls_ecp_group grp;
3436 mbedtls_ecp_point R, P;
3437 mbedtls_mpi m;
3438
3439 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
3440 /* Exponents especially adapted for secp192k1, which has the lowest
3441 * order n of all supported curves (secp192r1 is in a slightly larger
3442 * field but the order of its base point is slightly smaller). */
3443 const char *sw_exponents[] =
3444 {
3445 "000000000000000000000000000000000000000000000001", /* one */
3446 "FFFFFFFFFFFFFFFFFFFFFFFE26F2FC170F69466A74DEFD8C", /* n - 1 */
3447 "5EA6F389A38B8BC81E767753B15AA5569E1782E30ABE7D25", /* random */
3448 "400000000000000000000000000000000000000000000000", /* one and zeros */
3449 "7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", /* all ones */
3450 "555555555555555555555555555555555555555555555555", /* 101010... */
3451 };
3452 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
3453 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
3454 const char *m_exponents[] =
3455 {
3456 /* Valid private values for Curve25519. In a build with Curve448
3457 * but not Curve25519, they will be adjusted in
3458 * self_test_adjust_exponent(). */
3459 "4000000000000000000000000000000000000000000000000000000000000000",
3460 "5C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C30",
3461 "5715ECCE24583F7A7023C24164390586842E816D7280A49EF6DF4EAE6B280BF8",
3462 "41A2B017516F6D254E1F002BCCBADD54BE30F8CEC737A0E912B4963B6BA74460",
3463 "5555555555555555555555555555555555555555555555555555555555555550",
3464 "7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF8",
3465 };
3466 #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
3467
3468 mbedtls_ecp_group_init( &grp );
3469 mbedtls_ecp_point_init( &R );
3470 mbedtls_ecp_point_init( &P );
3471 mbedtls_mpi_init( &m );
3472
3473 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
3474 /* Use secp192r1 if available, or any available curve */
3475 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
3476 MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, MBEDTLS_ECP_DP_SECP192R1 ) );
3477 #else
3478 MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, mbedtls_ecp_curve_list()->grp_id ) );
3479 #endif
3480
3481 if( verbose != 0 )
3482 mbedtls_printf( " ECP SW test #1 (constant op_count, base point G): " );
3483 /* Do a dummy multiplication first to trigger precomputation */
3484 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &m, 2 ) );
3485 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &P, &m, &grp.G, NULL, NULL ) );
3486 ret = self_test_point( verbose,
3487 &grp, &R, &m, &grp.G,
3488 sw_exponents,
3489 sizeof( sw_exponents ) / sizeof( sw_exponents[0] ));
3490 if( ret != 0 )
3491 goto cleanup;
3492
3493 if( verbose != 0 )
3494 mbedtls_printf( " ECP SW test #2 (constant op_count, other point): " );
3495 /* We computed P = 2G last time, use it */
3496 ret = self_test_point( verbose,
3497 &grp, &R, &m, &P,
3498 sw_exponents,
3499 sizeof( sw_exponents ) / sizeof( sw_exponents[0] ));
3500 if( ret != 0 )
3501 goto cleanup;
3502
3503 mbedtls_ecp_group_free( &grp );
3504 mbedtls_ecp_point_free( &R );
3505 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
3506
3507 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
3508 if( verbose != 0 )
3509 mbedtls_printf( " ECP Montgomery test (constant op_count): " );
3510 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
3511 MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, MBEDTLS_ECP_DP_CURVE25519 ) );
3512 #elif defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
3513 MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, MBEDTLS_ECP_DP_CURVE448 ) );
3514 #else
3515 #error "MBEDTLS_ECP_MONTGOMERY_ENABLED is defined, but no curve is supported for self-test"
3516 #endif
3517 ret = self_test_point( verbose,
3518 &grp, &R, &m, &grp.G,
3519 m_exponents,
3520 sizeof( m_exponents ) / sizeof( m_exponents[0] ));
3521 if( ret != 0 )
3522 goto cleanup;
3523 #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
3524
3525 cleanup:
3526
3527 if( ret < 0 && verbose != 0 )
3528 mbedtls_printf( "Unexpected error, return code = %08X\n", (unsigned int) ret );
3529
3530 mbedtls_ecp_group_free( &grp );
3531 mbedtls_ecp_point_free( &R );
3532 mbedtls_ecp_point_free( &P );
3533 mbedtls_mpi_free( &m );
3534
3535 if( verbose != 0 )
3536 mbedtls_printf( "\n" );
3537
3538 return( ret );
3539 }
3540
3541 #endif /* MBEDTLS_SELF_TEST */
3542
3543 #endif /* !MBEDTLS_ECP_ALT */
3544
3545 #endif /* MBEDTLS_ECP_C */
3546