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 #include "mbedtls/bn_mul.h"
80
81 #include "ecp_invasive.h"
82
83 #include <string.h>
84
85 #if !defined(MBEDTLS_ECP_ALT)
86
87 /* Parameter validation macros based on platform_util.h */
88 #define ECP_VALIDATE_RET( cond ) \
89 MBEDTLS_INTERNAL_VALIDATE_RET( cond, MBEDTLS_ERR_ECP_BAD_INPUT_DATA )
90 #define ECP_VALIDATE( cond ) \
91 MBEDTLS_INTERNAL_VALIDATE( cond )
92
93 #if defined(MBEDTLS_PLATFORM_C)
94 #include "mbedtls/platform.h"
95 #else
96 #include <stdlib.h>
97 #include <stdio.h>
98 #define mbedtls_printf printf
99 #define mbedtls_calloc calloc
100 #define mbedtls_free free
101 #endif
102
103 #include "mbedtls/ecp_internal.h"
104
105 #if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
106 #if defined(MBEDTLS_HMAC_DRBG_C)
107 #include "mbedtls/hmac_drbg.h"
108 #elif defined(MBEDTLS_CTR_DRBG_C)
109 #include "mbedtls/ctr_drbg.h"
110 #else
111 #error "Invalid configuration detected. Include check_config.h to ensure that the configuration is valid."
112 #endif
113 #endif /* MBEDTLS_ECP_NO_INTERNAL_RNG */
114
115 #if ( defined(__ARMCC_VERSION) || defined(_MSC_VER) ) && \
116 !defined(inline) && !defined(__cplusplus)
117 #define inline __inline
118 #endif
119
120 #if defined(MBEDTLS_SELF_TEST)
121 /*
122 * Counts of point addition and doubling, and field multiplications.
123 * Used to test resistance of point multiplication to simple timing attacks.
124 */
125 static unsigned long add_count, dbl_count, mul_count;
126 #endif
127
128 #if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
129 /*
130 * Currently ecp_mul() takes a RNG function as an argument, used for
131 * side-channel protection, but it can be NULL. The initial reasoning was
132 * that people will pass non-NULL RNG when they care about side-channels, but
133 * unfortunately we have some APIs that call ecp_mul() with a NULL RNG, with
134 * no opportunity for the user to do anything about it.
135 *
136 * The obvious strategies for addressing that include:
137 * - change those APIs so that they take RNG arguments;
138 * - require a global RNG to be available to all crypto modules.
139 *
140 * Unfortunately those would break compatibility. So what we do instead is
141 * have our own internal DRBG instance, seeded from the secret scalar.
142 *
143 * The following is a light-weight abstraction layer for doing that with
144 * HMAC_DRBG (first choice) or CTR_DRBG.
145 */
146
147 #if defined(MBEDTLS_HMAC_DRBG_C)
148
149 /* DRBG context type */
150 typedef mbedtls_hmac_drbg_context ecp_drbg_context;
151
152 /* DRBG context init */
ecp_drbg_init(ecp_drbg_context * ctx)153 static inline void ecp_drbg_init( ecp_drbg_context *ctx )
154 {
155 mbedtls_hmac_drbg_init( ctx );
156 }
157
158 /* DRBG context free */
ecp_drbg_free(ecp_drbg_context * ctx)159 static inline void ecp_drbg_free( ecp_drbg_context *ctx )
160 {
161 mbedtls_hmac_drbg_free( ctx );
162 }
163
164 /* DRBG function */
ecp_drbg_random(void * p_rng,unsigned char * output,size_t output_len)165 static inline int ecp_drbg_random( void *p_rng,
166 unsigned char *output, size_t output_len )
167 {
168 return( mbedtls_hmac_drbg_random( p_rng, output, output_len ) );
169 }
170
171 /* DRBG context seeding */
ecp_drbg_seed(ecp_drbg_context * ctx,const mbedtls_mpi * secret,size_t secret_len)172 static int ecp_drbg_seed( ecp_drbg_context *ctx,
173 const mbedtls_mpi *secret, size_t secret_len )
174 {
175 int ret;
176 unsigned char secret_bytes[MBEDTLS_ECP_MAX_BYTES];
177 /* The list starts with strong hashes */
178 const mbedtls_md_type_t md_type = mbedtls_md_list()[0];
179 const mbedtls_md_info_t *md_info = mbedtls_md_info_from_type( md_type );
180
181 if( secret_len > MBEDTLS_ECP_MAX_BYTES )
182 {
183 ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
184 goto cleanup;
185 }
186
187 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( secret,
188 secret_bytes, secret_len ) );
189
190 ret = mbedtls_hmac_drbg_seed_buf( ctx, md_info, secret_bytes, secret_len );
191
192 cleanup:
193 mbedtls_platform_zeroize( secret_bytes, secret_len );
194
195 return( ret );
196 }
197
198 #elif defined(MBEDTLS_CTR_DRBG_C)
199
200 /* DRBG context type */
201 typedef mbedtls_ctr_drbg_context ecp_drbg_context;
202
203 /* DRBG context init */
ecp_drbg_init(ecp_drbg_context * ctx)204 static inline void ecp_drbg_init( ecp_drbg_context *ctx )
205 {
206 mbedtls_ctr_drbg_init( ctx );
207 }
208
209 /* DRBG context free */
ecp_drbg_free(ecp_drbg_context * ctx)210 static inline void ecp_drbg_free( ecp_drbg_context *ctx )
211 {
212 mbedtls_ctr_drbg_free( ctx );
213 }
214
215 /* DRBG function */
ecp_drbg_random(void * p_rng,unsigned char * output,size_t output_len)216 static inline int ecp_drbg_random( void *p_rng,
217 unsigned char *output, size_t output_len )
218 {
219 return( mbedtls_ctr_drbg_random( p_rng, output, output_len ) );
220 }
221
222 /*
223 * Since CTR_DRBG doesn't have a seed_buf() function the way HMAC_DRBG does,
224 * we need to pass an entropy function when seeding. So we use a dummy
225 * function for that, and pass the actual entropy as customisation string.
226 * (During seeding of CTR_DRBG the entropy input and customisation string are
227 * concatenated before being used to update the secret state.)
228 */
ecp_ctr_drbg_null_entropy(void * ctx,unsigned char * out,size_t len)229 static int ecp_ctr_drbg_null_entropy(void *ctx, unsigned char *out, size_t len)
230 {
231 (void) ctx;
232 memset( out, 0, len );
233 return( 0 );
234 }
235
236 /* DRBG context seeding */
ecp_drbg_seed(ecp_drbg_context * ctx,const mbedtls_mpi * secret,size_t secret_len)237 static int ecp_drbg_seed( ecp_drbg_context *ctx,
238 const mbedtls_mpi *secret, size_t secret_len )
239 {
240 int ret;
241 unsigned char secret_bytes[MBEDTLS_ECP_MAX_BYTES];
242
243 if( secret_len > MBEDTLS_ECP_MAX_BYTES )
244 {
245 ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
246 goto cleanup;
247 }
248
249 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( secret,
250 secret_bytes, secret_len ) );
251
252 ret = mbedtls_ctr_drbg_seed( ctx, ecp_ctr_drbg_null_entropy, NULL,
253 secret_bytes, secret_len );
254
255 cleanup:
256 mbedtls_platform_zeroize( secret_bytes, secret_len );
257
258 return( ret );
259 }
260
261 #else
262 #error "Invalid configuration detected. Include check_config.h to ensure that the configuration is valid."
263 #endif /* DRBG modules */
264 #endif /* MBEDTLS_ECP_NO_INTERNAL_RNG */
265
266 #if defined(MBEDTLS_ECP_RESTARTABLE)
267 /*
268 * Maximum number of "basic operations" to be done in a row.
269 *
270 * Default value 0 means that ECC operations will not yield.
271 * Note that regardless of the value of ecp_max_ops, always at
272 * least one step is performed before yielding.
273 *
274 * Setting ecp_max_ops=1 can be suitable for testing purposes
275 * as it will interrupt computation at all possible points.
276 */
277 static unsigned ecp_max_ops = 0;
278
279 /*
280 * Set ecp_max_ops
281 */
mbedtls_ecp_set_max_ops(unsigned max_ops)282 void mbedtls_ecp_set_max_ops( unsigned max_ops )
283 {
284 ecp_max_ops = max_ops;
285 }
286
287 /*
288 * Check if restart is enabled
289 */
mbedtls_ecp_restart_is_enabled(void)290 int mbedtls_ecp_restart_is_enabled( void )
291 {
292 return( ecp_max_ops != 0 );
293 }
294
295 /*
296 * Restart sub-context for ecp_mul_comb()
297 */
298 struct mbedtls_ecp_restart_mul
299 {
300 mbedtls_ecp_point R; /* current intermediate result */
301 size_t i; /* current index in various loops, 0 outside */
302 mbedtls_ecp_point *T; /* table for precomputed points */
303 unsigned char T_size; /* number of points in table T */
304 enum { /* what were we doing last time we returned? */
305 ecp_rsm_init = 0, /* nothing so far, dummy initial state */
306 ecp_rsm_pre_dbl, /* precompute 2^n multiples */
307 ecp_rsm_pre_norm_dbl, /* normalize precomputed 2^n multiples */
308 ecp_rsm_pre_add, /* precompute remaining points by adding */
309 ecp_rsm_pre_norm_add, /* normalize all precomputed points */
310 ecp_rsm_comb_core, /* ecp_mul_comb_core() */
311 ecp_rsm_final_norm, /* do the final normalization */
312 } state;
313 #if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
314 ecp_drbg_context drbg_ctx;
315 unsigned char drbg_seeded;
316 #endif
317 };
318
319 /*
320 * Init restart_mul sub-context
321 */
ecp_restart_rsm_init(mbedtls_ecp_restart_mul_ctx * ctx)322 static void ecp_restart_rsm_init( mbedtls_ecp_restart_mul_ctx *ctx )
323 {
324 mbedtls_ecp_point_init( &ctx->R );
325 ctx->i = 0;
326 ctx->T = NULL;
327 ctx->T_size = 0;
328 ctx->state = ecp_rsm_init;
329 #if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
330 ecp_drbg_init( &ctx->drbg_ctx );
331 ctx->drbg_seeded = 0;
332 #endif
333 }
334
335 /*
336 * Free the components of a restart_mul sub-context
337 */
ecp_restart_rsm_free(mbedtls_ecp_restart_mul_ctx * ctx)338 static void ecp_restart_rsm_free( mbedtls_ecp_restart_mul_ctx *ctx )
339 {
340 unsigned char i;
341
342 if( ctx == NULL )
343 return;
344
345 mbedtls_ecp_point_free( &ctx->R );
346
347 if( ctx->T != NULL )
348 {
349 for( i = 0; i < ctx->T_size; i++ )
350 mbedtls_ecp_point_free( ctx->T + i );
351 mbedtls_free( ctx->T );
352 }
353
354 #if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
355 ecp_drbg_free( &ctx->drbg_ctx );
356 #endif
357
358 ecp_restart_rsm_init( ctx );
359 }
360
361 /*
362 * Restart context for ecp_muladd()
363 */
364 struct mbedtls_ecp_restart_muladd
365 {
366 mbedtls_ecp_point mP; /* mP value */
367 mbedtls_ecp_point R; /* R intermediate result */
368 enum { /* what should we do next? */
369 ecp_rsma_mul1 = 0, /* first multiplication */
370 ecp_rsma_mul2, /* second multiplication */
371 ecp_rsma_add, /* addition */
372 ecp_rsma_norm, /* normalization */
373 } state;
374 };
375
376 /*
377 * Init restart_muladd sub-context
378 */
ecp_restart_ma_init(mbedtls_ecp_restart_muladd_ctx * ctx)379 static void ecp_restart_ma_init( mbedtls_ecp_restart_muladd_ctx *ctx )
380 {
381 mbedtls_ecp_point_init( &ctx->mP );
382 mbedtls_ecp_point_init( &ctx->R );
383 ctx->state = ecp_rsma_mul1;
384 }
385
386 /*
387 * Free the components of a restart_muladd sub-context
388 */
ecp_restart_ma_free(mbedtls_ecp_restart_muladd_ctx * ctx)389 static void ecp_restart_ma_free( mbedtls_ecp_restart_muladd_ctx *ctx )
390 {
391 if( ctx == NULL )
392 return;
393
394 mbedtls_ecp_point_free( &ctx->mP );
395 mbedtls_ecp_point_free( &ctx->R );
396
397 ecp_restart_ma_init( ctx );
398 }
399
400 /*
401 * Initialize a restart context
402 */
mbedtls_ecp_restart_init(mbedtls_ecp_restart_ctx * ctx)403 void mbedtls_ecp_restart_init( mbedtls_ecp_restart_ctx *ctx )
404 {
405 ECP_VALIDATE( ctx != NULL );
406 ctx->ops_done = 0;
407 ctx->depth = 0;
408 ctx->rsm = NULL;
409 ctx->ma = NULL;
410 }
411
412 /*
413 * Free the components of a restart context
414 */
mbedtls_ecp_restart_free(mbedtls_ecp_restart_ctx * ctx)415 void mbedtls_ecp_restart_free( mbedtls_ecp_restart_ctx *ctx )
416 {
417 if( ctx == NULL )
418 return;
419
420 ecp_restart_rsm_free( ctx->rsm );
421 mbedtls_free( ctx->rsm );
422
423 ecp_restart_ma_free( ctx->ma );
424 mbedtls_free( ctx->ma );
425
426 mbedtls_ecp_restart_init( ctx );
427 }
428
429 /*
430 * Check if we can do the next step
431 */
mbedtls_ecp_check_budget(const mbedtls_ecp_group * grp,mbedtls_ecp_restart_ctx * rs_ctx,unsigned ops)432 int mbedtls_ecp_check_budget( const mbedtls_ecp_group *grp,
433 mbedtls_ecp_restart_ctx *rs_ctx,
434 unsigned ops )
435 {
436 ECP_VALIDATE_RET( grp != NULL );
437
438 if( rs_ctx != NULL && ecp_max_ops != 0 )
439 {
440 /* scale depending on curve size: the chosen reference is 256-bit,
441 * and multiplication is quadratic. Round to the closest integer. */
442 if( grp->pbits >= 512 )
443 ops *= 4;
444 else if( grp->pbits >= 384 )
445 ops *= 2;
446
447 /* Avoid infinite loops: always allow first step.
448 * Because of that, however, it's not generally true
449 * that ops_done <= ecp_max_ops, so the check
450 * ops_done > ecp_max_ops below is mandatory. */
451 if( ( rs_ctx->ops_done != 0 ) &&
452 ( rs_ctx->ops_done > ecp_max_ops ||
453 ops > ecp_max_ops - rs_ctx->ops_done ) )
454 {
455 return( MBEDTLS_ERR_ECP_IN_PROGRESS );
456 }
457
458 /* update running count */
459 rs_ctx->ops_done += ops;
460 }
461
462 return( 0 );
463 }
464
465 /* Call this when entering a function that needs its own sub-context */
466 #define ECP_RS_ENTER( SUB ) do { \
467 /* reset ops count for this call if top-level */ \
468 if( rs_ctx != NULL && rs_ctx->depth++ == 0 ) \
469 rs_ctx->ops_done = 0; \
470 \
471 /* set up our own sub-context if needed */ \
472 if( mbedtls_ecp_restart_is_enabled() && \
473 rs_ctx != NULL && rs_ctx->SUB == NULL ) \
474 { \
475 rs_ctx->SUB = mbedtls_calloc( 1, sizeof( *rs_ctx->SUB ) ); \
476 if( rs_ctx->SUB == NULL ) \
477 return( MBEDTLS_ERR_ECP_ALLOC_FAILED ); \
478 \
479 ecp_restart_## SUB ##_init( rs_ctx->SUB ); \
480 } \
481 } while( 0 )
482
483 /* Call this when leaving a function that needs its own sub-context */
484 #define ECP_RS_LEAVE( SUB ) do { \
485 /* clear our sub-context when not in progress (done or error) */ \
486 if( rs_ctx != NULL && rs_ctx->SUB != NULL && \
487 ret != MBEDTLS_ERR_ECP_IN_PROGRESS ) \
488 { \
489 ecp_restart_## SUB ##_free( rs_ctx->SUB ); \
490 mbedtls_free( rs_ctx->SUB ); \
491 rs_ctx->SUB = NULL; \
492 } \
493 \
494 if( rs_ctx != NULL ) \
495 rs_ctx->depth--; \
496 } while( 0 )
497
498 #else /* MBEDTLS_ECP_RESTARTABLE */
499
500 #define ECP_RS_ENTER( sub ) (void) rs_ctx;
501 #define ECP_RS_LEAVE( sub ) (void) rs_ctx;
502
503 #endif /* MBEDTLS_ECP_RESTARTABLE */
504
505 /*
506 * List of supported curves:
507 * - internal ID
508 * - TLS NamedCurve ID (RFC 4492 sec. 5.1.1, RFC 7071 sec. 2, RFC 8446 sec. 4.2.7)
509 * - size in bits
510 * - readable name
511 *
512 * Curves are listed in order: largest curves first, and for a given size,
513 * fastest curves first. This provides the default order for the SSL module.
514 *
515 * Reminder: update profiles in x509_crt.c when adding a new curves!
516 */
517 static const mbedtls_ecp_curve_info ecp_supported_curves[] =
518 {
519 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
520 { MBEDTLS_ECP_DP_SECP521R1, 25, 521, "secp521r1" },
521 #endif
522 #if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED)
523 { MBEDTLS_ECP_DP_BP512R1, 28, 512, "brainpoolP512r1" },
524 #endif
525 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
526 { MBEDTLS_ECP_DP_SECP384R1, 24, 384, "secp384r1" },
527 #endif
528 #if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED)
529 { MBEDTLS_ECP_DP_BP384R1, 27, 384, "brainpoolP384r1" },
530 #endif
531 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
532 { MBEDTLS_ECP_DP_SECP256R1, 23, 256, "secp256r1" },
533 #endif
534 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
535 { MBEDTLS_ECP_DP_SECP256K1, 22, 256, "secp256k1" },
536 #endif
537 #if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED)
538 { MBEDTLS_ECP_DP_BP256R1, 26, 256, "brainpoolP256r1" },
539 #endif
540 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
541 { MBEDTLS_ECP_DP_SECP224R1, 21, 224, "secp224r1" },
542 #endif
543 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
544 { MBEDTLS_ECP_DP_SECP224K1, 20, 224, "secp224k1" },
545 #endif
546 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
547 { MBEDTLS_ECP_DP_SECP192R1, 19, 192, "secp192r1" },
548 #endif
549 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
550 { MBEDTLS_ECP_DP_SECP192K1, 18, 192, "secp192k1" },
551 #endif
552 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
553 { MBEDTLS_ECP_DP_CURVE25519, 29, 256, "x25519" },
554 #endif
555 #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
556 { MBEDTLS_ECP_DP_CURVE448, 30, 448, "x448" },
557 #endif
558 #if defined(MBEDTLS_ECP_DP_SM2_ENABLED)
559 /* https://tools.ietf.org/id/draft-yang-tls-tls13-sm-suites-05.html */
560 { MBEDTLS_ECP_DP_SM2, 41, 256, "sm2" },
561 #endif
562 { MBEDTLS_ECP_DP_NONE, 0, 0, NULL },
563 };
564
565 #define ECP_NB_CURVES sizeof( ecp_supported_curves ) / \
566 sizeof( ecp_supported_curves[0] )
567
568 static mbedtls_ecp_group_id ecp_supported_grp_id[ECP_NB_CURVES];
569
570 /*
571 * List of supported curves and associated info
572 */
mbedtls_ecp_curve_list(void)573 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_list( void )
574 {
575 return( ecp_supported_curves );
576 }
577
578 /*
579 * List of supported curves, group ID only
580 */
mbedtls_ecp_grp_id_list(void)581 const mbedtls_ecp_group_id *mbedtls_ecp_grp_id_list( void )
582 {
583 static int init_done = 0;
584
585 if( ! init_done )
586 {
587 size_t i = 0;
588 const mbedtls_ecp_curve_info *curve_info;
589
590 for( curve_info = mbedtls_ecp_curve_list();
591 curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
592 curve_info++ )
593 {
594 ecp_supported_grp_id[i++] = curve_info->grp_id;
595 }
596 ecp_supported_grp_id[i] = MBEDTLS_ECP_DP_NONE;
597
598 init_done = 1;
599 }
600
601 return( ecp_supported_grp_id );
602 }
603
604 /*
605 * Get the curve info for the internal identifier
606 */
mbedtls_ecp_curve_info_from_grp_id(mbedtls_ecp_group_id grp_id)607 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_grp_id( mbedtls_ecp_group_id grp_id )
608 {
609 const mbedtls_ecp_curve_info *curve_info;
610
611 for( curve_info = mbedtls_ecp_curve_list();
612 curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
613 curve_info++ )
614 {
615 if( curve_info->grp_id == grp_id )
616 return( curve_info );
617 }
618
619 return( NULL );
620 }
621
622 /*
623 * Get the curve info from the TLS identifier
624 */
mbedtls_ecp_curve_info_from_tls_id(uint16_t tls_id)625 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_tls_id( uint16_t tls_id )
626 {
627 const mbedtls_ecp_curve_info *curve_info;
628
629 for( curve_info = mbedtls_ecp_curve_list();
630 curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
631 curve_info++ )
632 {
633 if( curve_info->tls_id == tls_id )
634 return( curve_info );
635 }
636
637 return( NULL );
638 }
639
640 /*
641 * Get the curve info from the name
642 */
mbedtls_ecp_curve_info_from_name(const char * name)643 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_name( const char *name )
644 {
645 const mbedtls_ecp_curve_info *curve_info;
646
647 if( name == NULL )
648 return( NULL );
649
650 for( curve_info = mbedtls_ecp_curve_list();
651 curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
652 curve_info++ )
653 {
654 if( strcmp( curve_info->name, name ) == 0 )
655 return( curve_info );
656 }
657
658 return( NULL );
659 }
660
661 /*
662 * Get the type of a curve
663 */
mbedtls_ecp_get_type(const mbedtls_ecp_group * grp)664 mbedtls_ecp_curve_type mbedtls_ecp_get_type( const mbedtls_ecp_group *grp )
665 {
666 if( grp->G.X.p == NULL )
667 return( MBEDTLS_ECP_TYPE_NONE );
668
669 if( grp->G.Y.p == NULL )
670 return( MBEDTLS_ECP_TYPE_MONTGOMERY );
671 else
672 return( MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS );
673 }
674
675 /*
676 * Initialize (the components of) a point
677 */
mbedtls_ecp_point_init(mbedtls_ecp_point * pt)678 void mbedtls_ecp_point_init( mbedtls_ecp_point *pt )
679 {
680 ECP_VALIDATE( pt != NULL );
681
682 mbedtls_mpi_init( &pt->X );
683 mbedtls_mpi_init( &pt->Y );
684 mbedtls_mpi_init( &pt->Z );
685 }
686
687 /*
688 * Initialize (the components of) a group
689 */
mbedtls_ecp_group_init(mbedtls_ecp_group * grp)690 void mbedtls_ecp_group_init( mbedtls_ecp_group *grp )
691 {
692 ECP_VALIDATE( grp != NULL );
693
694 grp->id = MBEDTLS_ECP_DP_NONE;
695 mbedtls_mpi_init( &grp->P );
696 mbedtls_mpi_init( &grp->A );
697 mbedtls_mpi_init( &grp->B );
698 mbedtls_ecp_point_init( &grp->G );
699 mbedtls_mpi_init( &grp->N );
700 grp->pbits = 0;
701 grp->nbits = 0;
702 grp->h = 0;
703 grp->modp = NULL;
704 grp->t_pre = NULL;
705 grp->t_post = NULL;
706 grp->t_data = NULL;
707 grp->T = NULL;
708 grp->T_size = 0;
709 }
710
711 /*
712 * Initialize (the components of) a key pair
713 */
mbedtls_ecp_keypair_init(mbedtls_ecp_keypair * key)714 void mbedtls_ecp_keypair_init( mbedtls_ecp_keypair *key )
715 {
716 ECP_VALIDATE( key != NULL );
717
718 mbedtls_ecp_group_init( &key->grp );
719 mbedtls_mpi_init( &key->d );
720 mbedtls_ecp_point_init( &key->Q );
721 }
722
723 /*
724 * Unallocate (the components of) a point
725 */
mbedtls_ecp_point_free(mbedtls_ecp_point * pt)726 void mbedtls_ecp_point_free( mbedtls_ecp_point *pt )
727 {
728 if( pt == NULL )
729 return;
730
731 mbedtls_mpi_free( &( pt->X ) );
732 mbedtls_mpi_free( &( pt->Y ) );
733 mbedtls_mpi_free( &( pt->Z ) );
734 }
735
736 /*
737 * Unallocate (the components of) a group
738 */
mbedtls_ecp_group_free(mbedtls_ecp_group * grp)739 void mbedtls_ecp_group_free( mbedtls_ecp_group *grp )
740 {
741 size_t i;
742
743 if( grp == NULL )
744 return;
745
746 if( grp->h != 1 )
747 {
748 mbedtls_mpi_free( &grp->P );
749 mbedtls_mpi_free( &grp->A );
750 mbedtls_mpi_free( &grp->B );
751 mbedtls_ecp_point_free( &grp->G );
752 mbedtls_mpi_free( &grp->N );
753 }
754
755 if( grp->T != NULL )
756 {
757 for( i = 0; i < grp->T_size; i++ )
758 mbedtls_ecp_point_free( &grp->T[i] );
759 mbedtls_free( grp->T );
760 }
761
762 mbedtls_platform_zeroize( grp, sizeof( mbedtls_ecp_group ) );
763 }
764
765 /*
766 * Unallocate (the components of) a key pair
767 */
mbedtls_ecp_keypair_free(mbedtls_ecp_keypair * key)768 void mbedtls_ecp_keypair_free( mbedtls_ecp_keypair *key )
769 {
770 if( key == NULL )
771 return;
772
773 mbedtls_ecp_group_free( &key->grp );
774 mbedtls_mpi_free( &key->d );
775 mbedtls_ecp_point_free( &key->Q );
776 }
777
778 /*
779 * Copy the contents of a point
780 */
mbedtls_ecp_copy(mbedtls_ecp_point * P,const mbedtls_ecp_point * Q)781 int mbedtls_ecp_copy( mbedtls_ecp_point *P, const mbedtls_ecp_point *Q )
782 {
783 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
784 ECP_VALIDATE_RET( P != NULL );
785 ECP_VALIDATE_RET( Q != NULL );
786
787 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->X, &Q->X ) );
788 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->Y, &Q->Y ) );
789 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->Z, &Q->Z ) );
790
791 cleanup:
792 return( ret );
793 }
794
795 /*
796 * Copy the contents of a group object
797 */
mbedtls_ecp_group_copy(mbedtls_ecp_group * dst,const mbedtls_ecp_group * src)798 int mbedtls_ecp_group_copy( mbedtls_ecp_group *dst, const mbedtls_ecp_group *src )
799 {
800 ECP_VALIDATE_RET( dst != NULL );
801 ECP_VALIDATE_RET( src != NULL );
802
803 return( mbedtls_ecp_group_load( dst, src->id ) );
804 }
805
806 /*
807 * Set point to zero
808 */
mbedtls_ecp_set_zero(mbedtls_ecp_point * pt)809 int mbedtls_ecp_set_zero( mbedtls_ecp_point *pt )
810 {
811 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
812 ECP_VALIDATE_RET( pt != NULL );
813
814 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->X , 1 ) );
815 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Y , 1 ) );
816 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z , 0 ) );
817
818 cleanup:
819 return( ret );
820 }
821
822 /*
823 * Tell if a point is zero
824 */
mbedtls_ecp_is_zero(mbedtls_ecp_point * pt)825 int mbedtls_ecp_is_zero( mbedtls_ecp_point *pt )
826 {
827 ECP_VALIDATE_RET( pt != NULL );
828
829 return( mbedtls_mpi_cmp_int( &pt->Z, 0 ) == 0 );
830 }
831
832 /*
833 * Compare two points lazily
834 */
mbedtls_ecp_point_cmp(const mbedtls_ecp_point * P,const mbedtls_ecp_point * Q)835 int mbedtls_ecp_point_cmp( const mbedtls_ecp_point *P,
836 const mbedtls_ecp_point *Q )
837 {
838 ECP_VALIDATE_RET( P != NULL );
839 ECP_VALIDATE_RET( Q != NULL );
840
841 if( mbedtls_mpi_cmp_mpi( &P->X, &Q->X ) == 0 &&
842 mbedtls_mpi_cmp_mpi( &P->Y, &Q->Y ) == 0 &&
843 mbedtls_mpi_cmp_mpi( &P->Z, &Q->Z ) == 0 )
844 {
845 return( 0 );
846 }
847
848 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
849 }
850
851 /*
852 * Import a non-zero point from ASCII strings
853 */
mbedtls_ecp_point_read_string(mbedtls_ecp_point * P,int radix,const char * x,const char * y)854 int mbedtls_ecp_point_read_string( mbedtls_ecp_point *P, int radix,
855 const char *x, const char *y )
856 {
857 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
858 ECP_VALIDATE_RET( P != NULL );
859 ECP_VALIDATE_RET( x != NULL );
860 ECP_VALIDATE_RET( y != NULL );
861
862 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &P->X, radix, x ) );
863 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &P->Y, radix, y ) );
864 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &P->Z, 1 ) );
865
866 cleanup:
867 return( ret );
868 }
869
870 /*
871 * Export a point into unsigned binary data (SEC1 2.3.3 and RFC7748)
872 */
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)873 int mbedtls_ecp_point_write_binary( const mbedtls_ecp_group *grp,
874 const mbedtls_ecp_point *P,
875 int format, size_t *olen,
876 unsigned char *buf, size_t buflen )
877 {
878 int ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
879 size_t plen;
880 ECP_VALIDATE_RET( grp != NULL );
881 ECP_VALIDATE_RET( P != NULL );
882 ECP_VALIDATE_RET( olen != NULL );
883 ECP_VALIDATE_RET( buf != NULL );
884 ECP_VALIDATE_RET( format == MBEDTLS_ECP_PF_UNCOMPRESSED ||
885 format == MBEDTLS_ECP_PF_COMPRESSED );
886
887 plen = mbedtls_mpi_size( &grp->P );
888
889 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
890 (void) format; /* Montgomery curves always use the same point format */
891 if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY )
892 {
893 *olen = plen;
894 if( buflen < *olen )
895 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
896
897 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary_le( &P->X, buf, plen ) );
898 }
899 #endif
900 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
901 if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
902 {
903 /*
904 * Common case: P == 0
905 */
906 if( mbedtls_mpi_cmp_int( &P->Z, 0 ) == 0 )
907 {
908 if( buflen < 1 )
909 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
910
911 buf[0] = 0x00;
912 *olen = 1;
913
914 return( 0 );
915 }
916
917 if( format == MBEDTLS_ECP_PF_UNCOMPRESSED )
918 {
919 *olen = 2 * plen + 1;
920
921 if( buflen < *olen )
922 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
923
924 buf[0] = 0x04;
925 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->X, buf + 1, plen ) );
926 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->Y, buf + 1 + plen, plen ) );
927 }
928 else if( format == MBEDTLS_ECP_PF_COMPRESSED )
929 {
930 *olen = plen + 1;
931
932 if( buflen < *olen )
933 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
934
935 buf[0] = 0x02 + mbedtls_mpi_get_bit( &P->Y, 0 );
936 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->X, buf + 1, plen ) );
937 }
938 }
939 #endif
940
941 cleanup:
942 return( ret );
943 }
944
945 /*
946 * Import a point from unsigned binary data (SEC1 2.3.4 and RFC7748)
947 */
mbedtls_ecp_point_read_binary(const mbedtls_ecp_group * grp,mbedtls_ecp_point * pt,const unsigned char * buf,size_t ilen)948 int mbedtls_ecp_point_read_binary( const mbedtls_ecp_group *grp,
949 mbedtls_ecp_point *pt,
950 const unsigned char *buf, size_t ilen )
951 {
952 int ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
953 size_t plen;
954 ECP_VALIDATE_RET( grp != NULL );
955 ECP_VALIDATE_RET( pt != NULL );
956 ECP_VALIDATE_RET( buf != NULL );
957
958 if( ilen < 1 )
959 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
960
961 plen = mbedtls_mpi_size( &grp->P );
962
963 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
964 if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY )
965 {
966 if( plen != ilen )
967 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
968
969 MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary_le( &pt->X, buf, plen ) );
970 mbedtls_mpi_free( &pt->Y );
971
972 if( grp->id == MBEDTLS_ECP_DP_CURVE25519 )
973 /* Set most significant bit to 0 as prescribed in RFC7748 §5 */
974 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &pt->X, plen * 8 - 1, 0 ) );
975
976 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) );
977 }
978 #endif
979 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
980 if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
981 {
982 if( buf[0] == 0x00 )
983 {
984 if( ilen == 1 )
985 return( mbedtls_ecp_set_zero( pt ) );
986 else
987 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
988 }
989
990 if( buf[0] != 0x04 )
991 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
992
993 if( ilen != 2 * plen + 1 )
994 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
995
996 MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &pt->X, buf + 1, plen ) );
997 MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &pt->Y,
998 buf + 1 + plen, plen ) );
999 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) );
1000 }
1001 #endif
1002
1003 cleanup:
1004 return( ret );
1005 }
1006
1007 /*
1008 * Import a point from a TLS ECPoint record (RFC 4492)
1009 * struct {
1010 * opaque point <1..2^8-1>;
1011 * } ECPoint;
1012 */
mbedtls_ecp_tls_read_point(const mbedtls_ecp_group * grp,mbedtls_ecp_point * pt,const unsigned char ** buf,size_t buf_len)1013 int mbedtls_ecp_tls_read_point( const mbedtls_ecp_group *grp,
1014 mbedtls_ecp_point *pt,
1015 const unsigned char **buf, size_t buf_len )
1016 {
1017 unsigned char data_len;
1018 const unsigned char *buf_start;
1019 ECP_VALIDATE_RET( grp != NULL );
1020 ECP_VALIDATE_RET( pt != NULL );
1021 ECP_VALIDATE_RET( buf != NULL );
1022 ECP_VALIDATE_RET( *buf != NULL );
1023
1024 /*
1025 * We must have at least two bytes (1 for length, at least one for data)
1026 */
1027 if( buf_len < 2 )
1028 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1029
1030 data_len = *(*buf)++;
1031 if( data_len < 1 || data_len > buf_len - 1 )
1032 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1033
1034 /*
1035 * Save buffer start for read_binary and update buf
1036 */
1037 buf_start = *buf;
1038 *buf += data_len;
1039
1040 return( mbedtls_ecp_point_read_binary( grp, pt, buf_start, data_len ) );
1041 }
1042
1043 /*
1044 * Export a point as a TLS ECPoint record (RFC 4492)
1045 * struct {
1046 * opaque point <1..2^8-1>;
1047 * } ECPoint;
1048 */
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)1049 int mbedtls_ecp_tls_write_point( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt,
1050 int format, size_t *olen,
1051 unsigned char *buf, size_t blen )
1052 {
1053 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1054 ECP_VALIDATE_RET( grp != NULL );
1055 ECP_VALIDATE_RET( pt != NULL );
1056 ECP_VALIDATE_RET( olen != NULL );
1057 ECP_VALIDATE_RET( buf != NULL );
1058 ECP_VALIDATE_RET( format == MBEDTLS_ECP_PF_UNCOMPRESSED ||
1059 format == MBEDTLS_ECP_PF_COMPRESSED );
1060
1061 /*
1062 * buffer length must be at least one, for our length byte
1063 */
1064 if( blen < 1 )
1065 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1066
1067 if( ( ret = mbedtls_ecp_point_write_binary( grp, pt, format,
1068 olen, buf + 1, blen - 1) ) != 0 )
1069 return( ret );
1070
1071 /*
1072 * write length to the first byte and update total length
1073 */
1074 buf[0] = (unsigned char) *olen;
1075 ++*olen;
1076
1077 return( 0 );
1078 }
1079
1080 /*
1081 * Set a group from an ECParameters record (RFC 4492)
1082 */
mbedtls_ecp_tls_read_group(mbedtls_ecp_group * grp,const unsigned char ** buf,size_t len)1083 int mbedtls_ecp_tls_read_group( mbedtls_ecp_group *grp,
1084 const unsigned char **buf, size_t len )
1085 {
1086 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1087 mbedtls_ecp_group_id grp_id;
1088 ECP_VALIDATE_RET( grp != NULL );
1089 ECP_VALIDATE_RET( buf != NULL );
1090 ECP_VALIDATE_RET( *buf != NULL );
1091
1092 if( ( ret = mbedtls_ecp_tls_read_group_id( &grp_id, buf, len ) ) != 0 )
1093 return( ret );
1094
1095 return( mbedtls_ecp_group_load( grp, grp_id ) );
1096 }
1097
1098 /*
1099 * Read a group id from an ECParameters record (RFC 4492) and convert it to
1100 * mbedtls_ecp_group_id.
1101 */
mbedtls_ecp_tls_read_group_id(mbedtls_ecp_group_id * grp,const unsigned char ** buf,size_t len)1102 int mbedtls_ecp_tls_read_group_id( mbedtls_ecp_group_id *grp,
1103 const unsigned char **buf, size_t len )
1104 {
1105 uint16_t tls_id;
1106 const mbedtls_ecp_curve_info *curve_info;
1107 ECP_VALIDATE_RET( grp != NULL );
1108 ECP_VALIDATE_RET( buf != NULL );
1109 ECP_VALIDATE_RET( *buf != NULL );
1110
1111 /*
1112 * We expect at least three bytes (see below)
1113 */
1114 if( len < 3 )
1115 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1116
1117 /*
1118 * First byte is curve_type; only named_curve is handled
1119 */
1120 if( *(*buf)++ != MBEDTLS_ECP_TLS_NAMED_CURVE )
1121 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1122
1123 /*
1124 * Next two bytes are the namedcurve value
1125 */
1126 tls_id = *(*buf)++;
1127 tls_id <<= 8;
1128 tls_id |= *(*buf)++;
1129
1130 if( ( curve_info = mbedtls_ecp_curve_info_from_tls_id( tls_id ) ) == NULL )
1131 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
1132
1133 *grp = curve_info->grp_id;
1134
1135 return( 0 );
1136 }
1137
1138 /*
1139 * Write the ECParameters record corresponding to a group (RFC 4492)
1140 */
mbedtls_ecp_tls_write_group(const mbedtls_ecp_group * grp,size_t * olen,unsigned char * buf,size_t blen)1141 int mbedtls_ecp_tls_write_group( const mbedtls_ecp_group *grp, size_t *olen,
1142 unsigned char *buf, size_t blen )
1143 {
1144 const mbedtls_ecp_curve_info *curve_info;
1145 ECP_VALIDATE_RET( grp != NULL );
1146 ECP_VALIDATE_RET( buf != NULL );
1147 ECP_VALIDATE_RET( olen != NULL );
1148
1149 if( ( curve_info = mbedtls_ecp_curve_info_from_grp_id( grp->id ) ) == NULL )
1150 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1151
1152 /*
1153 * We are going to write 3 bytes (see below)
1154 */
1155 *olen = 3;
1156 if( blen < *olen )
1157 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
1158
1159 /*
1160 * First byte is curve_type, always named_curve
1161 */
1162 *buf++ = MBEDTLS_ECP_TLS_NAMED_CURVE;
1163
1164 /*
1165 * Next two bytes are the namedcurve value
1166 */
1167 buf[0] = curve_info->tls_id >> 8;
1168 buf[1] = curve_info->tls_id & 0xFF;
1169
1170 return( 0 );
1171 }
1172
1173 /*
1174 * Wrapper around fast quasi-modp functions, with fall-back to mbedtls_mpi_mod_mpi.
1175 * See the documentation of struct mbedtls_ecp_group.
1176 *
1177 * This function is in the critial loop for mbedtls_ecp_mul, so pay attention to perf.
1178 */
ecp_modp(mbedtls_mpi * N,const mbedtls_ecp_group * grp)1179 static int ecp_modp( mbedtls_mpi *N, const mbedtls_ecp_group *grp )
1180 {
1181 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1182
1183 if( grp->modp == NULL )
1184 return( mbedtls_mpi_mod_mpi( N, N, &grp->P ) );
1185
1186 /* N->s < 0 is a much faster test, which fails only if N is 0 */
1187 if( ( N->s < 0 && mbedtls_mpi_cmp_int( N, 0 ) != 0 ) ||
1188 mbedtls_mpi_bitlen( N ) > 2 * grp->pbits )
1189 {
1190 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1191 }
1192
1193 MBEDTLS_MPI_CHK( grp->modp( N ) );
1194
1195 /* N->s < 0 is a much faster test, which fails only if N is 0 */
1196 while( N->s < 0 && mbedtls_mpi_cmp_int( N, 0 ) != 0 )
1197 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &grp->P ) );
1198
1199 while( mbedtls_mpi_cmp_mpi( N, &grp->P ) >= 0 )
1200 /* we known P, N and the result are positive */
1201 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( N, N, &grp->P ) );
1202
1203 cleanup:
1204 return( ret );
1205 }
1206
1207 /*
1208 * Fast mod-p functions expect their argument to be in the 0..p^2 range.
1209 *
1210 * In order to guarantee that, we need to ensure that operands of
1211 * mbedtls_mpi_mul_mpi are in the 0..p range. So, after each operation we will
1212 * bring the result back to this range.
1213 *
1214 * The following macros are shortcuts for doing that.
1215 */
1216
1217 /*
1218 * Reduce a mbedtls_mpi mod p in-place, general case, to use after mbedtls_mpi_mul_mpi
1219 */
1220 #if defined(MBEDTLS_SELF_TEST)
1221 #define INC_MUL_COUNT mul_count++;
1222 #else
1223 #define INC_MUL_COUNT
1224 #endif
1225
1226 #define MOD_MUL( N ) \
1227 do \
1228 { \
1229 MBEDTLS_MPI_CHK( ecp_modp( &(N), grp ) ); \
1230 INC_MUL_COUNT \
1231 } while( 0 )
1232
mbedtls_mpi_mul_mod(const mbedtls_ecp_group * grp,mbedtls_mpi * X,const mbedtls_mpi * A,const mbedtls_mpi * B)1233 static inline int mbedtls_mpi_mul_mod( const mbedtls_ecp_group *grp,
1234 mbedtls_mpi *X,
1235 const mbedtls_mpi *A,
1236 const mbedtls_mpi *B )
1237 {
1238 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1239 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( X, A, B ) );
1240 MOD_MUL( *X );
1241 cleanup:
1242 return( ret );
1243 }
1244
1245 /*
1246 * Reduce a mbedtls_mpi mod p in-place, to use after mbedtls_mpi_sub_mpi
1247 * N->s < 0 is a very fast test, which fails only if N is 0
1248 */
1249 #define MOD_SUB( N ) \
1250 while( (N).s < 0 && mbedtls_mpi_cmp_int( &(N), 0 ) != 0 ) \
1251 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &(N), &(N), &grp->P ) )
1252
1253 #if ( defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) && \
1254 !( defined(MBEDTLS_ECP_NO_FALLBACK) && \
1255 defined(MBEDTLS_ECP_DOUBLE_JAC_ALT) && \
1256 defined(MBEDTLS_ECP_ADD_MIXED_ALT) ) ) || \
1257 ( defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) && \
1258 !( defined(MBEDTLS_ECP_NO_FALLBACK) && \
1259 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)1260 static inline int mbedtls_mpi_sub_mod( const mbedtls_ecp_group *grp,
1261 mbedtls_mpi *X,
1262 const mbedtls_mpi *A,
1263 const mbedtls_mpi *B )
1264 {
1265 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1266 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( X, A, B ) );
1267 MOD_SUB( *X );
1268 cleanup:
1269 return( ret );
1270 }
1271 #endif /* All functions referencing mbedtls_mpi_sub_mod() are alt-implemented without fallback */
1272
1273 /*
1274 * Reduce a mbedtls_mpi mod p in-place, to use after mbedtls_mpi_add_mpi and mbedtls_mpi_mul_int.
1275 * We known P, N and the result are positive, so sub_abs is correct, and
1276 * a bit faster.
1277 */
1278 #define MOD_ADD( N ) \
1279 while( mbedtls_mpi_cmp_mpi( &(N), &grp->P ) >= 0 ) \
1280 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( &(N), &(N), &grp->P ) )
1281
mbedtls_mpi_add_mod(const mbedtls_ecp_group * grp,mbedtls_mpi * X,const mbedtls_mpi * A,const mbedtls_mpi * B)1282 static inline int mbedtls_mpi_add_mod( const mbedtls_ecp_group *grp,
1283 mbedtls_mpi *X,
1284 const mbedtls_mpi *A,
1285 const mbedtls_mpi *B )
1286 {
1287 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1288 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( X, A, B ) );
1289 MOD_ADD( *X );
1290 cleanup:
1291 return( ret );
1292 }
1293
1294 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) && \
1295 !( defined(MBEDTLS_ECP_NO_FALLBACK) && \
1296 defined(MBEDTLS_ECP_DOUBLE_JAC_ALT) && \
1297 defined(MBEDTLS_ECP_ADD_MIXED_ALT) )
mbedtls_mpi_shift_l_mod(const mbedtls_ecp_group * grp,mbedtls_mpi * X,size_t count)1298 static inline int mbedtls_mpi_shift_l_mod( const mbedtls_ecp_group *grp,
1299 mbedtls_mpi *X,
1300 size_t count )
1301 {
1302 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1303 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( X, count ) );
1304 MOD_ADD( *X );
1305 cleanup:
1306 return( ret );
1307 }
1308 #endif /* All functions referencing mbedtls_mpi_shift_l_mod() are alt-implemented without fallback */
1309
1310 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
1311 /*
1312 * For curves in short Weierstrass form, we do all the internal operations in
1313 * Jacobian coordinates.
1314 *
1315 * For multiplication, we'll use a comb method with coutermeasueres against
1316 * SPA, hence timing attacks.
1317 */
1318
1319 /*
1320 * Normalize jacobian coordinates so that Z == 0 || Z == 1 (GECC 3.2.1)
1321 * Cost: 1N := 1I + 3M + 1S
1322 */
ecp_normalize_jac(const mbedtls_ecp_group * grp,mbedtls_ecp_point * pt)1323 static int ecp_normalize_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt )
1324 {
1325 if( mbedtls_mpi_cmp_int( &pt->Z, 0 ) == 0 )
1326 return( 0 );
1327
1328 #if defined(MBEDTLS_ECP_NORMALIZE_JAC_ALT)
1329 if( mbedtls_internal_ecp_grp_capable( grp ) )
1330 return( mbedtls_internal_ecp_normalize_jac( grp, pt ) );
1331 #endif /* MBEDTLS_ECP_NORMALIZE_JAC_ALT */
1332
1333 #if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_NORMALIZE_JAC_ALT)
1334 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
1335 #else
1336 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1337 mbedtls_mpi Zi, ZZi;
1338 mbedtls_mpi_init( &Zi ); mbedtls_mpi_init( &ZZi );
1339
1340 /*
1341 * X = X / Z^2 mod p
1342 */
1343 MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &Zi, &pt->Z, &grp->P ) );
1344 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &ZZi, &Zi, &Zi ) );
1345 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &pt->X, &pt->X, &ZZi ) );
1346
1347 /*
1348 * Y = Y / Z^3 mod p
1349 */
1350 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &pt->Y, &pt->Y, &ZZi ) );
1351 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &pt->Y, &pt->Y, &Zi ) );
1352
1353 /*
1354 * Z = 1
1355 */
1356 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) );
1357
1358 cleanup:
1359
1360 mbedtls_mpi_free( &Zi ); mbedtls_mpi_free( &ZZi );
1361
1362 return( ret );
1363 #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_NORMALIZE_JAC_ALT) */
1364 }
1365
1366 /*
1367 * Normalize jacobian coordinates of an array of (pointers to) points,
1368 * using Montgomery's trick to perform only one inversion mod P.
1369 * (See for example Cohen's "A Course in Computational Algebraic Number
1370 * Theory", Algorithm 10.3.4.)
1371 *
1372 * Warning: fails (returning an error) if one of the points is zero!
1373 * This should never happen, see choice of w in ecp_mul_comb().
1374 *
1375 * Cost: 1N(t) := 1I + (6t - 3)M + 1S
1376 */
ecp_normalize_jac_many(const mbedtls_ecp_group * grp,mbedtls_ecp_point * T[],size_t T_size)1377 static int ecp_normalize_jac_many( const mbedtls_ecp_group *grp,
1378 mbedtls_ecp_point *T[], size_t T_size )
1379 {
1380 if( T_size < 2 )
1381 return( ecp_normalize_jac( grp, *T ) );
1382
1383 #if defined(MBEDTLS_ECP_NORMALIZE_JAC_MANY_ALT)
1384 if( mbedtls_internal_ecp_grp_capable( grp ) )
1385 return( mbedtls_internal_ecp_normalize_jac_many( grp, T, T_size ) );
1386 #endif
1387
1388 #if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_NORMALIZE_JAC_MANY_ALT)
1389 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
1390 #else
1391 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1392 size_t i;
1393 mbedtls_mpi *c, u, Zi, ZZi;
1394
1395 if( ( c = mbedtls_calloc( T_size, sizeof( mbedtls_mpi ) ) ) == NULL )
1396 return( MBEDTLS_ERR_ECP_ALLOC_FAILED );
1397
1398 for( i = 0; i < T_size; i++ )
1399 mbedtls_mpi_init( &c[i] );
1400
1401 mbedtls_mpi_init( &u ); mbedtls_mpi_init( &Zi ); mbedtls_mpi_init( &ZZi );
1402
1403 /*
1404 * c[i] = Z_0 * ... * Z_i
1405 */
1406 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &c[0], &T[0]->Z ) );
1407 for( i = 1; i < T_size; i++ )
1408 {
1409 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &c[i], &c[i-1], &T[i]->Z ) );
1410 }
1411
1412 /*
1413 * u = 1 / (Z_0 * ... * Z_n) mod P
1414 */
1415 MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &u, &c[T_size-1], &grp->P ) );
1416
1417 for( i = T_size - 1; ; i-- )
1418 {
1419 /*
1420 * Zi = 1 / Z_i mod p
1421 * u = 1 / (Z_0 * ... * Z_i) mod P
1422 */
1423 if( i == 0 ) {
1424 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &Zi, &u ) );
1425 }
1426 else
1427 {
1428 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &Zi, &u, &c[i-1] ) );
1429 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &u, &u, &T[i]->Z ) );
1430 }
1431
1432 /*
1433 * proceed as in normalize()
1434 */
1435 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &ZZi, &Zi, &Zi ) );
1436 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T[i]->X, &T[i]->X, &ZZi ) );
1437 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T[i]->Y, &T[i]->Y, &ZZi ) );
1438 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T[i]->Y, &T[i]->Y, &Zi ) );
1439
1440 /*
1441 * Post-precessing: reclaim some memory by shrinking coordinates
1442 * - not storing Z (always 1)
1443 * - shrinking other coordinates, but still keeping the same number of
1444 * limbs as P, as otherwise it will too likely be regrown too fast.
1445 */
1446 MBEDTLS_MPI_CHK( mbedtls_mpi_shrink( &T[i]->X, grp->P.n ) );
1447 MBEDTLS_MPI_CHK( mbedtls_mpi_shrink( &T[i]->Y, grp->P.n ) );
1448 mbedtls_mpi_free( &T[i]->Z );
1449
1450 if( i == 0 )
1451 break;
1452 }
1453
1454 cleanup:
1455
1456 mbedtls_mpi_free( &u ); mbedtls_mpi_free( &Zi ); mbedtls_mpi_free( &ZZi );
1457 for( i = 0; i < T_size; i++ )
1458 mbedtls_mpi_free( &c[i] );
1459 mbedtls_free( c );
1460
1461 return( ret );
1462 #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_NORMALIZE_JAC_MANY_ALT) */
1463 }
1464
1465 /*
1466 * Conditional point inversion: Q -> -Q = (Q.X, -Q.Y, Q.Z) without leak.
1467 * "inv" must be 0 (don't invert) or 1 (invert) or the result will be invalid
1468 */
ecp_safe_invert_jac(const mbedtls_ecp_group * grp,mbedtls_ecp_point * Q,unsigned char inv)1469 static int ecp_safe_invert_jac( const mbedtls_ecp_group *grp,
1470 mbedtls_ecp_point *Q,
1471 unsigned char inv )
1472 {
1473 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1474 unsigned char nonzero;
1475 mbedtls_mpi mQY;
1476
1477 mbedtls_mpi_init( &mQY );
1478
1479 /* Use the fact that -Q.Y mod P = P - Q.Y unless Q.Y == 0 */
1480 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &mQY, &grp->P, &Q->Y ) );
1481 nonzero = mbedtls_mpi_cmp_int( &Q->Y, 0 ) != 0;
1482 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &Q->Y, &mQY, inv & nonzero ) );
1483
1484 cleanup:
1485 mbedtls_mpi_free( &mQY );
1486
1487 return( ret );
1488 }
1489
1490 /*
1491 * Point doubling R = 2 P, Jacobian coordinates
1492 *
1493 * Based on http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#doubling-dbl-1998-cmo-2 .
1494 *
1495 * We follow the variable naming fairly closely. The formula variations that trade a MUL for a SQR
1496 * (plus a few ADDs) aren't useful as our bignum implementation doesn't distinguish squaring.
1497 *
1498 * Standard optimizations are applied when curve parameter A is one of { 0, -3 }.
1499 *
1500 * Cost: 1D := 3M + 4S (A == 0)
1501 * 4M + 4S (A == -3)
1502 * 3M + 6S + 1a otherwise
1503 */
ecp_double_jac(const mbedtls_ecp_group * grp,mbedtls_ecp_point * R,const mbedtls_ecp_point * P)1504 static int ecp_double_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
1505 const mbedtls_ecp_point *P )
1506 {
1507 #if defined(MBEDTLS_SELF_TEST)
1508 dbl_count++;
1509 #endif
1510
1511 #if defined(MBEDTLS_ECP_DOUBLE_JAC_ALT)
1512 if( mbedtls_internal_ecp_grp_capable( grp ) )
1513 return( mbedtls_internal_ecp_double_jac( grp, R, P ) );
1514 #endif /* MBEDTLS_ECP_DOUBLE_JAC_ALT */
1515
1516 #if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_DOUBLE_JAC_ALT)
1517 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
1518 #else
1519 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1520 mbedtls_mpi M, S, T, U;
1521
1522 mbedtls_mpi_init( &M ); mbedtls_mpi_init( &S ); mbedtls_mpi_init( &T ); mbedtls_mpi_init( &U );
1523
1524 /* Special case for A = -3 */
1525 if( grp->A.p == NULL )
1526 {
1527 /* M = 3(X + Z^2)(X - Z^2) */
1528 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S, &P->Z, &P->Z ) );
1529 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &T, &P->X, &S ) );
1530 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &U, &P->X, &S ) );
1531 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S, &T, &U ) );
1532 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &S, 3 ) ); MOD_ADD( M );
1533 }
1534 else
1535 {
1536 /* M = 3.X^2 */
1537 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S, &P->X, &P->X ) );
1538 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &S, 3 ) ); MOD_ADD( M );
1539
1540 /* Optimize away for "koblitz" curves with A = 0 */
1541 if( mbedtls_mpi_cmp_int( &grp->A, 0 ) != 0 )
1542 {
1543 /* M += A.Z^4 */
1544 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S, &P->Z, &P->Z ) );
1545 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T, &S, &S ) );
1546 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S, &T, &grp->A ) );
1547 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &M, &M, &S ) );
1548 }
1549 }
1550
1551 /* S = 4.X.Y^2 */
1552 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T, &P->Y, &P->Y ) );
1553 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l_mod( grp, &T, 1 ) );
1554 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S, &P->X, &T ) );
1555 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l_mod( grp, &S, 1 ) );
1556
1557 /* U = 8.Y^4 */
1558 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &U, &T, &T ) );
1559 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l_mod( grp, &U, 1 ) );
1560
1561 /* T = M^2 - 2.S */
1562 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T, &M, &M ) );
1563 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &T, &T, &S ) );
1564 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &T, &T, &S ) );
1565
1566 /* S = M(S - T) - U */
1567 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &S, &S, &T ) );
1568 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S, &S, &M ) );
1569 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &S, &S, &U ) );
1570
1571 /* U = 2.Y.Z */
1572 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &U, &P->Y, &P->Z ) );
1573 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l_mod( grp, &U, 1 ) );
1574
1575 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->X, &T ) );
1576 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Y, &S ) );
1577 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Z, &U ) );
1578
1579 cleanup:
1580 mbedtls_mpi_free( &M ); mbedtls_mpi_free( &S ); mbedtls_mpi_free( &T ); mbedtls_mpi_free( &U );
1581
1582 return( ret );
1583 #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_DOUBLE_JAC_ALT) */
1584 }
1585
1586 /*
1587 * Addition: R = P + Q, mixed affine-Jacobian coordinates (GECC 3.22)
1588 *
1589 * The coordinates of Q must be normalized (= affine),
1590 * but those of P don't need to. R is not normalized.
1591 *
1592 * Special cases: (1) P or Q is zero, (2) R is zero, (3) P == Q.
1593 * None of these cases can happen as intermediate step in ecp_mul_comb():
1594 * - at each step, P, Q and R are multiples of the base point, the factor
1595 * being less than its order, so none of them is zero;
1596 * - Q is an odd multiple of the base point, P an even multiple,
1597 * due to the choice of precomputed points in the modified comb method.
1598 * So branches for these cases do not leak secret information.
1599 *
1600 * We accept Q->Z being unset (saving memory in tables) as meaning 1.
1601 *
1602 * Cost: 1A := 8M + 3S
1603 */
ecp_add_mixed(const mbedtls_ecp_group * grp,mbedtls_ecp_point * R,const mbedtls_ecp_point * P,const mbedtls_ecp_point * Q)1604 static int ecp_add_mixed( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
1605 const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q )
1606 {
1607 #if defined(MBEDTLS_SELF_TEST)
1608 add_count++;
1609 #endif
1610
1611 #if defined(MBEDTLS_ECP_ADD_MIXED_ALT)
1612 if( mbedtls_internal_ecp_grp_capable( grp ) )
1613 return( mbedtls_internal_ecp_add_mixed( grp, R, P, Q ) );
1614 #endif /* MBEDTLS_ECP_ADD_MIXED_ALT */
1615
1616 #if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_ADD_MIXED_ALT)
1617 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
1618 #else
1619 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1620 mbedtls_mpi T1, T2, T3, T4, X, Y, Z;
1621
1622 /*
1623 * Trivial cases: P == 0 or Q == 0 (case 1)
1624 */
1625 if( mbedtls_mpi_cmp_int( &P->Z, 0 ) == 0 )
1626 return( mbedtls_ecp_copy( R, Q ) );
1627
1628 if( Q->Z.p != NULL && mbedtls_mpi_cmp_int( &Q->Z, 0 ) == 0 )
1629 return( mbedtls_ecp_copy( R, P ) );
1630
1631 /*
1632 * Make sure Q coordinates are normalized
1633 */
1634 if( Q->Z.p != NULL && mbedtls_mpi_cmp_int( &Q->Z, 1 ) != 0 )
1635 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1636
1637 mbedtls_mpi_init( &T1 ); mbedtls_mpi_init( &T2 ); mbedtls_mpi_init( &T3 ); mbedtls_mpi_init( &T4 );
1638 mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Y ); mbedtls_mpi_init( &Z );
1639
1640 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T1, &P->Z, &P->Z ) );
1641 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T2, &T1, &P->Z ) );
1642 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T1, &T1, &Q->X ) );
1643 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T2, &T2, &Q->Y ) );
1644 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &T1, &T1, &P->X ) );
1645 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &T2, &T2, &P->Y ) );
1646
1647 /* Special cases (2) and (3) */
1648 if( mbedtls_mpi_cmp_int( &T1, 0 ) == 0 )
1649 {
1650 if( mbedtls_mpi_cmp_int( &T2, 0 ) == 0 )
1651 {
1652 ret = ecp_double_jac( grp, R, P );
1653 goto cleanup;
1654 }
1655 else
1656 {
1657 ret = mbedtls_ecp_set_zero( R );
1658 goto cleanup;
1659 }
1660 }
1661
1662 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &Z, &P->Z, &T1 ) );
1663 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T3, &T1, &T1 ) );
1664 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T4, &T3, &T1 ) );
1665 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T3, &T3, &P->X ) );
1666 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &T1, &T3 ) );
1667 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l_mod( grp, &T1, 1 ) );
1668 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &X, &T2, &T2 ) );
1669 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &X, &X, &T1 ) );
1670 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &X, &X, &T4 ) );
1671 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &T3, &T3, &X ) );
1672 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T3, &T3, &T2 ) );
1673 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T4, &T4, &P->Y ) );
1674 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &Y, &T3, &T4 ) );
1675
1676 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->X, &X ) );
1677 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Y, &Y ) );
1678 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Z, &Z ) );
1679
1680 cleanup:
1681
1682 mbedtls_mpi_free( &T1 ); mbedtls_mpi_free( &T2 ); mbedtls_mpi_free( &T3 ); mbedtls_mpi_free( &T4 );
1683 mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Y ); mbedtls_mpi_free( &Z );
1684
1685 return( ret );
1686 #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_ADD_MIXED_ALT) */
1687 }
1688
1689 /*
1690 * Randomize jacobian coordinates:
1691 * (X, Y, Z) -> (l^2 X, l^3 Y, l Z) for random l
1692 * This is sort of the reverse operation of ecp_normalize_jac().
1693 *
1694 * This countermeasure was first suggested in [2].
1695 */
ecp_randomize_jac(const mbedtls_ecp_group * grp,mbedtls_ecp_point * pt,int (* f_rng)(void *,unsigned char *,size_t),void * p_rng)1696 static int ecp_randomize_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt,
1697 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
1698 {
1699 #if defined(MBEDTLS_ECP_RANDOMIZE_JAC_ALT)
1700 if( mbedtls_internal_ecp_grp_capable( grp ) )
1701 return( mbedtls_internal_ecp_randomize_jac( grp, pt, f_rng, p_rng ) );
1702 #endif /* MBEDTLS_ECP_RANDOMIZE_JAC_ALT */
1703
1704 #if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_RANDOMIZE_JAC_ALT)
1705 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
1706 #else
1707 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1708 mbedtls_mpi l, ll;
1709
1710 mbedtls_mpi_init( &l ); mbedtls_mpi_init( &ll );
1711
1712 /* Generate l such that 1 < l < p */
1713 MBEDTLS_MPI_CHK( mbedtls_mpi_random( &l, 2, &grp->P, f_rng, p_rng ) );
1714
1715 /* Z = l * Z */
1716 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &pt->Z, &pt->Z, &l ) );
1717
1718 /* X = l^2 * X */
1719 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &ll, &l, &l ) );
1720 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &pt->X, &pt->X, &ll ) );
1721
1722 /* Y = l^3 * Y */
1723 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &ll, &ll, &l ) );
1724 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &pt->Y, &pt->Y, &ll ) );
1725
1726 cleanup:
1727 mbedtls_mpi_free( &l ); mbedtls_mpi_free( &ll );
1728
1729 if( ret == MBEDTLS_ERR_MPI_NOT_ACCEPTABLE )
1730 ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
1731 return( ret );
1732 #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_RANDOMIZE_JAC_ALT) */
1733 }
1734
1735 /*
1736 * Check and define parameters used by the comb method (see below for details)
1737 */
1738 #if MBEDTLS_ECP_WINDOW_SIZE < 2 || MBEDTLS_ECP_WINDOW_SIZE > 7
1739 #error "MBEDTLS_ECP_WINDOW_SIZE out of bounds"
1740 #endif
1741
1742 /* d = ceil( n / w ) */
1743 #define COMB_MAX_D ( MBEDTLS_ECP_MAX_BITS + 1 ) / 2
1744
1745 /* number of precomputed points */
1746 #define COMB_MAX_PRE ( 1 << ( MBEDTLS_ECP_WINDOW_SIZE - 1 ) )
1747
1748 /*
1749 * Compute the representation of m that will be used with our comb method.
1750 *
1751 * The basic comb method is described in GECC 3.44 for example. We use a
1752 * modified version that provides resistance to SPA by avoiding zero
1753 * digits in the representation as in [3]. We modify the method further by
1754 * requiring that all K_i be odd, which has the small cost that our
1755 * representation uses one more K_i, due to carries, but saves on the size of
1756 * the precomputed table.
1757 *
1758 * Summary of the comb method and its modifications:
1759 *
1760 * - The goal is to compute m*P for some w*d-bit integer m.
1761 *
1762 * - The basic comb method splits m into the w-bit integers
1763 * x[0] .. x[d-1] where x[i] consists of the bits in m whose
1764 * index has residue i modulo d, and computes m * P as
1765 * S[x[0]] + 2 * S[x[1]] + .. + 2^(d-1) S[x[d-1]], where
1766 * S[i_{w-1} .. i_0] := i_{w-1} 2^{(w-1)d} P + ... + i_1 2^d P + i_0 P.
1767 *
1768 * - If it happens that, say, x[i+1]=0 (=> S[x[i+1]]=0), one can replace the sum by
1769 * .. + 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]] ..,
1770 * thereby successively converting it into a form where all summands
1771 * are nonzero, at the cost of negative summands. This is the basic idea of [3].
1772 *
1773 * - More generally, even if x[i+1] != 0, we can first transform the sum as
1774 * .. - 2^i S[x[i]] + 2^{i+1} ( S[x[i]] + S[x[i+1]] ) + 2^{i+2} S[x[i+2]] ..,
1775 * and then replace S[x[i]] + S[x[i+1]] = S[x[i] ^ x[i+1]] + 2 S[x[i] & x[i+1]].
1776 * Performing and iterating this procedure for those x[i] that are even
1777 * (keeping track of carry), we can transform the original sum into one of the form
1778 * S[x'[0]] +- 2 S[x'[1]] +- .. +- 2^{d-1} S[x'[d-1]] + 2^d S[x'[d]]
1779 * with all x'[i] odd. It is therefore only necessary to know S at odd indices,
1780 * which is why we are only computing half of it in the first place in
1781 * ecp_precompute_comb and accessing it with index abs(i) / 2 in ecp_select_comb.
1782 *
1783 * - For the sake of compactness, only the seven low-order bits of x[i]
1784 * are used to represent its absolute value (K_i in the paper), and the msb
1785 * of x[i] encodes the sign (s_i in the paper): it is set if and only if
1786 * if s_i == -1;
1787 *
1788 * Calling conventions:
1789 * - x is an array of size d + 1
1790 * - w is the size, ie number of teeth, of the comb, and must be between
1791 * 2 and 7 (in practice, between 2 and MBEDTLS_ECP_WINDOW_SIZE)
1792 * - m is the MPI, expected to be odd and such that bitlength(m) <= w * d
1793 * (the result will be incorrect if these assumptions are not satisfied)
1794 */
ecp_comb_recode_core(unsigned char x[],size_t d,unsigned char w,const mbedtls_mpi * m)1795 static void ecp_comb_recode_core( unsigned char x[], size_t d,
1796 unsigned char w, const mbedtls_mpi *m )
1797 {
1798 size_t i, j;
1799 unsigned char c, cc, adjust;
1800
1801 memset( x, 0, d+1 );
1802
1803 /* First get the classical comb values (except for x_d = 0) */
1804 for( i = 0; i < d; i++ )
1805 for( j = 0; j < w; j++ )
1806 x[i] |= mbedtls_mpi_get_bit( m, i + d * j ) << j;
1807
1808 /* Now make sure x_1 .. x_d are odd */
1809 c = 0;
1810 for( i = 1; i <= d; i++ )
1811 {
1812 /* Add carry and update it */
1813 cc = x[i] & c;
1814 x[i] = x[i] ^ c;
1815 c = cc;
1816
1817 /* Adjust if needed, avoiding branches */
1818 adjust = 1 - ( x[i] & 0x01 );
1819 c |= x[i] & ( x[i-1] * adjust );
1820 x[i] = x[i] ^ ( x[i-1] * adjust );
1821 x[i-1] |= adjust << 7;
1822 }
1823 }
1824
1825 /*
1826 * Precompute points for the adapted comb method
1827 *
1828 * Assumption: T must be able to hold 2^{w - 1} elements.
1829 *
1830 * Operation: If i = i_{w-1} ... i_1 is the binary representation of i,
1831 * sets T[i] = i_{w-1} 2^{(w-1)d} P + ... + i_1 2^d P + P.
1832 *
1833 * Cost: d(w-1) D + (2^{w-1} - 1) A + 1 N(w-1) + 1 N(2^{w-1} - 1)
1834 *
1835 * Note: Even comb values (those where P would be omitted from the
1836 * sum defining T[i] above) are not needed in our adaption
1837 * the comb method. See ecp_comb_recode_core().
1838 *
1839 * This function currently works in four steps:
1840 * (1) [dbl] Computation of intermediate T[i] for 2-power values of i
1841 * (2) [norm_dbl] Normalization of coordinates of these T[i]
1842 * (3) [add] Computation of all T[i]
1843 * (4) [norm_add] Normalization of all T[i]
1844 *
1845 * Step 1 can be interrupted but not the others; together with the final
1846 * coordinate normalization they are the largest steps done at once, depending
1847 * on the window size. Here are operation counts for P-256:
1848 *
1849 * step (2) (3) (4)
1850 * w = 5 142 165 208
1851 * w = 4 136 77 160
1852 * w = 3 130 33 136
1853 * w = 2 124 11 124
1854 *
1855 * So if ECC operations are blocking for too long even with a low max_ops
1856 * value, it's useful to set MBEDTLS_ECP_WINDOW_SIZE to a lower value in order
1857 * to minimize maximum blocking time.
1858 */
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)1859 static int ecp_precompute_comb( const mbedtls_ecp_group *grp,
1860 mbedtls_ecp_point T[], const mbedtls_ecp_point *P,
1861 unsigned char w, size_t d,
1862 mbedtls_ecp_restart_ctx *rs_ctx )
1863 {
1864 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1865 unsigned char i;
1866 size_t j = 0;
1867 const unsigned char T_size = 1U << ( w - 1 );
1868 mbedtls_ecp_point *cur, *TT[COMB_MAX_PRE - 1];
1869
1870 #if defined(MBEDTLS_ECP_RESTARTABLE)
1871 if( rs_ctx != NULL && rs_ctx->rsm != NULL )
1872 {
1873 if( rs_ctx->rsm->state == ecp_rsm_pre_dbl )
1874 goto dbl;
1875 if( rs_ctx->rsm->state == ecp_rsm_pre_norm_dbl )
1876 goto norm_dbl;
1877 if( rs_ctx->rsm->state == ecp_rsm_pre_add )
1878 goto add;
1879 if( rs_ctx->rsm->state == ecp_rsm_pre_norm_add )
1880 goto norm_add;
1881 }
1882 #else
1883 (void) rs_ctx;
1884 #endif
1885
1886 #if defined(MBEDTLS_ECP_RESTARTABLE)
1887 if( rs_ctx != NULL && rs_ctx->rsm != NULL )
1888 {
1889 rs_ctx->rsm->state = ecp_rsm_pre_dbl;
1890
1891 /* initial state for the loop */
1892 rs_ctx->rsm->i = 0;
1893 }
1894
1895 dbl:
1896 #endif
1897 /*
1898 * Set T[0] = P and
1899 * T[2^{l-1}] = 2^{dl} P for l = 1 .. w-1 (this is not the final value)
1900 */
1901 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( &T[0], P ) );
1902
1903 #if defined(MBEDTLS_ECP_RESTARTABLE)
1904 if( rs_ctx != NULL && rs_ctx->rsm != NULL && rs_ctx->rsm->i != 0 )
1905 j = rs_ctx->rsm->i;
1906 else
1907 #endif
1908 j = 0;
1909
1910 for( ; j < d * ( w - 1 ); j++ )
1911 {
1912 MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_DBL );
1913
1914 i = 1U << ( j / d );
1915 cur = T + i;
1916
1917 if( j % d == 0 )
1918 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( cur, T + ( i >> 1 ) ) );
1919
1920 MBEDTLS_MPI_CHK( ecp_double_jac( grp, cur, cur ) );
1921 }
1922
1923 #if defined(MBEDTLS_ECP_RESTARTABLE)
1924 if( rs_ctx != NULL && rs_ctx->rsm != NULL )
1925 rs_ctx->rsm->state = ecp_rsm_pre_norm_dbl;
1926
1927 norm_dbl:
1928 #endif
1929 /*
1930 * Normalize current elements in T. As T has holes,
1931 * use an auxiliary array of pointers to elements in T.
1932 */
1933 j = 0;
1934 for( i = 1; i < T_size; i <<= 1 )
1935 TT[j++] = T + i;
1936
1937 MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_INV + 6 * j - 2 );
1938
1939 MBEDTLS_MPI_CHK( ecp_normalize_jac_many( grp, TT, j ) );
1940
1941 #if defined(MBEDTLS_ECP_RESTARTABLE)
1942 if( rs_ctx != NULL && rs_ctx->rsm != NULL )
1943 rs_ctx->rsm->state = ecp_rsm_pre_add;
1944
1945 add:
1946 #endif
1947 /*
1948 * Compute the remaining ones using the minimal number of additions
1949 * Be careful to update T[2^l] only after using it!
1950 */
1951 MBEDTLS_ECP_BUDGET( ( T_size - 1 ) * MBEDTLS_ECP_OPS_ADD );
1952
1953 for( i = 1; i < T_size; i <<= 1 )
1954 {
1955 j = i;
1956 while( j-- )
1957 MBEDTLS_MPI_CHK( ecp_add_mixed( grp, &T[i + j], &T[j], &T[i] ) );
1958 }
1959
1960 #if defined(MBEDTLS_ECP_RESTARTABLE)
1961 if( rs_ctx != NULL && rs_ctx->rsm != NULL )
1962 rs_ctx->rsm->state = ecp_rsm_pre_norm_add;
1963
1964 norm_add:
1965 #endif
1966 /*
1967 * Normalize final elements in T. Even though there are no holes now, we
1968 * still need the auxiliary array for homogeneity with the previous
1969 * call. Also, skip T[0] which is already normalised, being a copy of P.
1970 */
1971 for( j = 0; j + 1 < T_size; j++ )
1972 TT[j] = T + j + 1;
1973
1974 MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_INV + 6 * j - 2 );
1975
1976 MBEDTLS_MPI_CHK( ecp_normalize_jac_many( grp, TT, j ) );
1977
1978 cleanup:
1979 #if defined(MBEDTLS_ECP_RESTARTABLE)
1980 if( rs_ctx != NULL && rs_ctx->rsm != NULL &&
1981 ret == MBEDTLS_ERR_ECP_IN_PROGRESS )
1982 {
1983 if( rs_ctx->rsm->state == ecp_rsm_pre_dbl )
1984 rs_ctx->rsm->i = j;
1985 }
1986 #endif
1987
1988 return( ret );
1989 }
1990
1991 /*
1992 * Select precomputed point: R = sign(i) * T[ abs(i) / 2 ]
1993 *
1994 * See ecp_comb_recode_core() for background
1995 */
ecp_select_comb(const mbedtls_ecp_group * grp,mbedtls_ecp_point * R,const mbedtls_ecp_point T[],unsigned char T_size,unsigned char i)1996 static int ecp_select_comb( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
1997 const mbedtls_ecp_point T[], unsigned char T_size,
1998 unsigned char i )
1999 {
2000 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
2001 unsigned char ii, j;
2002
2003 /* Ignore the "sign" bit and scale down */
2004 ii = ( i & 0x7Fu ) >> 1;
2005
2006 /* Read the whole table to thwart cache-based timing attacks */
2007 for( j = 0; j < T_size; j++ )
2008 {
2009 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &R->X, &T[j].X, j == ii ) );
2010 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &R->Y, &T[j].Y, j == ii ) );
2011 }
2012
2013 /* Safely invert result if i is "negative" */
2014 MBEDTLS_MPI_CHK( ecp_safe_invert_jac( grp, R, i >> 7 ) );
2015
2016 cleanup:
2017 return( ret );
2018 }
2019
2020 /*
2021 * Core multiplication algorithm for the (modified) comb method.
2022 * This part is actually common with the basic comb method (GECC 3.44)
2023 *
2024 * Cost: d A + d D + 1 R
2025 */
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)2026 static int ecp_mul_comb_core( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
2027 const mbedtls_ecp_point T[], unsigned char T_size,
2028 const unsigned char x[], size_t d,
2029 int (*f_rng)(void *, unsigned char *, size_t),
2030 void *p_rng,
2031 mbedtls_ecp_restart_ctx *rs_ctx )
2032 {
2033 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
2034 mbedtls_ecp_point Txi;
2035 size_t i;
2036
2037 mbedtls_ecp_point_init( &Txi );
2038
2039 #if !defined(MBEDTLS_ECP_RESTARTABLE)
2040 (void) rs_ctx;
2041 #endif
2042
2043 #if defined(MBEDTLS_ECP_RESTARTABLE)
2044 if( rs_ctx != NULL && rs_ctx->rsm != NULL &&
2045 rs_ctx->rsm->state != ecp_rsm_comb_core )
2046 {
2047 rs_ctx->rsm->i = 0;
2048 rs_ctx->rsm->state = ecp_rsm_comb_core;
2049 }
2050
2051 /* new 'if' instead of nested for the sake of the 'else' branch */
2052 if( rs_ctx != NULL && rs_ctx->rsm != NULL && rs_ctx->rsm->i != 0 )
2053 {
2054 /* restore current index (R already pointing to rs_ctx->rsm->R) */
2055 i = rs_ctx->rsm->i;
2056 }
2057 else
2058 #endif
2059 {
2060 /* Start with a non-zero point and randomize its coordinates */
2061 i = d;
2062 MBEDTLS_MPI_CHK( ecp_select_comb( grp, R, T, T_size, x[i] ) );
2063 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->Z, 1 ) );
2064 #if defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
2065 if( f_rng != 0 )
2066 #endif
2067 MBEDTLS_MPI_CHK( ecp_randomize_jac( grp, R, f_rng, p_rng ) );
2068 }
2069
2070 while( i != 0 )
2071 {
2072 MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_DBL + MBEDTLS_ECP_OPS_ADD );
2073 --i;
2074
2075 MBEDTLS_MPI_CHK( ecp_double_jac( grp, R, R ) );
2076 MBEDTLS_MPI_CHK( ecp_select_comb( grp, &Txi, T, T_size, x[i] ) );
2077 MBEDTLS_MPI_CHK( ecp_add_mixed( grp, R, R, &Txi ) );
2078 }
2079
2080 cleanup:
2081
2082 mbedtls_ecp_point_free( &Txi );
2083
2084 #if defined(MBEDTLS_ECP_RESTARTABLE)
2085 if( rs_ctx != NULL && rs_ctx->rsm != NULL &&
2086 ret == MBEDTLS_ERR_ECP_IN_PROGRESS )
2087 {
2088 rs_ctx->rsm->i = i;
2089 /* no need to save R, already pointing to rs_ctx->rsm->R */
2090 }
2091 #endif
2092
2093 return( ret );
2094 }
2095
2096 /*
2097 * Recode the scalar to get constant-time comb multiplication
2098 *
2099 * As the actual scalar recoding needs an odd scalar as a starting point,
2100 * this wrapper ensures that by replacing m by N - m if necessary, and
2101 * informs the caller that the result of multiplication will be negated.
2102 *
2103 * This works because we only support large prime order for Short Weierstrass
2104 * curves, so N is always odd hence either m or N - m is.
2105 *
2106 * See ecp_comb_recode_core() for background.
2107 */
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)2108 static int ecp_comb_recode_scalar( const mbedtls_ecp_group *grp,
2109 const mbedtls_mpi *m,
2110 unsigned char k[COMB_MAX_D + 1],
2111 size_t d,
2112 unsigned char w,
2113 unsigned char *parity_trick )
2114 {
2115 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
2116 mbedtls_mpi M, mm;
2117
2118 mbedtls_mpi_init( &M );
2119 mbedtls_mpi_init( &mm );
2120
2121 /* N is always odd (see above), just make extra sure */
2122 if( mbedtls_mpi_get_bit( &grp->N, 0 ) != 1 )
2123 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
2124
2125 /* do we need the parity trick? */
2126 *parity_trick = ( mbedtls_mpi_get_bit( m, 0 ) == 0 );
2127
2128 /* execute parity fix in constant time */
2129 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &M, m ) );
2130 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &mm, &grp->N, m ) );
2131 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &M, &mm, *parity_trick ) );
2132
2133 /* actual scalar recoding */
2134 ecp_comb_recode_core( k, d, w, &M );
2135
2136 cleanup:
2137 mbedtls_mpi_free( &mm );
2138 mbedtls_mpi_free( &M );
2139
2140 return( ret );
2141 }
2142
2143 /*
2144 * Perform comb multiplication (for short Weierstrass curves)
2145 * once the auxiliary table has been pre-computed.
2146 *
2147 * Scalar recoding may use a parity trick that makes us compute -m * P,
2148 * if that is the case we'll need to recover m * P at the end.
2149 */
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)2150 static int ecp_mul_comb_after_precomp( const mbedtls_ecp_group *grp,
2151 mbedtls_ecp_point *R,
2152 const mbedtls_mpi *m,
2153 const mbedtls_ecp_point *T,
2154 unsigned char T_size,
2155 unsigned char w,
2156 size_t d,
2157 int (*f_rng)(void *, unsigned char *, size_t),
2158 void *p_rng,
2159 mbedtls_ecp_restart_ctx *rs_ctx )
2160 {
2161 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
2162 unsigned char parity_trick;
2163 unsigned char k[COMB_MAX_D + 1];
2164 mbedtls_ecp_point *RR = R;
2165
2166 #if defined(MBEDTLS_ECP_RESTARTABLE)
2167 if( rs_ctx != NULL && rs_ctx->rsm != NULL )
2168 {
2169 RR = &rs_ctx->rsm->R;
2170
2171 if( rs_ctx->rsm->state == ecp_rsm_final_norm )
2172 goto final_norm;
2173 }
2174 #endif
2175
2176 MBEDTLS_MPI_CHK( ecp_comb_recode_scalar( grp, m, k, d, w,
2177 &parity_trick ) );
2178 MBEDTLS_MPI_CHK( ecp_mul_comb_core( grp, RR, T, T_size, k, d,
2179 f_rng, p_rng, rs_ctx ) );
2180 MBEDTLS_MPI_CHK( ecp_safe_invert_jac( grp, RR, parity_trick ) );
2181
2182 #if defined(MBEDTLS_ECP_RESTARTABLE)
2183 if( rs_ctx != NULL && rs_ctx->rsm != NULL )
2184 rs_ctx->rsm->state = ecp_rsm_final_norm;
2185
2186 final_norm:
2187 MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_INV );
2188 #endif
2189 /*
2190 * Knowledge of the jacobian coordinates may leak the last few bits of the
2191 * scalar [1], and since our MPI implementation isn't constant-flow,
2192 * inversion (used for coordinate normalization) may leak the full value
2193 * of its input via side-channels [2].
2194 *
2195 * [1] https://eprint.iacr.org/2003/191
2196 * [2] https://eprint.iacr.org/2020/055
2197 *
2198 * Avoid the leak by randomizing coordinates before we normalize them.
2199 */
2200 #if defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
2201 if( f_rng != 0 )
2202 #endif
2203 MBEDTLS_MPI_CHK( ecp_randomize_jac( grp, RR, f_rng, p_rng ) );
2204
2205 MBEDTLS_MPI_CHK( ecp_normalize_jac( grp, RR ) );
2206
2207 #if defined(MBEDTLS_ECP_RESTARTABLE)
2208 if( rs_ctx != NULL && rs_ctx->rsm != NULL )
2209 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, RR ) );
2210 #endif
2211
2212 cleanup:
2213 return( ret );
2214 }
2215
2216 /*
2217 * Pick window size based on curve size and whether we optimize for base point
2218 */
ecp_pick_window_size(const mbedtls_ecp_group * grp,unsigned char p_eq_g)2219 static unsigned char ecp_pick_window_size( const mbedtls_ecp_group *grp,
2220 unsigned char p_eq_g )
2221 {
2222 unsigned char w;
2223
2224 /*
2225 * Minimize the number of multiplications, that is minimize
2226 * 10 * d * w + 18 * 2^(w-1) + 11 * d + 7 * w, with d = ceil( nbits / w )
2227 * (see costs of the various parts, with 1S = 1M)
2228 */
2229 w = grp->nbits >= 384 ? 5 : 4;
2230
2231 /*
2232 * If P == G, pre-compute a bit more, since this may be re-used later.
2233 * Just adding one avoids upping the cost of the first mul too much,
2234 * and the memory cost too.
2235 */
2236 if( p_eq_g )
2237 w++;
2238
2239 /*
2240 * Make sure w is within bounds.
2241 * (The last test is useful only for very small curves in the test suite.)
2242 */
2243 #if( MBEDTLS_ECP_WINDOW_SIZE < 6 )
2244 if( w > MBEDTLS_ECP_WINDOW_SIZE )
2245 w = MBEDTLS_ECP_WINDOW_SIZE;
2246 #endif
2247 if( w >= grp->nbits )
2248 w = 2;
2249
2250 return( w );
2251 }
2252
2253 /*
2254 * Multiplication using the comb method - for curves in short Weierstrass form
2255 *
2256 * This function is mainly responsible for administrative work:
2257 * - managing the restart context if enabled
2258 * - managing the table of precomputed points (passed between the below two
2259 * functions): allocation, computation, ownership tranfer, freeing.
2260 *
2261 * It delegates the actual arithmetic work to:
2262 * ecp_precompute_comb() and ecp_mul_comb_with_precomp()
2263 *
2264 * See comments on ecp_comb_recode_core() regarding the computation strategy.
2265 */
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)2266 static int ecp_mul_comb( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
2267 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
2268 int (*f_rng)(void *, unsigned char *, size_t),
2269 void *p_rng,
2270 mbedtls_ecp_restart_ctx *rs_ctx )
2271 {
2272 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
2273 unsigned char w, p_eq_g, i;
2274 size_t d;
2275 unsigned char T_size = 0, T_ok = 0;
2276 mbedtls_ecp_point *T = NULL;
2277 #if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
2278 ecp_drbg_context drbg_ctx;
2279
2280 ecp_drbg_init( &drbg_ctx );
2281 #endif
2282
2283 ECP_RS_ENTER( rsm );
2284
2285 #if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
2286 if( f_rng == NULL )
2287 {
2288 /* Adjust pointers */
2289 f_rng = &ecp_drbg_random;
2290 #if defined(MBEDTLS_ECP_RESTARTABLE)
2291 if( rs_ctx != NULL && rs_ctx->rsm != NULL )
2292 p_rng = &rs_ctx->rsm->drbg_ctx;
2293 else
2294 #endif
2295 p_rng = &drbg_ctx;
2296
2297 /* Initialize internal DRBG if necessary */
2298 #if defined(MBEDTLS_ECP_RESTARTABLE)
2299 if( rs_ctx == NULL || rs_ctx->rsm == NULL ||
2300 rs_ctx->rsm->drbg_seeded == 0 )
2301 #endif
2302 {
2303 const size_t m_len = ( grp->nbits + 7 ) / 8;
2304 MBEDTLS_MPI_CHK( ecp_drbg_seed( p_rng, m, m_len ) );
2305 }
2306 #if defined(MBEDTLS_ECP_RESTARTABLE)
2307 if( rs_ctx != NULL && rs_ctx->rsm != NULL )
2308 rs_ctx->rsm->drbg_seeded = 1;
2309 #endif
2310 }
2311 #endif /* !MBEDTLS_ECP_NO_INTERNAL_RNG */
2312
2313 /* Is P the base point ? */
2314 #if MBEDTLS_ECP_FIXED_POINT_OPTIM == 1
2315 p_eq_g = ( mbedtls_mpi_cmp_mpi( &P->Y, &grp->G.Y ) == 0 &&
2316 mbedtls_mpi_cmp_mpi( &P->X, &grp->G.X ) == 0 );
2317 #else
2318 p_eq_g = 0;
2319 #endif
2320
2321 /* Pick window size and deduce related sizes */
2322 w = ecp_pick_window_size( grp, p_eq_g );
2323 T_size = 1U << ( w - 1 );
2324 d = ( grp->nbits + w - 1 ) / w;
2325
2326 /* Pre-computed table: do we have it already for the base point? */
2327 if( p_eq_g && grp->T != NULL )
2328 {
2329 /* second pointer to the same table, will be deleted on exit */
2330 T = grp->T;
2331 T_ok = 1;
2332 }
2333 else
2334 #if defined(MBEDTLS_ECP_RESTARTABLE)
2335 /* Pre-computed table: do we have one in progress? complete? */
2336 if( rs_ctx != NULL && rs_ctx->rsm != NULL && rs_ctx->rsm->T != NULL )
2337 {
2338 /* transfer ownership of T from rsm to local function */
2339 T = rs_ctx->rsm->T;
2340 rs_ctx->rsm->T = NULL;
2341 rs_ctx->rsm->T_size = 0;
2342
2343 /* This effectively jumps to the call to mul_comb_after_precomp() */
2344 T_ok = rs_ctx->rsm->state >= ecp_rsm_comb_core;
2345 }
2346 else
2347 #endif
2348 /* Allocate table if we didn't have any */
2349 {
2350 T = mbedtls_calloc( T_size, sizeof( mbedtls_ecp_point ) );
2351 if( T == NULL )
2352 {
2353 ret = MBEDTLS_ERR_ECP_ALLOC_FAILED;
2354 goto cleanup;
2355 }
2356
2357 for( i = 0; i < T_size; i++ )
2358 mbedtls_ecp_point_init( &T[i] );
2359
2360 T_ok = 0;
2361 }
2362
2363 /* Compute table (or finish computing it) if not done already */
2364 if( !T_ok )
2365 {
2366 MBEDTLS_MPI_CHK( ecp_precompute_comb( grp, T, P, w, d, rs_ctx ) );
2367
2368 if( p_eq_g )
2369 {
2370 /* almost transfer ownership of T to the group, but keep a copy of
2371 * the pointer to use for calling the next function more easily */
2372 grp->T = T;
2373 grp->T_size = T_size;
2374 }
2375 }
2376
2377 /* Actual comb multiplication using precomputed points */
2378 MBEDTLS_MPI_CHK( ecp_mul_comb_after_precomp( grp, R, m,
2379 T, T_size, w, d,
2380 f_rng, p_rng, rs_ctx ) );
2381
2382 cleanup:
2383
2384 #if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
2385 ecp_drbg_free( &drbg_ctx );
2386 #endif
2387
2388 /* does T belong to the group? */
2389 if( T == grp->T )
2390 T = NULL;
2391
2392 /* does T belong to the restart context? */
2393 #if defined(MBEDTLS_ECP_RESTARTABLE)
2394 if( rs_ctx != NULL && rs_ctx->rsm != NULL && ret == MBEDTLS_ERR_ECP_IN_PROGRESS && T != NULL )
2395 {
2396 /* transfer ownership of T from local function to rsm */
2397 rs_ctx->rsm->T_size = T_size;
2398 rs_ctx->rsm->T = T;
2399 T = NULL;
2400 }
2401 #endif
2402
2403 /* did T belong to us? then let's destroy it! */
2404 if( T != NULL )
2405 {
2406 for( i = 0; i < T_size; i++ )
2407 mbedtls_ecp_point_free( &T[i] );
2408 mbedtls_free( T );
2409 }
2410
2411 /* don't free R while in progress in case R == P */
2412 #if defined(MBEDTLS_ECP_RESTARTABLE)
2413 if( ret != MBEDTLS_ERR_ECP_IN_PROGRESS )
2414 #endif
2415 /* prevent caller from using invalid value */
2416 if( ret != 0 )
2417 mbedtls_ecp_point_free( R );
2418
2419 ECP_RS_LEAVE( rsm );
2420
2421 return( ret );
2422 }
2423
2424 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
2425
2426 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
2427 /*
2428 * For Montgomery curves, we do all the internal arithmetic in projective
2429 * coordinates. Import/export of points uses only the x coordinates, which is
2430 * internaly represented as X / Z.
2431 *
2432 * For scalar multiplication, we'll use a Montgomery ladder.
2433 */
2434
2435 /*
2436 * Normalize Montgomery x/z coordinates: X = X/Z, Z = 1
2437 * Cost: 1M + 1I
2438 */
ecp_normalize_mxz(const mbedtls_ecp_group * grp,mbedtls_ecp_point * P)2439 static int ecp_normalize_mxz( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P )
2440 {
2441 #if defined(MBEDTLS_ECP_NORMALIZE_MXZ_ALT)
2442 if( mbedtls_internal_ecp_grp_capable( grp ) )
2443 return( mbedtls_internal_ecp_normalize_mxz( grp, P ) );
2444 #endif /* MBEDTLS_ECP_NORMALIZE_MXZ_ALT */
2445
2446 #if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_NORMALIZE_MXZ_ALT)
2447 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
2448 #else
2449 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
2450 MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &P->Z, &P->Z, &grp->P ) );
2451 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &P->X, &P->X, &P->Z ) );
2452 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &P->Z, 1 ) );
2453
2454 cleanup:
2455 return( ret );
2456 #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_NORMALIZE_MXZ_ALT) */
2457 }
2458
2459 /*
2460 * Randomize projective x/z coordinates:
2461 * (X, Z) -> (l X, l Z) for random l
2462 * This is sort of the reverse operation of ecp_normalize_mxz().
2463 *
2464 * This countermeasure was first suggested in [2].
2465 * Cost: 2M
2466 */
ecp_randomize_mxz(const mbedtls_ecp_group * grp,mbedtls_ecp_point * P,int (* f_rng)(void *,unsigned char *,size_t),void * p_rng)2467 static int ecp_randomize_mxz( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P,
2468 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
2469 {
2470 #if defined(MBEDTLS_ECP_RANDOMIZE_MXZ_ALT)
2471 if( mbedtls_internal_ecp_grp_capable( grp ) )
2472 return( mbedtls_internal_ecp_randomize_mxz( grp, P, f_rng, p_rng ) );
2473 #endif /* MBEDTLS_ECP_RANDOMIZE_MXZ_ALT */
2474
2475 #if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_RANDOMIZE_MXZ_ALT)
2476 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
2477 #else
2478 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
2479 mbedtls_mpi l;
2480 mbedtls_mpi_init( &l );
2481
2482 /* Generate l such that 1 < l < p */
2483 MBEDTLS_MPI_CHK( mbedtls_mpi_random( &l, 2, &grp->P, f_rng, p_rng ) );
2484
2485 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &P->X, &P->X, &l ) );
2486 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &P->Z, &P->Z, &l ) );
2487
2488 cleanup:
2489 mbedtls_mpi_free( &l );
2490
2491 if( ret == MBEDTLS_ERR_MPI_NOT_ACCEPTABLE )
2492 ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
2493 return( ret );
2494 #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_RANDOMIZE_MXZ_ALT) */
2495 }
2496
2497 /*
2498 * Double-and-add: R = 2P, S = P + Q, with d = X(P - Q),
2499 * for Montgomery curves in x/z coordinates.
2500 *
2501 * http://www.hyperelliptic.org/EFD/g1p/auto-code/montgom/xz/ladder/mladd-1987-m.op3
2502 * with
2503 * d = X1
2504 * P = (X2, Z2)
2505 * Q = (X3, Z3)
2506 * R = (X4, Z4)
2507 * S = (X5, Z5)
2508 * and eliminating temporary variables tO, ..., t4.
2509 *
2510 * Cost: 5M + 4S
2511 */
ecp_double_add_mxz(const mbedtls_ecp_group * grp,mbedtls_ecp_point * R,mbedtls_ecp_point * S,const mbedtls_ecp_point * P,const mbedtls_ecp_point * Q,const mbedtls_mpi * d)2512 static int ecp_double_add_mxz( const mbedtls_ecp_group *grp,
2513 mbedtls_ecp_point *R, mbedtls_ecp_point *S,
2514 const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q,
2515 const mbedtls_mpi *d )
2516 {
2517 #if defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT)
2518 if( mbedtls_internal_ecp_grp_capable( grp ) )
2519 return( mbedtls_internal_ecp_double_add_mxz( grp, R, S, P, Q, d ) );
2520 #endif /* MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT */
2521
2522 #if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT)
2523 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
2524 #else
2525 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
2526 mbedtls_mpi A, AA, B, BB, E, C, D, DA, CB;
2527
2528 mbedtls_mpi_init( &A ); mbedtls_mpi_init( &AA ); mbedtls_mpi_init( &B );
2529 mbedtls_mpi_init( &BB ); mbedtls_mpi_init( &E ); mbedtls_mpi_init( &C );
2530 mbedtls_mpi_init( &D ); mbedtls_mpi_init( &DA ); mbedtls_mpi_init( &CB );
2531
2532 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &A, &P->X, &P->Z ) );
2533 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &AA, &A, &A ) );
2534 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &B, &P->X, &P->Z ) );
2535 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &BB, &B, &B ) );
2536 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &E, &AA, &BB ) );
2537 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &C, &Q->X, &Q->Z ) );
2538 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &D, &Q->X, &Q->Z ) );
2539 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &DA, &D, &A ) );
2540 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &CB, &C, &B ) );
2541 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &S->X, &DA, &CB ) );
2542 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S->X, &S->X, &S->X ) );
2543 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &S->Z, &DA, &CB ) );
2544 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S->Z, &S->Z, &S->Z ) );
2545 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S->Z, d, &S->Z ) );
2546 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &R->X, &AA, &BB ) );
2547 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &R->Z, &grp->A, &E ) );
2548 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &R->Z, &BB, &R->Z ) );
2549 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &R->Z, &E, &R->Z ) );
2550
2551 cleanup:
2552 mbedtls_mpi_free( &A ); mbedtls_mpi_free( &AA ); mbedtls_mpi_free( &B );
2553 mbedtls_mpi_free( &BB ); mbedtls_mpi_free( &E ); mbedtls_mpi_free( &C );
2554 mbedtls_mpi_free( &D ); mbedtls_mpi_free( &DA ); mbedtls_mpi_free( &CB );
2555
2556 return( ret );
2557 #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT) */
2558 }
2559
2560 /*
2561 * Multiplication with Montgomery ladder in x/z coordinates,
2562 * for curves in Montgomery form
2563 */
ecp_mul_mxz(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)2564 static int ecp_mul_mxz( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
2565 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
2566 int (*f_rng)(void *, unsigned char *, size_t),
2567 void *p_rng )
2568 {
2569 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
2570 size_t i;
2571 unsigned char b;
2572 mbedtls_ecp_point RP;
2573 mbedtls_mpi PX;
2574 #if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
2575 ecp_drbg_context drbg_ctx;
2576
2577 ecp_drbg_init( &drbg_ctx );
2578 #endif
2579 mbedtls_ecp_point_init( &RP ); mbedtls_mpi_init( &PX );
2580
2581 #if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
2582 if( f_rng == NULL )
2583 {
2584 const size_t m_len = ( grp->nbits + 7 ) / 8;
2585 MBEDTLS_MPI_CHK( ecp_drbg_seed( &drbg_ctx, m, m_len ) );
2586 f_rng = &ecp_drbg_random;
2587 p_rng = &drbg_ctx;
2588 }
2589 #endif /* !MBEDTLS_ECP_NO_INTERNAL_RNG */
2590
2591 /* Save PX and read from P before writing to R, in case P == R */
2592 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &PX, &P->X ) );
2593 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( &RP, P ) );
2594
2595 /* Set R to zero in modified x/z coordinates */
2596 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->X, 1 ) );
2597 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->Z, 0 ) );
2598 mbedtls_mpi_free( &R->Y );
2599
2600 /* RP.X might be sligtly larger than P, so reduce it */
2601 MOD_ADD( RP.X );
2602
2603 /* Randomize coordinates of the starting point */
2604 #if defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
2605 if( f_rng != NULL )
2606 #endif
2607 MBEDTLS_MPI_CHK( ecp_randomize_mxz( grp, &RP, f_rng, p_rng ) );
2608
2609 /* Loop invariant: R = result so far, RP = R + P */
2610 i = mbedtls_mpi_bitlen( m ); /* one past the (zero-based) most significant bit */
2611 while( i-- > 0 )
2612 {
2613 b = mbedtls_mpi_get_bit( m, i );
2614 /*
2615 * if (b) R = 2R + P else R = 2R,
2616 * which is:
2617 * if (b) double_add( RP, R, RP, R )
2618 * else double_add( R, RP, R, RP )
2619 * but using safe conditional swaps to avoid leaks
2620 */
2621 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->X, &RP.X, b ) );
2622 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->Z, &RP.Z, b ) );
2623 MBEDTLS_MPI_CHK( ecp_double_add_mxz( grp, R, &RP, R, &RP, &PX ) );
2624 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->X, &RP.X, b ) );
2625 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->Z, &RP.Z, b ) );
2626 }
2627
2628 /*
2629 * Knowledge of the projective coordinates may leak the last few bits of the
2630 * scalar [1], and since our MPI implementation isn't constant-flow,
2631 * inversion (used for coordinate normalization) may leak the full value
2632 * of its input via side-channels [2].
2633 *
2634 * [1] https://eprint.iacr.org/2003/191
2635 * [2] https://eprint.iacr.org/2020/055
2636 *
2637 * Avoid the leak by randomizing coordinates before we normalize them.
2638 */
2639 #if defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
2640 if( f_rng != NULL )
2641 #endif
2642 MBEDTLS_MPI_CHK( ecp_randomize_mxz( grp, R, f_rng, p_rng ) );
2643
2644 MBEDTLS_MPI_CHK( ecp_normalize_mxz( grp, R ) );
2645
2646 cleanup:
2647 #if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
2648 ecp_drbg_free( &drbg_ctx );
2649 #endif
2650
2651 mbedtls_ecp_point_free( &RP ); mbedtls_mpi_free( &PX );
2652
2653 return( ret );
2654 }
2655
2656 #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
2657
2658 /*
2659 * Restartable multiplication R = m * P
2660 */
mbedtls_ecp_mul_restartable(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)2661 int mbedtls_ecp_mul_restartable( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
2662 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
2663 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng,
2664 mbedtls_ecp_restart_ctx *rs_ctx )
2665 {
2666 int ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
2667 #if defined(MBEDTLS_ECP_INTERNAL_ALT)
2668 char is_grp_capable = 0;
2669 #endif
2670 ECP_VALIDATE_RET( grp != NULL );
2671 ECP_VALIDATE_RET( R != NULL );
2672 ECP_VALIDATE_RET( m != NULL );
2673 ECP_VALIDATE_RET( P != NULL );
2674
2675 #if defined(MBEDTLS_ECP_RESTARTABLE)
2676 /* reset ops count for this call if top-level */
2677 if( rs_ctx != NULL && rs_ctx->depth++ == 0 )
2678 rs_ctx->ops_done = 0;
2679 #else
2680 (void) rs_ctx;
2681 #endif
2682
2683 #if defined(MBEDTLS_ECP_INTERNAL_ALT)
2684 if( ( is_grp_capable = mbedtls_internal_ecp_grp_capable( grp ) ) )
2685 MBEDTLS_MPI_CHK( mbedtls_internal_ecp_init( grp ) );
2686 #endif /* MBEDTLS_ECP_INTERNAL_ALT */
2687
2688 #if defined(MBEDTLS_ECP_RESTARTABLE)
2689 /* skip argument check when restarting */
2690 if( rs_ctx == NULL || rs_ctx->rsm == NULL )
2691 #endif
2692 {
2693 /* check_privkey is free */
2694 MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_CHK );
2695
2696 /* Common sanity checks */
2697 MBEDTLS_MPI_CHK( mbedtls_ecp_check_privkey( grp, m ) );
2698 MBEDTLS_MPI_CHK( mbedtls_ecp_check_pubkey( grp, P ) );
2699 }
2700
2701 ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
2702 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
2703 if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY )
2704 MBEDTLS_MPI_CHK( ecp_mul_mxz( grp, R, m, P, f_rng, p_rng ) );
2705 #endif
2706 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
2707 if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
2708 MBEDTLS_MPI_CHK( ecp_mul_comb( grp, R, m, P, f_rng, p_rng, rs_ctx ) );
2709 #endif
2710
2711 cleanup:
2712
2713 #if defined(MBEDTLS_ECP_INTERNAL_ALT)
2714 if( is_grp_capable )
2715 mbedtls_internal_ecp_free( grp );
2716 #endif /* MBEDTLS_ECP_INTERNAL_ALT */
2717
2718 #if defined(MBEDTLS_ECP_RESTARTABLE)
2719 if( rs_ctx != NULL )
2720 rs_ctx->depth--;
2721 #endif
2722
2723 return( ret );
2724 }
2725
2726 /*
2727 * Multiplication R = m * P
2728 */
mbedtls_ecp_mul(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)2729 int mbedtls_ecp_mul( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
2730 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
2731 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
2732 {
2733 ECP_VALIDATE_RET( grp != NULL );
2734 ECP_VALIDATE_RET( R != NULL );
2735 ECP_VALIDATE_RET( m != NULL );
2736 ECP_VALIDATE_RET( P != NULL );
2737 return( mbedtls_ecp_mul_restartable( grp, R, m, P, f_rng, p_rng, NULL ) );
2738 }
2739
2740 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
2741 /*
2742 * Check that an affine point is valid as a public key,
2743 * short weierstrass curves (SEC1 3.2.3.1)
2744 */
ecp_check_pubkey_sw(const mbedtls_ecp_group * grp,const mbedtls_ecp_point * pt)2745 static int ecp_check_pubkey_sw( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt )
2746 {
2747 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
2748 mbedtls_mpi YY, RHS;
2749
2750 /* pt coordinates must be normalized for our checks */
2751 if( mbedtls_mpi_cmp_int( &pt->X, 0 ) < 0 ||
2752 mbedtls_mpi_cmp_int( &pt->Y, 0 ) < 0 ||
2753 mbedtls_mpi_cmp_mpi( &pt->X, &grp->P ) >= 0 ||
2754 mbedtls_mpi_cmp_mpi( &pt->Y, &grp->P ) >= 0 )
2755 return( MBEDTLS_ERR_ECP_INVALID_KEY );
2756
2757 mbedtls_mpi_init( &YY ); mbedtls_mpi_init( &RHS );
2758
2759 /*
2760 * YY = Y^2
2761 * RHS = X (X^2 + A) + B = X^3 + A X + B
2762 */
2763 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &YY, &pt->Y, &pt->Y ) );
2764 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &RHS, &pt->X, &pt->X ) );
2765
2766 /* Special case for A = -3 */
2767 if( grp->A.p == NULL )
2768 {
2769 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &RHS, &RHS, 3 ) ); MOD_SUB( RHS );
2770 }
2771 else
2772 {
2773 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &RHS, &RHS, &grp->A ) );
2774 }
2775
2776 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &RHS, &RHS, &pt->X ) );
2777 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &RHS, &RHS, &grp->B ) );
2778
2779 if( mbedtls_mpi_cmp_mpi( &YY, &RHS ) != 0 )
2780 ret = MBEDTLS_ERR_ECP_INVALID_KEY;
2781
2782 cleanup:
2783
2784 mbedtls_mpi_free( &YY ); mbedtls_mpi_free( &RHS );
2785
2786 return( ret );
2787 }
2788 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
2789
2790 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
2791 /*
2792 * R = m * P with shortcuts for m == 0, m == 1 and m == -1
2793 * NOT constant-time - ONLY for short Weierstrass!
2794 */
mbedtls_ecp_mul_shortcuts(mbedtls_ecp_group * grp,mbedtls_ecp_point * R,const mbedtls_mpi * m,const mbedtls_ecp_point * P,mbedtls_ecp_restart_ctx * rs_ctx)2795 static int mbedtls_ecp_mul_shortcuts( mbedtls_ecp_group *grp,
2796 mbedtls_ecp_point *R,
2797 const mbedtls_mpi *m,
2798 const mbedtls_ecp_point *P,
2799 mbedtls_ecp_restart_ctx *rs_ctx )
2800 {
2801 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
2802
2803 if( mbedtls_mpi_cmp_int( m, 0 ) == 0 )
2804 {
2805 MBEDTLS_MPI_CHK( mbedtls_ecp_set_zero( R ) );
2806 }
2807 else if( mbedtls_mpi_cmp_int( m, 1 ) == 0 )
2808 {
2809 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, P ) );
2810 }
2811 else if( mbedtls_mpi_cmp_int( m, -1 ) == 0 )
2812 {
2813 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, P ) );
2814 if( mbedtls_mpi_cmp_int( &R->Y, 0 ) != 0 )
2815 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &R->Y, &grp->P, &R->Y ) );
2816 }
2817 else
2818 {
2819 MBEDTLS_MPI_CHK( mbedtls_ecp_mul_restartable( grp, R, m, P,
2820 NULL, NULL, rs_ctx ) );
2821 }
2822
2823 cleanup:
2824 return( ret );
2825 }
2826
2827 /*
2828 * Restartable linear combination
2829 * NOT constant-time
2830 */
mbedtls_ecp_muladd_restartable(mbedtls_ecp_group * grp,mbedtls_ecp_point * R,const mbedtls_mpi * m,const mbedtls_ecp_point * P,const mbedtls_mpi * n,const mbedtls_ecp_point * Q,mbedtls_ecp_restart_ctx * rs_ctx)2831 int mbedtls_ecp_muladd_restartable(
2832 mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
2833 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
2834 const mbedtls_mpi *n, const mbedtls_ecp_point *Q,
2835 mbedtls_ecp_restart_ctx *rs_ctx )
2836 {
2837 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
2838 mbedtls_ecp_point mP;
2839 mbedtls_ecp_point *pmP = &mP;
2840 mbedtls_ecp_point *pR = R;
2841 #if defined(MBEDTLS_ECP_INTERNAL_ALT)
2842 char is_grp_capable = 0;
2843 #endif
2844 ECP_VALIDATE_RET( grp != NULL );
2845 ECP_VALIDATE_RET( R != NULL );
2846 ECP_VALIDATE_RET( m != NULL );
2847 ECP_VALIDATE_RET( P != NULL );
2848 ECP_VALIDATE_RET( n != NULL );
2849 ECP_VALIDATE_RET( Q != NULL );
2850
2851 if( mbedtls_ecp_get_type( grp ) != MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
2852 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
2853
2854 mbedtls_ecp_point_init( &mP );
2855
2856 ECP_RS_ENTER( ma );
2857
2858 #if defined(MBEDTLS_ECP_RESTARTABLE)
2859 if( rs_ctx != NULL && rs_ctx->ma != NULL )
2860 {
2861 /* redirect intermediate results to restart context */
2862 pmP = &rs_ctx->ma->mP;
2863 pR = &rs_ctx->ma->R;
2864
2865 /* jump to next operation */
2866 if( rs_ctx->ma->state == ecp_rsma_mul2 )
2867 goto mul2;
2868 if( rs_ctx->ma->state == ecp_rsma_add )
2869 goto add;
2870 if( rs_ctx->ma->state == ecp_rsma_norm )
2871 goto norm;
2872 }
2873 #endif /* MBEDTLS_ECP_RESTARTABLE */
2874
2875 MBEDTLS_MPI_CHK( mbedtls_ecp_mul_shortcuts( grp, pmP, m, P, rs_ctx ) );
2876 #if defined(MBEDTLS_ECP_RESTARTABLE)
2877 if( rs_ctx != NULL && rs_ctx->ma != NULL )
2878 rs_ctx->ma->state = ecp_rsma_mul2;
2879
2880 mul2:
2881 #endif
2882 MBEDTLS_MPI_CHK( mbedtls_ecp_mul_shortcuts( grp, pR, n, Q, rs_ctx ) );
2883
2884 #if defined(MBEDTLS_ECP_INTERNAL_ALT)
2885 if( ( is_grp_capable = mbedtls_internal_ecp_grp_capable( grp ) ) )
2886 MBEDTLS_MPI_CHK( mbedtls_internal_ecp_init( grp ) );
2887 #endif /* MBEDTLS_ECP_INTERNAL_ALT */
2888
2889 #if defined(MBEDTLS_ECP_RESTARTABLE)
2890 if( rs_ctx != NULL && rs_ctx->ma != NULL )
2891 rs_ctx->ma->state = ecp_rsma_add;
2892
2893 add:
2894 #endif
2895 MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_ADD );
2896 MBEDTLS_MPI_CHK( ecp_add_mixed( grp, pR, pmP, pR ) );
2897 #if defined(MBEDTLS_ECP_RESTARTABLE)
2898 if( rs_ctx != NULL && rs_ctx->ma != NULL )
2899 rs_ctx->ma->state = ecp_rsma_norm;
2900
2901 norm:
2902 #endif
2903 MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_INV );
2904 MBEDTLS_MPI_CHK( ecp_normalize_jac( grp, pR ) );
2905
2906 #if defined(MBEDTLS_ECP_RESTARTABLE)
2907 if( rs_ctx != NULL && rs_ctx->ma != NULL )
2908 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, pR ) );
2909 #endif
2910
2911 cleanup:
2912 #if defined(MBEDTLS_ECP_INTERNAL_ALT)
2913 if( is_grp_capable )
2914 mbedtls_internal_ecp_free( grp );
2915 #endif /* MBEDTLS_ECP_INTERNAL_ALT */
2916
2917 mbedtls_ecp_point_free( &mP );
2918
2919 ECP_RS_LEAVE( ma );
2920
2921 return( ret );
2922 }
2923
2924 /*
2925 * Linear combination
2926 * NOT constant-time
2927 */
mbedtls_ecp_muladd(mbedtls_ecp_group * grp,mbedtls_ecp_point * R,const mbedtls_mpi * m,const mbedtls_ecp_point * P,const mbedtls_mpi * n,const mbedtls_ecp_point * Q)2928 int mbedtls_ecp_muladd( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
2929 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
2930 const mbedtls_mpi *n, const mbedtls_ecp_point *Q )
2931 {
2932 ECP_VALIDATE_RET( grp != NULL );
2933 ECP_VALIDATE_RET( R != NULL );
2934 ECP_VALIDATE_RET( m != NULL );
2935 ECP_VALIDATE_RET( P != NULL );
2936 ECP_VALIDATE_RET( n != NULL );
2937 ECP_VALIDATE_RET( Q != NULL );
2938 return( mbedtls_ecp_muladd_restartable( grp, R, m, P, n, Q, NULL ) );
2939 }
2940 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
2941
2942 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
2943 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
2944 #define ECP_MPI_INIT(s, n, p) {s, 0, (n), (mbedtls_mpi_uint *)(p)}
2945 #define ECP_MPI_INIT_ARRAY(x) \
2946 ECP_MPI_INIT(1, sizeof(x) / sizeof(mbedtls_mpi_uint), x)
2947 /*
2948 * Constants for the two points other than 0, 1, -1 (mod p) in
2949 * https://cr.yp.to/ecdh.html#validate
2950 * See ecp_check_pubkey_x25519().
2951 */
2952 static const mbedtls_mpi_uint x25519_bad_point_1[] = {
2953 MBEDTLS_BYTES_TO_T_UINT_8( 0xe0, 0xeb, 0x7a, 0x7c, 0x3b, 0x41, 0xb8, 0xae ),
2954 MBEDTLS_BYTES_TO_T_UINT_8( 0x16, 0x56, 0xe3, 0xfa, 0xf1, 0x9f, 0xc4, 0x6a ),
2955 MBEDTLS_BYTES_TO_T_UINT_8( 0xda, 0x09, 0x8d, 0xeb, 0x9c, 0x32, 0xb1, 0xfd ),
2956 MBEDTLS_BYTES_TO_T_UINT_8( 0x86, 0x62, 0x05, 0x16, 0x5f, 0x49, 0xb8, 0x00 ),
2957 };
2958 static const mbedtls_mpi_uint x25519_bad_point_2[] = {
2959 MBEDTLS_BYTES_TO_T_UINT_8( 0x5f, 0x9c, 0x95, 0xbc, 0xa3, 0x50, 0x8c, 0x24 ),
2960 MBEDTLS_BYTES_TO_T_UINT_8( 0xb1, 0xd0, 0xb1, 0x55, 0x9c, 0x83, 0xef, 0x5b ),
2961 MBEDTLS_BYTES_TO_T_UINT_8( 0x04, 0x44, 0x5c, 0xc4, 0x58, 0x1c, 0x8e, 0x86 ),
2962 MBEDTLS_BYTES_TO_T_UINT_8( 0xd8, 0x22, 0x4e, 0xdd, 0xd0, 0x9f, 0x11, 0x57 ),
2963 };
2964 static const mbedtls_mpi ecp_x25519_bad_point_1 = ECP_MPI_INIT_ARRAY(
2965 x25519_bad_point_1 );
2966 static const mbedtls_mpi ecp_x25519_bad_point_2 = ECP_MPI_INIT_ARRAY(
2967 x25519_bad_point_2 );
2968 #endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */
2969
2970 /*
2971 * Check that the input point is not one of the low-order points.
2972 * This is recommended by the "May the Fourth" paper:
2973 * https://eprint.iacr.org/2017/806.pdf
2974 * Those points are never sent by an honest peer.
2975 */
ecp_check_bad_points_mx(const mbedtls_mpi * X,const mbedtls_mpi * P,const mbedtls_ecp_group_id grp_id)2976 static int ecp_check_bad_points_mx( const mbedtls_mpi *X, const mbedtls_mpi *P,
2977 const mbedtls_ecp_group_id grp_id )
2978 {
2979 int ret;
2980 mbedtls_mpi XmP;
2981
2982 mbedtls_mpi_init( &XmP );
2983
2984 /* Reduce X mod P so that we only need to check values less than P.
2985 * We know X < 2^256 so we can proceed by subtraction. */
2986 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &XmP, X ) );
2987 while( mbedtls_mpi_cmp_mpi( &XmP, P ) >= 0 )
2988 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &XmP, &XmP, P ) );
2989
2990 /* Check against the known bad values that are less than P. For Curve448
2991 * these are 0, 1 and -1. For Curve25519 we check the values less than P
2992 * from the following list: https://cr.yp.to/ecdh.html#validate */
2993 if( mbedtls_mpi_cmp_int( &XmP, 1 ) <= 0 ) /* takes care of 0 and 1 */
2994 {
2995 ret = MBEDTLS_ERR_ECP_INVALID_KEY;
2996 goto cleanup;
2997 }
2998
2999 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
3000 if( grp_id == MBEDTLS_ECP_DP_CURVE25519 )
3001 {
3002 if( mbedtls_mpi_cmp_mpi( &XmP, &ecp_x25519_bad_point_1 ) == 0 )
3003 {
3004 ret = MBEDTLS_ERR_ECP_INVALID_KEY;
3005 goto cleanup;
3006 }
3007
3008 if( mbedtls_mpi_cmp_mpi( &XmP, &ecp_x25519_bad_point_2 ) == 0 )
3009 {
3010 ret = MBEDTLS_ERR_ECP_INVALID_KEY;
3011 goto cleanup;
3012 }
3013 }
3014 #else
3015 (void) grp_id;
3016 #endif
3017
3018 /* Final check: check if XmP + 1 is P (final because it changes XmP!) */
3019 MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( &XmP, &XmP, 1 ) );
3020 if( mbedtls_mpi_cmp_mpi( &XmP, P ) == 0 )
3021 {
3022 ret = MBEDTLS_ERR_ECP_INVALID_KEY;
3023 goto cleanup;
3024 }
3025
3026 ret = 0;
3027
3028 cleanup:
3029 mbedtls_mpi_free( &XmP );
3030
3031 return( ret );
3032 }
3033
3034 /*
3035 * Check validity of a public key for Montgomery curves with x-only schemes
3036 */
ecp_check_pubkey_mx(const mbedtls_ecp_group * grp,const mbedtls_ecp_point * pt)3037 static int ecp_check_pubkey_mx( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt )
3038 {
3039 /* [Curve25519 p. 5] Just check X is the correct number of bytes */
3040 /* Allow any public value, if it's too big then we'll just reduce it mod p
3041 * (RFC 7748 sec. 5 para. 3). */
3042 if( mbedtls_mpi_size( &pt->X ) > ( grp->nbits + 7 ) / 8 )
3043 return( MBEDTLS_ERR_ECP_INVALID_KEY );
3044
3045 /* Implicit in all standards (as they don't consider negative numbers):
3046 * X must be non-negative. This is normally ensured by the way it's
3047 * encoded for transmission, but let's be extra sure. */
3048 if( mbedtls_mpi_cmp_int( &pt->X, 0 ) < 0 )
3049 return( MBEDTLS_ERR_ECP_INVALID_KEY );
3050
3051 return( ecp_check_bad_points_mx( &pt->X, &grp->P, grp->id ) );
3052 }
3053 #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
3054
3055 /*
3056 * Check that a point is valid as a public key
3057 */
mbedtls_ecp_check_pubkey(const mbedtls_ecp_group * grp,const mbedtls_ecp_point * pt)3058 int mbedtls_ecp_check_pubkey( const mbedtls_ecp_group *grp,
3059 const mbedtls_ecp_point *pt )
3060 {
3061 ECP_VALIDATE_RET( grp != NULL );
3062 ECP_VALIDATE_RET( pt != NULL );
3063
3064 /* Must use affine coordinates */
3065 if( mbedtls_mpi_cmp_int( &pt->Z, 1 ) != 0 )
3066 return( MBEDTLS_ERR_ECP_INVALID_KEY );
3067
3068 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
3069 if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY )
3070 return( ecp_check_pubkey_mx( grp, pt ) );
3071 #endif
3072 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
3073 if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
3074 return( ecp_check_pubkey_sw( grp, pt ) );
3075 #endif
3076 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
3077 }
3078
3079 /*
3080 * Check that an mbedtls_mpi is valid as a private key
3081 */
mbedtls_ecp_check_privkey(const mbedtls_ecp_group * grp,const mbedtls_mpi * d)3082 int mbedtls_ecp_check_privkey( const mbedtls_ecp_group *grp,
3083 const mbedtls_mpi *d )
3084 {
3085 ECP_VALIDATE_RET( grp != NULL );
3086 ECP_VALIDATE_RET( d != NULL );
3087
3088 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
3089 if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY )
3090 {
3091 /* see RFC 7748 sec. 5 para. 5 */
3092 if( mbedtls_mpi_get_bit( d, 0 ) != 0 ||
3093 mbedtls_mpi_get_bit( d, 1 ) != 0 ||
3094 mbedtls_mpi_bitlen( d ) - 1 != grp->nbits ) /* mbedtls_mpi_bitlen is one-based! */
3095 return( MBEDTLS_ERR_ECP_INVALID_KEY );
3096
3097 /* see [Curve25519] page 5 */
3098 if( grp->nbits == 254 && mbedtls_mpi_get_bit( d, 2 ) != 0 )
3099 return( MBEDTLS_ERR_ECP_INVALID_KEY );
3100
3101 return( 0 );
3102 }
3103 #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
3104 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
3105 if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
3106 {
3107 /* see SEC1 3.2 */
3108 if( mbedtls_mpi_cmp_int( d, 1 ) < 0 ||
3109 mbedtls_mpi_cmp_mpi( d, &grp->N ) >= 0 )
3110 return( MBEDTLS_ERR_ECP_INVALID_KEY );
3111 else
3112 return( 0 );
3113 }
3114 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
3115
3116 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
3117 }
3118
3119 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
3120 MBEDTLS_STATIC_TESTABLE
mbedtls_ecp_gen_privkey_mx(size_t high_bit,mbedtls_mpi * d,int (* f_rng)(void *,unsigned char *,size_t),void * p_rng)3121 int mbedtls_ecp_gen_privkey_mx( size_t high_bit,
3122 mbedtls_mpi *d,
3123 int (*f_rng)(void *, unsigned char *, size_t),
3124 void *p_rng )
3125 {
3126 int ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
3127 size_t n_random_bytes = high_bit / 8 + 1;
3128
3129 /* [Curve25519] page 5 */
3130 /* Generate a (high_bit+1)-bit random number by generating just enough
3131 * random bytes, then shifting out extra bits from the top (necessary
3132 * when (high_bit+1) is not a multiple of 8). */
3133 MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( d, n_random_bytes,
3134 f_rng, p_rng ) );
3135 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( d, 8 * n_random_bytes - high_bit - 1 ) );
3136
3137 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, high_bit, 1 ) );
3138
3139 /* Make sure the last two bits are unset for Curve448, three bits for
3140 Curve25519 */
3141 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 0, 0 ) );
3142 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 1, 0 ) );
3143 if( high_bit == 254 )
3144 {
3145 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 2, 0 ) );
3146 }
3147
3148 cleanup:
3149 return( ret );
3150 }
3151 #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
3152
3153 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
mbedtls_ecp_gen_privkey_sw(const mbedtls_mpi * N,mbedtls_mpi * d,int (* f_rng)(void *,unsigned char *,size_t),void * p_rng)3154 static int mbedtls_ecp_gen_privkey_sw(
3155 const mbedtls_mpi *N, mbedtls_mpi *d,
3156 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
3157 {
3158 int ret = mbedtls_mpi_random( d, 1, N, f_rng, p_rng );
3159 switch( ret )
3160 {
3161 case MBEDTLS_ERR_MPI_NOT_ACCEPTABLE:
3162 return( MBEDTLS_ERR_ECP_RANDOM_FAILED );
3163 default:
3164 return( ret );
3165 }
3166 }
3167 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
3168
3169 /*
3170 * Generate a private key
3171 */
mbedtls_ecp_gen_privkey(const mbedtls_ecp_group * grp,mbedtls_mpi * d,int (* f_rng)(void *,unsigned char *,size_t),void * p_rng)3172 int mbedtls_ecp_gen_privkey( const mbedtls_ecp_group *grp,
3173 mbedtls_mpi *d,
3174 int (*f_rng)(void *, unsigned char *, size_t),
3175 void *p_rng )
3176 {
3177 ECP_VALIDATE_RET( grp != NULL );
3178 ECP_VALIDATE_RET( d != NULL );
3179 ECP_VALIDATE_RET( f_rng != NULL );
3180
3181 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
3182 if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY )
3183 return( mbedtls_ecp_gen_privkey_mx( grp->nbits, d, f_rng, p_rng ) );
3184 #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
3185
3186 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
3187 if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
3188 return( mbedtls_ecp_gen_privkey_sw( &grp->N, d, f_rng, p_rng ) );
3189 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
3190
3191 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
3192 }
3193
3194 /*
3195 * Generate a keypair with configurable base point
3196 */
mbedtls_ecp_gen_keypair_base(mbedtls_ecp_group * grp,const mbedtls_ecp_point * G,mbedtls_mpi * d,mbedtls_ecp_point * Q,int (* f_rng)(void *,unsigned char *,size_t),void * p_rng)3197 int mbedtls_ecp_gen_keypair_base( mbedtls_ecp_group *grp,
3198 const mbedtls_ecp_point *G,
3199 mbedtls_mpi *d, mbedtls_ecp_point *Q,
3200 int (*f_rng)(void *, unsigned char *, size_t),
3201 void *p_rng )
3202 {
3203 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
3204 ECP_VALIDATE_RET( grp != NULL );
3205 ECP_VALIDATE_RET( d != NULL );
3206 ECP_VALIDATE_RET( G != NULL );
3207 ECP_VALIDATE_RET( Q != NULL );
3208 ECP_VALIDATE_RET( f_rng != NULL );
3209
3210 MBEDTLS_MPI_CHK( mbedtls_ecp_gen_privkey( grp, d, f_rng, p_rng ) );
3211 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( grp, Q, d, G, f_rng, p_rng ) );
3212
3213 cleanup:
3214 return( ret );
3215 }
3216
3217 /*
3218 * Generate key pair, wrapper for conventional base point
3219 */
mbedtls_ecp_gen_keypair(mbedtls_ecp_group * grp,mbedtls_mpi * d,mbedtls_ecp_point * Q,int (* f_rng)(void *,unsigned char *,size_t),void * p_rng)3220 int mbedtls_ecp_gen_keypair( mbedtls_ecp_group *grp,
3221 mbedtls_mpi *d, mbedtls_ecp_point *Q,
3222 int (*f_rng)(void *, unsigned char *, size_t),
3223 void *p_rng )
3224 {
3225 ECP_VALIDATE_RET( grp != NULL );
3226 ECP_VALIDATE_RET( d != NULL );
3227 ECP_VALIDATE_RET( Q != NULL );
3228 ECP_VALIDATE_RET( f_rng != NULL );
3229
3230 return( mbedtls_ecp_gen_keypair_base( grp, &grp->G, d, Q, f_rng, p_rng ) );
3231 }
3232
3233 /*
3234 * Generate a keypair, prettier wrapper
3235 */
mbedtls_ecp_gen_key(mbedtls_ecp_group_id grp_id,mbedtls_ecp_keypair * key,int (* f_rng)(void *,unsigned char *,size_t),void * p_rng)3236 int mbedtls_ecp_gen_key( mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key,
3237 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
3238 {
3239 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
3240 ECP_VALIDATE_RET( key != NULL );
3241 ECP_VALIDATE_RET( f_rng != NULL );
3242
3243 if( ( ret = mbedtls_ecp_group_load( &key->grp, grp_id ) ) != 0 )
3244 return( ret );
3245
3246 return( mbedtls_ecp_gen_keypair( &key->grp, &key->d, &key->Q, f_rng, p_rng ) );
3247 }
3248
3249 #define ECP_CURVE25519_KEY_SIZE 32
3250 /*
3251 * Read a private key.
3252 */
mbedtls_ecp_read_key(mbedtls_ecp_group_id grp_id,mbedtls_ecp_keypair * key,const unsigned char * buf,size_t buflen)3253 int mbedtls_ecp_read_key( mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key,
3254 const unsigned char *buf, size_t buflen )
3255 {
3256 int ret = 0;
3257
3258 ECP_VALIDATE_RET( key != NULL );
3259 ECP_VALIDATE_RET( buf != NULL );
3260
3261 if( ( ret = mbedtls_ecp_group_load( &key->grp, grp_id ) ) != 0 )
3262 return( ret );
3263
3264 ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
3265
3266 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
3267 if( mbedtls_ecp_get_type( &key->grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY )
3268 {
3269 /*
3270 * If it is Curve25519 curve then mask the key as mandated by RFC7748
3271 */
3272 if( grp_id == MBEDTLS_ECP_DP_CURVE25519 )
3273 {
3274 if( buflen != ECP_CURVE25519_KEY_SIZE )
3275 return MBEDTLS_ERR_ECP_INVALID_KEY;
3276
3277 MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary_le( &key->d, buf, buflen ) );
3278
3279 /* Set the three least significant bits to 0 */
3280 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &key->d, 0, 0 ) );
3281 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &key->d, 1, 0 ) );
3282 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &key->d, 2, 0 ) );
3283
3284 /* Set the most significant bit to 0 */
3285 MBEDTLS_MPI_CHK(
3286 mbedtls_mpi_set_bit( &key->d,
3287 ECP_CURVE25519_KEY_SIZE * 8 - 1, 0 )
3288 );
3289
3290 /* Set the second most significant bit to 1 */
3291 MBEDTLS_MPI_CHK(
3292 mbedtls_mpi_set_bit( &key->d,
3293 ECP_CURVE25519_KEY_SIZE * 8 - 2, 1 )
3294 );
3295 }
3296 else
3297 ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
3298 }
3299
3300 #endif
3301 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
3302 if( mbedtls_ecp_get_type( &key->grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
3303 {
3304 MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &key->d, buf, buflen ) );
3305
3306 MBEDTLS_MPI_CHK( mbedtls_ecp_check_privkey( &key->grp, &key->d ) );
3307 }
3308
3309 #endif
3310 cleanup:
3311
3312 if( ret != 0 )
3313 mbedtls_mpi_free( &key->d );
3314
3315 return( ret );
3316 }
3317
3318 /*
3319 * Write a private key.
3320 */
mbedtls_ecp_write_key(mbedtls_ecp_keypair * key,unsigned char * buf,size_t buflen)3321 int mbedtls_ecp_write_key( mbedtls_ecp_keypair *key,
3322 unsigned char *buf, size_t buflen )
3323 {
3324 int ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
3325
3326 ECP_VALIDATE_RET( key != NULL );
3327 ECP_VALIDATE_RET( buf != NULL );
3328
3329 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
3330 if( mbedtls_ecp_get_type( &key->grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY )
3331 {
3332 if( key->grp.id == MBEDTLS_ECP_DP_CURVE25519 )
3333 {
3334 if( buflen < ECP_CURVE25519_KEY_SIZE )
3335 return MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL;
3336
3337 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary_le( &key->d, buf, buflen ) );
3338 }
3339 else
3340 ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
3341 }
3342
3343 #endif
3344 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
3345 if( mbedtls_ecp_get_type( &key->grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
3346 {
3347 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &key->d, buf, buflen ) );
3348 }
3349
3350 #endif
3351 cleanup:
3352
3353 return( ret );
3354 }
3355
3356
3357 /*
3358 * Check a public-private key pair
3359 */
mbedtls_ecp_check_pub_priv(const mbedtls_ecp_keypair * pub,const mbedtls_ecp_keypair * prv)3360 int mbedtls_ecp_check_pub_priv( const mbedtls_ecp_keypair *pub, const mbedtls_ecp_keypair *prv )
3361 {
3362 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
3363 mbedtls_ecp_point Q;
3364 mbedtls_ecp_group grp;
3365 ECP_VALIDATE_RET( pub != NULL );
3366 ECP_VALIDATE_RET( prv != NULL );
3367
3368 if( pub->grp.id == MBEDTLS_ECP_DP_NONE ||
3369 pub->grp.id != prv->grp.id ||
3370 mbedtls_mpi_cmp_mpi( &pub->Q.X, &prv->Q.X ) ||
3371 mbedtls_mpi_cmp_mpi( &pub->Q.Y, &prv->Q.Y ) ||
3372 mbedtls_mpi_cmp_mpi( &pub->Q.Z, &prv->Q.Z ) )
3373 {
3374 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
3375 }
3376
3377 mbedtls_ecp_point_init( &Q );
3378 mbedtls_ecp_group_init( &grp );
3379
3380 /* mbedtls_ecp_mul() needs a non-const group... */
3381 mbedtls_ecp_group_copy( &grp, &prv->grp );
3382
3383 /* Also checks d is valid */
3384 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &Q, &prv->d, &prv->grp.G, NULL, NULL ) );
3385
3386 if( mbedtls_mpi_cmp_mpi( &Q.X, &prv->Q.X ) ||
3387 mbedtls_mpi_cmp_mpi( &Q.Y, &prv->Q.Y ) ||
3388 mbedtls_mpi_cmp_mpi( &Q.Z, &prv->Q.Z ) )
3389 {
3390 ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
3391 goto cleanup;
3392 }
3393
3394 cleanup:
3395 mbedtls_ecp_point_free( &Q );
3396 mbedtls_ecp_group_free( &grp );
3397
3398 return( ret );
3399 }
3400
3401 #if defined(MBEDTLS_SELF_TEST)
3402
3403 /* Adjust the exponent to be a valid private point for the specified curve.
3404 * This is sometimes necessary because we use a single set of exponents
3405 * for all curves but the validity of values depends on the curve. */
self_test_adjust_exponent(const mbedtls_ecp_group * grp,mbedtls_mpi * m)3406 static int self_test_adjust_exponent( const mbedtls_ecp_group *grp,
3407 mbedtls_mpi *m )
3408 {
3409 int ret = 0;
3410 switch( grp->id )
3411 {
3412 /* If Curve25519 is available, then that's what we use for the
3413 * Montgomery test, so we don't need the adjustment code. */
3414 #if ! defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
3415 #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
3416 case MBEDTLS_ECP_DP_CURVE448:
3417 /* Move highest bit from 254 to N-1. Setting bit N-1 is
3418 * necessary to enforce the highest-bit-set constraint. */
3419 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( m, 254, 0 ) );
3420 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( m, grp->nbits, 1 ) );
3421 /* Copy second-highest bit from 253 to N-2. This is not
3422 * necessary but improves the test variety a bit. */
3423 MBEDTLS_MPI_CHK(
3424 mbedtls_mpi_set_bit( m, grp->nbits - 1,
3425 mbedtls_mpi_get_bit( m, 253 ) ) );
3426 break;
3427 #endif
3428 #endif /* ! defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) */
3429 default:
3430 /* Non-Montgomery curves and Curve25519 need no adjustment. */
3431 (void) grp;
3432 (void) m;
3433 goto cleanup;
3434 }
3435 cleanup:
3436 return( ret );
3437 }
3438
3439 /* Calculate R = m.P for each m in exponents. Check that the number of
3440 * basic operations doesn't depend on the value of m. */
self_test_point(int verbose,mbedtls_ecp_group * grp,mbedtls_ecp_point * R,mbedtls_mpi * m,const mbedtls_ecp_point * P,const char * const * exponents,size_t n_exponents)3441 static int self_test_point( int verbose,
3442 mbedtls_ecp_group *grp,
3443 mbedtls_ecp_point *R,
3444 mbedtls_mpi *m,
3445 const mbedtls_ecp_point *P,
3446 const char *const *exponents,
3447 size_t n_exponents )
3448 {
3449 int ret = 0;
3450 size_t i = 0;
3451 unsigned long add_c_prev, dbl_c_prev, mul_c_prev;
3452 add_count = 0;
3453 dbl_count = 0;
3454 mul_count = 0;
3455
3456 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( m, 16, exponents[0] ) );
3457 MBEDTLS_MPI_CHK( self_test_adjust_exponent( grp, m ) );
3458 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( grp, R, m, P, NULL, NULL ) );
3459
3460 for( i = 1; i < n_exponents; i++ )
3461 {
3462 add_c_prev = add_count;
3463 dbl_c_prev = dbl_count;
3464 mul_c_prev = mul_count;
3465 add_count = 0;
3466 dbl_count = 0;
3467 mul_count = 0;
3468
3469 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( m, 16, exponents[i] ) );
3470 MBEDTLS_MPI_CHK( self_test_adjust_exponent( grp, m ) );
3471 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( grp, R, m, P, NULL, NULL ) );
3472
3473 if( add_count != add_c_prev ||
3474 dbl_count != dbl_c_prev ||
3475 mul_count != mul_c_prev )
3476 {
3477 ret = 1;
3478 break;
3479 }
3480 }
3481
3482 cleanup:
3483 if( verbose != 0 )
3484 {
3485 if( ret != 0 )
3486 mbedtls_printf( "failed (%u)\n", (unsigned int) i );
3487 else
3488 mbedtls_printf( "passed\n" );
3489 }
3490 return( ret );
3491 }
3492
3493 /*
3494 * Checkup routine
3495 */
mbedtls_ecp_self_test(int verbose)3496 int mbedtls_ecp_self_test( int verbose )
3497 {
3498 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
3499 mbedtls_ecp_group grp;
3500 mbedtls_ecp_point R, P;
3501 mbedtls_mpi m;
3502
3503 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
3504 /* Exponents especially adapted for secp192k1, which has the lowest
3505 * order n of all supported curves (secp192r1 is in a slightly larger
3506 * field but the order of its base point is slightly smaller). */
3507 const char *sw_exponents[] =
3508 {
3509 "000000000000000000000000000000000000000000000001", /* one */
3510 "FFFFFFFFFFFFFFFFFFFFFFFE26F2FC170F69466A74DEFD8C", /* n - 1 */
3511 "5EA6F389A38B8BC81E767753B15AA5569E1782E30ABE7D25", /* random */
3512 "400000000000000000000000000000000000000000000000", /* one and zeros */
3513 "7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", /* all ones */
3514 "555555555555555555555555555555555555555555555555", /* 101010... */
3515 };
3516 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
3517 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
3518 const char *m_exponents[] =
3519 {
3520 /* Valid private values for Curve25519. In a build with Curve448
3521 * but not Curve25519, they will be adjusted in
3522 * self_test_adjust_exponent(). */
3523 "4000000000000000000000000000000000000000000000000000000000000000",
3524 "5C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C30",
3525 "5715ECCE24583F7A7023C24164390586842E816D7280A49EF6DF4EAE6B280BF8",
3526 "41A2B017516F6D254E1F002BCCBADD54BE30F8CEC737A0E912B4963B6BA74460",
3527 "5555555555555555555555555555555555555555555555555555555555555550",
3528 "7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF8",
3529 };
3530 #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
3531
3532 mbedtls_ecp_group_init( &grp );
3533 mbedtls_ecp_point_init( &R );
3534 mbedtls_ecp_point_init( &P );
3535 mbedtls_mpi_init( &m );
3536
3537 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
3538 /* Use secp192r1 if available, or any available curve */
3539 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
3540 MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, MBEDTLS_ECP_DP_SECP192R1 ) );
3541 #else
3542 MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, mbedtls_ecp_curve_list()->grp_id ) );
3543 #endif
3544
3545 if( verbose != 0 )
3546 mbedtls_printf( " ECP SW test #1 (constant op_count, base point G): " );
3547 /* Do a dummy multiplication first to trigger precomputation */
3548 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &m, 2 ) );
3549 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &P, &m, &grp.G, NULL, NULL ) );
3550 ret = self_test_point( verbose,
3551 &grp, &R, &m, &grp.G,
3552 sw_exponents,
3553 sizeof( sw_exponents ) / sizeof( sw_exponents[0] ));
3554 if( ret != 0 )
3555 goto cleanup;
3556
3557 if( verbose != 0 )
3558 mbedtls_printf( " ECP SW test #2 (constant op_count, other point): " );
3559 /* We computed P = 2G last time, use it */
3560 ret = self_test_point( verbose,
3561 &grp, &R, &m, &P,
3562 sw_exponents,
3563 sizeof( sw_exponents ) / sizeof( sw_exponents[0] ));
3564 if( ret != 0 )
3565 goto cleanup;
3566
3567 mbedtls_ecp_group_free( &grp );
3568 mbedtls_ecp_point_free( &R );
3569 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
3570
3571 #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
3572 if( verbose != 0 )
3573 mbedtls_printf( " ECP Montgomery test (constant op_count): " );
3574 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
3575 MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, MBEDTLS_ECP_DP_CURVE25519 ) );
3576 #elif defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
3577 MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, MBEDTLS_ECP_DP_CURVE448 ) );
3578 #else
3579 #error "MBEDTLS_ECP_MONTGOMERY_ENABLED is defined, but no curve is supported for self-test"
3580 #endif
3581 ret = self_test_point( verbose,
3582 &grp, &R, &m, &grp.G,
3583 m_exponents,
3584 sizeof( m_exponents ) / sizeof( m_exponents[0] ));
3585 if( ret != 0 )
3586 goto cleanup;
3587 #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
3588
3589 cleanup:
3590
3591 if( ret < 0 && verbose != 0 )
3592 mbedtls_printf( "Unexpected error, return code = %08X\n", (unsigned int) ret );
3593
3594 mbedtls_ecp_group_free( &grp );
3595 mbedtls_ecp_point_free( &R );
3596 mbedtls_ecp_point_free( &P );
3597 mbedtls_mpi_free( &m );
3598
3599 if( verbose != 0 )
3600 mbedtls_printf( "\n" );
3601
3602 return( ret );
3603 }
3604
3605 #endif /* MBEDTLS_SELF_TEST */
3606
3607 #endif /* !MBEDTLS_ECP_ALT */
3608
3609 #endif /* MBEDTLS_ECP_C */
3610