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