1 /*
2 * Elliptic curves over GF(p): generic functions
3 *
4 * Copyright (C) 2006-2015, ARM Limited, All Rights Reserved
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 * This file is part of mbed TLS (https://tls.mbed.org)
20 */
21
22 /*
23 * References:
24 *
25 * SEC1 http://www.secg.org/index.php?action=secg,docs_secg
26 * GECC = Guide to Elliptic Curve Cryptography - Hankerson, Menezes, Vanstone
27 * FIPS 186-3 http://csrc.nist.gov/publications/fips/fips186-3/fips_186-3.pdf
28 * RFC 4492 for the related TLS structures and constants
29 *
30 * [Curve25519] http://cr.yp.to/ecdh/curve25519-20060209.pdf
31 *
32 * [2] CORON, Jean-S'ebastien. Resistance against differential power analysis
33 * for elliptic curve cryptosystems. In : Cryptographic Hardware and
34 * Embedded Systems. Springer Berlin Heidelberg, 1999. p. 292-302.
35 * <http://link.springer.com/chapter/10.1007/3-540-48059-5_25>
36 *
37 * [3] HEDABOU, Mustapha, PINEL, Pierre, et B'EN'ETEAU, Lucien. A comb method to
38 * render ECC resistant against Side Channel Attacks. IACR Cryptology
39 * ePrint Archive, 2004, vol. 2004, p. 342.
40 * <http://eprint.iacr.org/2004/342.pdf>
41 */
42
43 #if !defined(MBEDTLS_CONFIG_FILE)
44 #include "mbedtls/config.h"
45 #else
46 #include MBEDTLS_CONFIG_FILE
47 #endif
48
49 #if defined(MBEDTLS_ECP_C)
50
51 #include "mbedtls/ecp.h"
52
53 #include <string.h>
54
55 #if defined(MBEDTLS_PLATFORM_C)
56 #include "mbedtls/platform.h"
57 #else
58 #include <stdlib.h>
59 #include <stdio.h>
60 #define mbedtls_printf printf
61 #define mbedtls_calloc calloc
62 #define mbedtls_free free
63 #endif
64
65 #if ( defined(__ARMCC_VERSION) || defined(_MSC_VER) ) && \
66 !defined(inline) && !defined(__cplusplus)
67 #define inline __inline
68 #endif
69
70 /* Implementation that should never be optimized out by the compiler */
mbedtls_zeroize(void * v,size_t n)71 static void mbedtls_zeroize( void *v, size_t n ) {
72 volatile unsigned char *p = v; while( n-- ) *p++ = 0;
73 }
74
75 #if defined(MBEDTLS_SELF_TEST)
76 /*
77 * Counts of point addition and doubling, and field multiplications.
78 * Used to test resistance of point multiplication to simple timing attacks.
79 */
80 static unsigned long add_count, dbl_count, mul_count;
81 #endif
82
83 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) || \
84 defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) || \
85 defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) || \
86 defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) || \
87 defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) || \
88 defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) || \
89 defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) || \
90 defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) || \
91 defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) || \
92 defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) || \
93 defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
94 #define ECP_SHORTWEIERSTRASS
95 #endif
96
97 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
98 #define ECP_MONTGOMERY
99 #endif
100
101 /*
102 * Curve types: internal for now, might be exposed later
103 */
104 typedef enum
105 {
106 ECP_TYPE_NONE = 0,
107 ECP_TYPE_SHORT_WEIERSTRASS, /* y^2 = x^3 + a x + b */
108 ECP_TYPE_MONTGOMERY, /* y^2 = x^3 + a x^2 + x */
109 } ecp_curve_type;
110
111 /*
112 * List of supported curves:
113 * - internal ID
114 * - TLS NamedCurve ID (RFC 4492 sec. 5.1.1, RFC 7071 sec. 2)
115 * - size in bits
116 * - readable name
117 *
118 * Curves are listed in order: largest curves first, and for a given size,
119 * fastest curves first. This provides the default order for the SSL module.
120 *
121 * Reminder: update profiles in x509_crt.c when adding a new curves!
122 */
123 static const mbedtls_ecp_curve_info ecp_supported_curves[] =
124 {
125 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
126 { MBEDTLS_ECP_DP_SECP521R1, 25, 521, "secp521r1" },
127 #endif
128 #if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED)
129 { MBEDTLS_ECP_DP_BP512R1, 28, 512, "brainpoolP512r1" },
130 #endif
131 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
132 { MBEDTLS_ECP_DP_SECP384R1, 24, 384, "secp384r1" },
133 #endif
134 #if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED)
135 { MBEDTLS_ECP_DP_BP384R1, 27, 384, "brainpoolP384r1" },
136 #endif
137 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
138 { MBEDTLS_ECP_DP_SECP256R1, 23, 256, "secp256r1" },
139 #endif
140 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
141 { MBEDTLS_ECP_DP_SECP256K1, 22, 256, "secp256k1" },
142 #endif
143 #if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED)
144 { MBEDTLS_ECP_DP_BP256R1, 26, 256, "brainpoolP256r1" },
145 #endif
146 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
147 { MBEDTLS_ECP_DP_SECP224R1, 21, 224, "secp224r1" },
148 #endif
149 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
150 { MBEDTLS_ECP_DP_SECP224K1, 20, 224, "secp224k1" },
151 #endif
152 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
153 { MBEDTLS_ECP_DP_SECP192R1, 19, 192, "secp192r1" },
154 #endif
155 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
156 { MBEDTLS_ECP_DP_SECP192K1, 18, 192, "secp192k1" },
157 #endif
158 { MBEDTLS_ECP_DP_NONE, 0, 0, NULL },
159 };
160
161 #define ECP_NB_CURVES sizeof( ecp_supported_curves ) / \
162 sizeof( ecp_supported_curves[0] )
163
164 static mbedtls_ecp_group_id ecp_supported_grp_id[ECP_NB_CURVES];
165
166 /*
167 * List of supported curves and associated info
168 */
mbedtls_ecp_curve_list(void)169 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_list( void )
170 {
171 return( ecp_supported_curves );
172 }
173
174 /*
175 * List of supported curves, group ID only
176 */
mbedtls_ecp_grp_id_list(void)177 const mbedtls_ecp_group_id *mbedtls_ecp_grp_id_list( void )
178 {
179 static int init_done = 0;
180
181 if( ! init_done )
182 {
183 size_t i = 0;
184 const mbedtls_ecp_curve_info *curve_info;
185
186 for( curve_info = mbedtls_ecp_curve_list();
187 curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
188 curve_info++ )
189 {
190 ecp_supported_grp_id[i++] = curve_info->grp_id;
191 }
192 ecp_supported_grp_id[i] = MBEDTLS_ECP_DP_NONE;
193
194 init_done = 1;
195 }
196
197 return( ecp_supported_grp_id );
198 }
199
200 /*
201 * Get the curve info for the internal identifier
202 */
mbedtls_ecp_curve_info_from_grp_id(mbedtls_ecp_group_id grp_id)203 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_grp_id( mbedtls_ecp_group_id grp_id )
204 {
205 const mbedtls_ecp_curve_info *curve_info;
206
207 for( curve_info = mbedtls_ecp_curve_list();
208 curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
209 curve_info++ )
210 {
211 if( curve_info->grp_id == grp_id )
212 return( curve_info );
213 }
214
215 return( NULL );
216 }
217
218 /*
219 * Get the curve info from the TLS identifier
220 */
mbedtls_ecp_curve_info_from_tls_id(uint16_t tls_id)221 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_tls_id( uint16_t tls_id )
222 {
223 const mbedtls_ecp_curve_info *curve_info;
224
225 for( curve_info = mbedtls_ecp_curve_list();
226 curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
227 curve_info++ )
228 {
229 if( curve_info->tls_id == tls_id )
230 return( curve_info );
231 }
232
233 return( NULL );
234 }
235
236 /*
237 * Get the curve info from the name
238 */
mbedtls_ecp_curve_info_from_name(const char * name)239 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_name( const char *name )
240 {
241 const mbedtls_ecp_curve_info *curve_info;
242
243 for( curve_info = mbedtls_ecp_curve_list();
244 curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
245 curve_info++ )
246 {
247 if( strcmp( curve_info->name, name ) == 0 )
248 return( curve_info );
249 }
250
251 return( NULL );
252 }
253
254 /*
255 * Get the type of a curve
256 */
ecp_get_type(const mbedtls_ecp_group * grp)257 static inline ecp_curve_type ecp_get_type( const mbedtls_ecp_group *grp )
258 {
259 if( grp->G.X.p == NULL )
260 return( ECP_TYPE_NONE );
261
262 if( grp->G.Y.p == NULL )
263 return( ECP_TYPE_MONTGOMERY );
264 else
265 return( ECP_TYPE_SHORT_WEIERSTRASS );
266 }
267
268 /*
269 * Initialize (the components of) a point
270 */
mbedtls_ecp_point_init(mbedtls_ecp_point * pt)271 void mbedtls_ecp_point_init( mbedtls_ecp_point *pt )
272 {
273 if( pt == NULL )
274 return;
275
276 mbedtls_mpi_init( &pt->X );
277 mbedtls_mpi_init( &pt->Y );
278 mbedtls_mpi_init( &pt->Z );
279 }
280
281 /*
282 * Initialize (the components of) a group
283 */
mbedtls_ecp_group_init(mbedtls_ecp_group * grp)284 void mbedtls_ecp_group_init( mbedtls_ecp_group *grp )
285 {
286 if( grp == NULL )
287 return;
288
289 memset( grp, 0, sizeof( mbedtls_ecp_group ) );
290 }
291
292 /*
293 * Initialize (the components of) a key pair
294 */
mbedtls_ecp_keypair_init(mbedtls_ecp_keypair * key)295 void mbedtls_ecp_keypair_init( mbedtls_ecp_keypair *key )
296 {
297 if( key == NULL )
298 return;
299
300 mbedtls_ecp_group_init( &key->grp );
301 mbedtls_mpi_init( &key->d );
302 mbedtls_ecp_point_init( &key->Q );
303 }
304
305 /*
306 * Unallocate (the components of) a point
307 */
mbedtls_ecp_point_free(mbedtls_ecp_point * pt)308 void mbedtls_ecp_point_free( mbedtls_ecp_point *pt )
309 {
310 if( pt == NULL )
311 return;
312
313 mbedtls_mpi_free( &( pt->X ) );
314 mbedtls_mpi_free( &( pt->Y ) );
315 mbedtls_mpi_free( &( pt->Z ) );
316 }
317
318 /*
319 * Unallocate (the components of) a group
320 */
mbedtls_ecp_group_free(mbedtls_ecp_group * grp)321 void mbedtls_ecp_group_free( mbedtls_ecp_group *grp )
322 {
323 size_t i;
324
325 if( grp == NULL )
326 return;
327
328 if( grp->h != 1 )
329 {
330 mbedtls_mpi_free( &grp->P );
331 mbedtls_mpi_free( &grp->A );
332 mbedtls_mpi_free( &grp->B );
333 mbedtls_ecp_point_free( &grp->G );
334 mbedtls_mpi_free( &grp->N );
335 }
336
337 if( grp->T != NULL )
338 {
339 for( i = 0; i < grp->T_size; i++ )
340 mbedtls_ecp_point_free( &grp->T[i] );
341 mbedtls_free( grp->T );
342 }
343
344 mbedtls_zeroize( grp, sizeof( mbedtls_ecp_group ) );
345 }
346
347 /*
348 * Unallocate (the components of) a key pair
349 */
mbedtls_ecp_keypair_free(mbedtls_ecp_keypair * key)350 void mbedtls_ecp_keypair_free( mbedtls_ecp_keypair *key )
351 {
352 if( key == NULL )
353 return;
354
355 mbedtls_ecp_group_free( &key->grp );
356 mbedtls_mpi_free( &key->d );
357 mbedtls_ecp_point_free( &key->Q );
358 }
359
360 /*
361 * Copy the contents of a point
362 */
mbedtls_ecp_copy(mbedtls_ecp_point * P,const mbedtls_ecp_point * Q)363 int mbedtls_ecp_copy( mbedtls_ecp_point *P, const mbedtls_ecp_point *Q )
364 {
365 int ret;
366
367 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->X, &Q->X ) );
368 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->Y, &Q->Y ) );
369 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->Z, &Q->Z ) );
370
371 cleanup:
372 return( ret );
373 }
374
375 /*
376 * Copy the contents of a group object
377 */
mbedtls_ecp_group_copy(mbedtls_ecp_group * dst,const mbedtls_ecp_group * src)378 int mbedtls_ecp_group_copy( mbedtls_ecp_group *dst, const mbedtls_ecp_group *src )
379 {
380 return mbedtls_ecp_group_load( dst, src->id );
381 }
382
383 /*
384 * Set point to zero
385 */
mbedtls_ecp_set_zero(mbedtls_ecp_point * pt)386 int mbedtls_ecp_set_zero( mbedtls_ecp_point *pt )
387 {
388 int ret;
389
390 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->X , 1 ) );
391 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Y , 1 ) );
392 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z , 0 ) );
393
394 cleanup:
395 return( ret );
396 }
397
398 /*
399 * Tell if a point is zero
400 */
mbedtls_ecp_is_zero(mbedtls_ecp_point * pt)401 int mbedtls_ecp_is_zero( mbedtls_ecp_point *pt )
402 {
403 return( mbedtls_mpi_cmp_int( &pt->Z, 0 ) == 0 );
404 }
405
406 /*
407 * Compare two points lazyly
408 */
mbedtls_ecp_point_cmp(const mbedtls_ecp_point * P,const mbedtls_ecp_point * Q)409 int mbedtls_ecp_point_cmp( const mbedtls_ecp_point *P,
410 const mbedtls_ecp_point *Q )
411 {
412 if( mbedtls_mpi_cmp_mpi( &P->X, &Q->X ) == 0 &&
413 mbedtls_mpi_cmp_mpi( &P->Y, &Q->Y ) == 0 &&
414 mbedtls_mpi_cmp_mpi( &P->Z, &Q->Z ) == 0 )
415 {
416 return( 0 );
417 }
418
419 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
420 }
421
422 /*
423 * Import a non-zero point from ASCII strings
424 */
mbedtls_ecp_point_read_string(mbedtls_ecp_point * P,int radix,const char * x,const char * y)425 int mbedtls_ecp_point_read_string( mbedtls_ecp_point *P, int radix,
426 const char *x, const char *y )
427 {
428 int ret;
429
430 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &P->X, radix, x ) );
431 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &P->Y, radix, y ) );
432 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &P->Z, 1 ) );
433
434 cleanup:
435 return( ret );
436 }
437
438 /*
439 * Export a point into unsigned binary data (SEC1 2.3.3)
440 */
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)441 int mbedtls_ecp_point_write_binary( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *P,
442 int format, size_t *olen,
443 unsigned char *buf, size_t buflen )
444 {
445 int ret = 0;
446 size_t plen;
447
448 if( format != MBEDTLS_ECP_PF_UNCOMPRESSED &&
449 format != MBEDTLS_ECP_PF_COMPRESSED )
450 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
451
452 /*
453 * Common case: P == 0
454 */
455 if( mbedtls_mpi_cmp_int( &P->Z, 0 ) == 0 )
456 {
457 if( buflen < 1 )
458 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
459
460 buf[0] = 0x00;
461 *olen = 1;
462
463 return( 0 );
464 }
465
466 plen = mbedtls_mpi_size( &grp->P );
467
468 if( format == MBEDTLS_ECP_PF_UNCOMPRESSED )
469 {
470 *olen = 2 * plen + 1;
471
472 if( buflen < *olen )
473 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
474
475 buf[0] = 0x04;
476 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->X, buf + 1, plen ) );
477 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->Y, buf + 1 + plen, plen ) );
478 }
479 else if( format == MBEDTLS_ECP_PF_COMPRESSED )
480 {
481 *olen = plen + 1;
482
483 if( buflen < *olen )
484 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
485
486 buf[0] = 0x02 + mbedtls_mpi_get_bit( &P->Y, 0 );
487 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->X, buf + 1, plen ) );
488 }
489
490 cleanup:
491 return( ret );
492 }
493
494 /*
495 * Import a point from unsigned binary data (SEC1 2.3.4)
496 */
mbedtls_ecp_point_read_binary(const mbedtls_ecp_group * grp,mbedtls_ecp_point * pt,const unsigned char * buf,size_t ilen)497 int mbedtls_ecp_point_read_binary( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt,
498 const unsigned char *buf, size_t ilen )
499 {
500 int ret;
501 size_t plen;
502
503 if( ilen < 1 )
504 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
505
506 if( buf[0] == 0x00 )
507 {
508 if( ilen == 1 )
509 return( mbedtls_ecp_set_zero( pt ) );
510 else
511 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
512 }
513
514 plen = mbedtls_mpi_size( &grp->P );
515
516 if( buf[0] != 0x04 )
517 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
518
519 if( ilen != 2 * plen + 1 )
520 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
521
522 MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &pt->X, buf + 1, plen ) );
523 MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &pt->Y, buf + 1 + plen, plen ) );
524 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) );
525
526 cleanup:
527 return( ret );
528 }
529
530 /*
531 * Import a point from a TLS ECPoint record (RFC 4492)
532 * struct {
533 * opaque point <1..2^8-1>;
534 * } ECPoint;
535 */
mbedtls_ecp_tls_read_point(const mbedtls_ecp_group * grp,mbedtls_ecp_point * pt,const unsigned char ** buf,size_t buf_len)536 int mbedtls_ecp_tls_read_point( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt,
537 const unsigned char **buf, size_t buf_len )
538 {
539 unsigned char data_len;
540 const unsigned char *buf_start;
541
542 /*
543 * We must have at least two bytes (1 for length, at least one for data)
544 */
545 if( buf_len < 2 )
546 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
547
548 data_len = *(*buf)++;
549 if( data_len < 1 || data_len > buf_len - 1 )
550 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
551
552 /*
553 * Save buffer start for read_binary and update buf
554 */
555 buf_start = *buf;
556 *buf += data_len;
557
558 return mbedtls_ecp_point_read_binary( grp, pt, buf_start, data_len );
559 }
560
561 /*
562 * Export a point as a TLS ECPoint record (RFC 4492)
563 * struct {
564 * opaque point <1..2^8-1>;
565 * } ECPoint;
566 */
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)567 int mbedtls_ecp_tls_write_point( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt,
568 int format, size_t *olen,
569 unsigned char *buf, size_t blen )
570 {
571 int ret;
572
573 /*
574 * buffer length must be at least one, for our length byte
575 */
576 if( blen < 1 )
577 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
578
579 if( ( ret = mbedtls_ecp_point_write_binary( grp, pt, format,
580 olen, buf + 1, blen - 1) ) != 0 )
581 return( ret );
582
583 /*
584 * write length to the first byte and update total length
585 */
586 buf[0] = (unsigned char) *olen;
587 ++*olen;
588
589 return( 0 );
590 }
591
592 /*
593 * Set a group from an ECParameters record (RFC 4492)
594 */
mbedtls_ecp_tls_read_group(mbedtls_ecp_group * grp,const unsigned char ** buf,size_t len)595 int mbedtls_ecp_tls_read_group( mbedtls_ecp_group *grp, const unsigned char **buf, size_t len )
596 {
597 uint16_t tls_id;
598 const mbedtls_ecp_curve_info *curve_info;
599
600 /*
601 * We expect at least three bytes (see below)
602 */
603 if( len < 3 )
604 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
605
606 /*
607 * First byte is curve_type; only named_curve is handled
608 */
609 if( *(*buf)++ != MBEDTLS_ECP_TLS_NAMED_CURVE )
610 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
611
612 /*
613 * Next two bytes are the namedcurve value
614 */
615 tls_id = *(*buf)++;
616 tls_id <<= 8;
617 tls_id |= *(*buf)++;
618
619 if( ( curve_info = mbedtls_ecp_curve_info_from_tls_id( tls_id ) ) == NULL )
620 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
621
622 return mbedtls_ecp_group_load( grp, curve_info->grp_id );
623 }
624
625 /*
626 * Write the ECParameters record corresponding to a group (RFC 4492)
627 */
mbedtls_ecp_tls_write_group(const mbedtls_ecp_group * grp,size_t * olen,unsigned char * buf,size_t blen)628 int mbedtls_ecp_tls_write_group( const mbedtls_ecp_group *grp, size_t *olen,
629 unsigned char *buf, size_t blen )
630 {
631 const mbedtls_ecp_curve_info *curve_info;
632
633 if( ( curve_info = mbedtls_ecp_curve_info_from_grp_id( grp->id ) ) == NULL )
634 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
635
636 /*
637 * We are going to write 3 bytes (see below)
638 */
639 *olen = 3;
640 if( blen < *olen )
641 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
642
643 /*
644 * First byte is curve_type, always named_curve
645 */
646 *buf++ = MBEDTLS_ECP_TLS_NAMED_CURVE;
647
648 /*
649 * Next two bytes are the namedcurve value
650 */
651 buf[0] = curve_info->tls_id >> 8;
652 buf[1] = curve_info->tls_id & 0xFF;
653
654 return( 0 );
655 }
656
657 /*
658 * Wrapper around fast quasi-modp functions, with fall-back to mbedtls_mpi_mod_mpi.
659 * See the documentation of struct mbedtls_ecp_group.
660 *
661 * This function is in the critial loop for mbedtls_ecp_mul, so pay attention to perf.
662 */
ecp_modp(mbedtls_mpi * N,const mbedtls_ecp_group * grp)663 static int ecp_modp( mbedtls_mpi *N, const mbedtls_ecp_group *grp )
664 {
665 int ret;
666
667 if( grp->modp == NULL )
668 return( mbedtls_mpi_mod_mpi( N, N, &grp->P ) );
669
670 /* N->s < 0 is a much faster test, which fails only if N is 0 */
671 if( ( N->s < 0 && mbedtls_mpi_cmp_int( N, 0 ) != 0 ) ||
672 mbedtls_mpi_bitlen( N ) > 2 * grp->pbits )
673 {
674 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
675 }
676
677 MBEDTLS_MPI_CHK( grp->modp( N ) );
678
679 /* N->s < 0 is a much faster test, which fails only if N is 0 */
680 while( N->s < 0 && mbedtls_mpi_cmp_int( N, 0 ) != 0 )
681 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &grp->P ) );
682
683 while( mbedtls_mpi_cmp_mpi( N, &grp->P ) >= 0 )
684 /* we known P, N and the result are positive */
685 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( N, N, &grp->P ) );
686
687 cleanup:
688 return( ret );
689 }
690
691 /*
692 * Fast mod-p functions expect their argument to be in the 0..p^2 range.
693 *
694 * In order to guarantee that, we need to ensure that operands of
695 * mbedtls_mpi_mul_mpi are in the 0..p range. So, after each operation we will
696 * bring the result back to this range.
697 *
698 * The following macros are shortcuts for doing that.
699 */
700
701 /*
702 * Reduce a mbedtls_mpi mod p in-place, general case, to use after mbedtls_mpi_mul_mpi
703 */
704 #if defined(MBEDTLS_SELF_TEST)
705 #define INC_MUL_COUNT mul_count++;
706 #else
707 #define INC_MUL_COUNT
708 #endif
709
710 #define MOD_MUL( N ) do { MBEDTLS_MPI_CHK( ecp_modp( &N, grp ) ); INC_MUL_COUNT } \
711 while( 0 )
712
713 /*
714 * Reduce a mbedtls_mpi mod p in-place, to use after mbedtls_mpi_sub_mpi
715 * N->s < 0 is a very fast test, which fails only if N is 0
716 */
717 #define MOD_SUB( N ) \
718 while( N.s < 0 && mbedtls_mpi_cmp_int( &N, 0 ) != 0 ) \
719 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &N, &N, &grp->P ) )
720
721 /*
722 * Reduce a mbedtls_mpi mod p in-place, to use after mbedtls_mpi_add_mpi and mbedtls_mpi_mul_int.
723 * We known P, N and the result are positive, so sub_abs is correct, and
724 * a bit faster.
725 */
726 #define MOD_ADD( N ) \
727 while( mbedtls_mpi_cmp_mpi( &N, &grp->P ) >= 0 ) \
728 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( &N, &N, &grp->P ) )
729
730 #if defined(ECP_SHORTWEIERSTRASS)
731 /*
732 * For curves in short Weierstrass form, we do all the internal operations in
733 * Jacobian coordinates.
734 *
735 * For multiplication, we'll use a comb method with coutermeasueres against
736 * SPA, hence timing attacks.
737 */
738
739 /*
740 * Normalize jacobian coordinates so that Z == 0 || Z == 1 (GECC 3.2.1)
741 * Cost: 1N := 1I + 3M + 1S
742 */
ecp_normalize_jac(const mbedtls_ecp_group * grp,mbedtls_ecp_point * pt)743 static int ecp_normalize_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt )
744 {
745 int ret;
746 mbedtls_mpi Zi, ZZi;
747
748 if( mbedtls_mpi_cmp_int( &pt->Z, 0 ) == 0 )
749 return( 0 );
750
751 mbedtls_mpi_init( &Zi ); mbedtls_mpi_init( &ZZi );
752
753 /*
754 * X = X / Z^2 mod p
755 */
756 MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &Zi, &pt->Z, &grp->P ) );
757 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ZZi, &Zi, &Zi ) ); MOD_MUL( ZZi );
758 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->X, &pt->X, &ZZi ) ); MOD_MUL( pt->X );
759
760 /*
761 * Y = Y / Z^3 mod p
762 */
763 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Y, &pt->Y, &ZZi ) ); MOD_MUL( pt->Y );
764 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Y, &pt->Y, &Zi ) ); MOD_MUL( pt->Y );
765
766 /*
767 * Z = 1
768 */
769 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) );
770
771 cleanup:
772
773 mbedtls_mpi_free( &Zi ); mbedtls_mpi_free( &ZZi );
774
775 return( ret );
776 }
777
778 /*
779 * Normalize jacobian coordinates of an array of (pointers to) points,
780 * using Montgomery's trick to perform only one inversion mod P.
781 * (See for example Cohen's "A Course in Computational Algebraic Number
782 * Theory", Algorithm 10.3.4.)
783 *
784 * Warning: fails (returning an error) if one of the points is zero!
785 * This should never happen, see choice of w in ecp_mul_comb().
786 *
787 * Cost: 1N(t) := 1I + (6t - 3)M + 1S
788 */
ecp_normalize_jac_many(const mbedtls_ecp_group * grp,mbedtls_ecp_point * T[],size_t t_len)789 static int ecp_normalize_jac_many( const mbedtls_ecp_group *grp,
790 mbedtls_ecp_point *T[], size_t t_len )
791 {
792 int ret;
793 size_t i;
794 mbedtls_mpi *c, u, Zi, ZZi;
795
796 if( t_len < 2 )
797 return( ecp_normalize_jac( grp, *T ) );
798
799 if( ( c = mbedtls_calloc( t_len, sizeof( mbedtls_mpi ) ) ) == NULL )
800 return( MBEDTLS_ERR_ECP_ALLOC_FAILED );
801
802 mbedtls_mpi_init( &u ); mbedtls_mpi_init( &Zi ); mbedtls_mpi_init( &ZZi );
803
804 /*
805 * c[i] = Z_0 * ... * Z_i
806 */
807 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &c[0], &T[0]->Z ) );
808 for( i = 1; i < t_len; i++ )
809 {
810 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &c[i], &c[i-1], &T[i]->Z ) );
811 MOD_MUL( c[i] );
812 }
813
814 /*
815 * u = 1 / (Z_0 * ... * Z_n) mod P
816 */
817 MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &u, &c[t_len-1], &grp->P ) );
818
819 for( i = t_len - 1; ; i-- )
820 {
821 /*
822 * Zi = 1 / Z_i mod p
823 * u = 1 / (Z_0 * ... * Z_i) mod P
824 */
825 if( i == 0 ) {
826 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &Zi, &u ) );
827 }
828 else
829 {
830 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &Zi, &u, &c[i-1] ) ); MOD_MUL( Zi );
831 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &u, &u, &T[i]->Z ) ); MOD_MUL( u );
832 }
833
834 /*
835 * proceed as in normalize()
836 */
837 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ZZi, &Zi, &Zi ) ); MOD_MUL( ZZi );
838 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T[i]->X, &T[i]->X, &ZZi ) ); MOD_MUL( T[i]->X );
839 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T[i]->Y, &T[i]->Y, &ZZi ) ); MOD_MUL( T[i]->Y );
840 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T[i]->Y, &T[i]->Y, &Zi ) ); MOD_MUL( T[i]->Y );
841
842 /*
843 * Post-precessing: reclaim some memory by shrinking coordinates
844 * - not storing Z (always 1)
845 * - shrinking other coordinates, but still keeping the same number of
846 * limbs as P, as otherwise it will too likely be regrown too fast.
847 */
848 MBEDTLS_MPI_CHK( mbedtls_mpi_shrink( &T[i]->X, grp->P.n ) );
849 MBEDTLS_MPI_CHK( mbedtls_mpi_shrink( &T[i]->Y, grp->P.n ) );
850 mbedtls_mpi_free( &T[i]->Z );
851
852 if( i == 0 )
853 break;
854 }
855
856 cleanup:
857
858 mbedtls_mpi_free( &u ); mbedtls_mpi_free( &Zi ); mbedtls_mpi_free( &ZZi );
859 for( i = 0; i < t_len; i++ )
860 mbedtls_mpi_free( &c[i] );
861 mbedtls_free( c );
862
863 return( ret );
864 }
865
866 /*
867 * Conditional point inversion: Q -> -Q = (Q.X, -Q.Y, Q.Z) without leak.
868 * "inv" must be 0 (don't invert) or 1 (invert) or the result will be invalid
869 */
ecp_safe_invert_jac(const mbedtls_ecp_group * grp,mbedtls_ecp_point * Q,unsigned char inv)870 static int ecp_safe_invert_jac( const mbedtls_ecp_group *grp,
871 mbedtls_ecp_point *Q,
872 unsigned char inv )
873 {
874 int ret;
875 unsigned char nonzero;
876 mbedtls_mpi mQY;
877
878 mbedtls_mpi_init( &mQY );
879
880 /* Use the fact that -Q.Y mod P = P - Q.Y unless Q.Y == 0 */
881 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &mQY, &grp->P, &Q->Y ) );
882 nonzero = mbedtls_mpi_cmp_int( &Q->Y, 0 ) != 0;
883 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &Q->Y, &mQY, inv & nonzero ) );
884
885 cleanup:
886 mbedtls_mpi_free( &mQY );
887
888 return( ret );
889 }
890
891 /*
892 * Point doubling R = 2 P, Jacobian coordinates
893 *
894 * Based on http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#doubling-dbl-1998-cmo-2 .
895 *
896 * We follow the variable naming fairly closely. The formula variations that trade a MUL for a SQR
897 * (plus a few ADDs) aren't useful as our bignum implementation doesn't distinguish squaring.
898 *
899 * Standard optimizations are applied when curve parameter A is one of { 0, -3 }.
900 *
901 * Cost: 1D := 3M + 4S (A == 0)
902 * 4M + 4S (A == -3)
903 * 3M + 6S + 1a otherwise
904 */
ecp_double_jac(const mbedtls_ecp_group * grp,mbedtls_ecp_point * R,const mbedtls_ecp_point * P)905 static int ecp_double_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
906 const mbedtls_ecp_point *P )
907 {
908 int ret;
909 mbedtls_mpi M, S, T, U;
910
911 #if defined(MBEDTLS_SELF_TEST)
912 dbl_count++;
913 #endif
914
915 mbedtls_mpi_init( &M ); mbedtls_mpi_init( &S ); mbedtls_mpi_init( &T ); mbedtls_mpi_init( &U );
916
917 /* Special case for A = -3 */
918 if( grp->A.p == NULL )
919 {
920 /* M = 3(X + Z^2)(X - Z^2) */
921 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->Z, &P->Z ) ); MOD_MUL( S );
922 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &T, &P->X, &S ) ); MOD_ADD( T );
923 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &U, &P->X, &S ) ); MOD_SUB( U );
924 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &T, &U ) ); MOD_MUL( S );
925 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &S, 3 ) ); MOD_ADD( M );
926 }
927 else
928 {
929 /* M = 3.X^2 */
930 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->X, &P->X ) ); MOD_MUL( S );
931 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &S, 3 ) ); MOD_ADD( M );
932
933 /* Optimize away for "koblitz" curves with A = 0 */
934 if( mbedtls_mpi_cmp_int( &grp->A, 0 ) != 0 )
935 {
936 /* M += A.Z^4 */
937 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->Z, &P->Z ) ); MOD_MUL( S );
938 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &S, &S ) ); MOD_MUL( T );
939 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &T, &grp->A ) ); MOD_MUL( S );
940 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &M, &M, &S ) ); MOD_ADD( M );
941 }
942 }
943
944 /* S = 4.X.Y^2 */
945 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &P->Y, &P->Y ) ); MOD_MUL( T );
946 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &T, 1 ) ); MOD_ADD( T );
947 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->X, &T ) ); MOD_MUL( S );
948 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &S, 1 ) ); MOD_ADD( S );
949
950 /* U = 8.Y^4 */
951 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &U, &T, &T ) ); MOD_MUL( U );
952 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &U, 1 ) ); MOD_ADD( U );
953
954 /* T = M^2 - 2.S */
955 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &M, &M ) ); MOD_MUL( T );
956 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T, &T, &S ) ); MOD_SUB( T );
957 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T, &T, &S ) ); MOD_SUB( T );
958
959 /* S = M(S - T) - U */
960 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &S, &S, &T ) ); MOD_SUB( S );
961 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &S, &M ) ); MOD_MUL( S );
962 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &S, &S, &U ) ); MOD_SUB( S );
963
964 /* U = 2.Y.Z */
965 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &U, &P->Y, &P->Z ) ); MOD_MUL( U );
966 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &U, 1 ) ); MOD_ADD( U );
967
968 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->X, &T ) );
969 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Y, &S ) );
970 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Z, &U ) );
971
972 cleanup:
973 mbedtls_mpi_free( &M ); mbedtls_mpi_free( &S ); mbedtls_mpi_free( &T ); mbedtls_mpi_free( &U );
974
975 return( ret );
976 }
977
978 /*
979 * Addition: R = P + Q, mixed affine-Jacobian coordinates (GECC 3.22)
980 *
981 * The coordinates of Q must be normalized (= affine),
982 * but those of P don't need to. R is not normalized.
983 *
984 * Special cases: (1) P or Q is zero, (2) R is zero, (3) P == Q.
985 * None of these cases can happen as intermediate step in ecp_mul_comb():
986 * - at each step, P, Q and R are multiples of the base point, the factor
987 * being less than its order, so none of them is zero;
988 * - Q is an odd multiple of the base point, P an even multiple,
989 * due to the choice of precomputed points in the modified comb method.
990 * So branches for these cases do not leak secret information.
991 *
992 * We accept Q->Z being unset (saving memory in tables) as meaning 1.
993 *
994 * Cost: 1A := 8M + 3S
995 */
ecp_add_mixed(const mbedtls_ecp_group * grp,mbedtls_ecp_point * R,const mbedtls_ecp_point * P,const mbedtls_ecp_point * Q)996 static int ecp_add_mixed( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
997 const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q )
998 {
999 int ret;
1000 mbedtls_mpi T1, T2, T3, T4, X, Y, Z;
1001
1002 #if defined(MBEDTLS_SELF_TEST)
1003 add_count++;
1004 #endif
1005
1006 /*
1007 * Trivial cases: P == 0 or Q == 0 (case 1)
1008 */
1009 if( mbedtls_mpi_cmp_int( &P->Z, 0 ) == 0 )
1010 return( mbedtls_ecp_copy( R, Q ) );
1011
1012 if( Q->Z.p != NULL && mbedtls_mpi_cmp_int( &Q->Z, 0 ) == 0 )
1013 return( mbedtls_ecp_copy( R, P ) );
1014
1015 /*
1016 * Make sure Q coordinates are normalized
1017 */
1018 if( Q->Z.p != NULL && mbedtls_mpi_cmp_int( &Q->Z, 1 ) != 0 )
1019 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1020
1021 mbedtls_mpi_init( &T1 ); mbedtls_mpi_init( &T2 ); mbedtls_mpi_init( &T3 ); mbedtls_mpi_init( &T4 );
1022 mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Y ); mbedtls_mpi_init( &Z );
1023
1024 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T1, &P->Z, &P->Z ) ); MOD_MUL( T1 );
1025 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T2, &T1, &P->Z ) ); MOD_MUL( T2 );
1026 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T1, &T1, &Q->X ) ); MOD_MUL( T1 );
1027 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T2, &T2, &Q->Y ) ); MOD_MUL( T2 );
1028 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T1, &T1, &P->X ) ); MOD_SUB( T1 );
1029 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T2, &T2, &P->Y ) ); MOD_SUB( T2 );
1030
1031 /* Special cases (2) and (3) */
1032 if( mbedtls_mpi_cmp_int( &T1, 0 ) == 0 )
1033 {
1034 if( mbedtls_mpi_cmp_int( &T2, 0 ) == 0 )
1035 {
1036 ret = ecp_double_jac( grp, R, P );
1037 goto cleanup;
1038 }
1039 else
1040 {
1041 ret = mbedtls_ecp_set_zero( R );
1042 goto cleanup;
1043 }
1044 }
1045
1046 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &Z, &P->Z, &T1 ) ); MOD_MUL( Z );
1047 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T3, &T1, &T1 ) ); MOD_MUL( T3 );
1048 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T4, &T3, &T1 ) ); MOD_MUL( T4 );
1049 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T3, &T3, &P->X ) ); MOD_MUL( T3 );
1050 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &T1, &T3, 2 ) ); MOD_ADD( T1 );
1051 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &X, &T2, &T2 ) ); MOD_MUL( X );
1052 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &X, &X, &T1 ) ); MOD_SUB( X );
1053 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &X, &X, &T4 ) ); MOD_SUB( X );
1054 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T3, &T3, &X ) ); MOD_SUB( T3 );
1055 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T3, &T3, &T2 ) ); MOD_MUL( T3 );
1056 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T4, &T4, &P->Y ) ); MOD_MUL( T4 );
1057 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &Y, &T3, &T4 ) ); MOD_SUB( Y );
1058
1059 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->X, &X ) );
1060 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Y, &Y ) );
1061 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Z, &Z ) );
1062
1063 cleanup:
1064
1065 mbedtls_mpi_free( &T1 ); mbedtls_mpi_free( &T2 ); mbedtls_mpi_free( &T3 ); mbedtls_mpi_free( &T4 );
1066 mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Y ); mbedtls_mpi_free( &Z );
1067
1068 return( ret );
1069 }
1070
1071 /*
1072 * Randomize jacobian coordinates:
1073 * (X, Y, Z) -> (l^2 X, l^3 Y, l Z) for random l
1074 * This is sort of the reverse operation of ecp_normalize_jac().
1075 *
1076 * This countermeasure was first suggested in [2].
1077 */
ecp_randomize_jac(const mbedtls_ecp_group * grp,mbedtls_ecp_point * pt,int (* f_rng)(void *,unsigned char *,size_t),void * p_rng)1078 static int ecp_randomize_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt,
1079 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
1080 {
1081 int ret;
1082 mbedtls_mpi l, ll;
1083 size_t p_size = ( grp->pbits + 7 ) / 8;
1084 int count = 0;
1085
1086 mbedtls_mpi_init( &l ); mbedtls_mpi_init( &ll );
1087
1088 /* Generate l such that 1 < l < p */
1089 do
1090 {
1091 mbedtls_mpi_fill_random( &l, p_size, f_rng, p_rng );
1092
1093 while( mbedtls_mpi_cmp_mpi( &l, &grp->P ) >= 0 )
1094 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &l, 1 ) );
1095
1096 if( count++ > 10 )
1097 return( MBEDTLS_ERR_ECP_RANDOM_FAILED );
1098 }
1099 while( mbedtls_mpi_cmp_int( &l, 1 ) <= 0 );
1100
1101 /* Z = l * Z */
1102 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Z, &pt->Z, &l ) ); MOD_MUL( pt->Z );
1103
1104 /* X = l^2 * X */
1105 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ll, &l, &l ) ); MOD_MUL( ll );
1106 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->X, &pt->X, &ll ) ); MOD_MUL( pt->X );
1107
1108 /* Y = l^3 * Y */
1109 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ll, &ll, &l ) ); MOD_MUL( ll );
1110 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Y, &pt->Y, &ll ) ); MOD_MUL( pt->Y );
1111
1112 cleanup:
1113 mbedtls_mpi_free( &l ); mbedtls_mpi_free( &ll );
1114
1115 return( ret );
1116 }
1117
1118 /*
1119 * Check and define parameters used by the comb method (see below for details)
1120 */
1121 #if MBEDTLS_ECP_WINDOW_SIZE < 2 || MBEDTLS_ECP_WINDOW_SIZE > 7
1122 #error "MBEDTLS_ECP_WINDOW_SIZE out of bounds"
1123 #endif
1124
1125 /* d = ceil( n / w ) */
1126 #define COMB_MAX_D ( MBEDTLS_ECP_MAX_BITS + 1 ) / 2
1127
1128 /* number of precomputed points */
1129 #define COMB_MAX_PRE ( 1 << ( MBEDTLS_ECP_WINDOW_SIZE - 1 ) )
1130
1131 /*
1132 * Compute the representation of m that will be used with our comb method.
1133 *
1134 * The basic comb method is described in GECC 3.44 for example. We use a
1135 * modified version that provides resistance to SPA by avoiding zero
1136 * digits in the representation as in [3]. We modify the method further by
1137 * requiring that all K_i be odd, which has the small cost that our
1138 * representation uses one more K_i, due to carries.
1139 *
1140 * Also, for the sake of compactness, only the seven low-order bits of x[i]
1141 * are used to represent K_i, and the msb of x[i] encodes the the sign (s_i in
1142 * the paper): it is set if and only if if s_i == -1;
1143 *
1144 * Calling conventions:
1145 * - x is an array of size d + 1
1146 * - w is the size, ie number of teeth, of the comb, and must be between
1147 * 2 and 7 (in practice, between 2 and MBEDTLS_ECP_WINDOW_SIZE)
1148 * - m is the MPI, expected to be odd and such that bitlength(m) <= w * d
1149 * (the result will be incorrect if these assumptions are not satisfied)
1150 */
ecp_comb_fixed(unsigned char x[],size_t d,unsigned char w,const mbedtls_mpi * m)1151 static void ecp_comb_fixed( unsigned char x[], size_t d,
1152 unsigned char w, const mbedtls_mpi *m )
1153 {
1154 size_t i, j;
1155 unsigned char c, cc, adjust;
1156
1157 memset( x, 0, d+1 );
1158
1159 /* First get the classical comb values (except for x_d = 0) */
1160 for( i = 0; i < d; i++ )
1161 for( j = 0; j < w; j++ )
1162 x[i] |= mbedtls_mpi_get_bit( m, i + d * j ) << j;
1163
1164 /* Now make sure x_1 .. x_d are odd */
1165 c = 0;
1166 for( i = 1; i <= d; i++ )
1167 {
1168 /* Add carry and update it */
1169 cc = x[i] & c;
1170 x[i] = x[i] ^ c;
1171 c = cc;
1172
1173 /* Adjust if needed, avoiding branches */
1174 adjust = 1 - ( x[i] & 0x01 );
1175 c |= x[i] & ( x[i-1] * adjust );
1176 x[i] = x[i] ^ ( x[i-1] * adjust );
1177 x[i-1] |= adjust << 7;
1178 }
1179 }
1180
1181 /*
1182 * Precompute points for the comb method
1183 *
1184 * If i = i_{w-1} ... i_1 is the binary representation of i, then
1185 * T[i] = i_{w-1} 2^{(w-1)d} P + ... + i_1 2^d P + P
1186 *
1187 * T must be able to hold 2^{w - 1} elements
1188 *
1189 * Cost: d(w-1) D + (2^{w-1} - 1) A + 1 N(w-1) + 1 N(2^{w-1} - 1)
1190 */
ecp_precompute_comb(const mbedtls_ecp_group * grp,mbedtls_ecp_point T[],const mbedtls_ecp_point * P,unsigned char w,size_t d)1191 static int ecp_precompute_comb( const mbedtls_ecp_group *grp,
1192 mbedtls_ecp_point T[], const mbedtls_ecp_point *P,
1193 unsigned char w, size_t d )
1194 {
1195 int ret;
1196 unsigned char i, k;
1197 size_t j;
1198 mbedtls_ecp_point *cur, *TT[COMB_MAX_PRE - 1];
1199
1200 /*
1201 * Set T[0] = P and
1202 * T[2^{l-1}] = 2^{dl} P for l = 1 .. w-1 (this is not the final value)
1203 */
1204 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( &T[0], P ) );
1205
1206 k = 0;
1207 for( i = 1; i < ( 1U << ( w - 1 ) ); i <<= 1 )
1208 {
1209 cur = T + i;
1210 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( cur, T + ( i >> 1 ) ) );
1211 for( j = 0; j < d; j++ )
1212 MBEDTLS_MPI_CHK( ecp_double_jac( grp, cur, cur ) );
1213
1214 TT[k++] = cur;
1215 }
1216
1217 MBEDTLS_MPI_CHK( ecp_normalize_jac_many( grp, TT, k ) );
1218
1219 /*
1220 * Compute the remaining ones using the minimal number of additions
1221 * Be careful to update T[2^l] only after using it!
1222 */
1223 k = 0;
1224 for( i = 1; i < ( 1U << ( w - 1 ) ); i <<= 1 )
1225 {
1226 j = i;
1227 while( j-- )
1228 {
1229 MBEDTLS_MPI_CHK( ecp_add_mixed( grp, &T[i + j], &T[j], &T[i] ) );
1230 TT[k++] = &T[i + j];
1231 }
1232 }
1233
1234 MBEDTLS_MPI_CHK( ecp_normalize_jac_many( grp, TT, k ) );
1235
1236 cleanup:
1237 return( ret );
1238 }
1239
1240 /*
1241 * Select precomputed point: R = sign(i) * T[ abs(i) / 2 ]
1242 */
ecp_select_comb(const mbedtls_ecp_group * grp,mbedtls_ecp_point * R,const mbedtls_ecp_point T[],unsigned char t_len,unsigned char i)1243 static int ecp_select_comb( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
1244 const mbedtls_ecp_point T[], unsigned char t_len,
1245 unsigned char i )
1246 {
1247 int ret;
1248 unsigned char ii, j;
1249
1250 /* Ignore the "sign" bit and scale down */
1251 ii = ( i & 0x7Fu ) >> 1;
1252
1253 /* Read the whole table to thwart cache-based timing attacks */
1254 for( j = 0; j < t_len; j++ )
1255 {
1256 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &R->X, &T[j].X, j == ii ) );
1257 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &R->Y, &T[j].Y, j == ii ) );
1258 }
1259
1260 /* Safely invert result if i is "negative" */
1261 MBEDTLS_MPI_CHK( ecp_safe_invert_jac( grp, R, i >> 7 ) );
1262
1263 cleanup:
1264 return( ret );
1265 }
1266
1267 /*
1268 * Core multiplication algorithm for the (modified) comb method.
1269 * This part is actually common with the basic comb method (GECC 3.44)
1270 *
1271 * Cost: d A + d D + 1 R
1272 */
ecp_mul_comb_core(const mbedtls_ecp_group * grp,mbedtls_ecp_point * R,const mbedtls_ecp_point T[],unsigned char t_len,const unsigned char x[],size_t d,int (* f_rng)(void *,unsigned char *,size_t),void * p_rng)1273 static int ecp_mul_comb_core( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
1274 const mbedtls_ecp_point T[], unsigned char t_len,
1275 const unsigned char x[], size_t d,
1276 int (*f_rng)(void *, unsigned char *, size_t),
1277 void *p_rng )
1278 {
1279 int ret;
1280 mbedtls_ecp_point Txi;
1281 size_t i;
1282
1283 mbedtls_ecp_point_init( &Txi );
1284
1285 /* Start with a non-zero point and randomize its coordinates */
1286 i = d;
1287 MBEDTLS_MPI_CHK( ecp_select_comb( grp, R, T, t_len, x[i] ) );
1288 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->Z, 1 ) );
1289 if( f_rng != 0 )
1290 MBEDTLS_MPI_CHK( ecp_randomize_jac( grp, R, f_rng, p_rng ) );
1291
1292 while( i-- != 0 )
1293 {
1294 MBEDTLS_MPI_CHK( ecp_double_jac( grp, R, R ) );
1295 MBEDTLS_MPI_CHK( ecp_select_comb( grp, &Txi, T, t_len, x[i] ) );
1296 MBEDTLS_MPI_CHK( ecp_add_mixed( grp, R, R, &Txi ) );
1297 }
1298
1299 cleanup:
1300 mbedtls_ecp_point_free( &Txi );
1301
1302 return( ret );
1303 }
1304
1305 /*
1306 * Multiplication using the comb method,
1307 * for curves in short Weierstrass form
1308 */
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)1309 static int ecp_mul_comb( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
1310 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
1311 int (*f_rng)(void *, unsigned char *, size_t),
1312 void *p_rng )
1313 {
1314 int ret;
1315 unsigned char w, m_is_odd, p_eq_g, pre_len, i;
1316 size_t d;
1317 unsigned char k[COMB_MAX_D + 1];
1318 mbedtls_ecp_point *T;
1319 mbedtls_mpi M, mm;
1320
1321 mbedtls_mpi_init( &M );
1322 mbedtls_mpi_init( &mm );
1323
1324 /* we need N to be odd to trnaform m in an odd number, check now */
1325 if( mbedtls_mpi_get_bit( &grp->N, 0 ) != 1 )
1326 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1327
1328 /*
1329 * Minimize the number of multiplications, that is minimize
1330 * 10 * d * w + 18 * 2^(w-1) + 11 * d + 7 * w, with d = ceil( nbits / w )
1331 * (see costs of the various parts, with 1S = 1M)
1332 */
1333 w = grp->nbits >= 384 ? 5 : 4;
1334
1335 /*
1336 * If P == G, pre-compute a bit more, since this may be re-used later.
1337 * Just adding one avoids upping the cost of the first mul too much,
1338 * and the memory cost too.
1339 */
1340 #if MBEDTLS_ECP_FIXED_POINT_OPTIM == 1
1341 p_eq_g = ( mbedtls_mpi_cmp_mpi( &P->Y, &grp->G.Y ) == 0 &&
1342 mbedtls_mpi_cmp_mpi( &P->X, &grp->G.X ) == 0 );
1343 if( p_eq_g )
1344 w++;
1345 #else
1346 p_eq_g = 0;
1347 #endif
1348
1349 /*
1350 * Make sure w is within bounds.
1351 * (The last test is useful only for very small curves in the test suite.)
1352 */
1353 if( w > MBEDTLS_ECP_WINDOW_SIZE )
1354 w = MBEDTLS_ECP_WINDOW_SIZE;
1355 if( w >= grp->nbits )
1356 w = 2;
1357
1358 /* Other sizes that depend on w */
1359 pre_len = 1U << ( w - 1 );
1360 d = ( grp->nbits + w - 1 ) / w;
1361
1362 /*
1363 * Prepare precomputed points: if P == G we want to
1364 * use grp->T if already initialized, or initialize it.
1365 */
1366 T = p_eq_g ? grp->T : NULL;
1367
1368 if( T == NULL )
1369 {
1370 T = mbedtls_calloc( pre_len, sizeof( mbedtls_ecp_point ) );
1371 if( T == NULL )
1372 {
1373 ret = MBEDTLS_ERR_ECP_ALLOC_FAILED;
1374 goto cleanup;
1375 }
1376
1377 MBEDTLS_MPI_CHK( ecp_precompute_comb( grp, T, P, w, d ) );
1378
1379 if( p_eq_g )
1380 {
1381 grp->T = T;
1382 grp->T_size = pre_len;
1383 }
1384 }
1385
1386 /*
1387 * Make sure M is odd (M = m or M = N - m, since N is odd)
1388 * using the fact that m * P = - (N - m) * P
1389 */
1390 m_is_odd = ( mbedtls_mpi_get_bit( m, 0 ) == 1 );
1391 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &M, m ) );
1392 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &mm, &grp->N, m ) );
1393 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &M, &mm, ! m_is_odd ) );
1394
1395 /*
1396 * Go for comb multiplication, R = M * P
1397 */
1398 ecp_comb_fixed( k, d, w, &M );
1399 MBEDTLS_MPI_CHK( ecp_mul_comb_core( grp, R, T, pre_len, k, d, f_rng, p_rng ) );
1400
1401 /*
1402 * Now get m * P from M * P and normalize it
1403 */
1404 MBEDTLS_MPI_CHK( ecp_safe_invert_jac( grp, R, ! m_is_odd ) );
1405 MBEDTLS_MPI_CHK( ecp_normalize_jac( grp, R ) );
1406
1407 cleanup:
1408
1409 if( T != NULL && ! p_eq_g )
1410 {
1411 for( i = 0; i < pre_len; i++ )
1412 mbedtls_ecp_point_free( &T[i] );
1413 mbedtls_free( T );
1414 }
1415
1416 mbedtls_mpi_free( &M );
1417 mbedtls_mpi_free( &mm );
1418
1419 if( ret != 0 )
1420 mbedtls_ecp_point_free( R );
1421
1422 return( ret );
1423 }
1424
1425 #endif /* ECP_SHORTWEIERSTRASS */
1426
1427 #if defined(ECP_MONTGOMERY)
1428 /*
1429 * For Montgomery curves, we do all the internal arithmetic in projective
1430 * coordinates. Import/export of points uses only the x coordinates, which is
1431 * internaly represented as X / Z.
1432 *
1433 * For scalar multiplication, we'll use a Montgomery ladder.
1434 */
1435
1436 /*
1437 * Normalize Montgomery x/z coordinates: X = X/Z, Z = 1
1438 * Cost: 1M + 1I
1439 */
ecp_normalize_mxz(const mbedtls_ecp_group * grp,mbedtls_ecp_point * P)1440 static int ecp_normalize_mxz( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P )
1441 {
1442 int ret;
1443
1444 MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &P->Z, &P->Z, &grp->P ) );
1445 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &P->X, &P->X, &P->Z ) ); MOD_MUL( P->X );
1446 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &P->Z, 1 ) );
1447
1448 cleanup:
1449 return( ret );
1450 }
1451
1452 /*
1453 * Randomize projective x/z coordinates:
1454 * (X, Z) -> (l X, l Z) for random l
1455 * This is sort of the reverse operation of ecp_normalize_mxz().
1456 *
1457 * This countermeasure was first suggested in [2].
1458 * Cost: 2M
1459 */
ecp_randomize_mxz(const mbedtls_ecp_group * grp,mbedtls_ecp_point * P,int (* f_rng)(void *,unsigned char *,size_t),void * p_rng)1460 static int ecp_randomize_mxz( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P,
1461 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
1462 {
1463 int ret;
1464 mbedtls_mpi l;
1465 size_t p_size = ( grp->pbits + 7 ) / 8;
1466 int count = 0;
1467
1468 mbedtls_mpi_init( &l );
1469
1470 /* Generate l such that 1 < l < p */
1471 do
1472 {
1473 mbedtls_mpi_fill_random( &l, p_size, f_rng, p_rng );
1474
1475 while( mbedtls_mpi_cmp_mpi( &l, &grp->P ) >= 0 )
1476 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &l, 1 ) );
1477
1478 if( count++ > 10 )
1479 return( MBEDTLS_ERR_ECP_RANDOM_FAILED );
1480 }
1481 while( mbedtls_mpi_cmp_int( &l, 1 ) <= 0 );
1482
1483 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &P->X, &P->X, &l ) ); MOD_MUL( P->X );
1484 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &P->Z, &P->Z, &l ) ); MOD_MUL( P->Z );
1485
1486 cleanup:
1487 mbedtls_mpi_free( &l );
1488
1489 return( ret );
1490 }
1491
1492 /*
1493 * Double-and-add: R = 2P, S = P + Q, with d = X(P - Q),
1494 * for Montgomery curves in x/z coordinates.
1495 *
1496 * http://www.hyperelliptic.org/EFD/g1p/auto-code/montgom/xz/ladder/mladd-1987-m.op3
1497 * with
1498 * d = X1
1499 * P = (X2, Z2)
1500 * Q = (X3, Z3)
1501 * R = (X4, Z4)
1502 * S = (X5, Z5)
1503 * and eliminating temporary variables tO, ..., t4.
1504 *
1505 * Cost: 5M + 4S
1506 */
ecp_double_add_mxz(const mbedtls_ecp_group * grp,mbedtls_ecp_point * R,mbedtls_ecp_point * S,const mbedtls_ecp_point * P,const mbedtls_ecp_point * Q,const mbedtls_mpi * d)1507 static int ecp_double_add_mxz( const mbedtls_ecp_group *grp,
1508 mbedtls_ecp_point *R, mbedtls_ecp_point *S,
1509 const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q,
1510 const mbedtls_mpi *d )
1511 {
1512 int ret;
1513 mbedtls_mpi A, AA, B, BB, E, C, D, DA, CB;
1514
1515 mbedtls_mpi_init( &A ); mbedtls_mpi_init( &AA ); mbedtls_mpi_init( &B );
1516 mbedtls_mpi_init( &BB ); mbedtls_mpi_init( &E ); mbedtls_mpi_init( &C );
1517 mbedtls_mpi_init( &D ); mbedtls_mpi_init( &DA ); mbedtls_mpi_init( &CB );
1518
1519 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &A, &P->X, &P->Z ) ); MOD_ADD( A );
1520 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &AA, &A, &A ) ); MOD_MUL( AA );
1521 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &B, &P->X, &P->Z ) ); MOD_SUB( B );
1522 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &BB, &B, &B ) ); MOD_MUL( BB );
1523 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &E, &AA, &BB ) ); MOD_SUB( E );
1524 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &C, &Q->X, &Q->Z ) ); MOD_ADD( C );
1525 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &D, &Q->X, &Q->Z ) ); MOD_SUB( D );
1526 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &DA, &D, &A ) ); MOD_MUL( DA );
1527 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &CB, &C, &B ) ); MOD_MUL( CB );
1528 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &S->X, &DA, &CB ) ); MOD_MUL( S->X );
1529 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S->X, &S->X, &S->X ) ); MOD_MUL( S->X );
1530 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &S->Z, &DA, &CB ) ); MOD_SUB( S->Z );
1531 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S->Z, &S->Z, &S->Z ) ); MOD_MUL( S->Z );
1532 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S->Z, d, &S->Z ) ); MOD_MUL( S->Z );
1533 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &R->X, &AA, &BB ) ); MOD_MUL( R->X );
1534 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &R->Z, &grp->A, &E ) ); MOD_MUL( R->Z );
1535 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &R->Z, &BB, &R->Z ) ); MOD_ADD( R->Z );
1536 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &R->Z, &E, &R->Z ) ); MOD_MUL( R->Z );
1537
1538 cleanup:
1539 mbedtls_mpi_free( &A ); mbedtls_mpi_free( &AA ); mbedtls_mpi_free( &B );
1540 mbedtls_mpi_free( &BB ); mbedtls_mpi_free( &E ); mbedtls_mpi_free( &C );
1541 mbedtls_mpi_free( &D ); mbedtls_mpi_free( &DA ); mbedtls_mpi_free( &CB );
1542
1543 return( ret );
1544 }
1545
1546 /*
1547 * Multiplication with Montgomery ladder in x/z coordinates,
1548 * for curves in Montgomery form
1549 */
ecp_mul_mxz(mbedtls_ecp_group * grp,mbedtls_ecp_point * R,const mbedtls_mpi * m,const mbedtls_ecp_point * P,int (* f_rng)(void *,unsigned char *,size_t),void * p_rng)1550 static int ecp_mul_mxz( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
1551 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
1552 int (*f_rng)(void *, unsigned char *, size_t),
1553 void *p_rng )
1554 {
1555 int ret;
1556 size_t i;
1557 unsigned char b;
1558 mbedtls_ecp_point RP;
1559 mbedtls_mpi PX;
1560
1561 mbedtls_ecp_point_init( &RP ); mbedtls_mpi_init( &PX );
1562
1563 /* Save PX and read from P before writing to R, in case P == R */
1564 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &PX, &P->X ) );
1565 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( &RP, P ) );
1566
1567 /* Set R to zero in modified x/z coordinates */
1568 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->X, 1 ) );
1569 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->Z, 0 ) );
1570 mbedtls_mpi_free( &R->Y );
1571
1572 /* RP.X might be sligtly larger than P, so reduce it */
1573 MOD_ADD( RP.X );
1574
1575 /* Randomize coordinates of the starting point */
1576 if( f_rng != NULL )
1577 MBEDTLS_MPI_CHK( ecp_randomize_mxz( grp, &RP, f_rng, p_rng ) );
1578
1579 /* Loop invariant: R = result so far, RP = R + P */
1580 i = mbedtls_mpi_bitlen( m ); /* one past the (zero-based) most significant bit */
1581 while( i-- > 0 )
1582 {
1583 b = mbedtls_mpi_get_bit( m, i );
1584 /*
1585 * if (b) R = 2R + P else R = 2R,
1586 * which is:
1587 * if (b) double_add( RP, R, RP, R )
1588 * else double_add( R, RP, R, RP )
1589 * but using safe conditional swaps to avoid leaks
1590 */
1591 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->X, &RP.X, b ) );
1592 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->Z, &RP.Z, b ) );
1593 MBEDTLS_MPI_CHK( ecp_double_add_mxz( grp, R, &RP, R, &RP, &PX ) );
1594 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->X, &RP.X, b ) );
1595 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->Z, &RP.Z, b ) );
1596 }
1597
1598 MBEDTLS_MPI_CHK( ecp_normalize_mxz( grp, R ) );
1599
1600 cleanup:
1601 mbedtls_ecp_point_free( &RP ); mbedtls_mpi_free( &PX );
1602
1603 return( ret );
1604 }
1605
1606 #endif /* ECP_MONTGOMERY */
1607
1608 /*
1609 * Multiplication R = m * P
1610 */
mbedtls_ecp_mul(mbedtls_ecp_group * grp,mbedtls_ecp_point * R,const mbedtls_mpi * m,const mbedtls_ecp_point * P,int (* f_rng)(void *,unsigned char *,size_t),void * p_rng)1611 int mbedtls_ecp_mul( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
1612 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
1613 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
1614 {
1615 int ret;
1616
1617 /* Common sanity checks */
1618 if( mbedtls_mpi_cmp_int( &P->Z, 1 ) != 0 )
1619 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1620
1621 if( ( ret = mbedtls_ecp_check_privkey( grp, m ) ) != 0 ||
1622 ( ret = mbedtls_ecp_check_pubkey( grp, P ) ) != 0 )
1623 return( ret );
1624
1625 #if defined(ECP_MONTGOMERY)
1626 if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
1627 return( ecp_mul_mxz( grp, R, m, P, f_rng, p_rng ) );
1628 #endif
1629 #if defined(ECP_SHORTWEIERSTRASS)
1630 if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS )
1631 return( ecp_mul_comb( grp, R, m, P, f_rng, p_rng ) );
1632 #endif
1633 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1634 }
1635
1636 #if defined(ECP_SHORTWEIERSTRASS)
1637 /*
1638 * Check that an affine point is valid as a public key,
1639 * short weierstrass curves (SEC1 3.2.3.1)
1640 */
ecp_check_pubkey_sw(const mbedtls_ecp_group * grp,const mbedtls_ecp_point * pt)1641 static int ecp_check_pubkey_sw( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt )
1642 {
1643 int ret;
1644 mbedtls_mpi YY, RHS;
1645
1646 /* pt coordinates must be normalized for our checks */
1647 if( mbedtls_mpi_cmp_int( &pt->X, 0 ) < 0 ||
1648 mbedtls_mpi_cmp_int( &pt->Y, 0 ) < 0 ||
1649 mbedtls_mpi_cmp_mpi( &pt->X, &grp->P ) >= 0 ||
1650 mbedtls_mpi_cmp_mpi( &pt->Y, &grp->P ) >= 0 )
1651 return( MBEDTLS_ERR_ECP_INVALID_KEY );
1652
1653 mbedtls_mpi_init( &YY ); mbedtls_mpi_init( &RHS );
1654
1655 /*
1656 * YY = Y^2
1657 * RHS = X (X^2 + A) + B = X^3 + A X + B
1658 */
1659 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &YY, &pt->Y, &pt->Y ) ); MOD_MUL( YY );
1660 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &RHS, &pt->X, &pt->X ) ); MOD_MUL( RHS );
1661
1662 /* Special case for A = -3 */
1663 if( grp->A.p == NULL )
1664 {
1665 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &RHS, &RHS, 3 ) ); MOD_SUB( RHS );
1666 }
1667 else
1668 {
1669 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &RHS, &RHS, &grp->A ) ); MOD_ADD( RHS );
1670 }
1671
1672 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &RHS, &RHS, &pt->X ) ); MOD_MUL( RHS );
1673 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &RHS, &RHS, &grp->B ) ); MOD_ADD( RHS );
1674
1675 if( mbedtls_mpi_cmp_mpi( &YY, &RHS ) != 0 )
1676 ret = MBEDTLS_ERR_ECP_INVALID_KEY;
1677
1678 cleanup:
1679
1680 mbedtls_mpi_free( &YY ); mbedtls_mpi_free( &RHS );
1681
1682 return( ret );
1683 }
1684 #endif /* ECP_SHORTWEIERSTRASS */
1685
1686 /*
1687 * R = m * P with shortcuts for m == 1 and m == -1
1688 * NOT constant-time - ONLY for short Weierstrass!
1689 */
mbedtls_ecp_mul_shortcuts(mbedtls_ecp_group * grp,mbedtls_ecp_point * R,const mbedtls_mpi * m,const mbedtls_ecp_point * P)1690 static int mbedtls_ecp_mul_shortcuts( mbedtls_ecp_group *grp,
1691 mbedtls_ecp_point *R,
1692 const mbedtls_mpi *m,
1693 const mbedtls_ecp_point *P )
1694 {
1695 int ret;
1696
1697 if( mbedtls_mpi_cmp_int( m, 1 ) == 0 )
1698 {
1699 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, P ) );
1700 }
1701 else if( mbedtls_mpi_cmp_int( m, -1 ) == 0 )
1702 {
1703 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, P ) );
1704 if( mbedtls_mpi_cmp_int( &R->Y, 0 ) != 0 )
1705 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &R->Y, &grp->P, &R->Y ) );
1706 }
1707 else
1708 {
1709 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( grp, R, m, P, NULL, NULL ) );
1710 }
1711
1712 cleanup:
1713 return( ret );
1714 }
1715
1716 /*
1717 * Linear combination
1718 * NOT constant-time
1719 */
mbedtls_ecp_muladd(mbedtls_ecp_group * grp,mbedtls_ecp_point * R,const mbedtls_mpi * m,const mbedtls_ecp_point * P,const mbedtls_mpi * n,const mbedtls_ecp_point * Q)1720 int mbedtls_ecp_muladd( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
1721 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
1722 const mbedtls_mpi *n, const mbedtls_ecp_point *Q )
1723 {
1724 int ret;
1725 mbedtls_ecp_point mP;
1726
1727 if( ecp_get_type( grp ) != ECP_TYPE_SHORT_WEIERSTRASS )
1728 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
1729
1730 mbedtls_ecp_point_init( &mP );
1731
1732 MBEDTLS_MPI_CHK( mbedtls_ecp_mul_shortcuts( grp, &mP, m, P ) );
1733 MBEDTLS_MPI_CHK( mbedtls_ecp_mul_shortcuts( grp, R, n, Q ) );
1734
1735 MBEDTLS_MPI_CHK( ecp_add_mixed( grp, R, &mP, R ) );
1736 MBEDTLS_MPI_CHK( ecp_normalize_jac( grp, R ) );
1737
1738 cleanup:
1739 mbedtls_ecp_point_free( &mP );
1740
1741 return( ret );
1742 }
1743
1744
1745 #if defined(ECP_MONTGOMERY)
1746 /*
1747 * Check validity of a public key for Montgomery curves with x-only schemes
1748 */
ecp_check_pubkey_mx(const mbedtls_ecp_group * grp,const mbedtls_ecp_point * pt)1749 static int ecp_check_pubkey_mx( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt )
1750 {
1751 /* [Curve25519 p. 5] Just check X is the correct number of bytes */
1752 if( mbedtls_mpi_size( &pt->X ) > ( grp->nbits + 7 ) / 8 )
1753 return( MBEDTLS_ERR_ECP_INVALID_KEY );
1754
1755 return( 0 );
1756 }
1757 #endif /* ECP_MONTGOMERY */
1758
1759 /*
1760 * Check that a point is valid as a public key
1761 */
mbedtls_ecp_check_pubkey(const mbedtls_ecp_group * grp,const mbedtls_ecp_point * pt)1762 int mbedtls_ecp_check_pubkey( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt )
1763 {
1764 /* Must use affine coordinates */
1765 if( mbedtls_mpi_cmp_int( &pt->Z, 1 ) != 0 )
1766 return( MBEDTLS_ERR_ECP_INVALID_KEY );
1767
1768 #if defined(ECP_MONTGOMERY)
1769 if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
1770 return( ecp_check_pubkey_mx( grp, pt ) );
1771 #endif
1772 #if defined(ECP_SHORTWEIERSTRASS)
1773 if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS )
1774 return( ecp_check_pubkey_sw( grp, pt ) );
1775 #endif
1776 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1777 }
1778
1779 /*
1780 * Check that an mbedtls_mpi is valid as a private key
1781 */
mbedtls_ecp_check_privkey(const mbedtls_ecp_group * grp,const mbedtls_mpi * d)1782 int mbedtls_ecp_check_privkey( const mbedtls_ecp_group *grp, const mbedtls_mpi *d )
1783 {
1784 #if defined(ECP_MONTGOMERY)
1785 if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
1786 {
1787 /* see [Curve25519] page 5 */
1788 if( mbedtls_mpi_get_bit( d, 0 ) != 0 ||
1789 mbedtls_mpi_get_bit( d, 1 ) != 0 ||
1790 mbedtls_mpi_get_bit( d, 2 ) != 0 ||
1791 mbedtls_mpi_bitlen( d ) - 1 != grp->nbits ) /* mbedtls_mpi_bitlen is one-based! */
1792 return( MBEDTLS_ERR_ECP_INVALID_KEY );
1793 else
1794 return( 0 );
1795 }
1796 #endif /* ECP_MONTGOMERY */
1797 #if defined(ECP_SHORTWEIERSTRASS)
1798 if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS )
1799 {
1800 /* see SEC1 3.2 */
1801 if( mbedtls_mpi_cmp_int( d, 1 ) < 0 ||
1802 mbedtls_mpi_cmp_mpi( d, &grp->N ) >= 0 )
1803 return( MBEDTLS_ERR_ECP_INVALID_KEY );
1804 else
1805 return( 0 );
1806 }
1807 #endif /* ECP_SHORTWEIERSTRASS */
1808
1809 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1810 }
1811
1812 /*
1813 * Generate a keypair with configurable base point
1814 */
mbedtls_ecp_gen_keypair_base(mbedtls_ecp_group * grp,const mbedtls_ecp_point * G,mbedtls_mpi * d,mbedtls_ecp_point * Q,int (* f_rng)(void *,unsigned char *,size_t),void * p_rng)1815 int mbedtls_ecp_gen_keypair_base( mbedtls_ecp_group *grp,
1816 const mbedtls_ecp_point *G,
1817 mbedtls_mpi *d, mbedtls_ecp_point *Q,
1818 int (*f_rng)(void *, unsigned char *, size_t),
1819 void *p_rng )
1820 {
1821 int ret;
1822 size_t n_size = ( grp->nbits + 7 ) / 8;
1823
1824 #if defined(ECP_MONTGOMERY)
1825 if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
1826 {
1827 /* [M225] page 5 */
1828 size_t b;
1829
1830 do {
1831 MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( d, n_size, f_rng, p_rng ) );
1832 } while( mbedtls_mpi_bitlen( d ) == 0);
1833
1834 /* Make sure the most significant bit is nbits */
1835 b = mbedtls_mpi_bitlen( d ) - 1; /* mbedtls_mpi_bitlen is one-based */
1836 if( b > grp->nbits )
1837 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( d, b - grp->nbits ) );
1838 else
1839 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, grp->nbits, 1 ) );
1840
1841 /* Make sure the last three bits are unset */
1842 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 0, 0 ) );
1843 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 1, 0 ) );
1844 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 2, 0 ) );
1845 }
1846 else
1847 #endif /* ECP_MONTGOMERY */
1848 #if defined(ECP_SHORTWEIERSTRASS)
1849 if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS )
1850 {
1851 /* SEC1 3.2.1: Generate d such that 1 <= n < N */
1852 int count = 0;
1853 unsigned char rnd[MBEDTLS_ECP_MAX_BYTES];
1854
1855 /*
1856 * Match the procedure given in RFC 6979 (deterministic ECDSA):
1857 * - use the same byte ordering;
1858 * - keep the leftmost nbits bits of the generated octet string;
1859 * - try until result is in the desired range.
1860 * This also avoids any biais, which is especially important for ECDSA.
1861 */
1862 do
1863 {
1864 MBEDTLS_MPI_CHK( f_rng( p_rng, rnd, n_size ) );
1865 MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( d, rnd, n_size ) );
1866 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( d, 8 * n_size - grp->nbits ) );
1867
1868 /*
1869 * Each try has at worst a probability 1/2 of failing (the msb has
1870 * a probability 1/2 of being 0, and then the result will be < N),
1871 * so after 30 tries failure probability is a most 2**(-30).
1872 *
1873 * For most curves, 1 try is enough with overwhelming probability,
1874 * since N starts with a lot of 1s in binary, but some curves
1875 * such as secp224k1 are actually very close to the worst case.
1876 */
1877 if( ++count > 30 )
1878 return( MBEDTLS_ERR_ECP_RANDOM_FAILED );
1879 }
1880 while( mbedtls_mpi_cmp_int( d, 1 ) < 0 ||
1881 mbedtls_mpi_cmp_mpi( d, &grp->N ) >= 0 );
1882 }
1883 else
1884 #endif /* ECP_SHORTWEIERSTRASS */
1885 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1886
1887 cleanup:
1888 if( ret != 0 )
1889 return( ret );
1890
1891 return( mbedtls_ecp_mul( grp, Q, d, G, f_rng, p_rng ) );
1892 }
1893
1894 /*
1895 * Generate key pair, wrapper for conventional base point
1896 */
mbedtls_ecp_gen_keypair(mbedtls_ecp_group * grp,mbedtls_mpi * d,mbedtls_ecp_point * Q,int (* f_rng)(void *,unsigned char *,size_t),void * p_rng)1897 int mbedtls_ecp_gen_keypair( mbedtls_ecp_group *grp,
1898 mbedtls_mpi *d, mbedtls_ecp_point *Q,
1899 int (*f_rng)(void *, unsigned char *, size_t),
1900 void *p_rng )
1901 {
1902 return( mbedtls_ecp_gen_keypair_base( grp, &grp->G, d, Q, f_rng, p_rng ) );
1903 }
1904
1905 /*
1906 * Generate a keypair, prettier wrapper
1907 */
mbedtls_ecp_gen_key(mbedtls_ecp_group_id grp_id,mbedtls_ecp_keypair * key,int (* f_rng)(void *,unsigned char *,size_t),void * p_rng)1908 int mbedtls_ecp_gen_key( mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key,
1909 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
1910 {
1911 int ret;
1912
1913 if( ( ret = mbedtls_ecp_group_load( &key->grp, grp_id ) ) != 0 )
1914 return( ret );
1915
1916 return( mbedtls_ecp_gen_keypair( &key->grp, &key->d, &key->Q, f_rng, p_rng ) );
1917 }
1918
1919 /*
1920 * Check a public-private key pair
1921 */
mbedtls_ecp_check_pub_priv(const mbedtls_ecp_keypair * pub,const mbedtls_ecp_keypair * prv)1922 int mbedtls_ecp_check_pub_priv( const mbedtls_ecp_keypair *pub, const mbedtls_ecp_keypair *prv )
1923 {
1924 int ret;
1925 mbedtls_ecp_point Q;
1926 mbedtls_ecp_group grp;
1927
1928 if( pub->grp.id == MBEDTLS_ECP_DP_NONE ||
1929 pub->grp.id != prv->grp.id ||
1930 mbedtls_mpi_cmp_mpi( &pub->Q.X, &prv->Q.X ) ||
1931 mbedtls_mpi_cmp_mpi( &pub->Q.Y, &prv->Q.Y ) ||
1932 mbedtls_mpi_cmp_mpi( &pub->Q.Z, &prv->Q.Z ) )
1933 {
1934 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1935 }
1936
1937 mbedtls_ecp_point_init( &Q );
1938 mbedtls_ecp_group_init( &grp );
1939
1940 /* mbedtls_ecp_mul() needs a non-const group... */
1941 mbedtls_ecp_group_copy( &grp, &prv->grp );
1942
1943 /* Also checks d is valid */
1944 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &Q, &prv->d, &prv->grp.G, NULL, NULL ) );
1945
1946 if( mbedtls_mpi_cmp_mpi( &Q.X, &prv->Q.X ) ||
1947 mbedtls_mpi_cmp_mpi( &Q.Y, &prv->Q.Y ) ||
1948 mbedtls_mpi_cmp_mpi( &Q.Z, &prv->Q.Z ) )
1949 {
1950 ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
1951 goto cleanup;
1952 }
1953
1954 cleanup:
1955 mbedtls_ecp_point_free( &Q );
1956 mbedtls_ecp_group_free( &grp );
1957
1958 return( ret );
1959 }
1960
1961 #if defined(MBEDTLS_SELF_TEST)
1962
1963 /*
1964 * Checkup routine
1965 */
mbedtls_ecp_self_test(int verbose)1966 int mbedtls_ecp_self_test( int verbose )
1967 {
1968 int ret;
1969 size_t i;
1970 mbedtls_ecp_group grp;
1971 mbedtls_ecp_point R, P;
1972 mbedtls_mpi m;
1973 unsigned long add_c_prev, dbl_c_prev, mul_c_prev;
1974 /* exponents especially adapted for secp192r1 */
1975 const char *exponents[] =
1976 {
1977 "000000000000000000000000000000000000000000000001", /* one */
1978 "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22830", /* N - 1 */
1979 "5EA6F389A38B8BC81E767753B15AA5569E1782E30ABE7D25", /* random */
1980 "400000000000000000000000000000000000000000000000", /* one and zeros */
1981 "7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", /* all ones */
1982 "555555555555555555555555555555555555555555555555", /* 101010... */
1983 };
1984
1985 mbedtls_ecp_group_init( &grp );
1986 mbedtls_ecp_point_init( &R );
1987 mbedtls_ecp_point_init( &P );
1988 mbedtls_mpi_init( &m );
1989
1990 /* Use secp192r1 if available, or any available curve */
1991 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
1992 MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, MBEDTLS_ECP_DP_SECP192R1 ) );
1993 #else
1994 MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, mbedtls_ecp_curve_list()->grp_id ) );
1995 #endif
1996
1997 if( verbose != 0 )
1998 mbedtls_printf( " ECP test #1 (constant op_count, base point G): " );
1999
2000 /* Do a dummy multiplication first to trigger precomputation */
2001 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &m, 2 ) );
2002 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &P, &m, &grp.G, NULL, NULL ) );
2003
2004 add_count = 0;
2005 dbl_count = 0;
2006 mul_count = 0;
2007 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[0] ) );
2008 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &grp.G, NULL, NULL ) );
2009
2010 for( i = 1; i < sizeof( exponents ) / sizeof( exponents[0] ); i++ )
2011 {
2012 add_c_prev = add_count;
2013 dbl_c_prev = dbl_count;
2014 mul_c_prev = mul_count;
2015 add_count = 0;
2016 dbl_count = 0;
2017 mul_count = 0;
2018
2019 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[i] ) );
2020 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &grp.G, NULL, NULL ) );
2021
2022 if( add_count != add_c_prev ||
2023 dbl_count != dbl_c_prev ||
2024 mul_count != mul_c_prev )
2025 {
2026 if( verbose != 0 )
2027 mbedtls_printf( "failed (%u)\n", (unsigned int) i );
2028
2029 ret = 1;
2030 goto cleanup;
2031 }
2032 }
2033
2034 if( verbose != 0 )
2035 mbedtls_printf( "passed\n" );
2036
2037 if( verbose != 0 )
2038 mbedtls_printf( " ECP test #2 (constant op_count, other point): " );
2039 /* We computed P = 2G last time, use it */
2040
2041 add_count = 0;
2042 dbl_count = 0;
2043 mul_count = 0;
2044 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[0] ) );
2045 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &P, NULL, NULL ) );
2046
2047 for( i = 1; i < sizeof( exponents ) / sizeof( exponents[0] ); i++ )
2048 {
2049 add_c_prev = add_count;
2050 dbl_c_prev = dbl_count;
2051 mul_c_prev = mul_count;
2052 add_count = 0;
2053 dbl_count = 0;
2054 mul_count = 0;
2055
2056 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[i] ) );
2057 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &P, NULL, NULL ) );
2058
2059 if( add_count != add_c_prev ||
2060 dbl_count != dbl_c_prev ||
2061 mul_count != mul_c_prev )
2062 {
2063 if( verbose != 0 )
2064 mbedtls_printf( "failed (%u)\n", (unsigned int) i );
2065
2066 ret = 1;
2067 goto cleanup;
2068 }
2069 }
2070
2071 if( verbose != 0 )
2072 mbedtls_printf( "passed\n" );
2073
2074 cleanup:
2075
2076 if( ret < 0 && verbose != 0 )
2077 mbedtls_printf( "Unexpected error, return code = %08X\n", ret );
2078
2079 mbedtls_ecp_group_free( &grp );
2080 mbedtls_ecp_point_free( &R );
2081 mbedtls_ecp_point_free( &P );
2082 mbedtls_mpi_free( &m );
2083
2084 if( verbose != 0 )
2085 mbedtls_printf( "\n" );
2086
2087 return( ret );
2088 }
2089
2090 #endif /* MBEDTLS_SELF_TEST */
2091
2092 #endif /* MBEDTLS_ECP_C */
2093
