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move from polarssl to mbedtls (#708)
[proxmark3-svn] / common / mbedtls / ecp.c
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OM		 1/*
2 * Elliptic curves over GF(p): generic functions
3 *
4 * Copyright (C) 2006-2015, ARM Limited, All Rights Reserved
5 * SPDX-License-Identifier: GPL-2.0
6 *
7 * This program is free software; you can redistribute it and/or modify
8 * it under the terms of the GNU General Public License as published by
9 * the Free Software Foundation; either version 2 of the License, or
10 * (at your option) any later version.
11 *
12 * This program is distributed in the hope that it will be useful,
13 * but WITHOUT ANY WARRANTY; without even the implied warranty of
14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
15 * GNU General Public License for more details.
16 *
17 * You should have received a copy of the GNU General Public License along
18 * with this program; if not, write to the Free Software Foundation, Inc.,
19 * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
20 *
21 * This file is part of mbed TLS (https://tls.mbed.org)
22 */
23
24/*
25 * References:
26 *
27 * SEC1 http://www.secg.org/index.php?action=secg,docs_secg
28 * GECC = Guide to Elliptic Curve Cryptography - Hankerson, Menezes, Vanstone
29 * FIPS 186-3 http://csrc.nist.gov/publications/fips/fips186-3/fips_186-3.pdf
30 * RFC 4492 for the related TLS structures and constants
31 * RFC 7748 for the Curve448 and Curve25519 curve definitions
32 *
33 * [Curve25519] http://cr.yp.to/ecdh/curve25519-20060209.pdf
34 *
35 * [2] CORON, Jean-S'ebastien. Resistance against differential power analysis
36 * for elliptic curve cryptosystems. In : Cryptographic Hardware and
37 * Embedded Systems. Springer Berlin Heidelberg, 1999. p. 292-302.
38 * <http://link.springer.com/chapter/10.1007/3-540-48059-5_25>
39 *
40 * [3] HEDABOU, Mustapha, PINEL, Pierre, et B'EN'ETEAU, Lucien. A comb method to
41 * render ECC resistant against Side Channel Attacks. IACR Cryptology
42 * ePrint Archive, 2004, vol. 2004, p. 342.
43 * <http://eprint.iacr.org/2004/342.pdf>
44 */
45
46#if !defined(MBEDTLS_CONFIG_FILE)
47#include "mbedtls/config.h"
48#else
49#include MBEDTLS_CONFIG_FILE
50#endif
51
52#if defined(MBEDTLS_ECP_C)
53
54#include "mbedtls/ecp.h"
55#include "mbedtls/threading.h"
56#include "mbedtls/platform_util.h"
57
58#include <string.h>
59
60#if !defined(MBEDTLS_ECP_ALT)
61
62#if defined(MBEDTLS_PLATFORM_C)
63#include "mbedtls/platform.h"
64#else
65#include <stdlib.h>
66#include <stdio.h>
67#define mbedtls_printf printf
68#define mbedtls_calloc calloc
69#define mbedtls_free free
70#endif
71
72#include "mbedtls/ecp_internal.h"
73
74#if ( defined(__ARMCC_VERSION) || defined(_MSC_VER) ) && \
75 !defined(inline) && !defined(__cplusplus)
76#define inline __inline
77#endif
78
79#if defined(MBEDTLS_SELF_TEST)
80/*
81 * Counts of point addition and doubling, and field multiplications.
82 * Used to test resistance of point multiplication to simple timing attacks.
83 */
84static unsigned long add_count, dbl_count, mul_count;
85#endif
86
87#if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) || \
88 defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) || \
89 defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) || \
90 defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) || \
91 defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) || \
92 defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) || \
93 defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) || \
94 defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) || \
95 defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) || \
96 defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) || \
97 defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
98#define ECP_SHORTWEIERSTRASS
99#endif
100
101#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) || \
102 defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
103#define ECP_MONTGOMERY
104#endif
105
106/*
107 * Curve types: internal for now, might be exposed later
108 */
109typedef enum
110{
111 ECP_TYPE_NONE = 0,
112 ECP_TYPE_SHORT_WEIERSTRASS, /* y^2 = x^3 + a x + b */
113 ECP_TYPE_MONTGOMERY, /* y^2 = x^3 + a x^2 + x */
114} ecp_curve_type;
115
116/*
117 * List of supported curves:
118 * - internal ID
119 * - TLS NamedCurve ID (RFC 4492 sec. 5.1.1, RFC 7071 sec. 2)
120 * - size in bits
121 * - readable name
122 *
123 * Curves are listed in order: largest curves first, and for a given size,
124 * fastest curves first. This provides the default order for the SSL module.
125 *
126 * Reminder: update profiles in x509_crt.c when adding a new curves!
127 */
128static const mbedtls_ecp_curve_info ecp_supported_curves[] =
129{
130#if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
131 { MBEDTLS_ECP_DP_SECP521R1, 25, 521, "secp521r1" },
132#endif
133#if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED)
134 { MBEDTLS_ECP_DP_BP512R1, 28, 512, "brainpoolP512r1" },
135#endif
136#if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
137 { MBEDTLS_ECP_DP_SECP384R1, 24, 384, "secp384r1" },
138#endif
139#if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED)
140 { MBEDTLS_ECP_DP_BP384R1, 27, 384, "brainpoolP384r1" },
141#endif
142#if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
143 { MBEDTLS_ECP_DP_SECP256R1, 23, 256, "secp256r1" },
144#endif
145#if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
146 { MBEDTLS_ECP_DP_SECP256K1, 22, 256, "secp256k1" },
147#endif
148#if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED)
149 { MBEDTLS_ECP_DP_BP256R1, 26, 256, "brainpoolP256r1" },
150#endif
151#if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
152 { MBEDTLS_ECP_DP_SECP224R1, 21, 224, "secp224r1" },
153#endif
154#if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
155 { MBEDTLS_ECP_DP_SECP224K1, 20, 224, "secp224k1" },
156#endif
157#if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
158 { MBEDTLS_ECP_DP_SECP192R1, 19, 192, "secp192r1" },
159#endif
160#if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
161 { MBEDTLS_ECP_DP_SECP192K1, 18, 192, "secp192k1" },
162#endif
163 { MBEDTLS_ECP_DP_NONE, 0, 0, NULL },
164};
165
166#define ECP_NB_CURVES sizeof( ecp_supported_curves ) / \
167 sizeof( ecp_supported_curves[0] )
168
169static mbedtls_ecp_group_id ecp_supported_grp_id[ECP_NB_CURVES];
170
171/*
172 * List of supported curves and associated info
173 */
174const mbedtls_ecp_curve_info *mbedtls_ecp_curve_list( void )
175{
176 return( ecp_supported_curves );
177}
178
179/*
180 * List of supported curves, group ID only
181 */
182const mbedtls_ecp_group_id *mbedtls_ecp_grp_id_list( void )
183{
184 static int init_done = 0;
185
186 if( ! init_done )
187 {
188 size_t i = 0;
189 const mbedtls_ecp_curve_info *curve_info;
190
191 for( curve_info = mbedtls_ecp_curve_list();
192 curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
193 curve_info++ )
194 {
195 ecp_supported_grp_id[i++] = curve_info->grp_id;
196 }
197 ecp_supported_grp_id[i] = MBEDTLS_ECP_DP_NONE;
198
199 init_done = 1;
200 }
201
202 return( ecp_supported_grp_id );
203}
204
205/*
206 * Get the curve info for the internal identifier
207 */
208const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_grp_id( mbedtls_ecp_group_id grp_id )
209{
210 const mbedtls_ecp_curve_info *curve_info;
211
212 for( curve_info = mbedtls_ecp_curve_list();
213 curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
214 curve_info++ )
215 {
216 if( curve_info->grp_id == grp_id )
217 return( curve_info );
218 }
219
220 return( NULL );
221}
222
223/*
224 * Get the curve info from the TLS identifier
225 */
226const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_tls_id( uint16_t tls_id )
227{
228 const mbedtls_ecp_curve_info *curve_info;
229
230 for( curve_info = mbedtls_ecp_curve_list();
231 curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
232 curve_info++ )
233 {
234 if( curve_info->tls_id == tls_id )
235 return( curve_info );
236 }
237
238 return( NULL );
239}
240
241/*
242 * Get the curve info from the name
243 */
244const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_name( const char *name )
245{
246 const mbedtls_ecp_curve_info *curve_info;
247
248 for( curve_info = mbedtls_ecp_curve_list();
249 curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
250 curve_info++ )
251 {
252 if( strcmp( curve_info->name, name ) == 0 )
253 return( curve_info );
254 }
255
256 return( NULL );
257}
258
259/*
260 * Get the type of a curve
261 */
262static inline ecp_curve_type ecp_get_type( const mbedtls_ecp_group *grp )
263{
264 if( grp->G.X.p == NULL )
265 return( ECP_TYPE_NONE );
266
267 if( grp->G.Y.p == NULL )
268 return( ECP_TYPE_MONTGOMERY );
269 else
270 return( ECP_TYPE_SHORT_WEIERSTRASS );
271}
272
273/*
274 * Initialize (the components of) a point
275 */
276void mbedtls_ecp_point_init( mbedtls_ecp_point *pt )
277{
278 if( pt == NULL )
279 return;
280
281 mbedtls_mpi_init( &pt->X );
282 mbedtls_mpi_init( &pt->Y );
283 mbedtls_mpi_init( &pt->Z );
284}
285
286/*
287 * Initialize (the components of) a group
288 */
289void mbedtls_ecp_group_init( mbedtls_ecp_group *grp )
290{
291 if( grp == NULL )
292 return;
293
294 memset( grp, 0, sizeof( mbedtls_ecp_group ) );
295}
296
297/*
298 * Initialize (the components of) a key pair
299 */
300void mbedtls_ecp_keypair_init( mbedtls_ecp_keypair *key )
301{
302 if( key == NULL )
303 return;
304
305 mbedtls_ecp_group_init( &key->grp );
306 mbedtls_mpi_init( &key->d );
307 mbedtls_ecp_point_init( &key->Q );
308}
309
310/*
311 * Unallocate (the components of) a point
312 */
313void mbedtls_ecp_point_free( mbedtls_ecp_point *pt )
314{
315 if( pt == NULL )
316 return;
317
318 mbedtls_mpi_free( &( pt->X ) );
319 mbedtls_mpi_free( &( pt->Y ) );
320 mbedtls_mpi_free( &( pt->Z ) );
321}
322
323/*
324 * Unallocate (the components of) a group
325 */
326void mbedtls_ecp_group_free( mbedtls_ecp_group *grp )
327{
328 size_t i;
329
330 if( grp == NULL )
331 return;
332
333 if( grp->h != 1 )
334 {
335 mbedtls_mpi_free( &grp->P );
336 mbedtls_mpi_free( &grp->A );
337 mbedtls_mpi_free( &grp->B );
338 mbedtls_ecp_point_free( &grp->G );
339 mbedtls_mpi_free( &grp->N );
340 }
341
342 if( grp->T != NULL )
343 {
344 for( i = 0; i < grp->T_size; i++ )
345 mbedtls_ecp_point_free( &grp->T[i] );
346 mbedtls_free( grp->T );
347 }
348
349 mbedtls_platform_zeroize( grp, sizeof( mbedtls_ecp_group ) );
350}
351
352/*
353 * Unallocate (the components of) a key pair
354 */
355void mbedtls_ecp_keypair_free( mbedtls_ecp_keypair *key )
356{
357 if( key == NULL )
358 return;
359
360 mbedtls_ecp_group_free( &key->grp );
361 mbedtls_mpi_free( &key->d );
362 mbedtls_ecp_point_free( &key->Q );
363}
364
365/*
366 * Copy the contents of a point
367 */
368int mbedtls_ecp_copy( mbedtls_ecp_point *P, const mbedtls_ecp_point *Q )
369{
370 int ret;
371
372 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->X, &Q->X ) );
373 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->Y, &Q->Y ) );
374 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->Z, &Q->Z ) );
375
376cleanup:
377 return( ret );
378}
379
380/*
381 * Copy the contents of a group object
382 */
383int mbedtls_ecp_group_copy( mbedtls_ecp_group *dst, const mbedtls_ecp_group *src )
384{
385 return mbedtls_ecp_group_load( dst, src->id );
386}
387
388/*
389 * Set point to zero
390 */
391int mbedtls_ecp_set_zero( mbedtls_ecp_point *pt )
392{
393 int ret;
394
395 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->X , 1 ) );
396 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Y , 1 ) );
397 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z , 0 ) );
398
399cleanup:
400 return( ret );
401}
402
403/*
404 * Tell if a point is zero
405 */
406int mbedtls_ecp_is_zero( mbedtls_ecp_point *pt )
407{
408 return( mbedtls_mpi_cmp_int( &pt->Z, 0 ) == 0 );
409}
410
411/*
412 * Compare two points lazyly
413 */
414int mbedtls_ecp_point_cmp( const mbedtls_ecp_point *P,
415 const mbedtls_ecp_point *Q )
416{
417 if( mbedtls_mpi_cmp_mpi( &P->X, &Q->X ) == 0 &&
418 mbedtls_mpi_cmp_mpi( &P->Y, &Q->Y ) == 0 &&
419 mbedtls_mpi_cmp_mpi( &P->Z, &Q->Z ) == 0 )
420 {
421 return( 0 );
422 }
423
424 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
425}
426
427/*
428 * Import a non-zero point from ASCII strings
429 */
430int mbedtls_ecp_point_read_string( mbedtls_ecp_point *P, int radix,
431 const char *x, const char *y )
432{
433 int ret;
434
435 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &P->X, radix, x ) );
436 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &P->Y, radix, y ) );
437 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &P->Z, 1 ) );
438
439cleanup:
440 return( ret );
441}
442
443/*
444 * Export a point into unsigned binary data (SEC1 2.3.3)
445 */
446int mbedtls_ecp_point_write_binary( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *P,
447 int format, size_t *olen,
448 unsigned char *buf, size_t buflen )
449{
450 int ret = 0;
451 size_t plen;
452
453 if( format != MBEDTLS_ECP_PF_UNCOMPRESSED &&
454 format != MBEDTLS_ECP_PF_COMPRESSED )
455 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
456
457 /*
458 * Common case: P == 0
459 */
460 if( mbedtls_mpi_cmp_int( &P->Z, 0 ) == 0 )
461 {
462 if( buflen < 1 )
463 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
464
465 buf[0] = 0x00;
466 *olen = 1;
467
468 return( 0 );
469 }
470
471 plen = mbedtls_mpi_size( &grp->P );
472
473 if( format == MBEDTLS_ECP_PF_UNCOMPRESSED )
474 {
475 *olen = 2 * plen + 1;
476
477 if( buflen < *olen )
478 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
479
480 buf[0] = 0x04;
481 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->X, buf + 1, plen ) );
482 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->Y, buf + 1 + plen, plen ) );
483 }
484 else if( format == MBEDTLS_ECP_PF_COMPRESSED )
485 {
486 *olen = plen + 1;
487
488 if( buflen < *olen )
489 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
490
491 buf[0] = 0x02 + mbedtls_mpi_get_bit( &P->Y, 0 );
492 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->X, buf + 1, plen ) );
493 }
494
495cleanup:
496 return( ret );
497}
498
499/*
500 * Import a point from unsigned binary data (SEC1 2.3.4)
501 */
502int mbedtls_ecp_point_read_binary( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt,
503 const unsigned char *buf, size_t ilen )
504{
505 int ret;
506 size_t plen;
507
508 if( ilen < 1 )
509 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
510
511 if( buf[0] == 0x00 )
512 {
513 if( ilen == 1 )
514 return( mbedtls_ecp_set_zero( pt ) );
515 else
516 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
517 }
518
519 plen = mbedtls_mpi_size( &grp->P );
520
521 if( buf[0] != 0x04 )
522 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
523
524 if( ilen != 2 * plen + 1 )
525 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
526
527 MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &pt->X, buf + 1, plen ) );
528 MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &pt->Y, buf + 1 + plen, plen ) );
529 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) );
530
531cleanup:
532 return( ret );
533}
534
535/*
536 * Import a point from a TLS ECPoint record (RFC 4492)
537 * struct {
538 * opaque point <1..2^8-1>;
539 * } ECPoint;
540 */
541int mbedtls_ecp_tls_read_point( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt,
542 const unsigned char **buf, size_t buf_len )
543{
544 unsigned char data_len;
545 const unsigned char *buf_start;
546
547 /*
548 * We must have at least two bytes (1 for length, at least one for data)
549 */
550 if( buf_len < 2 )
551 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
552
553 data_len = *(*buf)++;
554 if( data_len < 1 || data_len > buf_len - 1 )
555 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
556
557 /*
558 * Save buffer start for read_binary and update buf
559 */
560 buf_start = *buf;
561 *buf += data_len;
562
563 return mbedtls_ecp_point_read_binary( grp, pt, buf_start, data_len );
564}
565
566/*
567 * Export a point as a TLS ECPoint record (RFC 4492)
568 * struct {
569 * opaque point <1..2^8-1>;
570 * } ECPoint;
571 */
572int mbedtls_ecp_tls_write_point( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt,
573 int format, size_t *olen,
574 unsigned char *buf, size_t blen )
575{
576 int ret;
577
578 /*
579 * buffer length must be at least one, for our length byte
580 */
581 if( blen < 1 )
582 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
583
584 if( ( ret = mbedtls_ecp_point_write_binary( grp, pt, format,
585 olen, buf + 1, blen - 1) ) != 0 )
586 return( ret );
587
588 /*
589 * write length to the first byte and update total length
590 */
591 buf[0] = (unsigned char) *olen;
592 ++*olen;
593
594 return( 0 );
595}
596
597/*
598 * Set a group from an ECParameters record (RFC 4492)
599 */
600int mbedtls_ecp_tls_read_group( mbedtls_ecp_group *grp, const unsigned char **buf, size_t len )
601{
602 uint16_t tls_id;
603 const mbedtls_ecp_curve_info *curve_info;
604
605 /*
606 * We expect at least three bytes (see below)
607 */
608 if( len < 3 )
609 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
610
611 /*
612 * First byte is curve_type; only named_curve is handled
613 */
614 if( *(*buf)++ != MBEDTLS_ECP_TLS_NAMED_CURVE )
615 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
616
617 /*
618 * Next two bytes are the namedcurve value
619 */
620 tls_id = *(*buf)++;
621 tls_id <<= 8;
622 tls_id |= *(*buf)++;
623
624 if( ( curve_info = mbedtls_ecp_curve_info_from_tls_id( tls_id ) ) == NULL )
625 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
626
627 return mbedtls_ecp_group_load( grp, curve_info->grp_id );
628}
629
630/*
631 * Write the ECParameters record corresponding to a group (RFC 4492)
632 */
633int mbedtls_ecp_tls_write_group( const mbedtls_ecp_group *grp, size_t *olen,
634 unsigned char *buf, size_t blen )
635{
636 const mbedtls_ecp_curve_info *curve_info;
637
638 if( ( curve_info = mbedtls_ecp_curve_info_from_grp_id( grp->id ) ) == NULL )
639 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
640
641 /*
642 * We are going to write 3 bytes (see below)
643 */
644 *olen = 3;
645 if( blen < *olen )
646 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
647
648 /*
649 * First byte is curve_type, always named_curve
650 */
651 *buf++ = MBEDTLS_ECP_TLS_NAMED_CURVE;
652
653 /*
654 * Next two bytes are the namedcurve value
655 */
656 buf[0] = curve_info->tls_id >> 8;
657 buf[1] = curve_info->tls_id & 0xFF;
658
659 return( 0 );
660}
661
662/*
663 * Wrapper around fast quasi-modp functions, with fall-back to mbedtls_mpi_mod_mpi.
664 * See the documentation of struct mbedtls_ecp_group.
665 *
666 * This function is in the critial loop for mbedtls_ecp_mul, so pay attention to perf.
667 */
668static int ecp_modp( mbedtls_mpi *N, const mbedtls_ecp_group *grp )
669{
670 int ret;
671
672 if( grp->modp == NULL )
673 return( mbedtls_mpi_mod_mpi( N, N, &grp->P ) );
674
675 /* N->s < 0 is a much faster test, which fails only if N is 0 */
676 if( ( N->s < 0 && mbedtls_mpi_cmp_int( N, 0 ) != 0 ) ||
677 mbedtls_mpi_bitlen( N ) > 2 * grp->pbits )
678 {
679 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
680 }
681
682 MBEDTLS_MPI_CHK( grp->modp( N ) );
683
684 /* N->s < 0 is a much faster test, which fails only if N is 0 */
685 while( N->s < 0 && mbedtls_mpi_cmp_int( N, 0 ) != 0 )
686 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &grp->P ) );
687
688 while( mbedtls_mpi_cmp_mpi( N, &grp->P ) >= 0 )
689 /* we known P, N and the result are positive */
690 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( N, N, &grp->P ) );
691
692cleanup:
693 return( ret );
694}
695
696/*
697 * Fast mod-p functions expect their argument to be in the 0..p^2 range.
698 *
699 * In order to guarantee that, we need to ensure that operands of
700 * mbedtls_mpi_mul_mpi are in the 0..p range. So, after each operation we will
701 * bring the result back to this range.
702 *
703 * The following macros are shortcuts for doing that.
704 */
705
706/*
707 * Reduce a mbedtls_mpi mod p in-place, general case, to use after mbedtls_mpi_mul_mpi
708 */
709#if defined(MBEDTLS_SELF_TEST)
710#define INC_MUL_COUNT mul_count++;
711#else
712#define INC_MUL_COUNT
713#endif
714
715#define MOD_MUL( N ) do { MBEDTLS_MPI_CHK( ecp_modp( &N, grp ) ); INC_MUL_COUNT } \
716 while( 0 )
717
718/*
719 * Reduce a mbedtls_mpi mod p in-place, to use after mbedtls_mpi_sub_mpi
720 * N->s < 0 is a very fast test, which fails only if N is 0
721 */
722#define MOD_SUB( N ) \
723 while( N.s < 0 && mbedtls_mpi_cmp_int( &N, 0 ) != 0 ) \
724 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &N, &N, &grp->P ) )
725
726/*
727 * Reduce a mbedtls_mpi mod p in-place, to use after mbedtls_mpi_add_mpi and mbedtls_mpi_mul_int.
728 * We known P, N and the result are positive, so sub_abs is correct, and
729 * a bit faster.
730 */
731#define MOD_ADD( N ) \
732 while( mbedtls_mpi_cmp_mpi( &N, &grp->P ) >= 0 ) \
733 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( &N, &N, &grp->P ) )
734
735#if defined(ECP_SHORTWEIERSTRASS)
736/*
737 * For curves in short Weierstrass form, we do all the internal operations in
738 * Jacobian coordinates.
739 *
740 * For multiplication, we'll use a comb method with coutermeasueres against
741 * SPA, hence timing attacks.
742 */
743
744/*
745 * Normalize jacobian coordinates so that Z == 0 || Z == 1 (GECC 3.2.1)
746 * Cost: 1N := 1I + 3M + 1S
747 */
748static int ecp_normalize_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt )
749{
750 int ret;
751 mbedtls_mpi Zi, ZZi;
752
753 if( mbedtls_mpi_cmp_int( &pt->Z, 0 ) == 0 )
754 return( 0 );
755
756#if defined(MBEDTLS_ECP_NORMALIZE_JAC_ALT)
757 if ( mbedtls_internal_ecp_grp_capable( grp ) )
758 {
759 return mbedtls_internal_ecp_normalize_jac( grp, pt );
760 }
761#endif /* MBEDTLS_ECP_NORMALIZE_JAC_ALT */
762 mbedtls_mpi_init( &Zi ); mbedtls_mpi_init( &ZZi );
763
764 /*
765 * X = X / Z^2 mod p
766 */
767 MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &Zi, &pt->Z, &grp->P ) );
768 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ZZi, &Zi, &Zi ) ); MOD_MUL( ZZi );
769 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->X, &pt->X, &ZZi ) ); MOD_MUL( pt->X );
770
771 /*
772 * Y = Y / Z^3 mod p
773 */
774 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Y, &pt->Y, &ZZi ) ); MOD_MUL( pt->Y );
775 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Y, &pt->Y, &Zi ) ); MOD_MUL( pt->Y );
776
777 /*
778 * Z = 1
779 */
780 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) );
781
782cleanup:
783
784 mbedtls_mpi_free( &Zi ); mbedtls_mpi_free( &ZZi );
785
786 return( ret );
787}
788
789/*
790 * Normalize jacobian coordinates of an array of (pointers to) points,
791 * using Montgomery's trick to perform only one inversion mod P.
792 * (See for example Cohen's "A Course in Computational Algebraic Number
793 * Theory", Algorithm 10.3.4.)
794 *
795 * Warning: fails (returning an error) if one of the points is zero!
796 * This should never happen, see choice of w in ecp_mul_comb().
797 *
798 * Cost: 1N(t) := 1I + (6t - 3)M + 1S
799 */
800static int ecp_normalize_jac_many( const mbedtls_ecp_group *grp,
801 mbedtls_ecp_point *T[], size_t t_len )
802{
803 int ret;
804 size_t i;
805 mbedtls_mpi *c, u, Zi, ZZi;
806
807 if( t_len < 2 )
808 return( ecp_normalize_jac( grp, *T ) );
809
810#if defined(MBEDTLS_ECP_NORMALIZE_JAC_MANY_ALT)
811 if ( mbedtls_internal_ecp_grp_capable( grp ) )
812 {
813 return mbedtls_internal_ecp_normalize_jac_many(grp, T, t_len);
814 }
815#endif
816
817 if( ( c = mbedtls_calloc( t_len, sizeof( mbedtls_mpi ) ) ) == NULL )
818 return( MBEDTLS_ERR_ECP_ALLOC_FAILED );
819
820 mbedtls_mpi_init( &u ); mbedtls_mpi_init( &Zi ); mbedtls_mpi_init( &ZZi );
821
822 /*
823 * c[i] = Z_0 * ... * Z_i
824 */
825 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &c[0], &T[0]->Z ) );
826 for( i = 1; i < t_len; i++ )
827 {
828 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &c[i], &c[i-1], &T[i]->Z ) );
829 MOD_MUL( c[i] );
830 }
831
832 /*
833 * u = 1 / (Z_0 * ... * Z_n) mod P
834 */
835 MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &u, &c[t_len-1], &grp->P ) );
836
837 for( i = t_len - 1; ; i-- )
838 {
839 /*
840 * Zi = 1 / Z_i mod p
841 * u = 1 / (Z_0 * ... * Z_i) mod P
842 */
843 if( i == 0 ) {
844 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &Zi, &u ) );
845 }
846 else
847 {
848 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &Zi, &u, &c[i-1] ) ); MOD_MUL( Zi );
849 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &u, &u, &T[i]->Z ) ); MOD_MUL( u );
850 }
851
852 /*
853 * proceed as in normalize()
854 */
855 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ZZi, &Zi, &Zi ) ); MOD_MUL( ZZi );
856 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T[i]->X, &T[i]->X, &ZZi ) ); MOD_MUL( T[i]->X );
857 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T[i]->Y, &T[i]->Y, &ZZi ) ); MOD_MUL( T[i]->Y );
858 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T[i]->Y, &T[i]->Y, &Zi ) ); MOD_MUL( T[i]->Y );
859
860 /*
861 * Post-precessing: reclaim some memory by shrinking coordinates
862 * - not storing Z (always 1)
863 * - shrinking other coordinates, but still keeping the same number of
864 * limbs as P, as otherwise it will too likely be regrown too fast.
865 */
866 MBEDTLS_MPI_CHK( mbedtls_mpi_shrink( &T[i]->X, grp->P.n ) );
867 MBEDTLS_MPI_CHK( mbedtls_mpi_shrink( &T[i]->Y, grp->P.n ) );
868 mbedtls_mpi_free( &T[i]->Z );
869
870 if( i == 0 )
871 break;
872 }
873
874cleanup:
875
876 mbedtls_mpi_free( &u ); mbedtls_mpi_free( &Zi ); mbedtls_mpi_free( &ZZi );
877 for( i = 0; i < t_len; i++ )
878 mbedtls_mpi_free( &c[i] );
879 mbedtls_free( c );
880
881 return( ret );
882}
883
884/*
885 * Conditional point inversion: Q -> -Q = (Q.X, -Q.Y, Q.Z) without leak.
886 * "inv" must be 0 (don't invert) or 1 (invert) or the result will be invalid
887 */
888static int ecp_safe_invert_jac( const mbedtls_ecp_group *grp,
889 mbedtls_ecp_point *Q,
890 unsigned char inv )
891{
892 int ret;
893 unsigned char nonzero;
894 mbedtls_mpi mQY;
895
896 mbedtls_mpi_init( &mQY );
897
898 /* Use the fact that -Q.Y mod P = P - Q.Y unless Q.Y == 0 */
899 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &mQY, &grp->P, &Q->Y ) );
900 nonzero = mbedtls_mpi_cmp_int( &Q->Y, 0 ) != 0;
901 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &Q->Y, &mQY, inv & nonzero ) );
902
903cleanup:
904 mbedtls_mpi_free( &mQY );
905
906 return( ret );
907}
908
909/*
910 * Point doubling R = 2 P, Jacobian coordinates
911 *
912 * Based on http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#doubling-dbl-1998-cmo-2 .
913 *
914 * We follow the variable naming fairly closely. The formula variations that trade a MUL for a SQR
915 * (plus a few ADDs) aren't useful as our bignum implementation doesn't distinguish squaring.
916 *
917 * Standard optimizations are applied when curve parameter A is one of { 0, -3 }.
918 *
919 * Cost: 1D := 3M + 4S (A == 0)
920 * 4M + 4S (A == -3)
921 * 3M + 6S + 1a otherwise
922 */
923static int ecp_double_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
924 const mbedtls_ecp_point *P )
925{
926 int ret;
927 mbedtls_mpi M, S, T, U;
928
929#if defined(MBEDTLS_SELF_TEST)
930 dbl_count++;
931#endif
932
933#if defined(MBEDTLS_ECP_DOUBLE_JAC_ALT)
934 if ( mbedtls_internal_ecp_grp_capable( grp ) )
935 {
936 return mbedtls_internal_ecp_double_jac( grp, R, P );
937 }
938#endif /* MBEDTLS_ECP_DOUBLE_JAC_ALT */
939
940 mbedtls_mpi_init( &M ); mbedtls_mpi_init( &S ); mbedtls_mpi_init( &T ); mbedtls_mpi_init( &U );
941
942 /* Special case for A = -3 */
943 if( grp->A.p == NULL )
944 {
945 /* M = 3(X + Z^2)(X - Z^2) */
946 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->Z, &P->Z ) ); MOD_MUL( S );
947 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &T, &P->X, &S ) ); MOD_ADD( T );
948 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &U, &P->X, &S ) ); MOD_SUB( U );
949 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &T, &U ) ); MOD_MUL( S );
950 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &S, 3 ) ); MOD_ADD( M );
951 }
952 else
953 {
954 /* M = 3.X^2 */
955 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->X, &P->X ) ); MOD_MUL( S );
956 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &S, 3 ) ); MOD_ADD( M );
957
958 /* Optimize away for "koblitz" curves with A = 0 */
959 if( mbedtls_mpi_cmp_int( &grp->A, 0 ) != 0 )
960 {
961 /* M += A.Z^4 */
962 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->Z, &P->Z ) ); MOD_MUL( S );
963 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &S, &S ) ); MOD_MUL( T );
964 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &T, &grp->A ) ); MOD_MUL( S );
965 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &M, &M, &S ) ); MOD_ADD( M );
966 }
967 }
968
969 /* S = 4.X.Y^2 */
970 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &P->Y, &P->Y ) ); MOD_MUL( T );
971 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &T, 1 ) ); MOD_ADD( T );
972 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->X, &T ) ); MOD_MUL( S );
973 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &S, 1 ) ); MOD_ADD( S );
974
975 /* U = 8.Y^4 */
976 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &U, &T, &T ) ); MOD_MUL( U );
977 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &U, 1 ) ); MOD_ADD( U );
978
979 /* T = M^2 - 2.S */
980 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &M, &M ) ); MOD_MUL( T );
981 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T, &T, &S ) ); MOD_SUB( T );
982 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T, &T, &S ) ); MOD_SUB( T );
983
984 /* S = M(S - T) - U */
985 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &S, &S, &T ) ); MOD_SUB( S );
986 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &S, &M ) ); MOD_MUL( S );
987 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &S, &S, &U ) ); MOD_SUB( S );
988
989 /* U = 2.Y.Z */
990 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &U, &P->Y, &P->Z ) ); MOD_MUL( U );
991 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &U, 1 ) ); MOD_ADD( U );
992
993 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->X, &T ) );
994 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Y, &S ) );
995 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Z, &U ) );
996
997cleanup:
998 mbedtls_mpi_free( &M ); mbedtls_mpi_free( &S ); mbedtls_mpi_free( &T ); mbedtls_mpi_free( &U );
999
1000 return( ret );
1001}
1002
1003/*
1004 * Addition: R = P + Q, mixed affine-Jacobian coordinates (GECC 3.22)
1005 *
1006 * The coordinates of Q must be normalized (= affine),
1007 * but those of P don't need to. R is not normalized.
1008 *
1009 * Special cases: (1) P or Q is zero, (2) R is zero, (3) P == Q.
1010 * None of these cases can happen as intermediate step in ecp_mul_comb():
1011 * - at each step, P, Q and R are multiples of the base point, the factor
1012 * being less than its order, so none of them is zero;
1013 * - Q is an odd multiple of the base point, P an even multiple,
1014 * due to the choice of precomputed points in the modified comb method.
1015 * So branches for these cases do not leak secret information.
1016 *
1017 * We accept Q->Z being unset (saving memory in tables) as meaning 1.
1018 *
1019 * Cost: 1A := 8M + 3S
1020 */
1021static int ecp_add_mixed( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
1022 const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q )
1023{
1024 int ret;
1025 mbedtls_mpi T1, T2, T3, T4, X, Y, Z;
1026
1027#if defined(MBEDTLS_SELF_TEST)
1028 add_count++;
1029#endif
1030
1031#if defined(MBEDTLS_ECP_ADD_MIXED_ALT)
1032 if ( mbedtls_internal_ecp_grp_capable( grp ) )
1033 {
1034 return mbedtls_internal_ecp_add_mixed( grp, R, P, Q );
1035 }
1036#endif /* MBEDTLS_ECP_ADD_MIXED_ALT */
1037
1038 /*
1039 * Trivial cases: P == 0 or Q == 0 (case 1)
1040 */
1041 if( mbedtls_mpi_cmp_int( &P->Z, 0 ) == 0 )
1042 return( mbedtls_ecp_copy( R, Q ) );
1043
1044 if( Q->Z.p != NULL && mbedtls_mpi_cmp_int( &Q->Z, 0 ) == 0 )
1045 return( mbedtls_ecp_copy( R, P ) );
1046
1047 /*
1048 * Make sure Q coordinates are normalized
1049 */
1050 if( Q->Z.p != NULL && mbedtls_mpi_cmp_int( &Q->Z, 1 ) != 0 )
1051 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1052
1053 mbedtls_mpi_init( &T1 ); mbedtls_mpi_init( &T2 ); mbedtls_mpi_init( &T3 ); mbedtls_mpi_init( &T4 );
1054 mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Y ); mbedtls_mpi_init( &Z );
1055
1056 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T1, &P->Z, &P->Z ) ); MOD_MUL( T1 );
1057 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T2, &T1, &P->Z ) ); MOD_MUL( T2 );
1058 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T1, &T1, &Q->X ) ); MOD_MUL( T1 );
1059 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T2, &T2, &Q->Y ) ); MOD_MUL( T2 );
1060 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T1, &T1, &P->X ) ); MOD_SUB( T1 );
1061 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T2, &T2, &P->Y ) ); MOD_SUB( T2 );
1062
1063 /* Special cases (2) and (3) */
1064 if( mbedtls_mpi_cmp_int( &T1, 0 ) == 0 )
1065 {
1066 if( mbedtls_mpi_cmp_int( &T2, 0 ) == 0 )
1067 {
1068 ret = ecp_double_jac( grp, R, P );
1069 goto cleanup;
1070 }
1071 else
1072 {
1073 ret = mbedtls_ecp_set_zero( R );
1074 goto cleanup;
1075 }
1076 }
1077
1078 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &Z, &P->Z, &T1 ) ); MOD_MUL( Z );
1079 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T3, &T1, &T1 ) ); MOD_MUL( T3 );
1080 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T4, &T3, &T1 ) ); MOD_MUL( T4 );
1081 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T3, &T3, &P->X ) ); MOD_MUL( T3 );
1082 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &T1, &T3, 2 ) ); MOD_ADD( T1 );
1083 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &X, &T2, &T2 ) ); MOD_MUL( X );
1084 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &X, &X, &T1 ) ); MOD_SUB( X );
1085 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &X, &X, &T4 ) ); MOD_SUB( X );
1086 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T3, &T3, &X ) ); MOD_SUB( T3 );
1087 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T3, &T3, &T2 ) ); MOD_MUL( T3 );
1088 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T4, &T4, &P->Y ) ); MOD_MUL( T4 );
1089 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &Y, &T3, &T4 ) ); MOD_SUB( Y );
1090
1091 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->X, &X ) );
1092 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Y, &Y ) );
1093 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Z, &Z ) );
1094
1095cleanup:
1096
1097 mbedtls_mpi_free( &T1 ); mbedtls_mpi_free( &T2 ); mbedtls_mpi_free( &T3 ); mbedtls_mpi_free( &T4 );
1098 mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Y ); mbedtls_mpi_free( &Z );
1099
1100 return( ret );
1101}
1102
1103/*
1104 * Randomize jacobian coordinates:
1105 * (X, Y, Z) -> (l^2 X, l^3 Y, l Z) for random l
1106 * This is sort of the reverse operation of ecp_normalize_jac().
1107 *
1108 * This countermeasure was first suggested in [2].
1109 */
1110static int ecp_randomize_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt,
1111 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
1112{
1113 int ret;
1114 mbedtls_mpi l, ll;
1115 size_t p_size;
1116 int count = 0;
1117
1118#if defined(MBEDTLS_ECP_RANDOMIZE_JAC_ALT)
1119 if ( mbedtls_internal_ecp_grp_capable( grp ) )
1120 {
1121 return mbedtls_internal_ecp_randomize_jac( grp, pt, f_rng, p_rng );
1122 }
1123#endif /* MBEDTLS_ECP_RANDOMIZE_JAC_ALT */
1124
1125 p_size = ( grp->pbits + 7 ) / 8;
1126 mbedtls_mpi_init( &l ); mbedtls_mpi_init( &ll );
1127
1128 /* Generate l such that 1 < l < p */
1129 do
1130 {
1131 MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &l, p_size, f_rng, p_rng ) );
1132
1133 while( mbedtls_mpi_cmp_mpi( &l, &grp->P ) >= 0 )
1134 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &l, 1 ) );
1135
1136 if( count++ > 10 )
1137 return( MBEDTLS_ERR_ECP_RANDOM_FAILED );
1138 }
1139 while( mbedtls_mpi_cmp_int( &l, 1 ) <= 0 );
1140
1141 /* Z = l * Z */
1142 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Z, &pt->Z, &l ) ); MOD_MUL( pt->Z );
1143
1144 /* X = l^2 * X */
1145 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ll, &l, &l ) ); MOD_MUL( ll );
1146 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->X, &pt->X, &ll ) ); MOD_MUL( pt->X );
1147
1148 /* Y = l^3 * Y */
1149 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ll, &ll, &l ) ); MOD_MUL( ll );
1150 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Y, &pt->Y, &ll ) ); MOD_MUL( pt->Y );
1151
1152cleanup:
1153 mbedtls_mpi_free( &l ); mbedtls_mpi_free( &ll );
1154
1155 return( ret );
1156}
1157
1158/*
1159 * Check and define parameters used by the comb method (see below for details)
1160 */
1161#if MBEDTLS_ECP_WINDOW_SIZE < 2 || MBEDTLS_ECP_WINDOW_SIZE > 7
1162#error "MBEDTLS_ECP_WINDOW_SIZE out of bounds"
1163#endif
1164
1165/* d = ceil( n / w ) */
1166#define COMB_MAX_D ( MBEDTLS_ECP_MAX_BITS + 1 ) / 2
1167
1168/* number of precomputed points */
1169#define COMB_MAX_PRE ( 1 << ( MBEDTLS_ECP_WINDOW_SIZE - 1 ) )
1170
1171/*
1172 * Compute the representation of m that will be used with our comb method.
1173 *
1174 * The basic comb method is described in GECC 3.44 for example. We use a
1175 * modified version that provides resistance to SPA by avoiding zero
1176 * digits in the representation as in [3]. We modify the method further by
1177 * requiring that all K_i be odd, which has the small cost that our
1178 * representation uses one more K_i, due to carries.
1179 *
1180 * Also, for the sake of compactness, only the seven low-order bits of x[i]
1181 * are used to represent K_i, and the msb of x[i] encodes the the sign (s_i in
1182 * the paper): it is set if and only if if s_i == -1;
1183 *
1184 * Calling conventions:
1185 * - x is an array of size d + 1
1186 * - w is the size, ie number of teeth, of the comb, and must be between
1187 * 2 and 7 (in practice, between 2 and MBEDTLS_ECP_WINDOW_SIZE)
1188 * - m is the MPI, expected to be odd and such that bitlength(m) <= w * d
1189 * (the result will be incorrect if these assumptions are not satisfied)
1190 */
1191static void ecp_comb_fixed( unsigned char x[], size_t d,
1192 unsigned char w, const mbedtls_mpi *m )
1193{
1194 size_t i, j;
1195 unsigned char c, cc, adjust;
1196
1197 memset( x, 0, d+1 );
1198
1199 /* First get the classical comb values (except for x_d = 0) */
1200 for( i = 0; i < d; i++ )
1201 for( j = 0; j < w; j++ )
1202 x[i] |= mbedtls_mpi_get_bit( m, i + d * j ) << j;
1203
1204 /* Now make sure x_1 .. x_d are odd */
1205 c = 0;
1206 for( i = 1; i <= d; i++ )
1207 {
1208 /* Add carry and update it */
1209 cc = x[i] & c;
1210 x[i] = x[i] ^ c;
1211 c = cc;
1212
1213 /* Adjust if needed, avoiding branches */
1214 adjust = 1 - ( x[i] & 0x01 );
1215 c |= x[i] & ( x[i-1] * adjust );
1216 x[i] = x[i] ^ ( x[i-1] * adjust );
1217 x[i-1] |= adjust << 7;
1218 }
1219}
1220
1221/*
1222 * Precompute points for the comb method
1223 *
1224 * If i = i_{w-1} ... i_1 is the binary representation of i, then
1225 * T[i] = i_{w-1} 2^{(w-1)d} P + ... + i_1 2^d P + P
1226 *
1227 * T must be able to hold 2^{w - 1} elements
1228 *
1229 * Cost: d(w-1) D + (2^{w-1} - 1) A + 1 N(w-1) + 1 N(2^{w-1} - 1)
1230 */
1231static int ecp_precompute_comb( const mbedtls_ecp_group *grp,
1232 mbedtls_ecp_point T[], const mbedtls_ecp_point *P,
1233 unsigned char w, size_t d )
1234{
1235 int ret;
1236 unsigned char i, k;
1237 size_t j;
1238 mbedtls_ecp_point *cur, *TT[COMB_MAX_PRE - 1];
1239
1240 /*
1241 * Set T[0] = P and
1242 * T[2^{l-1}] = 2^{dl} P for l = 1 .. w-1 (this is not the final value)
1243 */
1244 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( &T[0], P ) );
1245
1246 k = 0;
1247 for( i = 1; i < ( 1U << ( w - 1 ) ); i <<= 1 )
1248 {
1249 cur = T + i;
1250 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( cur, T + ( i >> 1 ) ) );
1251 for( j = 0; j < d; j++ )
1252 MBEDTLS_MPI_CHK( ecp_double_jac( grp, cur, cur ) );
1253
1254 TT[k++] = cur;
1255 }
1256
1257 MBEDTLS_MPI_CHK( ecp_normalize_jac_many( grp, TT, k ) );
1258
1259 /*
1260 * Compute the remaining ones using the minimal number of additions
1261 * Be careful to update T[2^l] only after using it!
1262 */
1263 k = 0;
1264 for( i = 1; i < ( 1U << ( w - 1 ) ); i <<= 1 )
1265 {
1266 j = i;
1267 while( j-- )
1268 {
1269 MBEDTLS_MPI_CHK( ecp_add_mixed( grp, &T[i + j], &T[j], &T[i] ) );
1270 TT[k++] = &T[i + j];
1271 }
1272 }
1273
1274 MBEDTLS_MPI_CHK( ecp_normalize_jac_many( grp, TT, k ) );
1275
1276cleanup:
1277
1278 return( ret );
1279}
1280
1281/*
1282 * Select precomputed point: R = sign(i) * T[ abs(i) / 2 ]
1283 */
1284static int ecp_select_comb( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
1285 const mbedtls_ecp_point T[], unsigned char t_len,
1286 unsigned char i )
1287{
1288 int ret;
1289 unsigned char ii, j;
1290
1291 /* Ignore the "sign" bit and scale down */
1292 ii = ( i & 0x7Fu ) >> 1;
1293
1294 /* Read the whole table to thwart cache-based timing attacks */
1295 for( j = 0; j < t_len; j++ )
1296 {
1297 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &R->X, &T[j].X, j == ii ) );
1298 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &R->Y, &T[j].Y, j == ii ) );
1299 }
1300
1301 /* Safely invert result if i is "negative" */
1302 MBEDTLS_MPI_CHK( ecp_safe_invert_jac( grp, R, i >> 7 ) );
1303
1304cleanup:
1305 return( ret );
1306}
1307
1308/*
1309 * Core multiplication algorithm for the (modified) comb method.
1310 * This part is actually common with the basic comb method (GECC 3.44)
1311 *
1312 * Cost: d A + d D + 1 R
1313 */
1314static int ecp_mul_comb_core( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
1315 const mbedtls_ecp_point T[], unsigned char t_len,
1316 const unsigned char x[], size_t d,
1317 int (*f_rng)(void *, unsigned char *, size_t),
1318 void *p_rng )
1319{
1320 int ret;
1321 mbedtls_ecp_point Txi;
1322 size_t i;
1323
1324 mbedtls_ecp_point_init( &Txi );
1325
1326 /* Start with a non-zero point and randomize its coordinates */
1327 i = d;
1328 MBEDTLS_MPI_CHK( ecp_select_comb( grp, R, T, t_len, x[i] ) );
1329 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->Z, 1 ) );
1330 if( f_rng != 0 )
1331 MBEDTLS_MPI_CHK( ecp_randomize_jac( grp, R, f_rng, p_rng ) );
1332
1333 while( i-- != 0 )
1334 {
1335 MBEDTLS_MPI_CHK( ecp_double_jac( grp, R, R ) );
1336 MBEDTLS_MPI_CHK( ecp_select_comb( grp, &Txi, T, t_len, x[i] ) );
1337 MBEDTLS_MPI_CHK( ecp_add_mixed( grp, R, R, &Txi ) );
1338 }
1339
1340cleanup:
1341
1342 mbedtls_ecp_point_free( &Txi );
1343
1344 return( ret );
1345}
1346
1347/*
1348 * Multiplication using the comb method,
1349 * for curves in short Weierstrass form
1350 */
1351static int ecp_mul_comb( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
1352 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
1353 int (*f_rng)(void *, unsigned char *, size_t),
1354 void *p_rng )
1355{
1356 int ret;
1357 unsigned char w, m_is_odd, p_eq_g, pre_len, i;
1358 size_t d;
1359 unsigned char k[COMB_MAX_D + 1];
1360 mbedtls_ecp_point *T;
1361 mbedtls_mpi M, mm;
1362
1363 mbedtls_mpi_init( &M );
1364 mbedtls_mpi_init( &mm );
1365
1366 /* we need N to be odd to trnaform m in an odd number, check now */
1367 if( mbedtls_mpi_get_bit( &grp->N, 0 ) != 1 )
1368 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1369
1370 /*
1371 * Minimize the number of multiplications, that is minimize
1372 * 10 * d * w + 18 * 2^(w-1) + 11 * d + 7 * w, with d = ceil( nbits / w )
1373 * (see costs of the various parts, with 1S = 1M)
1374 */
1375 w = grp->nbits >= 384 ? 5 : 4;
1376
1377 /*
1378 * If P == G, pre-compute a bit more, since this may be re-used later.
1379 * Just adding one avoids upping the cost of the first mul too much,
1380 * and the memory cost too.
1381 */
1382#if MBEDTLS_ECP_FIXED_POINT_OPTIM == 1
1383 p_eq_g = ( mbedtls_mpi_cmp_mpi( &P->Y, &grp->G.Y ) == 0 &&
1384 mbedtls_mpi_cmp_mpi( &P->X, &grp->G.X ) == 0 );
1385 if( p_eq_g )
1386 w++;
1387#else
1388 p_eq_g = 0;
1389#endif
1390
1391 /*
1392 * Make sure w is within bounds.
1393 * (The last test is useful only for very small curves in the test suite.)
1394 */
1395 if( w > MBEDTLS_ECP_WINDOW_SIZE )
1396 w = MBEDTLS_ECP_WINDOW_SIZE;
1397 if( w >= grp->nbits )
1398 w = 2;
1399
1400 /* Other sizes that depend on w */
1401 pre_len = 1U << ( w - 1 );
1402 d = ( grp->nbits + w - 1 ) / w;
1403
1404 /*
1405 * Prepare precomputed points: if P == G we want to
1406 * use grp->T if already initialized, or initialize it.
1407 */
1408 T = p_eq_g ? grp->T : NULL;
1409
1410 if( T == NULL )
1411 {
1412 T = mbedtls_calloc( pre_len, sizeof( mbedtls_ecp_point ) );
1413 if( T == NULL )
1414 {
1415 ret = MBEDTLS_ERR_ECP_ALLOC_FAILED;
1416 goto cleanup;
1417 }
1418
1419 MBEDTLS_MPI_CHK( ecp_precompute_comb( grp, T, P, w, d ) );
1420
1421 if( p_eq_g )
1422 {
1423 grp->T = T;
1424 grp->T_size = pre_len;
1425 }
1426 }
1427
1428 /*
1429 * Make sure M is odd (M = m or M = N - m, since N is odd)
1430 * using the fact that m * P = - (N - m) * P
1431 */
1432 m_is_odd = ( mbedtls_mpi_get_bit( m, 0 ) == 1 );
1433 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &M, m ) );
1434 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &mm, &grp->N, m ) );
1435 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &M, &mm, ! m_is_odd ) );
1436
1437 /*
1438 * Go for comb multiplication, R = M * P
1439 */
1440 ecp_comb_fixed( k, d, w, &M );
1441 MBEDTLS_MPI_CHK( ecp_mul_comb_core( grp, R, T, pre_len, k, d, f_rng, p_rng ) );
1442
1443 /*
1444 * Now get m * P from M * P and normalize it
1445 */
1446 MBEDTLS_MPI_CHK( ecp_safe_invert_jac( grp, R, ! m_is_odd ) );
1447 MBEDTLS_MPI_CHK( ecp_normalize_jac( grp, R ) );
1448
1449cleanup:
1450
1451 /* There are two cases where T is not stored in grp:
1452 * - P != G
1453 * - An intermediate operation failed before setting grp->T
1454 * In either case, T must be freed.
1455 */
1456 if( T != NULL && T != grp->T )
1457 {
1458 for( i = 0; i < pre_len; i++ )
1459 mbedtls_ecp_point_free( &T[i] );
1460 mbedtls_free( T );
1461 }
1462
1463 mbedtls_mpi_free( &M );
1464 mbedtls_mpi_free( &mm );
1465
1466 if( ret != 0 )
1467 mbedtls_ecp_point_free( R );
1468
1469 return( ret );
1470}
1471
1472#endif /* ECP_SHORTWEIERSTRASS */
1473
1474#if defined(ECP_MONTGOMERY)
1475/*
1476 * For Montgomery curves, we do all the internal arithmetic in projective
1477 * coordinates. Import/export of points uses only the x coordinates, which is
1478 * internaly represented as X / Z.
1479 *
1480 * For scalar multiplication, we'll use a Montgomery ladder.
1481 */
1482
1483/*
1484 * Normalize Montgomery x/z coordinates: X = X/Z, Z = 1
1485 * Cost: 1M + 1I
1486 */
1487static int ecp_normalize_mxz( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P )
1488{
1489 int ret;
1490
1491#if defined(MBEDTLS_ECP_NORMALIZE_MXZ_ALT)
1492 if ( mbedtls_internal_ecp_grp_capable( grp ) )
1493 {
1494 return mbedtls_internal_ecp_normalize_mxz( grp, P );
1495 }
1496#endif /* MBEDTLS_ECP_NORMALIZE_MXZ_ALT */
1497
1498 MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &P->Z, &P->Z, &grp->P ) );
1499 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &P->X, &P->X, &P->Z ) ); MOD_MUL( P->X );
1500 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &P->Z, 1 ) );
1501
1502cleanup:
1503 return( ret );
1504}
1505
1506/*
1507 * Randomize projective x/z coordinates:
1508 * (X, Z) -> (l X, l Z) for random l
1509 * This is sort of the reverse operation of ecp_normalize_mxz().
1510 *
1511 * This countermeasure was first suggested in [2].
1512 * Cost: 2M
1513 */
1514static int ecp_randomize_mxz( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P,
1515 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
1516{
1517 int ret;
1518 mbedtls_mpi l;
1519 size_t p_size;
1520 int count = 0;
1521
1522#if defined(MBEDTLS_ECP_RANDOMIZE_MXZ_ALT)
1523 if ( mbedtls_internal_ecp_grp_capable( grp ) )
1524 {
1525 return mbedtls_internal_ecp_randomize_mxz( grp, P, f_rng, p_rng );
1526 }
1527#endif /* MBEDTLS_ECP_RANDOMIZE_MXZ_ALT */
1528
1529 p_size = ( grp->pbits + 7 ) / 8;
1530 mbedtls_mpi_init( &l );
1531
1532 /* Generate l such that 1 < l < p */
1533 do
1534 {
1535 MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &l, p_size, f_rng, p_rng ) );
1536
1537 while( mbedtls_mpi_cmp_mpi( &l, &grp->P ) >= 0 )
1538 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &l, 1 ) );
1539
1540 if( count++ > 10 )
1541 return( MBEDTLS_ERR_ECP_RANDOM_FAILED );
1542 }
1543 while( mbedtls_mpi_cmp_int( &l, 1 ) <= 0 );
1544
1545 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &P->X, &P->X, &l ) ); MOD_MUL( P->X );
1546 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &P->Z, &P->Z, &l ) ); MOD_MUL( P->Z );
1547
1548cleanup:
1549 mbedtls_mpi_free( &l );
1550
1551 return( ret );
1552}
1553
1554/*
1555 * Double-and-add: R = 2P, S = P + Q, with d = X(P - Q),
1556 * for Montgomery curves in x/z coordinates.
1557 *
1558 * http://www.hyperelliptic.org/EFD/g1p/auto-code/montgom/xz/ladder/mladd-1987-m.op3
1559 * with
1560 * d = X1
1561 * P = (X2, Z2)
1562 * Q = (X3, Z3)
1563 * R = (X4, Z4)
1564 * S = (X5, Z5)
1565 * and eliminating temporary variables tO, ..., t4.
1566 *
1567 * Cost: 5M + 4S
1568 */
1569static int ecp_double_add_mxz( const mbedtls_ecp_group *grp,
1570 mbedtls_ecp_point *R, mbedtls_ecp_point *S,
1571 const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q,
1572 const mbedtls_mpi *d )
1573{
1574 int ret;
1575 mbedtls_mpi A, AA, B, BB, E, C, D, DA, CB;
1576
1577#if defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT)
1578 if ( mbedtls_internal_ecp_grp_capable( grp ) )
1579 {
1580 return mbedtls_internal_ecp_double_add_mxz( grp, R, S, P, Q, d );
1581 }
1582#endif /* MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT */
1583
1584 mbedtls_mpi_init( &A ); mbedtls_mpi_init( &AA ); mbedtls_mpi_init( &B );
1585 mbedtls_mpi_init( &BB ); mbedtls_mpi_init( &E ); mbedtls_mpi_init( &C );
1586 mbedtls_mpi_init( &D ); mbedtls_mpi_init( &DA ); mbedtls_mpi_init( &CB );
1587
1588 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &A, &P->X, &P->Z ) ); MOD_ADD( A );
1589 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &AA, &A, &A ) ); MOD_MUL( AA );
1590 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &B, &P->X, &P->Z ) ); MOD_SUB( B );
1591 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &BB, &B, &B ) ); MOD_MUL( BB );
1592 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &E, &AA, &BB ) ); MOD_SUB( E );
1593 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &C, &Q->X, &Q->Z ) ); MOD_ADD( C );
1594 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &D, &Q->X, &Q->Z ) ); MOD_SUB( D );
1595 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &DA, &D, &A ) ); MOD_MUL( DA );
1596 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &CB, &C, &B ) ); MOD_MUL( CB );
1597 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &S->X, &DA, &CB ) ); MOD_MUL( S->X );
1598 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S->X, &S->X, &S->X ) ); MOD_MUL( S->X );
1599 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &S->Z, &DA, &CB ) ); MOD_SUB( S->Z );
1600 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S->Z, &S->Z, &S->Z ) ); MOD_MUL( S->Z );
1601 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S->Z, d, &S->Z ) ); MOD_MUL( S->Z );
1602 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &R->X, &AA, &BB ) ); MOD_MUL( R->X );
1603 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &R->Z, &grp->A, &E ) ); MOD_MUL( R->Z );
1604 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &R->Z, &BB, &R->Z ) ); MOD_ADD( R->Z );
1605 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &R->Z, &E, &R->Z ) ); MOD_MUL( R->Z );
1606
1607cleanup:
1608 mbedtls_mpi_free( &A ); mbedtls_mpi_free( &AA ); mbedtls_mpi_free( &B );
1609 mbedtls_mpi_free( &BB ); mbedtls_mpi_free( &E ); mbedtls_mpi_free( &C );
1610 mbedtls_mpi_free( &D ); mbedtls_mpi_free( &DA ); mbedtls_mpi_free( &CB );
1611
1612 return( ret );
1613}
1614
1615/*
1616 * Multiplication with Montgomery ladder in x/z coordinates,
1617 * for curves in Montgomery form
1618 */
1619static int ecp_mul_mxz( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
1620 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
1621 int (*f_rng)(void *, unsigned char *, size_t),
1622 void *p_rng )
1623{
1624 int ret;
1625 size_t i;
1626 unsigned char b;
1627 mbedtls_ecp_point RP;
1628 mbedtls_mpi PX;
1629
1630 mbedtls_ecp_point_init( &RP ); mbedtls_mpi_init( &PX );
1631
1632 /* Save PX and read from P before writing to R, in case P == R */
1633 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &PX, &P->X ) );
1634 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( &RP, P ) );
1635
1636 /* Set R to zero in modified x/z coordinates */
1637 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->X, 1 ) );
1638 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->Z, 0 ) );
1639 mbedtls_mpi_free( &R->Y );
1640
1641 /* RP.X might be sligtly larger than P, so reduce it */
1642 MOD_ADD( RP.X );
1643
1644 /* Randomize coordinates of the starting point */
1645 if( f_rng != NULL )
1646 MBEDTLS_MPI_CHK( ecp_randomize_mxz( grp, &RP, f_rng, p_rng ) );
1647
1648 /* Loop invariant: R = result so far, RP = R + P */
1649 i = mbedtls_mpi_bitlen( m ); /* one past the (zero-based) most significant bit */
1650 while( i-- > 0 )
1651 {
1652 b = mbedtls_mpi_get_bit( m, i );
1653 /*
1654 * if (b) R = 2R + P else R = 2R,
1655 * which is:
1656 * if (b) double_add( RP, R, RP, R )
1657 * else double_add( R, RP, R, RP )
1658 * but using safe conditional swaps to avoid leaks
1659 */
1660 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->X, &RP.X, b ) );
1661 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->Z, &RP.Z, b ) );
1662 MBEDTLS_MPI_CHK( ecp_double_add_mxz( grp, R, &RP, R, &RP, &PX ) );
1663 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->X, &RP.X, b ) );
1664 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->Z, &RP.Z, b ) );
1665 }
1666
1667 MBEDTLS_MPI_CHK( ecp_normalize_mxz( grp, R ) );
1668
1669cleanup:
1670 mbedtls_ecp_point_free( &RP ); mbedtls_mpi_free( &PX );
1671
1672 return( ret );
1673}
1674
1675#endif /* ECP_MONTGOMERY */
1676
1677/*
1678 * Multiplication R = m * P
1679 */
1680int mbedtls_ecp_mul( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
1681 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
1682 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
1683{
1684 int ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
1685#if defined(MBEDTLS_ECP_INTERNAL_ALT)
1686 char is_grp_capable = 0;
1687#endif
1688
1689 /* Common sanity checks */
1690 if( mbedtls_mpi_cmp_int( &P->Z, 1 ) != 0 )
1691 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1692
1693 if( ( ret = mbedtls_ecp_check_privkey( grp, m ) ) != 0 ||
1694 ( ret = mbedtls_ecp_check_pubkey( grp, P ) ) != 0 )
1695 return( ret );
1696
1697#if defined(MBEDTLS_ECP_INTERNAL_ALT)
1698 if ( is_grp_capable = mbedtls_internal_ecp_grp_capable( grp ) )
1699 {
1700 MBEDTLS_MPI_CHK( mbedtls_internal_ecp_init( grp ) );
1701 }
1702
1703#endif /* MBEDTLS_ECP_INTERNAL_ALT */
1704#if defined(ECP_MONTGOMERY)
1705 if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
1706 ret = ecp_mul_mxz( grp, R, m, P, f_rng, p_rng );
1707
1708#endif
1709#if defined(ECP_SHORTWEIERSTRASS)
1710 if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS )
1711 ret = ecp_mul_comb( grp, R, m, P, f_rng, p_rng );
1712
1713#endif
1714#if defined(MBEDTLS_ECP_INTERNAL_ALT)
1715cleanup:
1716
1717 if ( is_grp_capable )
1718 {
1719 mbedtls_internal_ecp_free( grp );
1720 }
1721
1722#endif /* MBEDTLS_ECP_INTERNAL_ALT */
1723 return( ret );
1724}
1725
1726#if defined(ECP_SHORTWEIERSTRASS)
1727/*
1728 * Check that an affine point is valid as a public key,
1729 * short weierstrass curves (SEC1 3.2.3.1)
1730 */
1731static int ecp_check_pubkey_sw( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt )
1732{
1733 int ret;
1734 mbedtls_mpi YY, RHS;
1735
1736 /* pt coordinates must be normalized for our checks */
1737 if( mbedtls_mpi_cmp_int( &pt->X, 0 ) < 0 ||
1738 mbedtls_mpi_cmp_int( &pt->Y, 0 ) < 0 ||
1739 mbedtls_mpi_cmp_mpi( &pt->X, &grp->P ) >= 0 ||
1740 mbedtls_mpi_cmp_mpi( &pt->Y, &grp->P ) >= 0 )
1741 return( MBEDTLS_ERR_ECP_INVALID_KEY );
1742
1743 mbedtls_mpi_init( &YY ); mbedtls_mpi_init( &RHS );
1744
1745 /*
1746 * YY = Y^2
1747 * RHS = X (X^2 + A) + B = X^3 + A X + B
1748 */
1749 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &YY, &pt->Y, &pt->Y ) ); MOD_MUL( YY );
1750 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &RHS, &pt->X, &pt->X ) ); MOD_MUL( RHS );
1751
1752 /* Special case for A = -3 */
1753 if( grp->A.p == NULL )
1754 {
1755 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &RHS, &RHS, 3 ) ); MOD_SUB( RHS );
1756 }
1757 else
1758 {
1759 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &RHS, &RHS, &grp->A ) ); MOD_ADD( RHS );
1760 }
1761
1762 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &RHS, &RHS, &pt->X ) ); MOD_MUL( RHS );
1763 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &RHS, &RHS, &grp->B ) ); MOD_ADD( RHS );
1764
1765 if( mbedtls_mpi_cmp_mpi( &YY, &RHS ) != 0 )
1766 ret = MBEDTLS_ERR_ECP_INVALID_KEY;
1767
1768cleanup:
1769
1770 mbedtls_mpi_free( &YY ); mbedtls_mpi_free( &RHS );
1771
1772 return( ret );
1773}
1774#endif /* ECP_SHORTWEIERSTRASS */
1775
1776/*
1777 * R = m * P with shortcuts for m == 1 and m == -1
1778 * NOT constant-time - ONLY for short Weierstrass!
1779 */
1780static int mbedtls_ecp_mul_shortcuts( mbedtls_ecp_group *grp,
1781 mbedtls_ecp_point *R,
1782 const mbedtls_mpi *m,
1783 const mbedtls_ecp_point *P )
1784{
1785 int ret;
1786
1787 if( mbedtls_mpi_cmp_int( m, 1 ) == 0 )
1788 {
1789 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, P ) );
1790 }
1791 else if( mbedtls_mpi_cmp_int( m, -1 ) == 0 )
1792 {
1793 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, P ) );
1794 if( mbedtls_mpi_cmp_int( &R->Y, 0 ) != 0 )
1795 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &R->Y, &grp->P, &R->Y ) );
1796 }
1797 else
1798 {
1799 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( grp, R, m, P, NULL, NULL ) );
1800 }
1801
1802cleanup:
1803 return( ret );
1804}
1805
1806/*
1807 * Linear combination
1808 * NOT constant-time
1809 */
1810int mbedtls_ecp_muladd( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
1811 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
1812 const mbedtls_mpi *n, const mbedtls_ecp_point *Q )
1813{
1814 int ret;
1815 mbedtls_ecp_point mP;
1816#if defined(MBEDTLS_ECP_INTERNAL_ALT)
1817 char is_grp_capable = 0;
1818#endif
1819
1820 if( ecp_get_type( grp ) != ECP_TYPE_SHORT_WEIERSTRASS )
1821 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
1822
1823 mbedtls_ecp_point_init( &mP );
1824
1825 MBEDTLS_MPI_CHK( mbedtls_ecp_mul_shortcuts( grp, &mP, m, P ) );
1826 MBEDTLS_MPI_CHK( mbedtls_ecp_mul_shortcuts( grp, R, n, Q ) );
1827
1828#if defined(MBEDTLS_ECP_INTERNAL_ALT)
1829 if ( is_grp_capable = mbedtls_internal_ecp_grp_capable( grp ) )
1830 {
1831 MBEDTLS_MPI_CHK( mbedtls_internal_ecp_init( grp ) );
1832 }
1833
1834#endif /* MBEDTLS_ECP_INTERNAL_ALT */
1835 MBEDTLS_MPI_CHK( ecp_add_mixed( grp, R, &mP, R ) );
1836 MBEDTLS_MPI_CHK( ecp_normalize_jac( grp, R ) );
1837
1838cleanup:
1839
1840#if defined(MBEDTLS_ECP_INTERNAL_ALT)
1841 if ( is_grp_capable )
1842 {
1843 mbedtls_internal_ecp_free( grp );
1844 }
1845
1846#endif /* MBEDTLS_ECP_INTERNAL_ALT */
1847 mbedtls_ecp_point_free( &mP );
1848
1849 return( ret );
1850}
1851
1852
1853#if defined(ECP_MONTGOMERY)
1854/*
1855 * Check validity of a public key for Montgomery curves with x-only schemes
1856 */
1857static int ecp_check_pubkey_mx( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt )
1858{
1859 /* [Curve25519 p. 5] Just check X is the correct number of bytes */
1860 /* Allow any public value, if it's too big then we'll just reduce it mod p
1861 * (RFC 7748 sec. 5 para. 3). */
1862 if( mbedtls_mpi_size( &pt->X ) > ( grp->nbits + 7 ) / 8 )
1863 return( MBEDTLS_ERR_ECP_INVALID_KEY );
1864
1865 return( 0 );
1866}
1867#endif /* ECP_MONTGOMERY */
1868
1869/*
1870 * Check that a point is valid as a public key
1871 */
1872int mbedtls_ecp_check_pubkey( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt )
1873{
1874 /* Must use affine coordinates */
1875 if( mbedtls_mpi_cmp_int( &pt->Z, 1 ) != 0 )
1876 return( MBEDTLS_ERR_ECP_INVALID_KEY );
1877
1878#if defined(ECP_MONTGOMERY)
1879 if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
1880 return( ecp_check_pubkey_mx( grp, pt ) );
1881#endif
1882#if defined(ECP_SHORTWEIERSTRASS)
1883 if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS )
1884 return( ecp_check_pubkey_sw( grp, pt ) );
1885#endif
1886 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1887}
1888
1889/*
1890 * Check that an mbedtls_mpi is valid as a private key
1891 */
1892int mbedtls_ecp_check_privkey( const mbedtls_ecp_group *grp, const mbedtls_mpi *d )
1893{
1894#if defined(ECP_MONTGOMERY)
1895 if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
1896 {
1897 /* see RFC 7748 sec. 5 para. 5 */
1898 if( mbedtls_mpi_get_bit( d, 0 ) != 0 ||
1899 mbedtls_mpi_get_bit( d, 1 ) != 0 ||
1900 mbedtls_mpi_bitlen( d ) - 1 != grp->nbits ) /* mbedtls_mpi_bitlen is one-based! */
1901 return( MBEDTLS_ERR_ECP_INVALID_KEY );
1902
1903 /* see [Curve25519] page 5 */
1904 if( grp->nbits == 254 && mbedtls_mpi_get_bit( d, 2 ) != 0 )
1905 return( MBEDTLS_ERR_ECP_INVALID_KEY );
1906
1907 return( 0 );
1908 }
1909#endif /* ECP_MONTGOMERY */
1910#if defined(ECP_SHORTWEIERSTRASS)
1911 if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS )
1912 {
1913 /* see SEC1 3.2 */
1914 if( mbedtls_mpi_cmp_int( d, 1 ) < 0 ||
1915 mbedtls_mpi_cmp_mpi( d, &grp->N ) >= 0 )
1916 return( MBEDTLS_ERR_ECP_INVALID_KEY );
1917 else
1918 return( 0 );
1919 }
1920#endif /* ECP_SHORTWEIERSTRASS */
1921
1922 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1923}
1924
1925/*
1926 * Generate a keypair with configurable base point
1927 */
1928int mbedtls_ecp_gen_keypair_base( mbedtls_ecp_group *grp,
1929 const mbedtls_ecp_point *G,
1930 mbedtls_mpi *d, mbedtls_ecp_point *Q,
1931 int (*f_rng)(void *, unsigned char *, size_t),
1932 void *p_rng )
1933{
1934 int ret;
1935 size_t n_size = ( grp->nbits + 7 ) / 8;
1936
1937#if defined(ECP_MONTGOMERY)
1938 if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
1939 {
1940 /* [M225] page 5 */
1941 size_t b;
1942
1943 do {
1944 MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( d, n_size, f_rng, p_rng ) );
1945 } while( mbedtls_mpi_bitlen( d ) == 0);
1946
1947 /* Make sure the most significant bit is nbits */
1948 b = mbedtls_mpi_bitlen( d ) - 1; /* mbedtls_mpi_bitlen is one-based */
1949 if( b > grp->nbits )
1950 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( d, b - grp->nbits ) );
1951 else
1952 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, grp->nbits, 1 ) );
1953
1954 /* Make sure the last two bits are unset for Curve448, three bits for
1955 Curve25519 */
1956 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 0, 0 ) );
1957 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 1, 0 ) );
1958 if( grp->nbits == 254 )
1959 {
1960 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 2, 0 ) );
1961 }
1962 }
1963 else
1964#endif /* ECP_MONTGOMERY */
1965#if defined(ECP_SHORTWEIERSTRASS)
1966 if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS )
1967 {
1968 /* SEC1 3.2.1: Generate d such that 1 <= n < N */
1969 int count = 0;
1970
1971 /*
1972 * Match the procedure given in RFC 6979 (deterministic ECDSA):
1973 * - use the same byte ordering;
1974 * - keep the leftmost nbits bits of the generated octet string;
1975 * - try until result is in the desired range.
1976 * This also avoids any biais, which is especially important for ECDSA.
1977 */
1978 do
1979 {
1980 MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( d, n_size, f_rng, p_rng ) );
1981 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( d, 8 * n_size - grp->nbits ) );
1982
1983 /*
1984 * Each try has at worst a probability 1/2 of failing (the msb has
1985 * a probability 1/2 of being 0, and then the result will be < N),
1986 * so after 30 tries failure probability is a most 2**(-30).
1987 *
1988 * For most curves, 1 try is enough with overwhelming probability,
1989 * since N starts with a lot of 1s in binary, but some curves
1990 * such as secp224k1 are actually very close to the worst case.
1991 */
1992 if( ++count > 30 )
1993 return( MBEDTLS_ERR_ECP_RANDOM_FAILED );
1994 }
1995 while( mbedtls_mpi_cmp_int( d, 1 ) < 0 ||
1996 mbedtls_mpi_cmp_mpi( d, &grp->N ) >= 0 );
1997 }
1998 else
1999#endif /* ECP_SHORTWEIERSTRASS */
2000 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
2001
2002cleanup:
2003 if( ret != 0 )
2004 return( ret );
2005
2006 return( mbedtls_ecp_mul( grp, Q, d, G, f_rng, p_rng ) );
2007}
2008
2009/*
2010 * Generate key pair, wrapper for conventional base point
2011 */
2012int mbedtls_ecp_gen_keypair( mbedtls_ecp_group *grp,
2013 mbedtls_mpi *d, mbedtls_ecp_point *Q,
2014 int (*f_rng)(void *, unsigned char *, size_t),
2015 void *p_rng )
2016{
2017 return( mbedtls_ecp_gen_keypair_base( grp, &grp->G, d, Q, f_rng, p_rng ) );
2018}
2019
2020/*
2021 * Generate a keypair, prettier wrapper
2022 */
2023int mbedtls_ecp_gen_key( mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key,
2024 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
2025{
2026 int ret;
2027
2028 if( ( ret = mbedtls_ecp_group_load( &key->grp, grp_id ) ) != 0 )
2029 return( ret );
2030
2031 return( mbedtls_ecp_gen_keypair( &key->grp, &key->d, &key->Q, f_rng, p_rng ) );
2032}
2033
2034/*
2035 * Check a public-private key pair
2036 */
2037int mbedtls_ecp_check_pub_priv( const mbedtls_ecp_keypair *pub, const mbedtls_ecp_keypair *prv )
2038{
2039 int ret;
2040 mbedtls_ecp_point Q;
2041 mbedtls_ecp_group grp;
2042
2043 if( pub->grp.id == MBEDTLS_ECP_DP_NONE ||
2044 pub->grp.id != prv->grp.id ||
2045 mbedtls_mpi_cmp_mpi( &pub->Q.X, &prv->Q.X ) ||
2046 mbedtls_mpi_cmp_mpi( &pub->Q.Y, &prv->Q.Y ) ||
2047 mbedtls_mpi_cmp_mpi( &pub->Q.Z, &prv->Q.Z ) )
2048 {
2049 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
2050 }
2051
2052 mbedtls_ecp_point_init( &Q );
2053 mbedtls_ecp_group_init( &grp );
2054
2055 /* mbedtls_ecp_mul() needs a non-const group... */
2056 mbedtls_ecp_group_copy( &grp, &prv->grp );
2057
2058 /* Also checks d is valid */
2059 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &Q, &prv->d, &prv->grp.G, NULL, NULL ) );
2060
2061 if( mbedtls_mpi_cmp_mpi( &Q.X, &prv->Q.X ) ||
2062 mbedtls_mpi_cmp_mpi( &Q.Y, &prv->Q.Y ) ||
2063 mbedtls_mpi_cmp_mpi( &Q.Z, &prv->Q.Z ) )
2064 {
2065 ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
2066 goto cleanup;
2067 }
2068
2069cleanup:
2070 mbedtls_ecp_point_free( &Q );
2071 mbedtls_ecp_group_free( &grp );
2072
2073 return( ret );
2074}
2075
2076#if defined(MBEDTLS_SELF_TEST)
2077
2078/*
2079 * Checkup routine
2080 */
2081int mbedtls_ecp_self_test( int verbose )
2082{
2083 int ret;
2084 size_t i;
2085 mbedtls_ecp_group grp;
2086 mbedtls_ecp_point R, P;
2087 mbedtls_mpi m;
2088 unsigned long add_c_prev, dbl_c_prev, mul_c_prev;
2089 /* exponents especially adapted for secp192r1 */
2090 const char *exponents[] =
2091 {
2092 "000000000000000000000000000000000000000000000001", /* one */
2093 "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22830", /* N - 1 */
2094 "5EA6F389A38B8BC81E767753B15AA5569E1782E30ABE7D25", /* random */
2095 "400000000000000000000000000000000000000000000000", /* one and zeros */
2096 "7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", /* all ones */
2097 "555555555555555555555555555555555555555555555555", /* 101010... */
2098 };
2099
2100 mbedtls_ecp_group_init( &grp );
2101 mbedtls_ecp_point_init( &R );
2102 mbedtls_ecp_point_init( &P );
2103 mbedtls_mpi_init( &m );
2104
2105 /* Use secp192r1 if available, or any available curve */
2106#if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
2107 MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, MBEDTLS_ECP_DP_SECP192R1 ) );
2108#else
2109 MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, mbedtls_ecp_curve_list()->grp_id ) );
2110#endif
2111
2112 if( verbose != 0 )
2113 mbedtls_printf( " ECP test #1 (constant op_count, base point G): " );
2114
2115 /* Do a dummy multiplication first to trigger precomputation */
2116 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &m, 2 ) );
2117 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &P, &m, &grp.G, NULL, NULL ) );
2118
2119 add_count = 0;
2120 dbl_count = 0;
2121 mul_count = 0;
2122 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[0] ) );
2123 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &grp.G, NULL, NULL ) );
2124
2125 for( i = 1; i < sizeof( exponents ) / sizeof( exponents[0] ); i++ )
2126 {
2127 add_c_prev = add_count;
2128 dbl_c_prev = dbl_count;
2129 mul_c_prev = mul_count;
2130 add_count = 0;
2131 dbl_count = 0;
2132 mul_count = 0;
2133
2134 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[i] ) );
2135 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &grp.G, NULL, NULL ) );
2136
2137 if( add_count != add_c_prev ||
2138 dbl_count != dbl_c_prev ||
2139 mul_count != mul_c_prev )
2140 {
2141 if( verbose != 0 )
2142 mbedtls_printf( "failed (%u)\n", (unsigned int) i );
2143
2144 ret = 1;
2145 goto cleanup;
2146 }
2147 }
2148
2149 if( verbose != 0 )
2150 mbedtls_printf( "passed\n" );
2151
2152 if( verbose != 0 )
2153 mbedtls_printf( " ECP test #2 (constant op_count, other point): " );
2154 /* We computed P = 2G last time, use it */
2155
2156 add_count = 0;
2157 dbl_count = 0;
2158 mul_count = 0;
2159 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[0] ) );
2160 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &P, NULL, NULL ) );
2161
2162 for( i = 1; i < sizeof( exponents ) / sizeof( exponents[0] ); i++ )
2163 {
2164 add_c_prev = add_count;
2165 dbl_c_prev = dbl_count;
2166 mul_c_prev = mul_count;
2167 add_count = 0;
2168 dbl_count = 0;
2169 mul_count = 0;
2170
2171 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[i] ) );
2172 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &P, NULL, NULL ) );
2173
2174 if( add_count != add_c_prev ||
2175 dbl_count != dbl_c_prev ||
2176 mul_count != mul_c_prev )
2177 {
2178 if( verbose != 0 )
2179 mbedtls_printf( "failed (%u)\n", (unsigned int) i );
2180
2181 ret = 1;
2182 goto cleanup;
2183 }
2184 }
2185
2186 if( verbose != 0 )
2187 mbedtls_printf( "passed\n" );
2188
2189cleanup:
2190
2191 if( ret < 0 && verbose != 0 )
2192 mbedtls_printf( "Unexpected error, return code = %08X\n", ret );
2193
2194 mbedtls_ecp_group_free( &grp );
2195 mbedtls_ecp_point_free( &R );
2196 mbedtls_ecp_point_free( &P );
2197 mbedtls_mpi_free( &m );
2198
2199 if( verbose != 0 )
2200 mbedtls_printf( "\n" );
2201
2202 return( ret );
2203}
2204
2205#endif /* MBEDTLS_SELF_TEST */
2206
2207#endif /* !MBEDTLS_ECP_ALT */
2208
2209#endif /* MBEDTLS_ECP_C */
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