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[reactos.git] / reactos / dll / 3rdparty / mbedtls / ecp.c
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 */
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 */
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 */
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 */
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 */
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 */
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 */
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 */
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 */
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 */
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 */
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 */
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 */
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 */
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 */
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 */
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 */
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 * Import a non-zero point from ASCII strings
408 */
409 int mbedtls_ecp_point_read_string( mbedtls_ecp_point *P, int radix,
410 const char *x, const char *y )
411 {
412 int ret;
413
414 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &P->X, radix, x ) );
415 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &P->Y, radix, y ) );
416 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &P->Z, 1 ) );
417
418 cleanup:
419 return( ret );
420 }
421
422 /*
423 * Export a point into unsigned binary data (SEC1 2.3.3)
424 */
425 int mbedtls_ecp_point_write_binary( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *P,
426 int format, size_t *olen,
427 unsigned char *buf, size_t buflen )
428 {
429 int ret = 0;
430 size_t plen;
431
432 if( format != MBEDTLS_ECP_PF_UNCOMPRESSED &&
433 format != MBEDTLS_ECP_PF_COMPRESSED )
434 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
435
436 /*
437 * Common case: P == 0
438 */
439 if( mbedtls_mpi_cmp_int( &P->Z, 0 ) == 0 )
440 {
441 if( buflen < 1 )
442 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
443
444 buf[0] = 0x00;
445 *olen = 1;
446
447 return( 0 );
448 }
449
450 plen = mbedtls_mpi_size( &grp->P );
451
452 if( format == MBEDTLS_ECP_PF_UNCOMPRESSED )
453 {
454 *olen = 2 * plen + 1;
455
456 if( buflen < *olen )
457 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
458
459 buf[0] = 0x04;
460 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->X, buf + 1, plen ) );
461 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->Y, buf + 1 + plen, plen ) );
462 }
463 else if( format == MBEDTLS_ECP_PF_COMPRESSED )
464 {
465 *olen = plen + 1;
466
467 if( buflen < *olen )
468 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
469
470 buf[0] = 0x02 + mbedtls_mpi_get_bit( &P->Y, 0 );
471 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->X, buf + 1, plen ) );
472 }
473
474 cleanup:
475 return( ret );
476 }
477
478 /*
479 * Import a point from unsigned binary data (SEC1 2.3.4)
480 */
481 int mbedtls_ecp_point_read_binary( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt,
482 const unsigned char *buf, size_t ilen )
483 {
484 int ret;
485 size_t plen;
486
487 if( ilen < 1 )
488 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
489
490 if( buf[0] == 0x00 )
491 {
492 if( ilen == 1 )
493 return( mbedtls_ecp_set_zero( pt ) );
494 else
495 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
496 }
497
498 plen = mbedtls_mpi_size( &grp->P );
499
500 if( buf[0] != 0x04 )
501 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
502
503 if( ilen != 2 * plen + 1 )
504 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
505
506 MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &pt->X, buf + 1, plen ) );
507 MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &pt->Y, buf + 1 + plen, plen ) );
508 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) );
509
510 cleanup:
511 return( ret );
512 }
513
514 /*
515 * Import a point from a TLS ECPoint record (RFC 4492)
516 * struct {
517 * opaque point <1..2^8-1>;
518 * } ECPoint;
519 */
520 int mbedtls_ecp_tls_read_point( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt,
521 const unsigned char **buf, size_t buf_len )
522 {
523 unsigned char data_len;
524 const unsigned char *buf_start;
525
526 /*
527 * We must have at least two bytes (1 for length, at least one for data)
528 */
529 if( buf_len < 2 )
530 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
531
532 data_len = *(*buf)++;
533 if( data_len < 1 || data_len > buf_len - 1 )
534 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
535
536 /*
537 * Save buffer start for read_binary and update buf
538 */
539 buf_start = *buf;
540 *buf += data_len;
541
542 return mbedtls_ecp_point_read_binary( grp, pt, buf_start, data_len );
543 }
544
545 /*
546 * Export a point as a TLS ECPoint record (RFC 4492)
547 * struct {
548 * opaque point <1..2^8-1>;
549 * } ECPoint;
550 */
551 int mbedtls_ecp_tls_write_point( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt,
552 int format, size_t *olen,
553 unsigned char *buf, size_t blen )
554 {
555 int ret;
556
557 /*
558 * buffer length must be at least one, for our length byte
559 */
560 if( blen < 1 )
561 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
562
563 if( ( ret = mbedtls_ecp_point_write_binary( grp, pt, format,
564 olen, buf + 1, blen - 1) ) != 0 )
565 return( ret );
566
567 /*
568 * write length to the first byte and update total length
569 */
570 buf[0] = (unsigned char) *olen;
571 ++*olen;
572
573 return( 0 );
574 }
575
576 /*
577 * Set a group from an ECParameters record (RFC 4492)
578 */
579 int mbedtls_ecp_tls_read_group( mbedtls_ecp_group *grp, const unsigned char **buf, size_t len )
580 {
581 uint16_t tls_id;
582 const mbedtls_ecp_curve_info *curve_info;
583
584 /*
585 * We expect at least three bytes (see below)
586 */
587 if( len < 3 )
588 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
589
590 /*
591 * First byte is curve_type; only named_curve is handled
592 */
593 if( *(*buf)++ != MBEDTLS_ECP_TLS_NAMED_CURVE )
594 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
595
596 /*
597 * Next two bytes are the namedcurve value
598 */
599 tls_id = *(*buf)++;
600 tls_id <<= 8;
601 tls_id |= *(*buf)++;
602
603 if( ( curve_info = mbedtls_ecp_curve_info_from_tls_id( tls_id ) ) == NULL )
604 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
605
606 return mbedtls_ecp_group_load( grp, curve_info->grp_id );
607 }
608
609 /*
610 * Write the ECParameters record corresponding to a group (RFC 4492)
611 */
612 int mbedtls_ecp_tls_write_group( const mbedtls_ecp_group *grp, size_t *olen,
613 unsigned char *buf, size_t blen )
614 {
615 const mbedtls_ecp_curve_info *curve_info;
616
617 if( ( curve_info = mbedtls_ecp_curve_info_from_grp_id( grp->id ) ) == NULL )
618 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
619
620 /*
621 * We are going to write 3 bytes (see below)
622 */
623 *olen = 3;
624 if( blen < *olen )
625 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
626
627 /*
628 * First byte is curve_type, always named_curve
629 */
630 *buf++ = MBEDTLS_ECP_TLS_NAMED_CURVE;
631
632 /*
633 * Next two bytes are the namedcurve value
634 */
635 buf[0] = curve_info->tls_id >> 8;
636 buf[1] = curve_info->tls_id & 0xFF;
637
638 return( 0 );
639 }
640
641 /*
642 * Wrapper around fast quasi-modp functions, with fall-back to mbedtls_mpi_mod_mpi.
643 * See the documentation of struct mbedtls_ecp_group.
644 *
645 * This function is in the critial loop for mbedtls_ecp_mul, so pay attention to perf.
646 */
647 static int ecp_modp( mbedtls_mpi *N, const mbedtls_ecp_group *grp )
648 {
649 int ret;
650
651 if( grp->modp == NULL )
652 return( mbedtls_mpi_mod_mpi( N, N, &grp->P ) );
653
654 /* N->s < 0 is a much faster test, which fails only if N is 0 */
655 if( ( N->s < 0 && mbedtls_mpi_cmp_int( N, 0 ) != 0 ) ||
656 mbedtls_mpi_bitlen( N ) > 2 * grp->pbits )
657 {
658 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
659 }
660
661 MBEDTLS_MPI_CHK( grp->modp( N ) );
662
663 /* N->s < 0 is a much faster test, which fails only if N is 0 */
664 while( N->s < 0 && mbedtls_mpi_cmp_int( N, 0 ) != 0 )
665 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &grp->P ) );
666
667 while( mbedtls_mpi_cmp_mpi( N, &grp->P ) >= 0 )
668 /* we known P, N and the result are positive */
669 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( N, N, &grp->P ) );
670
671 cleanup:
672 return( ret );
673 }
674
675 /*
676 * Fast mod-p functions expect their argument to be in the 0..p^2 range.
677 *
678 * In order to guarantee that, we need to ensure that operands of
679 * mbedtls_mpi_mul_mpi are in the 0..p range. So, after each operation we will
680 * bring the result back to this range.
681 *
682 * The following macros are shortcuts for doing that.
683 */
684
685 /*
686 * Reduce a mbedtls_mpi mod p in-place, general case, to use after mbedtls_mpi_mul_mpi
687 */
688 #if defined(MBEDTLS_SELF_TEST)
689 #define INC_MUL_COUNT mul_count++;
690 #else
691 #define INC_MUL_COUNT
692 #endif
693
694 #define MOD_MUL( N ) do { MBEDTLS_MPI_CHK( ecp_modp( &N, grp ) ); INC_MUL_COUNT } \
695 while( 0 )
696
697 /*
698 * Reduce a mbedtls_mpi mod p in-place, to use after mbedtls_mpi_sub_mpi
699 * N->s < 0 is a very fast test, which fails only if N is 0
700 */
701 #define MOD_SUB( N ) \
702 while( N.s < 0 && mbedtls_mpi_cmp_int( &N, 0 ) != 0 ) \
703 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &N, &N, &grp->P ) )
704
705 /*
706 * Reduce a mbedtls_mpi mod p in-place, to use after mbedtls_mpi_add_mpi and mbedtls_mpi_mul_int.
707 * We known P, N and the result are positive, so sub_abs is correct, and
708 * a bit faster.
709 */
710 #define MOD_ADD( N ) \
711 while( mbedtls_mpi_cmp_mpi( &N, &grp->P ) >= 0 ) \
712 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( &N, &N, &grp->P ) )
713
714 #if defined(ECP_SHORTWEIERSTRASS)
715 /*
716 * For curves in short Weierstrass form, we do all the internal operations in
717 * Jacobian coordinates.
718 *
719 * For multiplication, we'll use a comb method with coutermeasueres against
720 * SPA, hence timing attacks.
721 */
722
723 /*
724 * Normalize jacobian coordinates so that Z == 0 || Z == 1 (GECC 3.2.1)
725 * Cost: 1N := 1I + 3M + 1S
726 */
727 static int ecp_normalize_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt )
728 {
729 int ret;
730 mbedtls_mpi Zi, ZZi;
731
732 if( mbedtls_mpi_cmp_int( &pt->Z, 0 ) == 0 )
733 return( 0 );
734
735 mbedtls_mpi_init( &Zi ); mbedtls_mpi_init( &ZZi );
736
737 /*
738 * X = X / Z^2 mod p
739 */
740 MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &Zi, &pt->Z, &grp->P ) );
741 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ZZi, &Zi, &Zi ) ); MOD_MUL( ZZi );
742 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->X, &pt->X, &ZZi ) ); MOD_MUL( pt->X );
743
744 /*
745 * Y = Y / Z^3 mod p
746 */
747 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Y, &pt->Y, &ZZi ) ); MOD_MUL( pt->Y );
748 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Y, &pt->Y, &Zi ) ); MOD_MUL( pt->Y );
749
750 /*
751 * Z = 1
752 */
753 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) );
754
755 cleanup:
756
757 mbedtls_mpi_free( &Zi ); mbedtls_mpi_free( &ZZi );
758
759 return( ret );
760 }
761
762 /*
763 * Normalize jacobian coordinates of an array of (pointers to) points,
764 * using Montgomery's trick to perform only one inversion mod P.
765 * (See for example Cohen's "A Course in Computational Algebraic Number
766 * Theory", Algorithm 10.3.4.)
767 *
768 * Warning: fails (returning an error) if one of the points is zero!
769 * This should never happen, see choice of w in ecp_mul_comb().
770 *
771 * Cost: 1N(t) := 1I + (6t - 3)M + 1S
772 */
773 static int ecp_normalize_jac_many( const mbedtls_ecp_group *grp,
774 mbedtls_ecp_point *T[], size_t t_len )
775 {
776 int ret;
777 size_t i;
778 mbedtls_mpi *c, u, Zi, ZZi;
779
780 if( t_len < 2 )
781 return( ecp_normalize_jac( grp, *T ) );
782
783 if( ( c = mbedtls_calloc( t_len, sizeof( mbedtls_mpi ) ) ) == NULL )
784 return( MBEDTLS_ERR_ECP_ALLOC_FAILED );
785
786 mbedtls_mpi_init( &u ); mbedtls_mpi_init( &Zi ); mbedtls_mpi_init( &ZZi );
787
788 /*
789 * c[i] = Z_0 * ... * Z_i
790 */
791 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &c[0], &T[0]->Z ) );
792 for( i = 1; i < t_len; i++ )
793 {
794 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &c[i], &c[i-1], &T[i]->Z ) );
795 MOD_MUL( c[i] );
796 }
797
798 /*
799 * u = 1 / (Z_0 * ... * Z_n) mod P
800 */
801 MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &u, &c[t_len-1], &grp->P ) );
802
803 for( i = t_len - 1; ; i-- )
804 {
805 /*
806 * Zi = 1 / Z_i mod p
807 * u = 1 / (Z_0 * ... * Z_i) mod P
808 */
809 if( i == 0 ) {
810 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &Zi, &u ) );
811 }
812 else
813 {
814 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &Zi, &u, &c[i-1] ) ); MOD_MUL( Zi );
815 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &u, &u, &T[i]->Z ) ); MOD_MUL( u );
816 }
817
818 /*
819 * proceed as in normalize()
820 */
821 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ZZi, &Zi, &Zi ) ); MOD_MUL( ZZi );
822 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T[i]->X, &T[i]->X, &ZZi ) ); MOD_MUL( T[i]->X );
823 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T[i]->Y, &T[i]->Y, &ZZi ) ); MOD_MUL( T[i]->Y );
824 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T[i]->Y, &T[i]->Y, &Zi ) ); MOD_MUL( T[i]->Y );
825
826 /*
827 * Post-precessing: reclaim some memory by shrinking coordinates
828 * - not storing Z (always 1)
829 * - shrinking other coordinates, but still keeping the same number of
830 * limbs as P, as otherwise it will too likely be regrown too fast.
831 */
832 MBEDTLS_MPI_CHK( mbedtls_mpi_shrink( &T[i]->X, grp->P.n ) );
833 MBEDTLS_MPI_CHK( mbedtls_mpi_shrink( &T[i]->Y, grp->P.n ) );
834 mbedtls_mpi_free( &T[i]->Z );
835
836 if( i == 0 )
837 break;
838 }
839
840 cleanup:
841
842 mbedtls_mpi_free( &u ); mbedtls_mpi_free( &Zi ); mbedtls_mpi_free( &ZZi );
843 for( i = 0; i < t_len; i++ )
844 mbedtls_mpi_free( &c[i] );
845 mbedtls_free( c );
846
847 return( ret );
848 }
849
850 /*
851 * Conditional point inversion: Q -> -Q = (Q.X, -Q.Y, Q.Z) without leak.
852 * "inv" must be 0 (don't invert) or 1 (invert) or the result will be invalid
853 */
854 static int ecp_safe_invert_jac( const mbedtls_ecp_group *grp,
855 mbedtls_ecp_point *Q,
856 unsigned char inv )
857 {
858 int ret;
859 unsigned char nonzero;
860 mbedtls_mpi mQY;
861
862 mbedtls_mpi_init( &mQY );
863
864 /* Use the fact that -Q.Y mod P = P - Q.Y unless Q.Y == 0 */
865 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &mQY, &grp->P, &Q->Y ) );
866 nonzero = mbedtls_mpi_cmp_int( &Q->Y, 0 ) != 0;
867 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &Q->Y, &mQY, inv & nonzero ) );
868
869 cleanup:
870 mbedtls_mpi_free( &mQY );
871
872 return( ret );
873 }
874
875 /*
876 * Point doubling R = 2 P, Jacobian coordinates
877 *
878 * Based on http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#doubling-dbl-1998-cmo-2 .
879 *
880 * We follow the variable naming fairly closely. The formula variations that trade a MUL for a SQR
881 * (plus a few ADDs) aren't useful as our bignum implementation doesn't distinguish squaring.
882 *
883 * Standard optimizations are applied when curve parameter A is one of { 0, -3 }.
884 *
885 * Cost: 1D := 3M + 4S (A == 0)
886 * 4M + 4S (A == -3)
887 * 3M + 6S + 1a otherwise
888 */
889 static int ecp_double_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
890 const mbedtls_ecp_point *P )
891 {
892 int ret;
893 mbedtls_mpi M, S, T, U;
894
895 #if defined(MBEDTLS_SELF_TEST)
896 dbl_count++;
897 #endif
898
899 mbedtls_mpi_init( &M ); mbedtls_mpi_init( &S ); mbedtls_mpi_init( &T ); mbedtls_mpi_init( &U );
900
901 /* Special case for A = -3 */
902 if( grp->A.p == NULL )
903 {
904 /* M = 3(X + Z^2)(X - Z^2) */
905 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->Z, &P->Z ) ); MOD_MUL( S );
906 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &T, &P->X, &S ) ); MOD_ADD( T );
907 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &U, &P->X, &S ) ); MOD_SUB( U );
908 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &T, &U ) ); MOD_MUL( S );
909 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &S, 3 ) ); MOD_ADD( M );
910 }
911 else
912 {
913 /* M = 3.X^2 */
914 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->X, &P->X ) ); MOD_MUL( S );
915 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &S, 3 ) ); MOD_ADD( M );
916
917 /* Optimize away for "koblitz" curves with A = 0 */
918 if( mbedtls_mpi_cmp_int( &grp->A, 0 ) != 0 )
919 {
920 /* M += A.Z^4 */
921 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->Z, &P->Z ) ); MOD_MUL( S );
922 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &S, &S ) ); MOD_MUL( T );
923 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &T, &grp->A ) ); MOD_MUL( S );
924 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &M, &M, &S ) ); MOD_ADD( M );
925 }
926 }
927
928 /* S = 4.X.Y^2 */
929 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &P->Y, &P->Y ) ); MOD_MUL( T );
930 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &T, 1 ) ); MOD_ADD( T );
931 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->X, &T ) ); MOD_MUL( S );
932 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &S, 1 ) ); MOD_ADD( S );
933
934 /* U = 8.Y^4 */
935 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &U, &T, &T ) ); MOD_MUL( U );
936 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &U, 1 ) ); MOD_ADD( U );
937
938 /* T = M^2 - 2.S */
939 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &M, &M ) ); MOD_MUL( T );
940 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T, &T, &S ) ); MOD_SUB( T );
941 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T, &T, &S ) ); MOD_SUB( T );
942
943 /* S = M(S - T) - U */
944 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &S, &S, &T ) ); MOD_SUB( S );
945 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &S, &M ) ); MOD_MUL( S );
946 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &S, &S, &U ) ); MOD_SUB( S );
947
948 /* U = 2.Y.Z */
949 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &U, &P->Y, &P->Z ) ); MOD_MUL( U );
950 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &U, 1 ) ); MOD_ADD( U );
951
952 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->X, &T ) );
953 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Y, &S ) );
954 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Z, &U ) );
955
956 cleanup:
957 mbedtls_mpi_free( &M ); mbedtls_mpi_free( &S ); mbedtls_mpi_free( &T ); mbedtls_mpi_free( &U );
958
959 return( ret );
960 }
961
962 /*
963 * Addition: R = P + Q, mixed affine-Jacobian coordinates (GECC 3.22)
964 *
965 * The coordinates of Q must be normalized (= affine),
966 * but those of P don't need to. R is not normalized.
967 *
968 * Special cases: (1) P or Q is zero, (2) R is zero, (3) P == Q.
969 * None of these cases can happen as intermediate step in ecp_mul_comb():
970 * - at each step, P, Q and R are multiples of the base point, the factor
971 * being less than its order, so none of them is zero;
972 * - Q is an odd multiple of the base point, P an even multiple,
973 * due to the choice of precomputed points in the modified comb method.
974 * So branches for these cases do not leak secret information.
975 *
976 * We accept Q->Z being unset (saving memory in tables) as meaning 1.
977 *
978 * Cost: 1A := 8M + 3S
979 */
980 static int ecp_add_mixed( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
981 const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q )
982 {
983 int ret;
984 mbedtls_mpi T1, T2, T3, T4, X, Y, Z;
985
986 #if defined(MBEDTLS_SELF_TEST)
987 add_count++;
988 #endif
989
990 /*
991 * Trivial cases: P == 0 or Q == 0 (case 1)
992 */
993 if( mbedtls_mpi_cmp_int( &P->Z, 0 ) == 0 )
994 return( mbedtls_ecp_copy( R, Q ) );
995
996 if( Q->Z.p != NULL && mbedtls_mpi_cmp_int( &Q->Z, 0 ) == 0 )
997 return( mbedtls_ecp_copy( R, P ) );
998
999 /*
1000 * Make sure Q coordinates are normalized
1001 */
1002 if( Q->Z.p != NULL && mbedtls_mpi_cmp_int( &Q->Z, 1 ) != 0 )
1003 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1004
1005 mbedtls_mpi_init( &T1 ); mbedtls_mpi_init( &T2 ); mbedtls_mpi_init( &T3 ); mbedtls_mpi_init( &T4 );
1006 mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Y ); mbedtls_mpi_init( &Z );
1007
1008 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T1, &P->Z, &P->Z ) ); MOD_MUL( T1 );
1009 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T2, &T1, &P->Z ) ); MOD_MUL( T2 );
1010 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T1, &T1, &Q->X ) ); MOD_MUL( T1 );
1011 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T2, &T2, &Q->Y ) ); MOD_MUL( T2 );
1012 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T1, &T1, &P->X ) ); MOD_SUB( T1 );
1013 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T2, &T2, &P->Y ) ); MOD_SUB( T2 );
1014
1015 /* Special cases (2) and (3) */
1016 if( mbedtls_mpi_cmp_int( &T1, 0 ) == 0 )
1017 {
1018 if( mbedtls_mpi_cmp_int( &T2, 0 ) == 0 )
1019 {
1020 ret = ecp_double_jac( grp, R, P );
1021 goto cleanup;
1022 }
1023 else
1024 {
1025 ret = mbedtls_ecp_set_zero( R );
1026 goto cleanup;
1027 }
1028 }
1029
1030 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &Z, &P->Z, &T1 ) ); MOD_MUL( Z );
1031 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T3, &T1, &T1 ) ); MOD_MUL( T3 );
1032 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T4, &T3, &T1 ) ); MOD_MUL( T4 );
1033 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T3, &T3, &P->X ) ); MOD_MUL( T3 );
1034 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &T1, &T3, 2 ) ); MOD_ADD( T1 );
1035 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &X, &T2, &T2 ) ); MOD_MUL( X );
1036 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &X, &X, &T1 ) ); MOD_SUB( X );
1037 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &X, &X, &T4 ) ); MOD_SUB( X );
1038 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T3, &T3, &X ) ); MOD_SUB( T3 );
1039 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T3, &T3, &T2 ) ); MOD_MUL( T3 );
1040 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T4, &T4, &P->Y ) ); MOD_MUL( T4 );
1041 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &Y, &T3, &T4 ) ); MOD_SUB( Y );
1042
1043 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->X, &X ) );
1044 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Y, &Y ) );
1045 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Z, &Z ) );
1046
1047 cleanup:
1048
1049 mbedtls_mpi_free( &T1 ); mbedtls_mpi_free( &T2 ); mbedtls_mpi_free( &T3 ); mbedtls_mpi_free( &T4 );
1050 mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Y ); mbedtls_mpi_free( &Z );
1051
1052 return( ret );
1053 }
1054
1055 /*
1056 * Randomize jacobian coordinates:
1057 * (X, Y, Z) -> (l^2 X, l^3 Y, l Z) for random l
1058 * This is sort of the reverse operation of ecp_normalize_jac().
1059 *
1060 * This countermeasure was first suggested in [2].
1061 */
1062 static int ecp_randomize_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt,
1063 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
1064 {
1065 int ret;
1066 mbedtls_mpi l, ll;
1067 size_t p_size = ( grp->pbits + 7 ) / 8;
1068 int count = 0;
1069
1070 mbedtls_mpi_init( &l ); mbedtls_mpi_init( &ll );
1071
1072 /* Generate l such that 1 < l < p */
1073 do
1074 {
1075 mbedtls_mpi_fill_random( &l, p_size, f_rng, p_rng );
1076
1077 while( mbedtls_mpi_cmp_mpi( &l, &grp->P ) >= 0 )
1078 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &l, 1 ) );
1079
1080 if( count++ > 10 )
1081 return( MBEDTLS_ERR_ECP_RANDOM_FAILED );
1082 }
1083 while( mbedtls_mpi_cmp_int( &l, 1 ) <= 0 );
1084
1085 /* Z = l * Z */
1086 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Z, &pt->Z, &l ) ); MOD_MUL( pt->Z );
1087
1088 /* X = l^2 * X */
1089 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ll, &l, &l ) ); MOD_MUL( ll );
1090 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->X, &pt->X, &ll ) ); MOD_MUL( pt->X );
1091
1092 /* Y = l^3 * Y */
1093 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ll, &ll, &l ) ); MOD_MUL( ll );
1094 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Y, &pt->Y, &ll ) ); MOD_MUL( pt->Y );
1095
1096 cleanup:
1097 mbedtls_mpi_free( &l ); mbedtls_mpi_free( &ll );
1098
1099 return( ret );
1100 }
1101
1102 /*
1103 * Check and define parameters used by the comb method (see below for details)
1104 */
1105 #if MBEDTLS_ECP_WINDOW_SIZE < 2 || MBEDTLS_ECP_WINDOW_SIZE > 7
1106 #error "MBEDTLS_ECP_WINDOW_SIZE out of bounds"
1107 #endif
1108
1109 /* d = ceil( n / w ) */
1110 #define COMB_MAX_D ( MBEDTLS_ECP_MAX_BITS + 1 ) / 2
1111
1112 /* number of precomputed points */
1113 #define COMB_MAX_PRE ( 1 << ( MBEDTLS_ECP_WINDOW_SIZE - 1 ) )
1114
1115 /*
1116 * Compute the representation of m that will be used with our comb method.
1117 *
1118 * The basic comb method is described in GECC 3.44 for example. We use a
1119 * modified version that provides resistance to SPA by avoiding zero
1120 * digits in the representation as in [3]. We modify the method further by
1121 * requiring that all K_i be odd, which has the small cost that our
1122 * representation uses one more K_i, due to carries.
1123 *
1124 * Also, for the sake of compactness, only the seven low-order bits of x[i]
1125 * are used to represent K_i, and the msb of x[i] encodes the the sign (s_i in
1126 * the paper): it is set if and only if if s_i == -1;
1127 *
1128 * Calling conventions:
1129 * - x is an array of size d + 1
1130 * - w is the size, ie number of teeth, of the comb, and must be between
1131 * 2 and 7 (in practice, between 2 and MBEDTLS_ECP_WINDOW_SIZE)
1132 * - m is the MPI, expected to be odd and such that bitlength(m) <= w * d
1133 * (the result will be incorrect if these assumptions are not satisfied)
1134 */
1135 static void ecp_comb_fixed( unsigned char x[], size_t d,
1136 unsigned char w, const mbedtls_mpi *m )
1137 {
1138 size_t i, j;
1139 unsigned char c, cc, adjust;
1140
1141 memset( x, 0, d+1 );
1142
1143 /* First get the classical comb values (except for x_d = 0) */
1144 for( i = 0; i < d; i++ )
1145 for( j = 0; j < w; j++ )
1146 x[i] |= mbedtls_mpi_get_bit( m, i + d * j ) << j;
1147
1148 /* Now make sure x_1 .. x_d are odd */
1149 c = 0;
1150 for( i = 1; i <= d; i++ )
1151 {
1152 /* Add carry and update it */
1153 cc = x[i] & c;
1154 x[i] = x[i] ^ c;
1155 c = cc;
1156
1157 /* Adjust if needed, avoiding branches */
1158 adjust = 1 - ( x[i] & 0x01 );
1159 c |= x[i] & ( x[i-1] * adjust );
1160 x[i] = x[i] ^ ( x[i-1] * adjust );
1161 x[i-1] |= adjust << 7;
1162 }
1163 }
1164
1165 /*
1166 * Precompute points for the comb method
1167 *
1168 * If i = i_{w-1} ... i_1 is the binary representation of i, then
1169 * T[i] = i_{w-1} 2^{(w-1)d} P + ... + i_1 2^d P + P
1170 *
1171 * T must be able to hold 2^{w - 1} elements
1172 *
1173 * Cost: d(w-1) D + (2^{w-1} - 1) A + 1 N(w-1) + 1 N(2^{w-1} - 1)
1174 */
1175 static int ecp_precompute_comb( const mbedtls_ecp_group *grp,
1176 mbedtls_ecp_point T[], const mbedtls_ecp_point *P,
1177 unsigned char w, size_t d )
1178 {
1179 int ret;
1180 unsigned char i, k;
1181 size_t j;
1182 mbedtls_ecp_point *cur, *TT[COMB_MAX_PRE - 1];
1183
1184 /*
1185 * Set T[0] = P and
1186 * T[2^{l-1}] = 2^{dl} P for l = 1 .. w-1 (this is not the final value)
1187 */
1188 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( &T[0], P ) );
1189
1190 k = 0;
1191 for( i = 1; i < ( 1U << ( w - 1 ) ); i <<= 1 )
1192 {
1193 cur = T + i;
1194 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( cur, T + ( i >> 1 ) ) );
1195 for( j = 0; j < d; j++ )
1196 MBEDTLS_MPI_CHK( ecp_double_jac( grp, cur, cur ) );
1197
1198 TT[k++] = cur;
1199 }
1200
1201 MBEDTLS_MPI_CHK( ecp_normalize_jac_many( grp, TT, k ) );
1202
1203 /*
1204 * Compute the remaining ones using the minimal number of additions
1205 * Be careful to update T[2^l] only after using it!
1206 */
1207 k = 0;
1208 for( i = 1; i < ( 1U << ( w - 1 ) ); i <<= 1 )
1209 {
1210 j = i;
1211 while( j-- )
1212 {
1213 MBEDTLS_MPI_CHK( ecp_add_mixed( grp, &T[i + j], &T[j], &T[i] ) );
1214 TT[k++] = &T[i + j];
1215 }
1216 }
1217
1218 MBEDTLS_MPI_CHK( ecp_normalize_jac_many( grp, TT, k ) );
1219
1220 cleanup:
1221 return( ret );
1222 }
1223
1224 /*
1225 * Select precomputed point: R = sign(i) * T[ abs(i) / 2 ]
1226 */
1227 static int ecp_select_comb( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
1228 const mbedtls_ecp_point T[], unsigned char t_len,
1229 unsigned char i )
1230 {
1231 int ret;
1232 unsigned char ii, j;
1233
1234 /* Ignore the "sign" bit and scale down */
1235 ii = ( i & 0x7Fu ) >> 1;
1236
1237 /* Read the whole table to thwart cache-based timing attacks */
1238 for( j = 0; j < t_len; j++ )
1239 {
1240 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &R->X, &T[j].X, j == ii ) );
1241 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &R->Y, &T[j].Y, j == ii ) );
1242 }
1243
1244 /* Safely invert result if i is "negative" */
1245 MBEDTLS_MPI_CHK( ecp_safe_invert_jac( grp, R, i >> 7 ) );
1246
1247 cleanup:
1248 return( ret );
1249 }
1250
1251 /*
1252 * Core multiplication algorithm for the (modified) comb method.
1253 * This part is actually common with the basic comb method (GECC 3.44)
1254 *
1255 * Cost: d A + d D + 1 R
1256 */
1257 static int ecp_mul_comb_core( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
1258 const mbedtls_ecp_point T[], unsigned char t_len,
1259 const unsigned char x[], size_t d,
1260 int (*f_rng)(void *, unsigned char *, size_t),
1261 void *p_rng )
1262 {
1263 int ret;
1264 mbedtls_ecp_point Txi;
1265 size_t i;
1266
1267 mbedtls_ecp_point_init( &Txi );
1268
1269 /* Start with a non-zero point and randomize its coordinates */
1270 i = d;
1271 MBEDTLS_MPI_CHK( ecp_select_comb( grp, R, T, t_len, x[i] ) );
1272 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->Z, 1 ) );
1273 if( f_rng != 0 )
1274 MBEDTLS_MPI_CHK( ecp_randomize_jac( grp, R, f_rng, p_rng ) );
1275
1276 while( i-- != 0 )
1277 {
1278 MBEDTLS_MPI_CHK( ecp_double_jac( grp, R, R ) );
1279 MBEDTLS_MPI_CHK( ecp_select_comb( grp, &Txi, T, t_len, x[i] ) );
1280 MBEDTLS_MPI_CHK( ecp_add_mixed( grp, R, R, &Txi ) );
1281 }
1282
1283 cleanup:
1284 mbedtls_ecp_point_free( &Txi );
1285
1286 return( ret );
1287 }
1288
1289 /*
1290 * Multiplication using the comb method,
1291 * for curves in short Weierstrass form
1292 */
1293 static int ecp_mul_comb( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
1294 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
1295 int (*f_rng)(void *, unsigned char *, size_t),
1296 void *p_rng )
1297 {
1298 int ret;
1299 unsigned char w, m_is_odd, p_eq_g, pre_len, i;
1300 size_t d;
1301 unsigned char k[COMB_MAX_D + 1];
1302 mbedtls_ecp_point *T;
1303 mbedtls_mpi M, mm;
1304
1305 mbedtls_mpi_init( &M );
1306 mbedtls_mpi_init( &mm );
1307
1308 /* we need N to be odd to trnaform m in an odd number, check now */
1309 if( mbedtls_mpi_get_bit( &grp->N, 0 ) != 1 )
1310 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1311
1312 /*
1313 * Minimize the number of multiplications, that is minimize
1314 * 10 * d * w + 18 * 2^(w-1) + 11 * d + 7 * w, with d = ceil( nbits / w )
1315 * (see costs of the various parts, with 1S = 1M)
1316 */
1317 w = grp->nbits >= 384 ? 5 : 4;
1318
1319 /*
1320 * If P == G, pre-compute a bit more, since this may be re-used later.
1321 * Just adding one avoids upping the cost of the first mul too much,
1322 * and the memory cost too.
1323 */
1324 #if MBEDTLS_ECP_FIXED_POINT_OPTIM == 1
1325 p_eq_g = ( mbedtls_mpi_cmp_mpi( &P->Y, &grp->G.Y ) == 0 &&
1326 mbedtls_mpi_cmp_mpi( &P->X, &grp->G.X ) == 0 );
1327 if( p_eq_g )
1328 w++;
1329 #else
1330 p_eq_g = 0;
1331 #endif
1332
1333 /*
1334 * Make sure w is within bounds.
1335 * (The last test is useful only for very small curves in the test suite.)
1336 */
1337 if( w > MBEDTLS_ECP_WINDOW_SIZE )
1338 w = MBEDTLS_ECP_WINDOW_SIZE;
1339 if( w >= grp->nbits )
1340 w = 2;
1341
1342 /* Other sizes that depend on w */
1343 pre_len = 1U << ( w - 1 );
1344 d = ( grp->nbits + w - 1 ) / w;
1345
1346 /*
1347 * Prepare precomputed points: if P == G we want to
1348 * use grp->T if already initialized, or initialize it.
1349 */
1350 T = p_eq_g ? grp->T : NULL;
1351
1352 if( T == NULL )
1353 {
1354 T = mbedtls_calloc( pre_len, sizeof( mbedtls_ecp_point ) );
1355 if( T == NULL )
1356 {
1357 ret = MBEDTLS_ERR_ECP_ALLOC_FAILED;
1358 goto cleanup;
1359 }
1360
1361 MBEDTLS_MPI_CHK( ecp_precompute_comb( grp, T, P, w, d ) );
1362
1363 if( p_eq_g )
1364 {
1365 grp->T = T;
1366 grp->T_size = pre_len;
1367 }
1368 }
1369
1370 /*
1371 * Make sure M is odd (M = m or M = N - m, since N is odd)
1372 * using the fact that m * P = - (N - m) * P
1373 */
1374 m_is_odd = ( mbedtls_mpi_get_bit( m, 0 ) == 1 );
1375 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &M, m ) );
1376 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &mm, &grp->N, m ) );
1377 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &M, &mm, ! m_is_odd ) );
1378
1379 /*
1380 * Go for comb multiplication, R = M * P
1381 */
1382 ecp_comb_fixed( k, d, w, &M );
1383 MBEDTLS_MPI_CHK( ecp_mul_comb_core( grp, R, T, pre_len, k, d, f_rng, p_rng ) );
1384
1385 /*
1386 * Now get m * P from M * P and normalize it
1387 */
1388 MBEDTLS_MPI_CHK( ecp_safe_invert_jac( grp, R, ! m_is_odd ) );
1389 MBEDTLS_MPI_CHK( ecp_normalize_jac( grp, R ) );
1390
1391 cleanup:
1392
1393 if( T != NULL && ! p_eq_g )
1394 {
1395 for( i = 0; i < pre_len; i++ )
1396 mbedtls_ecp_point_free( &T[i] );
1397 mbedtls_free( T );
1398 }
1399
1400 mbedtls_mpi_free( &M );
1401 mbedtls_mpi_free( &mm );
1402
1403 if( ret != 0 )
1404 mbedtls_ecp_point_free( R );
1405
1406 return( ret );
1407 }
1408
1409 #endif /* ECP_SHORTWEIERSTRASS */
1410
1411 #if defined(ECP_MONTGOMERY)
1412 /*
1413 * For Montgomery curves, we do all the internal arithmetic in projective
1414 * coordinates. Import/export of points uses only the x coordinates, which is
1415 * internaly represented as X / Z.
1416 *
1417 * For scalar multiplication, we'll use a Montgomery ladder.
1418 */
1419
1420 /*
1421 * Normalize Montgomery x/z coordinates: X = X/Z, Z = 1
1422 * Cost: 1M + 1I
1423 */
1424 static int ecp_normalize_mxz( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P )
1425 {
1426 int ret;
1427
1428 MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &P->Z, &P->Z, &grp->P ) );
1429 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &P->X, &P->X, &P->Z ) ); MOD_MUL( P->X );
1430 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &P->Z, 1 ) );
1431
1432 cleanup:
1433 return( ret );
1434 }
1435
1436 /*
1437 * Randomize projective x/z coordinates:
1438 * (X, Z) -> (l X, l Z) for random l
1439 * This is sort of the reverse operation of ecp_normalize_mxz().
1440 *
1441 * This countermeasure was first suggested in [2].
1442 * Cost: 2M
1443 */
1444 static int ecp_randomize_mxz( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P,
1445 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
1446 {
1447 int ret;
1448 mbedtls_mpi l;
1449 size_t p_size = ( grp->pbits + 7 ) / 8;
1450 int count = 0;
1451
1452 mbedtls_mpi_init( &l );
1453
1454 /* Generate l such that 1 < l < p */
1455 do
1456 {
1457 mbedtls_mpi_fill_random( &l, p_size, f_rng, p_rng );
1458
1459 while( mbedtls_mpi_cmp_mpi( &l, &grp->P ) >= 0 )
1460 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &l, 1 ) );
1461
1462 if( count++ > 10 )
1463 return( MBEDTLS_ERR_ECP_RANDOM_FAILED );
1464 }
1465 while( mbedtls_mpi_cmp_int( &l, 1 ) <= 0 );
1466
1467 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &P->X, &P->X, &l ) ); MOD_MUL( P->X );
1468 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &P->Z, &P->Z, &l ) ); MOD_MUL( P->Z );
1469
1470 cleanup:
1471 mbedtls_mpi_free( &l );
1472
1473 return( ret );
1474 }
1475
1476 /*
1477 * Double-and-add: R = 2P, S = P + Q, with d = X(P - Q),
1478 * for Montgomery curves in x/z coordinates.
1479 *
1480 * http://www.hyperelliptic.org/EFD/g1p/auto-code/montgom/xz/ladder/mladd-1987-m.op3
1481 * with
1482 * d = X1
1483 * P = (X2, Z2)
1484 * Q = (X3, Z3)
1485 * R = (X4, Z4)
1486 * S = (X5, Z5)
1487 * and eliminating temporary variables tO, ..., t4.
1488 *
1489 * Cost: 5M + 4S
1490 */
1491 static int ecp_double_add_mxz( const mbedtls_ecp_group *grp,
1492 mbedtls_ecp_point *R, mbedtls_ecp_point *S,
1493 const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q,
1494 const mbedtls_mpi *d )
1495 {
1496 int ret;
1497 mbedtls_mpi A, AA, B, BB, E, C, D, DA, CB;
1498
1499 mbedtls_mpi_init( &A ); mbedtls_mpi_init( &AA ); mbedtls_mpi_init( &B );
1500 mbedtls_mpi_init( &BB ); mbedtls_mpi_init( &E ); mbedtls_mpi_init( &C );
1501 mbedtls_mpi_init( &D ); mbedtls_mpi_init( &DA ); mbedtls_mpi_init( &CB );
1502
1503 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &A, &P->X, &P->Z ) ); MOD_ADD( A );
1504 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &AA, &A, &A ) ); MOD_MUL( AA );
1505 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &B, &P->X, &P->Z ) ); MOD_SUB( B );
1506 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &BB, &B, &B ) ); MOD_MUL( BB );
1507 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &E, &AA, &BB ) ); MOD_SUB( E );
1508 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &C, &Q->X, &Q->Z ) ); MOD_ADD( C );
1509 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &D, &Q->X, &Q->Z ) ); MOD_SUB( D );
1510 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &DA, &D, &A ) ); MOD_MUL( DA );
1511 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &CB, &C, &B ) ); MOD_MUL( CB );
1512 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &S->X, &DA, &CB ) ); MOD_MUL( S->X );
1513 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S->X, &S->X, &S->X ) ); MOD_MUL( S->X );
1514 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &S->Z, &DA, &CB ) ); MOD_SUB( S->Z );
1515 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S->Z, &S->Z, &S->Z ) ); MOD_MUL( S->Z );
1516 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S->Z, d, &S->Z ) ); MOD_MUL( S->Z );
1517 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &R->X, &AA, &BB ) ); MOD_MUL( R->X );
1518 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &R->Z, &grp->A, &E ) ); MOD_MUL( R->Z );
1519 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &R->Z, &BB, &R->Z ) ); MOD_ADD( R->Z );
1520 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &R->Z, &E, &R->Z ) ); MOD_MUL( R->Z );
1521
1522 cleanup:
1523 mbedtls_mpi_free( &A ); mbedtls_mpi_free( &AA ); mbedtls_mpi_free( &B );
1524 mbedtls_mpi_free( &BB ); mbedtls_mpi_free( &E ); mbedtls_mpi_free( &C );
1525 mbedtls_mpi_free( &D ); mbedtls_mpi_free( &DA ); mbedtls_mpi_free( &CB );
1526
1527 return( ret );
1528 }
1529
1530 /*
1531 * Multiplication with Montgomery ladder in x/z coordinates,
1532 * for curves in Montgomery form
1533 */
1534 static int ecp_mul_mxz( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
1535 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
1536 int (*f_rng)(void *, unsigned char *, size_t),
1537 void *p_rng )
1538 {
1539 int ret;
1540 size_t i;
1541 unsigned char b;
1542 mbedtls_ecp_point RP;
1543 mbedtls_mpi PX;
1544
1545 mbedtls_ecp_point_init( &RP ); mbedtls_mpi_init( &PX );
1546
1547 /* Save PX and read from P before writing to R, in case P == R */
1548 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &PX, &P->X ) );
1549 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( &RP, P ) );
1550
1551 /* Set R to zero in modified x/z coordinates */
1552 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->X, 1 ) );
1553 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->Z, 0 ) );
1554 mbedtls_mpi_free( &R->Y );
1555
1556 /* RP.X might be sligtly larger than P, so reduce it */
1557 MOD_ADD( RP.X );
1558
1559 /* Randomize coordinates of the starting point */
1560 if( f_rng != NULL )
1561 MBEDTLS_MPI_CHK( ecp_randomize_mxz( grp, &RP, f_rng, p_rng ) );
1562
1563 /* Loop invariant: R = result so far, RP = R + P */
1564 i = mbedtls_mpi_bitlen( m ); /* one past the (zero-based) most significant bit */
1565 while( i-- > 0 )
1566 {
1567 b = mbedtls_mpi_get_bit( m, i );
1568 /*
1569 * if (b) R = 2R + P else R = 2R,
1570 * which is:
1571 * if (b) double_add( RP, R, RP, R )
1572 * else double_add( R, RP, R, RP )
1573 * but using safe conditional swaps to avoid leaks
1574 */
1575 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->X, &RP.X, b ) );
1576 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->Z, &RP.Z, b ) );
1577 MBEDTLS_MPI_CHK( ecp_double_add_mxz( grp, R, &RP, R, &RP, &PX ) );
1578 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->X, &RP.X, b ) );
1579 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->Z, &RP.Z, b ) );
1580 }
1581
1582 MBEDTLS_MPI_CHK( ecp_normalize_mxz( grp, R ) );
1583
1584 cleanup:
1585 mbedtls_ecp_point_free( &RP ); mbedtls_mpi_free( &PX );
1586
1587 return( ret );
1588 }
1589
1590 #endif /* ECP_MONTGOMERY */
1591
1592 /*
1593 * Multiplication R = m * P
1594 */
1595 int mbedtls_ecp_mul( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
1596 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
1597 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
1598 {
1599 int ret;
1600
1601 /* Common sanity checks */
1602 if( mbedtls_mpi_cmp_int( &P->Z, 1 ) != 0 )
1603 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1604
1605 if( ( ret = mbedtls_ecp_check_privkey( grp, m ) ) != 0 ||
1606 ( ret = mbedtls_ecp_check_pubkey( grp, P ) ) != 0 )
1607 return( ret );
1608
1609 #if defined(ECP_MONTGOMERY)
1610 if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
1611 return( ecp_mul_mxz( grp, R, m, P, f_rng, p_rng ) );
1612 #endif
1613 #if defined(ECP_SHORTWEIERSTRASS)
1614 if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS )
1615 return( ecp_mul_comb( grp, R, m, P, f_rng, p_rng ) );
1616 #endif
1617 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1618 }
1619
1620 #if defined(ECP_SHORTWEIERSTRASS)
1621 /*
1622 * Check that an affine point is valid as a public key,
1623 * short weierstrass curves (SEC1 3.2.3.1)
1624 */
1625 static int ecp_check_pubkey_sw( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt )
1626 {
1627 int ret;
1628 mbedtls_mpi YY, RHS;
1629
1630 /* pt coordinates must be normalized for our checks */
1631 if( mbedtls_mpi_cmp_int( &pt->X, 0 ) < 0 ||
1632 mbedtls_mpi_cmp_int( &pt->Y, 0 ) < 0 ||
1633 mbedtls_mpi_cmp_mpi( &pt->X, &grp->P ) >= 0 ||
1634 mbedtls_mpi_cmp_mpi( &pt->Y, &grp->P ) >= 0 )
1635 return( MBEDTLS_ERR_ECP_INVALID_KEY );
1636
1637 mbedtls_mpi_init( &YY ); mbedtls_mpi_init( &RHS );
1638
1639 /*
1640 * YY = Y^2
1641 * RHS = X (X^2 + A) + B = X^3 + A X + B
1642 */
1643 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &YY, &pt->Y, &pt->Y ) ); MOD_MUL( YY );
1644 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &RHS, &pt->X, &pt->X ) ); MOD_MUL( RHS );
1645
1646 /* Special case for A = -3 */
1647 if( grp->A.p == NULL )
1648 {
1649 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &RHS, &RHS, 3 ) ); MOD_SUB( RHS );
1650 }
1651 else
1652 {
1653 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &RHS, &RHS, &grp->A ) ); MOD_ADD( RHS );
1654 }
1655
1656 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &RHS, &RHS, &pt->X ) ); MOD_MUL( RHS );
1657 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &RHS, &RHS, &grp->B ) ); MOD_ADD( RHS );
1658
1659 if( mbedtls_mpi_cmp_mpi( &YY, &RHS ) != 0 )
1660 ret = MBEDTLS_ERR_ECP_INVALID_KEY;
1661
1662 cleanup:
1663
1664 mbedtls_mpi_free( &YY ); mbedtls_mpi_free( &RHS );
1665
1666 return( ret );
1667 }
1668 #endif /* ECP_SHORTWEIERSTRASS */
1669
1670 /*
1671 * Linear combination
1672 */
1673 int mbedtls_ecp_muladd( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
1674 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
1675 const mbedtls_mpi *n, const mbedtls_ecp_point *Q )
1676 {
1677 int ret;
1678 mbedtls_ecp_point mP;
1679
1680 if( ecp_get_type( grp ) != ECP_TYPE_SHORT_WEIERSTRASS )
1681 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
1682
1683 mbedtls_ecp_point_init( &mP );
1684
1685 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( grp, &mP, m, P, NULL, NULL ) );
1686 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( grp, R, n, Q, NULL, NULL ) );
1687 MBEDTLS_MPI_CHK( ecp_add_mixed( grp, R, &mP, R ) );
1688 MBEDTLS_MPI_CHK( ecp_normalize_jac( grp, R ) );
1689
1690 cleanup:
1691 mbedtls_ecp_point_free( &mP );
1692
1693 return( ret );
1694 }
1695
1696
1697 #if defined(ECP_MONTGOMERY)
1698 /*
1699 * Check validity of a public key for Montgomery curves with x-only schemes
1700 */
1701 static int ecp_check_pubkey_mx( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt )
1702 {
1703 /* [Curve25519 p. 5] Just check X is the correct number of bytes */
1704 if( mbedtls_mpi_size( &pt->X ) > ( grp->nbits + 7 ) / 8 )
1705 return( MBEDTLS_ERR_ECP_INVALID_KEY );
1706
1707 return( 0 );
1708 }
1709 #endif /* ECP_MONTGOMERY */
1710
1711 /*
1712 * Check that a point is valid as a public key
1713 */
1714 int mbedtls_ecp_check_pubkey( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt )
1715 {
1716 /* Must use affine coordinates */
1717 if( mbedtls_mpi_cmp_int( &pt->Z, 1 ) != 0 )
1718 return( MBEDTLS_ERR_ECP_INVALID_KEY );
1719
1720 #if defined(ECP_MONTGOMERY)
1721 if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
1722 return( ecp_check_pubkey_mx( grp, pt ) );
1723 #endif
1724 #if defined(ECP_SHORTWEIERSTRASS)
1725 if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS )
1726 return( ecp_check_pubkey_sw( grp, pt ) );
1727 #endif
1728 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1729 }
1730
1731 /*
1732 * Check that an mbedtls_mpi is valid as a private key
1733 */
1734 int mbedtls_ecp_check_privkey( const mbedtls_ecp_group *grp, const mbedtls_mpi *d )
1735 {
1736 #if defined(ECP_MONTGOMERY)
1737 if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
1738 {
1739 /* see [Curve25519] page 5 */
1740 if( mbedtls_mpi_get_bit( d, 0 ) != 0 ||
1741 mbedtls_mpi_get_bit( d, 1 ) != 0 ||
1742 mbedtls_mpi_get_bit( d, 2 ) != 0 ||
1743 mbedtls_mpi_bitlen( d ) - 1 != grp->nbits ) /* mbedtls_mpi_bitlen is one-based! */
1744 return( MBEDTLS_ERR_ECP_INVALID_KEY );
1745 else
1746 return( 0 );
1747 }
1748 #endif /* ECP_MONTGOMERY */
1749 #if defined(ECP_SHORTWEIERSTRASS)
1750 if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS )
1751 {
1752 /* see SEC1 3.2 */
1753 if( mbedtls_mpi_cmp_int( d, 1 ) < 0 ||
1754 mbedtls_mpi_cmp_mpi( d, &grp->N ) >= 0 )
1755 return( MBEDTLS_ERR_ECP_INVALID_KEY );
1756 else
1757 return( 0 );
1758 }
1759 #endif /* ECP_SHORTWEIERSTRASS */
1760
1761 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1762 }
1763
1764 /*
1765 * Generate a keypair
1766 */
1767 int mbedtls_ecp_gen_keypair( mbedtls_ecp_group *grp, mbedtls_mpi *d, mbedtls_ecp_point *Q,
1768 int (*f_rng)(void *, unsigned char *, size_t),
1769 void *p_rng )
1770 {
1771 int ret;
1772 size_t n_size = ( grp->nbits + 7 ) / 8;
1773
1774 #if defined(ECP_MONTGOMERY)
1775 if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
1776 {
1777 /* [M225] page 5 */
1778 size_t b;
1779
1780 MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( d, n_size, f_rng, p_rng ) );
1781
1782 /* Make sure the most significant bit is nbits */
1783 b = mbedtls_mpi_bitlen( d ) - 1; /* mbedtls_mpi_bitlen is one-based */
1784 if( b > grp->nbits )
1785 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( d, b - grp->nbits ) );
1786 else
1787 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, grp->nbits, 1 ) );
1788
1789 /* Make sure the last three bits are unset */
1790 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 0, 0 ) );
1791 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 1, 0 ) );
1792 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 2, 0 ) );
1793 }
1794 else
1795 #endif /* ECP_MONTGOMERY */
1796 #if defined(ECP_SHORTWEIERSTRASS)
1797 if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS )
1798 {
1799 /* SEC1 3.2.1: Generate d such that 1 <= n < N */
1800 int count = 0;
1801 unsigned char rnd[MBEDTLS_ECP_MAX_BYTES];
1802
1803 /*
1804 * Match the procedure given in RFC 6979 (deterministic ECDSA):
1805 * - use the same byte ordering;
1806 * - keep the leftmost nbits bits of the generated octet string;
1807 * - try until result is in the desired range.
1808 * This also avoids any biais, which is especially important for ECDSA.
1809 */
1810 do
1811 {
1812 MBEDTLS_MPI_CHK( f_rng( p_rng, rnd, n_size ) );
1813 MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( d, rnd, n_size ) );
1814 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( d, 8 * n_size - grp->nbits ) );
1815
1816 /*
1817 * Each try has at worst a probability 1/2 of failing (the msb has
1818 * a probability 1/2 of being 0, and then the result will be < N),
1819 * so after 30 tries failure probability is a most 2**(-30).
1820 *
1821 * For most curves, 1 try is enough with overwhelming probability,
1822 * since N starts with a lot of 1s in binary, but some curves
1823 * such as secp224k1 are actually very close to the worst case.
1824 */
1825 if( ++count > 30 )
1826 return( MBEDTLS_ERR_ECP_RANDOM_FAILED );
1827 }
1828 while( mbedtls_mpi_cmp_int( d, 1 ) < 0 ||
1829 mbedtls_mpi_cmp_mpi( d, &grp->N ) >= 0 );
1830 }
1831 else
1832 #endif /* ECP_SHORTWEIERSTRASS */
1833 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1834
1835 cleanup:
1836 if( ret != 0 )
1837 return( ret );
1838
1839 return( mbedtls_ecp_mul( grp, Q, d, &grp->G, f_rng, p_rng ) );
1840 }
1841
1842 /*
1843 * Generate a keypair, prettier wrapper
1844 */
1845 int mbedtls_ecp_gen_key( mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key,
1846 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
1847 {
1848 int ret;
1849
1850 if( ( ret = mbedtls_ecp_group_load( &key->grp, grp_id ) ) != 0 )
1851 return( ret );
1852
1853 return( mbedtls_ecp_gen_keypair( &key->grp, &key->d, &key->Q, f_rng, p_rng ) );
1854 }
1855
1856 /*
1857 * Check a public-private key pair
1858 */
1859 int mbedtls_ecp_check_pub_priv( const mbedtls_ecp_keypair *pub, const mbedtls_ecp_keypair *prv )
1860 {
1861 int ret;
1862 mbedtls_ecp_point Q;
1863 mbedtls_ecp_group grp;
1864
1865 if( pub->grp.id == MBEDTLS_ECP_DP_NONE ||
1866 pub->grp.id != prv->grp.id ||
1867 mbedtls_mpi_cmp_mpi( &pub->Q.X, &prv->Q.X ) ||
1868 mbedtls_mpi_cmp_mpi( &pub->Q.Y, &prv->Q.Y ) ||
1869 mbedtls_mpi_cmp_mpi( &pub->Q.Z, &prv->Q.Z ) )
1870 {
1871 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
1872 }
1873
1874 mbedtls_ecp_point_init( &Q );
1875 mbedtls_ecp_group_init( &grp );
1876
1877 /* mbedtls_ecp_mul() needs a non-const group... */
1878 mbedtls_ecp_group_copy( &grp, &prv->grp );
1879
1880 /* Also checks d is valid */
1881 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &Q, &prv->d, &prv->grp.G, NULL, NULL ) );
1882
1883 if( mbedtls_mpi_cmp_mpi( &Q.X, &prv->Q.X ) ||
1884 mbedtls_mpi_cmp_mpi( &Q.Y, &prv->Q.Y ) ||
1885 mbedtls_mpi_cmp_mpi( &Q.Z, &prv->Q.Z ) )
1886 {
1887 ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
1888 goto cleanup;
1889 }
1890
1891 cleanup:
1892 mbedtls_ecp_point_free( &Q );
1893 mbedtls_ecp_group_free( &grp );
1894
1895 return( ret );
1896 }
1897
1898 #if defined(MBEDTLS_SELF_TEST)
1899
1900 /*
1901 * Checkup routine
1902 */
1903 int mbedtls_ecp_self_test( int verbose )
1904 {
1905 int ret;
1906 size_t i;
1907 mbedtls_ecp_group grp;
1908 mbedtls_ecp_point R, P;
1909 mbedtls_mpi m;
1910 unsigned long add_c_prev, dbl_c_prev, mul_c_prev;
1911 /* exponents especially adapted for secp192r1 */
1912 const char *exponents[] =
1913 {
1914 "000000000000000000000000000000000000000000000001", /* one */
1915 "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22830", /* N - 1 */
1916 "5EA6F389A38B8BC81E767753B15AA5569E1782E30ABE7D25", /* random */
1917 "400000000000000000000000000000000000000000000000", /* one and zeros */
1918 "7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", /* all ones */
1919 "555555555555555555555555555555555555555555555555", /* 101010... */
1920 };
1921
1922 mbedtls_ecp_group_init( &grp );
1923 mbedtls_ecp_point_init( &R );
1924 mbedtls_ecp_point_init( &P );
1925 mbedtls_mpi_init( &m );
1926
1927 /* Use secp192r1 if available, or any available curve */
1928 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
1929 MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, MBEDTLS_ECP_DP_SECP192R1 ) );
1930 #else
1931 MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, mbedtls_ecp_curve_list()->grp_id ) );
1932 #endif
1933
1934 if( verbose != 0 )
1935 mbedtls_printf( " ECP test #1 (constant op_count, base point G): " );
1936
1937 /* Do a dummy multiplication first to trigger precomputation */
1938 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &m, 2 ) );
1939 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &P, &m, &grp.G, NULL, NULL ) );
1940
1941 add_count = 0;
1942 dbl_count = 0;
1943 mul_count = 0;
1944 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[0] ) );
1945 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &grp.G, NULL, NULL ) );
1946
1947 for( i = 1; i < sizeof( exponents ) / sizeof( exponents[0] ); i++ )
1948 {
1949 add_c_prev = add_count;
1950 dbl_c_prev = dbl_count;
1951 mul_c_prev = mul_count;
1952 add_count = 0;
1953 dbl_count = 0;
1954 mul_count = 0;
1955
1956 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[i] ) );
1957 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &grp.G, NULL, NULL ) );
1958
1959 if( add_count != add_c_prev ||
1960 dbl_count != dbl_c_prev ||
1961 mul_count != mul_c_prev )
1962 {
1963 if( verbose != 0 )
1964 mbedtls_printf( "failed (%u)\n", (unsigned int) i );
1965
1966 ret = 1;
1967 goto cleanup;
1968 }
1969 }
1970
1971 if( verbose != 0 )
1972 mbedtls_printf( "passed\n" );
1973
1974 if( verbose != 0 )
1975 mbedtls_printf( " ECP test #2 (constant op_count, other point): " );
1976 /* We computed P = 2G last time, use it */
1977
1978 add_count = 0;
1979 dbl_count = 0;
1980 mul_count = 0;
1981 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[0] ) );
1982 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &P, NULL, NULL ) );
1983
1984 for( i = 1; i < sizeof( exponents ) / sizeof( exponents[0] ); i++ )
1985 {
1986 add_c_prev = add_count;
1987 dbl_c_prev = dbl_count;
1988 mul_c_prev = mul_count;
1989 add_count = 0;
1990 dbl_count = 0;
1991 mul_count = 0;
1992
1993 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[i] ) );
1994 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &P, NULL, NULL ) );
1995
1996 if( add_count != add_c_prev ||
1997 dbl_count != dbl_c_prev ||
1998 mul_count != mul_c_prev )
1999 {
2000 if( verbose != 0 )
2001 mbedtls_printf( "failed (%u)\n", (unsigned int) i );
2002
2003 ret = 1;
2004 goto cleanup;
2005 }
2006 }
2007
2008 if( verbose != 0 )
2009 mbedtls_printf( "passed\n" );
2010
2011 cleanup:
2012
2013 if( ret < 0 && verbose != 0 )
2014 mbedtls_printf( "Unexpected error, return code = %08X\n", ret );
2015
2016 mbedtls_ecp_group_free( &grp );
2017 mbedtls_ecp_point_free( &R );
2018 mbedtls_ecp_point_free( &P );
2019 mbedtls_mpi_free( &m );
2020
2021 if( verbose != 0 )
2022 mbedtls_printf( "\n" );
2023
2024 return( ret );
2025 }
2026
2027 #endif /* MBEDTLS_SELF_TEST */
2028
2029 #endif /* MBEDTLS_ECP_C */
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