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