xref: /reactos/dll/3rdparty/mbedtls/ecdsa.c (revision f7cab5a1)
1 /*
2  *  Elliptic curve DSA
3  *
4  *  Copyright (C) 2006-2015, ARM Limited, All Rights Reserved
5  *  SPDX-License-Identifier: GPL-2.0
6  *
7  *  This program is free software; you can redistribute it and/or modify
8  *  it under the terms of the GNU General Public License as published by
9  *  the Free Software Foundation; either version 2 of the License, or
10  *  (at your option) any later version.
11  *
12  *  This program is distributed in the hope that it will be useful,
13  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
14  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
15  *  GNU General Public License for more details.
16  *
17  *  You should have received a copy of the GNU General Public License along
18  *  with this program; if not, write to the Free Software Foundation, Inc.,
19  *  51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
20  *
21  *  This file is part of mbed TLS (https://tls.mbed.org)
22  */
23 
24 /*
25  * References:
26  *
27  * SEC1 http://www.secg.org/index.php?action=secg,docs_secg
28  */
29 
30 #if !defined(MBEDTLS_CONFIG_FILE)
31 #include "mbedtls/config.h"
32 #else
33 #include MBEDTLS_CONFIG_FILE
34 #endif
35 
36 #if defined(MBEDTLS_ECDSA_C)
37 
38 #include "mbedtls/ecdsa.h"
39 #include "mbedtls/asn1write.h"
40 
41 #include <string.h>
42 
43 #if defined(MBEDTLS_ECDSA_DETERMINISTIC)
44 #include "mbedtls/hmac_drbg.h"
45 #endif
46 
47 /*
48  * Derive a suitable integer for group grp from a buffer of length len
49  * SEC1 4.1.3 step 5 aka SEC1 4.1.4 step 3
50  */
51 static int derive_mpi( const mbedtls_ecp_group *grp, mbedtls_mpi *x,
52                        const unsigned char *buf, size_t blen )
53 {
54     int ret;
55     size_t n_size = ( grp->nbits + 7 ) / 8;
56     size_t use_size = blen > n_size ? n_size : blen;
57 
58     MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( x, buf, use_size ) );
59     if( use_size * 8 > grp->nbits )
60         MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( x, use_size * 8 - grp->nbits ) );
61 
62     /* While at it, reduce modulo N */
63     if( mbedtls_mpi_cmp_mpi( x, &grp->N ) >= 0 )
64         MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( x, x, &grp->N ) );
65 
66 cleanup:
67     return( ret );
68 }
69 
70 #if !defined(MBEDTLS_ECDSA_SIGN_ALT)
71 /*
72  * Compute ECDSA signature of a hashed message (SEC1 4.1.3)
73  * Obviously, compared to SEC1 4.1.3, we skip step 4 (hash message)
74  */
75 static int ecdsa_sign_internal( mbedtls_ecp_group *grp, mbedtls_mpi *r,
76                                 mbedtls_mpi *s, const mbedtls_mpi *d,
77                                 const unsigned char *buf, size_t blen,
78                                 int (*f_rng)(void *, unsigned char *, size_t),
79                                 void *p_rng,
80                                 int (*f_rng_blind)(void *, unsigned char *,
81                                                    size_t),
82                                 void *p_rng_blind )
83 {
84     int ret, key_tries, sign_tries, blind_tries;
85     mbedtls_ecp_point R;
86     mbedtls_mpi k, e, t;
87 
88     /* Fail cleanly on curves such as Curve25519 that can't be used for ECDSA */
89     if( grp->N.p == NULL )
90         return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
91 
92     /* Make sure d is in range 1..n-1 */
93     if( mbedtls_mpi_cmp_int( d, 1 ) < 0 || mbedtls_mpi_cmp_mpi( d, &grp->N ) >= 0 )
94         return( MBEDTLS_ERR_ECP_INVALID_KEY );
95 
96     mbedtls_ecp_point_init( &R );
97     mbedtls_mpi_init( &k ); mbedtls_mpi_init( &e ); mbedtls_mpi_init( &t );
98 
99     sign_tries = 0;
100     do
101     {
102         /*
103          * Steps 1-3: generate a suitable ephemeral keypair
104          * and set r = xR mod n
105          */
106         key_tries = 0;
107         do
108         {
109             MBEDTLS_MPI_CHK( mbedtls_ecp_gen_privkey( grp, &k, f_rng, p_rng ) );
110 
111             MBEDTLS_MPI_CHK( mbedtls_ecp_mul( grp, &R, &k, &grp->G,
112                                               f_rng_blind, p_rng_blind ) );
113             MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( r, &R.X, &grp->N ) );
114 
115             if( key_tries++ > 10 )
116             {
117                 ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
118                 goto cleanup;
119             }
120         }
121         while( mbedtls_mpi_cmp_int( r, 0 ) == 0 );
122 
123         /*
124          * Step 5: derive MPI from hashed message
125          */
126         MBEDTLS_MPI_CHK( derive_mpi( grp, &e, buf, blen ) );
127 
128         /*
129          * Generate a random value to blind inv_mod in next step,
130          * avoiding a potential timing leak.
131          *
132          * This loop does the same job as mbedtls_ecp_gen_privkey() and it is
133          * replaced by a call to it in the mainline. This change is not
134          * necessary to backport the fix separating the blinding and ephemeral
135          * key generating RNGs, therefore the original code is kept.
136          */
137         blind_tries = 0;
138         do
139         {
140             size_t n_size = ( grp->nbits + 7 ) / 8;
141             MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &t, n_size, f_rng_blind,
142                                                       p_rng_blind ) );
143             MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &t, 8 * n_size - grp->nbits ) );
144 
145             if( ++blind_tries > 30 )
146                 return( MBEDTLS_ERR_ECP_RANDOM_FAILED );
147         }
148         while( mbedtls_mpi_cmp_int( &t, 1 ) < 0 ||
149                mbedtls_mpi_cmp_mpi( &t, &grp->N ) >= 0 );
150 
151         /*
152          * Step 6: compute s = (e + r * d) / k = t (e + rd) / (kt) mod n
153          */
154         MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( s, r, d ) );
155         MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &e, &e, s ) );
156         MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &e, &e, &t ) );
157         MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &k, &k, &t ) );
158         MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &k, &k, &grp->N ) );
159         MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( s, &k, &grp->N ) );
160         MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( s, s, &e ) );
161         MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( s, s, &grp->N ) );
162 
163         if( sign_tries++ > 10 )
164         {
165             ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
166             goto cleanup;
167         }
168     }
169     while( mbedtls_mpi_cmp_int( s, 0 ) == 0 );
170 
171 cleanup:
172     mbedtls_ecp_point_free( &R );
173     mbedtls_mpi_free( &k ); mbedtls_mpi_free( &e ); mbedtls_mpi_free( &t );
174 
175     return( ret );
176 }
177 
178 int mbedtls_ecdsa_sign( mbedtls_ecp_group *grp, mbedtls_mpi *r, mbedtls_mpi *s,
179                         const mbedtls_mpi *d, const unsigned char *buf,
180                         size_t blen,
181                         int (*f_rng)(void *, unsigned char *, size_t),
182                         void *p_rng )
183 {
184     /* Use the same RNG for both blinding and ephemeral key generation */
185     return( ecdsa_sign_internal( grp, r, s, d, buf, blen, f_rng, p_rng,
186                                  f_rng, p_rng ) );
187 }
188 #endif /* MBEDTLS_ECDSA_SIGN_ALT */
189 
190 #if defined(MBEDTLS_ECDSA_DETERMINISTIC)
191 static int ecdsa_sign_det_internal( mbedtls_ecp_group *grp, mbedtls_mpi *r,
192                                     mbedtls_mpi *s, const mbedtls_mpi *d,
193                                     const unsigned char *buf, size_t blen,
194                                     mbedtls_md_type_t md_alg,
195                                     int (*f_rng_blind)(void *, unsigned char *,
196                                                        size_t),
197                                     void *p_rng_blind )
198 {
199     int ret;
200     mbedtls_hmac_drbg_context rng_ctx;
201     unsigned char data[2 * MBEDTLS_ECP_MAX_BYTES];
202     size_t grp_len = ( grp->nbits + 7 ) / 8;
203     const mbedtls_md_info_t *md_info;
204     mbedtls_mpi h;
205     /* Variables for deterministic blinding fallback */
206     const char* blind_label = "BLINDING CONTEXT";
207     mbedtls_hmac_drbg_context rng_ctx_blind;
208 
209     if( ( md_info = mbedtls_md_info_from_type( md_alg ) ) == NULL )
210         return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
211 
212     mbedtls_mpi_init( &h );
213     mbedtls_hmac_drbg_init( &rng_ctx );
214     mbedtls_hmac_drbg_init( &rng_ctx_blind );
215 
216     /* Use private key and message hash (reduced) to initialize HMAC_DRBG */
217     MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( d, data, grp_len ) );
218     MBEDTLS_MPI_CHK( derive_mpi( grp, &h, buf, blen ) );
219     MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &h, data + grp_len, grp_len ) );
220     mbedtls_hmac_drbg_seed_buf( &rng_ctx, md_info, data, 2 * grp_len );
221 
222     if( f_rng_blind != NULL )
223         ret = ecdsa_sign_internal( grp, r, s, d, buf, blen,
224                                    mbedtls_hmac_drbg_random, &rng_ctx,
225                                    f_rng_blind, p_rng_blind );
226     else
227     {
228         /*
229          * To avoid reusing rng_ctx and risking incorrect behavior we seed a
230          * second HMAC-DRBG with the same seed. We also apply a label to avoid
231          * reusing the bits of the ephemeral key for blinding and eliminate the
232          * risk that they leak this way.
233          */
234 
235         mbedtls_hmac_drbg_seed_buf( &rng_ctx_blind, md_info,
236                                     data, 2 * grp_len );
237         ret = mbedtls_hmac_drbg_update_ret( &rng_ctx_blind,
238                                             (const unsigned char*) blind_label,
239                                             strlen( blind_label ) );
240         if( ret != 0 )
241             goto cleanup;
242 
243         /*
244          * Since the output of the RNGs is always the same for the same key and
245          * message, this limits the efficiency of blinding and leaks information
246          * through side channels. After mbedtls_ecdsa_sign_det() is removed NULL
247          * won't be a valid value for f_rng_blind anymore. Therefore it should
248          * be checked by the caller and this branch and check can be removed.
249          */
250         ret = ecdsa_sign_internal( grp, r, s, d, buf, blen,
251                                    mbedtls_hmac_drbg_random, &rng_ctx,
252                                    mbedtls_hmac_drbg_random, &rng_ctx_blind );
253 
254     }
255 
256 cleanup:
257     mbedtls_hmac_drbg_free( &rng_ctx );
258     mbedtls_hmac_drbg_free( &rng_ctx_blind );
259     mbedtls_mpi_free( &h );
260 
261     return( ret );
262 }
263 
264 /*
265  * Deterministic signature wrappers
266  */
267 int mbedtls_ecdsa_sign_det( mbedtls_ecp_group *grp, mbedtls_mpi *r,
268                             mbedtls_mpi *s, const mbedtls_mpi *d,
269                             const unsigned char *buf, size_t blen,
270                             mbedtls_md_type_t md_alg )
271 {
272     return( ecdsa_sign_det_internal( grp, r, s, d, buf, blen, md_alg,
273                                      NULL, NULL ) );
274 }
275 
276 int mbedtls_ecdsa_sign_det_ext( mbedtls_ecp_group *grp, mbedtls_mpi *r,
277                                 mbedtls_mpi *s, const mbedtls_mpi *d,
278                                 const unsigned char *buf, size_t blen,
279                                 mbedtls_md_type_t md_alg,
280                                 int (*f_rng_blind)(void *, unsigned char *,
281                                                    size_t),
282                                 void *p_rng_blind )
283 {
284     return( ecdsa_sign_det_internal( grp, r, s, d, buf, blen, md_alg,
285                                      f_rng_blind, p_rng_blind ) );
286 }
287 #endif /* MBEDTLS_ECDSA_DETERMINISTIC */
288 
289 #if !defined(MBEDTLS_ECDSA_VERIFY_ALT)
290 /*
291  * Verify ECDSA signature of hashed message (SEC1 4.1.4)
292  * Obviously, compared to SEC1 4.1.3, we skip step 2 (hash message)
293  */
294 int mbedtls_ecdsa_verify( mbedtls_ecp_group *grp,
295                   const unsigned char *buf, size_t blen,
296                   const mbedtls_ecp_point *Q, const mbedtls_mpi *r, const mbedtls_mpi *s)
297 {
298     int ret;
299     mbedtls_mpi e, s_inv, u1, u2;
300     mbedtls_ecp_point R;
301 
302     mbedtls_ecp_point_init( &R );
303     mbedtls_mpi_init( &e ); mbedtls_mpi_init( &s_inv ); mbedtls_mpi_init( &u1 ); mbedtls_mpi_init( &u2 );
304 
305     /* Fail cleanly on curves such as Curve25519 that can't be used for ECDSA */
306     if( grp->N.p == NULL )
307         return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
308 
309     /*
310      * Step 1: make sure r and s are in range 1..n-1
311      */
312     if( mbedtls_mpi_cmp_int( r, 1 ) < 0 || mbedtls_mpi_cmp_mpi( r, &grp->N ) >= 0 ||
313         mbedtls_mpi_cmp_int( s, 1 ) < 0 || mbedtls_mpi_cmp_mpi( s, &grp->N ) >= 0 )
314     {
315         ret = MBEDTLS_ERR_ECP_VERIFY_FAILED;
316         goto cleanup;
317     }
318 
319     /*
320      * Additional precaution: make sure Q is valid
321      */
322     MBEDTLS_MPI_CHK( mbedtls_ecp_check_pubkey( grp, Q ) );
323 
324     /*
325      * Step 3: derive MPI from hashed message
326      */
327     MBEDTLS_MPI_CHK( derive_mpi( grp, &e, buf, blen ) );
328 
329     /*
330      * Step 4: u1 = e / s mod n, u2 = r / s mod n
331      */
332     MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &s_inv, s, &grp->N ) );
333 
334     MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &u1, &e, &s_inv ) );
335     MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &u1, &u1, &grp->N ) );
336 
337     MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &u2, r, &s_inv ) );
338     MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &u2, &u2, &grp->N ) );
339 
340     /*
341      * Step 5: R = u1 G + u2 Q
342      *
343      * Since we're not using any secret data, no need to pass a RNG to
344      * mbedtls_ecp_mul() for countermesures.
345      */
346     MBEDTLS_MPI_CHK( mbedtls_ecp_muladd( grp, &R, &u1, &grp->G, &u2, Q ) );
347 
348     if( mbedtls_ecp_is_zero( &R ) )
349     {
350         ret = MBEDTLS_ERR_ECP_VERIFY_FAILED;
351         goto cleanup;
352     }
353 
354     /*
355      * Step 6: convert xR to an integer (no-op)
356      * Step 7: reduce xR mod n (gives v)
357      */
358     MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &R.X, &R.X, &grp->N ) );
359 
360     /*
361      * Step 8: check if v (that is, R.X) is equal to r
362      */
363     if( mbedtls_mpi_cmp_mpi( &R.X, r ) != 0 )
364     {
365         ret = MBEDTLS_ERR_ECP_VERIFY_FAILED;
366         goto cleanup;
367     }
368 
369 cleanup:
370     mbedtls_ecp_point_free( &R );
371     mbedtls_mpi_free( &e ); mbedtls_mpi_free( &s_inv ); mbedtls_mpi_free( &u1 ); mbedtls_mpi_free( &u2 );
372 
373     return( ret );
374 }
375 #endif /* MBEDTLS_ECDSA_VERIFY_ALT */
376 
377 /*
378  * Convert a signature (given by context) to ASN.1
379  */
380 static int ecdsa_signature_to_asn1( const mbedtls_mpi *r, const mbedtls_mpi *s,
381                                     unsigned char *sig, size_t *slen )
382 {
383     int ret;
384     unsigned char buf[MBEDTLS_ECDSA_MAX_LEN];
385     unsigned char *p = buf + sizeof( buf );
386     size_t len = 0;
387 
388     MBEDTLS_ASN1_CHK_ADD( len, mbedtls_asn1_write_mpi( &p, buf, s ) );
389     MBEDTLS_ASN1_CHK_ADD( len, mbedtls_asn1_write_mpi( &p, buf, r ) );
390 
391     MBEDTLS_ASN1_CHK_ADD( len, mbedtls_asn1_write_len( &p, buf, len ) );
392     MBEDTLS_ASN1_CHK_ADD( len, mbedtls_asn1_write_tag( &p, buf,
393                                        MBEDTLS_ASN1_CONSTRUCTED | MBEDTLS_ASN1_SEQUENCE ) );
394 
395     memcpy( sig, p, len );
396     *slen = len;
397 
398     return( 0 );
399 }
400 
401 /*
402  * Compute and write signature
403  */
404 int mbedtls_ecdsa_write_signature( mbedtls_ecdsa_context *ctx, mbedtls_md_type_t md_alg,
405                            const unsigned char *hash, size_t hlen,
406                            unsigned char *sig, size_t *slen,
407                            int (*f_rng)(void *, unsigned char *, size_t),
408                            void *p_rng )
409 {
410     int ret;
411     mbedtls_mpi r, s;
412 
413     mbedtls_mpi_init( &r );
414     mbedtls_mpi_init( &s );
415 
416 #if defined(MBEDTLS_ECDSA_DETERMINISTIC)
417     MBEDTLS_MPI_CHK( ecdsa_sign_det_internal( &ctx->grp, &r, &s, &ctx->d,
418                                               hash, hlen, md_alg,
419                                               f_rng, p_rng ) );
420 #else
421     (void) md_alg;
422 
423     MBEDTLS_MPI_CHK( mbedtls_ecdsa_sign( &ctx->grp, &r, &s, &ctx->d,
424                          hash, hlen, f_rng, p_rng ) );
425 #endif /* MBEDTLS_ECDSA_DETERMINISTIC */
426 
427     MBEDTLS_MPI_CHK( ecdsa_signature_to_asn1( &r, &s, sig, slen ) );
428 
429 cleanup:
430     mbedtls_mpi_free( &r );
431     mbedtls_mpi_free( &s );
432 
433     return( ret );
434 }
435 
436 #if ! defined(MBEDTLS_DEPRECATED_REMOVED) && \
437     defined(MBEDTLS_ECDSA_DETERMINISTIC)
438 int mbedtls_ecdsa_write_signature_det( mbedtls_ecdsa_context *ctx,
439                                const unsigned char *hash, size_t hlen,
440                                unsigned char *sig, size_t *slen,
441                                mbedtls_md_type_t md_alg )
442 {
443     return( mbedtls_ecdsa_write_signature( ctx, md_alg, hash, hlen, sig, slen,
444                                    NULL, NULL ) );
445 }
446 #endif
447 
448 /*
449  * Read and check signature
450  */
451 int mbedtls_ecdsa_read_signature( mbedtls_ecdsa_context *ctx,
452                           const unsigned char *hash, size_t hlen,
453                           const unsigned char *sig, size_t slen )
454 {
455     int ret;
456     unsigned char *p = (unsigned char *) sig;
457     const unsigned char *end = sig + slen;
458     size_t len;
459     mbedtls_mpi r, s;
460 
461     mbedtls_mpi_init( &r );
462     mbedtls_mpi_init( &s );
463 
464     if( ( ret = mbedtls_asn1_get_tag( &p, end, &len,
465                     MBEDTLS_ASN1_CONSTRUCTED | MBEDTLS_ASN1_SEQUENCE ) ) != 0 )
466     {
467         ret += MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
468         goto cleanup;
469     }
470 
471     if( p + len != end )
472     {
473         ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA +
474               MBEDTLS_ERR_ASN1_LENGTH_MISMATCH;
475         goto cleanup;
476     }
477 
478     if( ( ret = mbedtls_asn1_get_mpi( &p, end, &r ) ) != 0 ||
479         ( ret = mbedtls_asn1_get_mpi( &p, end, &s ) ) != 0 )
480     {
481         ret += MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
482         goto cleanup;
483     }
484 
485     if( ( ret = mbedtls_ecdsa_verify( &ctx->grp, hash, hlen,
486                               &ctx->Q, &r, &s ) ) != 0 )
487         goto cleanup;
488 
489     /* At this point we know that the buffer starts with a valid signature.
490      * Return 0 if the buffer just contains the signature, and a specific
491      * error code if the valid signature is followed by more data. */
492     if( p != end )
493         ret = MBEDTLS_ERR_ECP_SIG_LEN_MISMATCH;
494 
495 cleanup:
496     mbedtls_mpi_free( &r );
497     mbedtls_mpi_free( &s );
498 
499     return( ret );
500 }
501 
502 #if !defined(MBEDTLS_ECDSA_GENKEY_ALT)
503 /*
504  * Generate key pair
505  */
506 int mbedtls_ecdsa_genkey( mbedtls_ecdsa_context *ctx, mbedtls_ecp_group_id gid,
507                   int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
508 {
509     int ret = 0;
510     ret = mbedtls_ecp_group_load( &ctx->grp, gid );
511     if( ret != 0 )
512         return( ret );
513 
514    return( mbedtls_ecp_gen_keypair( &ctx->grp, &ctx->d,
515                                     &ctx->Q, f_rng, p_rng ) );
516 }
517 #endif /* MBEDTLS_ECDSA_GENKEY_ALT */
518 
519 /*
520  * Set context from an mbedtls_ecp_keypair
521  */
522 int mbedtls_ecdsa_from_keypair( mbedtls_ecdsa_context *ctx, const mbedtls_ecp_keypair *key )
523 {
524     int ret;
525 
526     if( ( ret = mbedtls_ecp_group_copy( &ctx->grp, &key->grp ) ) != 0 ||
527         ( ret = mbedtls_mpi_copy( &ctx->d, &key->d ) ) != 0 ||
528         ( ret = mbedtls_ecp_copy( &ctx->Q, &key->Q ) ) != 0 )
529     {
530         mbedtls_ecdsa_free( ctx );
531     }
532 
533     return( ret );
534 }
535 
536 /*
537  * Initialize context
538  */
539 void mbedtls_ecdsa_init( mbedtls_ecdsa_context *ctx )
540 {
541     mbedtls_ecp_keypair_init( ctx );
542 }
543 
544 /*
545  * Free context
546  */
547 void mbedtls_ecdsa_free( mbedtls_ecdsa_context *ctx )
548 {
549     mbedtls_ecp_keypair_free( ctx );
550 }
551 
552 #endif /* MBEDTLS_ECDSA_C */
553