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Manuel Pégourié-Gonnard2aea1412013-01-26 16:33:44 +01001/*
2 * Elliptic curve DSA
3 *
Bence Szépkúti1e148272020-08-07 13:07:28 +02004 * Copyright The Mbed TLS Contributors
Dave Rodgman16799db2023-11-02 19:47:20 +00005 * SPDX-License-Identifier: Apache-2.0 OR GPL-2.0-or-later
Manuel Pégourié-Gonnard2aea1412013-01-26 16:33:44 +01006 */
7
8/*
9 * References:
10 *
Xiaokang Qianb92a2f62023-04-19 02:59:15 +000011 * SEC1 https://www.secg.org/sec1-v2.pdf
Manuel Pégourié-Gonnard2aea1412013-01-26 16:33:44 +010012 */
13
Gilles Peskinedb09ef62020-06-03 01:43:33 +020014#include "common.h"
Manuel Pégourié-Gonnard2aea1412013-01-26 16:33:44 +010015
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +020016#if defined(MBEDTLS_ECDSA_C)
Manuel Pégourié-Gonnard2aea1412013-01-26 16:33:44 +010017
Manuel Pégourié-Gonnard7f809972015-03-09 17:05:11 +000018#include "mbedtls/ecdsa.h"
19#include "mbedtls/asn1write.h"
Manuel Pégourié-Gonnard0d73de52025-07-10 22:59:39 +020020#include "bignum_internal.h"
Manuel Pégourié-Gonnard2aea1412013-01-26 16:33:44 +010021
Rich Evans00ab4702015-02-06 13:43:58 +000022#include <string.h>
23
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +020024#if defined(MBEDTLS_ECDSA_DETERMINISTIC)
Manuel Pégourié-Gonnard7f809972015-03-09 17:05:11 +000025#include "mbedtls/hmac_drbg.h"
Manuel Pégourié-Gonnard7845fc02014-01-27 14:24:03 +010026#endif
Manuel Pégourié-Gonnard461d4162014-01-06 10:16:28 +010027
Manuel Pégourié-Gonnarda0c5bcc2017-04-21 11:33:57 +020028#include "mbedtls/platform.h"
Manuel Pégourié-Gonnarda0c5bcc2017-04-21 11:33:57 +020029
Hanno Becker319ae112018-12-14 16:43:29 +000030#include "mbedtls/platform_util.h"
Janos Follath24eed8d2019-11-22 13:21:35 +000031#include "mbedtls/error.h"
Hanno Becker319ae112018-12-14 16:43:29 +000032
Manuel Pégourié-Gonnarda0c5bcc2017-04-21 11:33:57 +020033#if defined(MBEDTLS_ECP_RESTARTABLE)
Manuel Pégourié-Gonnard5314f232017-04-21 12:36:59 +020034
Manuel Pégourié-Gonnarda0c5bcc2017-04-21 11:33:57 +020035/*
Manuel Pégourié-Gonnarda4dd7832017-09-07 11:11:39 +020036 * Sub-context for ecdsa_verify()
Manuel Pégourié-Gonnarda0c5bcc2017-04-21 11:33:57 +020037 */
Gilles Peskine449bd832023-01-11 14:50:10 +010038struct mbedtls_ecdsa_restart_ver {
Manuel Pégourié-Gonnard5314f232017-04-21 12:36:59 +020039 mbedtls_mpi u1, u2; /* intermediate values */
40 enum { /* what to do next? */
41 ecdsa_ver_init = 0, /* getting started */
42 ecdsa_ver_muladd, /* muladd step */
43 } state;
Manuel Pégourié-Gonnarda0c5bcc2017-04-21 11:33:57 +020044};
45
46/*
47 * Init verify restart sub-context
48 */
Gilles Peskine449bd832023-01-11 14:50:10 +010049static void ecdsa_restart_ver_init(mbedtls_ecdsa_restart_ver_ctx *ctx)
Manuel Pégourié-Gonnarda0c5bcc2017-04-21 11:33:57 +020050{
Gilles Peskine449bd832023-01-11 14:50:10 +010051 mbedtls_mpi_init(&ctx->u1);
52 mbedtls_mpi_init(&ctx->u2);
Manuel Pégourié-Gonnard5bd38b12017-08-23 16:55:59 +020053 ctx->state = ecdsa_ver_init;
Manuel Pégourié-Gonnarda0c5bcc2017-04-21 11:33:57 +020054}
55
56/*
57 * Free the components of a verify restart sub-context
58 */
Gilles Peskine449bd832023-01-11 14:50:10 +010059static void ecdsa_restart_ver_free(mbedtls_ecdsa_restart_ver_ctx *ctx)
Manuel Pégourié-Gonnarda0c5bcc2017-04-21 11:33:57 +020060{
Gilles Peskine449bd832023-01-11 14:50:10 +010061 if (ctx == NULL) {
Manuel Pégourié-Gonnarda0c5bcc2017-04-21 11:33:57 +020062 return;
Gilles Peskine449bd832023-01-11 14:50:10 +010063 }
Manuel Pégourié-Gonnarda0c5bcc2017-04-21 11:33:57 +020064
Gilles Peskine449bd832023-01-11 14:50:10 +010065 mbedtls_mpi_free(&ctx->u1);
66 mbedtls_mpi_free(&ctx->u2);
Manuel Pégourié-Gonnard5314f232017-04-21 12:36:59 +020067
Gilles Peskine449bd832023-01-11 14:50:10 +010068 ecdsa_restart_ver_init(ctx);
Manuel Pégourié-Gonnarda0c5bcc2017-04-21 11:33:57 +020069}
70
Manuel Pégourié-Gonnardb90883d2017-04-25 11:33:10 +020071/*
Manuel Pégourié-Gonnarda4dd7832017-09-07 11:11:39 +020072 * Sub-context for ecdsa_sign()
Manuel Pégourié-Gonnardb90883d2017-04-25 11:33:10 +020073 */
Gilles Peskine449bd832023-01-11 14:50:10 +010074struct mbedtls_ecdsa_restart_sig {
Manuel Pégourié-Gonnardaf081f52017-04-25 13:44:19 +020075 int sign_tries;
76 int key_tries;
77 mbedtls_mpi k; /* per-signature random */
78 mbedtls_mpi r; /* r value */
Manuel Pégourié-Gonnardb90883d2017-04-25 11:33:10 +020079 enum { /* what to do next? */
80 ecdsa_sig_init = 0, /* getting started */
Manuel Pégourié-Gonnardaf081f52017-04-25 13:44:19 +020081 ecdsa_sig_mul, /* doing ecp_mul() */
82 ecdsa_sig_modn, /* mod N computations */
Manuel Pégourié-Gonnardb90883d2017-04-25 11:33:10 +020083 } state;
84};
85
86/*
87 * Init verify sign sub-context
88 */
Gilles Peskine449bd832023-01-11 14:50:10 +010089static void ecdsa_restart_sig_init(mbedtls_ecdsa_restart_sig_ctx *ctx)
Manuel Pégourié-Gonnardb90883d2017-04-25 11:33:10 +020090{
Manuel Pégourié-Gonnard5bd38b12017-08-23 16:55:59 +020091 ctx->sign_tries = 0;
92 ctx->key_tries = 0;
Gilles Peskine449bd832023-01-11 14:50:10 +010093 mbedtls_mpi_init(&ctx->k);
94 mbedtls_mpi_init(&ctx->r);
Manuel Pégourié-Gonnard5bd38b12017-08-23 16:55:59 +020095 ctx->state = ecdsa_sig_init;
Manuel Pégourié-Gonnardb90883d2017-04-25 11:33:10 +020096}
97
98/*
99 * Free the components of a sign restart sub-context
100 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100101static void ecdsa_restart_sig_free(mbedtls_ecdsa_restart_sig_ctx *ctx)
Manuel Pégourié-Gonnardb90883d2017-04-25 11:33:10 +0200102{
Gilles Peskine449bd832023-01-11 14:50:10 +0100103 if (ctx == NULL) {
Manuel Pégourié-Gonnardb90883d2017-04-25 11:33:10 +0200104 return;
Gilles Peskine449bd832023-01-11 14:50:10 +0100105 }
Manuel Pégourié-Gonnardb90883d2017-04-25 11:33:10 +0200106
Gilles Peskine449bd832023-01-11 14:50:10 +0100107 mbedtls_mpi_free(&ctx->k);
108 mbedtls_mpi_free(&ctx->r);
Manuel Pégourié-Gonnardb90883d2017-04-25 11:33:10 +0200109}
110
111#if defined(MBEDTLS_ECDSA_DETERMINISTIC)
112/*
Manuel Pégourié-Gonnarda4dd7832017-09-07 11:11:39 +0200113 * Sub-context for ecdsa_sign_det()
Manuel Pégourié-Gonnardb90883d2017-04-25 11:33:10 +0200114 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100115struct mbedtls_ecdsa_restart_det {
Manuel Pégourié-Gonnardaf081f52017-04-25 13:44:19 +0200116 mbedtls_hmac_drbg_context rng_ctx; /* DRBG state */
Manuel Pégourié-Gonnardb90883d2017-04-25 11:33:10 +0200117 enum { /* what to do next? */
Manuel Pégourié-Gonnardaf081f52017-04-25 13:44:19 +0200118 ecdsa_det_init = 0, /* getting started */
119 ecdsa_det_sign, /* make signature */
Manuel Pégourié-Gonnardb90883d2017-04-25 11:33:10 +0200120 } state;
121};
122
123/*
124 * Init verify sign_det sub-context
125 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100126static void ecdsa_restart_det_init(mbedtls_ecdsa_restart_det_ctx *ctx)
Manuel Pégourié-Gonnardb90883d2017-04-25 11:33:10 +0200127{
Gilles Peskine449bd832023-01-11 14:50:10 +0100128 mbedtls_hmac_drbg_init(&ctx->rng_ctx);
Manuel Pégourié-Gonnard5bd38b12017-08-23 16:55:59 +0200129 ctx->state = ecdsa_det_init;
Manuel Pégourié-Gonnardb90883d2017-04-25 11:33:10 +0200130}
131
132/*
133 * Free the components of a sign_det restart sub-context
134 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100135static void ecdsa_restart_det_free(mbedtls_ecdsa_restart_det_ctx *ctx)
Manuel Pégourié-Gonnardb90883d2017-04-25 11:33:10 +0200136{
Gilles Peskine449bd832023-01-11 14:50:10 +0100137 if (ctx == NULL) {
Manuel Pégourié-Gonnardb90883d2017-04-25 11:33:10 +0200138 return;
Gilles Peskine449bd832023-01-11 14:50:10 +0100139 }
Manuel Pégourié-Gonnardb90883d2017-04-25 11:33:10 +0200140
Gilles Peskine449bd832023-01-11 14:50:10 +0100141 mbedtls_hmac_drbg_free(&ctx->rng_ctx);
Manuel Pégourié-Gonnardaf081f52017-04-25 13:44:19 +0200142
Gilles Peskine449bd832023-01-11 14:50:10 +0100143 ecdsa_restart_det_init(ctx);
Manuel Pégourié-Gonnardb90883d2017-04-25 11:33:10 +0200144}
145#endif /* MBEDTLS_ECDSA_DETERMINISTIC */
146
Gilles Peskine449bd832023-01-11 14:50:10 +0100147#define ECDSA_RS_ECP (rs_ctx == NULL ? NULL : &rs_ctx->ecp)
Manuel Pégourié-Gonnarda0c5bcc2017-04-21 11:33:57 +0200148
Manuel Pégourié-Gonnard5314f232017-04-21 12:36:59 +0200149/* Utility macro for checking and updating ops budget */
Gilles Peskine449bd832023-01-11 14:50:10 +0100150#define ECDSA_BUDGET(ops) \
151 MBEDTLS_MPI_CHK(mbedtls_ecp_check_budget(grp, ECDSA_RS_ECP, ops));
Manuel Pégourié-Gonnard5314f232017-04-21 12:36:59 +0200152
Manuel Pégourié-Gonnardb948f7d2017-08-23 17:58:40 +0200153/* Call this when entering a function that needs its own sub-context */
Gilles Peskine449bd832023-01-11 14:50:10 +0100154#define ECDSA_RS_ENTER(SUB) do { \
155 /* reset ops count for this call if top-level */ \
156 if (rs_ctx != NULL && rs_ctx->ecp.depth++ == 0) \
Manuel Pégourié-Gonnardb90883d2017-04-25 11:33:10 +0200157 rs_ctx->ecp.ops_done = 0; \
158 \
Gilles Peskine449bd832023-01-11 14:50:10 +0100159 /* set up our own sub-context if needed */ \
160 if (mbedtls_ecp_restart_is_enabled() && \
161 rs_ctx != NULL && rs_ctx->SUB == NULL) \
162 { \
163 rs_ctx->SUB = mbedtls_calloc(1, sizeof(*rs_ctx->SUB)); \
164 if (rs_ctx->SUB == NULL) \
165 return MBEDTLS_ERR_ECP_ALLOC_FAILED; \
166 \
167 ecdsa_restart_## SUB ##_init(rs_ctx->SUB); \
168 } \
169} while (0)
Manuel Pégourié-Gonnardb90883d2017-04-25 11:33:10 +0200170
Manuel Pégourié-Gonnardb948f7d2017-08-23 17:58:40 +0200171/* Call this when leaving a function that needs its own sub-context */
Gilles Peskine449bd832023-01-11 14:50:10 +0100172#define ECDSA_RS_LEAVE(SUB) do { \
173 /* clear our sub-context when not in progress (done or error) */ \
174 if (rs_ctx != NULL && rs_ctx->SUB != NULL && \
175 ret != MBEDTLS_ERR_ECP_IN_PROGRESS) \
176 { \
177 ecdsa_restart_## SUB ##_free(rs_ctx->SUB); \
178 mbedtls_free(rs_ctx->SUB); \
179 rs_ctx->SUB = NULL; \
180 } \
Manuel Pégourié-Gonnardb90883d2017-04-25 11:33:10 +0200181 \
Gilles Peskine449bd832023-01-11 14:50:10 +0100182 if (rs_ctx != NULL) \
Manuel Pégourié-Gonnardb90883d2017-04-25 11:33:10 +0200183 rs_ctx->ecp.depth--; \
Gilles Peskine449bd832023-01-11 14:50:10 +0100184} while (0)
Manuel Pégourié-Gonnardb90883d2017-04-25 11:33:10 +0200185
Manuel Pégourié-Gonnarda0c5bcc2017-04-21 11:33:57 +0200186#else /* MBEDTLS_ECP_RESTARTABLE */
187
188#define ECDSA_RS_ECP NULL
189
Gilles Peskine449bd832023-01-11 14:50:10 +0100190#define ECDSA_BUDGET(ops) /* no-op; for compatibility */
Manuel Pégourié-Gonnard5314f232017-04-21 12:36:59 +0200191
Gilles Peskine449bd832023-01-11 14:50:10 +0100192#define ECDSA_RS_ENTER(SUB) (void) rs_ctx
193#define ECDSA_RS_LEAVE(SUB) (void) rs_ctx
Manuel Pégourié-Gonnardb90883d2017-04-25 11:33:10 +0200194
Manuel Pégourié-Gonnarda0c5bcc2017-04-21 11:33:57 +0200195#endif /* MBEDTLS_ECP_RESTARTABLE */
196
Steven Cooremanfa6641b2021-01-11 17:11:39 +0100197#if defined(MBEDTLS_ECDSA_DETERMINISTIC) || \
Steven Cooreman107409f2021-01-26 12:01:22 +0100198 !defined(MBEDTLS_ECDSA_SIGN_ALT) || \
199 !defined(MBEDTLS_ECDSA_VERIFY_ALT)
Manuel Pégourié-Gonnardb309ab22013-01-26 17:24:59 +0100200/*
Manuel Pégourié-Gonnard3aeb5a72013-01-26 18:05:50 +0100201 * Derive a suitable integer for group grp from a buffer of length len
202 * SEC1 4.1.3 step 5 aka SEC1 4.1.4 step 3
203 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100204static int derive_mpi(const mbedtls_ecp_group *grp, mbedtls_mpi *x,
205 const unsigned char *buf, size_t blen)
Manuel Pégourié-Gonnard3aeb5a72013-01-26 18:05:50 +0100206{
Janos Follath24eed8d2019-11-22 13:21:35 +0000207 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
Gilles Peskine449bd832023-01-11 14:50:10 +0100208 size_t n_size = (grp->nbits + 7) / 8;
Manuel Pégourié-Gonnard53048122014-01-03 12:55:15 +0100209 size_t use_size = blen > n_size ? n_size : blen;
210
Gilles Peskine449bd832023-01-11 14:50:10 +0100211 MBEDTLS_MPI_CHK(mbedtls_mpi_read_binary(x, buf, use_size));
212 if (use_size * 8 > grp->nbits) {
213 MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(x, use_size * 8 - grp->nbits));
214 }
Manuel Pégourié-Gonnard53048122014-01-03 12:55:15 +0100215
Manuel Pégourié-Gonnard461d4162014-01-06 10:16:28 +0100216 /* While at it, reduce modulo N */
Gilles Peskine449bd832023-01-11 14:50:10 +0100217 if (mbedtls_mpi_cmp_mpi(x, &grp->N) >= 0) {
218 MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(x, x, &grp->N));
219 }
Manuel Pégourié-Gonnard461d4162014-01-06 10:16:28 +0100220
Manuel Pégourié-Gonnard53048122014-01-03 12:55:15 +0100221cleanup:
Gilles Peskine449bd832023-01-11 14:50:10 +0100222 return ret;
Manuel Pégourié-Gonnard3aeb5a72013-01-26 18:05:50 +0100223}
Steven Cooremanfa6641b2021-01-11 17:11:39 +0100224#endif /* ECDSA_DETERMINISTIC || !ECDSA_SIGN_ALT || !ECDSA_VERIFY_ALT */
Manuel Pégourié-Gonnard3aeb5a72013-01-26 18:05:50 +0100225
JonathanWitthoeft405ec942023-04-26 10:24:12 -0500226int mbedtls_ecdsa_can_do(mbedtls_ecp_group_id gid)
227{
228 switch (gid) {
229#ifdef MBEDTLS_ECP_DP_CURVE25519_ENABLED
230 case MBEDTLS_ECP_DP_CURVE25519: return 0;
231#endif
232#ifdef MBEDTLS_ECP_DP_CURVE448_ENABLED
233 case MBEDTLS_ECP_DP_CURVE448: return 0;
234#endif
235 default: return 1;
236 }
237}
238
Ron Eldor936d2842018-11-01 13:05:52 +0200239#if !defined(MBEDTLS_ECDSA_SIGN_ALT)
Manuel Pégourié-Gonnard3aeb5a72013-01-26 18:05:50 +0100240/*
Manuel Pégourié-Gonnardb309ab22013-01-26 17:24:59 +0100241 * Compute ECDSA signature of a hashed message (SEC1 4.1.3)
242 * Obviously, compared to SEC1 4.1.3, we skip step 4 (hash message)
243 */
Paul Elliott2ba002c2022-12-09 18:59:26 +0000244int mbedtls_ecdsa_sign_restartable(mbedtls_ecp_group *grp,
245 mbedtls_mpi *r, mbedtls_mpi *s,
246 const mbedtls_mpi *d, const unsigned char *buf, size_t blen,
247 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng,
248 int (*f_rng_blind)(void *, unsigned char *, size_t),
249 void *p_rng_blind,
250 mbedtls_ecdsa_restart_ctx *rs_ctx)
Manuel Pégourié-Gonnardb309ab22013-01-26 17:24:59 +0100251{
Manuel Pégourié-Gonnard50b63ba2017-04-25 12:57:22 +0200252 int ret, key_tries, sign_tries;
Manuel Pégourié-Gonnardaf081f52017-04-25 13:44:19 +0200253 int *p_sign_tries = &sign_tries, *p_key_tries = &key_tries;
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200254 mbedtls_ecp_point R;
Manuel Pégourié-Gonnardb4643292025-08-26 11:33:12 +0200255 mbedtls_mpi k, e;
Manuel Pégourié-Gonnardaf081f52017-04-25 13:44:19 +0200256 mbedtls_mpi *pk = &k, *pr = r;
Manuel Pégourié-Gonnardb309ab22013-01-26 17:24:59 +0100257
Manuel Pégourié-Gonnard97871ef2013-12-04 20:52:04 +0100258 /* Fail cleanly on curves such as Curve25519 that can't be used for ECDSA */
Gilles Peskine449bd832023-01-11 14:50:10 +0100259 if (!mbedtls_ecdsa_can_do(grp->id) || grp->N.p == NULL) {
260 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
261 }
Manuel Pégourié-Gonnard97871ef2013-12-04 20:52:04 +0100262
Darryl Greenc64a48b2017-11-17 17:09:17 +0000263 /* Make sure d is in range 1..n-1 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100264 if (mbedtls_mpi_cmp_int(d, 1) < 0 || mbedtls_mpi_cmp_mpi(d, &grp->N) >= 0) {
265 return MBEDTLS_ERR_ECP_INVALID_KEY;
266 }
Darryl Greenc64a48b2017-11-17 17:09:17 +0000267
Gilles Peskine449bd832023-01-11 14:50:10 +0100268 mbedtls_ecp_point_init(&R);
Manuel Pégourié-Gonnardb4643292025-08-26 11:33:12 +0200269 mbedtls_mpi_init(&k); mbedtls_mpi_init(&e);
Manuel Pégourié-Gonnardb309ab22013-01-26 17:24:59 +0100270
Gilles Peskine449bd832023-01-11 14:50:10 +0100271 ECDSA_RS_ENTER(sig);
Manuel Pégourié-Gonnardb90883d2017-04-25 11:33:10 +0200272
273#if defined(MBEDTLS_ECP_RESTARTABLE)
Gilles Peskine449bd832023-01-11 14:50:10 +0100274 if (rs_ctx != NULL && rs_ctx->sig != NULL) {
Manuel Pégourié-Gonnardb90883d2017-04-25 11:33:10 +0200275 /* redirect to our context */
Manuel Pégourié-Gonnardaf081f52017-04-25 13:44:19 +0200276 p_sign_tries = &rs_ctx->sig->sign_tries;
277 p_key_tries = &rs_ctx->sig->key_tries;
278 pk = &rs_ctx->sig->k;
279 pr = &rs_ctx->sig->r;
280
Manuel Pégourié-Gonnardb90883d2017-04-25 11:33:10 +0200281 /* jump to current step */
Gilles Peskine449bd832023-01-11 14:50:10 +0100282 if (rs_ctx->sig->state == ecdsa_sig_mul) {
Manuel Pégourié-Gonnardaf081f52017-04-25 13:44:19 +0200283 goto mul;
Gilles Peskine449bd832023-01-11 14:50:10 +0100284 }
285 if (rs_ctx->sig->state == ecdsa_sig_modn) {
Manuel Pégourié-Gonnardaf081f52017-04-25 13:44:19 +0200286 goto modn;
Gilles Peskine449bd832023-01-11 14:50:10 +0100287 }
Manuel Pégourié-Gonnardb90883d2017-04-25 11:33:10 +0200288 }
289#endif /* MBEDTLS_ECP_RESTARTABLE */
290
Manuel Pégourié-Gonnardaf081f52017-04-25 13:44:19 +0200291 *p_sign_tries = 0;
Gilles Peskine449bd832023-01-11 14:50:10 +0100292 do {
293 if ((*p_sign_tries)++ > 10) {
Manuel Pégourié-Gonnard67543962017-04-21 13:19:43 +0200294 ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
295 goto cleanup;
296 }
297
Manuel Pégourié-Gonnardb309ab22013-01-26 17:24:59 +0100298 /*
299 * Steps 1-3: generate a suitable ephemeral keypair
Manuel Pégourié-Gonnard178d9ba2013-10-29 10:45:28 +0100300 * and set r = xR mod n
Manuel Pégourié-Gonnardb309ab22013-01-26 17:24:59 +0100301 */
Manuel Pégourié-Gonnardaf081f52017-04-25 13:44:19 +0200302 *p_key_tries = 0;
Gilles Peskine449bd832023-01-11 14:50:10 +0100303 do {
304 if ((*p_key_tries)++ > 10) {
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200305 ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
Paul Bakkercca998a2013-07-26 14:20:53 +0200306 goto cleanup;
307 }
Manuel Pégourié-Gonnard67543962017-04-21 13:19:43 +0200308
Gilles Peskine449bd832023-01-11 14:50:10 +0100309 MBEDTLS_MPI_CHK(mbedtls_ecp_gen_privkey(grp, pk, f_rng, p_rng));
Manuel Pégourié-Gonnard50b63ba2017-04-25 12:57:22 +0200310
Manuel Pégourié-Gonnardaf081f52017-04-25 13:44:19 +0200311#if defined(MBEDTLS_ECP_RESTARTABLE)
Gilles Peskine449bd832023-01-11 14:50:10 +0100312 if (rs_ctx != NULL && rs_ctx->sig != NULL) {
Manuel Pégourié-Gonnard63481812017-08-24 11:16:01 +0200313 rs_ctx->sig->state = ecdsa_sig_mul;
Gilles Peskine449bd832023-01-11 14:50:10 +0100314 }
Manuel Pégourié-Gonnardaf081f52017-04-25 13:44:19 +0200315
316mul:
317#endif
Gilles Peskine449bd832023-01-11 14:50:10 +0100318 MBEDTLS_MPI_CHK(mbedtls_ecp_mul_restartable(grp, &R, pk, &grp->G,
319 f_rng_blind,
320 p_rng_blind,
321 ECDSA_RS_ECP));
322 MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(pr, &R.X, &grp->N));
323 } while (mbedtls_mpi_cmp_int(pr, 0) == 0);
Manuel Pégourié-Gonnardaf081f52017-04-25 13:44:19 +0200324
Manuel Pégourié-Gonnardaf081f52017-04-25 13:44:19 +0200325#if defined(MBEDTLS_ECP_RESTARTABLE)
Gilles Peskine449bd832023-01-11 14:50:10 +0100326 if (rs_ctx != NULL && rs_ctx->sig != NULL) {
Manuel Pégourié-Gonnard63481812017-08-24 11:16:01 +0200327 rs_ctx->sig->state = ecdsa_sig_modn;
Gilles Peskine449bd832023-01-11 14:50:10 +0100328 }
Manuel Pégourié-Gonnardaf081f52017-04-25 13:44:19 +0200329
330modn:
331#endif
332 /*
333 * Accounting for everything up to the end of the loop
334 * (step 6, but checking now avoids saving e and t)
335 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100336 ECDSA_BUDGET(MBEDTLS_ECP_OPS_INV + 4);
Manuel Pégourié-Gonnardb309ab22013-01-26 17:24:59 +0100337
338 /*
339 * Step 5: derive MPI from hashed message
340 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100341 MBEDTLS_MPI_CHK(derive_mpi(grp, &e, buf, blen));
Manuel Pégourié-Gonnardb309ab22013-01-26 17:24:59 +0100342
343 /*
Manuel Pégourié-Gonnard0d73de52025-07-10 22:59:39 +0200344 * Step 6: compute s = (e + r * d) / k
Manuel Pégourié-Gonnardb309ab22013-01-26 17:24:59 +0100345 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100346 MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mpi(s, pr, d));
347 MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(&e, &e, s));
Manuel Pégourié-Gonnard0d73de52025-07-10 22:59:39 +0200348 MBEDTLS_MPI_CHK(mbedtls_mpi_gcd_modinv_odd(NULL, s, pk, &grp->N));
Gilles Peskine449bd832023-01-11 14:50:10 +0100349 MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mpi(s, s, &e));
350 MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(s, s, &grp->N));
351 } while (mbedtls_mpi_cmp_int(s, 0) == 0);
Manuel Pégourié-Gonnardb309ab22013-01-26 17:24:59 +0100352
Manuel Pégourié-Gonnardaf081f52017-04-25 13:44:19 +0200353#if defined(MBEDTLS_ECP_RESTARTABLE)
Gilles Peskine449bd832023-01-11 14:50:10 +0100354 if (rs_ctx != NULL && rs_ctx->sig != NULL) {
Chien Wonge2caf412023-08-01 21:38:46 +0800355 MBEDTLS_MPI_CHK(mbedtls_mpi_copy(r, pr));
Gilles Peskine449bd832023-01-11 14:50:10 +0100356 }
Manuel Pégourié-Gonnardaf081f52017-04-25 13:44:19 +0200357#endif
358
Manuel Pégourié-Gonnardb309ab22013-01-26 17:24:59 +0100359cleanup:
Gilles Peskine449bd832023-01-11 14:50:10 +0100360 mbedtls_ecp_point_free(&R);
Manuel Pégourié-Gonnardb4643292025-08-26 11:33:12 +0200361 mbedtls_mpi_free(&k); mbedtls_mpi_free(&e);
Manuel Pégourié-Gonnardb309ab22013-01-26 17:24:59 +0100362
Gilles Peskine449bd832023-01-11 14:50:10 +0100363 ECDSA_RS_LEAVE(sig);
Manuel Pégourié-Gonnardb90883d2017-04-25 11:33:10 +0200364
Gilles Peskine449bd832023-01-11 14:50:10 +0100365 return ret;
Manuel Pégourié-Gonnardb309ab22013-01-26 17:24:59 +0100366}
Manuel Pégourié-Gonnard2aea1412013-01-26 16:33:44 +0100367
Manuel Pégourié-Gonnardaddb10e2017-04-21 12:54:46 +0200368/*
369 * Compute ECDSA signature of a hashed message
370 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100371int mbedtls_ecdsa_sign(mbedtls_ecp_group *grp, mbedtls_mpi *r, mbedtls_mpi *s,
372 const mbedtls_mpi *d, const unsigned char *buf, size_t blen,
373 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng)
Manuel Pégourié-Gonnardaddb10e2017-04-21 12:54:46 +0200374{
Janos Follathdca667a2019-01-04 14:32:30 +0000375 /* Use the same RNG for both blinding and ephemeral key generation */
Paul Elliott2ba002c2022-12-09 18:59:26 +0000376 return mbedtls_ecdsa_sign_restartable(grp, r, s, d, buf, blen,
377 f_rng, p_rng, f_rng, p_rng, NULL);
Manuel Pégourié-Gonnardaddb10e2017-04-21 12:54:46 +0200378}
Ron Eldor936d2842018-11-01 13:05:52 +0200379#endif /* !MBEDTLS_ECDSA_SIGN_ALT */
Manuel Pégourié-Gonnardaddb10e2017-04-21 12:54:46 +0200380
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200381#if defined(MBEDTLS_ECDSA_DETERMINISTIC)
Manuel Pégourié-Gonnard4daaef72014-01-06 14:25:56 +0100382/*
383 * Deterministic signature wrapper
TRodziewicz18efb732021-04-29 23:12:19 +0200384 *
TRodziewicz7e9422d2021-04-30 10:32:58 +0200385 * note: The f_rng_blind parameter must not be NULL.
TRodziewicz18efb732021-04-29 23:12:19 +0200386 *
Manuel Pégourié-Gonnard4daaef72014-01-06 14:25:56 +0100387 */
Paul Elliott2ba002c2022-12-09 18:59:26 +0000388int mbedtls_ecdsa_sign_det_restartable(mbedtls_ecp_group *grp,
389 mbedtls_mpi *r, mbedtls_mpi *s,
390 const mbedtls_mpi *d, const unsigned char *buf, size_t blen,
391 mbedtls_md_type_t md_alg,
392 int (*f_rng_blind)(void *, unsigned char *, size_t),
393 void *p_rng_blind,
394 mbedtls_ecdsa_restart_ctx *rs_ctx)
Manuel Pégourié-Gonnard4daaef72014-01-06 14:25:56 +0100395{
Janos Follath24eed8d2019-11-22 13:21:35 +0000396 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200397 mbedtls_hmac_drbg_context rng_ctx;
Manuel Pégourié-Gonnardaf081f52017-04-25 13:44:19 +0200398 mbedtls_hmac_drbg_context *p_rng = &rng_ctx;
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200399 unsigned char data[2 * MBEDTLS_ECP_MAX_BYTES];
Gilles Peskine449bd832023-01-11 14:50:10 +0100400 size_t grp_len = (grp->nbits + 7) / 8;
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200401 const mbedtls_md_info_t *md_info;
402 mbedtls_mpi h;
Manuel Pégourié-Gonnard4daaef72014-01-06 14:25:56 +0100403
Gilles Peskine449bd832023-01-11 14:50:10 +0100404 if ((md_info = mbedtls_md_info_from_type(md_alg)) == NULL) {
405 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
406 }
Manuel Pégourié-Gonnard4daaef72014-01-06 14:25:56 +0100407
Gilles Peskine449bd832023-01-11 14:50:10 +0100408 mbedtls_mpi_init(&h);
409 mbedtls_hmac_drbg_init(&rng_ctx);
Manuel Pégourié-Gonnard4daaef72014-01-06 14:25:56 +0100410
Gilles Peskine449bd832023-01-11 14:50:10 +0100411 ECDSA_RS_ENTER(det);
Manuel Pégourié-Gonnardb90883d2017-04-25 11:33:10 +0200412
413#if defined(MBEDTLS_ECP_RESTARTABLE)
Gilles Peskine449bd832023-01-11 14:50:10 +0100414 if (rs_ctx != NULL && rs_ctx->det != NULL) {
Manuel Pégourié-Gonnardb90883d2017-04-25 11:33:10 +0200415 /* redirect to our context */
Manuel Pégourié-Gonnardaf081f52017-04-25 13:44:19 +0200416 p_rng = &rs_ctx->det->rng_ctx;
Manuel Pégourié-Gonnardb90883d2017-04-25 11:33:10 +0200417
418 /* jump to current step */
Gilles Peskine449bd832023-01-11 14:50:10 +0100419 if (rs_ctx->det->state == ecdsa_det_sign) {
Manuel Pégourié-Gonnardaf081f52017-04-25 13:44:19 +0200420 goto sign;
Gilles Peskine449bd832023-01-11 14:50:10 +0100421 }
Manuel Pégourié-Gonnardb90883d2017-04-25 11:33:10 +0200422 }
423#endif /* MBEDTLS_ECP_RESTARTABLE */
424
Manuel Pégourié-Gonnardf42bca62014-01-06 15:05:01 +0100425 /* Use private key and message hash (reduced) to initialize HMAC_DRBG */
Gilles Peskine449bd832023-01-11 14:50:10 +0100426 MBEDTLS_MPI_CHK(mbedtls_mpi_write_binary(d, data, grp_len));
427 MBEDTLS_MPI_CHK(derive_mpi(grp, &h, buf, blen));
428 MBEDTLS_MPI_CHK(mbedtls_mpi_write_binary(&h, data + grp_len, grp_len));
Chien Wonge2caf412023-08-01 21:38:46 +0800429 MBEDTLS_MPI_CHK(mbedtls_hmac_drbg_seed_buf(p_rng, md_info, data, 2 * grp_len));
Manuel Pégourié-Gonnard4daaef72014-01-06 14:25:56 +0100430
Manuel Pégourié-Gonnardaf081f52017-04-25 13:44:19 +0200431#if defined(MBEDTLS_ECP_RESTARTABLE)
Gilles Peskine449bd832023-01-11 14:50:10 +0100432 if (rs_ctx != NULL && rs_ctx->det != NULL) {
Manuel Pégourié-Gonnard63481812017-08-24 11:16:01 +0200433 rs_ctx->det->state = ecdsa_det_sign;
Gilles Peskine449bd832023-01-11 14:50:10 +0100434 }
Manuel Pégourié-Gonnardaf081f52017-04-25 13:44:19 +0200435
436sign:
437#endif
Ron Eldor8493f802018-11-01 11:32:15 +0200438#if defined(MBEDTLS_ECDSA_SIGN_ALT)
Steven Cooreman6dce4bb2021-02-10 17:07:20 +0100439 (void) f_rng_blind;
440 (void) p_rng_blind;
Gilles Peskine449bd832023-01-11 14:50:10 +0100441 ret = mbedtls_ecdsa_sign(grp, r, s, d, buf, blen,
442 mbedtls_hmac_drbg_random, p_rng);
Ron Eldor8493f802018-11-01 11:32:15 +0200443#else
Paul Elliott2ba002c2022-12-09 18:59:26 +0000444 ret = mbedtls_ecdsa_sign_restartable(grp, r, s, d, buf, blen,
445 mbedtls_hmac_drbg_random, p_rng,
446 f_rng_blind, p_rng_blind, rs_ctx);
Ron Eldor936d2842018-11-01 13:05:52 +0200447#endif /* MBEDTLS_ECDSA_SIGN_ALT */
Manuel Pégourié-Gonnard4daaef72014-01-06 14:25:56 +0100448
449cleanup:
Gilles Peskine449bd832023-01-11 14:50:10 +0100450 mbedtls_hmac_drbg_free(&rng_ctx);
451 mbedtls_mpi_free(&h);
Manuel Pégourié-Gonnard4daaef72014-01-06 14:25:56 +0100452
Gilles Peskine449bd832023-01-11 14:50:10 +0100453 ECDSA_RS_LEAVE(det);
Manuel Pégourié-Gonnardb90883d2017-04-25 11:33:10 +0200454
Gilles Peskine449bd832023-01-11 14:50:10 +0100455 return ret;
Manuel Pégourié-Gonnard4daaef72014-01-06 14:25:56 +0100456}
Manuel Pégourié-Gonnardaddb10e2017-04-21 12:54:46 +0200457
458/*
TRodziewicz18efb732021-04-29 23:12:19 +0200459 * Deterministic signature wrapper
Manuel Pégourié-Gonnardaddb10e2017-04-21 12:54:46 +0200460 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100461int mbedtls_ecdsa_sign_det_ext(mbedtls_ecp_group *grp, mbedtls_mpi *r,
462 mbedtls_mpi *s, const mbedtls_mpi *d,
463 const unsigned char *buf, size_t blen,
464 mbedtls_md_type_t md_alg,
465 int (*f_rng_blind)(void *, unsigned char *,
466 size_t),
467 void *p_rng_blind)
Janos Follathdca667a2019-01-04 14:32:30 +0000468{
Paul Elliott2ba002c2022-12-09 18:59:26 +0000469 return mbedtls_ecdsa_sign_det_restartable(grp, r, s, d, buf, blen, md_alg,
470 f_rng_blind, p_rng_blind, NULL);
Manuel Pégourié-Gonnardaddb10e2017-04-21 12:54:46 +0200471}
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200472#endif /* MBEDTLS_ECDSA_DETERMINISTIC */
Paul Bakker9f3c7d72014-01-23 16:11:14 +0100473
Ron Eldor936d2842018-11-01 13:05:52 +0200474#if !defined(MBEDTLS_ECDSA_VERIFY_ALT)
Manuel Pégourié-Gonnard3aeb5a72013-01-26 18:05:50 +0100475/*
476 * Verify ECDSA signature of hashed message (SEC1 4.1.4)
477 * Obviously, compared to SEC1 4.1.3, we skip step 2 (hash message)
478 */
Paul Elliott2ba002c2022-12-09 18:59:26 +0000479int mbedtls_ecdsa_verify_restartable(mbedtls_ecp_group *grp,
480 const unsigned char *buf, size_t blen,
481 const mbedtls_ecp_point *Q,
482 const mbedtls_mpi *r,
483 const mbedtls_mpi *s,
484 mbedtls_ecdsa_restart_ctx *rs_ctx)
Manuel Pégourié-Gonnard3aeb5a72013-01-26 18:05:50 +0100485{
Janos Follath24eed8d2019-11-22 13:21:35 +0000486 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200487 mbedtls_mpi e, s_inv, u1, u2;
Manuel Pégourié-Gonnard56cc88a2015-05-11 18:40:45 +0200488 mbedtls_ecp_point R;
Manuel Pégourié-Gonnard5314f232017-04-21 12:36:59 +0200489 mbedtls_mpi *pu1 = &u1, *pu2 = &u2;
Manuel Pégourié-Gonnard3aeb5a72013-01-26 18:05:50 +0100490
Gilles Peskine449bd832023-01-11 14:50:10 +0100491 mbedtls_ecp_point_init(&R);
492 mbedtls_mpi_init(&e); mbedtls_mpi_init(&s_inv);
493 mbedtls_mpi_init(&u1); mbedtls_mpi_init(&u2);
Manuel Pégourié-Gonnard3aeb5a72013-01-26 18:05:50 +0100494
Manuel Pégourié-Gonnard97871ef2013-12-04 20:52:04 +0100495 /* Fail cleanly on curves such as Curve25519 that can't be used for ECDSA */
Gilles Peskine449bd832023-01-11 14:50:10 +0100496 if (!mbedtls_ecdsa_can_do(grp->id) || grp->N.p == NULL) {
497 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
498 }
Manuel Pégourié-Gonnard97871ef2013-12-04 20:52:04 +0100499
Gilles Peskine449bd832023-01-11 14:50:10 +0100500 ECDSA_RS_ENTER(ver);
Manuel Pégourié-Gonnardb90883d2017-04-25 11:33:10 +0200501
Manuel Pégourié-Gonnarda0c5bcc2017-04-21 11:33:57 +0200502#if defined(MBEDTLS_ECP_RESTARTABLE)
Gilles Peskine449bd832023-01-11 14:50:10 +0100503 if (rs_ctx != NULL && rs_ctx->ver != NULL) {
Manuel Pégourié-Gonnard5314f232017-04-21 12:36:59 +0200504 /* redirect to our context */
505 pu1 = &rs_ctx->ver->u1;
506 pu2 = &rs_ctx->ver->u2;
507
508 /* jump to current step */
Gilles Peskine449bd832023-01-11 14:50:10 +0100509 if (rs_ctx->ver->state == ecdsa_ver_muladd) {
Manuel Pégourié-Gonnard5314f232017-04-21 12:36:59 +0200510 goto muladd;
Gilles Peskine449bd832023-01-11 14:50:10 +0100511 }
Manuel Pégourié-Gonnard5314f232017-04-21 12:36:59 +0200512 }
Manuel Pégourié-Gonnarda0c5bcc2017-04-21 11:33:57 +0200513#endif /* MBEDTLS_ECP_RESTARTABLE */
514
Manuel Pégourié-Gonnard3aeb5a72013-01-26 18:05:50 +0100515 /*
516 * Step 1: make sure r and s are in range 1..n-1
517 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100518 if (mbedtls_mpi_cmp_int(r, 1) < 0 || mbedtls_mpi_cmp_mpi(r, &grp->N) >= 0 ||
519 mbedtls_mpi_cmp_int(s, 1) < 0 || mbedtls_mpi_cmp_mpi(s, &grp->N) >= 0) {
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200520 ret = MBEDTLS_ERR_ECP_VERIFY_FAILED;
Paul Bakkercca998a2013-07-26 14:20:53 +0200521 goto cleanup;
Manuel Pégourié-Gonnard3aeb5a72013-01-26 18:05:50 +0100522 }
523
524 /*
Manuel Pégourié-Gonnard3aeb5a72013-01-26 18:05:50 +0100525 * Step 3: derive MPI from hashed message
526 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100527 MBEDTLS_MPI_CHK(derive_mpi(grp, &e, buf, blen));
Manuel Pégourié-Gonnard3aeb5a72013-01-26 18:05:50 +0100528
529 /*
530 * Step 4: u1 = e / s mod n, u2 = r / s mod n
531 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100532 ECDSA_BUDGET(MBEDTLS_ECP_OPS_CHK + MBEDTLS_ECP_OPS_INV + 2);
Manuel Pégourié-Gonnardbfa19722017-08-23 17:39:18 +0200533
Manuel Pégourié-Gonnard0d73de52025-07-10 22:59:39 +0200534 MBEDTLS_MPI_CHK(mbedtls_mpi_gcd_modinv_odd(NULL, &s_inv, s, &grp->N));
Manuel Pégourié-Gonnard3aeb5a72013-01-26 18:05:50 +0100535
Gilles Peskine449bd832023-01-11 14:50:10 +0100536 MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mpi(pu1, &e, &s_inv));
537 MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(pu1, pu1, &grp->N));
Manuel Pégourié-Gonnard3aeb5a72013-01-26 18:05:50 +0100538
Gilles Peskine449bd832023-01-11 14:50:10 +0100539 MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mpi(pu2, r, &s_inv));
540 MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(pu2, pu2, &grp->N));
Manuel Pégourié-Gonnard3aeb5a72013-01-26 18:05:50 +0100541
Manuel Pégourié-Gonnard5314f232017-04-21 12:36:59 +0200542#if defined(MBEDTLS_ECP_RESTARTABLE)
Gilles Peskine449bd832023-01-11 14:50:10 +0100543 if (rs_ctx != NULL && rs_ctx->ver != NULL) {
Manuel Pégourié-Gonnard63481812017-08-24 11:16:01 +0200544 rs_ctx->ver->state = ecdsa_ver_muladd;
Gilles Peskine449bd832023-01-11 14:50:10 +0100545 }
Manuel Pégourié-Gonnard5314f232017-04-21 12:36:59 +0200546
547muladd:
548#endif
Manuel Pégourié-Gonnard3aeb5a72013-01-26 18:05:50 +0100549 /*
550 * Step 5: R = u1 G + u2 Q
551 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100552 MBEDTLS_MPI_CHK(mbedtls_ecp_muladd_restartable(grp,
553 &R, pu1, &grp->G, pu2, Q, ECDSA_RS_ECP));
Manuel Pégourié-Gonnard3aeb5a72013-01-26 18:05:50 +0100554
Gilles Peskine449bd832023-01-11 14:50:10 +0100555 if (mbedtls_ecp_is_zero(&R)) {
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200556 ret = MBEDTLS_ERR_ECP_VERIFY_FAILED;
Paul Bakkercca998a2013-07-26 14:20:53 +0200557 goto cleanup;
558 }
Manuel Pégourié-Gonnard3aeb5a72013-01-26 18:05:50 +0100559
560 /*
Manuel Pégourié-Gonnard178d9ba2013-10-29 10:45:28 +0100561 * Step 6: convert xR to an integer (no-op)
562 * Step 7: reduce xR mod n (gives v)
563 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100564 MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(&R.X, &R.X, &grp->N));
Manuel Pégourié-Gonnard178d9ba2013-10-29 10:45:28 +0100565
566 /*
567 * Step 8: check if v (that is, R.X) is equal to r
Manuel Pégourié-Gonnard3aeb5a72013-01-26 18:05:50 +0100568 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100569 if (mbedtls_mpi_cmp_mpi(&R.X, r) != 0) {
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200570 ret = MBEDTLS_ERR_ECP_VERIFY_FAILED;
Paul Bakkercca998a2013-07-26 14:20:53 +0200571 goto cleanup;
572 }
Manuel Pégourié-Gonnard3aeb5a72013-01-26 18:05:50 +0100573
574cleanup:
Gilles Peskine449bd832023-01-11 14:50:10 +0100575 mbedtls_ecp_point_free(&R);
576 mbedtls_mpi_free(&e); mbedtls_mpi_free(&s_inv);
577 mbedtls_mpi_free(&u1); mbedtls_mpi_free(&u2);
Manuel Pégourié-Gonnard3aeb5a72013-01-26 18:05:50 +0100578
Gilles Peskine449bd832023-01-11 14:50:10 +0100579 ECDSA_RS_LEAVE(ver);
Manuel Pégourié-Gonnarda0c5bcc2017-04-21 11:33:57 +0200580
Gilles Peskine449bd832023-01-11 14:50:10 +0100581 return ret;
Manuel Pégourié-Gonnard3aeb5a72013-01-26 18:05:50 +0100582}
583
Manuel Pégourié-Gonnard7c8934e2013-06-27 12:54:02 +0200584/*
Manuel Pégourié-Gonnard32aa4372017-04-21 10:29:13 +0200585 * Verify ECDSA signature of hashed message
586 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100587int mbedtls_ecdsa_verify(mbedtls_ecp_group *grp,
588 const unsigned char *buf, size_t blen,
589 const mbedtls_ecp_point *Q,
590 const mbedtls_mpi *r,
591 const mbedtls_mpi *s)
Manuel Pégourié-Gonnard32aa4372017-04-21 10:29:13 +0200592{
Paul Elliott2ba002c2022-12-09 18:59:26 +0000593 return mbedtls_ecdsa_verify_restartable(grp, buf, blen, Q, r, s, NULL);
Manuel Pégourié-Gonnard32aa4372017-04-21 10:29:13 +0200594}
Ron Eldor936d2842018-11-01 13:05:52 +0200595#endif /* !MBEDTLS_ECDSA_VERIFY_ALT */
Manuel Pégourié-Gonnard32aa4372017-04-21 10:29:13 +0200596
597/*
Manuel Pégourié-Gonnard937340b2014-01-06 10:27:16 +0100598 * Convert a signature (given by context) to ASN.1
Manuel Pégourié-Gonnardb694b482013-08-08 13:30:57 +0200599 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100600static int ecdsa_signature_to_asn1(const mbedtls_mpi *r, const mbedtls_mpi *s,
601 unsigned char *sig, size_t sig_size,
602 size_t *slen)
Manuel Pégourié-Gonnardb694b482013-08-08 13:30:57 +0200603{
Janos Follath24eed8d2019-11-22 13:21:35 +0000604 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
Gilles Peskine449bd832023-01-11 14:50:10 +0100605 unsigned char buf[MBEDTLS_ECDSA_MAX_LEN] = { 0 };
606 unsigned char *p = buf + sizeof(buf);
Manuel Pégourié-Gonnardb694b482013-08-08 13:30:57 +0200607 size_t len = 0;
608
Gilles Peskine449bd832023-01-11 14:50:10 +0100609 MBEDTLS_ASN1_CHK_ADD(len, mbedtls_asn1_write_mpi(&p, buf, s));
610 MBEDTLS_ASN1_CHK_ADD(len, mbedtls_asn1_write_mpi(&p, buf, r));
Manuel Pégourié-Gonnardb694b482013-08-08 13:30:57 +0200611
Gilles Peskine449bd832023-01-11 14:50:10 +0100612 MBEDTLS_ASN1_CHK_ADD(len, mbedtls_asn1_write_len(&p, buf, len));
613 MBEDTLS_ASN1_CHK_ADD(len, mbedtls_asn1_write_tag(&p, buf,
614 MBEDTLS_ASN1_CONSTRUCTED |
615 MBEDTLS_ASN1_SEQUENCE));
Manuel Pégourié-Gonnardb694b482013-08-08 13:30:57 +0200616
Gilles Peskine449bd832023-01-11 14:50:10 +0100617 if (len > sig_size) {
618 return MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL;
619 }
Gilles Peskinef00f1522021-06-22 00:09:00 +0200620
Gilles Peskine449bd832023-01-11 14:50:10 +0100621 memcpy(sig, p, len);
Manuel Pégourié-Gonnardb694b482013-08-08 13:30:57 +0200622 *slen = len;
623
Gilles Peskine449bd832023-01-11 14:50:10 +0100624 return 0;
Manuel Pégourié-Gonnardb694b482013-08-08 13:30:57 +0200625}
626
627/*
Manuel Pégourié-Gonnard937340b2014-01-06 10:27:16 +0100628 * Compute and write signature
629 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100630int mbedtls_ecdsa_write_signature_restartable(mbedtls_ecdsa_context *ctx,
631 mbedtls_md_type_t md_alg,
632 const unsigned char *hash, size_t hlen,
633 unsigned char *sig, size_t sig_size, size_t *slen,
634 int (*f_rng)(void *, unsigned char *, size_t),
635 void *p_rng,
636 mbedtls_ecdsa_restart_ctx *rs_ctx)
Manuel Pégourié-Gonnard937340b2014-01-06 10:27:16 +0100637{
Janos Follath24eed8d2019-11-22 13:21:35 +0000638 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200639 mbedtls_mpi r, s;
Gilles Peskine449bd832023-01-11 14:50:10 +0100640 if (f_rng == NULL) {
641 return MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
642 }
Manuel Pégourié-Gonnard8fce9372015-03-31 13:06:41 +0200643
Gilles Peskine449bd832023-01-11 14:50:10 +0100644 mbedtls_mpi_init(&r);
645 mbedtls_mpi_init(&s);
Manuel Pégourié-Gonnard937340b2014-01-06 10:27:16 +0100646
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200647#if defined(MBEDTLS_ECDSA_DETERMINISTIC)
Paul Elliott2ba002c2022-12-09 18:59:26 +0000648 MBEDTLS_MPI_CHK(mbedtls_ecdsa_sign_det_restartable(&ctx->grp, &r, &s, &ctx->d,
649 hash, hlen, md_alg, f_rng,
650 p_rng, rs_ctx));
Manuel Pégourié-Gonnarddfdcac92015-03-31 11:41:42 +0200651#else
652 (void) md_alg;
653
Ron Eldor8493f802018-11-01 11:32:15 +0200654#if defined(MBEDTLS_ECDSA_SIGN_ALT)
Steven Cooremanfa6641b2021-01-11 17:11:39 +0100655 (void) rs_ctx;
656
Gilles Peskine449bd832023-01-11 14:50:10 +0100657 MBEDTLS_MPI_CHK(mbedtls_ecdsa_sign(&ctx->grp, &r, &s, &ctx->d,
658 hash, hlen, f_rng, p_rng));
Ron Eldor8493f802018-11-01 11:32:15 +0200659#else
Janos Follathdca667a2019-01-04 14:32:30 +0000660 /* Use the same RNG for both blinding and ephemeral key generation */
Paul Elliott2ba002c2022-12-09 18:59:26 +0000661 MBEDTLS_MPI_CHK(mbedtls_ecdsa_sign_restartable(&ctx->grp, &r, &s, &ctx->d,
662 hash, hlen, f_rng, p_rng, f_rng,
663 p_rng, rs_ctx));
Ron Eldor936d2842018-11-01 13:05:52 +0200664#endif /* MBEDTLS_ECDSA_SIGN_ALT */
Ron Eldor5ed8c1e2018-11-05 14:04:26 +0200665#endif /* MBEDTLS_ECDSA_DETERMINISTIC */
Manuel Pégourié-Gonnard937340b2014-01-06 10:27:16 +0100666
Gilles Peskine449bd832023-01-11 14:50:10 +0100667 MBEDTLS_MPI_CHK(ecdsa_signature_to_asn1(&r, &s, sig, sig_size, slen));
Manuel Pégourié-Gonnard8fce9372015-03-31 13:06:41 +0200668
669cleanup:
Gilles Peskine449bd832023-01-11 14:50:10 +0100670 mbedtls_mpi_free(&r);
671 mbedtls_mpi_free(&s);
Manuel Pégourié-Gonnard8fce9372015-03-31 13:06:41 +0200672
Gilles Peskine449bd832023-01-11 14:50:10 +0100673 return ret;
Manuel Pégourié-Gonnard937340b2014-01-06 10:27:16 +0100674}
675
Manuel Pégourié-Gonnardaddb10e2017-04-21 12:54:46 +0200676/*
677 * Compute and write signature
678 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100679int mbedtls_ecdsa_write_signature(mbedtls_ecdsa_context *ctx,
680 mbedtls_md_type_t md_alg,
681 const unsigned char *hash, size_t hlen,
682 unsigned char *sig, size_t sig_size, size_t *slen,
683 int (*f_rng)(void *, unsigned char *, size_t),
684 void *p_rng)
Manuel Pégourié-Gonnardaddb10e2017-04-21 12:54:46 +0200685{
Gilles Peskine449bd832023-01-11 14:50:10 +0100686 return mbedtls_ecdsa_write_signature_restartable(
687 ctx, md_alg, hash, hlen, sig, sig_size, slen,
688 f_rng, p_rng, NULL);
Manuel Pégourié-Gonnardaddb10e2017-04-21 12:54:46 +0200689}
690
Manuel Pégourié-Gonnard937340b2014-01-06 10:27:16 +0100691/*
Manuel Pégourié-Gonnardb694b482013-08-08 13:30:57 +0200692 * Read and check signature
693 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100694int mbedtls_ecdsa_read_signature(mbedtls_ecdsa_context *ctx,
695 const unsigned char *hash, size_t hlen,
696 const unsigned char *sig, size_t slen)
Manuel Pégourié-Gonnardb694b482013-08-08 13:30:57 +0200697{
Gilles Peskine449bd832023-01-11 14:50:10 +0100698 return mbedtls_ecdsa_read_signature_restartable(
699 ctx, hash, hlen, sig, slen, NULL);
Manuel Pégourié-Gonnard32aa4372017-04-21 10:29:13 +0200700}
701
702/*
703 * Restartable read and check signature
704 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100705int mbedtls_ecdsa_read_signature_restartable(mbedtls_ecdsa_context *ctx,
706 const unsigned char *hash, size_t hlen,
707 const unsigned char *sig, size_t slen,
708 mbedtls_ecdsa_restart_ctx *rs_ctx)
Manuel Pégourié-Gonnard32aa4372017-04-21 10:29:13 +0200709{
Janos Follath24eed8d2019-11-22 13:21:35 +0000710 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
Manuel Pégourié-Gonnardb694b482013-08-08 13:30:57 +0200711 unsigned char *p = (unsigned char *) sig;
712 const unsigned char *end = sig + slen;
713 size_t len;
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200714 mbedtls_mpi r, s;
Gilles Peskine449bd832023-01-11 14:50:10 +0100715 mbedtls_mpi_init(&r);
716 mbedtls_mpi_init(&s);
Manuel Pégourié-Gonnardb694b482013-08-08 13:30:57 +0200717
Gilles Peskine449bd832023-01-11 14:50:10 +0100718 if ((ret = mbedtls_asn1_get_tag(&p, end, &len,
719 MBEDTLS_ASN1_CONSTRUCTED | MBEDTLS_ASN1_SEQUENCE)) != 0) {
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200720 ret += MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
Manuel Pégourié-Gonnard8fce9372015-03-31 13:06:41 +0200721 goto cleanup;
Manuel Pégourié-Gonnardb694b482013-08-08 13:30:57 +0200722 }
723
Gilles Peskine449bd832023-01-11 14:50:10 +0100724 if (p + len != end) {
725 ret = MBEDTLS_ERROR_ADD(MBEDTLS_ERR_ECP_BAD_INPUT_DATA,
726 MBEDTLS_ERR_ASN1_LENGTH_MISMATCH);
Manuel Pégourié-Gonnard8fce9372015-03-31 13:06:41 +0200727 goto cleanup;
728 }
Manuel Pégourié-Gonnardb694b482013-08-08 13:30:57 +0200729
Gilles Peskine449bd832023-01-11 14:50:10 +0100730 if ((ret = mbedtls_asn1_get_mpi(&p, end, &r)) != 0 ||
731 (ret = mbedtls_asn1_get_mpi(&p, end, &s)) != 0) {
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200732 ret += MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
Manuel Pégourié-Gonnard8fce9372015-03-31 13:06:41 +0200733 goto cleanup;
734 }
Ron Eldor8493f802018-11-01 11:32:15 +0200735#if defined(MBEDTLS_ECDSA_VERIFY_ALT)
Steven Cooremanfa6641b2021-01-11 17:11:39 +0100736 (void) rs_ctx;
737
Gilles Peskine449bd832023-01-11 14:50:10 +0100738 if ((ret = mbedtls_ecdsa_verify(&ctx->grp, hash, hlen,
739 &ctx->Q, &r, &s)) != 0) {
Ron Eldor8493f802018-11-01 11:32:15 +0200740 goto cleanup;
Gilles Peskine449bd832023-01-11 14:50:10 +0100741 }
Ron Eldor8493f802018-11-01 11:32:15 +0200742#else
Paul Elliott2ba002c2022-12-09 18:59:26 +0000743 if ((ret = mbedtls_ecdsa_verify_restartable(&ctx->grp, hash, hlen,
744 &ctx->Q, &r, &s, rs_ctx)) != 0) {
Manuel Pégourié-Gonnard8fce9372015-03-31 13:06:41 +0200745 goto cleanup;
Gilles Peskine449bd832023-01-11 14:50:10 +0100746 }
Ron Eldor936d2842018-11-01 13:05:52 +0200747#endif /* MBEDTLS_ECDSA_VERIFY_ALT */
Manuel Pégourié-Gonnardb694b482013-08-08 13:30:57 +0200748
Gilles Peskine5114d3e2018-03-30 07:12:15 +0200749 /* At this point we know that the buffer starts with a valid signature.
750 * Return 0 if the buffer just contains the signature, and a specific
751 * error code if the valid signature is followed by more data. */
Gilles Peskine449bd832023-01-11 14:50:10 +0100752 if (p != end) {
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200753 ret = MBEDTLS_ERR_ECP_SIG_LEN_MISMATCH;
Gilles Peskine449bd832023-01-11 14:50:10 +0100754 }
Manuel Pégourié-Gonnard35e95dd2014-04-08 12:17:41 +0200755
Manuel Pégourié-Gonnard8fce9372015-03-31 13:06:41 +0200756cleanup:
Gilles Peskine449bd832023-01-11 14:50:10 +0100757 mbedtls_mpi_free(&r);
758 mbedtls_mpi_free(&s);
Manuel Pégourié-Gonnard8fce9372015-03-31 13:06:41 +0200759
Gilles Peskine449bd832023-01-11 14:50:10 +0100760 return ret;
Manuel Pégourié-Gonnardb694b482013-08-08 13:30:57 +0200761}
762
Ron Eldor314adb62017-10-10 18:28:25 +0300763#if !defined(MBEDTLS_ECDSA_GENKEY_ALT)
Manuel Pégourié-Gonnardb694b482013-08-08 13:30:57 +0200764/*
Manuel Pégourié-Gonnard8eebd012013-08-09 16:21:34 +0200765 * Generate key pair
766 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100767int mbedtls_ecdsa_genkey(mbedtls_ecdsa_context *ctx, mbedtls_ecp_group_id gid,
768 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng)
Manuel Pégourié-Gonnard8eebd012013-08-09 16:21:34 +0200769{
Ron Eldoradb52342018-12-17 10:06:12 +0200770 int ret = 0;
Gilles Peskine449bd832023-01-11 14:50:10 +0100771 ret = mbedtls_ecp_group_load(&ctx->grp, gid);
772 if (ret != 0) {
773 return ret;
774 }
Ron Eldoradb52342018-12-17 10:06:12 +0200775
Gilles Peskine449bd832023-01-11 14:50:10 +0100776 return mbedtls_ecp_gen_keypair(&ctx->grp, &ctx->d,
777 &ctx->Q, f_rng, p_rng);
Manuel Pégourié-Gonnard8eebd012013-08-09 16:21:34 +0200778}
Ron Eldor936d2842018-11-01 13:05:52 +0200779#endif /* !MBEDTLS_ECDSA_GENKEY_ALT */
Manuel Pégourié-Gonnard8eebd012013-08-09 16:21:34 +0200780
Manuel Pégourié-Gonnardf4999932013-08-12 17:02:59 +0200781/*
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200782 * Set context from an mbedtls_ecp_keypair
Manuel Pégourié-Gonnardf4999932013-08-12 17:02:59 +0200783 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100784int mbedtls_ecdsa_from_keypair(mbedtls_ecdsa_context *ctx, const mbedtls_ecp_keypair *key)
Manuel Pégourié-Gonnardf4999932013-08-12 17:02:59 +0200785{
Janos Follath24eed8d2019-11-22 13:21:35 +0000786 int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
Gilles Peskine449bd832023-01-11 14:50:10 +0100787 if ((ret = mbedtls_ecp_group_copy(&ctx->grp, &key->grp)) != 0 ||
788 (ret = mbedtls_mpi_copy(&ctx->d, &key->d)) != 0 ||
789 (ret = mbedtls_ecp_copy(&ctx->Q, &key->Q)) != 0) {
790 mbedtls_ecdsa_free(ctx);
Manuel Pégourié-Gonnard1001e322013-10-27 14:53:48 +0100791 }
Manuel Pégourié-Gonnardf4999932013-08-12 17:02:59 +0200792
Gilles Peskine449bd832023-01-11 14:50:10 +0100793 return ret;
Manuel Pégourié-Gonnardf4999932013-08-12 17:02:59 +0200794}
Manuel Pégourié-Gonnard8eebd012013-08-09 16:21:34 +0200795
796/*
Manuel Pégourié-Gonnard7c8934e2013-06-27 12:54:02 +0200797 * Initialize context
798 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100799void mbedtls_ecdsa_init(mbedtls_ecdsa_context *ctx)
Manuel Pégourié-Gonnard7c8934e2013-06-27 12:54:02 +0200800{
Gilles Peskine449bd832023-01-11 14:50:10 +0100801 mbedtls_ecp_keypair_init(ctx);
Manuel Pégourié-Gonnard7c8934e2013-06-27 12:54:02 +0200802}
803
804/*
805 * Free context
806 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100807void mbedtls_ecdsa_free(mbedtls_ecdsa_context *ctx)
Manuel Pégourié-Gonnard7c8934e2013-06-27 12:54:02 +0200808{
Gilles Peskine449bd832023-01-11 14:50:10 +0100809 if (ctx == NULL) {
Hanno Becker319ae112018-12-14 16:43:29 +0000810 return;
Gilles Peskine449bd832023-01-11 14:50:10 +0100811 }
Hanno Becker319ae112018-12-14 16:43:29 +0000812
Gilles Peskine449bd832023-01-11 14:50:10 +0100813 mbedtls_ecp_keypair_free(ctx);
Manuel Pégourié-Gonnard7c8934e2013-06-27 12:54:02 +0200814}
Manuel Pégourié-Gonnard3aeb5a72013-01-26 18:05:50 +0100815
Manuel Pégourié-Gonnard32aa4372017-04-21 10:29:13 +0200816#if defined(MBEDTLS_ECP_RESTARTABLE)
817/*
818 * Initialize a restart context
819 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100820void mbedtls_ecdsa_restart_init(mbedtls_ecdsa_restart_ctx *ctx)
Manuel Pégourié-Gonnard32aa4372017-04-21 10:29:13 +0200821{
Gilles Peskine449bd832023-01-11 14:50:10 +0100822 mbedtls_ecp_restart_init(&ctx->ecp);
Manuel Pégourié-Gonnarda0c5bcc2017-04-21 11:33:57 +0200823
824 ctx->ver = NULL;
Manuel Pégourié-Gonnardb90883d2017-04-25 11:33:10 +0200825 ctx->sig = NULL;
826#if defined(MBEDTLS_ECDSA_DETERMINISTIC)
827 ctx->det = NULL;
828#endif
Manuel Pégourié-Gonnard32aa4372017-04-21 10:29:13 +0200829}
830
831/*
832 * Free the components of a restart context
833 */
Gilles Peskine449bd832023-01-11 14:50:10 +0100834void mbedtls_ecdsa_restart_free(mbedtls_ecdsa_restart_ctx *ctx)
Manuel Pégourié-Gonnard32aa4372017-04-21 10:29:13 +0200835{
Gilles Peskine449bd832023-01-11 14:50:10 +0100836 if (ctx == NULL) {
Hanno Becker319ae112018-12-14 16:43:29 +0000837 return;
Gilles Peskine449bd832023-01-11 14:50:10 +0100838 }
Hanno Becker319ae112018-12-14 16:43:29 +0000839
Gilles Peskine449bd832023-01-11 14:50:10 +0100840 mbedtls_ecp_restart_free(&ctx->ecp);
Manuel Pégourié-Gonnarda0c5bcc2017-04-21 11:33:57 +0200841
Gilles Peskine449bd832023-01-11 14:50:10 +0100842 ecdsa_restart_ver_free(ctx->ver);
843 mbedtls_free(ctx->ver);
Manuel Pégourié-Gonnarda0c5bcc2017-04-21 11:33:57 +0200844 ctx->ver = NULL;
Manuel Pégourié-Gonnardb90883d2017-04-25 11:33:10 +0200845
Gilles Peskine449bd832023-01-11 14:50:10 +0100846 ecdsa_restart_sig_free(ctx->sig);
847 mbedtls_free(ctx->sig);
Manuel Pégourié-Gonnardb90883d2017-04-25 11:33:10 +0200848 ctx->sig = NULL;
849
850#if defined(MBEDTLS_ECDSA_DETERMINISTIC)
Gilles Peskine449bd832023-01-11 14:50:10 +0100851 ecdsa_restart_det_free(ctx->det);
852 mbedtls_free(ctx->det);
Manuel Pégourié-Gonnardb90883d2017-04-25 11:33:10 +0200853 ctx->det = NULL;
854#endif
Manuel Pégourié-Gonnard32aa4372017-04-21 10:29:13 +0200855}
856#endif /* MBEDTLS_ECP_RESTARTABLE */
857
Manuel Pégourié-Gonnard2cf5a7c2015-04-08 12:49:31 +0200858#endif /* MBEDTLS_ECDSA_C */