mbedtls/library/ecdsa.c

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/*
* Elliptic curve DSA
*
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* Copyright (C) 2006-2015, ARM Limited, All Rights Reserved
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* SPDX-License-Identifier: Apache-2.0
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*
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* Licensed under the Apache License, Version 2.0 (the "License"); you may
* not use this file except in compliance with the License.
* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
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*
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* This file is part of mbed TLS (https://tls.mbed.org)
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*/
/*
* References:
*
* SEC1 http://www.secg.org/index.php?action=secg,docs_secg
*/
#if !defined(MBEDTLS_CONFIG_FILE)
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#include "mbedtls/config.h"
#else
#include MBEDTLS_CONFIG_FILE
#endif
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#if defined(MBEDTLS_ECDSA_C)
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#include "mbedtls/ecdsa.h"
#include "mbedtls/asn1write.h"
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#include <string.h>
#if defined(MBEDTLS_ECDSA_DETERMINISTIC)
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#include "mbedtls/hmac_drbg.h"
#endif
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/*
* Derive a suitable integer for group grp from a buffer of length len
* SEC1 4.1.3 step 5 aka SEC1 4.1.4 step 3
*/
static int derive_mpi( const mbedtls_ecp_group *grp, mbedtls_mpi *x,
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const unsigned char *buf, size_t blen )
{
int ret;
size_t n_size = ( grp->nbits + 7 ) / 8;
size_t use_size = blen > n_size ? n_size : blen;
MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( x, buf, use_size ) );
if( use_size * 8 > grp->nbits )
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( x, use_size * 8 - grp->nbits ) );
/* While at it, reduce modulo N */
if( mbedtls_mpi_cmp_mpi( x, &grp->N ) >= 0 )
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( x, x, &grp->N ) );
cleanup:
return( ret );
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}
#if !defined(MBEDTLS_ECDSA_SIGN_ALT)
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/*
* Compute ECDSA signature of a hashed message (SEC1 4.1.3)
* Obviously, compared to SEC1 4.1.3, we skip step 4 (hash message)
*/
static int ecdsa_sign_internal( mbedtls_ecp_group *grp, mbedtls_mpi *r,
mbedtls_mpi *s, const mbedtls_mpi *d,
const unsigned char *buf, size_t blen,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng,
int (*f_rng_blind)(void *, unsigned char *,
size_t),
void *p_rng_blind )
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{
int ret, key_tries, sign_tries, blind_tries;
mbedtls_ecp_point R;
mbedtls_mpi k, e, t;
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/* Fail cleanly on curves such as Curve25519 that can't be used for ECDSA */
if( grp->N.p == NULL )
return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
/* Make sure d is in range 1..n-1 */
if( mbedtls_mpi_cmp_int( d, 1 ) < 0 || mbedtls_mpi_cmp_mpi( d, &grp->N ) >= 0 )
return( MBEDTLS_ERR_ECP_INVALID_KEY );
mbedtls_ecp_point_init( &R );
mbedtls_mpi_init( &k ); mbedtls_mpi_init( &e ); mbedtls_mpi_init( &t );
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sign_tries = 0;
do
{
/*
* Steps 1-3: generate a suitable ephemeral keypair
* and set r = xR mod n
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*/
key_tries = 0;
do
{
MBEDTLS_MPI_CHK( mbedtls_ecp_gen_privkey( grp, &k, f_rng, p_rng ) );
MBEDTLS_MPI_CHK( mbedtls_ecp_mul( grp, &R, &k, &grp->G,
f_rng_blind, p_rng_blind ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( r, &R.X, &grp->N ) );
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if( key_tries++ > 10 )
{
ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
goto cleanup;
}
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}
while( mbedtls_mpi_cmp_int( r, 0 ) == 0 );
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/*
* Step 5: derive MPI from hashed message
*/
MBEDTLS_MPI_CHK( derive_mpi( grp, &e, buf, blen ) );
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/*
* Generate a random value to blind inv_mod in next step,
* avoiding a potential timing leak.
*/
blind_tries = 0;
do
{
size_t n_size = ( grp->nbits + 7 ) / 8;
MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &t, n_size, f_rng_blind,
p_rng_blind ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &t, 8 * n_size - grp->nbits ) );
/* See mbedtls_ecp_gen_keypair() */
if( ++blind_tries > 30 )
return( MBEDTLS_ERR_ECP_RANDOM_FAILED );
}
while( mbedtls_mpi_cmp_int( &t, 1 ) < 0 ||
mbedtls_mpi_cmp_mpi( &t, &grp->N ) >= 0 );
/*
* Step 6: compute s = (e + r * d) / k = t (e + rd) / (kt) mod n
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*/
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( s, r, d ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &e, &e, s ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &e, &e, &t ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &k, &k, &t ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( s, &k, &grp->N ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( s, s, &e ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( s, s, &grp->N ) );
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if( sign_tries++ > 10 )
{
ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
goto cleanup;
}
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}
while( mbedtls_mpi_cmp_int( s, 0 ) == 0 );
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cleanup:
mbedtls_ecp_point_free( &R );
mbedtls_mpi_free( &k ); mbedtls_mpi_free( &e ); mbedtls_mpi_free( &t );
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return( ret );
}
int mbedtls_ecdsa_sign( mbedtls_ecp_group *grp, mbedtls_mpi *r, mbedtls_mpi *s,
const mbedtls_mpi *d, const unsigned char *buf,
size_t blen,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng )
{
/* Use the same RNG for both blinding and ephemeral key generation */
return( ecdsa_sign_internal( grp, r, s, d, buf, blen, f_rng, p_rng,
f_rng, p_rng ) );
}
#endif /* MBEDTLS_ECDSA_SIGN_ALT */
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#if defined(MBEDTLS_ECDSA_DETERMINISTIC)
static int ecdsa_sign_det_internal( mbedtls_ecp_group *grp, mbedtls_mpi *r,
mbedtls_mpi *s, const mbedtls_mpi *d,
const unsigned char *buf, size_t blen,
mbedtls_md_type_t md_alg,
int (*f_rng_blind)(void *, unsigned char *,
size_t),
void *p_rng_blind )
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{
int ret;
mbedtls_hmac_drbg_context rng_ctx;
unsigned char data[2 * MBEDTLS_ECP_MAX_BYTES];
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size_t grp_len = ( grp->nbits + 7 ) / 8;
const mbedtls_md_info_t *md_info;
mbedtls_mpi h;
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if( ( md_info = mbedtls_md_info_from_type( md_alg ) ) == NULL )
return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
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mbedtls_mpi_init( &h );
mbedtls_hmac_drbg_init( &rng_ctx );
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/* Use private key and message hash (reduced) to initialize HMAC_DRBG */
MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( d, data, grp_len ) );
MBEDTLS_MPI_CHK( derive_mpi( grp, &h, buf, blen ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &h, data + grp_len, grp_len ) );
mbedtls_hmac_drbg_seed_buf( &rng_ctx, md_info, data, 2 * grp_len );
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if( f_rng_blind != NULL )
ret = ecdsa_sign_internal( grp, r, s, d, buf, blen,
mbedtls_hmac_drbg_random, &rng_ctx,
f_rng_blind, p_rng_blind );
else
/*
* Use the same RNG for both blinding and ephemeral key generation.
* Since the RNG output is always the same for the same key and message,
* this limits the efficiency of blinding and leaks information through
* side channels.
*/
ret = ecdsa_sign_internal( grp, r, s, d, buf, blen,
mbedtls_hmac_drbg_random, &rng_ctx,
mbedtls_hmac_drbg_random, &rng_ctx );
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cleanup:
mbedtls_hmac_drbg_free( &rng_ctx );
mbedtls_mpi_free( &h );
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return( ret );
}
/*
* Deterministic signature wrappers
*/
int mbedtls_ecdsa_sign_det( mbedtls_ecp_group *grp, mbedtls_mpi *r,
mbedtls_mpi *s, const mbedtls_mpi *d,
const unsigned char *buf, size_t blen,
mbedtls_md_type_t md_alg )
{
return( ecdsa_sign_det_internal( grp, r, s, d, buf, blen, md_alg,
NULL, NULL ) );
}
int mbedtls_ecdsa_sign_det_ext( mbedtls_ecp_group *grp, mbedtls_mpi *r,
mbedtls_mpi *s, const mbedtls_mpi *d,
const unsigned char *buf, size_t blen,
mbedtls_md_type_t md_alg,
int (*f_rng_blind)(void *, unsigned char *,
size_t),
void *p_rng_blind )
{
return( ecdsa_sign_det_internal( grp, r, s, d, buf, blen, md_alg,
f_rng_blind, p_rng_blind ) );
}
#endif /* MBEDTLS_ECDSA_DETERMINISTIC */
#if !defined(MBEDTLS_ECDSA_VERIFY_ALT)
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/*
* Verify ECDSA signature of hashed message (SEC1 4.1.4)
* Obviously, compared to SEC1 4.1.3, we skip step 2 (hash message)
*/
int mbedtls_ecdsa_verify( mbedtls_ecp_group *grp,
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const unsigned char *buf, size_t blen,
const mbedtls_ecp_point *Q, const mbedtls_mpi *r, const mbedtls_mpi *s)
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{
int ret;
mbedtls_mpi e, s_inv, u1, u2;
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mbedtls_ecp_point R;
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mbedtls_ecp_point_init( &R );
mbedtls_mpi_init( &e ); mbedtls_mpi_init( &s_inv ); mbedtls_mpi_init( &u1 ); mbedtls_mpi_init( &u2 );
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/* Fail cleanly on curves such as Curve25519 that can't be used for ECDSA */
if( grp->N.p == NULL )
return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
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/*
* Step 1: make sure r and s are in range 1..n-1
*/
if( mbedtls_mpi_cmp_int( r, 1 ) < 0 || mbedtls_mpi_cmp_mpi( r, &grp->N ) >= 0 ||
mbedtls_mpi_cmp_int( s, 1 ) < 0 || mbedtls_mpi_cmp_mpi( s, &grp->N ) >= 0 )
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{
ret = MBEDTLS_ERR_ECP_VERIFY_FAILED;
goto cleanup;
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}
/*
* Additional precaution: make sure Q is valid
*/
MBEDTLS_MPI_CHK( mbedtls_ecp_check_pubkey( grp, Q ) );
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/*
* Step 3: derive MPI from hashed message
*/
MBEDTLS_MPI_CHK( derive_mpi( grp, &e, buf, blen ) );
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/*
* Step 4: u1 = e / s mod n, u2 = r / s mod n
*/
MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &s_inv, s, &grp->N ) );
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MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &u1, &e, &s_inv ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &u1, &u1, &grp->N ) );
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MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &u2, r, &s_inv ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &u2, &u2, &grp->N ) );
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/*
* Step 5: R = u1 G + u2 Q
*
* Since we're not using any secret data, no need to pass a RNG to
* mbedtls_ecp_mul() for countermesures.
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*/
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MBEDTLS_MPI_CHK( mbedtls_ecp_muladd( grp, &R, &u1, &grp->G, &u2, Q ) );
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if( mbedtls_ecp_is_zero( &R ) )
{
ret = MBEDTLS_ERR_ECP_VERIFY_FAILED;
goto cleanup;
}
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/*
* Step 6: convert xR to an integer (no-op)
* Step 7: reduce xR mod n (gives v)
*/
MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &R.X, &R.X, &grp->N ) );
/*
* Step 8: check if v (that is, R.X) is equal to r
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*/
if( mbedtls_mpi_cmp_mpi( &R.X, r ) != 0 )
{
ret = MBEDTLS_ERR_ECP_VERIFY_FAILED;
goto cleanup;
}
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cleanup:
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mbedtls_ecp_point_free( &R );
mbedtls_mpi_free( &e ); mbedtls_mpi_free( &s_inv ); mbedtls_mpi_free( &u1 ); mbedtls_mpi_free( &u2 );
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return( ret );
}
#endif /* MBEDTLS_ECDSA_VERIFY_ALT */
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/*
* Convert a signature (given by context) to ASN.1
*/
static int ecdsa_signature_to_asn1( const mbedtls_mpi *r, const mbedtls_mpi *s,
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unsigned char *sig, size_t *slen )
{
int ret;
unsigned char buf[MBEDTLS_ECDSA_MAX_LEN];
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unsigned char *p = buf + sizeof( buf );
size_t len = 0;
MBEDTLS_ASN1_CHK_ADD( len, mbedtls_asn1_write_mpi( &p, buf, s ) );
MBEDTLS_ASN1_CHK_ADD( len, mbedtls_asn1_write_mpi( &p, buf, r ) );
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MBEDTLS_ASN1_CHK_ADD( len, mbedtls_asn1_write_len( &p, buf, len ) );
MBEDTLS_ASN1_CHK_ADD( len, mbedtls_asn1_write_tag( &p, buf,
MBEDTLS_ASN1_CONSTRUCTED | MBEDTLS_ASN1_SEQUENCE ) );
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memcpy( sig, p, len );
*slen = len;
return( 0 );
}
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/*
* Compute and write signature
*/
int mbedtls_ecdsa_write_signature( mbedtls_ecdsa_context *ctx, mbedtls_md_type_t md_alg,
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const unsigned char *hash, size_t hlen,
unsigned char *sig, size_t *slen,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng )
{
int ret;
mbedtls_mpi r, s;
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mbedtls_mpi_init( &r );
mbedtls_mpi_init( &s );
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#if defined(MBEDTLS_ECDSA_DETERMINISTIC)
MBEDTLS_MPI_CHK( ecdsa_sign_det_internal( &ctx->grp, &r, &s, &ctx->d,
hash, hlen, md_alg,
f_rng, p_rng ) );
#else
(void) md_alg;
MBEDTLS_MPI_CHK( mbedtls_ecdsa_sign( &ctx->grp, &r, &s, &ctx->d,
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hash, hlen, f_rng, p_rng ) );
#endif /* MBEDTLS_ECDSA_DETERMINISTIC */
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MBEDTLS_MPI_CHK( ecdsa_signature_to_asn1( &r, &s, sig, slen ) );
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cleanup:
mbedtls_mpi_free( &r );
mbedtls_mpi_free( &s );
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return( ret );
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}
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#if ! defined(MBEDTLS_DEPRECATED_REMOVED) && \
defined(MBEDTLS_ECDSA_DETERMINISTIC)
int mbedtls_ecdsa_write_signature_det( mbedtls_ecdsa_context *ctx,
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const unsigned char *hash, size_t hlen,
unsigned char *sig, size_t *slen,
mbedtls_md_type_t md_alg )
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{
return( mbedtls_ecdsa_write_signature( ctx, md_alg, hash, hlen, sig, slen,
NULL, NULL ) );
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}
#endif
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/*
* Read and check signature
*/
int mbedtls_ecdsa_read_signature( mbedtls_ecdsa_context *ctx,
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const unsigned char *hash, size_t hlen,
const unsigned char *sig, size_t slen )
{
int ret;
unsigned char *p = (unsigned char *) sig;
const unsigned char *end = sig + slen;
size_t len;
mbedtls_mpi r, s;
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mbedtls_mpi_init( &r );
mbedtls_mpi_init( &s );
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if( ( ret = mbedtls_asn1_get_tag( &p, end, &len,
MBEDTLS_ASN1_CONSTRUCTED | MBEDTLS_ASN1_SEQUENCE ) ) != 0 )
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{
ret += MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
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goto cleanup;
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}
if( p + len != end )
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{
ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA +
MBEDTLS_ERR_ASN1_LENGTH_MISMATCH;
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goto cleanup;
}
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if( ( ret = mbedtls_asn1_get_mpi( &p, end, &r ) ) != 0 ||
( ret = mbedtls_asn1_get_mpi( &p, end, &s ) ) != 0 )
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{
ret += MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
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goto cleanup;
}
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if( ( ret = mbedtls_ecdsa_verify( &ctx->grp, hash, hlen,
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&ctx->Q, &r, &s ) ) != 0 )
goto cleanup;
/* At this point we know that the buffer starts with a valid signature.
* Return 0 if the buffer just contains the signature, and a specific
* error code if the valid signature is followed by more data. */
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if( p != end )
ret = MBEDTLS_ERR_ECP_SIG_LEN_MISMATCH;
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cleanup:
mbedtls_mpi_free( &r );
mbedtls_mpi_free( &s );
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return( ret );
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}
#if !defined(MBEDTLS_ECDSA_GENKEY_ALT)
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/*
* Generate key pair
*/
int mbedtls_ecdsa_genkey( mbedtls_ecdsa_context *ctx, mbedtls_ecp_group_id gid,
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int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
{
return( mbedtls_ecp_group_load( &ctx->grp, gid ) ||
mbedtls_ecp_gen_keypair( &ctx->grp, &ctx->d, &ctx->Q, f_rng, p_rng ) );
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}
#endif /* MBEDTLS_ECDSA_GENKEY_ALT */
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/*
* Set context from an mbedtls_ecp_keypair
*/
int mbedtls_ecdsa_from_keypair( mbedtls_ecdsa_context *ctx, const mbedtls_ecp_keypair *key )
{
int ret;
if( ( ret = mbedtls_ecp_group_copy( &ctx->grp, &key->grp ) ) != 0 ||
( ret = mbedtls_mpi_copy( &ctx->d, &key->d ) ) != 0 ||
( ret = mbedtls_ecp_copy( &ctx->Q, &key->Q ) ) != 0 )
{
mbedtls_ecdsa_free( ctx );
}
return( ret );
}
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/*
* Initialize context
*/
void mbedtls_ecdsa_init( mbedtls_ecdsa_context *ctx )
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{
mbedtls_ecp_keypair_init( ctx );
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}
/*
* Free context
*/
void mbedtls_ecdsa_free( mbedtls_ecdsa_context *ctx )
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{
mbedtls_ecp_keypair_free( ctx );
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}
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#endif /* MBEDTLS_ECDSA_C */