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mbedtls/library/ecdsa.c

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/*
* Elliptic curve DSA
*
* Copyright (C) 2006-2014, Brainspark B.V.
*
* This file is part of PolarSSL (http://www.polarssl.org)
* Lead Maintainer: Paul Bakker <polarssl_maintainer at polarssl.org>
*
* All rights reserved.
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License along
* with this program; if not, write to the Free Software Foundation, Inc.,
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
*/
/*
* References:
*
* SEC1 http://www.secg.org/index.php?action=secg,docs_secg
*/
#if !defined(POLARSSL_CONFIG_FILE)
#include "polarssl/config.h"
#else
#include POLARSSL_CONFIG_FILE
#endif
#if defined(POLARSSL_ECDSA_C)
#include "polarssl/ecdsa.h"
#include "polarssl/asn1write.h"
#if defined(POLARSSL_ECDSA_DETERMINISTIC)
#include "polarssl/hmac_drbg.h"
#endif
#if defined(POLARSSL_ECDSA_DETERMINISTIC)
/*
* This a hopefully temporary compatibility function.
*
* Since we can't ensure the caller will pass a valid md_alg before the next
* interface change, try to pick up a decent md by size.
*
* Argument is the minimum size in bytes of the MD output.
*/
static const md_info_t *md_info_by_size( size_t min_size )
{
const md_info_t *md_cur, *md_picked = NULL;
const int *md_alg;
for( md_alg = md_list(); *md_alg != 0; md_alg++ )
{
if( ( md_cur = md_info_from_type( *md_alg ) ) == NULL ||
(size_t) md_cur->size < min_size ||
( md_picked != NULL && md_cur->size > md_picked->size ) )
continue;
md_picked = md_cur;
}
return( md_picked );
}
#endif /* POLARSSL_ECDSA_DETERMINISTIC */
/*
* 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 ecp_group *grp, mpi *x,
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;
MPI_CHK( mpi_read_binary( x, buf, use_size ) );
if( use_size * 8 > grp->nbits )
MPI_CHK( mpi_shift_r( x, use_size * 8 - grp->nbits ) );
/* While at it, reduce modulo N */
if( mpi_cmp_mpi( x, &grp->N ) >= 0 )
MPI_CHK( mpi_sub_mpi( x, x, &grp->N ) );
cleanup:
return( ret );
}
/*
* Compute ECDSA signature of a hashed message (SEC1 4.1.3)
* Obviously, compared to SEC1 4.1.3, we skip step 4 (hash message)
*/
int ecdsa_sign( ecp_group *grp, mpi *r, mpi *s,
const mpi *d, const unsigned char *buf, size_t blen,
int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
{
int ret, key_tries, sign_tries, blind_tries;
ecp_point R;
mpi k, e, t;
/* Fail cleanly on curves such as Curve25519 that can't be used for ECDSA */
if( grp->N.p == NULL )
return( POLARSSL_ERR_ECP_BAD_INPUT_DATA );
ecp_point_init( &R );
mpi_init( &k ); mpi_init( &e ); mpi_init( &t );
sign_tries = 0;
do
{
/*
* Steps 1-3: generate a suitable ephemeral keypair
* and set r = xR mod n
*/
key_tries = 0;
do
{
MPI_CHK( ecp_gen_keypair( grp, &k, &R, f_rng, p_rng ) );
MPI_CHK( mpi_mod_mpi( r, &R.X, &grp->N ) );
if( key_tries++ > 10 )
{
ret = POLARSSL_ERR_ECP_RANDOM_FAILED;
goto cleanup;
}
}
while( mpi_cmp_int( r, 0 ) == 0 );
/*
* Step 5: derive MPI from hashed message
*/
MPI_CHK( derive_mpi( grp, &e, buf, blen ) );
/*
* 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;
MPI_CHK( mpi_fill_random( &t, n_size, f_rng, p_rng ) );
MPI_CHK( mpi_shift_r( &t, 8 * n_size - grp->nbits ) );
/* See ecp_gen_keypair() */
if( ++blind_tries > 30 )
return( POLARSSL_ERR_ECP_RANDOM_FAILED );
}
while( mpi_cmp_int( &t, 1 ) < 0 ||
mpi_cmp_mpi( &t, &grp->N ) >= 0 );
/*
* Step 6: compute s = (e + r * d) / k = t (e + rd) / (kt) mod n
*/
MPI_CHK( mpi_mul_mpi( s, r, d ) );
MPI_CHK( mpi_add_mpi( &e, &e, s ) );
MPI_CHK( mpi_mul_mpi( &e, &e, &t ) );
MPI_CHK( mpi_mul_mpi( &k, &k, &t ) );
MPI_CHK( mpi_inv_mod( s, &k, &grp->N ) );
MPI_CHK( mpi_mul_mpi( s, s, &e ) );
MPI_CHK( mpi_mod_mpi( s, s, &grp->N ) );
if( sign_tries++ > 10 )
{
ret = POLARSSL_ERR_ECP_RANDOM_FAILED;
goto cleanup;
}
}
while( mpi_cmp_int( s, 0 ) == 0 );
cleanup:
ecp_point_free( &R );
mpi_free( &k ); mpi_free( &e ); mpi_free( &t );
return( ret );
}
#if defined(POLARSSL_ECDSA_DETERMINISTIC)
/*
* Deterministic signature wrapper
*/
int ecdsa_sign_det( ecp_group *grp, mpi *r, mpi *s,
const mpi *d, const unsigned char *buf, size_t blen,
md_type_t md_alg )
{
int ret;
hmac_drbg_context rng_ctx;
unsigned char data[2 * POLARSSL_ECP_MAX_BYTES];
size_t grp_len = ( grp->nbits + 7 ) / 8;
const md_info_t *md_info;
mpi h;
/* Temporary fallback */
if( md_alg == POLARSSL_MD_NONE )
md_info = md_info_by_size( blen );
else
md_info = md_info_from_type( md_alg );
if( md_info == NULL )
return( POLARSSL_ERR_ECP_BAD_INPUT_DATA );
mpi_init( &h );
memset( &rng_ctx, 0, sizeof( hmac_drbg_context ) );
/* Use private key and message hash (reduced) to initialize HMAC_DRBG */
MPI_CHK( mpi_write_binary( d, data, grp_len ) );
MPI_CHK( derive_mpi( grp, &h, buf, blen ) );
MPI_CHK( mpi_write_binary( &h, data + grp_len, grp_len ) );
hmac_drbg_init_buf( &rng_ctx, md_info, data, 2 * grp_len );
ret = ecdsa_sign( grp, r, s, d, buf, blen,
hmac_drbg_random, &rng_ctx );
cleanup:
hmac_drbg_free( &rng_ctx );
mpi_free( &h );
return( ret );
}
#endif /* POLARSSL_ECDSA_DETERMINISTIC */
/*
* Verify ECDSA signature of hashed message (SEC1 4.1.4)
* Obviously, compared to SEC1 4.1.3, we skip step 2 (hash message)
*/
int ecdsa_verify( ecp_group *grp,
const unsigned char *buf, size_t blen,
const ecp_point *Q, const mpi *r, const mpi *s)
{
int ret;
mpi e, s_inv, u1, u2;
ecp_point R, P;
ecp_point_init( &R ); ecp_point_init( &P );
mpi_init( &e ); mpi_init( &s_inv ); mpi_init( &u1 ); mpi_init( &u2 );
/* Fail cleanly on curves such as Curve25519 that can't be used for ECDSA */
if( grp->N.p == NULL )
return( POLARSSL_ERR_ECP_BAD_INPUT_DATA );
/*
* Step 1: make sure r and s are in range 1..n-1
*/
if( mpi_cmp_int( r, 1 ) < 0 || mpi_cmp_mpi( r, &grp->N ) >= 0 ||
mpi_cmp_int( s, 1 ) < 0 || mpi_cmp_mpi( s, &grp->N ) >= 0 )
{
ret = POLARSSL_ERR_ECP_VERIFY_FAILED;
goto cleanup;
}
/*
* Additional precaution: make sure Q is valid
*/
MPI_CHK( ecp_check_pubkey( grp, Q ) );
/*
* Step 3: derive MPI from hashed message
*/
MPI_CHK( derive_mpi( grp, &e, buf, blen ) );
/*
* Step 4: u1 = e / s mod n, u2 = r / s mod n
*/
MPI_CHK( mpi_inv_mod( &s_inv, s, &grp->N ) );
MPI_CHK( mpi_mul_mpi( &u1, &e, &s_inv ) );
MPI_CHK( mpi_mod_mpi( &u1, &u1, &grp->N ) );
MPI_CHK( mpi_mul_mpi( &u2, r, &s_inv ) );
MPI_CHK( mpi_mod_mpi( &u2, &u2, &grp->N ) );
/*
* Step 5: R = u1 G + u2 Q
*
* Since we're not using any secret data, no need to pass a RNG to
* ecp_mul() for countermesures.
*/
MPI_CHK( ecp_mul( grp, &R, &u1, &grp->G, NULL, NULL ) );
MPI_CHK( ecp_mul( grp, &P, &u2, Q, NULL, NULL ) );
MPI_CHK( ecp_add( grp, &R, &R, &P ) );
if( ecp_is_zero( &R ) )
{
ret = POLARSSL_ERR_ECP_VERIFY_FAILED;
goto cleanup;
}
/*
* Step 6: convert xR to an integer (no-op)
* Step 7: reduce xR mod n (gives v)
*/
MPI_CHK( mpi_mod_mpi( &R.X, &R.X, &grp->N ) );
/*
* Step 8: check if v (that is, R.X) is equal to r
*/
if( mpi_cmp_mpi( &R.X, r ) != 0 )
{
ret = POLARSSL_ERR_ECP_VERIFY_FAILED;
goto cleanup;
}
cleanup:
ecp_point_free( &R ); ecp_point_free( &P );
mpi_free( &e ); mpi_free( &s_inv ); mpi_free( &u1 ); mpi_free( &u2 );
return( ret );
}
/*
* RFC 4492 page 20:
*
* Ecdsa-Sig-Value ::= SEQUENCE {
* r INTEGER,
* s INTEGER
* }
*
* Size is at most
* 1 (tag) + 1 (len) + 1 (initial 0) + ECP_MAX_BYTES for each of r and s,
* twice that + 1 (tag) + 2 (len) for the sequence
* (assuming ECP_MAX_BYTES is less than 126 for r and s,
* and less than 124 (total len <= 255) for the sequence)
*/
#if POLARSSL_ECP_MAX_BYTES > 124
#error "POLARSSL_ECP_MAX_BYTES bigger than expected, please fix MAX_SIG_LEN"
#endif
#define MAX_SIG_LEN ( 3 + 2 * ( 2 + POLARSSL_ECP_MAX_BYTES ) )
/*
* Convert a signature (given by context) to ASN.1
*/
static int ecdsa_signature_to_asn1( ecdsa_context *ctx,
unsigned char *sig, size_t *slen )
{
int ret;
unsigned char buf[MAX_SIG_LEN];
unsigned char *p = buf + sizeof( buf );
size_t len = 0;
ASN1_CHK_ADD( len, asn1_write_mpi( &p, buf, &ctx->s ) );
ASN1_CHK_ADD( len, asn1_write_mpi( &p, buf, &ctx->r ) );
ASN1_CHK_ADD( len, asn1_write_len( &p, buf, len ) );
ASN1_CHK_ADD( len, asn1_write_tag( &p, buf,
ASN1_CONSTRUCTED | ASN1_SEQUENCE ) );
memcpy( sig, p, len );
*slen = len;
return( 0 );
}
/*
* Compute and write signature
*/
int ecdsa_write_signature( ecdsa_context *ctx,
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;
if( ( ret = ecdsa_sign( &ctx->grp, &ctx->r, &ctx->s, &ctx->d,
hash, hlen, f_rng, p_rng ) ) != 0 )
{
return( ret );
}
return( ecdsa_signature_to_asn1( ctx, sig, slen ) );
}
#if defined(POLARSSL_ECDSA_DETERMINISTIC)
/*
* Compute and write signature deterministically
*/
int ecdsa_write_signature_det( ecdsa_context *ctx,
const unsigned char *hash, size_t hlen,
unsigned char *sig, size_t *slen,
md_type_t md_alg )
{
int ret;
if( ( ret = ecdsa_sign_det( &ctx->grp, &ctx->r, &ctx->s, &ctx->d,
hash, hlen, md_alg ) ) != 0 )
{
return( ret );
}
return( ecdsa_signature_to_asn1( ctx, sig, slen ) );
}
#endif /* POLARSSL_ECDSA_DETERMINISTIC */
/*
* Read and check signature
*/
int ecdsa_read_signature( ecdsa_context *ctx,
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;
if( ( ret = asn1_get_tag( &p, end, &len,
ASN1_CONSTRUCTED | ASN1_SEQUENCE ) ) != 0 )
{
return( POLARSSL_ERR_ECP_BAD_INPUT_DATA + ret );
}
if( p + len != end )
return( POLARSSL_ERR_ECP_BAD_INPUT_DATA +
POLARSSL_ERR_ASN1_LENGTH_MISMATCH );
if( ( ret = asn1_get_mpi( &p, end, &ctx->r ) ) != 0 ||
( ret = asn1_get_mpi( &p, end, &ctx->s ) ) != 0 )
return( POLARSSL_ERR_ECP_BAD_INPUT_DATA + ret );
if( ( ret = ecdsa_verify( &ctx->grp, hash, hlen,
&ctx->Q, &ctx->r, &ctx->s ) ) != 0 )
return( ret );
if( p != end )
return( POLARSSL_ERR_ECP_SIG_LEN_MISMATCH );
return( 0 );
}
/*
* Generate key pair
*/
int ecdsa_genkey( ecdsa_context *ctx, ecp_group_id gid,
int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
{
return( ecp_use_known_dp( &ctx->grp, gid ) ||
ecp_gen_keypair( &ctx->grp, &ctx->d, &ctx->Q, f_rng, p_rng ) );
}
/*
* Set context from an ecp_keypair
*/
int ecdsa_from_keypair( ecdsa_context *ctx, const ecp_keypair *key )
{
int ret;
if( ( ret = ecp_group_copy( &ctx->grp, &key->grp ) ) != 0 ||
( ret = mpi_copy( &ctx->d, &key->d ) ) != 0 ||
( ret = ecp_copy( &ctx->Q, &key->Q ) ) != 0 )
{
ecdsa_free( ctx );
}
return( ret );
}
/*
* Initialize context
*/
void ecdsa_init( ecdsa_context *ctx )
{
ecp_group_init( &ctx->grp );
mpi_init( &ctx->d );
ecp_point_init( &ctx->Q );
mpi_init( &ctx->r );
mpi_init( &ctx->s );
}
/*
* Free context
*/
void ecdsa_free( ecdsa_context *ctx )
{
ecp_group_free( &ctx->grp );
mpi_free( &ctx->d );
ecp_point_free( &ctx->Q );
mpi_free( &ctx->r );
mpi_free( &ctx->s );
}
#if defined(POLARSSL_SELF_TEST)
/*
* Checkup routine
*/
int ecdsa_self_test( int verbose )
{
((void) verbose );
return( 0 );
}
#endif /* POLARSSL_SELF_TEST */
#endif /* POLARSSL_ECDSA_C */
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