/*
* Compute shared secret (SEC1 3.3.1)
*/
int mbedtls_ecdh_compute_shared( mbedtls_ecp_group *grp, mbedtls_mpi *z,
const mbedtls_ecp_point *Q, const mbedtls_mpi *d,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng )
{
int ret;
mbedtls_ecp_point P;
mbedtls_ecp_point_init( &P );
/*
* Make sure Q is a valid pubkey before using it
*/
MBEDTLS_MPI_CHK( mbedtls_ecp_check_pubkey( grp, Q ) );
MBEDTLS_MPI_CHK( mbedtls_ecp_mul( grp, &P, d, Q, f_rng, p_rng ) );
if( mbedtls_ecp_is_zero( &P ) )
{
ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
goto cleanup;
}
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( z, &P.X ) );
cleanup:
mbedtls_ecp_point_free( &P );
return( ret );
}
/*
* Verify ECDSA signature of hashed message (SEC1 4.1.4)
* Obviously, compared to SEC1 4.1.3, we skip step 2 (hash message)
*/
static int ecdsa_verify_restartable( mbedtls_ecp_group *grp,
const unsigned char *buf, size_t blen,
const mbedtls_ecp_point *Q,
const mbedtls_mpi *r, const mbedtls_mpi *s,
mbedtls_ecdsa_restart_ctx *rs_ctx )
{
int ret;
mbedtls_mpi e, s_inv, u1, u2;
mbedtls_ecp_point R;
mbedtls_mpi *pu1 = &u1, *pu2 = &u2;
mbedtls_ecp_point_init( &R );
mbedtls_mpi_init( &e ); mbedtls_mpi_init( &s_inv );
mbedtls_mpi_init( &u1 ); mbedtls_mpi_init( &u2 );
/* 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 );
ECDSA_RS_ENTER( ver );
#if defined(MBEDTLS_ECP_RESTARTABLE)
if( rs_ctx != NULL && rs_ctx->ver != NULL )
{
/* redirect to our context */
pu1 = &rs_ctx->ver->u1;
pu2 = &rs_ctx->ver->u2;
/* jump to current step */
if( rs_ctx->ver->state == ecdsa_ver_muladd )
goto muladd;
}
#endif /* MBEDTLS_ECP_RESTARTABLE */
/*
* 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 )
{
ret = MBEDTLS_ERR_ECP_VERIFY_FAILED;
goto cleanup;
}
/*
* Step 3: derive MPI from hashed message
*/
MBEDTLS_MPI_CHK( derive_mpi( grp, &e, buf, blen ) );
/*
* Step 4: u1 = e / s mod n, u2 = r / s mod n
*/
ECDSA_BUDGET( MBEDTLS_ECP_OPS_CHK + MBEDTLS_ECP_OPS_INV + 2 );
MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &s_inv, s, &grp->N ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( pu1, &e, &s_inv ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( pu1, pu1, &grp->N ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( pu2, r, &s_inv ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( pu2, pu2, &grp->N ) );
#if defined(MBEDTLS_ECP_RESTARTABLE)
if( rs_ctx != NULL && rs_ctx->ver != NULL )
rs_ctx->ver->state = ecdsa_ver_muladd;
muladd:
#endif
/*
* Step 5: R = u1 G + u2 Q
*/
MBEDTLS_MPI_CHK( mbedtls_ecp_muladd_restartable( grp,
&R, pu1, &grp->G, pu2, Q, ECDSA_RS_ECP ) );
if( mbedtls_ecp_is_zero( &R ) )
{
ret = MBEDTLS_ERR_ECP_VERIFY_FAILED;
goto cleanup;
}
/*
* 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
*/
if( mbedtls_mpi_cmp_mpi( &R.X, r ) != 0 )
{
ret = MBEDTLS_ERR_ECP_VERIFY_FAILED;
goto cleanup;
}
cleanup:
mbedtls_ecp_point_free( &R );
mbedtls_mpi_free( &e ); mbedtls_mpi_free( &s_inv );
mbedtls_mpi_free( &u1 ); mbedtls_mpi_free( &u2 );
ECDSA_RS_LEAVE( ver );
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 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 )
{
int ret, key_tries, sign_tries, blind_tries;
mbedtls_ecp_point R;
mbedtls_mpi k, e, t;
/* 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 );
mbedtls_ecp_point_init( &R );
mbedtls_mpi_init( &k ); mbedtls_mpi_init( &e ); mbedtls_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
{
MBEDTLS_MPI_CHK( mbedtls_ecp_gen_keypair( grp, &k, &R, f_rng, p_rng ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( r, &R.X, &grp->N ) );
if( key_tries++ > 10 )
{
ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
goto cleanup;
}
}
while( mbedtls_mpi_cmp_int( r, 0 ) == 0 );
/*
* Step 5: derive MPI from hashed message
*/
MBEDTLS_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;
MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &t, n_size, f_rng, p_rng ) );
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
*/
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 ) );
if( sign_tries++ > 10 )
{
ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
goto cleanup;
}
}
while( mbedtls_mpi_cmp_int( s, 0 ) == 0 );
cleanup:
mbedtls_ecp_point_free( &R );
mbedtls_mpi_free( &k ); mbedtls_mpi_free( &e ); mbedtls_mpi_free( &t );
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)
*/
static int ecdsa_sign_restartable( 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,
mbedtls_ecdsa_restart_ctx *rs_ctx )
{
int ret, key_tries, sign_tries;
int *p_sign_tries = &sign_tries, *p_key_tries = &key_tries;
mbedtls_ecp_point R;
mbedtls_mpi k, e, t;
mbedtls_mpi *pk = &k, *pr = r;
/* 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 );
ECDSA_RS_ENTER( sig );
#if defined(MBEDTLS_ECP_RESTARTABLE)
if( rs_ctx != NULL && rs_ctx->sig != NULL )
{
/* redirect to our context */
p_sign_tries = &rs_ctx->sig->sign_tries;
p_key_tries = &rs_ctx->sig->key_tries;
pk = &rs_ctx->sig->k;
pr = &rs_ctx->sig->r;
/* jump to current step */
if( rs_ctx->sig->state == ecdsa_sig_mul )
goto mul;
if( rs_ctx->sig->state == ecdsa_sig_modn )
goto modn;
}
#endif /* MBEDTLS_ECP_RESTARTABLE */
*p_sign_tries = 0;
do
{
if( *p_sign_tries++ > 10 )
{
ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
goto cleanup;
}
/*
* Steps 1-3: generate a suitable ephemeral keypair
* and set r = xR mod n
*/
*p_key_tries = 0;
do
{
if( *p_key_tries++ > 10 )
{
ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
goto cleanup;
}
MBEDTLS_MPI_CHK( mbedtls_ecp_gen_privkey( grp, pk, f_rng, p_rng ) );
#if defined(MBEDTLS_ECP_RESTARTABLE)
if( rs_ctx != NULL && rs_ctx->sig != NULL )
rs_ctx->sig->state = ecdsa_sig_mul;
mul:
#endif
MBEDTLS_MPI_CHK( mbedtls_ecp_mul_restartable( grp, &R, pk, &grp->G,
f_rng, p_rng, ECDSA_RS_ECP ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( pr, &R.X, &grp->N ) );
}
while( mbedtls_mpi_cmp_int( pr, 0 ) == 0 );
#if defined(MBEDTLS_ECP_RESTARTABLE)
if( rs_ctx != NULL && rs_ctx->sig != NULL )
rs_ctx->sig->state = ecdsa_sig_modn;
modn:
#endif
/*
* Accounting for everything up to the end of the loop
* (step 6, but checking now avoids saving e and t)
*/
ECDSA_BUDGET( MBEDTLS_ECP_OPS_INV + 4 );
/*
* Step 5: derive MPI from hashed message
*/
MBEDTLS_MPI_CHK( derive_mpi( grp, &e, buf, blen ) );
/*
* Generate a random value to blind inv_mod in next step,
* avoiding a potential timing leak.
*/
MBEDTLS_MPI_CHK( mbedtls_ecp_gen_privkey( grp, &t, f_rng, p_rng ) );
/*
* Step 6: compute s = (e + r * d) / k = t (e + rd) / (kt) mod n
*/
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( s, pr, 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( pk, pk, &t ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( s, pk, &grp->N ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( s, s, &e ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( s, s, &grp->N ) );
}
while( mbedtls_mpi_cmp_int( s, 0 ) == 0 );
#if defined(MBEDTLS_ECP_RESTARTABLE)
if( rs_ctx != NULL && rs_ctx->sig != NULL )
mbedtls_mpi_copy( r, pr );
#endif
cleanup:
mbedtls_ecp_point_free( &R );
mbedtls_mpi_free( &k ); mbedtls_mpi_free( &e ); mbedtls_mpi_free( &t );
ECDSA_RS_LEAVE( sig );
return( ret );
}
/*
* 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,
const unsigned char *buf, size_t blen,
const mbedtls_ecp_point *Q, const mbedtls_mpi *r, const mbedtls_mpi *s)
{
int ret;
mbedtls_mpi e, s_inv, u1, u2;
mbedtls_ecp_point R;
mbedtls_ecp_point_init( &R );
mbedtls_mpi_init( &e ); mbedtls_mpi_init( &s_inv ); mbedtls_mpi_init( &u1 ); mbedtls_mpi_init( &u2 );
/* 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 );
/*
* 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 )
{
ret = MBEDTLS_ERR_ECP_VERIFY_FAILED;
goto cleanup;
}
/*
* Additional precaution: make sure Q is valid
*/
MBEDTLS_MPI_CHK( mbedtls_ecp_check_pubkey( grp, Q ) );
/*
* Step 3: derive MPI from hashed message
*/
MBEDTLS_MPI_CHK( derive_mpi( grp, &e, buf, blen ) );
/*
* Step 4: u1 = e / s mod n, u2 = r / s mod n
*/
MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &s_inv, s, &grp->N ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &u1, &e, &s_inv ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &u1, &u1, &grp->N ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &u2, r, &s_inv ) );
MBEDTLS_MPI_CHK( mbedtls_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
* mbedtls_ecp_mul() for countermesures.
*/
MBEDTLS_MPI_CHK( mbedtls_ecp_muladd( grp, &R, &u1, &grp->G, &u2, Q ) );
if( mbedtls_ecp_is_zero( &R ) )
{
ret = MBEDTLS_ERR_ECP_VERIFY_FAILED;
goto cleanup;
}
/*
* 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
*/
if( mbedtls_mpi_cmp_mpi( &R.X, r ) != 0 )
{
ret = MBEDTLS_ERR_ECP_VERIFY_FAILED;
goto cleanup;
}
cleanup:
mbedtls_ecp_point_free( &R );
mbedtls_mpi_free( &e ); mbedtls_mpi_free( &s_inv ); mbedtls_mpi_free( &u1 ); mbedtls_mpi_free( &u2 );
return( ret );
}
