/*
* Check a private RSA key
*/
int mbedtls_rsa_check_privkey( const mbedtls_rsa_context *ctx )
{
int ret;
mbedtls_mpi PQ, DE, P1, Q1, H, I, G, G2, L1, L2, DP, DQ, QP;
if( ( ret = mbedtls_rsa_check_pubkey( ctx ) ) != 0 )
return( ret );
if( !ctx->P.p || !ctx->Q.p || !ctx->D.p )
return( MBEDTLS_ERR_RSA_KEY_CHECK_FAILED );
mbedtls_mpi_init( &PQ ); mbedtls_mpi_init( &DE ); mbedtls_mpi_init( &P1 ); mbedtls_mpi_init( &Q1 );
mbedtls_mpi_init( &H ); mbedtls_mpi_init( &I ); mbedtls_mpi_init( &G ); mbedtls_mpi_init( &G2 );
mbedtls_mpi_init( &L1 ); mbedtls_mpi_init( &L2 ); mbedtls_mpi_init( &DP ); mbedtls_mpi_init( &DQ );
mbedtls_mpi_init( &QP );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &PQ, &ctx->P, &ctx->Q ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &DE, &ctx->D, &ctx->E ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &P1, &ctx->P, 1 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &Q1, &ctx->Q, 1 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &H, &P1, &Q1 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( &G, &ctx->E, &H ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( &G2, &P1, &Q1 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_div_mpi( &L1, &L2, &H, &G2 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &I, &DE, &L1 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &DP, &ctx->D, &P1 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &DQ, &ctx->D, &Q1 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &QP, &ctx->Q, &ctx->P ) );
/*
* Check for a valid PKCS1v2 private key
*/
if( mbedtls_mpi_cmp_mpi( &PQ, &ctx->N ) != 0 ||
mbedtls_mpi_cmp_mpi( &DP, &ctx->DP ) != 0 ||
mbedtls_mpi_cmp_mpi( &DQ, &ctx->DQ ) != 0 ||
mbedtls_mpi_cmp_mpi( &QP, &ctx->QP ) != 0 ||
mbedtls_mpi_cmp_int( &L2, 0 ) != 0 ||
mbedtls_mpi_cmp_int( &I, 1 ) != 0 ||
mbedtls_mpi_cmp_int( &G, 1 ) != 0 )
{
ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
}
cleanup:
mbedtls_mpi_free( &PQ ); mbedtls_mpi_free( &DE ); mbedtls_mpi_free( &P1 ); mbedtls_mpi_free( &Q1 );
mbedtls_mpi_free( &H ); mbedtls_mpi_free( &I ); mbedtls_mpi_free( &G ); mbedtls_mpi_free( &G2 );
mbedtls_mpi_free( &L1 ); mbedtls_mpi_free( &L2 ); mbedtls_mpi_free( &DP ); mbedtls_mpi_free( &DQ );
mbedtls_mpi_free( &QP );
if( ret == MBEDTLS_ERR_RSA_KEY_CHECK_FAILED )
return( ret );
if( ret != 0 )
return( MBEDTLS_ERR_RSA_KEY_CHECK_FAILED + ret );
return( 0 );
}
/*
* Use the blinding method and optimisation suggested in section 10 of:
* KOCHER, Paul C. Timing attacks on implementations of Diffie-Hellman, RSA,
* DSS, and other systems. In : Advances in Cryptology-CRYPTO'96. Springer
* Berlin Heidelberg, 1996. p. 104-113.
*/
static int dhm_update_blinding( mbedtls_dhm_context *ctx,
int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
{
int ret, count;
/*
* Don't use any blinding the first time a particular X is used,
* but remember it to use blinding next time.
*/
if( mbedtls_mpi_cmp_mpi( &ctx->X, &ctx->pX ) != 0 )
{
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &ctx->pX, &ctx->X ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &ctx->Vi, 1 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &ctx->Vf, 1 ) );
return( 0 );
}
/*
* Ok, we need blinding. Can we re-use existing values?
* If yes, just update them by squaring them.
*/
if( mbedtls_mpi_cmp_int( &ctx->Vi, 1 ) != 0 )
{
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ctx->Vi, &ctx->Vi, &ctx->Vi ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &ctx->Vi, &ctx->Vi, &ctx->P ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ctx->Vf, &ctx->Vf, &ctx->Vf ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &ctx->Vf, &ctx->Vf, &ctx->P ) );
return( 0 );
}
/*
* We need to generate blinding values from scratch
*/
/* Vi = random( 2, P-1 ) */
count = 0;
do
{
mbedtls_mpi_fill_random( &ctx->Vi, mbedtls_mpi_size( &ctx->P ), f_rng, p_rng );
while( mbedtls_mpi_cmp_mpi( &ctx->Vi, &ctx->P ) >= 0 )
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &ctx->Vi, 1 ) );
if( count++ > 10 )
return( MBEDTLS_ERR_MPI_NOT_ACCEPTABLE );
}
while( mbedtls_mpi_cmp_int( &ctx->Vi, 1 ) <= 0 );
/* Vf = Vi^-X mod P */
MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &ctx->Vf, &ctx->Vi, &ctx->P ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &ctx->Vf, &ctx->Vf, &ctx->X, &ctx->P, &ctx->RP ) );
cleanup:
return( ret );
}
/*
* Generate or update blinding values, see section 10 of:
* KOCHER, Paul C. Timing attacks on implementations of Diffie-Hellman, RSA,
* DSS, and other systems. In : Advances in Cryptology-CRYPTO'96. Springer
* Berlin Heidelberg, 1996. p. 104-113.
*/
static int rsa_prepare_blinding( mbedtls_rsa_context *ctx,
int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
{
int ret, count = 0;
if( ctx->Vf.p != NULL )
{
/* We already have blinding values, just update them by squaring */
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ctx->Vi, &ctx->Vi, &ctx->Vi ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &ctx->Vi, &ctx->Vi, &ctx->N ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ctx->Vf, &ctx->Vf, &ctx->Vf ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &ctx->Vf, &ctx->Vf, &ctx->N ) );
goto cleanup;
}
/* Unblinding value: Vf = random number, invertible mod N */
do {
if( count++ > 10 )
return( MBEDTLS_ERR_RSA_RNG_FAILED );
MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &ctx->Vf, ctx->len - 1, f_rng, p_rng ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( &ctx->Vi, &ctx->Vf, &ctx->N ) );
} while( mbedtls_mpi_cmp_int( &ctx->Vi, 1 ) != 0 );
/* Blinding value: Vi = Vf^(-e) mod N */
MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &ctx->Vi, &ctx->Vf, &ctx->N ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &ctx->Vi, &ctx->Vi, &ctx->E, &ctx->N, &ctx->RN ) );
cleanup:
return( ret );
}
bool TEE_BigIntRelativePrime(const TEE_BigInt *op1, const TEE_BigInt *op2)
{
bool rc;
mbedtls_mpi mpi_op1;
mbedtls_mpi mpi_op2;
mbedtls_mpi *pop2 = &mpi_op2;
mbedtls_mpi gcd;
get_mpi(&mpi_op1, op1);
if (op2 == op1)
pop2 = &mpi_op1;
else
get_mpi(&mpi_op2, op2);
get_mpi(&gcd, NULL);
MPI_CHECK(mbedtls_mpi_gcd(&gcd, &mpi_op1, &mpi_op2));
rc = !mbedtls_mpi_cmp_int(&gcd, 1);
mbedtls_mpi_free(&gcd);
mbedtls_mpi_free(&mpi_op1);
if (pop2 == &mpi_op2)
mbedtls_mpi_free(&mpi_op2);
return rc;
}
int32_t TEE_BigIntCmpS32(const TEE_BigInt *op, int32_t shortVal)
{
mbedtls_mpi mpi;
int32_t rc;
get_mpi(&mpi, op);
rc = mbedtls_mpi_cmp_int(&mpi, shortVal);
mbedtls_mpi_free(&mpi);
return rc;
}
/*
* Create own private value X and export G^X
*/
int mbedtls_dhm_make_public( mbedtls_dhm_context *ctx, int x_size,
unsigned char *output, size_t olen,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng )
{
int ret, count = 0;
if( ctx == NULL || olen < 1 || olen > ctx->len )
return( MBEDTLS_ERR_DHM_BAD_INPUT_DATA );
if( mbedtls_mpi_cmp_int( &ctx->P, 0 ) == 0 )
return( MBEDTLS_ERR_DHM_BAD_INPUT_DATA );
/*
* generate X and calculate GX = G^X mod P
*/
do
{
mbedtls_mpi_fill_random( &ctx->X, x_size, f_rng, p_rng );
while( mbedtls_mpi_cmp_mpi( &ctx->X, &ctx->P ) >= 0 )
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &ctx->X, 1 ) );
if( count++ > 10 )
return( MBEDTLS_ERR_DHM_MAKE_PUBLIC_FAILED );
}
while( dhm_check_range( &ctx->X, &ctx->P ) != 0 );
MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &ctx->GX, &ctx->G, &ctx->X,
&ctx->P , &ctx->RP ) );
if( ( ret = dhm_check_range( &ctx->GX, &ctx->P ) ) != 0 )
return( ret );
MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &ctx->GX, output, olen ) );
cleanup:
if( ret != 0 )
return( MBEDTLS_ERR_DHM_MAKE_PUBLIC_FAILED + ret );
return( 0 );
}
/*
* Setup and write the ServerKeyExchange parameters
*/
int mbedtls_dhm_make_params( mbedtls_dhm_context *ctx, int x_size,
unsigned char *output, size_t *olen,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng )
{
int ret, count = 0;
size_t n1, n2, n3;
unsigned char *p;
if( mbedtls_mpi_cmp_int( &ctx->P, 0 ) == 0 )
return( MBEDTLS_ERR_DHM_BAD_INPUT_DATA );
/*
* Generate X as large as possible ( < P )
*/
do
{
mbedtls_mpi_fill_random( &ctx->X, x_size, f_rng, p_rng );
while( mbedtls_mpi_cmp_mpi( &ctx->X, &ctx->P ) >= 0 )
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &ctx->X, 1 ) );
if( count++ > 10 )
return( MBEDTLS_ERR_DHM_MAKE_PARAMS_FAILED );
}
while( dhm_check_range( &ctx->X, &ctx->P ) != 0 );
/*
* Calculate GX = G^X mod P
*/
MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &ctx->GX, &ctx->G, &ctx->X,
&ctx->P , &ctx->RP ) );
if( ( ret = dhm_check_range( &ctx->GX, &ctx->P ) ) != 0 )
return( ret );
/*
* export P, G, GX
*/
#define DHM_MPI_EXPORT(X,n) \
MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( X, p + 2, n ) ); \
*p++ = (unsigned char)( n >> 8 ); \
*p++ = (unsigned char)( n ); p += n;
n1 = mbedtls_mpi_size( &ctx->P );
n2 = mbedtls_mpi_size( &ctx->G );
n3 = mbedtls_mpi_size( &ctx->GX );
p = output;
DHM_MPI_EXPORT( &ctx->P , n1 );
DHM_MPI_EXPORT( &ctx->G , n2 );
DHM_MPI_EXPORT( &ctx->GX, n3 );
*olen = p - output;
ctx->len = n1;
cleanup:
if( ret != 0 )
return( MBEDTLS_ERR_DHM_MAKE_PARAMS_FAILED + ret );
return( 0 );
}
/*
* 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)
*/
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 );
}
/*
* Generate an RSA keypair
*/
int mbedtls_rsa_gen_key( mbedtls_rsa_context *ctx,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng,
unsigned int nbits, int exponent )
{
int ret;
mbedtls_mpi P1, Q1, H, G;
if( f_rng == NULL || nbits < 128 || exponent < 3 )
return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
mbedtls_mpi_init( &P1 ); mbedtls_mpi_init( &Q1 ); mbedtls_mpi_init( &H ); mbedtls_mpi_init( &G );
/*
* find primes P and Q with Q < P so that:
* GCD( E, (P-1)*(Q-1) ) == 1
*/
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &ctx->E, exponent ) );
do
{
MBEDTLS_MPI_CHK( mbedtls_mpi_gen_prime( &ctx->P, ( nbits + 1 ) >> 1, 0,
f_rng, p_rng ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_gen_prime( &ctx->Q, ( nbits + 1 ) >> 1, 0,
f_rng, p_rng ) );
if( mbedtls_mpi_cmp_mpi( &ctx->P, &ctx->Q ) < 0 )
mbedtls_mpi_swap( &ctx->P, &ctx->Q );
if( mbedtls_mpi_cmp_mpi( &ctx->P, &ctx->Q ) == 0 )
continue;
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ctx->N, &ctx->P, &ctx->Q ) );
if( mbedtls_mpi_bitlen( &ctx->N ) != nbits )
continue;
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &P1, &ctx->P, 1 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &Q1, &ctx->Q, 1 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &H, &P1, &Q1 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( &G, &ctx->E, &H ) );
}
while( mbedtls_mpi_cmp_int( &G, 1 ) != 0 );
/*
* D = E^-1 mod ((P-1)*(Q-1))
* DP = D mod (P - 1)
* DQ = D mod (Q - 1)
* QP = Q^-1 mod P
*/
MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &ctx->D , &ctx->E, &H ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &ctx->DP, &ctx->D, &P1 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &ctx->DQ, &ctx->D, &Q1 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &ctx->QP, &ctx->Q, &ctx->P ) );
ctx->len = ( mbedtls_mpi_bitlen( &ctx->N ) + 7 ) >> 3;
cleanup:
mbedtls_mpi_free( &P1 ); mbedtls_mpi_free( &Q1 ); mbedtls_mpi_free( &H ); mbedtls_mpi_free( &G );
if( ret != 0 )
{
mbedtls_rsa_free( ctx );
return( MBEDTLS_ERR_RSA_KEY_GEN_FAILED + ret );
}
return( 0 );
}
/*
* 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 );
}
/*
* 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 );
}
/*
* Based on libmpa implementation __mpa_egcd(), modified to work with MPI
* instead.
*/
static void mpi_egcd(mbedtls_mpi *gcd, mbedtls_mpi *a, mbedtls_mpi *b,
mbedtls_mpi *x_in, mbedtls_mpi *y_in)
{
mbedtls_mpi_uint k;
mbedtls_mpi A;
mbedtls_mpi B;
mbedtls_mpi C;
mbedtls_mpi D;
mbedtls_mpi x;
mbedtls_mpi y;
mbedtls_mpi u;
get_mpi(&A, NULL);
get_mpi(&B, NULL);
get_mpi(&C, NULL);
get_mpi(&D, NULL);
get_mpi(&x, NULL);
get_mpi(&y, NULL);
get_mpi(&u, NULL);
/* have y < x from assumption */
if (!mbedtls_mpi_cmp_int(y_in, 0)) {
MPI_CHECK(mbedtls_mpi_lset(a, 1));
MPI_CHECK(mbedtls_mpi_lset(b, 0));
MPI_CHECK(mbedtls_mpi_copy(gcd, x_in));
goto out;
}
MPI_CHECK(mbedtls_mpi_copy(&x, x_in));
MPI_CHECK(mbedtls_mpi_copy(&y, y_in));
k = 0;
while (mpi_is_even(&x) && mpi_is_even(&y)) {
k++;
MPI_CHECK(mbedtls_mpi_shift_r(&x, 1));
MPI_CHECK(mbedtls_mpi_shift_r(&y, 1));
}
MPI_CHECK(mbedtls_mpi_copy(&u, &x));
MPI_CHECK(mbedtls_mpi_copy(gcd, &y));
MPI_CHECK(mbedtls_mpi_lset(&A, 1));
MPI_CHECK(mbedtls_mpi_lset(&B, 0));
MPI_CHECK(mbedtls_mpi_lset(&C, 0));
MPI_CHECK(mbedtls_mpi_lset(&D, 1));
while (mbedtls_mpi_cmp_int(&u, 0)) {
while (mpi_is_even(&u)) {
MPI_CHECK(mbedtls_mpi_shift_r(&u, 1));
if (mpi_is_odd(&A) || mpi_is_odd(&B)) {
MPI_CHECK(mbedtls_mpi_add_mpi(&A, &A, &y));
MPI_CHECK(mbedtls_mpi_sub_mpi(&B, &B, &x));
}
MPI_CHECK(mbedtls_mpi_shift_r(&A, 1));
MPI_CHECK(mbedtls_mpi_shift_r(&B, 1));
}
while (mpi_is_even(gcd)) {
MPI_CHECK(mbedtls_mpi_shift_r(gcd, 1));
if (mpi_is_odd(&C) || mpi_is_odd(&D)) {
MPI_CHECK(mbedtls_mpi_add_mpi(&C, &C, &y));
MPI_CHECK(mbedtls_mpi_sub_mpi(&D, &D, &x));
}
MPI_CHECK(mbedtls_mpi_shift_r(&C, 1));
MPI_CHECK(mbedtls_mpi_shift_r(&D, 1));
}
if (mbedtls_mpi_cmp_mpi(&u, gcd) >= 0) {
MPI_CHECK(mbedtls_mpi_sub_mpi(&u, &u, gcd));
MPI_CHECK(mbedtls_mpi_sub_mpi(&A, &A, &C));
MPI_CHECK(mbedtls_mpi_sub_mpi(&B, &B, &D));
} else {
MPI_CHECK(mbedtls_mpi_sub_mpi(gcd, gcd, &u));
MPI_CHECK(mbedtls_mpi_sub_mpi(&C, &C, &A));
MPI_CHECK(mbedtls_mpi_sub_mpi(&D, &D, &B));
}
}
MPI_CHECK(mbedtls_mpi_copy(a, &C));
MPI_CHECK(mbedtls_mpi_copy(b, &D));
MPI_CHECK(mbedtls_mpi_shift_l(gcd, k));
out:
mbedtls_mpi_free(&A);
mbedtls_mpi_free(&B);
mbedtls_mpi_free(&C);
mbedtls_mpi_free(&D);
mbedtls_mpi_free(&x);
mbedtls_mpi_free(&y);
mbedtls_mpi_free(&u);
}
