/*
* 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 );
}
/*
* 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 );
}
/*
* This function calculates:
* d = a^b mod c
*
* @a: base
* @b: exponent
* @c: modulus
* @d: destination
*/
static int exptmod(void *a, void *b, void *c, void *d)
{
int res;
if (d == a || d == b || d == c) {
mbedtls_mpi dest;
mbedtls_mpi_init_mempool(&dest);
res = mbedtls_mpi_exp_mod(&dest, a, b, c, NULL);
if (!res)
res = mbedtls_mpi_copy(d, &dest);
mbedtls_mpi_free(&dest);
} else {
res = mbedtls_mpi_exp_mod(d, a, b, c, NULL);
}
if (res)
return CRYPT_MEM;
else
return CRYPT_OK;
}
/*
* Derive and export the shared secret (G^Y)^X mod P
*/
int mbedtls_dhm_calc_secret( mbedtls_dhm_context *ctx,
unsigned char *output, size_t output_size, size_t *olen,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng )
{
int ret;
mbedtls_mpi GYb;
if( ctx == NULL || output_size < ctx->len )
return( MBEDTLS_ERR_DHM_BAD_INPUT_DATA );
if( ( ret = dhm_check_range( &ctx->GY, &ctx->P ) ) != 0 )
return( ret );
mbedtls_mpi_init( &GYb );
/* Blind peer's value */
if( f_rng != NULL )
{
MBEDTLS_MPI_CHK( dhm_update_blinding( ctx, f_rng, p_rng ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &GYb, &ctx->GY, &ctx->Vi ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &GYb, &GYb, &ctx->P ) );
}
else
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &GYb, &ctx->GY ) );
/* Do modular exponentiation */
MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &ctx->K, &GYb, &ctx->X,
&ctx->P, &ctx->RP ) );
/* Unblind secret value */
if( f_rng != NULL )
{
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ctx->K, &ctx->K, &ctx->Vf ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &ctx->K, &ctx->K, &ctx->P ) );
}
*olen = mbedtls_mpi_size( &ctx->K );
MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &ctx->K, output, *olen ) );
cleanup:
mbedtls_mpi_free( &GYb );
if( ret != 0 )
return( MBEDTLS_ERR_DHM_CALC_SECRET_FAILED + ret );
return( 0 );
}
/*
* 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 );
}
/*
* Do an RSA public key operation
*/
int mbedtls_rsa_public( mbedtls_rsa_context *ctx,
const unsigned char *input,
unsigned char *output )
{
int ret;
size_t olen;
mbedtls_mpi T;
mbedtls_mpi_init( &T );
#if defined(MBEDTLS_THREADING_C)
if( ( ret = mbedtls_mutex_lock( &ctx->mutex ) ) != 0 )
return( ret );
#endif
MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &T, input, ctx->len ) );
if( mbedtls_mpi_cmp_mpi( &T, &ctx->N ) >= 0 )
{
ret = MBEDTLS_ERR_MPI_BAD_INPUT_DATA;
goto cleanup;
}
olen = ctx->len;
MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &T, &T, &ctx->E, &ctx->N, &ctx->RN ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &T, output, olen ) );
cleanup:
#if defined(MBEDTLS_THREADING_C)
if( mbedtls_mutex_unlock( &ctx->mutex ) != 0 )
return( MBEDTLS_ERR_THREADING_MUTEX_ERROR );
#endif
mbedtls_mpi_free( &T );
if( ret != 0 )
return( MBEDTLS_ERR_RSA_PUBLIC_FAILED + ret );
return( 0 );
}
int main( void )
{
int ret;
mbedtls_mpi E, P, Q, N, H, D, X, Y, Z;
mbedtls_mpi_init( &E ); mbedtls_mpi_init( &P ); mbedtls_mpi_init( &Q ); mbedtls_mpi_init( &N );
mbedtls_mpi_init( &H ); mbedtls_mpi_init( &D ); mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Y );
mbedtls_mpi_init( &Z );
MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &P, 10, "2789" ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &Q, 10, "3203" ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &E, 10, "257" ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &N, &P, &Q ) );
mbedtls_printf( "\n Public key:\n\n" );
MBEDTLS_MPI_CHK( mbedtls_mpi_write_file( " N = ", &N, 10, NULL ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_write_file( " E = ", &E, 10, NULL ) );
mbedtls_printf( "\n Private key:\n\n" );
MBEDTLS_MPI_CHK( mbedtls_mpi_write_file( " P = ", &P, 10, NULL ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_write_file( " Q = ", &Q, 10, NULL ) );
#if defined(MBEDTLS_GENPRIME)
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &P, &P, 1 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &Q, &Q, 1 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &H, &P, &Q ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &D, &E, &H ) );
mbedtls_mpi_write_file( " D = E^-1 mod (P-1)*(Q-1) = ",
&D, 10, NULL );
#else
mbedtls_printf("\nTest skipped (MBEDTLS_GENPRIME not defined).\n\n");
#endif
MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &X, 10, "55555" ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &Y, &X, &E, &N, NULL ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &Z, &Y, &D, &N, NULL ) );
mbedtls_printf( "\n RSA operation:\n\n" );
MBEDTLS_MPI_CHK( mbedtls_mpi_write_file( " X (plaintext) = ", &X, 10, NULL ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_write_file( " Y (ciphertext) = X^E mod N = ", &Y, 10, NULL ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_write_file( " Z (decrypted) = Y^D mod N = ", &Z, 10, NULL ) );
mbedtls_printf( "\n" );
cleanup:
mbedtls_mpi_free( &E ); mbedtls_mpi_free( &P ); mbedtls_mpi_free( &Q ); mbedtls_mpi_free( &N );
mbedtls_mpi_free( &H ); mbedtls_mpi_free( &D ); mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Y );
mbedtls_mpi_free( &Z );
if( ret != 0 )
{
mbedtls_printf( "\nAn error occurred.\n" );
ret = 1;
}
#if defined(_WIN32)
mbedtls_printf( " Press Enter to exit this program.\n" );
fflush( stdout ); getchar();
#endif
return( ret );
}
/*
* 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 );
}
/*
* Do an RSA private key operation
*/
int mbedtls_rsa_private( mbedtls_rsa_context *ctx,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng,
const unsigned char *input,
unsigned char *output )
{
int ret;
size_t olen;
mbedtls_mpi T, T1, T2;
/* Make sure we have private key info, prevent possible misuse */
if( ctx->P.p == NULL || ctx->Q.p == NULL || ctx->D.p == NULL )
return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
mbedtls_mpi_init( &T ); mbedtls_mpi_init( &T1 ); mbedtls_mpi_init( &T2 );
#if defined(MBEDTLS_THREADING_C)
if( ( ret = mbedtls_mutex_lock( &ctx->mutex ) ) != 0 )
return( ret );
#endif
MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &T, input, ctx->len ) );
if( mbedtls_mpi_cmp_mpi( &T, &ctx->N ) >= 0 )
{
ret = MBEDTLS_ERR_MPI_BAD_INPUT_DATA;
goto cleanup;
}
if( f_rng != NULL )
{
/*
* Blinding
* T = T * Vi mod N
*/
MBEDTLS_MPI_CHK( rsa_prepare_blinding( ctx, f_rng, p_rng ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &T, &ctx->Vi ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &T, &T, &ctx->N ) );
}
#if defined(MBEDTLS_RSA_NO_CRT)
MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &T, &T, &ctx->D, &ctx->N, &ctx->RN ) );
#else
/*
* faster decryption using the CRT
*
* T1 = input ^ dP mod P
* T2 = input ^ dQ mod Q
*/
MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &T1, &T, &ctx->DP, &ctx->P, &ctx->RP ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &T2, &T, &ctx->DQ, &ctx->Q, &ctx->RQ ) );
/*
* T = (T1 - T2) * (Q^-1 mod P) mod P
*/
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T, &T1, &T2 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T1, &T, &ctx->QP ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &T, &T1, &ctx->P ) );
/*
* T = T2 + T * Q
*/
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T1, &T, &ctx->Q ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &T, &T2, &T1 ) );
#endif /* MBEDTLS_RSA_NO_CRT */
if( f_rng != NULL )
{
/*
* Unblind
* T = T * Vf mod N
*/
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &T, &ctx->Vf ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &T, &T, &ctx->N ) );
}
olen = ctx->len;
MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &T, output, olen ) );
cleanup:
#if defined(MBEDTLS_THREADING_C)
if( mbedtls_mutex_unlock( &ctx->mutex ) != 0 )
return( MBEDTLS_ERR_THREADING_MUTEX_ERROR );
#endif
mbedtls_mpi_free( &T ); mbedtls_mpi_free( &T1 ); mbedtls_mpi_free( &T2 );
if( ret != 0 )
return( MBEDTLS_ERR_RSA_PRIVATE_FAILED + ret );
return( 0 );
}
