Verify the result of RSA private key operations
If RSA-CRT is used for signing, and if an attacker can cause a glitch
in one of the two computations modulo P or Q, the difference between
the faulty and the correct signature (which is not secret) will be
divisible by P or Q, but not by both, allowing to recover the private
key by taking the GCD with the public RSA modulus N. This is known as
the Bellcore Glitch Attack. Verifying the RSA signature before handing
it out is a countermeasure against it.
diff --git a/library/rsa.c b/library/rsa.c
index 6526978..c9f7ba9 100644
--- a/library/rsa.c
+++ b/library/rsa.c
@@ -773,16 +773,38 @@
{
int ret;
size_t olen;
- mbedtls_mpi T, T1, T2;
+
+ /* Temporary holding the result */
+ mbedtls_mpi T;
+
+ /* Temporaries holding P-1, Q-1 and the
+ * exponent blinding factor, respectively. */
mbedtls_mpi P1, Q1, R;
-#if defined(MBEDTLS_RSA_NO_CRT)
- mbedtls_mpi D_blind;
- mbedtls_mpi *D = &ctx->D;
-#else
+
+#if !defined(MBEDTLS_RSA_NO_CRT)
+ /* Temporaries holding the results mod p resp. mod q. */
+ mbedtls_mpi TP, TQ;
+
+ /* Temporaries holding the blinded exponents for
+ * the mod p resp. mod q computation (if used). */
mbedtls_mpi DP_blind, DQ_blind;
+
+ /* Pointers to actual exponents to be used - either the unblinded
+ * or the blinded ones, depending on the presence of a PRNG. */
mbedtls_mpi *DP = &ctx->DP;
mbedtls_mpi *DQ = &ctx->DQ;
-#endif
+#else
+ /* Temporary holding the blinded exponent (if used). */
+ mbedtls_mpi D_blind;
+
+ /* Pointer to actual exponent to be used - either the unblinded
+ * or the blinded one, depending on the presence of a PRNG. */
+ mbedtls_mpi *D = &ctx->D;
+#endif /* MBEDTLS_RSA_NO_CRT */
+
+ /* Temporaries holding the initial input and the double
+ * checked result; should be the same in the end. */
+ mbedtls_mpi I, C;
if( rsa_check_context( ctx, 1 /* private key checks */,
f_rng != NULL /* blinding y/n */ ) != 0 )
@@ -790,8 +812,17 @@
return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
}
- mbedtls_mpi_init( &T ); mbedtls_mpi_init( &T1 ); mbedtls_mpi_init( &T2 );
- mbedtls_mpi_init( &P1 ); mbedtls_mpi_init( &Q1 ); mbedtls_mpi_init( &R );
+#if defined(MBEDTLS_THREADING_C)
+ if( ( ret = mbedtls_mutex_lock( &ctx->mutex ) ) != 0 )
+ return( ret );
+#endif
+
+ /* MPI Initialization */
+ mbedtls_mpi_init( &T );
+
+ mbedtls_mpi_init( &P1 );
+ mbedtls_mpi_init( &Q1 );
+ mbedtls_mpi_init( &R );
if( f_rng != NULL )
{
@@ -803,12 +834,15 @@
#endif
}
-
-#if defined(MBEDTLS_THREADING_C)
- if( ( ret = mbedtls_mutex_lock( &ctx->mutex ) ) != 0 )
- return( ret );
+#if !defined(MBEDTLS_RSA_NO_CRT)
+ mbedtls_mpi_init( &TP ); mbedtls_mpi_init( &TQ );
#endif
+ mbedtls_mpi_init( &I );
+ mbedtls_mpi_init( &C );
+
+ /* End of MPI initialization */
+
MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &T, input, ctx->len ) );
if( mbedtls_mpi_cmp_mpi( &T, &ctx->N ) >= 0 )
{
@@ -816,6 +850,8 @@
goto cleanup;
}
+ MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &I, &T ) );
+
if( f_rng != NULL )
{
/*
@@ -874,24 +910,25 @@
/*
* Faster decryption using the CRT
*
- * T1 = input ^ dP mod P
- * T2 = input ^ dQ mod Q
+ * TP = input ^ dP mod P
+ * TQ = input ^ dQ mod Q
*/
- MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &T1, &T, DP, &ctx->P, &ctx->RP ) );
- MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &T2, &T, DQ, &ctx->Q, &ctx->RQ ) );
+
+ MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &TP, &T, DP, &ctx->P, &ctx->RP ) );
+ MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &TQ, &T, DQ, &ctx->Q, &ctx->RQ ) );
/*
- * T = (T1 - T2) * (Q^-1 mod P) mod P
+ * T = (TP - TQ) * (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 ) );
+ MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T, &TP, &TQ ) );
+ MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &TP, &T, &ctx->QP ) );
+ MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &T, &TP, &ctx->P ) );
/*
- * T = T2 + T * Q
+ * T = TQ + T * Q
*/
- MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T1, &T, &ctx->Q ) );
- MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &T, &T2, &T1 ) );
+ MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &TP, &T, &ctx->Q ) );
+ MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &T, &TQ, &TP ) );
#endif /* MBEDTLS_RSA_NO_CRT */
if( f_rng != NULL )
@@ -904,6 +941,15 @@
MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &T, &T, &ctx->N ) );
}
+ /* Verify the result to prevent glitching attacks. */
+ MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &C, &T, &ctx->E,
+ &ctx->N, &ctx->RN ) );
+ if( mbedtls_mpi_cmp_mpi( &C, &I ) != 0 )
+ {
+ ret = MBEDTLS_ERR_RSA_VERIFY_FAILED;
+ goto cleanup;
+ }
+
olen = ctx->len;
MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &T, output, olen ) );
@@ -913,8 +959,9 @@
return( MBEDTLS_ERR_THREADING_MUTEX_ERROR );
#endif
- mbedtls_mpi_free( &T ); mbedtls_mpi_free( &T1 ); mbedtls_mpi_free( &T2 );
- mbedtls_mpi_free( &P1 ); mbedtls_mpi_free( &Q1 ); mbedtls_mpi_free( &R );
+ mbedtls_mpi_free( &P1 );
+ mbedtls_mpi_free( &Q1 );
+ mbedtls_mpi_free( &R );
if( f_rng != NULL )
{
@@ -926,6 +973,15 @@
#endif
}
+ mbedtls_mpi_free( &T );
+
+#if !defined(MBEDTLS_RSA_NO_CRT)
+ mbedtls_mpi_free( &TP ); mbedtls_mpi_free( &TQ );
+#endif
+
+ mbedtls_mpi_free( &C );
+ mbedtls_mpi_free( &I );
+
if( ret != 0 )
return( MBEDTLS_ERR_RSA_PRIVATE_FAILED + ret );
@@ -2222,7 +2278,8 @@
if( verbose != 0 )
mbedtls_printf( "failed\n" );
- return( 1 );
+ ret = 1;
+ goto cleanup;
}
if( verbose != 0 )
@@ -2237,7 +2294,8 @@
if( verbose != 0 )
mbedtls_printf( "failed\n" );
- return( 1 );
+ ret = 1;
+ goto cleanup;
}
if( verbose != 0 )
@@ -2250,7 +2308,8 @@
if( verbose != 0 )
mbedtls_printf( "failed\n" );
- return( 1 );
+ ret = 1;
+ goto cleanup;
}
if( memcmp( rsa_decrypted, rsa_plaintext, len ) != 0 )
@@ -2258,7 +2317,8 @@
if( verbose != 0 )
mbedtls_printf( "failed\n" );
- return( 1 );
+ ret = 1;
+ goto cleanup;
}
if( verbose != 0 )
@@ -2283,7 +2343,8 @@
if( verbose != 0 )
mbedtls_printf( "failed\n" );
- return( 1 );
+ ret = 1;
+ goto cleanup;
}
if( verbose != 0 )
@@ -2296,7 +2357,8 @@
if( verbose != 0 )
mbedtls_printf( "failed\n" );
- return( 1 );
+ ret = 1;
+ goto cleanup;
}
if( verbose != 0 )