Introduce new files rsa_internal.[ch] for RSA helper functions
This commit splits off the RSA helper functions into separate headers and
compilation units to have a clearer separation of the public RSA interface,
intended to be used by end-users, and the helper functions which are publicly
provided only for the benefit of designers of alternative RSA implementations.
diff --git a/library/rsa.c b/library/rsa.c
index 493cd1c..83e2b2b 100644
--- a/library/rsa.c
+++ b/library/rsa.c
@@ -46,6 +46,7 @@
#if defined(MBEDTLS_RSA_C)
#include "mbedtls/rsa.h"
+#include "mbedtls/rsa_internal.h"
#include "mbedtls/oid.h"
#include <string.h>
@@ -67,483 +68,13 @@
#define mbedtls_free free
#endif
+#if !defined(MBEDTLS_RSA_ALT)
+
/* Implementation that should never be optimized out by the compiler */
static void mbedtls_zeroize( void *v, size_t n ) {
volatile unsigned char *p = (unsigned char*)v; while( n-- ) *p++ = 0;
}
-/*
- * Context-independent RSA helper functions.
- *
- * There are two classes of helper functions:
- * (1) Parameter-generating helpers. These are:
- * - mbedtls_rsa_deduce_primes
- * - mbedtls_rsa_deduce_private_exponent
- * - mbedtls_rsa_deduce_crt
- * Each of these functions takes a set of core RSA parameters
- * and generates some other, or CRT related parameters.
- * (2) Parameter-checking helpers. These are:
- * - mbedtls_rsa_validate_params
- * - mbedtls_rsa_validate_crt
- * They take a set of core or CRT related RSA parameters
- * and check their validity.
- *
- * The helper functions do not use the RSA context structure
- * and therefore do not need to be replaced when providing
- * an alternative RSA implementation.
- *
- * Their main purpose is to provide common MPI operations in the context
- * of RSA that can be easily shared across multiple implementations.
- */
-
-/*
- *
- * Given the modulus N=PQ and a pair of public and private
- * exponents E and D, respectively, factor N.
- *
- * Setting F := lcm(P-1,Q-1), the idea is as follows:
- *
- * (a) For any 1 <= X < N with gcd(X,N)=1, we have X^F = 1 modulo N, so X^(F/2)
- * is a square root of 1 in Z/NZ. Since Z/NZ ~= Z/PZ x Z/QZ by CRT and the
- * square roots of 1 in Z/PZ and Z/QZ are +1 and -1, this leaves the four
- * possibilities X^(F/2) = (+-1, +-1). If it happens that X^(F/2) = (-1,+1)
- * or (+1,-1), then gcd(X^(F/2) + 1, N) will be equal to one of the prime
- * factors of N.
- *
- * (b) If we don't know F/2 but (F/2) * K for some odd (!) K, then the same
- * construction still applies since (-)^K is the identity on the set of
- * roots of 1 in Z/NZ.
- *
- * The public and private key primitives (-)^E and (-)^D are mutually inverse
- * bijections on Z/NZ if and only if (-)^(DE) is the identity on Z/NZ, i.e.
- * if and only if DE - 1 is a multiple of F, say DE - 1 = F * L.
- * Splitting L = 2^t * K with K odd, we have
- *
- * DE - 1 = FL = (F/2) * (2^(t+1)) * K,
- *
- * so (F / 2) * K is among the numbers
- *
- * (DE - 1) >> 1, (DE - 1) >> 2, ..., (DE - 1) >> ord
- *
- * where ord is the order of 2 in (DE - 1).
- * We can therefore iterate through these numbers apply the construction
- * of (a) and (b) above to attempt to factor N.
- *
- */
-int mbedtls_rsa_deduce_primes( mbedtls_mpi const *N,
- mbedtls_mpi const *D, mbedtls_mpi const *E,
- mbedtls_mpi *P, mbedtls_mpi *Q )
-{
- int ret = 0;
-
- uint16_t attempt; /* Number of current attempt */
- uint16_t iter; /* Number of squares computed in the current attempt */
-
- uint16_t order; /* Order of 2 in DE - 1 */
-
- mbedtls_mpi T; /* Holds largest odd divisor of DE - 1 */
- mbedtls_mpi K; /* During factorization attempts, stores a random integer
- * in the range of [0,..,N] */
-
- const unsigned int primes[] = { 2,
- 3, 5, 7, 11, 13, 17, 19, 23,
- 29, 31, 37, 41, 43, 47, 53, 59,
- 61, 67, 71, 73, 79, 83, 89, 97,
- 101, 103, 107, 109, 113, 127, 131, 137,
- 139, 149, 151, 157, 163, 167, 173, 179,
- 181, 191, 193, 197, 199, 211, 223, 227,
- 229, 233, 239, 241, 251, 257, 263, 269,
- 271, 277, 281, 283, 293, 307, 311, 313
- };
-
- const size_t num_primes = sizeof( primes ) / sizeof( *primes );
-
- if( P == NULL || Q == NULL || P->p != NULL || Q->p != NULL )
- return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
-
- if( mbedtls_mpi_cmp_int( N, 0 ) <= 0 ||
- mbedtls_mpi_cmp_int( D, 1 ) <= 0 ||
- mbedtls_mpi_cmp_mpi( D, N ) >= 0 ||
- mbedtls_mpi_cmp_int( E, 1 ) <= 0 ||
- mbedtls_mpi_cmp_mpi( E, N ) >= 0 )
- {
- return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
- }
-
- /*
- * Initializations and temporary changes
- */
-
- mbedtls_mpi_init( &K );
- mbedtls_mpi_init( &T );
-
- /* T := DE - 1 */
- MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, D, E ) );
- MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &T, &T, 1 ) );
-
- if( ( order = mbedtls_mpi_lsb( &T ) ) == 0 )
- {
- ret = MBEDTLS_ERR_MPI_BAD_INPUT_DATA;
- goto cleanup;
- }
-
- /* After this operation, T holds the largest odd divisor of DE - 1. */
- MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &T, order ) );
-
- /*
- * Actual work
- */
-
- /* Skip trying 2 if N == 1 mod 8 */
- attempt = 0;
- if( N->p[0] % 8 == 1 )
- attempt = 1;
-
- for( ; attempt < num_primes; ++attempt )
- {
- mbedtls_mpi_lset( &K, primes[attempt] );
-
- /* Check if gcd(K,N) = 1 */
- MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( P, &K, N ) );
- if( mbedtls_mpi_cmp_int( P, 1 ) != 0 )
- continue;
-
- /* Go through K^T + 1, K^(2T) + 1, K^(4T) + 1, ...
- * and check whether they have nontrivial GCD with N. */
- MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &K, &K, &T, N,
- Q /* temporarily use Q for storing Montgomery
- * multiplication helper values */ ) );
-
- for( iter = 1; iter < order; ++iter )
- {
- MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( &K, &K, 1 ) );
- MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( P, &K, N ) );
-
- if( mbedtls_mpi_cmp_int( P, 1 ) == 1 &&
- mbedtls_mpi_cmp_mpi( P, N ) == -1 )
- {
- /*
- * Have found a nontrivial divisor P of N.
- * Set Q := N / P.
- */
-
- MBEDTLS_MPI_CHK( mbedtls_mpi_div_mpi( Q, NULL, N, P ) );
- goto cleanup;
- }
-
- MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, &K, 1 ) );
- MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, &K, &K ) );
- MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &K, &K, N ) );
- }
- }
-
- ret = MBEDTLS_ERR_MPI_BAD_INPUT_DATA;
-
-cleanup:
-
- mbedtls_mpi_free( &K );
- mbedtls_mpi_free( &T );
- return( ret );
-}
-
-/*
- * Given P, Q and the public exponent E, deduce D.
- * This is essentially a modular inversion.
- */
-
-int mbedtls_rsa_deduce_private_exponent( mbedtls_mpi const *P,
- mbedtls_mpi const *Q,
- mbedtls_mpi const *E,
- mbedtls_mpi *D )
-{
- int ret = 0;
- mbedtls_mpi K, L;
-
- if( D == NULL || mbedtls_mpi_cmp_int( D, 0 ) != 0 )
- return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
-
- if( mbedtls_mpi_cmp_int( P, 1 ) <= 0 ||
- mbedtls_mpi_cmp_int( Q, 1 ) <= 0 ||
- mbedtls_mpi_cmp_int( E, 0 ) == 0 )
- {
- return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
- }
-
- mbedtls_mpi_init( &K );
- mbedtls_mpi_init( &L );
-
- /* Temporarily put K := P-1 and L := Q-1 */
- MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, P, 1 ) );
- MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &L, Q, 1 ) );
-
- /* Temporarily put D := gcd(P-1, Q-1) */
- MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( D, &K, &L ) );
-
- /* K := LCM(P-1, Q-1) */
- MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, &K, &L ) );
- MBEDTLS_MPI_CHK( mbedtls_mpi_div_mpi( &K, NULL, &K, D ) );
-
- /* Compute modular inverse of E in LCM(P-1, Q-1) */
- MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( D, E, &K ) );
-
-cleanup:
-
- mbedtls_mpi_free( &K );
- mbedtls_mpi_free( &L );
-
- return( ret );
-}
-
-/*
- * Check that RSA CRT parameters are in accordance with core parameters.
- */
-
-int mbedtls_rsa_validate_crt( const mbedtls_mpi *P, const mbedtls_mpi *Q,
- const mbedtls_mpi *D, const mbedtls_mpi *DP,
- const mbedtls_mpi *DQ, const mbedtls_mpi *QP )
-{
- int ret = 0;
-
- mbedtls_mpi K, L;
- mbedtls_mpi_init( &K );
- mbedtls_mpi_init( &L );
-
- /* Check that DP - D == 0 mod P - 1 */
- if( DP != NULL )
- {
- if( P == NULL )
- {
- ret = MBEDTLS_ERR_RSA_BAD_INPUT_DATA;
- goto cleanup;
- }
-
- MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, P, 1 ) );
- MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &L, DP, D ) );
- MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &L, &L, &K ) );
-
- if( mbedtls_mpi_cmp_int( &L, 0 ) != 0 )
- {
- ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
- goto cleanup;
- }
- }
-
- /* Check that DQ - D == 0 mod Q - 1 */
- if( DQ != NULL )
- {
- if( Q == NULL )
- {
- ret = MBEDTLS_ERR_RSA_BAD_INPUT_DATA;
- goto cleanup;
- }
-
- MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, Q, 1 ) );
- MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &L, DQ, D ) );
- MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &L, &L, &K ) );
-
- if( mbedtls_mpi_cmp_int( &L, 0 ) != 0 )
- {
- ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
- goto cleanup;
- }
- }
-
- /* Check that QP * Q - 1 == 0 mod P */
- if( QP != NULL )
- {
- if( P == NULL || Q == NULL )
- {
- ret = MBEDTLS_ERR_RSA_BAD_INPUT_DATA;
- goto cleanup;
- }
-
- MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, QP, Q ) );
- MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, &K, 1 ) );
- MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &K, &K, P ) );
- if( mbedtls_mpi_cmp_int( &K, 0 ) != 0 )
- {
- ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
- goto cleanup;
- }
- }
-
-cleanup:
-
- /* Wrap MPI error codes by RSA check failure error code */
- if( ret != 0 &&
- ret != MBEDTLS_ERR_RSA_KEY_CHECK_FAILED &&
- ret != MBEDTLS_ERR_RSA_BAD_INPUT_DATA )
- {
- ret += MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
- }
-
- mbedtls_mpi_free( &K );
- mbedtls_mpi_free( &L );
-
- return( ret );
-}
-
-/*
- * Check that core RSA parameters are sane.
- */
-
-int mbedtls_rsa_validate_params( const mbedtls_mpi *N, const mbedtls_mpi *P,
- const mbedtls_mpi *Q, const mbedtls_mpi *D,
- const mbedtls_mpi *E,
- int (*f_rng)(void *, unsigned char *, size_t),
- void *p_rng )
-{
- int ret = 0;
- mbedtls_mpi K, L;
-
- mbedtls_mpi_init( &K );
- mbedtls_mpi_init( &L );
-
- /*
- * Step 1: If PRNG provided, check that P and Q are prime
- */
-
-#if defined(MBEDTLS_GENPRIME)
- if( f_rng != NULL && P != NULL &&
- ( ret = mbedtls_mpi_is_prime( P, f_rng, p_rng ) ) != 0 )
- {
- ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
- goto cleanup;
- }
-
- if( f_rng != NULL && Q != NULL &&
- ( ret = mbedtls_mpi_is_prime( Q, f_rng, p_rng ) ) != 0 )
- {
- ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
- goto cleanup;
- }
-#else
- ((void) f_rng);
- ((void) p_rng);
-#endif /* MBEDTLS_GENPRIME */
-
- /*
- * Step 2: Check that 1 < N = PQ
- */
-
- if( P != NULL && Q != NULL && N != NULL )
- {
- MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, P, Q ) );
- if( mbedtls_mpi_cmp_int( N, 1 ) <= 0 ||
- mbedtls_mpi_cmp_mpi( &K, N ) != 0 )
- {
- ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
- goto cleanup;
- }
- }
-
- /*
- * Step 3: Check and 1 < D, E < N if present.
- */
-
- if( N != NULL && D != NULL && E != NULL )
- {
- if ( mbedtls_mpi_cmp_int( D, 1 ) <= 0 ||
- mbedtls_mpi_cmp_int( E, 1 ) <= 0 ||
- mbedtls_mpi_cmp_mpi( D, N ) >= 0 ||
- mbedtls_mpi_cmp_mpi( E, N ) >= 0 )
- {
- ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
- goto cleanup;
- }
- }
-
- /*
- * Step 4: Check that D, E are inverse modulo P-1 and Q-1
- */
-
- if( P != NULL && Q != NULL && D != NULL && E != NULL )
- {
- if( mbedtls_mpi_cmp_int( P, 1 ) <= 0 ||
- mbedtls_mpi_cmp_int( Q, 1 ) <= 0 )
- {
- ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
- goto cleanup;
- }
-
- /* Compute DE-1 mod P-1 */
- MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, D, E ) );
- MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, &K, 1 ) );
- MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &L, P, 1 ) );
- MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &K, &K, &L ) );
- if( mbedtls_mpi_cmp_int( &K, 0 ) != 0 )
- {
- ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
- goto cleanup;
- }
-
- /* Compute DE-1 mod Q-1 */
- MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, D, E ) );
- MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, &K, 1 ) );
- MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &L, Q, 1 ) );
- MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &K, &K, &L ) );
- if( mbedtls_mpi_cmp_int( &K, 0 ) != 0 )
- {
- ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
- goto cleanup;
- }
- }
-
-cleanup:
-
- mbedtls_mpi_free( &K );
- mbedtls_mpi_free( &L );
-
- /* Wrap MPI error codes by RSA check failure error code */
- if( ret != 0 && ret != MBEDTLS_ERR_RSA_KEY_CHECK_FAILED )
- {
- ret += MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
- }
-
- return( ret );
-}
-
-int mbedtls_rsa_deduce_crt( const mbedtls_mpi *P, const mbedtls_mpi *Q,
- const mbedtls_mpi *D, mbedtls_mpi *DP,
- mbedtls_mpi *DQ, mbedtls_mpi *QP )
-{
- int ret = 0;
- mbedtls_mpi K;
- mbedtls_mpi_init( &K );
-
- /* DP = D mod P-1 */
- if( DP != NULL )
- {
- MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, P, 1 ) );
- MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( DP, D, &K ) );
- }
-
- /* DQ = D mod Q-1 */
- if( DQ != NULL )
- {
- MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, Q, 1 ) );
- MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( DQ, D, &K ) );
- }
-
- /* QP = Q^{-1} mod P */
- if( QP != NULL )
- {
- MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( QP, Q, P ) );
- }
-
-cleanup:
- mbedtls_mpi_free( &K );
-
- return( ret );
-}
-
-
-/*
- * Default RSA interface implementation
- */
-
-#if !defined(MBEDTLS_RSA_ALT)
-
int mbedtls_rsa_import( mbedtls_rsa_context *ctx,
const mbedtls_mpi *N,
const mbedtls_mpi *P, const mbedtls_mpi *Q,
