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,