library/rsa.c

/*
 *  The RSA public-key cryptosystem
 *
 *  Copyright (C) 2006-2015, ARM Limited, All Rights Reserved
 *  SPDX-License-Identifier: Apache-2.0
 *
 *  Licensed under the Apache License, Version 2.0 (the "License"); you may
 *  not use this file except in compliance with the License.
 *  You may obtain a copy of the License at
 *
 *  http://www.apache.org/licenses/LICENSE-2.0
 *
 *  Unless required by applicable law or agreed to in writing, software
 *  distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
 *  WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 *  See the License for the specific language governing permissions and
 *  limitations under the License.
 *
 *  This file is part of mbed TLS (https://tls.mbed.org)
 */
/*
 *  The following sources were referenced in the design of this implementation
 *  of the RSA algorithm:
 *
 *  [1] A method for obtaining digital signatures and public-key cryptosystems
 *      R Rivest, A Shamir, and L Adleman
 *      http://people.csail.mit.edu/rivest/pubs.html#RSA78
 *
 *  [2] Handbook of Applied Cryptography - 1997, Chapter 8
 *      Menezes, van Oorschot and Vanstone
 *
 *  [3] Malware Guard Extension: Using SGX to Conceal Cache Attacks
 *      Michael Schwarz, Samuel Weiser, Daniel Gruss, Clémentine Maurice and
 *      Stefan Mangard
 *      https://arxiv.org/abs/1702.08719v2
 *
 */

#if !defined(MBEDTLS_CONFIG_FILE)
#include "mbedtls/config.h"
#else
#include MBEDTLS_CONFIG_FILE
#endif

#if defined(MBEDTLS_RSA_C)

#include "mbedtls/rsa.h"
#include "mbedtls/oid.h"

#include <string.h>

#if defined(MBEDTLS_PKCS1_V21)
#include "mbedtls/md.h"
#endif

#if defined(MBEDTLS_PKCS1_V15) && !defined(__OpenBSD__)
#include <stdlib.h>
#endif

#if defined(MBEDTLS_PLATFORM_C)
#include "mbedtls/platform.h"
#else
#include <stdio.h>
#define mbedtls_printf printf
#define mbedtls_calloc calloc
#define mbedtls_free   free
#endif

/* 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_moduli
 *     - mbedtls_rsa_deduce_private
 *     - 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_moduli( mbedtls_mpi const *N,
                     mbedtls_mpi const *D, mbedtls_mpi const *E,
                     int (*f_rng)(void *, unsigned char *, size_t), void *p_rng,
                     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 bitlen_half; /* Half the bitsize of the modulus N */
    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] */

    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 ) );

    /* This is used to generate a few numbers around N / 2
     * if no PRNG is provided. */
    if( f_rng == NULL )
        bitlen_half = mbedtls_mpi_bitlen( N ) / 2;

    /*
     * Actual work
     */

    for( attempt = 0; attempt < 30; ++attempt )
    {
        /* Generate some number in [0,N], either randomly
         * if a PRNG is given, or try numbers around N/2 */
        if( f_rng != NULL )
        {
            MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &K,
                                        mbedtls_mpi_size( N ),
                                        f_rng, p_rng ) );
        }
        else
        {
            MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &K, 1 ) ) ;
            MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &K, bitlen_half ) ) ;
            MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( &K, &K, attempt + 1 ) );
        }

        /* 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( mbedtls_mpi *P, mbedtls_mpi *Q,
                                mbedtls_mpi *D, mbedtls_mpi *E )
{
    int ret = 0;
    mbedtls_mpi K;

    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 );

    /* Temporarily replace P and Q by P-1 and Q-1, respectively. */
    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( P, P, 1 ) );
    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( Q, Q, 1 ) );

    /* Temporarily compute the gcd(P-1, Q-1) in D. */
    MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( D, P, Q ) );

    /* Compute LCM(P-1, Q-1) in K */
    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, P, Q ) );
    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 ) );

    /* Restore P and Q. */
    MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( P, P, 1 ) );
    MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( Q, Q, 1 ) );

cleanup:

    mbedtls_mpi_free( &K );

    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 - P == 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 )
        {
            return( MBEDTLS_ERR_RSA_KEY_CHECK_FAILED );
        }
    }

    /* Check that DQ - Q == 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 )
        {
            return( MBEDTLS_ERR_RSA_KEY_CHECK_FAILED );
        }
    }

    /* Check that QP * P - 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 )
        {
            return( MBEDTLS_ERR_RSA_KEY_CHECK_FAILED );
        }
    }

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 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 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 ||
            mbedtls_mpi_cmp_int( D, 1 ) <= 0 ||
            mbedtls_mpi_cmp_int( E, 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,
                        const mbedtls_mpi *D, const mbedtls_mpi *E )
{
    int ret;

    if( ( N != NULL && ( ret = mbedtls_mpi_copy( &ctx->N, N ) ) != 0 ) ||
        ( P != NULL && ( ret = mbedtls_mpi_copy( &ctx->P, P ) ) != 0 ) ||
        ( Q != NULL && ( ret = mbedtls_mpi_copy( &ctx->Q, Q ) ) != 0 ) ||
        ( D != NULL && ( ret = mbedtls_mpi_copy( &ctx->D, D ) ) != 0 ) ||
        ( E != NULL && ( ret = mbedtls_mpi_copy( &ctx->E, E ) ) != 0 ) )
    {
        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA + ret );
    }

    if( N != NULL )
        ctx->len = mbedtls_mpi_size( &ctx->N );

    return( 0 );
}

int mbedtls_rsa_import_raw( mbedtls_rsa_context *ctx,
                            unsigned char *N, size_t N_len,
                            unsigned char *P, size_t P_len,
                            unsigned char *Q, size_t Q_len,
                            unsigned char *D, size_t D_len,
                            unsigned char *E, size_t E_len )
{
    int ret;

    if( N != NULL )
    {
        MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &ctx->N, N, N_len ) );
        ctx->len = mbedtls_mpi_size( &ctx->N );
    }

    if( P != NULL )
        MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &ctx->P, P, P_len ) );

    if( Q != NULL )
        MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &ctx->Q, Q, Q_len ) );

    if( D != NULL )
        MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &ctx->D, D, D_len ) );

    if( E != NULL )
        MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &ctx->E, E, E_len ) );

cleanup:

    if( ret != 0 )
        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA + ret );

    return( 0 );
}

int mbedtls_rsa_complete( mbedtls_rsa_context *ctx,
                          int (*f_rng)(void *, unsigned char *, size_t),
                          void *p_rng )
{
    int ret = 0;

    const int have_N = ( mbedtls_mpi_cmp_int( &ctx->N, 0 ) != 0 );
    const int have_P = ( mbedtls_mpi_cmp_int( &ctx->P, 0 ) != 0 );
    const int have_Q = ( mbedtls_mpi_cmp_int( &ctx->Q, 0 ) != 0 );
    const int have_D = ( mbedtls_mpi_cmp_int( &ctx->D, 0 ) != 0 );
    const int have_E = ( mbedtls_mpi_cmp_int( &ctx->E, 0 ) != 0 );

    /*
     * Check whether provided parameters are enough
     * to deduce all others. The following incomplete
     * parameter sets for private keys are supported:
     *
     * (1) P, Q missing.
     * (2) D and potentially N missing.
     *
     */

    const int n_missing  =              have_P &&  have_Q &&  have_D && have_E;
    const int pq_missing =   have_N && !have_P && !have_Q &&  have_D && have_E;
    const int d_missing  =              have_P &&  have_Q && !have_D && have_E;
    const int is_pub     =   have_N && !have_P && !have_Q && !have_D && have_E;

    /* These three alternatives are mutually exclusive */
    const int is_priv = n_missing || pq_missing || d_missing;

    if( !is_priv && !is_pub )
        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );

    /*
     * Step 1: Deduce N if P, Q are provided.
     */

    if( !have_N && have_P && have_Q )
    {
        if( ( ret = mbedtls_mpi_mul_mpi( &ctx->N, &ctx->P,
                                         &ctx->Q ) ) != 0 )
        {
            return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA + ret );
        }

        ctx->len = mbedtls_mpi_size( &ctx->N );
    }

    /*
     * Step 2: Deduce and verify all remaining core parameters.
     */

    if( pq_missing )
    {
        /* This includes sanity checking of core parameters,
         * so no further checks necessary. */
        ret = mbedtls_rsa_deduce_moduli( &ctx->N, &ctx->D, &ctx->E,
                                         f_rng, p_rng,
                                         &ctx->P, &ctx->Q );
        if( ret != 0 )
            return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA + ret );

    }
    else if( d_missing )
    {
#if defined(MBEDTLS_GENPRIME)
        /* If a PRNG is provided, check if P, Q are prime. */
        if( f_rng != NULL  &&
            ( ( ret = mbedtls_mpi_is_prime( &ctx->P, f_rng, p_rng ) ) != 0 ||
              ( ret = mbedtls_mpi_is_prime( &ctx->Q, f_rng, p_rng ) ) != 0 ) )
        {
            return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA + ret );
        }
#endif /* MBEDTLS_GENPRIME */

        /* Deduce private exponent. This includes double-checking of the result,
         * so together with the primality test above all core parameters are
         * guaranteed to be sane if this call succeeds. */
        if( ( ret = mbedtls_rsa_deduce_private( &ctx->P, &ctx->Q,
                                                &ctx->D, &ctx->E ) ) != 0 )
        {
            return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA + ret );
        }
    }

    /* In the remaining case of a public key, there's nothing to check for. */

    /*
     * Step 3: Deduce all additional parameters specific
     *         to our current RSA implementaiton.
     */

#if !defined(MBEDTLS_RSA_NO_CRT)
    if( is_priv )
    {
        ret = mbedtls_rsa_deduce_crt( &ctx->P,  &ctx->Q,  &ctx->D,
                                      &ctx->DP, &ctx->DQ, &ctx->QP );
        if( ret != 0 )
            return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA + ret );
    }
#endif /* MBEDTLS_RSA_NO_CRT */

    /*
     * Step 3: Double check
     */

    if( is_priv )
    {
        if( ( ret = mbedtls_rsa_check_privkey( ctx ) ) != 0 )
            return( ret );
    }
    else
    {
        if( ( ret = mbedtls_rsa_check_pubkey( ctx ) ) != 0 )
            return( ret );
    }

    return( 0 );
}

/*
 * Check if CRT parameters match RSA context.
 * This has to be implemented even if CRT is not used,
 * in order to be able to validate DER encoded RSA keys,
 * which always contain CRT parameters.
 */
int mbedtls_rsa_check_crt( const mbedtls_rsa_context *ctx,
                           mbedtls_mpi *DP, mbedtls_mpi *DQ, mbedtls_mpi *QP )
{
    int ret = 0;

    /* Check if key is private or public */
    const int is_priv =
        mbedtls_mpi_cmp_int( &ctx->N, 0 ) != 0 &&
        mbedtls_mpi_cmp_int( &ctx->P, 0 ) != 0 &&
        mbedtls_mpi_cmp_int( &ctx->Q, 0 ) != 0 &&
        mbedtls_mpi_cmp_int( &ctx->D, 0 ) != 0 &&
        mbedtls_mpi_cmp_int( &ctx->E, 0 ) != 0;

    if( !is_priv )
    {
        /* Checking optional parameters only makes sense for private keys. */
        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
    }

#if !defined(MBEDTLS_RSA_NO_CRT)
    if( ( DP != NULL && mbedtls_mpi_cmp_mpi( DP, &ctx->DP ) != 0 ) ||
        ( DQ != NULL && mbedtls_mpi_cmp_mpi( DQ, &ctx->DQ ) != 0 ) ||
        ( QP != NULL && mbedtls_mpi_cmp_mpi( QP, &ctx->QP ) != 0 ) )
    {
        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
    }
#else /* MBEDTLS_RSA_NO_CRT */
    if( ( ret = mbedtls_rsa_validate_crt( &ctx->P, &ctx->Q, &ctx->D,
                                          DP, DQ, QP ) ) != 0 )
    {
        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
    }
#endif

    if( ret != 0 )
        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA + ret );

    return( 0 );
}

int mbedtls_rsa_export_raw( const mbedtls_rsa_context *ctx,
                            unsigned char *N, size_t N_len,
                            unsigned char *P, size_t P_len,
                            unsigned char *Q, size_t Q_len,
                            unsigned char *D, size_t D_len,
                            unsigned char *E, size_t E_len )
{
    int ret = 0;

    /* Check if key is private or public */
    const int is_priv =
        mbedtls_mpi_cmp_int( &ctx->N, 0 ) != 0 &&
        mbedtls_mpi_cmp_int( &ctx->P, 0 ) != 0 &&
        mbedtls_mpi_cmp_int( &ctx->Q, 0 ) != 0 &&
        mbedtls_mpi_cmp_int( &ctx->D, 0 ) != 0 &&
        mbedtls_mpi_cmp_int( &ctx->E, 0 ) != 0;

    if( !is_priv )
    {
        /* If we're trying to export private parameters for a public key,
         * something must be wrong. */
        if( P != NULL || Q != NULL || D != NULL )
            return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );

    }

    if( N != NULL )
        MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &ctx->N, N, N_len ) );

    if( P != NULL )
        MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &ctx->P, P, P_len ) );

    if( Q != NULL )
        MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &ctx->Q, Q, Q_len ) );

    if( D != NULL )
        MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &ctx->D, D, D_len ) );

    if( E != NULL )
        MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &ctx->E, E, E_len ) );

cleanup:

    return( ret );
}

int mbedtls_rsa_export( const mbedtls_rsa_context *ctx,
                        mbedtls_mpi *N, mbedtls_mpi *P, mbedtls_mpi *Q,
                        mbedtls_mpi *D, mbedtls_mpi *E )
{
    int ret;

    /* Check if key is private or public */
    int is_priv =
        mbedtls_mpi_cmp_int( &ctx->N, 0 ) != 0 &&
        mbedtls_mpi_cmp_int( &ctx->P, 0 ) != 0 &&
        mbedtls_mpi_cmp_int( &ctx->Q, 0 ) != 0 &&
        mbedtls_mpi_cmp_int( &ctx->D, 0 ) != 0 &&
        mbedtls_mpi_cmp_int( &ctx->E, 0 ) != 0;

    if( !is_priv )
    {
        /* If we're trying to export private parameters for a public key,
         * something must be wrong. */
        if( P != NULL || Q != NULL || D != NULL )
            return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );

    }

    /* Export all requested core parameters. */

    if( ( N != NULL && ( ret = mbedtls_mpi_copy( N, &ctx->N ) ) != 0 ) ||
        ( P != NULL && ( ret = mbedtls_mpi_copy( P, &ctx->P ) ) != 0 ) ||
        ( Q != NULL && ( ret = mbedtls_mpi_copy( Q, &ctx->Q ) ) != 0 ) ||
        ( D != NULL && ( ret = mbedtls_mpi_copy( D, &ctx->D ) ) != 0 ) ||
        ( E != NULL && ( ret = mbedtls_mpi_copy( E, &ctx->E ) ) != 0 ) )
    {
        return( ret );
    }

    return( 0 );
}

/*
 * Export CRT parameters
 * This must also be implemented if CRT is not used, for being able to
 * write DER encoded RSA keys. The helper function mbedtls_rsa_deduce_crt
 * can be used in this case.
 */
int mbedtls_rsa_export_crt( const mbedtls_rsa_context *ctx,
                            mbedtls_mpi *DP, mbedtls_mpi *DQ, mbedtls_mpi *QP )
{
    int ret;

    /* Check if key is private or public */
    int is_priv =
        mbedtls_mpi_cmp_int( &ctx->N, 0 ) != 0 &&
        mbedtls_mpi_cmp_int( &ctx->P, 0 ) != 0 &&
        mbedtls_mpi_cmp_int( &ctx->Q, 0 ) != 0 &&
        mbedtls_mpi_cmp_int( &ctx->D, 0 ) != 0 &&
        mbedtls_mpi_cmp_int( &ctx->E, 0 ) != 0;

    if( !is_priv )
        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );

#if !defined(MBEDTLS_RSA_NO_CRT)
    /* Export all requested blinding parameters. */
    if( ( DP != NULL && ( ret = mbedtls_mpi_copy( DP, &ctx->DP ) ) != 0 ) ||
        ( DQ != NULL && ( ret = mbedtls_mpi_copy( DQ, &ctx->DQ ) ) != 0 ) ||
        ( QP != NULL && ( ret = mbedtls_mpi_copy( QP, &ctx->QP ) ) != 0 ) )
    {
        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA + ret );
    }
#else
    if( ( ret = mbedtls_rsa_deduce_crt( &ctx->P, &ctx->Q, &ctx->D,
                                        DP, DQ, QP ) ) != 0 )
    {
        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA + ret );
    }
#endif

    return( 0 );
}

/*
 * Initialize an RSA context
 */
void mbedtls_rsa_init( mbedtls_rsa_context *ctx,
               int padding,
               int hash_id )
{
    memset( ctx, 0, sizeof( mbedtls_rsa_context ) );

    mbedtls_rsa_set_padding( ctx, padding, hash_id );

#if defined(MBEDTLS_THREADING_C)
    mbedtls_mutex_init( &ctx->mutex );
#endif
}

/*
 * Set padding for an existing RSA context
 */
void mbedtls_rsa_set_padding( mbedtls_rsa_context *ctx, int padding, int hash_id )
{
    ctx->padding = padding;
    ctx->hash_id = hash_id;
}

/*
 * Get length in bytes of RSA modulus
 */

size_t mbedtls_rsa_get_len( const mbedtls_rsa_context *ctx )
{
    return( ctx->len );
}


#if defined(MBEDTLS_GENPRIME)

/*
 * 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 H, G;

    if( f_rng == NULL || nbits < 128 || exponent < 3 )
        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );

    if( nbits % 2 )
        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );

    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, 0,
                                                f_rng, p_rng ) );

        MBEDTLS_MPI_CHK( mbedtls_mpi_gen_prime( &ctx->Q, nbits >> 1, 0,
                                                f_rng, p_rng ) );

        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;

        if( mbedtls_mpi_cmp_mpi( &ctx->P, &ctx->Q ) < 0 )
            mbedtls_mpi_swap( &ctx->P, &ctx->Q );

        /* Temporarily replace P,Q by P-1, Q-1 */
        MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &ctx->P, &ctx->P, 1 ) );
        MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &ctx->Q, &ctx->Q, 1 ) );
        MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &H, &ctx->P, &ctx->Q ) );
        MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( &G, &ctx->E, &H  ) );
    }
    while( mbedtls_mpi_cmp_int( &G, 1 ) != 0 );

    /* Restore P,Q */
    MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( &ctx->P,  &ctx->P, 1 ) );
    MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( &ctx->Q,  &ctx->Q, 1 ) );

    ctx->len = mbedtls_mpi_size( &ctx->N );

    /*
     * 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  ) );

#if !defined(MBEDTLS_RSA_NO_CRT)
    MBEDTLS_MPI_CHK( mbedtls_rsa_deduce_crt( &ctx->P, &ctx->Q, &ctx->D,
                                             &ctx->DP, &ctx->DQ, &ctx->QP ) );
#endif /* MBEDTLS_RSA_NO_CRT */

    /* Double-check */
    MBEDTLS_MPI_CHK( mbedtls_rsa_check_privkey( ctx ) );

cleanup:

    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 );
}

#endif /* MBEDTLS_GENPRIME */

/*
 * Check a public RSA key
 */
int mbedtls_rsa_check_pubkey( const mbedtls_rsa_context *ctx )
{
    if( !ctx->N.p || !ctx->E.p )
        return( MBEDTLS_ERR_RSA_KEY_CHECK_FAILED );

    if( ctx->len != mbedtls_mpi_size( &ctx->N ) )
        return( MBEDTLS_ERR_RSA_KEY_CHECK_FAILED );

    if( ( ctx->N.p[0] & 1 ) == 0 ||
        ( ctx->E.p[0] & 1 ) == 0 )
        return( MBEDTLS_ERR_RSA_KEY_CHECK_FAILED );

    if( mbedtls_mpi_bitlen( &ctx->N ) < 128 ||
        mbedtls_mpi_bitlen( &ctx->N ) > MBEDTLS_MPI_MAX_BITS )
        return( MBEDTLS_ERR_RSA_KEY_CHECK_FAILED );

    if( mbedtls_mpi_bitlen( &ctx->E ) < 2 ||
        mbedtls_mpi_cmp_mpi( &ctx->E, &ctx->N ) >= 0 )
        return( MBEDTLS_ERR_RSA_KEY_CHECK_FAILED );

    return( 0 );
}

/*
 * Check a private RSA key
 */
int mbedtls_rsa_check_privkey( const mbedtls_rsa_context *ctx )
{
    if( mbedtls_rsa_check_pubkey( ctx ) != 0 ||
        mbedtls_rsa_validate_params( &ctx->N, &ctx->P, &ctx->Q,
                                     &ctx->D, &ctx->E, NULL, NULL ) != 0 )
    {
        return( MBEDTLS_ERR_RSA_KEY_CHECK_FAILED );
    }
#if !defined(MBEDTLS_RSA_NO_CRT)
    else if( mbedtls_rsa_validate_crt( &ctx->P, &ctx->Q, &ctx->D,
                                       &ctx->DP, &ctx->DQ, &ctx->QP ) != 0 )
    {
        return( MBEDTLS_ERR_RSA_KEY_CHECK_FAILED );
    }
#endif

    return( 0 );
}

/*
 * Check if contexts holding a public and private key match
 */
int mbedtls_rsa_check_pub_priv( const mbedtls_rsa_context *pub, const mbedtls_rsa_context *prv )
{
    if( mbedtls_rsa_check_pubkey( pub ) != 0 ||
        mbedtls_rsa_check_privkey( prv ) != 0 )
    {
        return( MBEDTLS_ERR_RSA_KEY_CHECK_FAILED );
    }

    if( mbedtls_mpi_cmp_mpi( &pub->N, &prv->N ) != 0 ||
        mbedtls_mpi_cmp_mpi( &pub->E, &prv->E ) != 0 )
    {
        return( MBEDTLS_ERR_RSA_KEY_CHECK_FAILED );
    }

    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 );
}

/*
 * 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 );
}

/*
 * Exponent blinding supposed to prevent side-channel attacks using multiple
 * traces of measurements to recover the RSA key. The more collisions are there,
 * the more bits of the key can be recovered. See [3].
 *
 * Collecting n collisions with m bit long blinding value requires 2^(m-m/n)
 * observations on avarage.
 *
 * For example with 28 byte blinding to achieve 2 collisions the adversary has
 * to make 2^112 observations on avarage.
 *
 * (With the currently (as of 2017 April) known best algorithms breaking 2048
 * bit RSA requires approximately as much time as trying out 2^112 random keys.
 * Thus in this sense with 28 byte blinding the security is not reduced by
 * side-channel attacks like the one in [3])
 *
 * This countermeasure does not help if the key recovery is possible with a
 * single trace.
 */
#define RSA_EXPONENT_BLINDING 28

/*
 * 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;
    mbedtls_mpi P1, Q1, R;
#if defined(MBEDTLS_RSA_NO_CRT)
    mbedtls_mpi D_blind;
    mbedtls_mpi *D = &ctx->D;
#else
    mbedtls_mpi DP_blind, DQ_blind;
    mbedtls_mpi *DP = &ctx->DP;
    mbedtls_mpi *DQ = &ctx->DQ;
#endif

    /* Sanity-check that all relevant fields are at least set,
     * but don't perform a full keycheck. */
    if( mbedtls_mpi_cmp_int( &ctx->N, 0 ) == 0 ||
        mbedtls_mpi_cmp_int( &ctx->P, 0 ) == 0 ||
        mbedtls_mpi_cmp_int( &ctx->Q, 0 ) == 0 ||
        mbedtls_mpi_cmp_int( &ctx->D, 0 ) == 0 ||
        mbedtls_mpi_cmp_int( &ctx->E, 0 ) == 0 )
    {
        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
    }
#if !defined(MBEDTLS_RSA_NO_CRT)
    if( mbedtls_mpi_cmp_int( &ctx->DP, 0 ) == 0 ||
        mbedtls_mpi_cmp_int( &ctx->DQ, 0 ) == 0 ||
        mbedtls_mpi_cmp_int( &ctx->QP, 0 ) == 0 )
    {
        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
    }
#endif /* MBEDTLS_RSA_NO_CRT */

    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( f_rng != NULL )
    {
#if defined(MBEDTLS_RSA_NO_CRT)
        mbedtls_mpi_init( &D_blind );
#else
        mbedtls_mpi_init( &DP_blind );
        mbedtls_mpi_init( &DQ_blind );
#endif
    }


#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 ) );

        /*
         * Exponent blinding
         */
        MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &P1, &ctx->P, 1 ) );
        MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &Q1, &ctx->Q, 1 ) );

#if defined(MBEDTLS_RSA_NO_CRT)
        /*
         * D_blind = ( P - 1 ) * ( Q - 1 ) * R + D
         */
        MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &R, RSA_EXPONENT_BLINDING,
                         f_rng, p_rng ) );
        MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &D_blind, &P1, &Q1 ) );
        MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &D_blind, &D_blind, &R ) );
        MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &D_blind, &D_blind, &ctx->D ) );

        D = &D_blind;
#else
        /*
         * DP_blind = ( P - 1 ) * R + DP
         */
        MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &R, RSA_EXPONENT_BLINDING,
                         f_rng, p_rng ) );
        MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &DP_blind, &P1, &R ) );
        MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &DP_blind, &DP_blind,
                    &ctx->DP ) );

        DP = &DP_blind;

        /*
         * DQ_blind = ( Q - 1 ) * R + DQ
         */
        MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &R, RSA_EXPONENT_BLINDING,
                         f_rng, p_rng ) );
        MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &DQ_blind, &Q1, &R ) );
        MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &DQ_blind, &DQ_blind,
                    &ctx->DQ ) );

        DQ = &DQ_blind;
#endif /* MBEDTLS_RSA_NO_CRT */
    }

#if defined(MBEDTLS_RSA_NO_CRT)
    MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &T, &T, 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, DP, &ctx->P, &ctx->RP ) );
    MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &T2, &T, 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 );
    mbedtls_mpi_free( &P1 ); mbedtls_mpi_free( &Q1 ); mbedtls_mpi_free( &R );

    if( f_rng != NULL )
    {
#if defined(MBEDTLS_RSA_NO_CRT)
        mbedtls_mpi_free( &D_blind );
#else
        mbedtls_mpi_free( &DP_blind );
        mbedtls_mpi_free( &DQ_blind );
#endif
    }

    if( ret != 0 )
        return( MBEDTLS_ERR_RSA_PRIVATE_FAILED + ret );

    return( 0 );
}

#if defined(MBEDTLS_PKCS1_V21)
/**
 * Generate and apply the MGF1 operation (from PKCS#1 v2.1) to a buffer.
 *
 * \param dst       buffer to mask
 * \param dlen      length of destination buffer
 * \param src       source of the mask generation
 * \param slen      length of the source buffer
 * \param md_ctx    message digest context to use
 */
static void mgf_mask( unsigned char *dst, size_t dlen, unsigned char *src,
                      size_t slen, mbedtls_md_context_t *md_ctx )
{
    unsigned char mask[MBEDTLS_MD_MAX_SIZE];
    unsigned char counter[4];
    unsigned char *p;
    unsigned int hlen;
    size_t i, use_len;

    memset( mask, 0, MBEDTLS_MD_MAX_SIZE );
    memset( counter, 0, 4 );

    hlen = mbedtls_md_get_size( md_ctx->md_info );

    /* Generate and apply dbMask */
    p = dst;

    while( dlen > 0 )
    {
        use_len = hlen;
        if( dlen < hlen )
            use_len = dlen;

        mbedtls_md_starts( md_ctx );
        mbedtls_md_update( md_ctx, src, slen );
        mbedtls_md_update( md_ctx, counter, 4 );
        mbedtls_md_finish( md_ctx, mask );

        for( i = 0; i < use_len; ++i )
            *p++ ^= mask[i];

        counter[3]++;

        dlen -= use_len;
    }

    mbedtls_zeroize( mask, sizeof( mask ) );
}
#endif /* MBEDTLS_PKCS1_V21 */

#if defined(MBEDTLS_PKCS1_V21)
/*
 * Implementation of the PKCS#1 v2.1 RSAES-OAEP-ENCRYPT function
 */
int mbedtls_rsa_rsaes_oaep_encrypt( mbedtls_rsa_context *ctx,
                            int (*f_rng)(void *, unsigned char *, size_t),
                            void *p_rng,
                            int mode,
                            const unsigned char *label, size_t label_len,
                            size_t ilen,
                            const unsigned char *input,
                            unsigned char *output )
{
    size_t olen;
    int ret;
    unsigned char *p = output;
    unsigned int hlen;
    const mbedtls_md_info_t *md_info;
    mbedtls_md_context_t md_ctx;

    if( mode == MBEDTLS_RSA_PRIVATE && ctx->padding != MBEDTLS_RSA_PKCS_V21 )
        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );

    if( f_rng == NULL )
        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );

    md_info = mbedtls_md_info_from_type( (mbedtls_md_type_t) ctx->hash_id );
    if( md_info == NULL )
        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );

    olen = ctx->len;
    hlen = mbedtls_md_get_size( md_info );

    /* first comparison checks for overflow */
    if( ilen + 2 * hlen + 2 < ilen || olen < ilen + 2 * hlen + 2 )
        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );

    memset( output, 0, olen );

    *p++ = 0;

    /* Generate a random octet string seed */
    if( ( ret = f_rng( p_rng, p, hlen ) ) != 0 )
        return( MBEDTLS_ERR_RSA_RNG_FAILED + ret );

    p += hlen;

    /* Construct DB */
    mbedtls_md( md_info, label, label_len, p );
    p += hlen;
    p += olen - 2 * hlen - 2 - ilen;
    *p++ = 1;
    memcpy( p, input, ilen );

    mbedtls_md_init( &md_ctx );
    if( ( ret = mbedtls_md_setup( &md_ctx, md_info, 0 ) ) != 0 )
    {
        mbedtls_md_free( &md_ctx );
        return( ret );
    }

    /* maskedDB: Apply dbMask to DB */
    mgf_mask( output + hlen + 1, olen - hlen - 1, output + 1, hlen,
               &md_ctx );

    /* maskedSeed: Apply seedMask to seed */
    mgf_mask( output + 1, hlen, output + hlen + 1, olen - hlen - 1,
               &md_ctx );

    mbedtls_md_free( &md_ctx );

    return( ( mode == MBEDTLS_RSA_PUBLIC )
            ? mbedtls_rsa_public(  ctx, output, output )
            : mbedtls_rsa_private( ctx, f_rng, p_rng, output, output ) );
}
#endif /* MBEDTLS_PKCS1_V21 */

#if defined(MBEDTLS_PKCS1_V15)
/*
 * Implementation of the PKCS#1 v2.1 RSAES-PKCS1-V1_5-ENCRYPT function
 */
int mbedtls_rsa_rsaes_pkcs1_v15_encrypt( mbedtls_rsa_context *ctx,
                                 int (*f_rng)(void *, unsigned char *, size_t),
                                 void *p_rng,
                                 int mode, size_t ilen,
                                 const unsigned char *input,
                                 unsigned char *output )
{
    size_t nb_pad, olen;
    int ret;
    unsigned char *p = output;

    if( mode == MBEDTLS_RSA_PRIVATE && ctx->padding != MBEDTLS_RSA_PKCS_V15 )
        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );

    // We don't check p_rng because it won't be dereferenced here
    if( f_rng == NULL || input == NULL || output == NULL )
        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );

    olen = ctx->len;

    /* first comparison checks for overflow */
    if( ilen + 11 < ilen || olen < ilen + 11 )
        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );

    nb_pad = olen - 3 - ilen;

    *p++ = 0;
    if( mode == MBEDTLS_RSA_PUBLIC )
    {
        *p++ = MBEDTLS_RSA_CRYPT;

        while( nb_pad-- > 0 )
        {
            int rng_dl = 100;

            do {
                ret = f_rng( p_rng, p, 1 );
            } while( *p == 0 && --rng_dl && ret == 0 );

            /* Check if RNG failed to generate data */
            if( rng_dl == 0 || ret != 0 )
                return( MBEDTLS_ERR_RSA_RNG_FAILED + ret );

            p++;
        }
    }
    else
    {
        *p++ = MBEDTLS_RSA_SIGN;

        while( nb_pad-- > 0 )
            *p++ = 0xFF;
    }

    *p++ = 0;
    memcpy( p, input, ilen );

    return( ( mode == MBEDTLS_RSA_PUBLIC )
            ? mbedtls_rsa_public(  ctx, output, output )
            : mbedtls_rsa_private( ctx, f_rng, p_rng, output, output ) );
}
#endif /* MBEDTLS_PKCS1_V15 */

/*
 * Add the message padding, then do an RSA operation
 */
int mbedtls_rsa_pkcs1_encrypt( mbedtls_rsa_context *ctx,
                       int (*f_rng)(void *, unsigned char *, size_t),
                       void *p_rng,
                       int mode, size_t ilen,
                       const unsigned char *input,
                       unsigned char *output )
{
    switch( ctx->padding )
    {
#if defined(MBEDTLS_PKCS1_V15)
        case MBEDTLS_RSA_PKCS_V15:
            return mbedtls_rsa_rsaes_pkcs1_v15_encrypt( ctx, f_rng, p_rng, mode, ilen,
                                                input, output );
#endif

#if defined(MBEDTLS_PKCS1_V21)
        case MBEDTLS_RSA_PKCS_V21:
            return mbedtls_rsa_rsaes_oaep_encrypt( ctx, f_rng, p_rng, mode, NULL, 0,
                                           ilen, input, output );
#endif

        default:
            return( MBEDTLS_ERR_RSA_INVALID_PADDING );
    }
}

#if defined(MBEDTLS_PKCS1_V21)
/*
 * Implementation of the PKCS#1 v2.1 RSAES-OAEP-DECRYPT function
 */
int mbedtls_rsa_rsaes_oaep_decrypt( mbedtls_rsa_context *ctx,
                            int (*f_rng)(void *, unsigned char *, size_t),
                            void *p_rng,
                            int mode,
                            const unsigned char *label, size_t label_len,
                            size_t *olen,
                            const unsigned char *input,
                            unsigned char *output,
                            size_t output_max_len )
{
    int ret;
    size_t ilen, i, pad_len;
    unsigned char *p, bad, pad_done;
    unsigned char buf[MBEDTLS_MPI_MAX_SIZE];
    unsigned char lhash[MBEDTLS_MD_MAX_SIZE];
    unsigned int hlen;
    const mbedtls_md_info_t *md_info;
    mbedtls_md_context_t md_ctx;

    /*
     * Parameters sanity checks
     */
    if( mode == MBEDTLS_RSA_PRIVATE && ctx->padding != MBEDTLS_RSA_PKCS_V21 )
        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );

    ilen = ctx->len;

    if( ilen < 16 || ilen > sizeof( buf ) )
        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );

    md_info = mbedtls_md_info_from_type( (mbedtls_md_type_t) ctx->hash_id );
    if( md_info == NULL )
        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );

    hlen = mbedtls_md_get_size( md_info );

    // checking for integer underflow
    if( 2 * hlen + 2 > ilen )
        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );

    /*
     * RSA operation
     */
    ret = ( mode == MBEDTLS_RSA_PUBLIC )
          ? mbedtls_rsa_public(  ctx, input, buf )
          : mbedtls_rsa_private( ctx, f_rng, p_rng, input, buf );

    if( ret != 0 )
        goto cleanup;

    /*
     * Unmask data and generate lHash
     */
    mbedtls_md_init( &md_ctx );
    if( ( ret = mbedtls_md_setup( &md_ctx, md_info, 0 ) ) != 0 )
    {
        mbedtls_md_free( &md_ctx );
        goto cleanup;
    }


    /* Generate lHash */
    mbedtls_md( md_info, label, label_len, lhash );

    /* seed: Apply seedMask to maskedSeed */
    mgf_mask( buf + 1, hlen, buf + hlen + 1, ilen - hlen - 1,
               &md_ctx );

    /* DB: Apply dbMask to maskedDB */
    mgf_mask( buf + hlen + 1, ilen - hlen - 1, buf + 1, hlen,
               &md_ctx );

    mbedtls_md_free( &md_ctx );

    /*
     * Check contents, in "constant-time"
     */
    p = buf;
    bad = 0;

    bad |= *p++; /* First byte must be 0 */

    p += hlen; /* Skip seed */

    /* Check lHash */
    for( i = 0; i < hlen; i++ )
        bad |= lhash[i] ^ *p++;

    /* Get zero-padding len, but always read till end of buffer
     * (minus one, for the 01 byte) */
    pad_len = 0;
    pad_done = 0;
    for( i = 0; i < ilen - 2 * hlen - 2; i++ )
    {
        pad_done |= p[i];
        pad_len += ((pad_done | (unsigned char)-pad_done) >> 7) ^ 1;
    }

    p += pad_len;
    bad |= *p++ ^ 0x01;

    /*
     * The only information "leaked" is whether the padding was correct or not
     * (eg, no data is copied if it was not correct). This meets the
     * recommendations in PKCS#1 v2.2: an opponent cannot distinguish between
     * the different error conditions.
     */
    if( bad != 0 )
    {
        ret = MBEDTLS_ERR_RSA_INVALID_PADDING;
        goto cleanup;
    }

    if( ilen - ( p - buf ) > output_max_len )
    {
        ret = MBEDTLS_ERR_RSA_OUTPUT_TOO_LARGE;
        goto cleanup;
    }

    *olen = ilen - (p - buf);
    memcpy( output, p, *olen );
    ret = 0;

cleanup:
    mbedtls_zeroize( buf, sizeof( buf ) );
    mbedtls_zeroize( lhash, sizeof( lhash ) );

    return( ret );
}
#endif /* MBEDTLS_PKCS1_V21 */

#if defined(MBEDTLS_PKCS1_V15)
/*
 * Implementation of the PKCS#1 v2.1 RSAES-PKCS1-V1_5-DECRYPT function
 */
int mbedtls_rsa_rsaes_pkcs1_v15_decrypt( mbedtls_rsa_context *ctx,
                                 int (*f_rng)(void *, unsigned char *, size_t),
                                 void *p_rng,
                                 int mode, size_t *olen,
                                 const unsigned char *input,
                                 unsigned char *output,
                                 size_t output_max_len)
{
    int ret;
    size_t ilen, pad_count = 0, i;
    unsigned char *p, bad, pad_done = 0;
    unsigned char buf[MBEDTLS_MPI_MAX_SIZE];

    if( mode == MBEDTLS_RSA_PRIVATE && ctx->padding != MBEDTLS_RSA_PKCS_V15 )
        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );

    ilen = ctx->len;

    if( ilen < 16 || ilen > sizeof( buf ) )
        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );

    ret = ( mode == MBEDTLS_RSA_PUBLIC )
          ? mbedtls_rsa_public(  ctx, input, buf )
          : mbedtls_rsa_private( ctx, f_rng, p_rng, input, buf );

    if( ret != 0 )
        goto cleanup;

    p = buf;
    bad = 0;

    /*
     * Check and get padding len in "constant-time"
     */
    bad |= *p++; /* First byte must be 0 */

    /* This test does not depend on secret data */
    if( mode == MBEDTLS_RSA_PRIVATE )
    {
        bad |= *p++ ^ MBEDTLS_RSA_CRYPT;

        /* Get padding len, but always read till end of buffer
         * (minus one, for the 00 byte) */
        for( i = 0; i < ilen - 3; i++ )
        {
            pad_done  |= ((p[i] | (unsigned char)-p[i]) >> 7) ^ 1;
            pad_count += ((pad_done | (unsigned char)-pad_done) >> 7) ^ 1;
        }

        p += pad_count;
        bad |= *p++; /* Must be zero */
    }
    else
    {
        bad |= *p++ ^ MBEDTLS_RSA_SIGN;

        /* Get padding len, but always read till end of buffer
         * (minus one, for the 00 byte) */
        for( i = 0; i < ilen - 3; i++ )
        {
            pad_done |= ( p[i] != 0xFF );
            pad_count += ( pad_done == 0 );
        }

        p += pad_count;
        bad |= *p++; /* Must be zero */
    }

    bad |= ( pad_count < 8 );

    if( bad )
    {
        ret = MBEDTLS_ERR_RSA_INVALID_PADDING;
        goto cleanup;
    }

    if( ilen - ( p - buf ) > output_max_len )
    {
        ret = MBEDTLS_ERR_RSA_OUTPUT_TOO_LARGE;
        goto cleanup;
    }

    *olen = ilen - (p - buf);
    memcpy( output, p, *olen );
    ret = 0;

cleanup:
    mbedtls_zeroize( buf, sizeof( buf ) );

    return( ret );
}
#endif /* MBEDTLS_PKCS1_V15 */

/*
 * Do an RSA operation, then remove the message padding
 */
int mbedtls_rsa_pkcs1_decrypt( mbedtls_rsa_context *ctx,
                       int (*f_rng)(void *, unsigned char *, size_t),
                       void *p_rng,
                       int mode, size_t *olen,
                       const unsigned char *input,
                       unsigned char *output,
                       size_t output_max_len)
{
    switch( ctx->padding )
    {
#if defined(MBEDTLS_PKCS1_V15)
        case MBEDTLS_RSA_PKCS_V15:
            return mbedtls_rsa_rsaes_pkcs1_v15_decrypt( ctx, f_rng, p_rng, mode, olen,
                                                input, output, output_max_len );
#endif

#if defined(MBEDTLS_PKCS1_V21)
        case MBEDTLS_RSA_PKCS_V21:
            return mbedtls_rsa_rsaes_oaep_decrypt( ctx, f_rng, p_rng, mode, NULL, 0,
                                           olen, input, output,
                                           output_max_len );
#endif

        default:
            return( MBEDTLS_ERR_RSA_INVALID_PADDING );
    }
}

#if defined(MBEDTLS_PKCS1_V21)
/*
 * Implementation of the PKCS#1 v2.1 RSASSA-PSS-SIGN function
 */
int mbedtls_rsa_rsassa_pss_sign( mbedtls_rsa_context *ctx,
                         int (*f_rng)(void *, unsigned char *, size_t),
                         void *p_rng,
                         int mode,
                         mbedtls_md_type_t md_alg,
                         unsigned int hashlen,
                         const unsigned char *hash,
                         unsigned char *sig )
{
    size_t olen;
    unsigned char *p = sig;
    unsigned char salt[MBEDTLS_MD_MAX_SIZE];
    unsigned int slen, hlen, offset = 0;
    int ret;
    size_t msb;
    const mbedtls_md_info_t *md_info;
    mbedtls_md_context_t md_ctx;

    if( mode == MBEDTLS_RSA_PRIVATE && ctx->padding != MBEDTLS_RSA_PKCS_V21 )
        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );

    if( f_rng == NULL )
        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );

    olen = ctx->len;

    if( md_alg != MBEDTLS_MD_NONE )
    {
        /* Gather length of hash to sign */
        md_info = mbedtls_md_info_from_type( md_alg );
        if( md_info == NULL )
            return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );

        hashlen = mbedtls_md_get_size( md_info );
    }

    md_info = mbedtls_md_info_from_type( (mbedtls_md_type_t) ctx->hash_id );
    if( md_info == NULL )
        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );

    hlen = mbedtls_md_get_size( md_info );
    slen = hlen;

    if( olen < hlen + slen + 2 )
        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );

    memset( sig, 0, olen );

    /* Generate salt of length slen */
    if( ( ret = f_rng( p_rng, salt, slen ) ) != 0 )
        return( MBEDTLS_ERR_RSA_RNG_FAILED + ret );

    /* Note: EMSA-PSS encoding is over the length of N - 1 bits */
    msb = mbedtls_mpi_bitlen( &ctx->N ) - 1;
    p += olen - hlen * 2 - 2;
    *p++ = 0x01;
    memcpy( p, salt, slen );
    p += slen;

    mbedtls_md_init( &md_ctx );
    if( ( ret = mbedtls_md_setup( &md_ctx, md_info, 0 ) ) != 0 )
    {
        mbedtls_md_free( &md_ctx );
        /* No need to zeroize salt: we didn't use it. */
        return( ret );
    }

    /* Generate H = Hash( M' ) */
    mbedtls_md_starts( &md_ctx );
    mbedtls_md_update( &md_ctx, p, 8 );
    mbedtls_md_update( &md_ctx, hash, hashlen );
    mbedtls_md_update( &md_ctx, salt, slen );
    mbedtls_md_finish( &md_ctx, p );
    mbedtls_zeroize( salt, sizeof( salt ) );

    /* Compensate for boundary condition when applying mask */
    if( msb % 8 == 0 )
        offset = 1;

    /* maskedDB: Apply dbMask to DB */
    mgf_mask( sig + offset, olen - hlen - 1 - offset, p, hlen, &md_ctx );

    mbedtls_md_free( &md_ctx );

    msb = mbedtls_mpi_bitlen( &ctx->N ) - 1;
    sig[0] &= 0xFF >> ( olen * 8 - msb );

    p += hlen;
    *p++ = 0xBC;

    return( ( mode == MBEDTLS_RSA_PUBLIC )
            ? mbedtls_rsa_public(  ctx, sig, sig )
            : mbedtls_rsa_private( ctx, f_rng, p_rng, sig, sig ) );
}
#endif /* MBEDTLS_PKCS1_V21 */

#if defined(MBEDTLS_PKCS1_V15)
/*
 * Implementation of the PKCS#1 v2.1 RSASSA-PKCS1-V1_5-SIGN function
 */
/*
 * Do an RSA operation to sign the message digest
 */
int mbedtls_rsa_rsassa_pkcs1_v15_sign( mbedtls_rsa_context *ctx,
                               int (*f_rng)(void *, unsigned char *, size_t),
                               void *p_rng,
                               int mode,
                               mbedtls_md_type_t md_alg,
                               unsigned int hashlen,
                               const unsigned char *hash,
                               unsigned char *sig )
{
    size_t nb_pad, olen, oid_size = 0;
    unsigned char *p = sig;
    const char *oid = NULL;
    unsigned char *sig_try = NULL, *verif = NULL;
    size_t i;
    unsigned char diff;
    volatile unsigned char diff_no_optimize;
    int ret;

    if( mode == MBEDTLS_RSA_PRIVATE && ctx->padding != MBEDTLS_RSA_PKCS_V15 )
        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );

    olen = ctx->len;
    nb_pad = olen - 3;

    if( md_alg != MBEDTLS_MD_NONE )
    {
        const mbedtls_md_info_t *md_info = mbedtls_md_info_from_type( md_alg );
        if( md_info == NULL )
            return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );

        if( mbedtls_oid_get_oid_by_md( md_alg, &oid, &oid_size ) != 0 )
            return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );

        nb_pad -= 10 + oid_size;

        hashlen = mbedtls_md_get_size( md_info );
    }

    nb_pad -= hashlen;

    if( ( nb_pad < 8 ) || ( nb_pad > olen ) )
        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );

    *p++ = 0;
    *p++ = MBEDTLS_RSA_SIGN;
    memset( p, 0xFF, nb_pad );
    p += nb_pad;
    *p++ = 0;

    if( md_alg == MBEDTLS_MD_NONE )
    {
        memcpy( p, hash, hashlen );
    }
    else
    {
        /*
         * DigestInfo ::= SEQUENCE {
         *   digestAlgorithm DigestAlgorithmIdentifier,
         *   digest Digest }
         *
         * DigestAlgorithmIdentifier ::= AlgorithmIdentifier
         *
         * Digest ::= OCTET STRING
         */
        *p++ = MBEDTLS_ASN1_SEQUENCE | MBEDTLS_ASN1_CONSTRUCTED;
        *p++ = (unsigned char) ( 0x08 + oid_size + hashlen );
        *p++ = MBEDTLS_ASN1_SEQUENCE | MBEDTLS_ASN1_CONSTRUCTED;
        *p++ = (unsigned char) ( 0x04 + oid_size );
        *p++ = MBEDTLS_ASN1_OID;
        *p++ = oid_size & 0xFF;
        memcpy( p, oid, oid_size );
        p += oid_size;
        *p++ = MBEDTLS_ASN1_NULL;
        *p++ = 0x00;
        *p++ = MBEDTLS_ASN1_OCTET_STRING;
        *p++ = hashlen;
        memcpy( p, hash, hashlen );
    }

    if( mode == MBEDTLS_RSA_PUBLIC )
        return( mbedtls_rsa_public(  ctx, sig, sig ) );

    /*
     * In order to prevent Lenstra's attack, make the signature in a
     * temporary buffer and check it before returning it.
     */
    sig_try = mbedtls_calloc( 1, ctx->len );
    if( sig_try == NULL )
        return( MBEDTLS_ERR_MPI_ALLOC_FAILED );

    verif   = mbedtls_calloc( 1, ctx->len );
    if( verif == NULL )
    {
        mbedtls_free( sig_try );
        return( MBEDTLS_ERR_MPI_ALLOC_FAILED );
    }

    MBEDTLS_MPI_CHK( mbedtls_rsa_private( ctx, f_rng, p_rng, sig, sig_try ) );
    MBEDTLS_MPI_CHK( mbedtls_rsa_public( ctx, sig_try, verif ) );

    /* Compare in constant time just in case */
    for( diff = 0, i = 0; i < ctx->len; i++ )
        diff |= verif[i] ^ sig[i];
    diff_no_optimize = diff;

    if( diff_no_optimize != 0 )
    {
        ret = MBEDTLS_ERR_RSA_PRIVATE_FAILED;
        goto cleanup;
    }

    memcpy( sig, sig_try, ctx->len );

cleanup:
    mbedtls_free( sig_try );
    mbedtls_free( verif );

    return( ret );
}
#endif /* MBEDTLS_PKCS1_V15 */

/*
 * Do an RSA operation to sign the message digest
 */
int mbedtls_rsa_pkcs1_sign( mbedtls_rsa_context *ctx,
                    int (*f_rng)(void *, unsigned char *, size_t),
                    void *p_rng,
                    int mode,
                    mbedtls_md_type_t md_alg,
                    unsigned int hashlen,
                    const unsigned char *hash,
                    unsigned char *sig )
{
    switch( ctx->padding )
    {
#if defined(MBEDTLS_PKCS1_V15)
        case MBEDTLS_RSA_PKCS_V15:
            return mbedtls_rsa_rsassa_pkcs1_v15_sign( ctx, f_rng, p_rng, mode, md_alg,
                                              hashlen, hash, sig );
#endif

#if defined(MBEDTLS_PKCS1_V21)
        case MBEDTLS_RSA_PKCS_V21:
            return mbedtls_rsa_rsassa_pss_sign( ctx, f_rng, p_rng, mode, md_alg,
                                        hashlen, hash, sig );
#endif

        default:
            return( MBEDTLS_ERR_RSA_INVALID_PADDING );
    }
}

#if defined(MBEDTLS_PKCS1_V21)
/*
 * Implementation of the PKCS#1 v2.1 RSASSA-PSS-VERIFY function
 */
int mbedtls_rsa_rsassa_pss_verify_ext( mbedtls_rsa_context *ctx,
                               int (*f_rng)(void *, unsigned char *, size_t),
                               void *p_rng,
                               int mode,
                               mbedtls_md_type_t md_alg,
                               unsigned int hashlen,
                               const unsigned char *hash,
                               mbedtls_md_type_t mgf1_hash_id,
                               int expected_salt_len,
                               const unsigned char *sig )
{
    int ret;
    size_t siglen;
    unsigned char *p;
    unsigned char result[MBEDTLS_MD_MAX_SIZE];
    unsigned char zeros[8];
    unsigned int hlen;
    size_t slen, msb;
    const mbedtls_md_info_t *md_info;
    mbedtls_md_context_t md_ctx;
    unsigned char buf[MBEDTLS_MPI_MAX_SIZE];

    if( mode == MBEDTLS_RSA_PRIVATE && ctx->padding != MBEDTLS_RSA_PKCS_V21 )
        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );

    siglen = ctx->len;

    if( siglen < 16 || siglen > sizeof( buf ) )
        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );

    ret = ( mode == MBEDTLS_RSA_PUBLIC )
          ? mbedtls_rsa_public(  ctx, sig, buf )
          : mbedtls_rsa_private( ctx, f_rng, p_rng, sig, buf );

    if( ret != 0 )
        return( ret );

    p = buf;

    if( buf[siglen - 1] != 0xBC )
        return( MBEDTLS_ERR_RSA_INVALID_PADDING );

    if( md_alg != MBEDTLS_MD_NONE )
    {
        /* Gather length of hash to sign */
        md_info = mbedtls_md_info_from_type( md_alg );
        if( md_info == NULL )
            return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );

        hashlen = mbedtls_md_get_size( md_info );
    }

    md_info = mbedtls_md_info_from_type( mgf1_hash_id );
    if( md_info == NULL )
        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );

    hlen = mbedtls_md_get_size( md_info );
    slen = siglen - hlen - 1; /* Currently length of salt + padding */

    memset( zeros, 0, 8 );

    /*
     * Note: EMSA-PSS verification is over the length of N - 1 bits
     */
    msb = mbedtls_mpi_bitlen( &ctx->N ) - 1;

    /* Compensate for boundary condition when applying mask */
    if( msb % 8 == 0 )
    {
        p++;
        siglen -= 1;
    }
    if( buf[0] >> ( 8 - siglen * 8 + msb ) )
        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );

    mbedtls_md_init( &md_ctx );
    if( ( ret = mbedtls_md_setup( &md_ctx, md_info, 0 ) ) != 0 )
    {
        mbedtls_md_free( &md_ctx );
        return( ret );
    }

    mgf_mask( p, siglen - hlen - 1, p + siglen - hlen - 1, hlen, &md_ctx );

    buf[0] &= 0xFF >> ( siglen * 8 - msb );

    while( p < buf + siglen && *p == 0 )
        p++;

    if( p == buf + siglen ||
        *p++ != 0x01 )
    {
        mbedtls_md_free( &md_ctx );
        return( MBEDTLS_ERR_RSA_INVALID_PADDING );
    }

    /* Actual salt len */
    slen -= p - buf;

    if( expected_salt_len != MBEDTLS_RSA_SALT_LEN_ANY &&
        slen != (size_t) expected_salt_len )
    {
        mbedtls_md_free( &md_ctx );
        return( MBEDTLS_ERR_RSA_INVALID_PADDING );
    }

    /*
     * Generate H = Hash( M' )
     */
    mbedtls_md_starts( &md_ctx );
    mbedtls_md_update( &md_ctx, zeros, 8 );
    mbedtls_md_update( &md_ctx, hash, hashlen );
    mbedtls_md_update( &md_ctx, p, slen );
    mbedtls_md_finish( &md_ctx, result );

    mbedtls_md_free( &md_ctx );

    if( memcmp( p + slen, result, hlen ) == 0 )
        return( 0 );
    else
        return( MBEDTLS_ERR_RSA_VERIFY_FAILED );
}

/*
 * Simplified PKCS#1 v2.1 RSASSA-PSS-VERIFY function
 */
int mbedtls_rsa_rsassa_pss_verify( mbedtls_rsa_context *ctx,
                           int (*f_rng)(void *, unsigned char *, size_t),
                           void *p_rng,
                           int mode,
                           mbedtls_md_type_t md_alg,
                           unsigned int hashlen,
                           const unsigned char *hash,
                           const unsigned char *sig )
{
    mbedtls_md_type_t mgf1_hash_id = ( ctx->hash_id != MBEDTLS_MD_NONE )
                             ? (mbedtls_md_type_t) ctx->hash_id
                             : md_alg;

    return( mbedtls_rsa_rsassa_pss_verify_ext( ctx, f_rng, p_rng, mode,
                                       md_alg, hashlen, hash,
                                       mgf1_hash_id, MBEDTLS_RSA_SALT_LEN_ANY,
                                       sig ) );

}
#endif /* MBEDTLS_PKCS1_V21 */

#if defined(MBEDTLS_PKCS1_V15)
/*
 * Implementation of the PKCS#1 v2.1 RSASSA-PKCS1-v1_5-VERIFY function
 */
int mbedtls_rsa_rsassa_pkcs1_v15_verify( mbedtls_rsa_context *ctx,
                                 int (*f_rng)(void *, unsigned char *, size_t),
                                 void *p_rng,
                                 int mode,
                                 mbedtls_md_type_t md_alg,
                                 unsigned int hashlen,
                                 const unsigned char *hash,
                                 const unsigned char *sig )
{
    int ret;
    size_t len, siglen, asn1_len;
    unsigned char *p, *p0, *end;
    mbedtls_md_type_t msg_md_alg;
    const mbedtls_md_info_t *md_info;
    mbedtls_asn1_buf oid;
    unsigned char buf[MBEDTLS_MPI_MAX_SIZE];

    if( mode == MBEDTLS_RSA_PRIVATE && ctx->padding != MBEDTLS_RSA_PKCS_V15 )
        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );

    siglen = ctx->len;

    if( siglen < 16 || siglen > sizeof( buf ) )
        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );

    ret = ( mode == MBEDTLS_RSA_PUBLIC )
          ? mbedtls_rsa_public(  ctx, sig, buf )
          : mbedtls_rsa_private( ctx, f_rng, p_rng, sig, buf );

    if( ret != 0 )
        return( ret );

    p = buf;

    if( *p++ != 0 || *p++ != MBEDTLS_RSA_SIGN )
        return( MBEDTLS_ERR_RSA_INVALID_PADDING );

    while( *p != 0 )
    {
        if( p >= buf + siglen - 1 || *p != 0xFF )
            return( MBEDTLS_ERR_RSA_INVALID_PADDING );
        p++;
    }
    p++; /* skip 00 byte */

    /* We've read: 00 01 PS 00 where PS must be at least 8 bytes */
    if( p - buf < 11 )
        return( MBEDTLS_ERR_RSA_INVALID_PADDING );

    len = siglen - ( p - buf );

    if( len == hashlen && md_alg == MBEDTLS_MD_NONE )
    {
        if( memcmp( p, hash, hashlen ) == 0 )
            return( 0 );
        else
            return( MBEDTLS_ERR_RSA_VERIFY_FAILED );
    }

    md_info = mbedtls_md_info_from_type( md_alg );
    if( md_info == NULL )
        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
    hashlen = mbedtls_md_get_size( md_info );

    end = p + len;

    /*
     * Parse the ASN.1 structure inside the PKCS#1 v1.5 structure.
     * Insist on 2-byte length tags, to protect against variants of
     * Bleichenbacher's forgery attack against lax PKCS#1v1.5 verification.
     */
    p0 = p;
    if( ( ret = mbedtls_asn1_get_tag( &p, end, &asn1_len,
            MBEDTLS_ASN1_CONSTRUCTED | MBEDTLS_ASN1_SEQUENCE ) ) != 0 )
        return( MBEDTLS_ERR_RSA_VERIFY_FAILED );
    if( p != p0 + 2 || asn1_len + 2 != len )
        return( MBEDTLS_ERR_RSA_VERIFY_FAILED );

    p0 = p;
    if( ( ret = mbedtls_asn1_get_tag( &p, end, &asn1_len,
            MBEDTLS_ASN1_CONSTRUCTED | MBEDTLS_ASN1_SEQUENCE ) ) != 0 )
        return( MBEDTLS_ERR_RSA_VERIFY_FAILED );
    if( p != p0 + 2 || asn1_len + 6 + hashlen != len )
        return( MBEDTLS_ERR_RSA_VERIFY_FAILED );

    p0 = p;
    if( ( ret = mbedtls_asn1_get_tag( &p, end, &oid.len, MBEDTLS_ASN1_OID ) ) != 0 )
        return( MBEDTLS_ERR_RSA_VERIFY_FAILED );
    if( p != p0 + 2 )
        return( MBEDTLS_ERR_RSA_VERIFY_FAILED );

    oid.p = p;
    p += oid.len;

    if( mbedtls_oid_get_md_alg( &oid, &msg_md_alg ) != 0 )
        return( MBEDTLS_ERR_RSA_VERIFY_FAILED );

    if( md_alg != msg_md_alg )
        return( MBEDTLS_ERR_RSA_VERIFY_FAILED );

    /*
     * assume the algorithm parameters must be NULL
     */
    p0 = p;
    if( ( ret = mbedtls_asn1_get_tag( &p, end, &asn1_len, MBEDTLS_ASN1_NULL ) ) != 0 )
        return( MBEDTLS_ERR_RSA_VERIFY_FAILED );
    if( p != p0 + 2 )
        return( MBEDTLS_ERR_RSA_VERIFY_FAILED );

    p0 = p;
    if( ( ret = mbedtls_asn1_get_tag( &p, end, &asn1_len, MBEDTLS_ASN1_OCTET_STRING ) ) != 0 )
        return( MBEDTLS_ERR_RSA_VERIFY_FAILED );
    if( p != p0 + 2 || asn1_len != hashlen )
        return( MBEDTLS_ERR_RSA_VERIFY_FAILED );

    if( memcmp( p, hash, hashlen ) != 0 )
        return( MBEDTLS_ERR_RSA_VERIFY_FAILED );

    p += hashlen;

    if( p != end )
        return( MBEDTLS_ERR_RSA_VERIFY_FAILED );

    return( 0 );
}
#endif /* MBEDTLS_PKCS1_V15 */

/*
 * Do an RSA operation and check the message digest
 */
int mbedtls_rsa_pkcs1_verify( mbedtls_rsa_context *ctx,
                      int (*f_rng)(void *, unsigned char *, size_t),
                      void *p_rng,
                      int mode,
                      mbedtls_md_type_t md_alg,
                      unsigned int hashlen,
                      const unsigned char *hash,
                      const unsigned char *sig )
{
    switch( ctx->padding )
    {
#if defined(MBEDTLS_PKCS1_V15)
        case MBEDTLS_RSA_PKCS_V15:
            return mbedtls_rsa_rsassa_pkcs1_v15_verify( ctx, f_rng, p_rng, mode, md_alg,
                                                hashlen, hash, sig );
#endif

#if defined(MBEDTLS_PKCS1_V21)
        case MBEDTLS_RSA_PKCS_V21:
            return mbedtls_rsa_rsassa_pss_verify( ctx, f_rng, p_rng, mode, md_alg,
                                          hashlen, hash, sig );
#endif

        default:
            return( MBEDTLS_ERR_RSA_INVALID_PADDING );
    }
}

/*
 * Copy the components of an RSA key
 */
int mbedtls_rsa_copy( mbedtls_rsa_context *dst, const mbedtls_rsa_context *src )
{
    int ret;

    dst->ver = src->ver;
    dst->len = src->len;

    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &dst->N, &src->N ) );
    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &dst->E, &src->E ) );

    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &dst->D, &src->D ) );
    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &dst->P, &src->P ) );
    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &dst->Q, &src->Q ) );

#if !defined(MBEDTLS_RSA_NO_CRT)
    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &dst->DP, &src->DP ) );
    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &dst->DQ, &src->DQ ) );
    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &dst->QP, &src->QP ) );
    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &dst->RP, &src->RP ) );
    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &dst->RQ, &src->RQ ) );
#endif

    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &dst->RN, &src->RN ) );

    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &dst->Vi, &src->Vi ) );
    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &dst->Vf, &src->Vf ) );

    dst->padding = src->padding;
    dst->hash_id = src->hash_id;

cleanup:
    if( ret != 0 )
        mbedtls_rsa_free( dst );

    return( ret );
}

/*
 * Free the components of an RSA key
 */
void mbedtls_rsa_free( mbedtls_rsa_context *ctx )
{
    mbedtls_mpi_free( &ctx->Vi ); mbedtls_mpi_free( &ctx->Vf );
    mbedtls_mpi_free( &ctx->RN ); mbedtls_mpi_free( &ctx->D  );
    mbedtls_mpi_free( &ctx->Q  ); mbedtls_mpi_free( &ctx->P  );
    mbedtls_mpi_free( &ctx->E  ); mbedtls_mpi_free( &ctx->N  );

#if !defined(MBEDTLS_RSA_NO_CRT)
    mbedtls_mpi_free( &ctx->RQ ); mbedtls_mpi_free( &ctx->RP );
    mbedtls_mpi_free( &ctx->QP ); mbedtls_mpi_free( &ctx->DQ );
    mbedtls_mpi_free( &ctx->DP );
#endif /* MBEDTLS_RSA_NO_CRT */

#if defined(MBEDTLS_THREADING_C)
    mbedtls_mutex_free( &ctx->mutex );
#endif
}

#endif /* !MBEDTLS_RSA_ALT */

#if defined(MBEDTLS_SELF_TEST)

#include "mbedtls/sha1.h"

/*
 * Example RSA-1024 keypair, for test purposes
 */
#define KEY_LEN 128

#define RSA_N   "9292758453063D803DD603D5E777D788" \
                "8ED1D5BF35786190FA2F23EBC0848AEA" \
                "DDA92CA6C3D80B32C4D109BE0F36D6AE" \
                "7130B9CED7ACDF54CFC7555AC14EEBAB" \
                "93A89813FBF3C4F8066D2D800F7C38A8" \
                "1AE31942917403FF4946B0A83D3D3E05" \
                "EE57C6F5F5606FB5D4BC6CD34EE0801A" \
                "5E94BB77B07507233A0BC7BAC8F90F79"

#define RSA_E   "10001"

#define RSA_D   "24BF6185468786FDD303083D25E64EFC" \
                "66CA472BC44D253102F8B4A9D3BFA750" \
                "91386C0077937FE33FA3252D28855837" \
                "AE1B484A8A9A45F7EE8C0C634F99E8CD" \
                "DF79C5CE07EE72C7F123142198164234" \
                "CABB724CF78B8173B9F880FC86322407" \
                "AF1FEDFDDE2BEB674CA15F3E81A1521E" \
                "071513A1E85B5DFA031F21ECAE91A34D"

#define RSA_P   "C36D0EB7FCD285223CFB5AABA5BDA3D8" \
                "2C01CAD19EA484A87EA4377637E75500" \
                "FCB2005C5C7DD6EC4AC023CDA285D796" \
                "C3D9E75E1EFC42488BB4F1D13AC30A57"

#define RSA_Q   "C000DF51A7C77AE8D7C7370C1FF55B69" \
                "E211C2B9E5DB1ED0BF61D0D9899620F4" \
                "910E4168387E3C30AA1E00C339A79508" \
                "8452DD96A9A5EA5D9DCA68DA636032AF"

#define RSA_DP  "C1ACF567564274FB07A0BBAD5D26E298" \
                "3C94D22288ACD763FD8E5600ED4A702D" \
                "F84198A5F06C2E72236AE490C93F07F8" \
                "3CC559CD27BC2D1CA488811730BB5725"

#define RSA_DQ  "4959CBF6F8FEF750AEE6977C155579C7" \
                "D8AAEA56749EA28623272E4F7D0592AF" \
                "7C1F1313CAC9471B5C523BFE592F517B" \
                "407A1BD76C164B93DA2D32A383E58357"

#define RSA_QP  "9AE7FBC99546432DF71896FC239EADAE" \
                "F38D18D2B2F0E2DD275AA977E2BF4411" \
                "F5A3B2A5D33605AEBBCCBA7FEB9F2D2F" \
                "A74206CEC169D74BF5A8C50D6F48EA08"

#define PT_LEN  24
#define RSA_PT  "\xAA\xBB\xCC\x03\x02\x01\x00\xFF\xFF\xFF\xFF\xFF" \
                "\x11\x22\x33\x0A\x0B\x0C\xCC\xDD\xDD\xDD\xDD\xDD"

#if defined(MBEDTLS_PKCS1_V15)
static int myrand( void *rng_state, unsigned char *output, size_t len )
{
#if !defined(__OpenBSD__)
    size_t i;

    if( rng_state != NULL )
        rng_state  = NULL;

    for( i = 0; i < len; ++i )
        output[i] = rand();
#else
    if( rng_state != NULL )
        rng_state = NULL;

    arc4random_buf( output, len );
#endif /* !OpenBSD */

    return( 0 );
}
#endif /* MBEDTLS_PKCS1_V15 */

/*
 * Checkup routine
 */
int mbedtls_rsa_self_test( int verbose )
{
    int ret = 0;
#if defined(MBEDTLS_PKCS1_V15)
    size_t len;
    mbedtls_rsa_context rsa;
    unsigned char rsa_plaintext[PT_LEN];
    unsigned char rsa_decrypted[PT_LEN];
    unsigned char rsa_ciphertext[KEY_LEN];
#if defined(MBEDTLS_SHA1_C)
    unsigned char sha1sum[20];
#endif

    mbedtls_mpi K;

    mbedtls_mpi_init( &K );
    mbedtls_rsa_init( &rsa, MBEDTLS_RSA_PKCS_V15, 0 );

    MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &K, 16, RSA_N  ) );
    MBEDTLS_MPI_CHK( mbedtls_rsa_import( &rsa, &K, NULL, NULL, NULL, NULL ) );
    MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &K, 16, RSA_P  ) );
    MBEDTLS_MPI_CHK( mbedtls_rsa_import( &rsa, NULL, &K, NULL, NULL, NULL ) );
    MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &K, 16, RSA_Q  ) );
    MBEDTLS_MPI_CHK( mbedtls_rsa_import( &rsa, NULL, NULL, &K, NULL, NULL ) );
    MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &K, 16, RSA_D  ) );
    MBEDTLS_MPI_CHK( mbedtls_rsa_import( &rsa, NULL, NULL, NULL, &K, NULL ) );
    MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &K, 16, RSA_E  ) );
    MBEDTLS_MPI_CHK( mbedtls_rsa_import( &rsa, NULL, NULL, NULL, NULL, &K ) );

    MBEDTLS_MPI_CHK( mbedtls_rsa_complete( &rsa, NULL, NULL ) );

    if( verbose != 0 )
        mbedtls_printf( "  RSA key validation: " );

    if( mbedtls_rsa_check_pubkey(  &rsa ) != 0 ||
        mbedtls_rsa_check_privkey( &rsa ) != 0 )
    {
        if( verbose != 0 )
            mbedtls_printf( "failed\n" );

        return( 1 );
    }

    MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &K, 16, RSA_DP  ) );
    MBEDTLS_MPI_CHK( mbedtls_rsa_check_crt( &rsa, &K, NULL, NULL ) );

    MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &K, 16, RSA_DQ  ) );
    MBEDTLS_MPI_CHK( mbedtls_rsa_check_crt( &rsa, NULL, &K, NULL ) );

    MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &K, 16, RSA_QP  ) );
    MBEDTLS_MPI_CHK( mbedtls_rsa_check_crt( &rsa, NULL, NULL, &K ) );

    if( verbose != 0 )
        mbedtls_printf( "passed\n  PKCS#1 encryption : " );

    memcpy( rsa_plaintext, RSA_PT, PT_LEN );

    if( mbedtls_rsa_pkcs1_encrypt( &rsa, myrand, NULL, MBEDTLS_RSA_PUBLIC, PT_LEN,
                           rsa_plaintext, rsa_ciphertext ) != 0 )
    {
        if( verbose != 0 )
            mbedtls_printf( "failed\n" );

        return( 1 );
    }

    if( verbose != 0 )
        mbedtls_printf( "passed\n  PKCS#1 decryption : " );

    if( mbedtls_rsa_pkcs1_decrypt( &rsa, myrand, NULL, MBEDTLS_RSA_PRIVATE, &len,
                           rsa_ciphertext, rsa_decrypted,
                           sizeof(rsa_decrypted) ) != 0 )
    {
        if( verbose != 0 )
            mbedtls_printf( "failed\n" );

        return( 1 );
    }

    if( memcmp( rsa_decrypted, rsa_plaintext, len ) != 0 )
    {
        if( verbose != 0 )
            mbedtls_printf( "failed\n" );

        return( 1 );
    }

    if( verbose != 0 )
        mbedtls_printf( "passed\n" );

#if defined(MBEDTLS_SHA1_C)
    if( verbose != 0 )
        mbedtls_printf( "  PKCS#1 data sign  : " );

    mbedtls_sha1( rsa_plaintext, PT_LEN, sha1sum );

    if( mbedtls_rsa_pkcs1_sign( &rsa, myrand, NULL, MBEDTLS_RSA_PRIVATE, MBEDTLS_MD_SHA1, 0,
                        sha1sum, rsa_ciphertext ) != 0 )
    {
        if( verbose != 0 )
            mbedtls_printf( "failed\n" );

        return( 1 );
    }

    if( verbose != 0 )
        mbedtls_printf( "passed\n  PKCS#1 sig. verify: " );

    if( mbedtls_rsa_pkcs1_verify( &rsa, NULL, NULL, MBEDTLS_RSA_PUBLIC, MBEDTLS_MD_SHA1, 0,
                          sha1sum, rsa_ciphertext ) != 0 )
    {
        if( verbose != 0 )
            mbedtls_printf( "failed\n" );

        return( 1 );
    }

    if( verbose != 0 )
        mbedtls_printf( "passed\n" );
#endif /* MBEDTLS_SHA1_C */

    if( verbose != 0 )
        mbedtls_printf( "\n" );

cleanup:
    mbedtls_mpi_free( &K );
    mbedtls_rsa_free( &rsa );
#else /* MBEDTLS_PKCS1_V15 */
    ((void) verbose);
#endif /* MBEDTLS_PKCS1_V15 */
    return( ret );
}

#endif /* MBEDTLS_SELF_TEST */

#endif /* MBEDTLS_RSA_C */