text: /*
   *  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/rsa_internal.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
  
  #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;
  }
  
  #if defined(MBEDTLS_PKCS1_V15)
  /* constant-time buffer comparison */
  static inline int mbedtls_safer_memcmp( const void *a, const void *b, size_t n )
  {
      size_t i;
      const unsigned char *A = (const unsigned char *) a;
      const unsigned char *B = (const unsigned char *) b;
      unsigned char diff = 0;
  
      for( i = 0; i < n; i++ )
          diff |= A[i] ^ B[i];
  
      return( diff );
  }
  #endif /* MBEDTLS_PKCS1_V15 */
  
  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 const *N, size_t N_len,
                              unsigned char const *P, size_t P_len,
                              unsigned char const *Q, size_t Q_len,
                              unsigned char const *D, size_t D_len,
                              unsigned char const *E, size_t E_len )
  {
      int ret = 0;
  
      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 );
  }
  
  /*
   * Checks whether the context fields are set in such a way
   * that the RSA primitives will be able to execute without error.
   * It does *not* make guarantees for consistency of the parameters.
   */
  static int rsa_check_context( mbedtls_rsa_context const *ctx, int is_priv,
                                int blinding_needed )
  {
  #if !defined(MBEDTLS_RSA_NO_CRT)
      /* blinding_needed is only used for NO_CRT to decide whether
       * P,Q need to be present or not. */
      ((void) blinding_needed);
  #endif
  
      if( ctx->len != mbedtls_mpi_size( &ctx->N ) ||
          ctx->len > MBEDTLS_MPI_MAX_SIZE )
      {
          return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
      }
  
      /*
       * 1. Modular exponentiation needs positive, odd moduli.
       */
  
      /* Modular exponentiation wrt. N is always used for
       * RSA public key operations. */
      if( mbedtls_mpi_cmp_int( &ctx->N, 0 ) <= 0 ||
          mbedtls_mpi_get_bit( &ctx->N, 0 ) == 0  )
      {
          return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
      }
  
  #if !defined(MBEDTLS_RSA_NO_CRT)
      /* Modular exponentiation for P and Q is only
       * used for private key operations and if CRT
       * is used. */
      if( is_priv &&
          ( mbedtls_mpi_cmp_int( &ctx->P, 0 ) <= 0 ||
            mbedtls_mpi_get_bit( &ctx->P, 0 ) == 0 ||
            mbedtls_mpi_cmp_int( &ctx->Q, 0 ) <= 0 ||
            mbedtls_mpi_get_bit( &ctx->Q, 0 ) == 0  ) )
      {
          return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
      }
  #endif /* !MBEDTLS_RSA_NO_CRT */
  
      /*
       * 2. Exponents must be positive
       */
  
      /* Always need E for public key operations */
      if( mbedtls_mpi_cmp_int( &ctx->E, 0 ) <= 0 )
          return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
  
  #if defined(MBEDTLS_RSA_NO_CRT)
      /* For private key operations, use D or DP & DQ
       * as (unblinded) exponents. */
      if( is_priv && mbedtls_mpi_cmp_int( &ctx->D, 0 ) <= 0 )
          return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
  #else
      if( is_priv &&
          ( mbedtls_mpi_cmp_int( &ctx->DP, 0 ) <= 0 ||
            mbedtls_mpi_cmp_int( &ctx->DQ, 0 ) <= 0  ) )
      {
          return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
      }
  #endif /* MBEDTLS_RSA_NO_CRT */
  
      /* Blinding shouldn't make exponents negative either,
       * so check that P, Q >= 1 if that hasn't yet been
       * done as part of 1. */
  #if defined(MBEDTLS_RSA_NO_CRT)
      if( is_priv && blinding_needed &&
          ( mbedtls_mpi_cmp_int( &ctx->P, 0 ) <= 0 ||
            mbedtls_mpi_cmp_int( &ctx->Q, 0 ) <= 0 ) )
      {
          return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
      }
  #endif
  
      /* It wouldn't lead to an error if it wasn't satisfied,
       * but check for QP >= 1 nonetheless. */
  #if !defined(MBEDTLS_RSA_NO_CRT)
      if( is_priv &&
          mbedtls_mpi_cmp_int( &ctx->QP, 0 ) <= 0 )
      {
          return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
      }
  #endif
  
      return( 0 );
  }
  
  int mbedtls_rsa_complete( mbedtls_rsa_context *ctx )
  {
      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 )
      {
          ret = mbedtls_rsa_deduce_primes( &ctx->N, &ctx->E, &ctx->D,
                                           &ctx->P, &ctx->Q );
          if( ret != 0 )
              return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA + ret );
  
      }
      else if( d_missing )
      {
          if( ( ret = mbedtls_rsa_deduce_private_exponent( &ctx->P,
                                                           &ctx->Q,
                                                           &ctx->E,
                                                           &ctx->D ) ) != 0 )
          {
              return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA + ret );
          }
      }
  
      /*
       * Step 3: Deduce all additional parameters specific
       *         to our current RSA implementation.
       */
  
  #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: Basic sanity checks
       */
  
      return( rsa_check_context( ctx, is_priv, 1 ) );
  }
  
  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
   *
   * This generation method follows the RSA key pair generation procedure of
   * FIPS 186-4 if 2^16 < exponent < 2^256 and nbits = 2048 or nbits = 3072.
   */
  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, L;
  
      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 );
      mbedtls_mpi_init( &L );
  
      /*
       * find primes P and Q with Q < P so that:
       * 1.  |P-Q| > 2^( nbits / 2 - 100 )
       * 2.  GCD( E, (P-1)*(Q-1) ) == 1
       * 3.  E^-1 mod LCM(P-1, Q-1) > 2^( nbits / 2 )
       */
      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 ) );
  
          /* make sure the difference between p and q is not too small (FIPS 186-4 §B.3.3 step 5.4) */
          MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &H, &ctx->P, &ctx->Q ) );
          if( mbedtls_mpi_bitlen( &H ) <= ( ( nbits >= 200 ) ? ( ( nbits >> 1 ) - 99 ) : 0 ) )
              continue;
  
          /* not required by any standards, but some users rely on the fact that P > Q */
          if( H.s < 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 ) );
  
          /* check GCD( E, (P-1)*(Q-1) ) == 1 (FIPS 186-4 §B.3.1 criterion 2(a)) */
          MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( &G, &ctx->E, &H  ) );
          if( mbedtls_mpi_cmp_int( &G, 1 ) != 0 )
              continue;
  
          /* compute smallest possible D = E^-1 mod LCM(P-1, Q-1) (FIPS 186-4 §B.3.1 criterion 3(b)) */
          MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( &G, &ctx->P, &ctx->Q ) );
          MBEDTLS_MPI_CHK( mbedtls_mpi_div_mpi( &L, NULL, &H, &G ) );
          MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &ctx->D, &ctx->E, &L ) );
  
          if( mbedtls_mpi_bitlen( &ctx->D ) <= ( ( nbits + 1 ) / 2 ) ) // (FIPS 186-4 §B.3.1 criterion 3(a))
              continue;
  
          break;
      }
      while( 1 );
  
      /* 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 ) );
  
      MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ctx->N, &ctx->P, &ctx->Q ) );
  
      ctx->len = mbedtls_mpi_size( &ctx->N );
  
  #if !defined(MBEDTLS_RSA_NO_CRT)
      /*
       * DP = D mod (P - 1)
       * DQ = D mod (Q - 1)
       * QP = Q^-1 mod P
       */
      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 );
      mbedtls_mpi_free( &L );
  
      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( rsa_check_context( ctx, 0 /* public */, 0 /* no blinding */ ) != 0 )
          return( MBEDTLS_ERR_RSA_KEY_CHECK_FAILED );
  
      if( mbedtls_mpi_bitlen( &ctx->N ) < 128 )
      {
          return( MBEDTLS_ERR_RSA_KEY_CHECK_FAILED );
      }
  
      if( mbedtls_mpi_get_bit( &ctx->E, 0 ) == 0 ||
          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 for the consistency of all fields in an RSA private key context
   */
  int mbedtls_rsa_check_privkey( const mbedtls_rsa_context *ctx )
  {
      if( mbedtls_rsa_check_pubkey( ctx ) != 0 ||
          rsa_check_context( ctx, 1 /* private */, 1 /* blinding */ ) != 0 )
      {
          return( MBEDTLS_ERR_RSA_KEY_CHECK_FAILED );
      }
  
      if( 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 );
  }
  
  #if !defined(MBEDTLS_RSA_PUBLIC_ALT)
  /*
   * 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;
  
      if( rsa_check_context( ctx, 0 /* public */, 0 /* no blinding */ ) )
          return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
  
      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 );
  }
  
  #endif /* MBEDTLS_RSA_PUBLIC_ALT */
  
  /*
   * 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;
  
      /* Temporary holding the result */
      mbedtls_mpi T;
  
      /* Temporaries holding P-1, Q-1 and the
       * exponent blinding factor, respectively. */
      mbedtls_mpi P1, Q1, R;
  
  #if !defined(MBEDTLS_RSA_NO_CRT)
      /* Temporaries holding the results mod p resp. mod q. */
      mbedtls_mpi TP, TQ;
  
      /* Temporaries holding the blinded exponents for
       * the mod p resp. mod q computation (if used). */
      mbedtls_mpi DP_blind, DQ_blind;
  
      /* Pointers to actual exponents to be used - either the unblinded
       * or the blinded ones, depending on the presence of a PRNG. */
      mbedtls_mpi *DP = &ctx->DP;
      mbedtls_mpi *DQ = &ctx->DQ;
  #else
      /* Temporary holding the blinded exponent (if used). */
      mbedtls_mpi D_blind;
  
      /* Pointer to actual exponent to be used - either the unblinded
       * or the blinded one, depending on the presence of a PRNG. */
      mbedtls_mpi *D = &ctx->D;
  #endif /* MBEDTLS_RSA_NO_CRT */
  
      /* Temporaries holding the initial input and the double
       * checked result; should be the same in the end. */
      mbedtls_mpi I, C;
  
      if( rsa_check_context( ctx, 1             /* private key checks */,
                                  f_rng != NULL /* blinding y/n       */ ) != 0 )
      {
          return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
      }
  
  #if defined(MBEDTLS_THREADING_C)
      if( ( ret = mbedtls_mutex_lock( &ctx->mutex ) ) != 0 )
          return( ret );
  #endif
  
      /* MPI Initialization */
      mbedtls_mpi_init( &T );
  
      mbedtls_mpi_init( &P1 );
      mbedtls_mpi_init( &Q1 );
      mbedtls_mpi_init( &R );
  
      if( f_rng != NULL )
      {
  #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_RSA_NO_CRT)
      mbedtls_mpi_init( &TP ); mbedtls_mpi_init( &TQ );
  #endif
  
      mbedtls_mpi_init( &I );
      mbedtls_mpi_init( &C );
  
      /* End of MPI initialization */
  
      MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &T, input, ctx->len ) );
      if( mbedtls_mpi_cmp_mpi( &T, &ctx->N ) >= 0 )
      {
          ret = MBEDTLS_ERR_MPI_BAD_INPUT_DATA;
          goto cleanup;
      }
  
      MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &I, &T ) );
  
      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
       *
       * TP = input ^ dP mod P
       * TQ = input ^ dQ mod Q
       */
  
      MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &TP, &T, DP, &ctx->P, &ctx->RP ) );
      MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &TQ, &T, DQ, &ctx->Q, &ctx->RQ ) );
  
      /*
       * T = (TP - TQ) * (Q^-1 mod P) mod P
       */
      MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T, &TP, &TQ ) );
      MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &TP, &T, &ctx->QP ) );
      MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &T, &TP, &ctx->P ) );
  
      /*
       * T = TQ + T * Q
       */
      MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &TP, &T, &ctx->Q ) );
      MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &T, &TQ, &TP ) );
  #endif /* MBEDTLS_RSA_NO_CRT */
  
      if( f_rng != NULL )
      {
          /*
           * 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 ) );
      }
  
      /* Verify the result to prevent glitching attacks. */
      MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &C, &T, &ctx->E,
                                            &ctx->N, &ctx->RN ) );
      if( mbedtls_mpi_cmp_mpi( &C, &I ) != 0 )
      {
          ret = MBEDTLS_ERR_RSA_VERIFY_FAILED;
          goto cleanup;
      }
  
      olen = ctx->len;
      MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &T, output, olen ) );
  
  cleanup:
  #if defined(MBEDTLS_THREADING_C)
      if( mbedtls_mutex_unlock( &ctx->mutex ) != 0 )
          return( MBEDTLS_ERR_THREADING_MUTEX_ERROR );
  #endif
  
      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
      }
  
      mbedtls_mpi_free( &T );
  
  #if !defined(MBEDTLS_RSA_NO_CRT)
      mbedtls_mpi_free( &TP ); mbedtls_mpi_free( &TQ );
  #endif
  
      mbedtls_mpi_free( &C );
      mbedtls_mpi_free( &I );
  
      if( ret != 0 )
          return( MBEDTLS_ERR_RSA_PRIVATE_FAILED + ret );
  
      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 int 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;
      int ret = 0;
  
      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;
  
          if( ( ret = mbedtls_md_starts( md_ctx ) ) != 0 )
              goto exit;
          if( ( ret = mbedtls_md_update( md_ctx, src, slen ) ) != 0 )
              goto exit;
          if( ( ret = mbedtls_md_update( md_ctx, counter, 4 ) ) != 0 )
              goto exit;
          if( ( ret = mbedtls_md_finish( md_ctx, mask ) ) != 0 )
              goto exit;
  
          for( i = 0; i < use_len; ++i )
              *p++ ^= mask[i];
  
          counter[3]++;
  
          dlen -= use_len;
      }
  
  exit:
      mbedtls_zeroize( mask, sizeof( mask ) );
  
      return( ret );
  }
  #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 */
      if( ( ret = mbedtls_md( md_info, label, label_len, p ) ) != 0 )
          return( ret );
      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 )
          goto exit;
  
      /* maskedDB: Apply dbMask to DB */
      if( ( ret = mgf_mask( output + hlen + 1, olen - hlen - 1, output + 1, hlen,
                            &md_ctx ) ) != 0 )
          goto exit;
  
      /* maskedSeed: Apply seedMask to seed */
      if( ( ret = mgf_mask( output + 1, hlen, output + hlen + 1, olen - hlen - 1,
                            &md_ctx ) ) != 0 )
          goto exit;
  
  exit:
      mbedtls_md_free( &md_ctx );
  
      if( ret != 0 )
          return( ret );
  
      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;
      }
  
      /* seed: Apply seedMask to maskedSeed */
      if( ( ret = mgf_mask( buf + 1, hlen, buf + hlen + 1, ilen - hlen - 1,
                            &md_ctx ) ) != 0 ||
      /* DB: Apply dbMask to maskedDB */
          ( ret = mgf_mask( buf + hlen + 1, ilen - hlen - 1, buf + 1, hlen,
                            &md_ctx ) ) != 0 )
      {
          mbedtls_md_free( &md_ctx );
          goto cleanup;
      }
  
      mbedtls_md_free( &md_ctx );
  
      /* Generate lHash */
      if( ( ret = mbedtls_md( md_info, label, label_len, lhash ) ) != 0 )
          goto cleanup;
  
      /*
       * 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 )
          goto exit;
  
      /* Generate H = Hash( M' ) */
      if( ( ret = mbedtls_md_starts( &md_ctx ) ) != 0 )
          goto exit;
      if( ( ret = mbedtls_md_update( &md_ctx, p, 8 ) ) != 0 )
          goto exit;
      if( ( ret = mbedtls_md_update( &md_ctx, hash, hashlen ) ) != 0 )
          goto exit;
      if( ( ret = mbedtls_md_update( &md_ctx, salt, slen ) ) != 0 )
          goto exit;
      if( ( ret = mbedtls_md_finish( &md_ctx, p ) ) != 0 )
          goto exit;
  
      /* Compensate for boundary condition when applying mask */
      if( msb % 8 == 0 )
          offset = 1;
  
      /* maskedDB: Apply dbMask to DB */
      if( ( ret = mgf_mask( sig + offset, olen - hlen - 1 - offset, p, hlen,
                            &md_ctx ) ) != 0 )
          goto exit;
  
      msb = mbedtls_mpi_bitlen( &ctx->N ) - 1;
      sig[0] &= 0xFF >> ( olen * 8 - msb );
  
      p += hlen;
      *p++ = 0xBC;
  
      mbedtls_zeroize( salt, sizeof( salt ) );
  
  exit:
      mbedtls_md_free( &md_ctx );
  
      if( ret != 0 )
          return( ret );
  
      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
   */
  
  /* Construct a PKCS v1.5 encoding of a hashed message
   *
   * This is used both for signature generation and verification.
   *
   * Parameters:
   * - md_alg:  Identifies the hash algorithm used to generate the given hash;
   *            MBEDTLS_MD_NONE if raw data is signed.
   * - hashlen: Length of hash in case hashlen is MBEDTLS_MD_NONE.
   * - hash:    Buffer containing the hashed message or the raw data.
   * - dst_len: Length of the encoded message.
   * - dst:     Buffer to hold the encoded message.
   *
   * Assumptions:
   * - hash has size hashlen if md_alg == MBEDTLS_MD_NONE.
   * - hash has size corresponding to md_alg if md_alg != MBEDTLS_MD_NONE.
   * - dst points to a buffer of size at least dst_len.
   *
   */
  static int rsa_rsassa_pkcs1_v15_encode( mbedtls_md_type_t md_alg,
                                          unsigned int hashlen,
                                          const unsigned char *hash,
                                          size_t dst_len,
                                          unsigned char *dst )
  {
      size_t oid_size  = 0;
      size_t nb_pad    = dst_len;
      unsigned char *p = dst;
      const char *oid  = NULL;
  
      /* Are we signing hashed or raw data? */
      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 );
  
          hashlen = mbedtls_md_get_size( md_info );
  
          /* Double-check that 8 + hashlen + oid_size can be used as a
           * 1-byte ASN.1 length encoding and that there's no overflow. */
          if( 8 + hashlen + oid_size  >= 0x80         ||
              10 + hashlen            <  hashlen      ||
              10 + hashlen + oid_size <  10 + hashlen )
              return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
  
          /*
           * Static bounds check:
           * - Need 10 bytes for five tag-length pairs.
           *   (Insist on 1-byte length encodings to protect against variants of
           *    Bleichenbacher's forgery attack against lax PKCS#1v1.5 verification)
           * - Need hashlen bytes for hash
           * - Need oid_size bytes for hash alg OID.
           */
          if( nb_pad < 10 + hashlen + oid_size )
              return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
          nb_pad -= 10 + hashlen + oid_size;
      }
      else
      {
          if( nb_pad < hashlen )
              return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
  
          nb_pad -= hashlen;
      }
  
      /* Need space for signature header and padding delimiter (3 bytes),
       * and 8 bytes for the minimal padding */
      if( nb_pad < 3 + 8 )
          return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
      nb_pad -= 3;
  
      /* Now nb_pad is the amount of memory to be filled
       * with padding, and at least 8 bytes long. */
  
      /* Write signature header and padding */
      *p++ = 0;
      *p++ = MBEDTLS_RSA_SIGN;
      memset( p, 0xFF, nb_pad );
      p += nb_pad;
      *p++ = 0;
  
      /* Are we signing raw data? */
      if( md_alg == MBEDTLS_MD_NONE )
      {
          memcpy( p, hash, hashlen );
          return( 0 );
      }
  
      /* Signing hashed data, add corresponding ASN.1 structure
       *
       * DigestInfo ::= SEQUENCE {
       *   digestAlgorithm DigestAlgorithmIdentifier,
       *   digest Digest }
       * DigestAlgorithmIdentifier ::= AlgorithmIdentifier
       * Digest ::= OCTET STRING
       *
       * Schematic:
       * TAG-SEQ + LEN [ TAG-SEQ + LEN [ TAG-OID  + LEN [ OID  ]
       *                                 TAG-NULL + LEN [ NULL ] ]
       *                 TAG-OCTET + LEN [ HASH ] ]
       */
      *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++ = (unsigned char) oid_size;
      memcpy( p, oid, oid_size );
      p += oid_size;
      *p++ = MBEDTLS_ASN1_NULL;
      *p++ = 0x00;
      *p++ = MBEDTLS_ASN1_OCTET_STRING;
      *p++ = (unsigned char) hashlen;
      memcpy( p, hash, hashlen );
      p += hashlen;
  
      /* Just a sanity-check, should be automatic
       * after the initial bounds check. */
      if( p != dst + dst_len )
      {
          mbedtls_zeroize( dst, dst_len );
          return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
      }
  
      return( 0 );
  }
  
  /*
   * 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 )
  {
      int ret;
      unsigned char *sig_try = NULL, *verif = NULL;
  
      if( mode == MBEDTLS_RSA_PRIVATE && ctx->padding != MBEDTLS_RSA_PKCS_V15 )
          return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
  
      /*
       * Prepare PKCS1-v1.5 encoding (padding and hash identifier)
       */
  
      if( ( ret = rsa_rsassa_pkcs1_v15_encode( md_alg, hashlen, hash,
                                               ctx->len, sig ) ) != 0 )
          return( ret );
  
      /*
       * Call respective RSA primitive
       */
  
      if( mode == MBEDTLS_RSA_PUBLIC )
      {
          /* Skip verification on a public key operation */
          return( mbedtls_rsa_public( ctx, sig, sig ) );
      }
  
      /* Private key operation
       *
       * 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 ) );
  
      if( mbedtls_safer_memcmp( verif, sig, ctx->len ) != 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 *hash_start;
      unsigned char result[MBEDTLS_MD_MAX_SIZE];
      unsigned char zeros[8];
      unsigned int hlen;
      size_t observed_salt_len, 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 );
  
      memset( zeros, 0, 8 );
  
      /*
       * Note: EMSA-PSS verification is over the length of N - 1 bits
       */
      msb = mbedtls_mpi_bitlen( &ctx->N ) - 1;
  
      if( buf[0] >> ( 8 - siglen * 8 + msb ) )
          return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
  
      /* Compensate for boundary condition when applying mask */
      if( msb % 8 == 0 )
      {
          p++;
          siglen -= 1;
      }
  
      if( siglen < hlen + 2 )
          return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
      hash_start = p + siglen - hlen - 1;
  
      mbedtls_md_init( &md_ctx );
      if( ( ret = mbedtls_md_setup( &md_ctx, md_info, 0 ) ) != 0 )
          goto exit;
  
      ret = mgf_mask( p, siglen - hlen - 1, hash_start, hlen, &md_ctx );
      if( ret != 0 )
          goto exit;
  
      buf[0] &= 0xFF >> ( siglen * 8 - msb );
  
      while( p < hash_start - 1 && *p == 0 )
          p++;
  
      if( *p++ != 0x01 )
      {
          ret = MBEDTLS_ERR_RSA_INVALID_PADDING;
          goto exit;
      }
  
      observed_salt_len = hash_start - p;
  
      if( expected_salt_len != MBEDTLS_RSA_SALT_LEN_ANY &&
          observed_salt_len != (size_t) expected_salt_len )
      {
          ret = MBEDTLS_ERR_RSA_INVALID_PADDING;
          goto exit;
      }
  
      /*
       * Generate H = Hash( M' )
       */
      ret = mbedtls_md_starts( &md_ctx );
      if ( ret != 0 )
          goto exit;
      ret = mbedtls_md_update( &md_ctx, zeros, 8 );
      if ( ret != 0 )
          goto exit;
      ret = mbedtls_md_update( &md_ctx, hash, hashlen );
      if ( ret != 0 )
          goto exit;
      ret = mbedtls_md_update( &md_ctx, p, observed_salt_len );
      if ( ret != 0 )
          goto exit;
      ret = mbedtls_md_finish( &md_ctx, result );
      if ( ret != 0 )
          goto exit;
  
      if( memcmp( hash_start, result, hlen ) != 0 )
      {
          ret = MBEDTLS_ERR_RSA_VERIFY_FAILED;
          goto exit;
      }
  
  exit:
      mbedtls_md_free( &md_ctx );
  
      return( ret );
  }
  
  /*
   * 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 = 0;
      const size_t sig_len = ctx->len;
      unsigned char *encoded = NULL, *encoded_expected = NULL;
  
      if( mode == MBEDTLS_RSA_PRIVATE && ctx->padding != MBEDTLS_RSA_PKCS_V15 )
          return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
  
      /*
       * Prepare expected PKCS1 v1.5 encoding of hash.
       */
  
      if( ( encoded          = mbedtls_calloc( 1, sig_len ) ) == NULL ||
          ( encoded_expected = mbedtls_calloc( 1, sig_len ) ) == NULL )
      {
          ret = MBEDTLS_ERR_MPI_ALLOC_FAILED;
          goto cleanup;
      }
  
      if( ( ret = rsa_rsassa_pkcs1_v15_encode( md_alg, hashlen, hash, sig_len,
                                               encoded_expected ) ) != 0 )
          goto cleanup;
  
      /*
       * Apply RSA primitive to get what should be PKCS1 encoded hash.
       */
  
      ret = ( mode == MBEDTLS_RSA_PUBLIC )
            ? mbedtls_rsa_public(  ctx, sig, encoded )
            : mbedtls_rsa_private( ctx, f_rng, p_rng, sig, encoded );
      if( ret != 0 )
          goto cleanup;
  
      /*
       * Compare
       */
  
      if( ( ret = mbedtls_safer_memcmp( encoded, encoded_expected,
                                        sig_len ) ) != 0 )
      {
          ret = MBEDTLS_ERR_RSA_VERIFY_FAILED;
          goto cleanup;
      }
  
  cleanup:
  
      if( encoded != NULL )
      {
          mbedtls_zeroize( encoded, sig_len );
          mbedtls_free( encoded );
      }
  
      if( encoded_expected != NULL )
      {
          mbedtls_zeroize( encoded_expected, sig_len );
          mbedtls_free( encoded_expected );
      }
  
      return( ret );
  }
  #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"
  #if 0
  /*
   * 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"
  #endif
  #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_pk_context pk;
      mbedtls_rsa_context *rsa;
      unsigned char rsa_plaintext[PT_LEN];
      unsigned char rsa_decrypted[PT_LEN];
  #if defined(MBEDTLS_SHA1_C)
      unsigned char sha1sum[20];
  #endif
  #if defined(FREESCALE_PKHA_LONG_OPERANDS_ENABLE) \
      || (defined(FREESCALE_PKHA_INT_MAX_BYTES) && (FREESCALE_PKHA_INT_MAX_BYTES >= ((4096 / 8) * 2)))
      unsigned char rsa_ciphertext[4096 / 8];
      const char *rsa_keys[] = { RSA_PRIVATE_KEY_1024, RSA_PRIVATE_KEY_2048, RSA_PRIVATE_KEY_4096 };
  #elif defined(FREESCALE_PKHA_INT_MAX_BYTES) && (FREESCALE_PKHA_INT_MAX_BYTES >= ((2048 / 8) * 2))
      unsigned char rsa_ciphertext[2048 / 8];
      const char *rsa_keys[] = { RSA_PRIVATE_KEY_1024, RSA_PRIVATE_KEY_2048 };
  #else
      unsigned char rsa_ciphertext[1024 / 8];
      const char *rsa_keys[] = { RSA_PRIVATE_KEY_1024 };
  #endif
      size_t i;
  
      for (i = 0; i < sizeof(rsa_keys) / sizeof(rsa_keys[0]); i++)
      {
          mbedtls_pk_init(&pk);
          
          if( verbose != 0 )
              mbedtls_printf( "  RSA parse key #%d       : ", i + 1 );
  
          MBEDTLS_MPI_CHK( mbedtls_pk_parse_key(&pk, (const unsigned char *)rsa_keys[i], strlen(rsa_keys[i]) + 1, NULL, 0) );
  
          rsa = mbedtls_pk_rsa(pk);
  
          if( verbose != 0 )
              mbedtls_printf( "passed\n\r  RSA-%d key validation: ", mbedtls_pk_get_bitlen( &pk ) );
  
          MBEDTLS_MPI_CHK( mbedtls_rsa_check_pubkey( rsa ) );
          MBEDTLS_MPI_CHK( mbedtls_rsa_check_privkey( rsa ) );
  
          if( verbose != 0 )
              mbedtls_printf( "passed\n\r  PKCS#1 encryption      : " );
  
          memcpy( rsa_plaintext, RSA_PT, PT_LEN );
  
          MBEDTLS_MPI_CHK( mbedtls_rsa_pkcs1_encrypt( rsa, myrand, NULL, MBEDTLS_RSA_PUBLIC, PT_LEN,
                                 rsa_plaintext, rsa_ciphertext ) );
  
          if( verbose != 0 )
              mbedtls_printf( "passed\n\r  PKCS#1 decryption      : " );
  
          MBEDTLS_MPI_CHK( mbedtls_rsa_pkcs1_decrypt( rsa, myrand, NULL, MBEDTLS_RSA_PRIVATE, &len,
                                 rsa_ciphertext, rsa_decrypted,
                                 sizeof(rsa_decrypted) ) );
  
          MBEDTLS_MPI_CHK( memcmp( rsa_decrypted, rsa_plaintext, len ) );
  
          if( verbose != 0 )
              mbedtls_printf( "passed\n\r" );
  
      #if defined(MBEDTLS_SHA1_C)
          if( verbose != 0 )
              mbedtls_printf( "  PKCS#1 data sign       : " );
  
          mbedtls_sha1( rsa_plaintext, PT_LEN, sha1sum );
  
          MBEDTLS_MPI_CHK( mbedtls_rsa_pkcs1_sign( rsa, myrand, NULL, MBEDTLS_RSA_PRIVATE, MBEDTLS_MD_SHA1, 0,
                              sha1sum, rsa_ciphertext ) );
  
          if( verbose != 0 )
              mbedtls_printf( "passed\n\r  PKCS#1 sig. verify     : " );
  
          MBEDTLS_MPI_CHK( mbedtls_rsa_pkcs1_verify( rsa, NULL, NULL, MBEDTLS_RSA_PUBLIC, MBEDTLS_MD_SHA1, 0,
                                sha1sum, rsa_ciphertext ) );
  
          if( verbose != 0 )
              mbedtls_printf( "passed\n\r" );
      #endif /* MBEDTLS_SHA1_C */
  
          if( verbose != 0 )
              mbedtls_printf( "\n\r" );
  
      cleanup:
          mbedtls_pk_free( &pk );
          if( ret != 0 )
          {
              if( verbose != 0 )
                  mbedtls_printf( "failed\n\r" );
  
              return( 1 );
          }
      #else /* MBEDTLS_PKCS1_V15 */
          ((void) verbose);
      #endif /* MBEDTLS_PKCS1_V15 */
      }
      
      return( 0 );
  }
  
  #endif /* MBEDTLS_SELF_TEST */
  
  #endif /* MBEDTLS_RSA_C */
  