text: /**
   * \file rsa.h
   *
   * \brief 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)
   */
  #ifndef MBEDTLS_RSA_H
  #define MBEDTLS_RSA_H
  
  #if !defined(MBEDTLS_CONFIG_FILE)
  #include "config.h"
  #else
  #include MBEDTLS_CONFIG_FILE
  #endif
  
  #include "bignum.h"
  #include "md.h"
  
  #if defined(MBEDTLS_THREADING_C)
  #include "threading.h"
  #endif
  
  /*
   * RSA Error codes
   */
  #define MBEDTLS_ERR_RSA_BAD_INPUT_DATA                    -0x4080  /**< Bad input parameters to function. */
  #define MBEDTLS_ERR_RSA_INVALID_PADDING                   -0x4100  /**< Input data contains invalid padding and is rejected. */
  #define MBEDTLS_ERR_RSA_KEY_GEN_FAILED                    -0x4180  /**< Something failed during generation of a key. */
  #define MBEDTLS_ERR_RSA_KEY_CHECK_FAILED                  -0x4200  /**< Key failed to pass the library's validity check. */
  #define MBEDTLS_ERR_RSA_PUBLIC_FAILED                     -0x4280  /**< The public key operation failed. */
  #define MBEDTLS_ERR_RSA_PRIVATE_FAILED                    -0x4300  /**< The private key operation failed. */
  #define MBEDTLS_ERR_RSA_VERIFY_FAILED                     -0x4380  /**< The PKCS#1 verification failed. */
  #define MBEDTLS_ERR_RSA_OUTPUT_TOO_LARGE                  -0x4400  /**< The output buffer for decryption is not large enough. */
  #define MBEDTLS_ERR_RSA_RNG_FAILED                        -0x4480  /**< The random generator failed to generate non-zeros. */
  
  /*
   * RSA constants
   */
  #define MBEDTLS_RSA_PUBLIC      0
  #define MBEDTLS_RSA_PRIVATE     1
  
  #define MBEDTLS_RSA_PKCS_V15    0
  #define MBEDTLS_RSA_PKCS_V21    1
  
  #define MBEDTLS_RSA_SIGN        1
  #define MBEDTLS_RSA_CRYPT       2
  
  #define MBEDTLS_RSA_SALT_LEN_ANY    -1
  
  /*
   * The above constants may be used even if the RSA module is compile out,
   * eg for alternative (PKCS#11) RSA implemenations in the PK layers.
   */
  #if defined(MBEDTLS_RSA_C)
  
  #ifdef __cplusplus
  extern "C" {
  #endif
  
  /**
   * \brief          RSA context structure
   */
  typedef struct
  {
      int ver;                    /*!<  always 0          */
      size_t len;                 /*!<  size(N) in chars  */
  
      mbedtls_mpi N;                      /*!<  public modulus    */
      mbedtls_mpi E;                      /*!<  public exponent   */
  
      mbedtls_mpi D;                      /*!<  private exponent  */
      mbedtls_mpi P;                      /*!<  1st prime factor  */
      mbedtls_mpi Q;                      /*!<  2nd prime factor  */
      mbedtls_mpi DP;                     /*!<  D % (P - 1)       */
      mbedtls_mpi DQ;                     /*!<  D % (Q - 1)       */
      mbedtls_mpi QP;                     /*!<  1 / (Q % P)       */
  
      mbedtls_mpi RN;                     /*!<  cached R^2 mod N  */
      mbedtls_mpi RP;                     /*!<  cached R^2 mod P  */
      mbedtls_mpi RQ;                     /*!<  cached R^2 mod Q  */
  
      mbedtls_mpi Vi;                     /*!<  cached blinding value     */
      mbedtls_mpi Vf;                     /*!<  cached un-blinding value  */
  
      int padding;                /*!<  MBEDTLS_RSA_PKCS_V15 for 1.5 padding and
                                        MBEDTLS_RSA_PKCS_v21 for OAEP/PSS         */
      int hash_id;                /*!<  Hash identifier of mbedtls_md_type_t as
                                        specified in the mbedtls_md.h header file
                                        for the EME-OAEP and EMSA-PSS
                                        encoding                          */
  #if defined(MBEDTLS_THREADING_C)
      mbedtls_threading_mutex_t mutex;    /*!<  Thread-safety mutex       */
  #endif
  }
  mbedtls_rsa_context;
  
  /**
   * \brief          Initialize an RSA context
   *
   *                 Note: Set padding to MBEDTLS_RSA_PKCS_V21 for the RSAES-OAEP
   *                 encryption scheme and the RSASSA-PSS signature scheme.
   *
   * \param ctx      RSA context to be initialized
   * \param padding  MBEDTLS_RSA_PKCS_V15 or MBEDTLS_RSA_PKCS_V21
   * \param hash_id  MBEDTLS_RSA_PKCS_V21 hash identifier
   *
   * \note           The hash_id parameter is actually ignored
   *                 when using MBEDTLS_RSA_PKCS_V15 padding.
   *
   * \note           Choice of padding mode is strictly enforced for private key
   *                 operations, since there might be security concerns in
   *                 mixing padding modes. For public key operations it's merely
   *                 a default value, which can be overriden by calling specific
   *                 rsa_rsaes_xxx or rsa_rsassa_xxx functions.
   *
   * \note           The chosen hash is always used for OEAP encryption.
   *                 For PSS signatures, it's always used for making signatures,
   *                 but can be overriden (and always is, if set to
   *                 MBEDTLS_MD_NONE) for verifying them.
   */
  void mbedtls_rsa_init( mbedtls_rsa_context *ctx,
                 int padding,
                 int hash_id);
  
  /**
   * \brief          Set padding for an already initialized RSA context
   *                 See \c mbedtls_rsa_init() for details.
   *
   * \param ctx      RSA context to be set
   * \param padding  MBEDTLS_RSA_PKCS_V15 or MBEDTLS_RSA_PKCS_V21
   * \param hash_id  MBEDTLS_RSA_PKCS_V21 hash identifier
   */
  void mbedtls_rsa_set_padding( mbedtls_rsa_context *ctx, int padding, int hash_id);
  
  /**
   * \brief          Generate an RSA keypair
   *
   * \param ctx      RSA context that will hold the key
   * \param f_rng    RNG function
   * \param p_rng    RNG parameter
   * \param nbits    size of the public key in bits
   * \param exponent public exponent (e.g., 65537)
   *
   * \note           mbedtls_rsa_init() must be called beforehand to setup
   *                 the RSA context.
   *
   * \return         0 if successful, or an MBEDTLS_ERR_RSA_XXX error code
   */
  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 );
  
  /**
   * \brief          Check a public RSA key
   *
   * \param ctx      RSA context to be checked
   *
   * \return         0 if successful, or an MBEDTLS_ERR_RSA_XXX error code
   */
  int mbedtls_rsa_check_pubkey( const mbedtls_rsa_context *ctx );
  
  /**
   * \brief          Check a private RSA key
   *
   * \param ctx      RSA context to be checked
   *
   * \return         0 if successful, or an MBEDTLS_ERR_RSA_XXX error code
   */
  int mbedtls_rsa_check_privkey( const mbedtls_rsa_context *ctx );
  
  /**
   * \brief          Check a public-private RSA key pair.
   *                 Check each of the contexts, and make sure they match.
   *
   * \param pub      RSA context holding the public key
   * \param prv      RSA context holding the private key
   *
   * \return         0 if successful, or an MBEDTLS_ERR_RSA_XXX error code
   */
  int mbedtls_rsa_check_pub_priv( const mbedtls_rsa_context *pub, const mbedtls_rsa_context *prv );
  
  /**
   * \brief          Do an RSA public key operation
   *
   * \param ctx      RSA context
   * \param input    input buffer
   * \param output   output buffer
   *
   * \return         0 if successful, or an MBEDTLS_ERR_RSA_XXX error code
   *
   * \note           This function does NOT take care of message
   *                 padding. Also, be sure to set input[0] = 0 or assure that
   *                 input is smaller than N.
   *
   * \note           The input and output buffers must be large
   *                 enough (eg. 128 bytes if RSA-1024 is used).
   */
  int mbedtls_rsa_public( mbedtls_rsa_context *ctx,
                  const unsigned char *input,
                  unsigned char *output );
  
  /**
   * \brief          Do an RSA private key operation
   *
   * \param ctx      RSA context
   * \param f_rng    RNG function (Needed for blinding)
   * \param p_rng    RNG parameter
   * \param input    input buffer
   * \param output   output buffer
   *
   * \return         0 if successful, or an MBEDTLS_ERR_RSA_XXX error code
   *
   * \note           The input and output buffers must be large
   *                 enough (eg. 128 bytes if RSA-1024 is used).
   */
  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 );
  
  /**
   * \brief          Generic wrapper to perform a PKCS#1 encryption using the
   *                 mode from the context. Add the message padding, then do an
   *                 RSA operation.
   *
   * \param ctx      RSA context
   * \param f_rng    RNG function (Needed for padding and PKCS#1 v2.1 encoding
   *                               and MBEDTLS_RSA_PRIVATE)
   * \param p_rng    RNG parameter
   * \param mode     MBEDTLS_RSA_PUBLIC or MBEDTLS_RSA_PRIVATE
   * \param ilen     contains the plaintext length
   * \param input    buffer holding the data to be encrypted
   * \param output   buffer that will hold the ciphertext
   *
   * \return         0 if successful, or an MBEDTLS_ERR_RSA_XXX error code
   *
   * \note           The output buffer must be as large as the size
   *                 of ctx->N (eg. 128 bytes if RSA-1024 is used).
   */
  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 );
  
  /**
   * \brief          Perform a PKCS#1 v1.5 encryption (RSAES-PKCS1-v1_5-ENCRYPT)
   *
   * \param ctx      RSA context
   * \param f_rng    RNG function (Needed for padding and MBEDTLS_RSA_PRIVATE)
   * \param p_rng    RNG parameter
   * \param mode     MBEDTLS_RSA_PUBLIC or MBEDTLS_RSA_PRIVATE
   * \param ilen     contains the plaintext length
   * \param input    buffer holding the data to be encrypted
   * \param output   buffer that will hold the ciphertext
   *
   * \return         0 if successful, or an MBEDTLS_ERR_RSA_XXX error code
   *
   * \note           The output buffer must be as large as the size
   *                 of ctx->N (eg. 128 bytes if RSA-1024 is used).
   */
  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 );
  
  /**
   * \brief          Perform a PKCS#1 v2.1 OAEP encryption (RSAES-OAEP-ENCRYPT)
   *
   * \param ctx      RSA context
   * \param f_rng    RNG function (Needed for padding and PKCS#1 v2.1 encoding
   *                               and MBEDTLS_RSA_PRIVATE)
   * \param p_rng    RNG parameter
   * \param mode     MBEDTLS_RSA_PUBLIC or MBEDTLS_RSA_PRIVATE
   * \param label    buffer holding the custom label to use
   * \param label_len contains the label length
   * \param ilen     contains the plaintext length
   * \param input    buffer holding the data to be encrypted
   * \param output   buffer that will hold the ciphertext
   *
   * \return         0 if successful, or an MBEDTLS_ERR_RSA_XXX error code
   *
   * \note           The output buffer must be as large as the size
   *                 of ctx->N (eg. 128 bytes if RSA-1024 is used).
   */
  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 );
  
  /**
   * \brief          Generic wrapper to perform a PKCS#1 decryption using the
   *                 mode from the context. Do an RSA operation, then remove
   *                 the message padding
   *
   * \param ctx      RSA context
   * \param f_rng    RNG function (Only needed for MBEDTLS_RSA_PRIVATE)
   * \param p_rng    RNG parameter
   * \param mode     MBEDTLS_RSA_PUBLIC or MBEDTLS_RSA_PRIVATE
   * \param olen     will contain the plaintext length
   * \param input    buffer holding the encrypted data
   * \param output   buffer that will hold the plaintext
   * \param output_max_len    maximum length of the output buffer
   *
   * \return         0 if successful, or an MBEDTLS_ERR_RSA_XXX error code
   *
   * \note           The output buffer must be as large as the size
   *                 of ctx->N (eg. 128 bytes if RSA-1024 is used) otherwise
   *                 an error is thrown.
   */
  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 );
  
  /**
   * \brief          Perform a PKCS#1 v1.5 decryption (RSAES-PKCS1-v1_5-DECRYPT)
   *
   * \param ctx      RSA context
   * \param f_rng    RNG function (Only needed for MBEDTLS_RSA_PRIVATE)
   * \param p_rng    RNG parameter
   * \param mode     MBEDTLS_RSA_PUBLIC or MBEDTLS_RSA_PRIVATE
   * \param olen     will contain the plaintext length
   * \param input    buffer holding the encrypted data
   * \param output   buffer that will hold the plaintext
   * \param output_max_len    maximum length of the output buffer
   *
   * \return         0 if successful, or an MBEDTLS_ERR_RSA_XXX error code
   *
   * \note           The output buffer must be as large as the size
   *                 of ctx->N (eg. 128 bytes if RSA-1024 is used) otherwise
   *                 an error is thrown.
   */
  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 );
  
  /**
   * \brief          Perform a PKCS#1 v2.1 OAEP decryption (RSAES-OAEP-DECRYPT)
   *
   * \param ctx      RSA context
   * \param f_rng    RNG function (Only needed for MBEDTLS_RSA_PRIVATE)
   * \param p_rng    RNG parameter
   * \param mode     MBEDTLS_RSA_PUBLIC or MBEDTLS_RSA_PRIVATE
   * \param label    buffer holding the custom label to use
   * \param label_len contains the label length
   * \param olen     will contain the plaintext length
   * \param input    buffer holding the encrypted data
   * \param output   buffer that will hold the plaintext
   * \param output_max_len    maximum length of the output buffer
   *
   * \return         0 if successful, or an MBEDTLS_ERR_RSA_XXX error code
   *
   * \note           The output buffer must be as large as the size
   *                 of ctx->N (eg. 128 bytes if RSA-1024 is used) otherwise
   *                 an error is thrown.
   */
  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 );
  
  /**
   * \brief          Generic wrapper to perform a PKCS#1 signature using the
   *                 mode from the context. Do a private RSA operation to sign
   *                 a message digest
   *
   * \param ctx      RSA context
   * \param f_rng    RNG function (Needed for PKCS#1 v2.1 encoding and for
   *                               MBEDTLS_RSA_PRIVATE)
   * \param p_rng    RNG parameter
   * \param mode     MBEDTLS_RSA_PUBLIC or MBEDTLS_RSA_PRIVATE
   * \param md_alg   a MBEDTLS_MD_XXX (use MBEDTLS_MD_NONE for signing raw data)
   * \param hashlen  message digest length (for MBEDTLS_MD_NONE only)
   * \param hash     buffer holding the message digest
   * \param sig      buffer that will hold the ciphertext
   *
   * \return         0 if the signing operation was successful,
   *                 or an MBEDTLS_ERR_RSA_XXX error code
   *
   * \note           The "sig" buffer must be as large as the size
   *                 of ctx->N (eg. 128 bytes if RSA-1024 is used).
   *
   * \note           In case of PKCS#1 v2.1 encoding, see comments on
   * \note           \c mbedtls_rsa_rsassa_pss_sign() for details on md_alg and hash_id.
   */
  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 );
  
  /**
   * \brief          Perform a PKCS#1 v1.5 signature (RSASSA-PKCS1-v1_5-SIGN)
   *
   * \param ctx      RSA context
   * \param f_rng    RNG function (Only needed for MBEDTLS_RSA_PRIVATE)
   * \param p_rng    RNG parameter
   * \param mode     MBEDTLS_RSA_PUBLIC or MBEDTLS_RSA_PRIVATE
   * \param md_alg   a MBEDTLS_MD_XXX (use MBEDTLS_MD_NONE for signing raw data)
   * \param hashlen  message digest length (for MBEDTLS_MD_NONE only)
   * \param hash     buffer holding the message digest
   * \param sig      buffer that will hold the ciphertext
   *
   * \return         0 if the signing operation was successful,
   *                 or an MBEDTLS_ERR_RSA_XXX error code
   *
   * \note           The "sig" buffer must be as large as the size
   *                 of ctx->N (eg. 128 bytes if RSA-1024 is used).
   */
  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 );
  
  /**
   * \brief          Perform a PKCS#1 v2.1 PSS signature (RSASSA-PSS-SIGN)
   *
   * \param ctx      RSA context
   * \param f_rng    RNG function (Needed for PKCS#1 v2.1 encoding and for
   *                               MBEDTLS_RSA_PRIVATE)
   * \param p_rng    RNG parameter
   * \param mode     MBEDTLS_RSA_PUBLIC or MBEDTLS_RSA_PRIVATE
   * \param md_alg   a MBEDTLS_MD_XXX (use MBEDTLS_MD_NONE for signing raw data)
   * \param hashlen  message digest length (for MBEDTLS_MD_NONE only)
   * \param hash     buffer holding the message digest
   * \param sig      buffer that will hold the ciphertext
   *
   * \return         0 if the signing operation was successful,
   *                 or an MBEDTLS_ERR_RSA_XXX error code
   *
   * \note           The "sig" buffer must be as large as the size
   *                 of ctx->N (eg. 128 bytes if RSA-1024 is used).
   *
   * \note           The hash_id in the RSA context is the one used for the
   *                 encoding. md_alg in the function call is the type of hash
   *                 that is encoded. According to RFC 3447 it is advised to
   *                 keep both hashes the same.
   */
  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 );
  
  /**
   * \brief          Generic wrapper to perform a PKCS#1 verification using the
   *                 mode from the context. Do a public RSA operation and check
   *                 the message digest
   *
   * \param ctx      points to an RSA public key
   * \param f_rng    RNG function (Only needed for MBEDTLS_RSA_PRIVATE)
   * \param p_rng    RNG parameter
   * \param mode     MBEDTLS_RSA_PUBLIC or MBEDTLS_RSA_PRIVATE
   * \param md_alg   a MBEDTLS_MD_XXX (use MBEDTLS_MD_NONE for signing raw data)
   * \param hashlen  message digest length (for MBEDTLS_MD_NONE only)
   * \param hash     buffer holding the message digest
   * \param sig      buffer holding the ciphertext
   *
   * \return         0 if the verify operation was successful,
   *                 or an MBEDTLS_ERR_RSA_XXX error code
   *
   * \note           The "sig" buffer must be as large as the size
   *                 of ctx->N (eg. 128 bytes if RSA-1024 is used).
   *
   * \note           In case of PKCS#1 v2.1 encoding, see comments on
   *                 \c mbedtls_rsa_rsassa_pss_verify() about md_alg and hash_id.
   */
  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 );
  
  /**
   * \brief          Perform a PKCS#1 v1.5 verification (RSASSA-PKCS1-v1_5-VERIFY)
   *
   * \param ctx      points to an RSA public key
   * \param f_rng    RNG function (Only needed for MBEDTLS_RSA_PRIVATE)
   * \param p_rng    RNG parameter
   * \param mode     MBEDTLS_RSA_PUBLIC or MBEDTLS_RSA_PRIVATE
   * \param md_alg   a MBEDTLS_MD_XXX (use MBEDTLS_MD_NONE for signing raw data)
   * \param hashlen  message digest length (for MBEDTLS_MD_NONE only)
   * \param hash     buffer holding the message digest
   * \param sig      buffer holding the ciphertext
   *
   * \return         0 if the verify operation was successful,
   *                 or an MBEDTLS_ERR_RSA_XXX error code
   *
   * \note           The "sig" buffer must be as large as the size
   *                 of ctx->N (eg. 128 bytes if RSA-1024 is used).
   */
  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 );
  
  /**
   * \brief          Perform a PKCS#1 v2.1 PSS verification (RSASSA-PSS-VERIFY)
   *                 (This is the "simple" version.)
   *
   * \param ctx      points to an RSA public key
   * \param f_rng    RNG function (Only needed for MBEDTLS_RSA_PRIVATE)
   * \param p_rng    RNG parameter
   * \param mode     MBEDTLS_RSA_PUBLIC or MBEDTLS_RSA_PRIVATE
   * \param md_alg   a MBEDTLS_MD_XXX (use MBEDTLS_MD_NONE for signing raw data)
   * \param hashlen  message digest length (for MBEDTLS_MD_NONE only)
   * \param hash     buffer holding the message digest
   * \param sig      buffer holding the ciphertext
   *
   * \return         0 if the verify operation was successful,
   *                 or an MBEDTLS_ERR_RSA_XXX error code
   *
   * \note           The "sig" buffer must be as large as the size
   *                 of ctx->N (eg. 128 bytes if RSA-1024 is used).
   *
   * \note           The hash_id in the RSA context is the one used for the
   *                 verification. md_alg in the function call is the type of
   *                 hash that is verified. According to RFC 3447 it is advised to
   *                 keep both hashes the same. If hash_id in the RSA context is
   *                 unset, the md_alg from the function call is used.
   */
  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 );
  
  /**
   * \brief          Perform a PKCS#1 v2.1 PSS verification (RSASSA-PSS-VERIFY)
   *                 (This is the version with "full" options.)
   *
   * \param ctx      points to an RSA public key
   * \param f_rng    RNG function (Only needed for MBEDTLS_RSA_PRIVATE)
   * \param p_rng    RNG parameter
   * \param mode     MBEDTLS_RSA_PUBLIC or MBEDTLS_RSA_PRIVATE
   * \param md_alg   a MBEDTLS_MD_XXX (use MBEDTLS_MD_NONE for signing raw data)
   * \param hashlen  message digest length (for MBEDTLS_MD_NONE only)
   * \param hash     buffer holding the message digest
   * \param mgf1_hash_id message digest used for mask generation
   * \param expected_salt_len Length of the salt used in padding, use
   *                 MBEDTLS_RSA_SALT_LEN_ANY to accept any salt length
   * \param sig      buffer holding the ciphertext
   *
   * \return         0 if the verify operation was successful,
   *                 or an MBEDTLS_ERR_RSA_XXX error code
   *
   * \note           The "sig" buffer must be as large as the size
   *                 of ctx->N (eg. 128 bytes if RSA-1024 is used).
   *
   * \note           The hash_id in the RSA context is ignored.
   */
  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 );
  
  /**
   * \brief          Copy the components of an RSA context
   *
   * \param dst      Destination context
   * \param src      Source context
   *
   * \return         0 on success,
   *                 MBEDTLS_ERR_MPI_ALLOC_FAILED on memory allocation failure
   */
  int mbedtls_rsa_copy( mbedtls_rsa_context *dst, const mbedtls_rsa_context *src );
  
  /**
   * \brief          Free the components of an RSA key
   *
   * \param ctx      RSA Context to free
   */
  void mbedtls_rsa_free( mbedtls_rsa_context *ctx );
  
  /**
   * \brief          Checkup routine
   *
   * \return         0 if successful, or 1 if the test failed
   */
  int mbedtls_rsa_self_test( int verbose );
  
  #ifdef __cplusplus
  }
  #endif
  
  #endif /* MBEDTLS_RSA_C */
  
  #endif /* rsa.h */
  