include/polarssl/rsa.h - mirror/mbed-tls - TrustedFirmware Git Browser

 /**
  * \file rsa.h
  *
  *  Copyright (C) 2006-2009, Paul Bakker <polarssl_maintainer at polarssl.org>
  *  All rights reserved.
  *
  *  Joined copyright on original XySSL code with: Christophe Devine
  *
  *  This program is free software; you can redistribute it and/or modify
  *  it under the terms of the GNU General Public License as published by
  *  the Free Software Foundation; either version 2 of the License, or
  *  (at your option) any later version.
  *
  *  This program is distributed in the hope that it will be useful,
  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  *  GNU General Public License for more details.
  *
  *  You should have received a copy of the GNU General Public License along
  *  with this program; if not, write to the Free Software Foundation, Inc.,
  *  51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
  */
 #ifndef POLARSSL_RSA_H
 #define POLARSSL_RSA_H

 #include "polarssl/bignum.h"

 /*
  * RSA Error codes
  */
 #define POLARSSL_ERR_RSA_BAD_INPUT_DATA                    -0x0400
 #define POLARSSL_ERR_RSA_INVALID_PADDING                   -0x0410
 #define POLARSSL_ERR_RSA_KEY_GEN_FAILED                    -0x0420
 #define POLARSSL_ERR_RSA_KEY_CHECK_FAILED                  -0x0430
 #define POLARSSL_ERR_RSA_PUBLIC_FAILED                     -0x0440
 #define POLARSSL_ERR_RSA_PRIVATE_FAILED                    -0x0450
 #define POLARSSL_ERR_RSA_VERIFY_FAILED                     -0x0460
 #define POLARSSL_ERR_RSA_OUTPUT_TOO_LARGE                  -0x0470

 /*
  * PKCS#1 constants
  */
 #define SIG_RSA_RAW     0
 #define SIG_RSA_MD2     2
 #define SIG_RSA_MD4     3
 #define SIG_RSA_MD5     4
 #define SIG_RSA_SHA1	5
 #define SIG_RSA_SHA224	14
 #define SIG_RSA_SHA256	11
 #define	SIG_RSA_SHA384	12
 #define SIG_RSA_SHA512	13

 #define RSA_PUBLIC      0
 #define RSA_PRIVATE     1

 #define RSA_PKCS_V15    0
 #define RSA_PKCS_V21    1

 #define RSA_SIGN        1
 #define RSA_CRYPT       2

 #define ASN1_STR_CONSTRUCTED_SEQUENCE	"\x30"
 #define ASN1_STR_NULL			        "\x05"
 #define ASN1_STR_OID			        "\x06"
 #define ASN1_STR_OCTET_STRING		    "\x04"

 #define OID_DIGEST_ALG_MDX	        "\x2A\x86\x48\x86\xF7\x0D\x02\x00"
 #define OID_HASH_ALG_SHA1	        "\x2b\x0e\x03\x02\x1a"
 #define OID_HASH_ALG_SHA2X	        "\x60\x86\x48\x01\x65\x03\x04\x02\x00"

 #define OID_ISO_MEMBER_BODIES	    "\x2a"
 #define OID_ISO_IDENTIFIED_ORG	    "\x2b"

 /*
  * ISO Member bodies OID parts
  */
 #define OID_COUNTRY_US		        "\x86\x48"
 #define OID_RSA_DATA_SECURITY	    "\x86\xf7\x0d"

 /*
  * ISO Identified organization OID parts
  */
 #define OID_OIW_SECSIG_SHA1	        "\x0e\x03\x02\x1a"

 /*
  * DigestInfo ::= SEQUENCE {
  *   digestAlgorithm DigestAlgorithmIdentifier,
  *   digest Digest }
  *
  * DigestAlgorithmIdentifier ::= AlgorithmIdentifier
  *
  * Digest ::= OCTET STRING
  */
 #define ASN1_HASH_MDX					        \
 (							                    \
     ASN1_STR_CONSTRUCTED_SEQUENCE "\x20"		\
       ASN1_STR_CONSTRUCTED_SEQUENCE "\x0C"		\
         ASN1_STR_OID "\x08"				        \
 	  OID_DIGEST_ALG_MDX				        \
 	ASN1_STR_NULL "\x00"				        \
       ASN1_STR_OCTET_STRING "\x10"			    \
 )

 #define ASN1_HASH_SHA1					        \
     ASN1_STR_CONSTRUCTED_SEQUENCE "\x21"		\
       ASN1_STR_CONSTRUCTED_SEQUENCE "\x09"		\
         ASN1_STR_OID "\x05"				        \
 	  OID_HASH_ALG_SHA1				            \
         ASN1_STR_NULL "\x00"				    \
       ASN1_STR_OCTET_STRING "\x14"

 #define ASN1_HASH_SHA2X					        \
     ASN1_STR_CONSTRUCTED_SEQUENCE "\x11"		\
       ASN1_STR_CONSTRUCTED_SEQUENCE "\x0d"		\
         ASN1_STR_OID "\x09"				        \
 	  OID_HASH_ALG_SHA2X				        \
         ASN1_STR_NULL "\x00"				    \
       ASN1_STR_OCTET_STRING "\x00"

 /**
  * \brief          RSA context structure
  */
 typedef struct
 {
     int ver;                    /*!<  always 0          */
     int len;                    /*!<  size(N) in chars  */

     mpi N;                      /*!<  public modulus    */
     mpi E;                      /*!<  public exponent   */

     mpi D;                      /*!<  private exponent  */
     mpi P;                      /*!<  1st prime factor  */
     mpi Q;                      /*!<  2nd prime factor  */
     mpi DP;                     /*!<  D % (P - 1)       */
     mpi DQ;                     /*!<  D % (Q - 1)       */
     mpi QP;                     /*!<  1 / (Q % P)       */

     mpi RN;                     /*!<  cached R^2 mod N  */
     mpi RP;                     /*!<  cached R^2 mod P  */
     mpi RQ;                     /*!<  cached R^2 mod Q  */

     int padding;                /*!<  1.5 or OAEP/PSS   */
     int hash_id;                /*!<  hash identifier   */
     int (*f_rng)(void *);       /*!<  RNG function      */
     void *p_rng;                /*!<  RNG parameter     */
 }
 rsa_context;

 #ifdef __cplusplus
 extern "C" {
 #endif

 /**
  * \brief          Initialize an RSA context
  *
  * \param ctx      RSA context to be initialized
  * \param padding  RSA_PKCS_V15 or RSA_PKCS_V21
  * \param hash_id  RSA_PKCS_V21 hash identifier
  * \param f_rng    RNG function
  * \param p_rng    RNG parameter
  *
  * \note           The hash_id parameter is actually ignored
  *                 when using RSA_PKCS_V15 padding.
  *
  * \note           Currently (xyssl-0.8), RSA_PKCS_V21 padding
  *                 is not supported.
  */
 void rsa_init( rsa_context *ctx,
                int padding,
                int hash_id,
                int (*f_rng)(void *),
                void *p_rng );

 /**
  * \brief          Generate an RSA keypair
  *
  * \param ctx      RSA context that will hold the key
  * \param nbits    size of the public key in bits
  * \param exponent public exponent (e.g., 65537)
  *
  * \note           rsa_init() must be called beforehand to setup
  *                 the RSA context (especially f_rng and p_rng).
  *
  * \return         0 if successful, or an POLARSSL_ERR_RSA_XXX error code
  */
 int rsa_gen_key( rsa_context *ctx, int nbits, int exponent );

 /**
  * \brief          Check a public RSA key
  *
  * \param ctx      RSA context to be checked
  *
  * \return         0 if successful, or an POLARSSL_ERR_RSA_XXX error code
  */
 int rsa_check_pubkey( rsa_context *ctx );

 /**
  * \brief          Check a private RSA key
  *
  * \param ctx      RSA context to be checked
  *
  * \return         0 if successful, or an POLARSSL_ERR_RSA_XXX error code
  */
 int rsa_check_privkey( rsa_context *ctx );

 /**
  * \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 POLARSSL_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 rsa_public( rsa_context *ctx,
                 unsigned char *input,
                 unsigned char *output );

 /**
  * \brief          Do an RSA private key operation
  *
  * \param ctx      RSA context
  * \param input    input buffer
  * \param output   output buffer
  *
  * \return         0 if successful, or an POLARSSL_ERR_RSA_XXX error code
  *
  * \note           The input and output buffers must be large
  *                 enough (eg. 128 bytes if RSA-1024 is used).
  */
 int rsa_private( rsa_context *ctx,
                  unsigned char *input,
                  unsigned char *output );

 /**
  * \brief          Add the message padding, then do an RSA operation
  *
  * \param ctx      RSA context
  * \param mode     RSA_PUBLIC or 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 POLARSSL_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 rsa_pkcs1_encrypt( rsa_context *ctx,
                        int mode, int  ilen,
                        unsigned char *input,
                        unsigned char *output );

 /**
  * \brief          Do an RSA operation, then remove the message padding
  *
  * \param ctx      RSA context
  * \param mode     RSA_PUBLIC or RSA_PRIVATE
  * \param input    buffer holding the encrypted data
  * \param output   buffer that will hold the plaintext
  * \param olen     will contain the plaintext length
  * \param output_max_len	maximum length of the output buffer
  *
  * \return         0 if successful, or an POLARSSL_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 rsa_pkcs1_decrypt( rsa_context *ctx,
                        int mode, int *olen,
                        unsigned char *input,
                        unsigned char *output,
 		               int output_max_len );

 /**
  * \brief          Do a private RSA to sign a message digest
  *
  * \param ctx      RSA context
  * \param mode     RSA_PUBLIC or RSA_PRIVATE
  * \param hash_id  SIG_RSA_RAW, SIG_RSA_MD{2,4,5} or SIG_RSA_SHA{1,224,256,384,512}
  * \param hashlen  message digest length (for SIG_RSA_RAW 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 POLARSSL_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 rsa_pkcs1_sign( rsa_context *ctx,
                     int mode,
                     int hash_id,
                     int hashlen,
                     unsigned char *hash,
                     unsigned char *sig );

 /**
  * \brief          Do a public RSA and check the message digest
  *
  * \param ctx      points to an RSA public key
  * \param mode     RSA_PUBLIC or RSA_PRIVATE
  * \param hash_id  SIG_RSA_RAW, RSA_MD{2,4,5} or RSA_SHA{1,256}
  * \param hashlen  message digest length (for SIG_RSA_RAW only)
  * \param hash     buffer holding the message digest
  * \param sig      buffer holding the ciphertext
  *
  * \return         0 if the verify operation was successful,
  *                 or an POLARSSL_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 rsa_pkcs1_verify( rsa_context *ctx,
                       int mode,
                       int hash_id,
                       int hashlen,
                       unsigned char *hash,
                       unsigned char *sig );

 /**
  * \brief          Free the components of an RSA key
  *
  * \param ctx      RSA Context to free
  */
 void rsa_free( rsa_context *ctx );

 /**
  * \brief          Checkup routine
  *
  * \return         0 if successful, or 1 if the test failed
  */
 int rsa_self_test( int verbose );

 #ifdef __cplusplus
 }
 #endif

 #endif /* rsa.h */
	/**
	* \file rsa.h
	*
	* Copyright (C) 2006-2009, Paul Bakker <polarssl_maintainer at polarssl.org>
	* All rights reserved.
	*
	* Joined copyright on original XySSL code with: Christophe Devine
	*
	* This program is free software; you can redistribute it and/or modify
	* it under the terms of the GNU General Public License as published by
	* the Free Software Foundation; either version 2 of the License, or
	* (at your option) any later version.
	*
	* This program is distributed in the hope that it will be useful,
	* but WITHOUT ANY WARRANTY; without even the implied warranty of
	* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
	* GNU General Public License for more details.
	*
	* You should have received a copy of the GNU General Public License along
	* with this program; if not, write to the Free Software Foundation, Inc.,
	* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
	*/
	#ifndef POLARSSL_RSA_H
	#define POLARSSL_RSA_H

	#include "polarssl/bignum.h"

	/*
	* RSA Error codes
	*/
	#define POLARSSL_ERR_RSA_BAD_INPUT_DATA -0x0400
	#define POLARSSL_ERR_RSA_INVALID_PADDING -0x0410
	#define POLARSSL_ERR_RSA_KEY_GEN_FAILED -0x0420
	#define POLARSSL_ERR_RSA_KEY_CHECK_FAILED -0x0430
	#define POLARSSL_ERR_RSA_PUBLIC_FAILED -0x0440
	#define POLARSSL_ERR_RSA_PRIVATE_FAILED -0x0450
	#define POLARSSL_ERR_RSA_VERIFY_FAILED -0x0460
	#define POLARSSL_ERR_RSA_OUTPUT_TOO_LARGE -0x0470

	/*
	* PKCS#1 constants
	*/
	#define SIG_RSA_RAW 0
	#define SIG_RSA_MD2 2
	#define SIG_RSA_MD4 3
	#define SIG_RSA_MD5 4
	#define SIG_RSA_SHA1 5
	#define SIG_RSA_SHA224 14
	#define SIG_RSA_SHA256 11
	#define SIG_RSA_SHA384 12
	#define SIG_RSA_SHA512 13

	#define RSA_PUBLIC 0
	#define RSA_PRIVATE 1

	#define RSA_PKCS_V15 0
	#define RSA_PKCS_V21 1

	#define RSA_SIGN 1
	#define RSA_CRYPT 2

	#define ASN1_STR_CONSTRUCTED_SEQUENCE "\x30"
	#define ASN1_STR_NULL "\x05"
	#define ASN1_STR_OID "\x06"
	#define ASN1_STR_OCTET_STRING "\x04"

	#define OID_DIGEST_ALG_MDX "\x2A\x86\x48\x86\xF7\x0D\x02\x00"
	#define OID_HASH_ALG_SHA1 "\x2b\x0e\x03\x02\x1a"
	#define OID_HASH_ALG_SHA2X "\x60\x86\x48\x01\x65\x03\x04\x02\x00"

	#define OID_ISO_MEMBER_BODIES "\x2a"
	#define OID_ISO_IDENTIFIED_ORG "\x2b"

	/*
	* ISO Member bodies OID parts
	*/
	#define OID_COUNTRY_US "\x86\x48"
	#define OID_RSA_DATA_SECURITY "\x86\xf7\x0d"

	/*
	* ISO Identified organization OID parts
	*/
	#define OID_OIW_SECSIG_SHA1 "\x0e\x03\x02\x1a"

	/*
	* DigestInfo ::= SEQUENCE {
	* digestAlgorithm DigestAlgorithmIdentifier,
	* digest Digest }
	*
	* DigestAlgorithmIdentifier ::= AlgorithmIdentifier
	*
	* Digest ::= OCTET STRING
	*/
	#define ASN1_HASH_MDX \
	( \
	ASN1_STR_CONSTRUCTED_SEQUENCE "\x20" \
	ASN1_STR_CONSTRUCTED_SEQUENCE "\x0C" \
	ASN1_STR_OID "\x08" \
	OID_DIGEST_ALG_MDX \
	ASN1_STR_NULL "\x00" \
	ASN1_STR_OCTET_STRING "\x10" \
	)

	#define ASN1_HASH_SHA1 \
	ASN1_STR_CONSTRUCTED_SEQUENCE "\x21" \
	ASN1_STR_CONSTRUCTED_SEQUENCE "\x09" \
	ASN1_STR_OID "\x05" \
	OID_HASH_ALG_SHA1 \
	ASN1_STR_NULL "\x00" \
	ASN1_STR_OCTET_STRING "\x14"

	#define ASN1_HASH_SHA2X \
	ASN1_STR_CONSTRUCTED_SEQUENCE "\x11" \
	ASN1_STR_CONSTRUCTED_SEQUENCE "\x0d" \
	ASN1_STR_OID "\x09" \
	OID_HASH_ALG_SHA2X \
	ASN1_STR_NULL "\x00" \
	ASN1_STR_OCTET_STRING "\x00"

	/**
	* \brief RSA context structure
	*/
	typedef struct
	{
	int ver; /!< always 0 /
	int len; /!< size(N) in chars /

	mpi N; /!< public modulus /
	mpi E; /!< public exponent /

	mpi D; /!< private exponent /
	mpi P; /!< 1st prime factor /
	mpi Q; /!< 2nd prime factor /
	mpi DP; /!< D % (P - 1) /
	mpi DQ; /!< D % (Q - 1) /
	mpi QP; /!< 1 / (Q % P) /

	mpi RN; /!< cached R^2 mod N /
	mpi RP; /!< cached R^2 mod P /
	mpi RQ; /!< cached R^2 mod Q /

	int padding; /!< 1.5 or OAEP/PSS /
	int hash_id; /!< hash identifier /
	int (f_rng)(void ); /!< RNG function /
	void p_rng; /!< RNG parameter */
	}
	rsa_context;

	#ifdef __cplusplus
	extern "C" {
	#endif

	/**
	* \brief Initialize an RSA context
	*
	* \param ctx RSA context to be initialized
	* \param padding RSA_PKCS_V15 or RSA_PKCS_V21
	* \param hash_id RSA_PKCS_V21 hash identifier
	* \param f_rng RNG function
	* \param p_rng RNG parameter
	*
	* \note The hash_id parameter is actually ignored
	* when using RSA_PKCS_V15 padding.
	*
	* \note Currently (xyssl-0.8), RSA_PKCS_V21 padding
	* is not supported.
	*/
	void rsa_init( rsa_context *ctx,
	int padding,
	int hash_id,
	int (f_rng)(void ),
	void *p_rng );

	/**
	* \brief Generate an RSA keypair
	*
	* \param ctx RSA context that will hold the key
	* \param nbits size of the public key in bits
	* \param exponent public exponent (e.g., 65537)
	*
	* \note rsa_init() must be called beforehand to setup
	* the RSA context (especially f_rng and p_rng).
	*
	* \return 0 if successful, or an POLARSSL_ERR_RSA_XXX error code
	*/
	int rsa_gen_key( rsa_context *ctx, int nbits, int exponent );

	/**
	* \brief Check a public RSA key
	*
	* \param ctx RSA context to be checked
	*
	* \return 0 if successful, or an POLARSSL_ERR_RSA_XXX error code
	*/
	int rsa_check_pubkey( rsa_context *ctx );

	/**
	* \brief Check a private RSA key
	*
	* \param ctx RSA context to be checked
	*
	* \return 0 if successful, or an POLARSSL_ERR_RSA_XXX error code
	*/
	int rsa_check_privkey( rsa_context *ctx );

	/**
	* \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 POLARSSL_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 rsa_public( rsa_context *ctx,
	unsigned char *input,
	unsigned char *output );

	/**
	* \brief Do an RSA private key operation
	*
	* \param ctx RSA context
	* \param input input buffer
	* \param output output buffer
	*
	* \return 0 if successful, or an POLARSSL_ERR_RSA_XXX error code
	*
	* \note The input and output buffers must be large
	* enough (eg. 128 bytes if RSA-1024 is used).
	*/
	int rsa_private( rsa_context *ctx,
	unsigned char *input,
	unsigned char *output );

	/**
	* \brief Add the message padding, then do an RSA operation
	*
	* \param ctx RSA context
	* \param mode RSA_PUBLIC or 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 POLARSSL_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 rsa_pkcs1_encrypt( rsa_context *ctx,
	int mode, int ilen,
	unsigned char *input,
	unsigned char *output );

	/**
	* \brief Do an RSA operation, then remove the message padding
	*
	* \param ctx RSA context
	* \param mode RSA_PUBLIC or RSA_PRIVATE
	* \param input buffer holding the encrypted data
	* \param output buffer that will hold the plaintext
	* \param olen will contain the plaintext length
	* \param output_max_len maximum length of the output buffer
	*
	* \return 0 if successful, or an POLARSSL_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 rsa_pkcs1_decrypt( rsa_context *ctx,
	int mode, int *olen,
	unsigned char *input,
	unsigned char *output,
	int output_max_len );

	/**
	* \brief Do a private RSA to sign a message digest
	*
	* \param ctx RSA context
	* \param mode RSA_PUBLIC or RSA_PRIVATE
	* \param hash_id SIG_RSA_RAW, SIG_RSA_MD{2,4,5} or SIG_RSA_SHA{1,224,256,384,512}
	* \param hashlen message digest length (for SIG_RSA_RAW 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 POLARSSL_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 rsa_pkcs1_sign( rsa_context *ctx,
	int mode,
	int hash_id,
	int hashlen,
	unsigned char *hash,
	unsigned char *sig );

	/**
	* \brief Do a public RSA and check the message digest
	*
	* \param ctx points to an RSA public key
	* \param mode RSA_PUBLIC or RSA_PRIVATE
	* \param hash_id SIG_RSA_RAW, RSA_MD{2,4,5} or RSA_SHA{1,256}
	* \param hashlen message digest length (for SIG_RSA_RAW only)
	* \param hash buffer holding the message digest
	* \param sig buffer holding the ciphertext
	*
	* \return 0 if the verify operation was successful,
	* or an POLARSSL_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 rsa_pkcs1_verify( rsa_context *ctx,
	int mode,
	int hash_id,
	int hashlen,
	unsigned char *hash,
	unsigned char *sig );

	/**
	* \brief Free the components of an RSA key
	*
	* \param ctx RSA Context to free
	*/
	void rsa_free( rsa_context *ctx );

	/**
	* \brief Checkup routine
	*
	* \return 0 if successful, or 1 if the test failed
	*/
	int rsa_self_test( int verbose );

	#ifdef __cplusplus
	}
	#endif

	#endif /* rsa.h */