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+.\" ========================================================================
+.\"
+.IX Title "rsa 3"
+.TH rsa 3 "2014-06-05" "0.9.8za" "OpenSSL"
+.\" For nroff, turn off justification.  Always turn off hyphenation; it makes
+.\" way too many mistakes in technical documents.
+.if n .ad l
+.nh
+.SH "NAME"
+rsa \- RSA public key cryptosystem
+.SH "SYNOPSIS"
+.IX Header "SYNOPSIS"
+.Vb 2
+\& #include <openssl/rsa.h>
+\& #include <openssl/engine.h>
+\&
+\& RSA * RSA_new(void);
+\& void RSA_free(RSA *rsa);
+\&
+\& int RSA_public_encrypt(int flen, unsigned char *from,
+\&    unsigned char *to, RSA *rsa, int padding);
+\& int RSA_private_decrypt(int flen, unsigned char *from,
+\&    unsigned char *to, RSA *rsa, int padding);
+\& int RSA_private_encrypt(int flen, unsigned char *from,
+\&    unsigned char *to, RSA *rsa,int padding);
+\& int RSA_public_decrypt(int flen, unsigned char *from, 
+\&    unsigned char *to, RSA *rsa,int padding);
+\&
+\& int RSA_sign(int type, unsigned char *m, unsigned int m_len,
+\&    unsigned char *sigret, unsigned int *siglen, RSA *rsa);
+\& int RSA_verify(int type, unsigned char *m, unsigned int m_len,
+\&    unsigned char *sigbuf, unsigned int siglen, RSA *rsa);
+\&
+\& int RSA_size(const RSA *rsa);
+\&
+\& RSA *RSA_generate_key(int num, unsigned long e,
+\&    void (*callback)(int,int,void *), void *cb_arg);
+\&
+\& int RSA_check_key(RSA *rsa);
+\&
+\& int RSA_blinding_on(RSA *rsa, BN_CTX *ctx);
+\& void RSA_blinding_off(RSA *rsa);
+\&
+\& void RSA_set_default_method(const RSA_METHOD *meth);
+\& const RSA_METHOD *RSA_get_default_method(void);
+\& int RSA_set_method(RSA *rsa, const RSA_METHOD *meth);
+\& const RSA_METHOD *RSA_get_method(const RSA *rsa);
+\& RSA_METHOD *RSA_PKCS1_SSLeay(void);
+\& RSA_METHOD *RSA_null_method(void);
+\& int RSA_flags(const RSA *rsa);
+\& RSA *RSA_new_method(ENGINE *engine);
+\&
+\& int RSA_print(BIO *bp, RSA *x, int offset);
+\& int RSA_print_fp(FILE *fp, RSA *x, int offset);
+\&
+\& int RSA_get_ex_new_index(long argl, char *argp, int (*new_func)(),
+\&    int (*dup_func)(), void (*free_func)());
+\& int RSA_set_ex_data(RSA *r,int idx,char *arg);
+\& char *RSA_get_ex_data(RSA *r, int idx);
+\&
+\& int RSA_sign_ASN1_OCTET_STRING(int dummy, unsigned char *m,
+\&    unsigned int m_len, unsigned char *sigret, unsigned int *siglen,
+\&    RSA *rsa);
+\& int RSA_verify_ASN1_OCTET_STRING(int dummy, unsigned char *m,
+\&    unsigned int m_len, unsigned char *sigbuf, unsigned int siglen,
+\&    RSA *rsa);
+.Ve
+.SH "DESCRIPTION"
+.IX Header "DESCRIPTION"
+These functions implement \s-1RSA\s0 public key encryption and signatures
+as defined in \s-1PKCS\s0 #1 v2.0 [\s-1RFC 2437\s0].
+.PP
+The \fB\s-1RSA\s0\fR structure consists of several \s-1BIGNUM\s0 components. It can
+contain public as well as private \s-1RSA\s0 keys:
+.PP
+.Vb 10
+\& struct
+\&        {
+\&        BIGNUM *n;              // public modulus
+\&        BIGNUM *e;              // public exponent
+\&        BIGNUM *d;              // private exponent
+\&        BIGNUM *p;              // secret prime factor
+\&        BIGNUM *q;              // secret prime factor
+\&        BIGNUM *dmp1;           // d mod (p\-1)
+\&        BIGNUM *dmq1;           // d mod (q\-1)
+\&        BIGNUM *iqmp;           // q^\-1 mod p
+\&        // ...
+\&        };
+\& RSA
+.Ve
+.PP
+In public keys, the private exponent and the related secret values are
+\&\fB\s-1NULL\s0\fR.
+.PP
+\&\fBp\fR, \fBq\fR, \fBdmp1\fR, \fBdmq1\fR and \fBiqmp\fR may be \fB\s-1NULL\s0\fR in private
+keys, but the \s-1RSA\s0 operations are much faster when these values are
+available.
+.PP
+Note that \s-1RSA\s0 keys may use non-standard \fB\s-1RSA_METHOD\s0\fR implementations,
+either directly or by the use of \fB\s-1ENGINE\s0\fR modules. In some cases (eg. an
+\&\s-1ENGINE\s0 providing support for hardware-embedded keys), these \s-1BIGNUM\s0 values
+will not be used by the implementation or may be used for alternative data
+storage. For this reason, applications should generally avoid using \s-1RSA\s0
+structure elements directly and instead use \s-1API\s0 functions to query or
+modify keys.
+.SH "CONFORMING TO"
+.IX Header "CONFORMING TO"
+\&\s-1SSL, PKCS\s0 #1 v2.0
+.SH "PATENTS"
+.IX Header "PATENTS"
+\&\s-1RSA\s0 was covered by a \s-1US\s0 patent which expired in September 2000.
+.SH "SEE ALSO"
+.IX Header "SEE ALSO"
+\&\fIrsa\fR\|(1), \fIbn\fR\|(3), \fIdsa\fR\|(3), \fIdh\fR\|(3),
+\&\fIrand\fR\|(3), \fIengine\fR\|(3), \fIRSA_new\fR\|(3),
+\&\fIRSA_public_encrypt\fR\|(3),
+\&\fIRSA_sign\fR\|(3), \fIRSA_size\fR\|(3),
+\&\fIRSA_generate_key\fR\|(3),
+\&\fIRSA_check_key\fR\|(3),
+\&\fIRSA_blinding_on\fR\|(3),
+\&\fIRSA_set_method\fR\|(3), \fIRSA_print\fR\|(3),
+\&\fIRSA_get_ex_new_index\fR\|(3),
+\&\fIRSA_private_encrypt\fR\|(3),
+\&\fIRSA_sign_ASN1_OCTET_STRING\fR\|(3),
+\&\fIRSA_padding_add_PKCS1_type_1\fR\|(3)