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+.\" Automatically generated by Pod::Man version 1.15
+.\" Thu May 9 13:16:34 2002
+.\"
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+.\" ======================================================================
+.\"
+.IX Title "BN_MOD_MUL_MONTGOMERY 1"
+.TH BN_MOD_MUL_MONTGOMERY 1 "perl v5.6.1" "2000-11-13" "User Contributed Perl Documentation"
+.UC
+.SH "NAME"
+BN_mod_mul_montgomery, BN_MONT_CTX_new, BN_MONT_CTX_init,
+BN_MONT_CTX_free, BN_MONT_CTX_set, BN_MONT_CTX_copy,
+BN_from_montgomery, BN_to_montgomery \- Montgomery multiplication
+.SH "SYNOPSIS"
+.IX Header "SYNOPSIS"
+.Vb 1
+\& #include <openssl/bn.h>
+.Ve
+.Vb 3
+\& BN_MONT_CTX *BN_MONT_CTX_new(void);
+\& void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
+\& void BN_MONT_CTX_free(BN_MONT_CTX *mont);
+.Ve
+.Vb 2
+\& int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *m, BN_CTX *ctx);
+\& BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from);
+.Ve
+.Vb 2
+\& int BN_mod_mul_montgomery(BIGNUM *r, BIGNUM *a, BIGNUM *b,
+\& BN_MONT_CTX *mont, BN_CTX *ctx);
+.Ve
+.Vb 2
+\& int BN_from_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
+\& BN_CTX *ctx);
+.Ve
+.Vb 2
+\& int BN_to_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
+\& BN_CTX *ctx);
+.Ve
+.SH "DESCRIPTION"
+.IX Header "DESCRIPTION"
+These functions implement Montgomery multiplication. They are used
+automatically when BN_mod_exp(3) is called with suitable input,
+but they may be useful when several operations are to be performed
+using the same modulus.
+.PP
+\&\fIBN_MONT_CTX_new()\fR allocates and initializes a \fB\s-1BN_MONT_CTX\s0\fR structure.
+\&\fIBN_MONT_CTX_init()\fR initializes an existing uninitialized \fB\s-1BN_MONT_CTX\s0\fR.
+.PP
+\&\fIBN_MONT_CTX_set()\fR sets up the \fBmont\fR structure from the modulus \fBm\fR
+by precomputing its inverse and a value R.
+.PP
+\&\fIBN_MONT_CTX_copy()\fR copies the \fB\s-1BN_MONT_CTX\s0\fR \fBfrom\fR to \fBto\fR.
+.PP
+\&\fIBN_MONT_CTX_free()\fR frees the components of the \fB\s-1BN_MONT_CTX\s0\fR, and, if
+it was created by \fIBN_MONT_CTX_new()\fR, also the structure itself.
+.PP
+\&\fIBN_mod_mul_montgomery()\fR computes Mont(\fBa\fR,\fBb\fR):=\fBa\fR*\fBb\fR*R^\-1 and places
+the result in \fBr\fR.
+.PP
+\&\fIBN_from_montgomery()\fR performs the Montgomery reduction \fBr\fR = \fBa\fR*R^\-1.
+.PP
+\&\fIBN_to_montgomery()\fR computes Mont(\fBa\fR,R^2), i.e. \fBa\fR*R.
+.PP
+For all functions, \fBctx\fR is a previously allocated \fB\s-1BN_CTX\s0\fR used for
+temporary variables.
+.PP
+The \fB\s-1BN_MONT_CTX\s0\fR structure is defined as follows:
+.PP
+.Vb 10
+\& typedef struct bn_mont_ctx_st
+\& {
+\& int ri; /* number of bits in R */
+\& BIGNUM RR; /* R^2 (used to convert to Montgomery form) */
+\& BIGNUM N; /* The modulus */
+\& BIGNUM Ni; /* R*(1/R mod N) - N*Ni = 1
+\& * (Ni is only stored for bignum algorithm) */
+\& BN_ULONG n0; /* least significant word of Ni */
+\& int flags;
+\& } BN_MONT_CTX;
+.Ve
+\&\fIBN_to_montgomery()\fR is a macro.
+.SH "RETURN VALUES"
+.IX Header "RETURN VALUES"
+\&\fIBN_MONT_CTX_new()\fR returns the newly allocated \fB\s-1BN_MONT_CTX\s0\fR, and \s-1NULL\s0
+on error.
+.PP
+\&\fIBN_MONT_CTX_init()\fR and \fIBN_MONT_CTX_free()\fR have no return values.
+.PP
+For the other functions, 1 is returned for success, 0 on error.
+The error codes can be obtained by ERR_get_error(3).
+.SH "SEE ALSO"
+.IX Header "SEE ALSO"
+bn(3), err(3), BN_add(3),
+BN_CTX_new(3)
+.SH "HISTORY"
+.IX Header "HISTORY"
+\&\fIBN_MONT_CTX_new()\fR, \fIBN_MONT_CTX_free()\fR, \fIBN_MONT_CTX_set()\fR,
+\&\fIBN_mod_mul_montgomery()\fR, \fIBN_from_montgomery()\fR and \fIBN_to_montgomery()\fR
+are available in all versions of SSLeay and OpenSSL.
+.PP
+\&\fIBN_MONT_CTX_init()\fR and \fIBN_MONT_CTX_copy()\fR were added in SSLeay 0.9.1b.
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