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.\" ========================================================================
.\"
.IX Title "BN_mod_mul_montgomery 3"
.TH BN_mod_mul_montgomery 3 "2019-12-20" "1.0.2u" "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"
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>
\&
\& 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);
\&
\& 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);
\&
\& int BN_mod_mul_montgomery(BIGNUM *r, BIGNUM *a, BIGNUM *b,
\&         BN_MONT_CTX *mont, BN_CTX *ctx);
\&
\& int BN_from_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
\&         BN_CTX *ctx);
\&
\& 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 \fBBN_mod_exp\fR\|(3) is called with suitable input,
but they may be useful when several operations are to be performed
using the same modulus.
.PP
\&\fBBN_MONT_CTX_new()\fR allocates and initializes a \fB\s-1BN_MONT_CTX\s0\fR structure.
\&\fBBN_MONT_CTX_init()\fR initializes an existing uninitialized \fB\s-1BN_MONT_CTX\s0\fR.
.PP
\&\fBBN_MONT_CTX_set()\fR sets up the \fImont\fR structure from the modulus \fIm\fR
by precomputing its inverse and a value R.
.PP
\&\fBBN_MONT_CTX_copy()\fR copies the \fB\s-1BN_MONT_CTX\s0\fR \fIfrom\fR to \fIto\fR.
.PP
\&\fBBN_MONT_CTX_free()\fR frees the components of the \fB\s-1BN_MONT_CTX\s0\fR, and, if
it was created by \fBBN_MONT_CTX_new()\fR, also the structure itself.
.PP
\&\fBBN_mod_mul_montgomery()\fR computes Mont(\fIa\fR,\fIb\fR):=\fIa\fR*\fIb\fR*R^\-1 and places
the result in \fIr\fR.
.PP
\&\fBBN_from_montgomery()\fR performs the Montgomery reduction \fIr\fR = \fIa\fR*R^\-1.
.PP
\&\fBBN_to_montgomery()\fR computes Mont(\fIa\fR,R^2), i.e. \fIa\fR*R.
Note that \fIa\fR must be non-negative and smaller than the modulus.
.PP
For all functions, \fIctx\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
.PP
\&\fBBN_to_montgomery()\fR is a macro.
.SH "RETURN VALUES"
.IX Header "RETURN VALUES"
\&\fBBN_MONT_CTX_new()\fR returns the newly allocated \fB\s-1BN_MONT_CTX\s0\fR, and \s-1NULL\s0
on error.
.PP
\&\fBBN_MONT_CTX_init()\fR and \fBBN_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 \fBERR_get_error\fR\|(3).
.SH "WARNING"
.IX Header "WARNING"
The inputs must be reduced modulo \fBm\fR, otherwise the result will be
outside the expected range.
.SH "SEE ALSO"
.IX Header "SEE ALSO"
\&\fBbn\fR\|(3), \fBERR_get_error\fR\|(3), \fBBN_add\fR\|(3),
\&\fBBN_CTX_new\fR\|(3)
.SH "HISTORY"
.IX Header "HISTORY"
\&\fBBN_MONT_CTX_new()\fR, \fBBN_MONT_CTX_free()\fR, \fBBN_MONT_CTX_set()\fR,
\&\fBBN_mod_mul_montgomery()\fR, \fBBN_from_montgomery()\fR and \fBBN_to_montgomery()\fR
are available in all versions of SSLeay and OpenSSL.
.PP
\&\fBBN_MONT_CTX_init()\fR and \fBBN_MONT_CTX_copy()\fR were added in SSLeay 0.9.1b.
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