.rn '' }`
'''
'''
.de Sh
.br
.if t .Sp
.ne 5
.PP
\fB\\$1\fR
.PP
..
.de Sp
.if t .sp .5v
.if n .sp
..
.de Ip
.br
.ie \\n(.$>=3 .ne \\$3
.el .ne 3
.IP "\\$1" \\$2
..
.de Vb
.ft CW
.nf
.ne \\$1
..
.de Ve
.ft R

.fi
..
'''
'''
'''     Set up \*(-- to give an unbreakable dash;
'''     string Tr holds user defined translation string.
'''     Bell System Logo is used as a dummy character.
'''
.tr \(*W-|\(bv\*(Tr
.ie n \{\
.ds -- \(*W-
.ds PI pi
.if (\n(.H=4u)&(1m=24u) .ds -- \(*W\h'-12u'\(*W\h'-12u'-\" diablo 10 pitch
.if (\n(.H=4u)&(1m=20u) .ds -- \(*W\h'-12u'\(*W\h'-8u'-\" diablo 12 pitch
.ds L" ""
.ds R" ""
'''   \*(M", \*(S", \*(N" and \*(T" are the equivalent of
'''   \*(L" and \*(R", except that they are used on ".xx" lines,
'''   such as .IP and .SH, which do another additional levels of
'''   double-quote interpretation
.ds M" """
.ds S" """
.ds N" """""
.ds T" """""
.ds L' '
.ds R' '
.ds M' '
.ds S' '
.ds N' '
.ds T' '
'br\}
.el\{\
.ds -- \(em\|
.tr \*(Tr
.ds L" ``
.ds R" ''
.ds M" ``
.ds S" ''
.ds N" ``
.ds T" ''
.ds L' `
.ds R' '
.ds M' `
.ds S' '
.ds N' `
.ds T' '
.ds PI \(*p
'br\}
.\"	If the F register is turned on, we'll generate
.\"	index entries out stderr for the following things:
.\"		TH	Title 
.\"		SH	Header
.\"		Sh	Subsection 
.\"		Ip	Item
.\"		X<>	Xref  (embedded
.\"	Of course, you have to process the output yourself
.\"	in some meaninful fashion.
.if \nF \{
.de IX
.tm Index:\\$1\t\\n%\t"\\$2"
..
.nr % 0
.rr F
.\}
.TH BN_mod_mul_montgomery 3 "0.9.5a" "22/Jul/2000" "OpenSSL"
.UC
.if n .hy 0
.if n .na
.ds C+ C\v'-.1v'\h'-1p'\s-2+\h'-1p'+\s0\v'.1v'\h'-1p'
.de CQ          \" put $1 in typewriter font
.ft CW
'if n "\c
'if t \\&\\$1\c
'if n \\&\\$1\c
'if n \&"
\\&\\$2 \\$3 \\$4 \\$5 \\$6 \\$7
'.ft R
..
.\" @(#)ms.acc 1.5 88/02/08 SMI; from UCB 4.2
.	\" AM - accent mark definitions
.bd B 3
.	\" fudge factors for nroff and troff
.if n \{\
.	ds #H 0
.	ds #V .8m
.	ds #F .3m
.	ds #[ \f1
.	ds #] \fP
.\}
.if t \{\
.	ds #H ((1u-(\\\\n(.fu%2u))*.13m)
.	ds #V .6m
.	ds #F 0
.	ds #[ \&
.	ds #] \&
.\}
.	\" simple accents for nroff and troff
.if n \{\
.	ds ' \&
.	ds ` \&
.	ds ^ \&
.	ds , \&
.	ds ~ ~
.	ds ? ?
.	ds ! !
.	ds /
.	ds q
.\}
.if t \{\
.	ds ' \\k:\h'-(\\n(.wu*8/10-\*(#H)'\'\h"|\\n:u"
.	ds ` \\k:\h'-(\\n(.wu*8/10-\*(#H)'\`\h'|\\n:u'
.	ds ^ \\k:\h'-(\\n(.wu*10/11-\*(#H)'^\h'|\\n:u'
.	ds , \\k:\h'-(\\n(.wu*8/10)',\h'|\\n:u'
.	ds ~ \\k:\h'-(\\n(.wu-\*(#H-.1m)'~\h'|\\n:u'
.	ds ? \s-2c\h'-\w'c'u*7/10'\u\h'\*(#H'\zi\d\s+2\h'\w'c'u*8/10'
.	ds ! \s-2\(or\s+2\h'-\w'\(or'u'\v'-.8m'.\v'.8m'
.	ds / \\k:\h'-(\\n(.wu*8/10-\*(#H)'\z\(sl\h'|\\n:u'
.	ds q o\h'-\w'o'u*8/10'\s-4\v'.4m'\z\(*i\v'-.4m'\s+4\h'\w'o'u*8/10'
.\}
.	\" troff and (daisy-wheel) nroff accents
.ds : \\k:\h'-(\\n(.wu*8/10-\*(#H+.1m+\*(#F)'\v'-\*(#V'\z.\h'.2m+\*(#F'.\h'|\\n:u'\v'\*(#V'
.ds 8 \h'\*(#H'\(*b\h'-\*(#H'
.ds v \\k:\h'-(\\n(.wu*9/10-\*(#H)'\v'-\*(#V'\*(#[\s-4v\s0\v'\*(#V'\h'|\\n:u'\*(#]
.ds _ \\k:\h'-(\\n(.wu*9/10-\*(#H+(\*(#F*2/3))'\v'-.4m'\z\(hy\v'.4m'\h'|\\n:u'
.ds . \\k:\h'-(\\n(.wu*8/10)'\v'\*(#V*4/10'\z.\v'-\*(#V*4/10'\h'|\\n:u'
.ds 3 \*(#[\v'.2m'\s-2\&3\s0\v'-.2m'\*(#]
.ds o \\k:\h'-(\\n(.wu+\w'\(de'u-\*(#H)/2u'\v'-.3n'\*(#[\z\(de\v'.3n'\h'|\\n:u'\*(#]
.ds d- \h'\*(#H'\(pd\h'-\w'~'u'\v'-.25m'\f2\(hy\fP\v'.25m'\h'-\*(#H'
.ds D- D\\k:\h'-\w'D'u'\v'-.11m'\z\(hy\v'.11m'\h'|\\n:u'
.ds th \*(#[\v'.3m'\s+1I\s-1\v'-.3m'\h'-(\w'I'u*2/3)'\s-1o\s+1\*(#]
.ds Th \*(#[\s+2I\s-2\h'-\w'I'u*3/5'\v'-.3m'o\v'.3m'\*(#]
.ds ae a\h'-(\w'a'u*4/10)'e
.ds Ae A\h'-(\w'A'u*4/10)'E
.ds oe o\h'-(\w'o'u*4/10)'e
.ds Oe O\h'-(\w'O'u*4/10)'E
.	\" corrections for vroff
.if v .ds ~ \\k:\h'-(\\n(.wu*9/10-\*(#H)'\s-2\u~\d\s+2\h'|\\n:u'
.if v .ds ^ \\k:\h'-(\\n(.wu*10/11-\*(#H)'\v'-.4m'^\v'.4m'\h'|\\n:u'
.	\" for low resolution devices (crt and lpr)
.if \n(.H>23 .if \n(.V>19 \
\{\
.	ds : e
.	ds 8 ss
.	ds v \h'-1'\o'\(aa\(ga'
.	ds _ \h'-1'^
.	ds . \h'-1'.
.	ds 3 3
.	ds o a
.	ds d- d\h'-1'\(ga
.	ds D- D\h'-1'\(hy
.	ds th \o'bp'
.	ds Th \o'LP'
.	ds ae ae
.	ds Ae AE
.	ds oe oe
.	ds Oe OE
.\}
.rm #[ #] #H #V #F C
.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 "LIBRARY"
libcrypto, -lcrypto
.SH "SYNOPSIS"
.PP
.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"
These functions implement Montgomery multiplication. They are used
automatically when the \fIBN_mod_exp(3)|BN_mod_exp(3)\fR manpage 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 \fBBN_MONT_CTX\fR structure.
\fIBN_MONT_CTX_init()\fR initializes an existing uninitialized \fBBN_MONT_CTX\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 \fBN_MONT_CTX\fR \fBfrom\fR to \fBto\fR.
.PP
\fIBN_MONT_CTX_free()\fR frees the components of the \fBBN_MONT_CTX\fR, and, if
it was created by \fIBN_MONT_CTX_new()\fR, also the structure itself.
.PP
\fIBN_mod_mul_montgomery()\fR computes \fIMont\fR\|(\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 \fIMont\fR\|(\fBa\fR,R^2).
.PP
For all functions, \fBctx\fR is a previously allocated \fBBN_CTX\fR used for
temporary variables.
.PP
The \fBBN_MONT_CTX\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"
\fIBN_MONT_CTX_new()\fR returns the newly allocated \fBBN_MONT_CTX\fR, and NULL
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 the \fIERR_get_error(3)|ERR_get_error(3)\fR manpage.
.SH "SEE ALSO"
the \fIbn(3)|bn(3)\fR manpage, the \fIerr(3)|err(3)\fR manpage, the \fIBN_add(3)|BN_add(3)\fR manpage,
the \fIBN_CTX_new(3)|BN_CTX_new(3)\fR manpage
.SH "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.

.rn }` ''
.IX Title "BN_mod_mul_montgomery 3"
.IX 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"

.IX Header "NAME"

.IX Header "SYNOPSIS"

.IX Header "DESCRIPTION"

.IX Header "RETURN VALUES"

.IX Header "SEE ALSO"

.IX Header "HISTORY"