22

✏️ Editing: BN_sqr.3

.\" Automatically generated by Pod::Man 4.11 (Pod::Simple 3.35)
.\"
.\" Standard preamble:
.\" ========================================================================
.de Sp \" Vertical space (when we can't use .PP)
.if t .sp .5v
.if n .sp
..
.de Vb \" Begin verbatim text
.ft CW
.nf
.ne \\$1
..
.de Ve \" End verbatim text
.ft R
.fi
..
.\" Set up some character translations and predefined strings.  \*(-- will
.\" give an unbreakable dash, \*(PI will give pi, \*(L" will give a left
.\" double quote, and \*(R" will give a right double quote.  \*(C+ will
.\" give a nicer C++.  Capital omega is used to do unbreakable dashes and
.\" therefore won't be available.  \*(C` and \*(C' expand to `' in nroff,
.\" nothing in troff, for use with C<>.
.tr \(*W-
.ds C+ C\v'-.1v'\h'-1p'\s-2+\h'-1p'+\s0\v'.1v'\h'-1p'
.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" ""
.    ds C` ""
.    ds C' ""
'br\}
.el\{\
.    ds -- \|\(em\|
.    ds PI \(*p
.    ds L" ``
.    ds R" ''
.    ds C`
.    ds C'
'br\}
.\"
.\" Escape single quotes in literal strings from groff's Unicode transform.
.ie \n(.g .ds Aq \(aq
.el       .ds Aq '
.\"
.\" If the F register is >0, we'll generate index entries on stderr for
.\" titles (.TH), headers (.SH), subsections (.SS), items (.Ip), and index
.\" entries marked with X<> in POD.  Of course, you'll have to process the
.\" output yourself in some meaningful fashion.
.\"
.\" Avoid warning from groff about undefined register 'F'.
.de IX
..
.nr rF 0
.if \n(.g .if rF .nr rF 1
.if (\n(rF:(\n(.g==0)) \{\
.    if \nF \{\
.        de IX
.        tm Index:\\$1\t\\n%\t"\\$2"
..
.        if !\nF==2 \{\
.            nr % 0
.            nr F 2
.        \}
.    \}
.\}
.rr rF
.\"
.\" Accent mark definitions (@(#)ms.acc 1.5 88/02/08 SMI; from UCB 4.2).
.\" Fear.  Run.  Save yourself.  No user-serviceable parts.
.    \" 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 /
.\}
.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 / \\k:\h'-(\\n(.wu*8/10-\*(#H)'\z\(sl\h'|\\n:u'
.\}
.    \" 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 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
.    \" 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 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
.\}
.rm #[ #] #H #V #F C
.\" ========================================================================
.\"
.IX Title "BN_ADD 3"
.TH BN_ADD 3 "2023-09-11" "1.1.1w" "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_add, BN_sub, BN_mul, BN_sqr, BN_div, BN_mod, BN_nnmod, BN_mod_add, BN_mod_sub, BN_mod_mul, BN_mod_sqr, BN_mod_sqrt, BN_exp, BN_mod_exp, BN_gcd \- arithmetic operations on BIGNUMs
.SH "SYNOPSIS"
.IX Header "SYNOPSIS"
.Vb 1
\& #include <openssl/bn.h>
\&
\& int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
\&
\& int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
\&
\& int BN_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
\&
\& int BN_sqr(BIGNUM *r, BIGNUM *a, BN_CTX *ctx);
\&
\& int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *a, const BIGNUM *d,
\&            BN_CTX *ctx);
\&
\& int BN_mod(BIGNUM *rem, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
\&
\& int BN_nnmod(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
\&
\& int BN_mod_add(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
\&                BN_CTX *ctx);
\&
\& int BN_mod_sub(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
\&                BN_CTX *ctx);
\&
\& int BN_mod_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
\&                BN_CTX *ctx);
\&
\& int BN_mod_sqr(BIGNUM *r, BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
\&
\& BIGNUM *BN_mod_sqrt(BIGNUM *in, BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
\&
\& int BN_exp(BIGNUM *r, BIGNUM *a, BIGNUM *p, BN_CTX *ctx);
\&
\& int BN_mod_exp(BIGNUM *r, BIGNUM *a, const BIGNUM *p,
\&                const BIGNUM *m, BN_CTX *ctx);
\&
\& int BN_gcd(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
.Ve
.SH "DESCRIPTION"
.IX Header "DESCRIPTION"
\&\fBBN_add()\fR adds \fIa\fR and \fIb\fR and places the result in \fIr\fR (\f(CW\*(C`r=a+b\*(C'\fR).
\&\fIr\fR may be the same \fB\s-1BIGNUM\s0\fR as \fIa\fR or \fIb\fR.
.PP
\&\fBBN_sub()\fR subtracts \fIb\fR from \fIa\fR and places the result in \fIr\fR (\f(CW\*(C`r=a\-b\*(C'\fR).
\&\fIr\fR may be the same \fB\s-1BIGNUM\s0\fR as \fIa\fR or \fIb\fR.
.PP
\&\fBBN_mul()\fR multiplies \fIa\fR and \fIb\fR and places the result in \fIr\fR (\f(CW\*(C`r=a*b\*(C'\fR).
\&\fIr\fR may be the same \fB\s-1BIGNUM\s0\fR as \fIa\fR or \fIb\fR.
For multiplication by powers of 2, use \fBBN_lshift\fR\|(3).
.PP
\&\fBBN_sqr()\fR takes the square of \fIa\fR and places the result in \fIr\fR
(\f(CW\*(C`r=a^2\*(C'\fR). \fIr\fR and \fIa\fR may be the same \fB\s-1BIGNUM\s0\fR.
This function is faster than BN_mul(r,a,a).
.PP
\&\fBBN_div()\fR divides \fIa\fR by \fId\fR and places the result in \fIdv\fR and the
remainder in \fIrem\fR (\f(CW\*(C`dv=a/d, rem=a%d\*(C'\fR). Either of \fIdv\fR and \fIrem\fR may
be \fB\s-1NULL\s0\fR, in which case the respective value is not returned.
The result is rounded towards zero; thus if \fIa\fR is negative, the
remainder will be zero or negative.
For division by powers of 2, use \fBBN_rshift\fR\|(3).
.PP
\&\fBBN_mod()\fR corresponds to \fBBN_div()\fR with \fIdv\fR set to \fB\s-1NULL\s0\fR.
.PP
\&\fBBN_nnmod()\fR reduces \fIa\fR modulo \fIm\fR and places the nonnegative
remainder in \fIr\fR.
.PP
\&\fBBN_mod_add()\fR adds \fIa\fR to \fIb\fR modulo \fIm\fR and places the nonnegative
result in \fIr\fR.
.PP
\&\fBBN_mod_sub()\fR subtracts \fIb\fR from \fIa\fR modulo \fIm\fR and places the
nonnegative result in \fIr\fR.
.PP
\&\fBBN_mod_mul()\fR multiplies \fIa\fR by \fIb\fR and finds the nonnegative
remainder respective to modulus \fIm\fR (\f(CW\*(C`r=(a*b) mod m\*(C'\fR). \fIr\fR may be
the same \fB\s-1BIGNUM\s0\fR as \fIa\fR or \fIb\fR. For more efficient algorithms for
repeated computations using the same modulus, see
\&\fBBN_mod_mul_montgomery\fR\|(3) and
\&\fBBN_mod_mul_reciprocal\fR\|(3).
.PP
\&\fBBN_mod_sqr()\fR takes the square of \fIa\fR modulo \fBm\fR and places the
result in \fIr\fR.
.PP
\&\fBBN_mod_sqrt()\fR returns the modular square root of \fIa\fR such that
\&\f(CW\*(C`in^2 = a (mod p)\*(C'\fR. The modulus \fIp\fR must be a
prime, otherwise an error or an incorrect \*(L"result\*(R" will be returned.
The result is stored into \fIin\fR which can be \s-1NULL.\s0 The result will be
newly allocated in that case.
.PP
\&\fBBN_exp()\fR raises \fIa\fR to the \fIp\fR\-th power and places the result in \fIr\fR
(\f(CW\*(C`r=a^p\*(C'\fR). This function is faster than repeated applications of
\&\fBBN_mul()\fR.
.PP
\&\fBBN_mod_exp()\fR computes \fIa\fR to the \fIp\fR\-th power modulo \fIm\fR (\f(CW\*(C`r=a^p %
m\*(C'\fR). This function uses less time and space than \fBBN_exp()\fR. Do not call this
function when \fBm\fR is even and any of the parameters have the
\&\fB\s-1BN_FLG_CONSTTIME\s0\fR flag set.
.PP
\&\fBBN_gcd()\fR computes the greatest common divisor of \fIa\fR and \fIb\fR and
places the result in \fIr\fR. \fIr\fR may be the same \fB\s-1BIGNUM\s0\fR as \fIa\fR or
\&\fIb\fR.
.PP
For all functions, \fIctx\fR is a previously allocated \fB\s-1BN_CTX\s0\fR used for
temporary variables; see \fBBN_CTX_new\fR\|(3).
.PP
Unless noted otherwise, the result \fB\s-1BIGNUM\s0\fR must be different from
the arguments.
.SH "RETURN VALUES"
.IX Header "RETURN VALUES"
The \fBBN_mod_sqrt()\fR returns the result (possibly incorrect if \fIp\fR is
not a prime), or \s-1NULL.\s0
.PP
For all remaining functions, 1 is returned for success, 0 on error. The return
value should always be checked (e.g., \f(CW\*(C`if (!BN_add(r,a,b)) goto err;\*(C'\fR).
The error codes can be obtained by \fBERR_get_error\fR\|(3).
.SH "SEE ALSO"
.IX Header "SEE ALSO"
\&\fBERR_get_error\fR\|(3), \fBBN_CTX_new\fR\|(3),
\&\fBBN_add_word\fR\|(3), \fBBN_set_bit\fR\|(3)
.SH "COPYRIGHT"
.IX Header "COPYRIGHT"
Copyright 2000\-2022 The OpenSSL Project Authors. All Rights Reserved.
.PP
Licensed under the OpenSSL license (the \*(L"License\*(R").  You may not use
this file except in compliance with the License.  You can obtain a copy
in the file \s-1LICENSE\s0 in the source distribution or at
<https://www.openssl.org/source/license.html>.

MR SKB