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BN_mod_exp.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>.
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