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.\" ========================================================================
.\"
.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"
\&\fIBN_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
\&\fIBN_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
\&\fIBN_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 \fIBN_lshift\fR\|(3).
.PP
\&\fIBN_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
\&\fIBN_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 \fIBN_rshift\fR\|(3).
.PP
\&\fIBN_mod()\fR corresponds to \fIBN_div()\fR with \fIdv\fR set to \fB\s-1NULL\s0\fR.
.PP
\&\fIBN_nnmod()\fR reduces \fIa\fR modulo \fIm\fR and places the nonnegative
remainder in \fIr\fR.
.PP
\&\fIBN_mod_add()\fR adds \fIa\fR to \fIb\fR modulo \fIm\fR and places the nonnegative
result in \fIr\fR.
.PP
\&\fIBN_mod_sub()\fR subtracts \fIb\fR from \fIa\fR modulo \fIm\fR and places the
nonnegative result in \fIr\fR.
.PP
\&\fIBN_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
\&\fIBN_mod_mul_montgomery\fR\|(3) and
\&\fIBN_mod_mul_reciprocal\fR\|(3).
.PP
\&\fIBN_mod_sqr()\fR takes the square of \fIa\fR modulo \fBm\fR and places the
result in \fIr\fR.
.PP
\&\fIBN_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
\&\fIBN_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
\&\fIBN_mul()\fR.
.PP
\&\fIBN_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 \fIBN_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
\&\fIBN_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 \fIBN_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 \fIBN_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 \fIERR_get_error\fR\|(3).
.SH "SEE ALSO"
.IX Header "SEE ALSO"
\&\fIERR_get_error\fR\|(3), \fIBN_CTX_new\fR\|(3),
\&\fIBN_add_word\fR\|(3), \fIBN_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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