BN_ADD(3SSL) OpenSSL BN_ADD(3SSL)
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
SYNOPSIS
#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, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
int BN_sqr(BIGNUM *r, const 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, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
BN_CTX *ctx);
int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
BN_CTX *ctx);
int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
BN_CTX *ctx);
int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
const BIGNUM *m, BN_CTX *ctx);
int BN_gcd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
DESCRIPTION
BN_add() adds a and b and places the result in r ("r=a+b"). r may be
the same BIGNUM as a or b.
BN_sub() subtracts b from a and places the result in r ("r=a-b"). r may
be the same BIGNUM as a or b.
BN_mul() multiplies a and b and places the result in r ("r=a*b"). r may
be the same BIGNUM as a or b. For multiplication by powers of 2, use
BN_lshift(3).
BN_sqr() takes the square of a and places the result in r ("r=a^2"). r
and a may be the same BIGNUM. This function is faster than
BN_mul(r,a,a).
BN_div() divides a by d and places the result in dv and the remainder in
rem ("dv=a/d, rem=a%d"). Either of dv and rem may be NULL, in which case
the respective value is not returned. The result is rounded towards
zero; thus if a is negative, the remainder will be zero or negative.
For division by powers of 2, use BN_rshift(3).
BN_mod() corresponds to BN_div() with dv set to NULL.
BN_nnmod() reduces a modulo m and places the nonnegative remainder in r.
BN_mod_add() adds a to b modulo m and places the nonnegative result in
r.
BN_mod_sub() subtracts b from a modulo m and places the nonnegative
result in r.
BN_mod_mul() multiplies a by b and finds the nonnegative remainder
respective to modulus m ("r=(a*b) mod m"). r may be the same BIGNUM as a
or b. For more efficient algorithms for repeated computations using the
same modulus, see BN_mod_mul_montgomery(3) and BN_mod_mul_reciprocal(3).
BN_mod_sqr() takes the square of a modulo m and places the result in r.
BN_mod_sqrt() returns the modular square root of a such that "in^2 = a
(mod p)". The modulus p must be a prime, otherwise an error or an
incorrect "result" will be returned. The result is stored into in which
can be NULL. The result will be newly allocated in that case.
BN_exp() raises a to the p-th power and places the result in r
("r=a^p"). This function is faster than repeated applications of
BN_mul().
BN_mod_exp() computes a to the p-th power modulo m ("r=a^p % m"). This
function uses less time and space than BN_exp(). Do not call this
function when m is even and any of the parameters have the
BN_FLG_CONSTTIME flag set.
BN_gcd() computes the greatest common divisor of a and b and places the
result in r. r may be the same BIGNUM as a or b.
For all functions that take a ctx parameter, it must be a previously
allocated BN_CTX used for temporary variables; see BN_CTX_new(3).
Unless stated otherwise in the documentation for a specific function,
the ctx parameter must not be NULL.
Unless noted otherwise, the result BIGNUM must be different from the
arguments.
NOTES
For modular operations such as BN_nnmod() or BN_mod_exp() it is an error
to use the same BIGNUM object for the modulus as for the output.
RETURN VALUES
The BN_mod_sqrt() returns the result (possibly incorrect if p is not a
prime), or NULL.
For all remaining functions, 1 is returned for success, 0 on error. The
return value should always be checked (e.g., "if (!BN_add(r,a,b)) goto
err;"). The error codes can be obtained by ERR_get_error(3).
SEE ALSO
ERR_get_error(3), BN_CTX_new(3), BN_add_word(3), BN_set_bit(3)
COPYRIGHT
Copyright 2000-2026 The OpenSSL Project Authors. All Rights Reserved.
Licensed under the Apache License 2.0 (the "License"). You may not use
this file except in compliance with the License. You can obtain a copy
in the file LICENSE in the source distribution or at
<https://www.openssl.org/source/license.html>.
3.5.7 2026-06-09 BN_ADD(3SSL)
Generated by dwww version 1.16 on Sat Oct 3 06:49:07 CEST 2026.