BN_ADD(3)

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>.