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BN_add(3)                           OpenSSL                          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

LIBRARY
       libcrypto, -lcrypto

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, 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);

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, ctx is a previously allocated BN_CTX used for
       temporary variables; see BN_CTX_new(3).

       Unless noted otherwise, the result BIGNUM must be different from the
       arguments.

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 2000-2022 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>.



3.0.12                            2023-05-07                         BN_add(3)