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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
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 2000-2020 The OpenSSL Project Authors. All Rights Reserved.
       Licensed under the OpenSSL license (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>;.
1.1.1k                            2024-10-09                         BN_ADD(3)