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.

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 2000-2022 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>.