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 non-negative remainder in r.

       BN_mod_add() adds a to b modulo m and places the non-negative result in r.

       BN_mod_sub() subtracts b from a modulo m and places the non-negative result in r.

       BN_mod_mul() multiplies a by b and finds the non-negative 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 2000-2018 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>.