NAME
SYNOPSIS
DESCRIPTION
RETURN VALUES
HISTORY

## NAME

 BN_add, BN_sub, BN_mul, BN_div, BN_sqr, BN_mod, BN_mod_mul, BN_exp, BN_mod_exp, BN_gcd − arithmetic operations on BIGNUMs

## SYNOPSIS

 ``` #include ``` ``` 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_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *a, const BIGNUM *d, BN_CTX *ctx); ``` ``` int BN_sqr(BIGNUM *r, BIGNUM *a, BN_CTX *ctx); ``` ``` int BN_mod(BIGNUM *rem, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx); ``` ``` int BN_mod_mul(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m, 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). 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_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. For division by powers of 2, use BN_rshift(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_mod() find the remainder of a divided by m and places it in rem (rem=a%m). BN_mod_mul() multiplies a by b and finds the remainder when divided by m (r=(a*b)%m). r may be the same BIGNUM as a or b. For a more efficient algorithm, see BN_mod_mul_montgomery(3); for repeated computations using the same modulus, see BN_mod_mul_reciprocal(3). 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(). 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

 For all 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).