- NAME
- SYNOPSIS
- DESCRIPTION
- RETURN VALUES
- SEE ALSO
- COPYRIGHT

# 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 2000-2022 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.