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<ul id="index">
 <li><a href="#NAME">NAME</a></li>
 <li><a href="#SYNOPSIS">SYNOPSIS</a></li>
 <li><a href="#DESCRIPTION">DESCRIPTION</a></li>
 <li><a href="#RETURN-VALUES">RETURN VALUES</a></li>
 <li><a href="#SEE-ALSO">SEE ALSO</a></li>
 <li><a href="#COPYRIGHT">COPYRIGHT</a></li>
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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

<h1 id="SYNOPSIS">SYNOPSIS</h1>

<pre><code> #include &lt;openssl/bn.h&gt;

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);</code></pre>

<h1 id="DESCRIPTION">DESCRIPTION</h1>

BN_add() adds a and b and places the result in r (<code>r=a+b</code>). r may be the same BIGNUM as a or b.

BN_sub() subtracts b from a and places the result in r (<code>r=a-b</code>). r may be the same BIGNUM as a or b.

BN_mul() multiplies a and b and places the result in r (<code>r=a*b</code>). r may be the same BIGNUM as a or b. For multiplication by powers of 2, use <a href="../man3/BN_lshift.html">BN_lshift(3)</a>.

BN_sqr() takes the square of a and places the result in r (<code>r=a^2</code>). 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 (<code>dv=a/d, rem=a%d</code>). 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 (<code>r=(a*b) mod m</code>). r may be the same BIGNUM as a or b. For more efficient algorithms for repeated computations using the same modulus, see <a href="../man3/BN_mod_mul_montgomery.html">BN_mod_mul_montgomery(3)</a> and <a href="../man3/BN_mod_mul_reciprocal.html">BN_mod_mul_reciprocal(3)</a>.

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 <code>in^2 = a (mod p)</code>. The modulus p must be a prime, otherwise an error or an incorrect &quot;result&quot; 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 (<code>r=a^p</code>). This function is faster than repeated applications of BN_mul().

BN_mod_exp() computes a to the p-th power modulo m (<code>r=a^p % m</code>). 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 <a href="../man3/BN_CTX_new.html">BN_CTX_new(3)</a>.

Unless noted otherwise, the result BIGNUM must be different from the arguments.

<h1 id="RETURN-VALUES">RETURN VALUES</h1>

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., <code>if (!BN_add(r,a,b)) goto err;</code>). The error codes can be obtained by <a href="../man3/ERR_get_error.html">ERR_get_error(3)</a>.

<a href="../man3/ERR_get_error.html">ERR_get_error(3)</a>, <a href="../man3/BN_CTX_new.html">BN_CTX_new(3)</a>, <a href="../man3/BN_add_word.html">BN_add_word(3)</a>, <a href="../man3/BN_set_bit.html">BN_set_bit(3)</a>

<h1 id="COPYRIGHT">COPYRIGHT</h1>

Licensed under the OpenSSL license (the &quot;License&quot;). 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 <a href="https://www.openssl.org/source/license.html">https://www.openssl.org/source/license.html</a>.

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