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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="#REMOVED-FUNCTIONALITY">REMOVED FUNCTIONALITY</a></li>
  <li><a href="#SEE-ALSO">SEE ALSO</a></li>
  <li><a href="#HISTORY">HISTORY</a></li>
  <li><a href="#COPYRIGHT">COPYRIGHT</a></li>
</ul>

<h1 id="NAME">NAME</h1>

<p>BN_generate_prime_ex, BN_is_prime_ex, BN_is_prime_fasttest_ex, BN_GENCB_call, BN_GENCB_new, BN_GENCB_free, BN_GENCB_set_old, BN_GENCB_set, BN_GENCB_get_arg, BN_generate_prime, BN_is_prime, BN_is_prime_fasttest - generate primes and test for primality</p>

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

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

 int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *add,
                          const BIGNUM *rem, BN_GENCB *cb);

 int BN_is_prime_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx, BN_GENCB *cb);

 int BN_is_prime_fasttest_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx,
                             int do_trial_division, BN_GENCB *cb);

 int BN_GENCB_call(BN_GENCB *cb, int a, int b);

 BN_GENCB *BN_GENCB_new(void);

 void BN_GENCB_free(BN_GENCB *cb);

 void BN_GENCB_set_old(BN_GENCB *gencb,
                       void (*callback)(int, int, void *), void *cb_arg);

 void BN_GENCB_set(BN_GENCB *gencb,
                   int (*callback)(int, int, BN_GENCB *), void *cb_arg);

 void *BN_GENCB_get_arg(BN_GENCB *cb);</code></pre>

<p>Deprecated:</p>

<pre><code> #if OPENSSL_API_COMPAT &lt; 0x00908000L
 BIGNUM *BN_generate_prime(BIGNUM *ret, int num, int safe, BIGNUM *add,
                           BIGNUM *rem, void (*callback)(int, int, void *),
                           void *cb_arg);

 int BN_is_prime(const BIGNUM *a, int checks,
                 void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg);

 int BN_is_prime_fasttest(const BIGNUM *a, int checks,
                          void (*callback)(int, int, void *), BN_CTX *ctx,
                          void *cb_arg, int do_trial_division);
 #endif</code></pre>

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

<p>BN_generate_prime_ex() generates a pseudo-random prime number of at least bit length <b>bits</b>. The returned number is probably prime with a negligible error. If <b>add</b> is <b>NULL</b> the returned prime number will have exact bit length <b>bits</b> with the top most two bits set.</p>

<p>If <b>ret</b> is not <b>NULL</b>, it will be used to store the number.</p>

<p>If <b>cb</b> is not <b>NULL</b>, it is used as follows:</p>

<ul>

<li><p><b>BN_GENCB_call(cb, 0, i)</b> is called after generating the i-th potential prime number.</p>

</li>
<li><p>While the number is being tested for primality, <b>BN_GENCB_call(cb, 1, j)</b> is called as described below.</p>

</li>
<li><p>When a prime has been found, <b>BN_GENCB_call(cb, 2, i)</b> is called.</p>

</li>
<li><p>The callers of BN_generate_prime_ex() may call <b>BN_GENCB_call(cb, i, j)</b> with other values as described in their respective man pages; see <a href="#SEE-ALSO">&quot;SEE ALSO&quot;</a>.</p>

</li>
</ul>

<p>The prime may have to fulfill additional requirements for use in Diffie-Hellman key exchange:</p>

<p>If <b>add</b> is not <b>NULL</b>, the prime will fulfill the condition p % <b>add</b> == <b>rem</b> (p % <b>add</b> == 1 if <b>rem</b> == <b>NULL</b>) in order to suit a given generator.</p>

<p>If <b>safe</b> is true, it will be a safe prime (i.e. a prime p so that (p-1)/2 is also prime). If <b>safe</b> is true, and <b>rem</b> == <b>NULL</b> the condition will be p % <b>add</b> == 3. It is recommended that <b>add</b> is a multiple of 4.</p>

<p>The random generator must be seeded prior to calling BN_generate_prime_ex(). If the automatic seeding or reseeding of the OpenSSL CSPRNG fails due to external circumstances (see <a href="../man7/RAND.html">RAND(7)</a>), the operation will fail.</p>

<p>BN_is_prime_ex() and BN_is_prime_fasttest_ex() test if the number <b>p</b> is prime. The following tests are performed until one of them shows that <b>p</b> is composite; if <b>p</b> passes all these tests, it is considered prime.</p>

<p>BN_is_prime_fasttest_ex(), when called with <b>do_trial_division == 1</b>, first attempts trial division by a number of small primes; if no divisors are found by this test and <b>cb</b> is not <b>NULL</b>, <b>BN_GENCB_call(cb, 1, -1)</b> is called. If <b>do_trial_division == 0</b>, this test is skipped.</p>

<p>Both BN_is_prime_ex() and BN_is_prime_fasttest_ex() perform a Miller-Rabin probabilistic primality test with <b>nchecks</b> iterations. If <b>nchecks == BN_prime_checks</b>, a number of iterations is used that yields a false positive rate of at most 2^-64 for random input. The error rate depends on the size of the prime and goes down for bigger primes. The rate is 2^-80 starting at 308 bits, 2^-112 at 852 bits, 2^-128 at 1080 bits, 2^-192 at 3747 bits and 2^-256 at 6394 bits.</p>

<p>When the source of the prime is not random or not trusted, the number of checks needs to be much higher to reach the same level of assurance: It should equal half of the targeted security level in bits (rounded up to the next integer if necessary). For instance, to reach the 128 bit security level, <b>nchecks</b> should be set to 64.</p>

<p>If <b>cb</b> is not <b>NULL</b>, <b>BN_GENCB_call(cb, 1, j)</b> is called after the j-th iteration (j = 0, 1, ...). <b>ctx</b> is a preallocated <b>BN_CTX</b> (to save the overhead of allocating and freeing the structure in a loop), or <b>NULL</b>.</p>

<p>BN_GENCB_call() calls the callback function held in the <b>BN_GENCB</b> structure and passes the ints <b>a</b> and <b>b</b> as arguments. There are two types of <b>BN_GENCB</b> structure that are supported: &quot;new&quot; style and &quot;old&quot; style. New programs should prefer the &quot;new&quot; style, whilst the &quot;old&quot; style is provided for backwards compatibility purposes.</p>

<p>A <b>BN_GENCB</b> structure should be created through a call to BN_GENCB_new(), and freed through a call to BN_GENCB_free().</p>

<p>For &quot;new&quot; style callbacks a BN_GENCB structure should be initialised with a call to BN_GENCB_set(), where <b>gencb</b> is a <b>BN_GENCB *</b>, <b>callback</b> is of type <b>int (*callback)(int, int, BN_GENCB *)</b> and <b>cb_arg</b> is a <b>void *</b>. &quot;Old&quot; style callbacks are the same except they are initialised with a call to BN_GENCB_set_old() and <b>callback</b> is of type <b>void (*callback)(int, int, void *)</b>.</p>

<p>A callback is invoked through a call to <b>BN_GENCB_call</b>. This will check the type of the callback and will invoke <b>callback(a, b, gencb)</b> for new style callbacks or <b>callback(a, b, cb_arg)</b> for old style.</p>

<p>It is possible to obtain the argument associated with a BN_GENCB structure (set via a call to BN_GENCB_set or BN_GENCB_set_old) using BN_GENCB_get_arg.</p>

<p>BN_generate_prime() (deprecated) works in the same way as BN_generate_prime_ex() but expects an old-style callback function directly in the <b>callback</b> parameter, and an argument to pass to it in the <b>cb_arg</b>. BN_is_prime() and BN_is_prime_fasttest() can similarly be compared to BN_is_prime_ex() and BN_is_prime_fasttest_ex(), respectively.</p>

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

<p>BN_generate_prime_ex() return 1 on success or 0 on error.</p>

<p>BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime() and BN_is_prime_fasttest() return 0 if the number is composite, 1 if it is prime with an error probability of less than 0.25^<b>nchecks</b>, and -1 on error.</p>

<p>BN_generate_prime() returns the prime number on success, <b>NULL</b> otherwise.</p>

<p>BN_GENCB_new returns a pointer to a BN_GENCB structure on success, or <b>NULL</b> otherwise.</p>

<p>BN_GENCB_get_arg returns the argument previously associated with a BN_GENCB structure.</p>

<p>Callback functions should return 1 on success or 0 on error.</p>

<p>The error codes can be obtained by <a href="../man3/ERR_get_error.html">ERR_get_error(3)</a>.</p>

<h1 id="REMOVED-FUNCTIONALITY">REMOVED FUNCTIONALITY</h1>

<p>As of OpenSSL 1.1.0 it is no longer possible to create a BN_GENCB structure directly, as in:</p>

<pre><code> BN_GENCB callback;</code></pre>

<p>Instead applications should create a BN_GENCB structure using BN_GENCB_new:</p>

<pre><code> BN_GENCB *callback;
 callback = BN_GENCB_new();
 if (!callback)
     /* error */
 ...
 BN_GENCB_free(callback);</code></pre>

<h1 id="SEE-ALSO">SEE ALSO</h1>

<p><a href="../man3/DH_generate_parameters.html">DH_generate_parameters(3)</a>, <a href="../man3/DSA_generate_parameters.html">DSA_generate_parameters(3)</a>, <a href="../man3/RSA_generate_key.html">RSA_generate_key(3)</a>, <a href="../man3/ERR_get_error.html">ERR_get_error(3)</a>, <a href="../man3/RAND_bytes.html">RAND_bytes(3)</a>, <a href="../man7/RAND.html">RAND(7)</a></p>

<h1 id="HISTORY">HISTORY</h1>

<p>The BN_GENCB_new(), BN_GENCB_free(), and BN_GENCB_get_arg() functions were added in OpenSSL 1.1.0.</p>

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

<p>Copyright 2000-2020 The OpenSSL Project Authors. All Rights Reserved.</p>

<p>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>.</p>


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