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257 lines
9.1 KiB
Plaintext
257 lines
9.1 KiB
Plaintext
=pod
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=head1 NAME
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BN_generate_prime_ex2, BN_generate_prime_ex, BN_is_prime_ex, BN_check_prime,
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BN_is_prime_fasttest_ex, BN_GENCB_call, BN_GENCB_new, BN_GENCB_free,
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BN_GENCB_set_old, BN_GENCB_set, BN_GENCB_get_arg, BN_generate_prime,
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BN_is_prime, BN_is_prime_fasttest - generate primes and test for primality
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=head1 SYNOPSIS
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#include <openssl/bn.h>
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int BN_generate_prime_ex2(BIGNUM *ret, int bits, int safe,
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const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb,
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BN_CTX *ctx);
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int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *add,
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const BIGNUM *rem, BN_GENCB *cb);
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int BN_check_prime(const BIGNUM *p, BN_CTX *ctx, BN_GENCB *cb);
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int BN_GENCB_call(BN_GENCB *cb, int a, int b);
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BN_GENCB *BN_GENCB_new(void);
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void BN_GENCB_free(BN_GENCB *cb);
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void BN_GENCB_set_old(BN_GENCB *gencb,
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void (*callback)(int, int, void *), void *cb_arg);
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void BN_GENCB_set(BN_GENCB *gencb,
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int (*callback)(int, int, BN_GENCB *), void *cb_arg);
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void *BN_GENCB_get_arg(BN_GENCB *cb);
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The following functions have been deprecated since OpenSSL 0.9.8, and can be
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hidden entirely by defining B<OPENSSL_API_COMPAT> with a suitable version value,
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see L<openssl_user_macros(7)>:
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BIGNUM *BN_generate_prime(BIGNUM *ret, int num, int safe, BIGNUM *add,
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BIGNUM *rem, void (*callback)(int, int, void *),
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void *cb_arg);
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int BN_is_prime(const BIGNUM *p, int nchecks,
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void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg);
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int BN_is_prime_fasttest(const BIGNUM *p, int nchecks,
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void (*callback)(int, int, void *), BN_CTX *ctx,
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void *cb_arg, int do_trial_division);
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The following functions have been deprecated since OpenSSL 3.0, and can be
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hidden entirely by defining B<OPENSSL_API_COMPAT> with a suitable version value,
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see L<openssl_user_macros(7)>:
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int BN_is_prime_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx, BN_GENCB *cb);
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int BN_is_prime_fasttest_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx,
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int do_trial_division, BN_GENCB *cb);
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=head1 DESCRIPTION
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BN_generate_prime_ex2() generates a pseudo-random prime number of
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at least bit length B<bits> using the BN_CTX provided in B<ctx>. The value of
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B<ctx> must not be NULL.
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The returned number is probably prime with a negligible error.
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The maximum error rate is 2^-128.
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It's 2^-287 for a 512 bit prime, 2^-435 for a 1024 bit prime,
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2^-648 for a 2048 bit prime, and lower than 2^-882 for primes larger
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than 2048 bit.
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If B<add> is B<NULL> the returned prime number will have exact bit
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length B<bits> with the top most two bits set.
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If B<ret> is not B<NULL>, it will be used to store the number.
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If B<cb> is not B<NULL>, it is used as follows:
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=over 2
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=item *
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B<BN_GENCB_call(cb, 0, i)> is called after generating the i-th
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potential prime number.
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=item *
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While the number is being tested for primality,
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B<BN_GENCB_call(cb, 1, j)> is called as described below.
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=item *
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When a prime has been found, B<BN_GENCB_call(cb, 2, i)> is called.
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=item *
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The callers of BN_generate_prime_ex() may call B<BN_GENCB_call(cb, i, j)> with
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other values as described in their respective man pages; see L</SEE ALSO>.
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=back
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The prime may have to fulfill additional requirements for use in
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Diffie-Hellman key exchange:
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If B<add> is not B<NULL>, the prime will fulfill the condition p % B<add>
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== B<rem> (p % B<add> == 1 if B<rem> == B<NULL>) in order to suit a given
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generator.
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If B<safe> is true, it will be a safe prime (i.e. a prime p so
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that (p-1)/2 is also prime). If B<safe> is true, and B<rem> == B<NULL>
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the condition will be p % B<add> == 3.
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It is recommended that B<add> is a multiple of 4.
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The random generator must be seeded prior to calling BN_generate_prime_ex().
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If the automatic seeding or reseeding of the OpenSSL CSPRNG fails due to
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external circumstances (see L<RAND(7)>), the operation will fail.
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The random number generator configured for the OSSL_LIB_CTX associated with
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B<ctx> will be used.
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BN_generate_prime_ex() is the same as BN_generate_prime_ex2() except that no
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B<ctx> parameter is passed.
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In this case the random number generator associated with the default OSSL_LIB_CTX
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will be used.
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BN_check_prime(), BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime()
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and BN_is_prime_fasttest() test if the number B<p> is prime.
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The functions tests until one of the tests shows that B<p> is composite,
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or all the tests passed.
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If B<p> passes all these tests, it is considered a probable prime.
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The test performed on B<p> are trial division by a number of small primes
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and rounds of the of the Miller-Rabin probabilistic primality test.
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The functions do at least 64 rounds of the Miller-Rabin test giving a maximum
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false positive rate of 2^-128.
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If the size of B<p> is more than 2048 bits, they do at least 128 rounds
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giving a maximum false positive rate of 2^-256.
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If B<nchecks> is larger than the minimum above (64 or 128), B<nchecks>
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rounds of the Miller-Rabin test will be done.
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If B<do_trial_division> set to B<0>, the trial division will be skipped.
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BN_is_prime_ex() and BN_is_prime() always skip the trial division.
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BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime()
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and BN_is_prime_fasttest() are deprecated.
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BN_is_prime_fasttest() and BN_is_prime() behave just like
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BN_is_prime_fasttest_ex() and BN_is_prime_ex() respectively, but with the old
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style call back.
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B<ctx> is a preallocated B<BN_CTX> (to save the overhead of allocating and
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freeing the structure in a loop), or B<NULL>.
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If the trial division is done, and no divisors are found and B<cb>
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is not B<NULL>, B<BN_GENCB_call(cb, 1, -1)> is called.
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After each round of the Miller-Rabin probabilistic primality test,
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if B<cb> is not B<NULL>, B<BN_GENCB_call(cb, 1, j)> is called
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with B<j> the iteration (j = 0, 1, ...).
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BN_GENCB_call() calls the callback function held in the B<BN_GENCB> structure
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and passes the ints B<a> and B<b> as arguments. There are two types of
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B<BN_GENCB> structure that are supported: "new" style and "old" style. New
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programs should prefer the "new" style, whilst the "old" style is provided
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for backwards compatibility purposes.
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A B<BN_GENCB> structure should be created through a call to BN_GENCB_new(),
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and freed through a call to BN_GENCB_free(). If the argument is NULL,
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nothing is done.
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For "new" style callbacks a BN_GENCB structure should be initialised with a
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call to BN_GENCB_set(), where B<gencb> is a B<BN_GENCB *>, B<callback> is of
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type B<int (*callback)(int, int, BN_GENCB *)> and B<cb_arg> is a B<void *>.
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"Old" style callbacks are the same except they are initialised with a call
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to BN_GENCB_set_old() and B<callback> is of type
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B<void (*callback)(int, int, void *)>.
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A callback is invoked through a call to B<BN_GENCB_call>. This will check
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the type of the callback and will invoke B<callback(a, b, gencb)> for new
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style callbacks or B<callback(a, b, cb_arg)> for old style.
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It is possible to obtain the argument associated with a BN_GENCB structure
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(set via a call to BN_GENCB_set or BN_GENCB_set_old) using BN_GENCB_get_arg.
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BN_generate_prime() (deprecated) works in the same way as
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BN_generate_prime_ex() but expects an old-style callback function
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directly in the B<callback> parameter, and an argument to pass to it in
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the B<cb_arg>. BN_is_prime() and BN_is_prime_fasttest()
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can similarly be compared to BN_is_prime_ex() and
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BN_is_prime_fasttest_ex(), respectively.
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=head1 RETURN VALUES
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BN_generate_prime_ex() return 1 on success or 0 on error.
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BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime(),
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BN_is_prime_fasttest() and BN_check_prime return 0 if the number is composite,
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1 if it is prime with an error probability of less than 0.25^B<nchecks>, and
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-1 on error.
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BN_generate_prime() returns the prime number on success, B<NULL> otherwise.
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BN_GENCB_new returns a pointer to a BN_GENCB structure on success, or B<NULL>
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otherwise.
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BN_GENCB_get_arg returns the argument previously associated with a BN_GENCB
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structure.
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Callback functions should return 1 on success or 0 on error.
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The error codes can be obtained by L<ERR_get_error(3)>.
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=head1 REMOVED FUNCTIONALITY
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As of OpenSSL 1.1.0 it is no longer possible to create a BN_GENCB structure
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directly, as in:
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BN_GENCB callback;
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Instead applications should create a BN_GENCB structure using BN_GENCB_new:
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BN_GENCB *callback;
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callback = BN_GENCB_new();
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if (!callback)
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/* error */
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...
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BN_GENCB_free(callback);
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=head1 SEE ALSO
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L<DH_generate_parameters(3)>, L<DSA_generate_parameters(3)>,
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L<RSA_generate_key(3)>, L<ERR_get_error(3)>, L<RAND_bytes(3)>,
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L<RAND(7)>
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=head1 HISTORY
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The BN_is_prime_ex() and BN_is_prime_fasttest_ex() functions were
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deprecated in OpenSSL 3.0.
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The BN_GENCB_new(), BN_GENCB_free(),
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and BN_GENCB_get_arg() functions were added in OpenSSL 1.1.0.
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BN_check_prime() was added in OpenSSL 3.0.
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=head1 COPYRIGHT
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Copyright 2000-2024 The OpenSSL Project Authors. All Rights Reserved.
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Licensed under the Apache License 2.0 (the "License"). You may not use
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this file except in compliance with the License. You can obtain a copy
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in the file LICENSE in the source distribution or at
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L<https://www.openssl.org/source/license.html>.
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=cut
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