5 BN_generate_prime_ex, BN_is_prime_ex, BN_is_prime_fasttest_ex, BN_GENCB_call,
6 BN_GENCB_set_old, BN_GENCB_set, BN_generate_prime, BN_is_prime,
7 BN_is_prime_fasttest - generate primes and test for primality
11 #include <openssl/bn.h>
13 int BN_generate_prime_ex(BIGNUM *ret,int bits,int safe, const BIGNUM *add,
14 const BIGNUM *rem, BN_GENCB *cb);
16 int BN_is_prime_ex(const BIGNUM *p,int nchecks, BN_CTX *ctx, BN_GENCB *cb);
18 int BN_is_prime_fasttest_ex(const BIGNUM *p,int nchecks, BN_CTX *ctx,
19 int do_trial_division, BN_GENCB *cb);
21 int BN_GENCB_call(BN_GENCB *cb, int a, int b);
23 #define BN_GENCB_set_old(gencb, callback, cb_arg) ...
25 #define BN_GENCB_set(gencb, callback, cb_arg) ...
30 BIGNUM *BN_generate_prime(BIGNUM *ret, int num, int safe, BIGNUM *add,
31 BIGNUM *rem, void (*callback)(int, int, void *), void *cb_arg);
33 int BN_is_prime(const BIGNUM *a, int checks, void (*callback)(int, int,
34 void *), BN_CTX *ctx, void *cb_arg);
36 int BN_is_prime_fasttest(const BIGNUM *a, int checks,
37 void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg,
38 int do_trial_division);
42 BN_generate_prime_ex() generates a pseudo-random prime number of
44 If B<ret> is not B<NULL>, it will be used to store the number.
46 If B<cb> is not B<NULL>, it is used as follows:
52 B<BN_GENCB_call(cb, 0, i)> is called after generating the i-th
53 potential prime number.
57 While the number is being tested for primality,
58 B<BN_GENCB_call(cb, 1, j)> is called as described below.
62 When a prime has been found, B<BN_GENCB_call(cb, 2, i)> is called.
66 The prime may have to fulfill additional requirements for use in
67 Diffie-Hellman key exchange:
69 If B<add> is not B<NULL>, the prime will fulfill the condition p % B<add>
70 == B<rem> (p % B<add> == 1 if B<rem> == B<NULL>) in order to suit a given
73 If B<safe> is true, it will be a safe prime (i.e. a prime p so
74 that (p-1)/2 is also prime).
76 The PRNG must be seeded prior to calling BN_generate_prime_ex().
77 The prime number generation has a negligible error probability.
79 BN_is_prime_ex() and BN_is_prime_fasttest_ex() test if the number B<p> is
80 prime. The following tests are performed until one of them shows that
81 B<p> is composite; if B<p> passes all these tests, it is considered
84 BN_is_prime_fasttest_ex(), when called with B<do_trial_division == 1>,
85 first attempts trial division by a number of small primes;
86 if no divisors are found by this test and B<cb> is not B<NULL>,
87 B<BN_GENCB_call(cb, 1, -1)> is called.
88 If B<do_trial_division == 0>, this test is skipped.
90 Both BN_is_prime_ex() and BN_is_prime_fasttest_ex() perform a Miller-Rabin
91 probabilistic primality test with B<nchecks> iterations. If
92 B<nchecks == BN_prime_checks>, a number of iterations is used that
93 yields a false positive rate of at most 2^-80 for random input.
95 If B<cb> is not B<NULL>, B<BN_GENCB_call(cb, 1, j)> is called
96 after the j-th iteration (j = 0, 1, ...). B<ctx> is a
97 pre-allocated B<BN_CTX> (to save the overhead of allocating and
98 freeing the structure in a loop), or B<NULL>.
100 BN_GENCB_call calls the callback function held in the B<BN_GENCB> structure
101 and passes the ints B<a> and B<b> as arguments. There are two types of
102 B<BN_GENCB> structure that are supported: "new" style and "old" style. New
103 programs should prefer the "new" style, whilst the "old" style is provided
104 for backwards compatibility purposes.
106 For "new" style callbacks a BN_GENCB structure should be initialised with a
107 call to BN_GENCB_set, where B<gencb> is a B<BN_GENCB *>, B<callback> is of
108 type B<int (*callback)(int, int, BN_GENCB *)> and B<cb_arg> is a B<void *>.
109 "Old" style callbacks are the same except they are initialised with a call
110 to BN_GENCB_set_old and B<callback> is of type
111 B<void (*callback)(int, int, void *)>.
113 A callback is invoked through a call to B<BN_GENCB_call>. This will check
114 the type of the callback and will invoke B<callback(a, b, gencb)> for new
115 style callbacks or B<callback(a, b, cb_arg)> for old style.
117 BN_generate_prime (deprecated) works in the same way as
118 BN_generate_prime_ex but expects an old style callback function
119 directly in the B<callback> parameter, and an argument to pass to it in
120 the B<cb_arg>. Similarly BN_is_prime and BN_is_prime_fasttest are
121 deprecated and can be compared to BN_is_prime_ex and
122 BN_is_prime_fasttest_ex respectively.
126 BN_generate_prime_ex() return 1 on success or 0 on error.
128 BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime() and
129 BN_is_prime_fasttest() return 0 if the number is composite, 1 if it is
130 prime with an error probability of less than 0.25^B<nchecks>, and
133 BN_generate_prime() returns the prime number on success, B<NULL> otherwise.
135 Callback functions should return 1 on success or 0 on error.
137 The error codes can be obtained by L<ERR_get_error(3)|ERR_get_error(3)>.
141 L<bn(3)|bn(3)>, L<ERR_get_error(3)|ERR_get_error(3)>, L<rand(3)|rand(3)>
145 The B<cb_arg> arguments to BN_generate_prime() and to BN_is_prime()
146 were added in SSLeay 0.9.0. The B<ret> argument to BN_generate_prime()
147 was added in SSLeay 0.9.1.
148 BN_is_prime_fasttest() was added in OpenSSL 0.9.5.