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^-64 for random input.
94 The error rate depends on the size of the prime and goes down for bigger primes.
95 The rate is 2^-80 starting at 308 bits, 2^-112 at 852 bits, 2^-128 at 1080 bits,
96 2^-192 at 3747 bits and 2^-256 at 6394 bits.
98 When the source of the prime is not random or not trusted, the number
99 of checks needs to be much higher to reach the same level of assurance:
100 It should equal half of the targeted security level in bits (rounded up to the
101 next integer if necessary).
102 For instance, to reach the 128 bit security level, B<nchecks> should be set to
105 If B<cb> is not B<NULL>, B<BN_GENCB_call(cb, 1, j)> is called
106 after the j-th iteration (j = 0, 1, ...). B<ctx> is a
107 pre-allocated B<BN_CTX> (to save the overhead of allocating and
108 freeing the structure in a loop), or B<NULL>.
110 BN_GENCB_call calls the callback function held in the B<BN_GENCB> structure
111 and passes the ints B<a> and B<b> as arguments. There are two types of
112 B<BN_GENCB> structure that are supported: "new" style and "old" style. New
113 programs should prefer the "new" style, whilst the "old" style is provided
114 for backwards compatibility purposes.
116 For "new" style callbacks a BN_GENCB structure should be initialised with a
117 call to BN_GENCB_set, where B<gencb> is a B<BN_GENCB *>, B<callback> is of
118 type B<int (*callback)(int, int, BN_GENCB *)> and B<cb_arg> is a B<void *>.
119 "Old" style callbacks are the same except they are initialised with a call
120 to BN_GENCB_set_old and B<callback> is of type
121 B<void (*callback)(int, int, void *)>.
123 A callback is invoked through a call to B<BN_GENCB_call>. This will check
124 the type of the callback and will invoke B<callback(a, b, gencb)> for new
125 style callbacks or B<callback(a, b, cb_arg)> for old style.
127 BN_generate_prime (deprecated) works in the same way as
128 BN_generate_prime_ex but expects an old style callback function
129 directly in the B<callback> parameter, and an argument to pass to it in
130 the B<cb_arg>. Similarly BN_is_prime and BN_is_prime_fasttest are
131 deprecated and can be compared to BN_is_prime_ex and
132 BN_is_prime_fasttest_ex respectively.
136 BN_generate_prime_ex() return 1 on success or 0 on error.
138 BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime() and
139 BN_is_prime_fasttest() return 0 if the number is composite, 1 if it is
140 prime with an error probability of less than 0.25^B<nchecks>, and
143 BN_generate_prime() returns the prime number on success, B<NULL> otherwise.
145 Callback functions should return 1 on success or 0 on error.
147 The error codes can be obtained by L<ERR_get_error(3)|ERR_get_error(3)>.
151 L<bn(3)|bn(3)>, L<ERR_get_error(3)|ERR_get_error(3)>, L<rand(3)|rand(3)>
155 The B<cb_arg> arguments to BN_generate_prime() and to BN_is_prime()
156 were added in SSLeay 0.9.0. The B<ret> argument to BN_generate_prime()
157 was added in SSLeay 0.9.1.
158 BN_is_prime_fasttest() was added in OpenSSL 0.9.5.