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1 | =pod | ||
2 | |||
3 | =head1 NAME | ||
4 | |||
5 | BN_generate_prime, BN_is_prime, BN_is_prime_fasttest - generate primes and test for primality | ||
6 | |||
7 | =head1 SYNOPSIS | ||
8 | |||
9 | #include <openssl/bn.h> | ||
10 | |||
11 | BIGNUM *BN_generate_prime(BIGNUM *ret, int num, int safe, BIGNUM *add, | ||
12 | BIGNUM *rem, void (*callback)(int, int, void *), void *cb_arg); | ||
13 | |||
14 | int BN_is_prime(const BIGNUM *a, int checks, void (*callback)(int, int, | ||
15 | void *), BN_CTX *ctx, void *cb_arg); | ||
16 | |||
17 | int BN_is_prime_fasttest(const BIGNUM *a, int checks, | ||
18 | void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg, | ||
19 | int do_trial_division); | ||
20 | |||
21 | =head1 DESCRIPTION | ||
22 | |||
23 | BN_generate_prime() generates a pseudo-random prime number of B<num> | ||
24 | bits. | ||
25 | If B<ret> is not B<NULL>, it will be used to store the number. | ||
26 | |||
27 | If B<callback> is not B<NULL>, it is called as follows: | ||
28 | |||
29 | =over 4 | ||
30 | |||
31 | =item * | ||
32 | |||
33 | B<callback(0, i, cb_arg)> is called after generating the i-th | ||
34 | potential prime number. | ||
35 | |||
36 | =item * | ||
37 | |||
38 | While the number is being tested for primality, B<callback(1, j, | ||
39 | cb_arg)> is called as described below. | ||
40 | |||
41 | =item * | ||
42 | |||
43 | When a prime has been found, B<callback(2, i, cb_arg)> is called. | ||
44 | |||
45 | =back | ||
46 | |||
47 | The prime may have to fulfill additional requirements for use in | ||
48 | Diffie-Hellman key exchange: | ||
49 | |||
50 | If B<add> is not B<NULL>, the prime will fulfill the condition p % B<add> | ||
51 | == B<rem> (p % B<add> == 1 if B<rem> == B<NULL>) in order to suit a given | ||
52 | generator. | ||
53 | |||
54 | If B<safe> is true, it will be a safe prime (i.e. a prime p so | ||
55 | that (p-1)/2 is also prime). | ||
56 | |||
57 | The PRNG must be seeded prior to calling BN_generate_prime(). | ||
58 | The prime number generation has a negligible error probability. | ||
59 | |||
60 | BN_is_prime() and BN_is_prime_fasttest() test if the number B<a> is | ||
61 | prime. The following tests are performed until one of them shows that | ||
62 | B<a> is composite; if B<a> passes all these tests, it is considered | ||
63 | prime. | ||
64 | |||
65 | BN_is_prime_fasttest(), when called with B<do_trial_division == 1>, | ||
66 | first attempts trial division by a number of small primes; | ||
67 | if no divisors are found by this test and B<callback> is not B<NULL>, | ||
68 | B<callback(1, -1, cb_arg)> is called. | ||
69 | If B<do_trial_division == 0>, this test is skipped. | ||
70 | |||
71 | Both BN_is_prime() and BN_is_prime_fasttest() perform a Miller-Rabin | ||
72 | probabilistic primality test with B<checks> iterations. If | ||
73 | B<checks == BN_prime_check>, a number of iterations is used that | ||
74 | yields a false positive rate of at most 2^-80 for random input. | ||
75 | |||
76 | If B<callback> is not B<NULL>, B<callback(1, j, cb_arg)> is called | ||
77 | after the j-th iteration (j = 0, 1, ...). B<ctx> is a | ||
78 | pre-allocated B<BN_CTX> (to save the overhead of allocating and | ||
79 | freeing the structure in a loop), or B<NULL>. | ||
80 | |||
81 | =head1 RETURN VALUES | ||
82 | |||
83 | BN_generate_prime() returns the prime number on success, B<NULL> otherwise. | ||
84 | |||
85 | BN_is_prime() returns 0 if the number is composite, 1 if it is | ||
86 | prime with an error probability of less than 0.25^B<checks>, and | ||
87 | -1 on error. | ||
88 | |||
89 | The error codes can be obtained by L<ERR_get_error(3)|ERR_get_error(3)>. | ||
90 | |||
91 | =head1 SEE ALSO | ||
92 | |||
93 | L<bn(3)|bn(3)>, L<err(3)|err(3)>, L<rand(3)|rand(3)> | ||
94 | |||
95 | =head1 HISTORY | ||
96 | |||
97 | The B<cb_arg> arguments to BN_generate_prime() and to BN_is_prime() | ||
98 | were added in SSLeay 0.9.0. The B<ret> argument to BN_generate_prime() | ||
99 | was added in SSLeay 0.9.1. | ||
100 | BN_is_prime_fasttest() was added in OpenSSL 0.9.5. | ||
101 | |||
102 | =cut | ||