BN_is_prime_ex(3ssl)

1BN_GENERATE_PRIME(3)                OpenSSL               BN_GENERATE_PRIME(3)
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NAME

6       BN_generate_prime_ex, BN_is_prime_ex, BN_is_prime_fasttest_ex,
7       BN_GENCB_call, BN_GENCB_new, BN_GENCB_free, BN_GENCB_set_old,
8       BN_GENCB_set, BN_GENCB_get_arg, BN_generate_prime, BN_is_prime,
9       BN_is_prime_fasttest - generate primes and test for primality
10

SYNOPSIS

12        #include <openssl/bn.h>
13
14        int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *add,
15                                 const BIGNUM *rem, BN_GENCB *cb);
16
17        int BN_is_prime_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx, BN_GENCB *cb);
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19        int BN_is_prime_fasttest_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx,
20                                    int do_trial_division, BN_GENCB *cb);
21
22        int BN_GENCB_call(BN_GENCB *cb, int a, int b);
23
24        BN_GENCB *BN_GENCB_new(void);
25
26        void BN_GENCB_free(BN_GENCB *cb);
27
28        void BN_GENCB_set_old(BN_GENCB *gencb,
29                              void (*callback)(int, int, void *), void *cb_arg);
30
31        void BN_GENCB_set(BN_GENCB *gencb,
32                          int (*callback)(int, int, BN_GENCB *), void *cb_arg);
33
34        void *BN_GENCB_get_arg(BN_GENCB *cb);
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36       Deprecated:
37
38        #if OPENSSL_API_COMPAT < 0x00908000L
39        BIGNUM *BN_generate_prime(BIGNUM *ret, int num, int safe, BIGNUM *add,
40                                  BIGNUM *rem, void (*callback)(int, int, void *),
41                                  void *cb_arg);
42
43        int BN_is_prime(const BIGNUM *a, int checks,
44                        void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg);
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46        int BN_is_prime_fasttest(const BIGNUM *a, int checks,
47                                 void (*callback)(int, int, void *), BN_CTX *ctx,
48                                 void *cb_arg, int do_trial_division);
49        #endif
50

DESCRIPTION

52       BN_generate_prime_ex() generates a pseudo-random prime number of at
53       least bit length bits.  If ret is not NULL, it will be used to store
54       the number.
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56       If cb is not NULL, it is used as follows:
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58       · BN_GENCB_call(cb, 0, i) is called after generating the i-th potential
59         prime number.
60
61       · While the number is being tested for primality, BN_GENCB_call(cb, 1,
62         j) is called as described below.
63
64       · When a prime has been found, BN_GENCB_call(cb, 2, i) is called.
65
66       · The callers of BN_generate_prime_ex() may call BN_GENCB_call(cb, i,
67         j) with other values as described in their respective man pages; see
68         "SEE ALSO".
69
70       The prime may have to fulfill additional requirements for use in
71       Diffie-Hellman key exchange:
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73       If add is not NULL, the prime will fulfill the condition p % add == rem
74       (p % add == 1 if rem == NULL) in order to suit a given generator.
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76       If safe is true, it will be a safe prime (i.e. a prime p so that
77       (p-1)/2 is also prime).
78
79       The PRNG must be seeded prior to calling BN_generate_prime_ex().  The
80       prime number generation has a negligible error probability.
81
82       BN_is_prime_ex() and BN_is_prime_fasttest_ex() test if the number p is
83       prime.  The following tests are performed until one of them shows that
84       p is composite; if p passes all these tests, it is considered prime.
85
86       BN_is_prime_fasttest_ex(), when called with do_trial_division == 1,
87       first attempts trial division by a number of small primes; if no
88       divisors are found by this test and cb is not NULL, BN_GENCB_call(cb,
89       1, -1) is called.  If do_trial_division == 0, this test is skipped.
90
91       Both BN_is_prime_ex() and BN_is_prime_fasttest_ex() perform a Miller-
92       Rabin probabilistic primality test with nchecks iterations. If nchecks
93       == BN_prime_checks, a number of iterations is used that yields a false
94       positive rate of at most 2^-64 for random input.  The error rate
95       depends on the size of the prime and goes down for bigger primes.  The
96       rate is 2^-80 starting at 308 bits, 2^-112 at 852 bits, 2^-128 at 1080
97       bits, 2^-192 at 3747 bits and 2^-256 at 6394 bits.
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99       When the source of the prime is not random or not trusted, the number
100       of checks needs to be much higher to reach the same level of assurance:
101       It should equal half of the targeted security level in bits (rounded up
102       to the next integer if necessary).  For instance, to reach the 128 bit
103       security level, nchecks should be set to 64.
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105       If cb is not NULL, BN_GENCB_call(cb, 1, j) is called after the j-th
106       iteration (j = 0, 1, ...). ctx is a pre-allocated BN_CTX (to save the
107       overhead of allocating and freeing the structure in a loop), or NULL.
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109       BN_GENCB_call() calls the callback function held in the BN_GENCB
110       structure and passes the ints a and b as arguments. There are two types
111       of BN_GENCB structure that are supported: "new" style and "old" style.
112       New programs should prefer the "new" style, whilst the "old" style is
113       provided for backwards compatibility purposes.
114
115       A BN_GENCB structure should be created through a call to
116       BN_GENCB_new(), and freed through a call to BN_GENCB_free().
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118       For "new" style callbacks a BN_GENCB structure should be initialised
119       with a call to BN_GENCB_set(), where gencb is a BN_GENCB *, callback is
120       of type int (*callback)(int, int, BN_GENCB *) and cb_arg is a void *.
121       "Old" style callbacks are the same except they are initialised with a
122       call to BN_GENCB_set_old() and callback is of type void
123       (*callback)(int, int, void *).
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125       A callback is invoked through a call to BN_GENCB_call. This will check
126       the type of the callback and will invoke callback(a, b, gencb) for new
127       style callbacks or callback(a, b, cb_arg) for old style.
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129       It is possible to obtain the argument associated with a BN_GENCB
130       structure (set via a call to BN_GENCB_set or BN_GENCB_set_old) using
131       BN_GENCB_get_arg.
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133       BN_generate_prime() (deprecated) works in the same way as
134       BN_generate_prime_ex() but expects an old-style callback function
135       directly in the callback parameter, and an argument to pass to it in
136       the cb_arg. BN_is_prime() and BN_is_prime_fasttest() can similarly be
137       compared to BN_is_prime_ex() and BN_is_prime_fasttest_ex(),
138       respectively.
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RETURN VALUES

141       BN_generate_prime_ex() return 1 on success or 0 on error.
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143       BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime() and
144       BN_is_prime_fasttest() return 0 if the number is composite, 1 if it is
145       prime with an error probability of less than 0.25^nchecks, and -1 on
146       error.
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148       BN_generate_prime() returns the prime number on success, NULL
149       otherwise.
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151       BN_GENCB_new returns a pointer to a BN_GENCB structure on success, or
152       NULL otherwise.
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154       BN_GENCB_get_arg returns the argument previously associated with a
155       BN_GENCB structure.
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157       Callback functions should return 1 on success or 0 on error.
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159       The error codes can be obtained by ERR_get_error(3).
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REMOVED FUNCTIONALITY

162       As of OpenSSL 1.1.0 it is no longer possible to create a BN_GENCB
163       structure directly, as in:
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165        BN_GENCB callback;
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167       Instead applications should create a BN_GENCB structure using
168       BN_GENCB_new:
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170        BN_GENCB *callback;
171        callback = BN_GENCB_new();
172        if (!callback)
173            /* error */
174        ...
175        BN_GENCB_free(callback);
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HISTORY

182       The BN_GENCB_new(), BN_GENCB_free(), and BN_GENCB_get_arg() functions
183       were added in OpenSSL 1.1.0.
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COPYRIGHT

186       Copyright 2000-2018 The OpenSSL Project Authors. All Rights Reserved.
187
188       Licensed under the OpenSSL license (the "License").  You may not use
189       this file except in compliance with the License.  You can obtain a copy
190       in the file LICENSE in the source distribution or at
191       <https://www.openssl.org/source/license.html>.
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1951.1.1c                            2019-05-28              BN_GENERATE_PRIME(3)