Standard preamble:
========================================================================
..
.... Set up some character translations and predefined strings. \*(-- will
give an unbreakable dash, \*(PI will give pi, \*(L" will give a left
double quote, and \*(R" will give a right double quote. \*(C+ will
give a nicer C++. Capital omega is used to do unbreakable dashes and
therefore won't be available. \*(C` and \*(C' expand to `' in nroff,
nothing in troff, for use with C<>.
.tr \(*W- . ds -- \(*W- . ds PI pi . if (\n(.H=4u)&(1m=24u) .ds -- \(*W\h'-12u'\(*W\h'-12u'-\" diablo 10 pitch . if (\n(.H=4u)&(1m=20u) .ds -- \(*W\h'-12u'\(*W\h'-8u'-\" diablo 12 pitch . ds L" "" . ds R" "" . ds C` "" . ds C' "" 'br\} . ds -- \|\(em\| . ds PI \(*p . ds L" `` . ds R" '' . ds C` . ds C' 'br\}
Escape single quotes in literal strings from groff's Unicode transform.
If the F register is >0, we'll generate index entries on stderr for
titles (.TH), headers (.SH), subsections (.SS), items (.Ip), and index
entries marked with X<> in POD. Of course, you'll have to process the
output yourself in some meaningful fashion.
Avoid warning from groff about undefined register 'F'.
.. .nr rF 0 . if \nF \{\ . de IX . tm Index:\\$1\t\\n%\t"\\$2" .. . if !\nF==2 \{\ . nr % 0 . nr F 2 . \} . \} .\} .rr rF
Accent mark definitions (@(#)ms.acc 1.5 88/02/08 SMI; from UCB 4.2).
Fear. Run. Save yourself. No user-serviceable parts.
. \" fudge factors for nroff and troff . ds #H 0 . ds #V .8m . ds #F .3m . ds #[ \f1 . ds #] .\} . ds #H ((1u-(\\\\n(.fu%2u))*.13m) . ds #V .6m . ds #F 0 . ds #[ \& . ds #] \& .\} . \" simple accents for nroff and troff . ds ' \& . ds ` \& . ds ^ \& . ds , \& . ds ~ ~ . ds / .\} . ds ' \\k:\h'-(\\n(.wu*8/10-\*(#H)'\'\h"|\\n:u" . ds ` \\k:\h'-(\\n(.wu*8/10-\*(#H)'\`\h'|\\n:u' . ds ^ \\k:\h'-(\\n(.wu*10/11-\*(#H)'^\h'|\\n:u' . ds , \\k:\h'-(\\n(.wu*8/10)',\h'|\\n:u' . ds ~ \\k:\h'-(\\n(.wu-\*(#H-.1m)'~\h'|\\n:u' . ds / \\k:\h'-(\\n(.wu*8/10-\*(#H)'\z\(sl\h'|\\n:u' .\} . \" troff and (daisy-wheel) nroff accents . \" corrections for vroff . \" for low resolution devices (crt and lpr) \{\ . ds : e . ds 8 ss . ds o a . ds d- d\h'-1'\(ga . ds D- D\h'-1'\(hy . ds th \o'bp' . ds Th \o'LP' . ds ae ae . ds Ae AE .\} ========================================================================
Title "BN_GENERATE_PRIME 3"
way too many mistakes in technical documents.
Deprecated:
.Vb 4 #if OPENSSL_API_COMPAT < 0x00908000L BIGNUM *BN_generate_prime(BIGNUM *ret, int num, int safe, BIGNUM *add, BIGNUM *rem, void (*callback)(int, int, void *), void *cb_arg); \& int BN_is_prime(const BIGNUM *a, int checks, void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg); \& int BN_is_prime_fasttest(const BIGNUM *a, int checks, void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg, int do_trial_division); #endif .Ve
If ret is not \s-1NULL\s0, it will be used to store the number.
If cb is not \s-1NULL\s0, it is used as follows:
The prime may have to fulfill additional requirements for use in Diffie-Hellman key exchange:
If add is not \s-1NULL\s0, the prime will fulfill the condition p % add == rem (p % add == 1 if rem == \s-1NULL\s0) in order to suit a given generator.
If safe is true, it will be a safe prime (i.e. a prime p so that (p-1)/2 is also prime). If safe is true, and rem == \s-1NULL\s0 the condition will be p % add == 3. It is recommended that add is a multiple of 4.
The random generator must be seeded prior to calling BN_generate_prime_ex(). If the automatic seeding or reseeding of the OpenSSL \s-1CSPRNG\s0 fails due to external circumstances (see \s-1RAND\s0\|(7)), the operation will fail.
\fBBN_is_prime_ex() and BN_is_prime_fasttest_ex() test if the number p is prime. The following tests are performed until one of them shows that \fBp is composite; if p passes all these tests, it is considered prime.
\fBBN_is_prime_fasttest_ex(), when called with do_trial_division == 1, first attempts trial division by a number of small primes; if no divisors are found by this test and cb is not \s-1NULL\s0, \fBBN_GENCB_call(cb, 1, -1) is called. If do_trial_division == 0, this test is skipped.
Both BN_is_prime_ex() and BN_is_prime_fasttest_ex() perform a Miller-Rabin probabilistic primality test with nchecks iterations. If \fBnchecks == BN_prime_checks, a number of iterations is used that yields a false positive rate of at most 2^-64 for random input. The error rate depends on the size of the prime and goes down for bigger primes. The rate is 2^-80 starting at 308 bits, 2^-112 at 852 bits, 2^-128 at 1080 bits, 2^-192 at 3747 bits and 2^-256 at 6394 bits.
When the source of the prime is not random or not trusted, the number of checks needs to be much higher to reach the same level of assurance: It should equal half of the targeted security level in bits (rounded up to the next integer if necessary). For instance, to reach the 128 bit security level, nchecks should be set to 64.
If cb is not \s-1NULL\s0, BN_GENCB_call(cb, 1, j) is called after the j-th iteration (j = 0, 1, ...). ctx is a preallocated \s-1BN_CTX\s0 (to save the overhead of allocating and freeing the structure in a loop), or \s-1NULL\s0.
\fBBN_GENCB_call() calls the callback function held in the \s-1BN_GENCB\s0 structure and passes the ints a and b as arguments. There are two types of \fB\s-1BN_GENCB\s0 structure that are supported: \*(L"new\*(R" style and \*(L"old\*(R" style. New programs should prefer the \*(L"new\*(R" style, whilst the \*(L"old\*(R" style is provided for backwards compatibility purposes.
A \s-1BN_GENCB\s0 structure should be created through a call to BN_GENCB_new(), and freed through a call to BN_GENCB_free().
For \*(L"new\*(R" style callbacks a \s-1BN_GENCB\s0 structure should be initialised with a call to BN_GENCB_set(), where gencb is a \s-1BN_GENCB\s0 *, callback is of type int (*callback)(int, int, \s-1BN_GENCB\s0 *) and cb_arg is a void *. \*(L"Old\*(R" style callbacks are the same except they are initialised with a call to BN_GENCB_set_old() and callback is of type \fBvoid (*callback)(int, int, void *).
A callback is invoked through a call to BN_GENCB_call. This will check the type of the callback and will invoke callback(a, b, gencb) for new style callbacks or callback(a, b, cb_arg) for old style.
It is possible to obtain the argument associated with a \s-1BN_GENCB\s0 structure (set via a call to BN_GENCB_set or BN_GENCB_set_old) using BN_GENCB_get_arg.
\fBBN_generate_prime() (deprecated) works in the same way as \fBBN_generate_prime_ex() but expects an old-style callback function directly in the callback parameter, and an argument to pass to it in the cb_arg. BN_is_prime() and BN_is_prime_fasttest() can similarly be compared to BN_is_prime_ex() and \fBBN_is_prime_fasttest_ex(), respectively.
\fBBN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime() and \fBBN_is_prime_fasttest() return 0 if the number is composite, 1 if it is prime with an error probability of less than 0.25^nchecks, and \-1 on error.
\fBBN_generate_prime() returns the prime number on success, \s-1NULL\s0 otherwise.
BN_GENCB_new returns a pointer to a \s-1BN_GENCB\s0 structure on success, or \s-1NULL\s0 otherwise.
BN_GENCB_get_arg returns the argument previously associated with a \s-1BN_GENCB\s0 structure.
Callback functions should return 1 on success or 0 on error.
The error codes can be obtained by ERR_get_error\|(3).
.Vb 1 BN_GENCB callback; .Ve
Instead applications should create a \s-1BN_GENCB\s0 structure using BN_GENCB_new:
.Vb 6 BN_GENCB *callback; callback = BN_GENCB_new(); if (!callback) /* error */ ... BN_GENCB_free(callback); .Ve
Licensed under the OpenSSL license (the \*(L"License\*(R"). You may not use this file except in compliance with the License. You can obtain a copy in the file \s-1LICENSE\s0 in the source distribution or at <https://www.openssl.org/source/license.html>.