296 lines
7.7 KiB
Groff
296 lines
7.7 KiB
Groff
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'''
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'''
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''' Set up \*(-- to give an unbreakable dash;
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''' string Tr holds user defined translation string.
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''' Bell System Logo is used as a dummy character.
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'''
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.tr \(*W-|\(bv\*(Tr
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.ie n \{\
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.ds -- \(*W-
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.ds PI pi
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.if (\n(.H=4u)&(1m=24u) .ds -- \(*W\h'-12u'\(*W\h'-12u'-\" diablo 10 pitch
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.\" If the F register is turned on, we'll generate
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.\" index entries out stderr for the following things:
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.\" TH Title
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.\" SH Header
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.\" Sh Subsection
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.\}
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.TH BN_generate_prime 3 "0.9.5a" "22/Jul/2000" "OpenSSL"
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.UC
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.if n .hy 0
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.if n .na
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.ds C+ C\v'-.1v'\h'-1p'\s-2+\h'-1p'+\s0\v'.1v'\h'-1p'
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..
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.\}
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.rm #[ #] #H #V #F C
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.SH "NAME"
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BN_generate_prime, BN_is_prime, BN_is_prime_fasttest \- generate primes and test for primality
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.SH "LIBRARY"
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libcrypto, -lcrypto
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.SH "SYNOPSIS"
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.PP
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.Vb 1
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\& #include <openssl/bn.h>
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.Ve
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.Vb 2
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\& BIGNUM *BN_generate_prime(BIGNUM *ret, int num, int safe, BIGNUM *add,
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\& BIGNUM *rem, void (*callback)(int, int, void *), void *cb_arg);
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.Ve
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.Vb 2
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\& int BN_is_prime(const BIGNUM *a, int checks, void (*callback)(int, int,
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\& void *), BN_CTX *ctx, void *cb_arg);
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.Ve
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.Vb 3
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\& int BN_is_prime_fasttest(const BIGNUM *a, int checks,
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\& void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg,
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\& int do_trial_division);
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.Ve
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.SH "DESCRIPTION"
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\fIBN_generate_prime()\fR generates a pseudo-random prime number of \fBnum\fR
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bits.
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If \fBret\fR is not \fBNULL\fR, it will be used to store the number.
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.PP
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If \fBcallback\fR is not \fBNULL\fR, it is called as follows:
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.Ip "\(bu" 4
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\fBcallback(0, i, cb_arg)\fR is called after generating the i-th
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potential prime number.
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.Ip "\(bu" 4
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While the number is being tested for primality, \fBcallback(1, j,
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cb_arg)\fR is called as described below.
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.Ip "\(bu" 4
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When a prime has been found, \fBcallback(2, i, cb_arg)\fR is called.
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.PP
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The prime may have to fulfill additional requirements for use in
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Diffie-Hellman key exchange:
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.PP
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If \fBadd\fR is not \fB\s-1NULL\s0\fR, the prime will fulfill the condition p % \fBadd\fR
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== \fBrem\fR (p % \fBadd\fR == 1 if \fBrem\fR == \fB\s-1NULL\s0\fR) in order to suit a given
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generator.
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.PP
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If \fBsafe\fR is true, it will be a safe prime (i.e. a prime p so
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that (p-1)/2 is also prime).
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.PP
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The \s-1PRNG\s0 must be seeded prior to calling \fIBN_generate_prime()\fR.
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The prime number generation has a negligible error probability.
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.PP
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\fIBN_is_prime()\fR and \fIBN_is_prime_fasttest()\fR test if the number \fBa\fR is
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prime. The following tests are performed until one of them shows that
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\fBa\fR is composite; if \fBa\fR passes all these tests, it is considered
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prime.
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.PP
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\fIBN_is_prime_fasttest()\fR, when called with \fBdo_trial_division == 1\fR,
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first attempts trial division by a number of small primes;
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if no divisors are found by this test and \fBcallback\fR is not \fB\s-1NULL\s0\fR,
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\fBcallback(1, \-1, cb_arg)\fR is called.
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If \fBdo_trial_division == 0\fR, this test is skipped.
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.PP
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Both \fIBN_is_prime()\fR and \fIBN_is_prime_fasttest()\fR perform a Miller-Rabin
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probabilistic primality test with \fBchecks\fR iterations. If
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\fBchecks == BN_prime_check\fR, a number of iterations is used that
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yields a false positive rate of at most 2^\-80 for random input.
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.PP
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If \fBcallback\fR is not \fB\s-1NULL\s0\fR, \fBcallback(1, j, cb_arg)\fR is called
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after the j-th iteration (j = 0, 1, ...). \fBctx\fR is a
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pre-allocated \fB\s-1BN_CTX\s0\fR (to save the overhead of allocating and
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freeing the structure in a loop), or \fB\s-1NULL\s0\fR.
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.SH "RETURN VALUES"
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\fIBN_generate_prime()\fR returns the prime number on success, \fBNULL\fR otherwise.
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.PP
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\fIBN_is_prime()\fR returns 0 if the number is composite, 1 if it is
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prime with an error probability of less than 0.25^\fBchecks\fR, and
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\-1 on error.
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.PP
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The error codes can be obtained by the \fIERR_get_error(3)|ERR_get_error(3)\fR manpage.
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.SH "SEE ALSO"
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the \fIbn(3)|bn(3)\fR manpage, the \fIerr(3)|err(3)\fR manpage, the \fIrand(3)|rand(3)\fR manpage
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.SH "HISTORY"
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The \fBcb_arg\fR arguments to \fIBN_generate_prime()\fR and to \fIBN_is_prime()\fR
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were added in SSLeay 0.9.0. The \fBret\fR argument to \fIBN_generate_prime()\fR
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was added in SSLeay 0.9.1.
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\fIBN_is_prime_fasttest()\fR was added in OpenSSL 0.9.5.
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.rn }` ''
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.IX Title "BN_generate_prime 3"
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.IX Name "BN_generate_prime, BN_is_prime, BN_is_prime_fasttest - generate primes and test for primality"
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.IX Header "NAME"
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.IX Header "SYNOPSIS"
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.IX Header "DESCRIPTION"
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.IX Item "\(bu"
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.IX Item "\(bu"
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.IX Item "\(bu"
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.IX Header "RETURN VALUES"
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.IX Header "SEE ALSO"
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.IX Header "HISTORY"
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