234 lines
7.4 KiB
Groff
234 lines
7.4 KiB
Groff
.\" $NetBSD: BN_generate_prime.3,v 1.10 2002/08/09 16:15:38 itojun Exp $
|
|
.\"
|
|
.\" Automatically generated by Pod::Man version 1.02
|
|
.\" Sat Aug 10 00:56:09 2002
|
|
.\"
|
|
.\" Standard preamble:
|
|
.\" ======================================================================
|
|
.de Sh \" Subsection heading
|
|
.br
|
|
.if t .Sp
|
|
.ne 5
|
|
.PP
|
|
\fB\\$1\fR
|
|
.PP
|
|
..
|
|
.de Sp \" Vertical space (when we can't use .PP)
|
|
.if t .sp .5v
|
|
.if n .sp
|
|
..
|
|
.de Ip \" List item
|
|
.br
|
|
.ie \\n(.$>=3 .ne \\$3
|
|
.el .ne 3
|
|
.IP "\\$1" \\$2
|
|
..
|
|
.de Vb \" Begin verbatim text
|
|
.ft CW
|
|
.nf
|
|
.ne \\$1
|
|
..
|
|
.de Ve \" End verbatim text
|
|
.ft R
|
|
|
|
.fi
|
|
..
|
|
.\" 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. | will give a
|
|
.\" real vertical bar. \*(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-|\(bv\*(Tr
|
|
.ds C+ C\v'-.1v'\h'-1p'\s-2+\h'-1p'+\s0\v'.1v'\h'-1p'
|
|
.ie n \{\
|
|
. 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\}
|
|
.el\{\
|
|
. ds -- \|\(em\|
|
|
. ds PI \(*p
|
|
. ds L" ``
|
|
. ds R" ''
|
|
'br\}
|
|
.\"
|
|
.\" If the F register is turned on, we'll generate index entries on stderr
|
|
.\" for titles (.TH), headers (.SH), subsections (.Sh), items (.Ip), and
|
|
.\" index entries marked with X<> in POD. Of course, you'll have to process
|
|
.\" the output yourself in some meaningful fashion.
|
|
.if \nF \{\
|
|
. de IX
|
|
. tm Index:\\$1\t\\n%\t"\\$2"
|
|
. .
|
|
. nr % 0
|
|
. rr F
|
|
.\}
|
|
.\"
|
|
.\" For nroff, turn off justification. Always turn off hyphenation; it
|
|
.\" makes way too many mistakes in technical documents.
|
|
.hy 0
|
|
.if n .na
|
|
.\"
|
|
.\" Accent mark definitions (@(#)ms.acc 1.5 88/02/08 SMI; from UCB 4.2).
|
|
.\" Fear. Run. Save yourself. No user-serviceable parts.
|
|
.bd B 3
|
|
. \" fudge factors for nroff and troff
|
|
.if n \{\
|
|
. ds #H 0
|
|
. ds #V .8m
|
|
. ds #F .3m
|
|
. ds #[ \f1
|
|
. ds #] \fP
|
|
.\}
|
|
.if t \{\
|
|
. ds #H ((1u-(\\\\n(.fu%2u))*.13m)
|
|
. ds #V .6m
|
|
. ds #F 0
|
|
. ds #[ \&
|
|
. ds #] \&
|
|
.\}
|
|
. \" simple accents for nroff and troff
|
|
.if n \{\
|
|
. ds ' \&
|
|
. ds ` \&
|
|
. ds ^ \&
|
|
. ds , \&
|
|
. ds ~ ~
|
|
. ds /
|
|
.\}
|
|
.if t \{\
|
|
. 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
|
|
.ds : \\k:\h'-(\\n(.wu*8/10-\*(#H+.1m+\*(#F)'\v'-\*(#V'\z.\h'.2m+\*(#F'.\h'|\\n:u'\v'\*(#V'
|
|
.ds 8 \h'\*(#H'\(*b\h'-\*(#H'
|
|
.ds o \\k:\h'-(\\n(.wu+\w'\(de'u-\*(#H)/2u'\v'-.3n'\*(#[\z\(de\v'.3n'\h'|\\n:u'\*(#]
|
|
.ds d- \h'\*(#H'\(pd\h'-\w'~'u'\v'-.25m'\f2\(hy\fP\v'.25m'\h'-\*(#H'
|
|
.ds D- D\\k:\h'-\w'D'u'\v'-.11m'\z\(hy\v'.11m'\h'|\\n:u'
|
|
.ds th \*(#[\v'.3m'\s+1I\s-1\v'-.3m'\h'-(\w'I'u*2/3)'\s-1o\s+1\*(#]
|
|
.ds Th \*(#[\s+2I\s-2\h'-\w'I'u*3/5'\v'-.3m'o\v'.3m'\*(#]
|
|
.ds ae a\h'-(\w'a'u*4/10)'e
|
|
.ds Ae A\h'-(\w'A'u*4/10)'E
|
|
. \" corrections for vroff
|
|
.if v .ds ~ \\k:\h'-(\\n(.wu*9/10-\*(#H)'\s-2\u~\d\s+2\h'|\\n:u'
|
|
.if v .ds ^ \\k:\h'-(\\n(.wu*10/11-\*(#H)'\v'-.4m'^\v'.4m'\h'|\\n:u'
|
|
. \" for low resolution devices (crt and lpr)
|
|
.if \n(.H>23 .if \n(.V>19 \
|
|
\{\
|
|
. 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
|
|
.\}
|
|
.rm #[ #] #H #V #F C
|
|
.\" ======================================================================
|
|
.\"
|
|
.IX Title "BN_generate_prime 3"
|
|
.TH BN_generate_prime 3 "0.9.6g" "2000-07-22" "OpenSSL"
|
|
.UC
|
|
.SH "NAME"
|
|
BN_generate_prime, BN_is_prime, BN_is_prime_fasttest \- generate primes and test for primality
|
|
.SH "LIBRARY"
|
|
libcrypto, -lcrypto
|
|
.SH "SYNOPSIS"
|
|
.IX Header "SYNOPSIS"
|
|
.Vb 1
|
|
\& #include <openssl/bn.h>
|
|
.Ve
|
|
.Vb 2
|
|
\& BIGNUM *BN_generate_prime(BIGNUM *ret, int num, int safe, BIGNUM *add,
|
|
\& BIGNUM *rem, void (*callback)(int, int, void *), void *cb_arg);
|
|
.Ve
|
|
.Vb 2
|
|
\& int BN_is_prime(const BIGNUM *a, int checks, void (*callback)(int, int,
|
|
\& void *), BN_CTX *ctx, void *cb_arg);
|
|
.Ve
|
|
.Vb 3
|
|
\& 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);
|
|
.Ve
|
|
.SH "DESCRIPTION"
|
|
.IX Header "DESCRIPTION"
|
|
\&\fIBN_generate_prime()\fR generates a pseudo-random prime number of \fBnum\fR
|
|
bits.
|
|
If \fBret\fR is not \fB\s-1NULL\s0\fR, it will be used to store the number.
|
|
.PP
|
|
If \fBcallback\fR is not \fB\s-1NULL\s0\fR, it is called as follows:
|
|
.Ip "\(bu" 4
|
|
\&\fBcallback(0, i, cb_arg)\fR is called after generating the i-th
|
|
potential prime number.
|
|
.Ip "\(bu" 4
|
|
While the number is being tested for primality, \fBcallback(1, j,
|
|
cb_arg)\fR is called as described below.
|
|
.Ip "\(bu" 4
|
|
When a prime has been found, \fBcallback(2, i, cb_arg)\fR is called.
|
|
.PP
|
|
The prime may have to fulfill additional requirements for use in
|
|
Diffie-Hellman key exchange:
|
|
.PP
|
|
If \fBadd\fR is not \fB\s-1NULL\s0\fR, the prime will fulfill the condition p % \fBadd\fR
|
|
== \fBrem\fR (p % \fBadd\fR == 1 if \fBrem\fR == \fB\s-1NULL\s0\fR) in order to suit a given
|
|
generator.
|
|
.PP
|
|
If \fBsafe\fR is true, it will be a safe prime (i.e. a prime p so
|
|
that (p-1)/2 is also prime).
|
|
.PP
|
|
The \s-1PRNG\s0 must be seeded prior to calling \fIBN_generate_prime()\fR.
|
|
The prime number generation has a negligible error probability.
|
|
.PP
|
|
\&\fIBN_is_prime()\fR and \fIBN_is_prime_fasttest()\fR test if the number \fBa\fR is
|
|
prime. The following tests are performed until one of them shows that
|
|
\&\fBa\fR is composite; if \fBa\fR passes all these tests, it is considered
|
|
prime.
|
|
.PP
|
|
\&\fIBN_is_prime_fasttest()\fR, when called with \fBdo_trial_division == 1\fR,
|
|
first attempts trial division by a number of small primes;
|
|
if no divisors are found by this test and \fBcallback\fR is not \fB\s-1NULL\s0\fR,
|
|
\&\fBcallback(1, \-1, cb_arg)\fR is called.
|
|
If \fBdo_trial_division == 0\fR, this test is skipped.
|
|
.PP
|
|
Both \fIBN_is_prime()\fR and \fIBN_is_prime_fasttest()\fR perform a Miller-Rabin
|
|
probabilistic primality test with \fBchecks\fR iterations. If
|
|
\&\fBchecks == BN_prime_check\fR, a number of iterations is used that
|
|
yields a false positive rate of at most 2^\-80 for random input.
|
|
.PP
|
|
If \fBcallback\fR is not \fB\s-1NULL\s0\fR, \fBcallback(1, j, cb_arg)\fR is called
|
|
after the j-th iteration (j = 0, 1, ...). \fBctx\fR is a
|
|
pre-allocated \fB\s-1BN_CTX\s0\fR (to save the overhead of allocating and
|
|
freeing the structure in a loop), or \fB\s-1NULL\s0\fR.
|
|
.SH "RETURN VALUES"
|
|
.IX Header "RETURN VALUES"
|
|
\&\fIBN_generate_prime()\fR returns the prime number on success, \fB\s-1NULL\s0\fR otherwise.
|
|
.PP
|
|
\&\fIBN_is_prime()\fR returns 0 if the number is composite, 1 if it is
|
|
prime with an error probability of less than 0.25^\fBchecks\fR, and
|
|
\&\-1 on error.
|
|
.PP
|
|
The error codes can be obtained by ERR_get_error(3).
|
|
.SH "SEE ALSO"
|
|
.IX Header "SEE ALSO"
|
|
openssl_bn(3), openssl_err(3), openssl_rand(3)
|
|
.SH "HISTORY"
|
|
.IX Header "HISTORY"
|
|
The \fBcb_arg\fR arguments to \fIBN_generate_prime()\fR and to \fIBN_is_prime()\fR
|
|
were added in SSLeay 0.9.0. The \fBret\fR argument to \fIBN_generate_prime()\fR
|
|
was added in SSLeay 0.9.1.
|
|
\&\fIBN_is_prime_fasttest()\fR was added in OpenSSL 0.9.5.
|