296 lines
7.7 KiB
Groff
296 lines
7.7 KiB
Groff
.rn '' }`
|
|
'''
|
|
'''
|
|
.de Sh
|
|
.br
|
|
.if t .Sp
|
|
.ne 5
|
|
.PP
|
|
\fB\\$1\fR
|
|
.PP
|
|
..
|
|
.de Sp
|
|
.if t .sp .5v
|
|
.if n .sp
|
|
..
|
|
.de Ip
|
|
.br
|
|
.ie \\n(.$>=3 .ne \\$3
|
|
.el .ne 3
|
|
.IP "\\$1" \\$2
|
|
..
|
|
.de Vb
|
|
.ft CW
|
|
.nf
|
|
.ne \\$1
|
|
..
|
|
.de Ve
|
|
.ft R
|
|
|
|
.fi
|
|
..
|
|
'''
|
|
'''
|
|
''' Set up \*(-- to give an unbreakable dash;
|
|
''' string Tr holds user defined translation string.
|
|
''' Bell System Logo is used as a dummy character.
|
|
'''
|
|
.tr \(*W-|\(bv\*(Tr
|
|
.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" ""
|
|
''' \*(M", \*(S", \*(N" and \*(T" are the equivalent of
|
|
''' \*(L" and \*(R", except that they are used on ".xx" lines,
|
|
''' such as .IP and .SH, which do another additional levels of
|
|
''' double-quote interpretation
|
|
.ds M" """
|
|
.ds S" """
|
|
.ds N" """""
|
|
.ds T" """""
|
|
.ds L' '
|
|
.ds R' '
|
|
.ds M' '
|
|
.ds S' '
|
|
.ds N' '
|
|
.ds T' '
|
|
'br\}
|
|
.el\{\
|
|
.ds -- \(em\|
|
|
.tr \*(Tr
|
|
.ds L" ``
|
|
.ds R" ''
|
|
.ds M" ``
|
|
.ds S" ''
|
|
.ds N" ``
|
|
.ds T" ''
|
|
.ds L' `
|
|
.ds R' '
|
|
.ds M' `
|
|
.ds S' '
|
|
.ds N' `
|
|
.ds T' '
|
|
.ds PI \(*p
|
|
'br\}
|
|
.\" If the F register is turned on, we'll generate
|
|
.\" index entries out stderr for the following things:
|
|
.\" TH Title
|
|
.\" SH Header
|
|
.\" Sh Subsection
|
|
.\" Ip Item
|
|
.\" X<> Xref (embedded
|
|
.\" Of course, you have to process the output yourself
|
|
.\" in some meaninful fashion.
|
|
.if \nF \{
|
|
.de IX
|
|
.tm Index:\\$1\t\\n%\t"\\$2"
|
|
..
|
|
.nr % 0
|
|
.rr F
|
|
.\}
|
|
.TH BN_generate_prime 3 "0.9.5a" "22/Jul/100" "OpenSSL"
|
|
.UC
|
|
.if n .hy 0
|
|
.if n .na
|
|
.ds C+ C\v'-.1v'\h'-1p'\s-2+\h'-1p'+\s0\v'.1v'\h'-1p'
|
|
.de CQ \" put $1 in typewriter font
|
|
.ft CW
|
|
'if n "\c
|
|
'if t \\&\\$1\c
|
|
'if n \\&\\$1\c
|
|
'if n \&"
|
|
\\&\\$2 \\$3 \\$4 \\$5 \\$6 \\$7
|
|
'.ft R
|
|
..
|
|
.\" @(#)ms.acc 1.5 88/02/08 SMI; from UCB 4.2
|
|
. \" AM - accent mark definitions
|
|
.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 ? ?
|
|
. ds ! !
|
|
. ds /
|
|
. ds q
|
|
.\}
|
|
.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 ? \s-2c\h'-\w'c'u*7/10'\u\h'\*(#H'\zi\d\s+2\h'\w'c'u*8/10'
|
|
. ds ! \s-2\(or\s+2\h'-\w'\(or'u'\v'-.8m'.\v'.8m'
|
|
. ds / \\k:\h'-(\\n(.wu*8/10-\*(#H)'\z\(sl\h'|\\n:u'
|
|
. ds q o\h'-\w'o'u*8/10'\s-4\v'.4m'\z\(*i\v'-.4m'\s+4\h'\w'o'u*8/10'
|
|
.\}
|
|
. \" 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 v \\k:\h'-(\\n(.wu*9/10-\*(#H)'\v'-\*(#V'\*(#[\s-4v\s0\v'\*(#V'\h'|\\n:u'\*(#]
|
|
.ds _ \\k:\h'-(\\n(.wu*9/10-\*(#H+(\*(#F*2/3))'\v'-.4m'\z\(hy\v'.4m'\h'|\\n:u'
|
|
.ds . \\k:\h'-(\\n(.wu*8/10)'\v'\*(#V*4/10'\z.\v'-\*(#V*4/10'\h'|\\n:u'
|
|
.ds 3 \*(#[\v'.2m'\s-2\&3\s0\v'-.2m'\*(#]
|
|
.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
|
|
.ds oe o\h'-(\w'o'u*4/10)'e
|
|
.ds Oe O\h'-(\w'O'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 v \h'-1'\o'\(aa\(ga'
|
|
. ds _ \h'-1'^
|
|
. ds . \h'-1'.
|
|
. ds 3 3
|
|
. 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
|
|
. ds oe oe
|
|
. ds Oe OE
|
|
.\}
|
|
.rm #[ #] #H #V #F C
|
|
.SH "NAME"
|
|
BN_generate_prime, BN_is_prime, BN_is_prime_fasttest \- generate primes and test for primality
|
|
.SH "LIBRARY"
|
|
libcrypto, -lcrypto
|
|
.SH "SYNOPSIS"
|
|
.PP
|
|
.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"
|
|
\fIBN_generate_prime()\fR generates a pseudo-random prime number of \fBnum\fR
|
|
bits.
|
|
If \fBret\fR is not \fBNULL\fR, it will be used to store the number.
|
|
.PP
|
|
If \fBcallback\fR is not \fBNULL\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"
|
|
\fIBN_generate_prime()\fR returns the prime number on success, \fBNULL\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 the \fIERR_get_error(3)|ERR_get_error(3)\fR manpage.
|
|
.SH "SEE ALSO"
|
|
the \fIbn(3)|bn(3)\fR manpage, the \fIerr(3)|err(3)\fR manpage, the \fIrand(3)|rand(3)\fR manpage
|
|
.SH "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.
|
|
|
|
.rn }` ''
|
|
.IX Title "BN_generate_prime 3"
|
|
.IX Name "BN_generate_prime, BN_is_prime, BN_is_prime_fasttest - generate primes and test for primality"
|
|
|
|
.IX Header "NAME"
|
|
|
|
.IX Header "SYNOPSIS"
|
|
|
|
.IX Header "DESCRIPTION"
|
|
|
|
.IX Item "\(bu"
|
|
|
|
.IX Item "\(bu"
|
|
|
|
.IX Item "\(bu"
|
|
|
|
.IX Header "RETURN VALUES"
|
|
|
|
.IX Header "SEE ALSO"
|
|
|
|
.IX Header "HISTORY"
|
|
|