436 lines
15 KiB
Groff
436 lines
15 KiB
Groff
.rn '' }`
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'''
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'''
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.de Sh
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.br
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.if t .Sp
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.ne 5
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.PP
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\fB\\$1\fR
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.PP
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..
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.de Sp
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.if t .sp .5v
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.if n .sp
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..
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.de Ip
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.br
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.ie \\n(.$>=3 .ne \\$3
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.el .ne 3
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.IP "\\$1" \\$2
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..
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.de Vb
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.ft CW
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.nf
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.ne \\$1
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..
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.de Ve
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.ft R
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.fi
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..
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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 (\n(.H=4u)&(1m=20u) .ds -- \(*W\h'-12u'\(*W\h'-8u'-\" diablo 12 pitch
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.ds L" ""
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.ds R" ""
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''' \*(M", \*(S", \*(N" and \*(T" are the equivalent of
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''' \*(L" and \*(R", except that they are used on ".xx" lines,
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''' such as .IP and .SH, which do another additional levels of
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''' double-quote interpretation
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.ds M" """
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.ds S" """
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.ds N" """""
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.ds T" """""
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.ds L' '
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.ds S' '
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.ds N' '
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.ds T' '
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'br\}
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.el\{\
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.ds -- \(em\|
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.tr \*(Tr
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.ds L" ``
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.ds R" ''
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.ds M" ``
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.ds S" ''
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.ds N" ``
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.ds T" ''
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.ds L' `
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.ds R' '
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.ds M' `
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.ds N' `
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.ds T' '
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.ds PI \(*p
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'br\}
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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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.\" Ip Item
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.\" X<> Xref (embedded
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.\" Of course, you have to process the output yourself
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.\" in some meaninful fashion.
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.if \nF \{
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.de IX
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.tm Index:\\$1\t\\n%\t"\\$2"
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..
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.nr % 0
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.rr F
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.\}
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.TH bn_internal 3 "0.9.5a" "22/Jul/100" "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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.de CQ \" put $1 in typewriter font
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.ft CW
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'if n "\c
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'if t \\&\\$1\c
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'if n \\&\\$1\c
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'if n \&"
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\\&\\$2 \\$3 \\$4 \\$5 \\$6 \\$7
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'.ft R
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..
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.\" @(#)ms.acc 1.5 88/02/08 SMI; from UCB 4.2
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. \" AM - accent mark definitions
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.bd B 3
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. \" fudge factors for nroff and troff
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.if n \{\
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. ds #H 0
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. ds #V .8m
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. ds #F .3m
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. ds #[ \f1
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. ds #] \fP
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.\}
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.if t \{\
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. ds #H ((1u-(\\\\n(.fu%2u))*.13m)
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. ds #V .6m
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. ds #F 0
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. ds #[ \&
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. ds #] \&
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.\}
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. \" simple accents for nroff and troff
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.if n \{\
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. ds ' \&
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. ds ` \&
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. ds ^ \&
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. ds , \&
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. ds ~ ~
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. ds ? ?
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. ds ! !
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. ds /
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. ds q
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.\}
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.if t \{\
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. ds ' \\k:\h'-(\\n(.wu*8/10-\*(#H)'\'\h"|\\n:u"
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. ds ` \\k:\h'-(\\n(.wu*8/10-\*(#H)'\`\h'|\\n:u'
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. ds ^ \\k:\h'-(\\n(.wu*10/11-\*(#H)'^\h'|\\n:u'
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. ds , \\k:\h'-(\\n(.wu*8/10)',\h'|\\n:u'
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. ds ~ \\k:\h'-(\\n(.wu-\*(#H-.1m)'~\h'|\\n:u'
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. ds ? \s-2c\h'-\w'c'u*7/10'\u\h'\*(#H'\zi\d\s+2\h'\w'c'u*8/10'
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. ds ! \s-2\(or\s+2\h'-\w'\(or'u'\v'-.8m'.\v'.8m'
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. ds / \\k:\h'-(\\n(.wu*8/10-\*(#H)'\z\(sl\h'|\\n:u'
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. 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'
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.\}
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. \" troff and (daisy-wheel) nroff accents
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.ds : \\k:\h'-(\\n(.wu*8/10-\*(#H+.1m+\*(#F)'\v'-\*(#V'\z.\h'.2m+\*(#F'.\h'|\\n:u'\v'\*(#V'
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.ds 8 \h'\*(#H'\(*b\h'-\*(#H'
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.ds v \\k:\h'-(\\n(.wu*9/10-\*(#H)'\v'-\*(#V'\*(#[\s-4v\s0\v'\*(#V'\h'|\\n:u'\*(#]
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.ds _ \\k:\h'-(\\n(.wu*9/10-\*(#H+(\*(#F*2/3))'\v'-.4m'\z\(hy\v'.4m'\h'|\\n:u'
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.ds . \\k:\h'-(\\n(.wu*8/10)'\v'\*(#V*4/10'\z.\v'-\*(#V*4/10'\h'|\\n:u'
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.ds 3 \*(#[\v'.2m'\s-2\&3\s0\v'-.2m'\*(#]
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.ds o \\k:\h'-(\\n(.wu+\w'\(de'u-\*(#H)/2u'\v'-.3n'\*(#[\z\(de\v'.3n'\h'|\\n:u'\*(#]
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.ds d- \h'\*(#H'\(pd\h'-\w'~'u'\v'-.25m'\f2\(hy\fP\v'.25m'\h'-\*(#H'
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.ds D- D\\k:\h'-\w'D'u'\v'-.11m'\z\(hy\v'.11m'\h'|\\n:u'
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.ds th \*(#[\v'.3m'\s+1I\s-1\v'-.3m'\h'-(\w'I'u*2/3)'\s-1o\s+1\*(#]
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.ds Th \*(#[\s+2I\s-2\h'-\w'I'u*3/5'\v'-.3m'o\v'.3m'\*(#]
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.ds ae a\h'-(\w'a'u*4/10)'e
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.ds Ae A\h'-(\w'A'u*4/10)'E
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.ds oe o\h'-(\w'o'u*4/10)'e
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.ds Oe O\h'-(\w'O'u*4/10)'E
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. \" corrections for vroff
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.if v .ds ~ \\k:\h'-(\\n(.wu*9/10-\*(#H)'\s-2\u~\d\s+2\h'|\\n:u'
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.if v .ds ^ \\k:\h'-(\\n(.wu*10/11-\*(#H)'\v'-.4m'^\v'.4m'\h'|\\n:u'
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. \" for low resolution devices (crt and lpr)
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.if \n(.H>23 .if \n(.V>19 \
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\{\
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. ds : e
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. ds 8 ss
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. ds v \h'-1'\o'\(aa\(ga'
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. ds _ \h'-1'^
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. ds . \h'-1'.
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. ds 3 3
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. ds o a
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. ds d- d\h'-1'\(ga
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. ds D- D\h'-1'\(hy
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. ds th \o'bp'
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. ds Th \o'LP'
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. ds ae ae
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. ds Ae AE
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. ds oe oe
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. ds Oe OE
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.\}
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.rm #[ #] #H #V #F C
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.SH "NAME"
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bn_mul_words, bn_mul_add_words, bn_sqr_words, bn_div_words,
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bn_add_words, bn_sub_words, bn_mul_comba4, bn_mul_comba8,
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bn_sqr_comba4, bn_sqr_comba8, bn_cmp_words, bn_mul_normal,
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bn_mul_low_normal, bn_mul_recursive, bn_mul_part_recursive,
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bn_mul_low_recursive, bn_mul_high, bn_sqr_normal, bn_sqr_recursive,
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bn_expand, bn_wexpand, bn_expand2, bn_fix_top, bn_check_top,
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bn_print, bn_dump, bn_set_max, bn_set_high, bn_set_low \- BIGNUM
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library internal functions
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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 9
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\& BN_ULONG bn_mul_words(BN_ULONG *rp, BN_ULONG *ap, int num, BN_ULONG w);
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\& BN_ULONG bn_mul_add_words(BN_ULONG *rp, BN_ULONG *ap, int num,
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\& BN_ULONG w);
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\& void bn_sqr_words(BN_ULONG *rp, BN_ULONG *ap, int num);
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\& BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d);
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\& BN_ULONG bn_add_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp,
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\& int num);
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\& BN_ULONG bn_sub_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp,
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\& int num);
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.Ve
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.Vb 4
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\& void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
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\& void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
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\& void bn_sqr_comba4(BN_ULONG *r, BN_ULONG *a);
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\& void bn_sqr_comba8(BN_ULONG *r, BN_ULONG *a);
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.Ve
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.Vb 1
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\& int bn_cmp_words(BN_ULONG *a, BN_ULONG *b, int n);
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.Ve
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.Vb 11
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\& void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b,
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\& int nb);
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\& void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n);
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\& void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
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\& BN_ULONG *tmp);
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\& void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b,
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\& int tn, int n, BN_ULONG *tmp);
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\& void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b,
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\& int n2, BN_ULONG *tmp);
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\& void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l,
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\& int n2, BN_ULONG *tmp);
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.Ve
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.Vb 2
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\& void bn_sqr_normal(BN_ULONG *r, BN_ULONG *a, int n, BN_ULONG *tmp);
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\& void bn_sqr_recursive(BN_ULONG *r, BN_ULONG *a, int n2, BN_ULONG *tmp);
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.Ve
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.Vb 3
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\& void mul(BN_ULONG r, BN_ULONG a, BN_ULONG w, BN_ULONG c);
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\& void mul_add(BN_ULONG r, BN_ULONG a, BN_ULONG w, BN_ULONG c);
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\& void sqr(BN_ULONG r0, BN_ULONG r1, BN_ULONG a);
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.Ve
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.Vb 4
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\& BIGNUM *bn_expand(BIGNUM *a, int bits);
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\& BIGNUM *bn_wexpand(BIGNUM *a, int n);
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\& BIGNUM *bn_expand2(BIGNUM *a, int n);
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\& void bn_fix_top(BIGNUM *a);
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.Ve
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.Vb 6
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\& void bn_check_top(BIGNUM *a);
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\& void bn_print(BIGNUM *a);
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\& void bn_dump(BN_ULONG *d, int n);
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\& void bn_set_max(BIGNUM *a);
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\& void bn_set_high(BIGNUM *r, BIGNUM *a, int n);
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\& void bn_set_low(BIGNUM *r, BIGNUM *a, int n);
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.Ve
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.SH "DESCRIPTION"
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This page documents the internal functions used by the OpenSSL
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\fBBIGNUM\fR implementation. They are described here to facilitate
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debugging and extending the library. They are \fInot\fR to be used by
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applications.
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.Sh "The \s-1BIGNUM\s0 structure"
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.PP
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.Vb 7
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\& typedef struct bignum_st
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\& {
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\& int top; /* index of last used d (most significant word) */
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\& BN_ULONG *d; /* pointer to an array of 'BITS2' bit chunks */
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\& int max; /* size of the d array */
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\& int neg; /* sign */
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\& } BIGNUM;
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.Ve
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The big number is stored in \fBd\fR, a \fImalloc()\fRed array of \fB\s-1BN_ULONG\s0\fRs,
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least significant first. A \fB\s-1BN_ULONG\s0\fR can be either 16, 32 or 64 bits
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in size (\fB\s-1BITS2\s0\fR), depending on the \*(L'number of bits\*(R' specified in
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\f(CWopenssl/bn.h\fR.
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.PP
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\fBmax\fR is the size of the \fBd\fR array that has been allocated. \fBtop\fR
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is the \*(L'last\*(R' entry being used, so for a value of 4, bn.d[0]=4 and
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bn.top=1. \fBneg\fR is 1 if the number is negative. When a \fB\s-1BIGNUM\s0\fR is
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\fB0\fR, the \fBd\fR field can be \fB\s-1NULL\s0\fR and \fBtop\fR == \fB0\fR.
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.PP
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Various routines in this library require the use of temporary
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\fB\s-1BIGNUM\s0\fR variables during their execution. Since dynamic memory
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allocation to create \fB\s-1BIGNUM\s0\fRs is rather expensive when used in
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conjunction with repeated subroutine calls, the \fB\s-1BN_CTX\s0\fR structure is
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used. This structure contains \fB\s-1BN_CTX_NUM\s0\fR \fB\s-1BIGNUM\s0\fRs, see
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the \fIBN_CTX_start(3)|BN_CTX_start(3)\fR manpage.
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.Sh "Low-level arithmetic operations"
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These functions are implemented in C and for several platforms in
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assembly language:
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.PP
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\fIbn_mul_words\fR\|(\fBrp\fR, \fBap\fR, \fBnum\fR, \fBw\fR) operates on the \fBnum\fR word
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arrays \fBrp\fR and \fBap\fR. It computes \fBap\fR * \fBw\fR, places the result
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in \fBrp\fR, and returns the high word (carry).
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.PP
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\fIbn_mul_add_words\fR\|(\fBrp\fR, \fBap\fR, \fBnum\fR, \fBw\fR) operates on the \fBnum\fR
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word arrays \fBrp\fR and \fBap\fR. It computes \fBap\fR * \fBw\fR + \fBrp\fR, places
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the result in \fBrp\fR, and returns the high word (carry).
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.PP
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\fIbn_sqr_words\fR\|(\fBrp\fR, \fBap\fR, \fBn\fR) operates on the \fBnum\fR word array
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\fBap\fR and the 2*\fBnum\fR word array \fBap\fR. It computes \fBap\fR * \fBap\fR
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word-wise, and places the low and high bytes of the result in \fBrp\fR.
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.PP
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\fIbn_div_words\fR\|(\fBh\fR, \fBl\fR, \fBd\fR) divides the two word number (\fBh\fR,\fBl\fR)
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by \fBd\fR and returns the result.
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.PP
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\fIbn_add_words\fR\|(\fBrp\fR, \fBap\fR, \fBbp\fR, \fBnum\fR) operates on the \fBnum\fR word
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arrays \fBap\fR, \fBbp\fR and \fBrp\fR. It computes \fBap\fR + \fBbp\fR, places the
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result in \fBrp\fR, and returns the high word (carry).
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.PP
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\fIbn_sub_words\fR\|(\fBrp\fR, \fBap\fR, \fBbp\fR, \fBnum\fR) operates on the \fBnum\fR word
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arrays \fBap\fR, \fBbp\fR and \fBrp\fR. It computes \fBap\fR \- \fBbp\fR, places the
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result in \fBrp\fR, and returns the carry (1 if \fBbp\fR > \fBap\fR, 0
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otherwise).
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.PP
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\fIbn_mul_comba4\fR\|(\fBr\fR, \fBa\fR, \fBb\fR) operates on the 4 word arrays \fBa\fR and
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\fBb\fR and the 8 word array \fBr\fR. It computes \fBa\fR*\fBb\fR and places the
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result in \fBr\fR.
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.PP
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\fIbn_mul_comba8\fR\|(\fBr\fR, \fBa\fR, \fBb\fR) operates on the 8 word arrays \fBa\fR and
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\fBb\fR and the 16 word array \fBr\fR. It computes \fBa\fR*\fBb\fR and places the
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result in \fBr\fR.
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.PP
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\fIbn_sqr_comba4\fR\|(\fBr\fR, \fBa\fR, \fBb\fR) operates on the 4 word arrays \fBa\fR and
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\fBb\fR and the 8 word array \fBr\fR.
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.PP
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\fIbn_sqr_comba8\fR\|(\fBr\fR, \fBa\fR, \fBb\fR) operates on the 8 word arrays \fBa\fR and
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\fBb\fR and the 16 word array \fBr\fR.
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.PP
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The following functions are implemented in C:
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.PP
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\fIbn_cmp_words\fR\|(\fBa\fR, \fBb\fR, \fBn\fR) operates on the \fBn\fR word arrays \fBa\fR
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and \fBb\fR. It returns 1, 0 and \-1 if \fBa\fR is greater than, equal and
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less than \fBb\fR.
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.PP
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\fIbn_mul_normal\fR\|(\fBr\fR, \fBa\fR, \fBna\fR, \fBb\fR, \fBnb\fR) operates on the \fBna\fR
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word array \fBa\fR, the \fBnb\fR word array \fBb\fR and the \fBna\fR+\fBnb\fR word
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array \fBr\fR. It computes \fBa\fR*\fBb\fR and places the result in \fBr\fR.
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.PP
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\fIbn_mul_low_normal\fR\|(\fBr\fR, \fBa\fR, \fBb\fR, \fBn\fR) operates on the \fBn\fR word
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arrays \fBr\fR, \fBa\fR und \fBb\fR. It computes the \fBn\fR low words of
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\fBa\fR*\fBb\fR and places the result in \fBr\fR.
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.PP
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\fIbn_mul_recursive\fR\|(\fBr\fR, \fBa\fR, \fBb\fR, \fBn2\fR, \fBt\fR) operates on the \fBn2\fR
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word arrays \fBa\fR and \fBb\fR and the 2*\fBn2\fR word arrays \fBr\fR and \fBt\fR.
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\fBn2\fR must be a power of 2. It computes \fBa\fR*\fBb\fR and places the
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result in \fBr\fR.
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.PP
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\fIbn_mul_part_recursive\fR\|(\fBr\fR, \fBa\fR, \fBb\fR, \fBtn\fR, \fBn\fR, \fBtmp\fR) operates
|
|
on the \fBn\fR+\fBtn\fR word arrays \fBa\fR and \fBb\fR and the 4*\fBn\fR word arrays
|
|
\fBr\fR and \fBtmp\fR.
|
|
.PP
|
|
\fIbn_mul_low_recursive\fR\|(\fBr\fR, \fBa\fR, \fBb\fR, \fBn2\fR, \fBtmp\fR) operates on the
|
|
\fBn2\fR word arrays \fBr\fR and \fBtmp\fR and the \fBn2\fR/2 word arrays \fBa\fR
|
|
and \fBb\fR.
|
|
.PP
|
|
\fIbn_mul_high\fR\|(\fBr\fR, \fBa\fR, \fBb\fR, \fBl\fR, \fBn2\fR, \fBtmp\fR) operates on the
|
|
\fBn2\fR word arrays \fBr\fR, \fBa\fR, \fBb\fR and \fBl\fR (?) and the 3*\fBn2\fR word
|
|
array \fBtmp\fR.
|
|
.PP
|
|
\fIBN_mul()\fR calls \fIbn_mul_normal()\fR, or an optimized implementation if the
|
|
factors have the same size: \fIbn_mul_comba8()\fR is used if they are 8
|
|
words long, \fIbn_mul_recursive()\fR if they are larger than
|
|
\fB\s-1BN_MULL_SIZE_NORMAL\s0\fR and the size is an exact multiple of the word
|
|
size, and \fIbn_mul_part_recursive()\fR for others that are larger than
|
|
\fB\s-1BN_MULL_SIZE_NORMAL\s0\fR.
|
|
.PP
|
|
\fIbn_sqr_normal\fR\|(\fBr\fR, \fBa\fR, \fBn\fR, \fBtmp\fR) operates on the \fBn\fR word array
|
|
\fBa\fR and the 2*\fBn\fR word arrays \fBtmp\fR and \fBr\fR.
|
|
.PP
|
|
The implementations use the following macros which, depending on the
|
|
architecture, may use \*(L"long long\*(R" C operations or inline assembler.
|
|
They are defined in \f(CWbn_lcl.h\fR.
|
|
.PP
|
|
\fImul\fR\|(\fBr\fR, \fBa\fR, \fBw\fR, \fBc\fR) computes \fBw\fR*\fBa\fR+\fBc\fR and places the
|
|
low word of the result in \fBr\fR and the high word in \fBc\fR.
|
|
.PP
|
|
\fImul_add\fR\|(\fBr\fR, \fBa\fR, \fBw\fR, \fBc\fR) computes \fBw\fR*\fBa\fR+\fBr\fR+\fBc\fR and
|
|
places the low word of the result in \fBr\fR and the high word in \fBc\fR.
|
|
.PP
|
|
\fIsqr\fR\|(\fBr0\fR, \fBr1\fR, \fBa\fR) computes \fBa\fR*\fBa\fR and places the low word
|
|
of the result in \fBr0\fR and the high word in \fBr1\fR.
|
|
.Sh "Size changes"
|
|
\fIbn_expand()\fR ensures that \fBb\fR has enough space for a \fBbits\fR bit
|
|
number. \fIbn_wexpand()\fR ensures that \fBb\fR has enough space for an
|
|
\fBn\fR word number. If the number has to be expanded, both macros
|
|
call \fIbn_expand2()\fR, which allocates a new \fBd\fR array and copies the
|
|
data. They return \fB\s-1NULL\s0\fR on error, \fBb\fR otherwise.
|
|
.PP
|
|
The \fIbn_fix_top()\fR macro reduces \fBa->top\fR to point to the most
|
|
significant non-zero word when \fBa\fR has shrunk.
|
|
.Sh "Debugging"
|
|
\fIbn_check_top()\fR verifies that \f(CW((a)->top >= 0 && (a)->top
|
|
<= (a)->max)\fR. A violation will cause the program to abort.
|
|
.PP
|
|
\fIbn_print()\fR prints \fBa\fR to stderr. \fIbn_dump()\fR prints \fBn\fR words at \fBd\fR
|
|
(in reverse order, i.e. most significant word first) to stderr.
|
|
.PP
|
|
\fIbn_set_max()\fR makes \fBa\fR a static number with a \fBmax\fR of its current size.
|
|
This is used by \fIbn_set_low()\fR and \fIbn_set_high()\fR to make \fBr\fR a read-only
|
|
\fB\s-1BIGNUM\s0\fR that contains the \fBn\fR low or high words of \fBa\fR.
|
|
.PP
|
|
If \fB\s-1BN_DEBUG\s0\fR is not defined, \fIbn_check_top()\fR, \fIbn_print()\fR, \fIbn_dump()\fR
|
|
and \fIbn_set_max()\fR are defined as empty macros.
|
|
.SH "SEE ALSO"
|
|
the \fIbn(3)|bn(3)\fR manpage
|
|
|
|
.rn }` ''
|
|
.IX Title "bn_internal 3"
|
|
.IX Name "bn_mul_words, bn_mul_add_words, bn_sqr_words, bn_div_words,
|
|
bn_add_words, bn_sub_words, bn_mul_comba4, bn_mul_comba8,
|
|
bn_sqr_comba4, bn_sqr_comba8, bn_cmp_words, bn_mul_normal,
|
|
bn_mul_low_normal, bn_mul_recursive, bn_mul_part_recursive,
|
|
bn_mul_low_recursive, bn_mul_high, bn_sqr_normal, bn_sqr_recursive,
|
|
bn_expand, bn_wexpand, bn_expand2, bn_fix_top, bn_check_top,
|
|
bn_print, bn_dump, bn_set_max, bn_set_high, bn_set_low - BIGNUM
|
|
library internal functions"
|
|
|
|
.IX Header "NAME"
|
|
|
|
.IX Header "SYNOPSIS"
|
|
|
|
.IX Header "DESCRIPTION"
|
|
|
|
.IX Subsection "The \s-1BIGNUM\s0 structure"
|
|
|
|
.IX Subsection "Low-level arithmetic operations"
|
|
|
|
.IX Subsection "Size changes"
|
|
|
|
.IX Subsection "Debugging"
|
|
|
|
.IX Header "SEE ALSO"
|
|
|