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diff --git a/secure/lib/libcrypto/man/bn_internal.3 b/secure/lib/libcrypto/man/bn_internal.3 new file mode 100644 index 0000000..245f380 --- /dev/null +++ b/secure/lib/libcrypto/man/bn_internal.3 @@ -0,0 +1,365 @@ +.\" Automatically generated by Pod::Man version 1.15 +.\" Thu May 9 13:18:55 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_INTERNAL 1" +.TH BN_INTERNAL 1 "perl v5.6.1" "2000-11-13" "User Contributed Perl Documentation" +.UC +.SH "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 \- \s-1BIGNUM\s0 +library internal functions +.SH "SYNOPSIS" +.IX Header "SYNOPSIS" +.Vb 9 +\& BN_ULONG bn_mul_words(BN_ULONG *rp, BN_ULONG *ap, int num, BN_ULONG w); +\& BN_ULONG bn_mul_add_words(BN_ULONG *rp, BN_ULONG *ap, int num, +\& BN_ULONG w); +\& void bn_sqr_words(BN_ULONG *rp, BN_ULONG *ap, int num); +\& BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d); +\& BN_ULONG bn_add_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp, +\& int num); +\& BN_ULONG bn_sub_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp, +\& int num); +.Ve +.Vb 4 +\& void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b); +\& void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b); +\& void bn_sqr_comba4(BN_ULONG *r, BN_ULONG *a); +\& void bn_sqr_comba8(BN_ULONG *r, BN_ULONG *a); +.Ve +.Vb 1 +\& int bn_cmp_words(BN_ULONG *a, BN_ULONG *b, int n); +.Ve +.Vb 11 +\& void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, +\& int nb); +\& void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n); +\& void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2, +\& BN_ULONG *tmp); +\& void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, +\& int tn, int n, BN_ULONG *tmp); +\& void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, +\& int n2, BN_ULONG *tmp); +\& void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, +\& int n2, BN_ULONG *tmp); +.Ve +.Vb 2 +\& void bn_sqr_normal(BN_ULONG *r, BN_ULONG *a, int n, BN_ULONG *tmp); +\& void bn_sqr_recursive(BN_ULONG *r, BN_ULONG *a, int n2, BN_ULONG *tmp); +.Ve +.Vb 3 +\& void mul(BN_ULONG r, BN_ULONG a, BN_ULONG w, BN_ULONG c); +\& void mul_add(BN_ULONG r, BN_ULONG a, BN_ULONG w, BN_ULONG c); +\& void sqr(BN_ULONG r0, BN_ULONG r1, BN_ULONG a); +.Ve +.Vb 4 +\& BIGNUM *bn_expand(BIGNUM *a, int bits); +\& BIGNUM *bn_wexpand(BIGNUM *a, int n); +\& BIGNUM *bn_expand2(BIGNUM *a, int n); +\& void bn_fix_top(BIGNUM *a); +.Ve +.Vb 6 +\& void bn_check_top(BIGNUM *a); +\& void bn_print(BIGNUM *a); +\& void bn_dump(BN_ULONG *d, int n); +\& void bn_set_max(BIGNUM *a); +\& void bn_set_high(BIGNUM *r, BIGNUM *a, int n); +\& void bn_set_low(BIGNUM *r, BIGNUM *a, int n); +.Ve +.SH "DESCRIPTION" +.IX Header "DESCRIPTION" +This page documents the internal functions used by the OpenSSL +\&\fB\s-1BIGNUM\s0\fR implementation. They are described here to facilitate +debugging and extending the library. They are \fInot\fR to be used by +applications. +.Sh "The \s-1BIGNUM\s0 structure" +.IX Subsection "The BIGNUM structure" +.Vb 7 +\& typedef struct bignum_st +\& { +\& int top; /* index of last used d (most significant word) */ +\& BN_ULONG *d; /* pointer to an array of 'BITS2' bit chunks */ +\& int max; /* size of the d array */ +\& int neg; /* sign */ +\& } BIGNUM; +.Ve +The big number is stored in \fBd\fR, a \fImalloc()\fRed array of \fB\s-1BN_ULONG\s0\fRs, +least significant first. A \fB\s-1BN_ULONG\s0\fR can be either 16, 32 or 64 bits +in size (\fB\s-1BITS2\s0\fR), depending on the 'number of bits' specified in +\&\f(CW\*(C`openssl/bn.h\*(C'\fR. +.PP +\&\fBmax\fR is the size of the \fBd\fR array that has been allocated. \fBtop\fR +is the 'last' entry being used, so for a value of 4, bn.d[0]=4 and +bn.top=1. \fBneg\fR is 1 if the number is negative. When a \fB\s-1BIGNUM\s0\fR is +\&\fB0\fR, the \fBd\fR field can be \fB\s-1NULL\s0\fR and \fBtop\fR == \fB0\fR. +.PP +Various routines in this library require the use of temporary +\&\fB\s-1BIGNUM\s0\fR variables during their execution. Since dynamic memory +allocation to create \fB\s-1BIGNUM\s0\fRs is rather expensive when used in +conjunction with repeated subroutine calls, the \fB\s-1BN_CTX\s0\fR structure is +used. This structure contains \fB\s-1BN_CTX_NUM\s0\fR \fB\s-1BIGNUM\s0\fRs, see +BN_CTX_start(3). +.Sh "Low-level arithmetic operations" +.IX Subsection "Low-level arithmetic operations" +These functions are implemented in C and for several platforms in +assembly language: +.PP +bn_mul_words(\fBrp\fR, \fBap\fR, \fBnum\fR, \fBw\fR) operates on the \fBnum\fR word +arrays \fBrp\fR and \fBap\fR. It computes \fBap\fR * \fBw\fR, places the result +in \fBrp\fR, and returns the high word (carry). +.PP +bn_mul_add_words(\fBrp\fR, \fBap\fR, \fBnum\fR, \fBw\fR) operates on the \fBnum\fR +word arrays \fBrp\fR and \fBap\fR. It computes \fBap\fR * \fBw\fR + \fBrp\fR, places +the result in \fBrp\fR, and returns the high word (carry). +.PP +bn_sqr_words(\fBrp\fR, \fBap\fR, \fBn\fR) operates on the \fBnum\fR word array +\&\fBap\fR and the 2*\fBnum\fR word array \fBap\fR. It computes \fBap\fR * \fBap\fR +word-wise, and places the low and high bytes of the result in \fBrp\fR. +.PP +bn_div_words(\fBh\fR, \fBl\fR, \fBd\fR) divides the two word number (\fBh\fR,\fBl\fR) +by \fBd\fR and returns the result. +.PP +bn_add_words(\fBrp\fR, \fBap\fR, \fBbp\fR, \fBnum\fR) operates on the \fBnum\fR word +arrays \fBap\fR, \fBbp\fR and \fBrp\fR. It computes \fBap\fR + \fBbp\fR, places the +result in \fBrp\fR, and returns the high word (carry). +.PP +bn_sub_words(\fBrp\fR, \fBap\fR, \fBbp\fR, \fBnum\fR) operates on the \fBnum\fR word +arrays \fBap\fR, \fBbp\fR and \fBrp\fR. It computes \fBap\fR \- \fBbp\fR, places the +result in \fBrp\fR, and returns the carry (1 if \fBbp\fR > \fBap\fR, 0 +otherwise). +.PP +bn_mul_comba4(\fBr\fR, \fBa\fR, \fBb\fR) operates on the 4 word arrays \fBa\fR and +\&\fBb\fR and the 8 word array \fBr\fR. It computes \fBa\fR*\fBb\fR and places the +result in \fBr\fR. +.PP +bn_mul_comba8(\fBr\fR, \fBa\fR, \fBb\fR) operates on the 8 word arrays \fBa\fR and +\&\fBb\fR and the 16 word array \fBr\fR. It computes \fBa\fR*\fBb\fR and places the +result in \fBr\fR. +.PP +bn_sqr_comba4(\fBr\fR, \fBa\fR, \fBb\fR) operates on the 4 word arrays \fBa\fR and +\&\fBb\fR and the 8 word array \fBr\fR. +.PP +bn_sqr_comba8(\fBr\fR, \fBa\fR, \fBb\fR) operates on the 8 word arrays \fBa\fR and +\&\fBb\fR and the 16 word array \fBr\fR. +.PP +The following functions are implemented in C: +.PP +bn_cmp_words(\fBa\fR, \fBb\fR, \fBn\fR) operates on the \fBn\fR word arrays \fBa\fR +and \fBb\fR. It returns 1, 0 and \-1 if \fBa\fR is greater than, equal and +less than \fBb\fR. +.PP +bn_mul_normal(\fBr\fR, \fBa\fR, \fBna\fR, \fBb\fR, \fBnb\fR) operates on the \fBna\fR +word array \fBa\fR, the \fBnb\fR word array \fBb\fR and the \fBna\fR+\fBnb\fR word +array \fBr\fR. It computes \fBa\fR*\fBb\fR and places the result in \fBr\fR. +.PP +bn_mul_low_normal(\fBr\fR, \fBa\fR, \fBb\fR, \fBn\fR) operates on the \fBn\fR word +arrays \fBr\fR, \fBa\fR and \fBb\fR. It computes the \fBn\fR low words of +\&\fBa\fR*\fBb\fR and places the result in \fBr\fR. +.PP +bn_mul_recursive(\fBr\fR, \fBa\fR, \fBb\fR, \fBn2\fR, \fBt\fR) operates on the \fBn2\fR +word arrays \fBa\fR and \fBb\fR and the 2*\fBn2\fR word arrays \fBr\fR and \fBt\fR. +\&\fBn2\fR must be a power of 2. It computes \fBa\fR*\fBb\fR and places the +result in \fBr\fR. +.PP +bn_mul_part_recursive(\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 +bn_mul_low_recursive(\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 +bn_mul_high(\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 +bn_sqr_normal(\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(CW\*(C`bn_lcl.h\*(C'\fR. +.PP +mul(\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 +mul_add(\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 +sqr(\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" +.IX Subsection "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" +.IX Subsection "Debugging" +\&\fIbn_check_top()\fR verifies that \f(CW\*(C`((a)\->top >= 0 && (a)\->top +<= (a)\->max)\*(C'\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" +.IX Header "SEE ALSO" +bn(3) |
