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.\" $NetBSD: openssl_bn_internal.3,v 1.3 2002/02/07 09:24:09 ross Exp $
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.\" ======================================================================
.\"
.IX Title "bn_internal 3"
.TH bn_internal 3 "0.9.6a" "2001-04-12" "OpenSSL"
.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 "LIBRARY"
libcrypto, -lcrypto
.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 \*[Gt] \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-\*[Gt]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)\-\*[Gt]top \*[Ge] 0 \*[Am]\*[Am] (a)\-\*[Gt]top
\*[Le] (a)\-\*[Gt]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"
openssl_bn(3)
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