365 lines
14 KiB
Groff
365 lines
14 KiB
Groff
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.\" ========================================================================
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.\"
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.IX Title "bn_internal 3"
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.TH bn_internal 3 "2009-06-14" "0.9.8k" "OpenSSL"
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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 "SYNOPSIS"
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.IX Header "SYNOPSIS"
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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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.PP
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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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.PP
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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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.PP
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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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\& int dna,int dnb,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 n, int tna,int tnb, 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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.PP
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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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.PP
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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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.PP
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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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.PP
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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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.IX Header "DESCRIPTION"
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This page documents the internal functions used by the OpenSSL
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\&\fB\s-1BIGNUM\s0\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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.IX Subsection "The BIGNUM structure"
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.Vb 7
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\& typedef struct bignum_st
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\& {
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\& int top; /* number of words used in d */
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\& BN_ULONG *d; /* pointer to an array containing the integer value */
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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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.PP
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The integer value is stored in \fBd\fR, a \fImalloc()\fRed array of words (\fB\s-1BN_ULONG\s0\fR),
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least significant word first. A \fB\s-1BN_ULONG\s0\fR can be either 16, 32 or 64 bits
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in size, depending on the 'number of bits' (\fB\s-1BITS2\s0\fR) specified in
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\&\f(CW\*(C`openssl/bn.h\*(C'\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 number of words 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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\&\fIBN_CTX_start\fR\|(3).
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.Sh "Low-level arithmetic operations"
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.IX Subsection "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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bn_mul_words(\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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bn_mul_add_words(\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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bn_sqr_words(\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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bn_div_words(\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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bn_add_words(\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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bn_sub_words(\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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bn_mul_comba4(\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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bn_mul_comba8(\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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bn_sqr_comba4(\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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bn_sqr_comba8(\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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bn_cmp_words(\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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bn_mul_normal(\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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bn_mul_low_normal(\fBr\fR, \fBa\fR, \fBb\fR, \fBn\fR) operates on the \fBn\fR word
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arrays \fBr\fR, \fBa\fR and \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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bn_mul_recursive(\fBr\fR, \fBa\fR, \fBb\fR, \fBn2\fR, \fBdna\fR, \fBdnb\fR, \fBt\fR) operates
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on the word arrays \fBa\fR and \fBb\fR of length \fBn2\fR+\fBdna\fR and \fBn2\fR+\fBdnb\fR
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(\fBdna\fR and \fBdnb\fR are currently allowed to be 0 or negative) and the 2*\fBn2\fR
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word arrays \fBr\fR and \fBt\fR. \fBn2\fR must be a power of 2. It computes
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\&\fBa\fR*\fBb\fR and places the result in \fBr\fR.
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.PP
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bn_mul_part_recursive(\fBr\fR, \fBa\fR, \fBb\fR, \fBn\fR, \fBtna\fR, \fBtnb\fR, \fBtmp\fR)
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operates on the word arrays \fBa\fR and \fBb\fR of length \fBn\fR+\fBtna\fR and
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\&\fBn\fR+\fBtnb\fR and the 4*\fBn\fR word arrays \fBr\fR and \fBtmp\fR.
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.PP
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bn_mul_low_recursive(\fBr\fR, \fBa\fR, \fBb\fR, \fBn2\fR, \fBtmp\fR) operates on the
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\&\fBn2\fR word arrays \fBr\fR and \fBtmp\fR and the \fBn2\fR/2 word arrays \fBa\fR
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and \fBb\fR.
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.PP
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bn_mul_high(\fBr\fR, \fBa\fR, \fBb\fR, \fBl\fR, \fBn2\fR, \fBtmp\fR) operates on the
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\&\fBn2\fR word arrays \fBr\fR, \fBa\fR, \fBb\fR and \fBl\fR (?) and the 3*\fBn2\fR word
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array \fBtmp\fR.
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.PP
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\&\fIBN_mul()\fR calls \fIbn_mul_normal()\fR, or an optimized implementation if the
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factors have the same size: \fIbn_mul_comba8()\fR is used if they are 8
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words long, \fIbn_mul_recursive()\fR if they are larger than
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\&\fB\s-1BN_MULL_SIZE_NORMAL\s0\fR and the size is an exact multiple of the word
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size, and \fIbn_mul_part_recursive()\fR for others that are larger than
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\&\fB\s-1BN_MULL_SIZE_NORMAL\s0\fR.
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.PP
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bn_sqr_normal(\fBr\fR, \fBa\fR, \fBn\fR, \fBtmp\fR) operates on the \fBn\fR word array
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\&\fBa\fR and the 2*\fBn\fR word arrays \fBtmp\fR and \fBr\fR.
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.PP
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The implementations use the following macros which, depending on the
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architecture, may use \*(L"long long\*(R" C operations or inline assembler.
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They are defined in \f(CW\*(C`bn_lcl.h\*(C'\fR.
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.PP
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mul(\fBr\fR, \fBa\fR, \fBw\fR, \fBc\fR) computes \fBw\fR*\fBa\fR+\fBc\fR and places the
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low word of the result in \fBr\fR and the high word in \fBc\fR.
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.PP
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mul_add(\fBr\fR, \fBa\fR, \fBw\fR, \fBc\fR) computes \fBw\fR*\fBa\fR+\fBr\fR+\fBc\fR and
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places the low word of the result in \fBr\fR and the high word in \fBc\fR.
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.PP
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sqr(\fBr0\fR, \fBr1\fR, \fBa\fR) computes \fBa\fR*\fBa\fR and places the low word
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of the result in \fBr0\fR and the high word in \fBr1\fR.
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.Sh "Size changes"
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.IX Subsection "Size changes"
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\&\fIbn_expand()\fR ensures that \fBb\fR has enough space for a \fBbits\fR bit
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number. \fIbn_wexpand()\fR ensures that \fBb\fR has enough space for an
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\&\fBn\fR word number. If the number has to be expanded, both macros
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call \fIbn_expand2()\fR, which allocates a new \fBd\fR array and copies the
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data. They return \fB\s-1NULL\s0\fR on error, \fBb\fR otherwise.
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.PP
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The \fIbn_fix_top()\fR macro reduces \fBa\->top\fR to point to the most
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significant non-zero word plus one when \fBa\fR has shrunk.
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.Sh "Debugging"
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.IX Subsection "Debugging"
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\&\fIbn_check_top()\fR verifies that \f(CW\*(C`((a)\->top >= 0 && (a)\->top
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<= (a)\->max)\*(C'\fR. A violation will cause the program to abort.
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.PP
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\&\fIbn_print()\fR prints \fBa\fR to stderr. \fIbn_dump()\fR prints \fBn\fR words at \fBd\fR
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(in reverse order, i.e. most significant word first) to stderr.
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.PP
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\&\fIbn_set_max()\fR makes \fBa\fR a static number with a \fBmax\fR of its current size.
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This is used by \fIbn_set_low()\fR and \fIbn_set_high()\fR to make \fBr\fR a read-only
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\&\fB\s-1BIGNUM\s0\fR that contains the \fBn\fR low or high words of \fBa\fR.
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.PP
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If \fB\s-1BN_DEBUG\s0\fR is not defined, \fIbn_check_top()\fR, \fIbn_print()\fR, \fIbn_dump()\fR
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and \fIbn_set_max()\fR are defined as empty macros.
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.SH "SEE ALSO"
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.IX Header "SEE ALSO"
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\&\fIbn\fR\|(3)
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