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bn_internal(3)
NAME
bn_internal, 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
SYNOPSIS
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 );
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 );
int bn_cmp_words(
BN_ULONG *a, BN_ULONG *b, int n );
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 );
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 );
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 );
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 );
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 );
DESCRIPTION
This page describes the internal functions used by the OpenSSL BIGNUM
implementation. They are described here to facilitate debugging and
extending the library. They are not to be used by applications.
The BIGNUM structure
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;
The big number is stored in d, a malloc array of BN_ULONGs, least
significant first. A BN_ULONG can be either 16, 32 or 64 bits in size
(BITS2), depending on the number of bits specified in openssl/bn.h.
The max is the size of the d array that has been allocated. The top is the
last entry being used. For a value of 4, for example, bn.d[0]=4 and
bn.top=1. The neg is 1 if the number is negative. When a BIGNUM is 0, the
d field can be NULL and top == 0.
Various routines in this library require the use of temporary BIGNUM
variables during their execution. Since dynamic memory allocation to
create BIGNUMs is rather expensive when used in conjunction with repeated
subroutine calls, the BN_CTX structure is used. This structure contains
BN_CTX_NUM BIGNUMs. See BN_CTX_start(3).
Low-level arithmetic operations
These functions are implemented in C and for several platforms in assembly
language:
bn_mul_words(rp, ap, num, w)
Operates on the num word arrays rp and ap. It computes ap * w,
places the result in rp, and returns the high word (carry).
bn_mul_add_words(rp, ap, num, w)
Operates on the num word arrays rp and ap. It computes ap * w +
rp, places the result in rp, and returns the high word (carry).
bn_sqr_words(rp, ap, n)
Operates on the num word array ap and the 2*num word array ap. It
computes ap * ap word-wise, and places the low and high bytes of
the result in rp.
bn_div_words(h, l, d)
Divides the two word number (h,l) by d and returns the result.
bn_add_words(rp, ap, bp, num)
Operates on the num word arrays ap, bp and rp. It computes ap +
bp, places the result in rp, and returns the high word (carry).
bn_sub_words(rp, ap, bp, num)
Operates on the num word arrays ap, bp and rp. It computes ap -
bp, places the result in rp, and returns the carry (1 if bp > ap, 0
otherwise).
bn_mul_comba4(r, a, b)
Operates on the 4 word arrays a and b and the 8 word array r. It
computes a*b and places the result in r.
bn_mul_comba8(r, a, b)
Operates on the 8-word arrays a and b and the 16-word array r. It
computes a*b and places the result in r.
bn_sqr_comba4(r, a, b)
Operates on the 4-word arrays a and b and the 8-word array r.
bn_sqr_comba8(r, a, b)
Operates on the 8-word arrays a and b and the 16-word array r.
The following functions are implemented in C:
bn_cmp_words(a, b, n)
Operates on the n word arrays a and b. It returns 1, 0 and -1 if a
is greater than, equal and less than b.
bn_mul_normal(r, a, na, b, nb)
Operates on the na word array a, the nb word array b and the na+nb
word array r. It computes a*b and places the result in r.
bn_mul_low_normal(r, a, b, n)
Operates on the n word arrays r, a and b. It computes the n low
words of a*b and places the result in r.
bn_mul_recursive(r, a, b, n2, t)
Operates on the n2 word arrays a and b and the 2*n2 word arrays r
and t. The n2 must be a power of 2. It computes a*b and places the
result in r.
bn_mul_part_recursive(r, a, b, tn, n, tmp)
Operates on the n+tn word arrays a and b and the 4*n word arrays r
and tmp.
bn_mul_low_recursive(r, a, b, n2, tmp)
Operates on the n2 word arrays r and tmp and the n2/2 word arrays a
and b.
bn_mul_high(r, a, b, l, n2, tmp)
Operates on the n2 word arrays r, a, b and l (?) and the 3*n2 word
array tmp.
BN_mul() calls bn_mul_normal(), or an optimized implementation if
the factors have the same size: bn_mul_comba8() is used if they are
8 words long, bn_mul_recursive() if they are larger than
BN_MULL_SIZE_NORMAL and the size is an exact multiple of the word
size, and bn_mul_part_recursive() for others that are larger than
BN_MULL_SIZE_NORMAL.
bn_sqr_normal(r, a, n, tmp)
Operates on the n word array a and the 2*n word arrays tmp and r.
The implementations use the following macros which, depending on the
architecture, may use "long long" C operations or inline assembler. They
are defined in bn_lcl.h.
mul(r, a, w, c)
Computes w*a+c and places the low word of the result in r and the
high word in c.
mul_add(r, a, w, c)
Computes w*a+r+c and places the low word of the result in r and the
high word in c.
sqr(r0, r1, a)
Computes a*a and places the low word of the result in r0 and the
high word in r1.
Size changes
The bn_expand() macro ensures that b has enough space for a bits bit
number. The bn_wexpand() macro ensures that b has enough space for an n
word number. If the number has to be expanded, both macros call
bn_expand2(), which allocates a new d array and copies the data. They
return NULL on error, b otherwise.
The bn_fix_top() macro reduces a->top to point to the most significant
non-zero word when a has shrunk.
Debugging
The bn_check_top() verifies that ((a)->top >= 0 && (a)->top <= (a)->max). A
violation will cause the program to abort.
The bn_print() prints a to stderr. bn_dump() prints n words at d (in
reverse order, i.e. most significant word first) to stderr.
The bn_set_max() makes a a static number with a max of its current size.
This is used by bn_set_low() and bn_set_high() to make r a read-only BIGNUM
that contains the n low or high words of a.
If BN_DEBUG is not defined, bn_check_top(), bn_print(), bn_dump(), and
bn_set_max() are defined as empty macros.
SEE ALSO
Functions: bn(3)
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Alphabetical
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