bn_internal(3) OpenSSL bn_internal(3)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
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);
26/Feb/2001 0.9.6 1
bn_internal(3) OpenSSL bn_internal(3)
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 documents 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()ed 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.
max is the size of the d array that has been allocated.
top is the 'last' entry being used, so for a value of 4,
bn.d[0]=4 and bn.top=1. 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
26/Feb/2001 0.9.6 2
bn_internal(3) OpenSSL bn_internal(3)
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. 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
26/Feb/2001 0.9.6 3
bn_internal(3) OpenSSL bn_internal(3)
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
bn_expand() ensures that b has enough space for a bits bit
number. bn_wexpand() 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
bn_check_top() verifies that ((a)->top >= 0 && (a)->top <=
(a)->max). A violation will cause the program to abort.
bn_print() prints a to stderr. bn_dump() prints n words at
d (in reverse order, i.e. most significant word first) to
stderr.
26/Feb/2001 0.9.6 4
bn_internal(3) OpenSSL bn_internal(3)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 ALSObn(3)
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"
26/Feb/2001 0.9.6 5
