bn_sqr_words (3)
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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 functionsSYNOPSIS
#include <openssl/bn.h> 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, int dna,int dnb,BN_ULONG *tmp); void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n, int tna,int tnb, 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 documents the internal functions used by the OpenSSLThe BIGNUM structure
typedef struct bignum_st BIGNUM; struct bignum_st { BN_ULONG *d; /* Pointer to an array of 'BN_BITS2' bit chunks. */ int top; /* Index of last used d +1. */ /* The next are internal book keeping for bn_expand. */ int dmax; /* Size of the d array. */ int neg; /* one if the number is negative */ int flags; };
The integer value is stored in d, a malloc()ed array of words (
dmax is the size of the d array that has been allocated. top is the number of words 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
flags is a bit field of flags which are defined in "openssl/bn.h". The flags begin with
Various routines in this library require the use of temporary
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, dna, dnb, t) operates on the word arrays a and b of length n2+dna and n2+dnb (dna and dnb are currently allowed to be 0 or negative) 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, n, tna, tnb, tmp) operates on the word arrays a and b of length n+tna and n+tnb 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_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 returnThe bn_fix_top() macro reduces a->top to point to the most significant non-zero word plus one when a has shrunk.
Debugging
bn_check_top() verifies that "((a)->top >= 0 && (a)->top <= (a)->dmax)". 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.
bn_set_max() makes a a static number with a dmax of its current size. This is used by bn_set_low() and bn_set_high() to make r a read-only
If