™.. bn_internal - Online Linux Manual PageSection : 3
Updated : 2013-02-11
Source : 1.0.1e
Note : OpenSSL
NAMEbn_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​ #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);
DESCRIPTIONThis 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 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 (BN_ULONG), least significant word first. A BN_ULONG can be either 16, 32 or 64 bits in size, depending on the 'number of bits' (BITS2) specified in ​\*(C`openssl/bn.h\*(C'\fR. ​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 BIGNUM is ​0, the d field can be NULL and top == 0. ​flags is a bit field of flags which are defined in \*(C`openssl/bn.h\*(C'\fR. The flags begin with BN_FLG_. The macros BN_set_flags(b,n) and BN_get_flags(b,n) exist to enable or fetch flag(s) n from BIGNUM structure b. 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 operationsThese 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_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 \*(C`bn_lcl.h\*(C'\fR. 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 plus one when a has shrunk.
Debugging​bn_check_top() verifies that \*(C`((a)\->top >= 0 && (a)\->top <= (a)−>dmax)\*(C'\fR. 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 ​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​bn (3) 0
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