=pod =head1 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_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 =head1 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_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); =head1 DESCRIPTION This page documents the internal functions used by the OpenSSL B<BIGNUM> implementation. They are described here to facilitate debugging and extending the library. They are I<not> to be used by applications. =head2 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 B<d>, a malloc()ed array of words (B<BN_ULONG>), least significant word first. A B<BN_ULONG> can be either 16, 32 or 64 bits in size, depending on the 'number of bits' (B<BITS2>) specified in C<openssl/bn.h>. B<dmax> is the size of the B<d> array that has been allocated. B<top> is the number of words being used, so for a value of 4, bn.d[0]=4 and bn.top=1. B<neg> is 1 if the number is negative. When a B<BIGNUM> is B<0>, the B<d> field can be B<NULL> and B<top> == B<0>. B<flags> is a bit field of flags which are defined in C<openssl/bn.h>. The flags begin with B<BN_FLG_>. The macros BN_set_flags(b, n) and BN_get_flags(b, n) exist to enable or fetch flag(s) B<n> from B<BIGNUM> structure B. Various routines in this library require the use of temporary B<BIGNUM> variables during their execution. Since dynamic memory allocation to create B<BIGNUM>s is rather expensive when used in conjunction with repeated subroutine calls, the B<BN_CTX> structure is used. This structure contains B<BN_CTX_NUM> B<BIGNUM>s, see L<BN_CTX_start(3)>. =head2 Low-level arithmetic operations These functions are implemented in C and for several platforms in assembly language: bn_mul_words(B<rp>, B<ap>, B<num>, B<w>) operates on the B<num> word arrays B<rp> and B<ap>. It computes B<ap> * B<w>, places the result in B<rp>, and returns the high word (carry). bn_mul_add_words(B<rp>, B<ap>, B<num>, B<w>) operates on the B<num> word arrays B<rp> and B<ap>. It computes B<ap> * B<w> + B<rp>, places the result in B<rp>, and returns the high word (carry). bn_sqr_words(B<rp>, B<ap>, B<n>) operates on the B<num> word array B<ap> and the 2*B<num> word array B<ap>. It computes B<ap> * B<ap> word-wise, and places the low and high bytes of the result in B<rp>. bn_div_words(B<h>, B<l>, B<d>) divides the two word number (B<h>, B<l>) by B<d> and returns the result. bn_add_words(B<rp>, B<ap>, B<bp>, B<num>) operates on the B<num> word arrays B<ap>, B<bp> and B<rp>. It computes B<ap> + B<bp>, places the result in B<rp>, and returns the high word (carry). bn_sub_words(B<rp>, B<ap>, B<bp>, B<num>) operates on the B<num> word arrays B<ap>, B<bp> and B<rp>. It computes B<ap> - B<bp>, places the result in B<rp>, and returns the carry (1 if B<bp> E<gt> B<ap>, 0 otherwise). bn_mul_comba4(B<r>, B, B) operates on the 4 word arrays B and B and the 8 word array B<r>. It computes B*B and places the result in B<r>. bn_mul_comba8(B<r>, B, B) operates on the 8 word arrays B and B and the 16 word array B<r>. It computes B*B and places the result in B<r>. bn_sqr_comba4(B<r>, B, B) operates on the 4 word arrays B and B and the 8 word array B<r>. bn_sqr_comba8(B<r>, B, B) operates on the 8 word arrays B and B and the 16 word array B<r>. The following functions are implemented in C: bn_cmp_words(B, B, B<n>) operates on the B<n> word arrays B and B. It returns 1, 0 and -1 if B is greater than, equal and less than B. bn_mul_normal(B<r>, B, B<na>, B, B<nb>) operates on the B<na> word array B, the B<nb> word array B and the B<na>+B<nb> word array B<r>. It computes B*B and places the result in B<r>. bn_mul_low_normal(B<r>, B, B, B<n>) operates on the B<n> word arrays B<r>, B and B. It computes the B<n> low words of B*B and places the result in B<r>. bn_mul_recursive(B<r>, B, B, B<n2>, B<dna>, B<dnb>, B<t>) operates on the word arrays B and B of length B<n2>+B<dna> and B<n2>+B<dnb> (B<dna> and B<dnb> are currently allowed to be 0 or negative) and the 2*B<n2> word arrays B<r> and B<t>. B<n2> must be a power of 2. It computes B*B and places the result in B<r>. bn_mul_part_recursive(B<r>, B, B, B<n>, B<tna>, B<tnb>, B<tmp>) operates on the word arrays B and B of length B<n>+B<tna> and B<n>+B<tnb> and the 4*B<n> word arrays B<r> and B<tmp>. bn_mul_low_recursive(B<r>, B, B, B<n2>, B<tmp>) operates on the B<n2> word arrays B<r> and B<tmp> and the B<n2>/2 word arrays B and B. 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 B<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 B<BN_MULL_SIZE_NORMAL>. bn_sqr_normal(B<r>, B, B<n>, B<tmp>) operates on the B<n> word array B and the 2*B<n> word arrays B<tmp> and B<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_local.h>. mul(B<r>, B, B<w>, B<c>) computes B<w>*B+B<c> and places the low word of the result in B<r> and the high word in B<c>. mul_add(B<r>, B, B<w>, B<c>) computes B<w>*B+B<r>+B<c> and places the low word of the result in B<r> and the high word in B<c>. sqr(B<r0>, B<r1>, B) computes B*B and places the low word of the result in B<r0> and the high word in B<r1>. =head2 Size changes bn_expand() ensures that B has enough space for a B<bits> bit number. bn_wexpand() ensures that B has enough space for an B<n> word number. If the number has to be expanded, both macros call bn_expand2(), which allocates a new B<d> array and copies the data. They return B<NULL> on error, B otherwise. The bn_fix_top() macro reduces B<a-E<gt>top> to point to the most significant non-zero word plus one when B has shrunk. =head2 Debugging bn_check_top() verifies that C<((a)-E<gt>top E<gt>= 0 && (a)-E<gt>top E<lt>= (a)-E<gt>dmax)>. A violation will cause the program to abort. bn_print() prints B to stderr. bn_dump() prints B<n> words at B<d> (in reverse order, i.e. most significant word first) to stderr. bn_set_max() makes B a static number with a B<dmax> of its current size. This is used by bn_set_low() and bn_set_high() to make B<r> a read-only B<BIGNUM> that contains the B<n> low or high words of B. If B<BN_DEBUG> is not defined, bn_check_top(), bn_print(), bn_dump() and bn_set_max() are defined as empty macros. =head1 SEE ALSO L<bn(3)> =head1 COPYRIGHT Copyright 2000-2016 The OpenSSL Project Authors. All Rights Reserved. Licensed under the OpenSSL license (the "License"). You may not use this file except in compliance with the License. You can obtain a copy in the file LICENSE in the source distribution or at L<https://www.openssl.org/source/license.html>. =cut