1=pod
2
3=head1 NAME
4
5bn_mul_words, bn_mul_add_words, bn_sqr_words, bn_div_words,
6bn_add_words, bn_sub_words, bn_mul_comba4, bn_mul_comba8,
7bn_sqr_comba4, bn_sqr_comba8, bn_cmp_words, bn_mul_normal,
8bn_mul_low_normal, bn_mul_recursive, bn_mul_part_recursive,
9bn_mul_low_recursive, bn_sqr_normal, bn_sqr_recursive,
10bn_expand, bn_wexpand, bn_expand2, bn_fix_top, bn_check_top,
11bn_print, bn_dump, bn_set_max, bn_set_high, bn_set_low - BIGNUM
12library internal functions
13
14=head1 SYNOPSIS
15
16 #include <openssl/bn.h>
17
18 BN_ULONG bn_mul_words(BN_ULONG *rp, BN_ULONG *ap, int num, BN_ULONG w);
19 BN_ULONG bn_mul_add_words(BN_ULONG *rp, BN_ULONG *ap, int num,
20 BN_ULONG w);
21 void bn_sqr_words(BN_ULONG *rp, BN_ULONG *ap, int num);
22 BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d);
23 BN_ULONG bn_add_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp,
24 int num);
25 BN_ULONG bn_sub_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp,
26 int num);
27
28 void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
29 void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
30 void bn_sqr_comba4(BN_ULONG *r, BN_ULONG *a);
31 void bn_sqr_comba8(BN_ULONG *r, BN_ULONG *a);
32
33 int bn_cmp_words(BN_ULONG *a, BN_ULONG *b, int n);
34
35 void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b,
36 int nb);
37 void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n);
38 void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
39 int dna, int dnb, BN_ULONG *tmp);
40 void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b,
41 int n, int tna, int tnb, BN_ULONG *tmp);
42 void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b,
43 int n2, BN_ULONG *tmp);
44
45 void bn_sqr_normal(BN_ULONG *r, BN_ULONG *a, int n, BN_ULONG *tmp);
46 void bn_sqr_recursive(BN_ULONG *r, BN_ULONG *a, int n2, BN_ULONG *tmp);
47
48 void mul(BN_ULONG r, BN_ULONG a, BN_ULONG w, BN_ULONG c);
49 void mul_add(BN_ULONG r, BN_ULONG a, BN_ULONG w, BN_ULONG c);
50 void sqr(BN_ULONG r0, BN_ULONG r1, BN_ULONG a);
51
52 BIGNUM *bn_expand(BIGNUM *a, int bits);
53 BIGNUM *bn_wexpand(BIGNUM *a, int n);
54 BIGNUM *bn_expand2(BIGNUM *a, int n);
55 void bn_fix_top(BIGNUM *a);
56
57 void bn_check_top(BIGNUM *a);
58 void bn_print(BIGNUM *a);
59 void bn_dump(BN_ULONG *d, int n);
60 void bn_set_max(BIGNUM *a);
61 void bn_set_high(BIGNUM *r, BIGNUM *a, int n);
62 void bn_set_low(BIGNUM *r, BIGNUM *a, int n);
63
64=head1 DESCRIPTION
65
66This page documents the internal functions used by the OpenSSL
67B<BIGNUM> implementation. They are described here to facilitate
68debugging and extending the library. They are I<not> to be used by
69applications.
70
71=head2 The BIGNUM structure
72
73 typedef struct bignum_st BIGNUM;
74
75 struct bignum_st
76 {
77 BN_ULONG *d; /* Pointer to an array of 'BN_BITS2' bit chunks. */
78 int top; /* Index of last used d +1. */
79 /* The next are internal book keeping for bn_expand. */
80 int dmax; /* Size of the d array. */
81 int neg; /* one if the number is negative */
82 int flags;
83 };
84
85
86The integer value is stored in B<d>, a malloc()ed array of words (B<BN_ULONG>),
87least significant word first. A B<BN_ULONG> can be either 16, 32 or 64 bits
88in size, depending on the 'number of bits' (B<BITS2>) specified in
89C<openssl/bn.h>.
90
91B<dmax> is the size of the B<d> array that has been allocated. B<top>
92is the number of words being used, so for a value of 4, bn.d[0]=4 and
93bn.top=1. B<neg> is 1 if the number is negative. When a B<BIGNUM> is
94B<0>, the B<d> field can be B<NULL> and B<top> == B<0>.
95
96B<flags> is a bit field of flags which are defined in C<openssl/bn.h>. The
97flags begin with B<BN_FLG_>. The macros BN_set_flags(b, n) and
98BN_get_flags(b, n) exist to enable or fetch flag(s) B<n> from B<BIGNUM>
99structure B<b>.
100
101Various routines in this library require the use of temporary
102B<BIGNUM> variables during their execution. Since dynamic memory
103allocation to create B<BIGNUM>s is rather expensive when used in
104conjunction with repeated subroutine calls, the B<BN_CTX> structure is
105used. This structure contains B<BN_CTX_NUM> B<BIGNUM>s, see
106L<BN_CTX_start(3)>.
107
108=head2 Low-level arithmetic operations
109
110These functions are implemented in C and for several platforms in
111assembly language:
112
113bn_mul_words(B<rp>, B<ap>, B<num>, B<w>) operates on the B<num> word
114arrays B<rp> and B<ap>. It computes B<ap> * B<w>, places the result
115in B<rp>, and returns the high word (carry).
116
117bn_mul_add_words(B<rp>, B<ap>, B<num>, B<w>) operates on the B<num>
118word arrays B<rp> and B<ap>. It computes B<ap> * B<w> + B<rp>, places
119the result in B<rp>, and returns the high word (carry).
120
121bn_sqr_words(B<rp>, B<ap>, B<n>) operates on the B<num> word array
122B<ap> and the 2*B<num> word array B<ap>. It computes B<ap> * B<ap>
123word-wise, and places the low and high bytes of the result in B<rp>.
124
125bn_div_words(B<h>, B<l>, B<d>) divides the two word number (B<h>, B<l>)
126by B<d> and returns the result.
127
128bn_add_words(B<rp>, B<ap>, B<bp>, B<num>) operates on the B<num> word
129arrays B<ap>, B<bp> and B<rp>. It computes B<ap> + B<bp>, places the
130result in B<rp>, and returns the high word (carry).
131
132bn_sub_words(B<rp>, B<ap>, B<bp>, B<num>) operates on the B<num> word
133arrays B<ap>, B<bp> and B<rp>. It computes B<ap> - B<bp>, places the
134result in B<rp>, and returns the carry (1 if B<bp> E<gt> B<ap>, 0
135otherwise).
136
137bn_mul_comba4(B<r>, B<a>, B<b>) operates on the 4 word arrays B<a> and
138B<b> and the 8 word array B<r>. It computes B<a>*B<b> and places the
139result in B<r>.
140
141bn_mul_comba8(B<r>, B<a>, B<b>) operates on the 8 word arrays B<a> and
142B<b> and the 16 word array B<r>. It computes B<a>*B<b> and places the
143result in B<r>.
144
145bn_sqr_comba4(B<r>, B<a>, B<b>) operates on the 4 word arrays B<a> and
146B<b> and the 8 word array B<r>.
147
148bn_sqr_comba8(B<r>, B<a>, B<b>) operates on the 8 word arrays B<a> and
149B<b> and the 16 word array B<r>.
150
151The following functions are implemented in C:
152
153bn_cmp_words(B<a>, B<b>, B<n>) operates on the B<n> word arrays B<a>
154and B<b>. It returns 1, 0 and -1 if B<a> is greater than, equal and
155less than B<b>.
156
157bn_mul_normal(B<r>, B<a>, B<na>, B<b>, B<nb>) operates on the B<na>
158word array B<a>, the B<nb> word array B<b> and the B<na>+B<nb> word
159array B<r>. It computes B<a>*B<b> and places the result in B<r>.
160
161bn_mul_low_normal(B<r>, B<a>, B<b>, B<n>) operates on the B<n> word
162arrays B<r>, B<a> and B<b>. It computes the B<n> low words of
163B<a>*B<b> and places the result in B<r>.
164
165bn_mul_recursive(B<r>, B<a>, B<b>, B<n2>, B<dna>, B<dnb>, B<t>) operates
166on the word arrays B<a> and B<b> of length B<n2>+B<dna> and B<n2>+B<dnb>
167(B<dna> and B<dnb> are currently allowed to be 0 or negative) and the 2*B<n2>
168word arrays B<r> and B<t>. B<n2> must be a power of 2. It computes
169B<a>*B<b> and places the result in B<r>.
170
171bn_mul_part_recursive(B<r>, B<a>, B<b>, B<n>, B<tna>, B<tnb>, B<tmp>)
172operates on the word arrays B<a> and B<b> of length B<n>+B<tna> and
173B<n>+B<tnb> and the 4*B<n> word arrays B<r> and B<tmp>.
174
175bn_mul_low_recursive(B<r>, B<a>, B<b>, B<n2>, B<tmp>) operates on the
176B<n2> word arrays B<r> and B<tmp> and the B<n2>/2 word arrays B<a>
177and B<b>.
178
179BN_mul() calls bn_mul_normal(), or an optimized implementation if the
180factors have the same size: bn_mul_comba8() is used if they are 8
181words long, bn_mul_recursive() if they are larger than
182B<BN_MULL_SIZE_NORMAL> and the size is an exact multiple of the word
183size, and bn_mul_part_recursive() for others that are larger than
184B<BN_MULL_SIZE_NORMAL>.
185
186bn_sqr_normal(B<r>, B<a>, B<n>, B<tmp>) operates on the B<n> word array
187B<a> and the 2*B<n> word arrays B<tmp> and B<r>.
188
189The implementations use the following macros which, depending on the
190architecture, may use "long long" C operations or inline assembler.
191They are defined in C<bn_local.h>.
192
193mul(B<r>, B<a>, B<w>, B<c>) computes B<w>*B<a>+B<c> and places the
194low word of the result in B<r> and the high word in B<c>.
195
196mul_add(B<r>, B<a>, B<w>, B<c>) computes B<w>*B<a>+B<r>+B<c> and
197places the low word of the result in B<r> and the high word in B<c>.
198
199sqr(B<r0>, B<r1>, B<a>) computes B<a>*B<a> and places the low word
200of the result in B<r0> and the high word in B<r1>.
201
202=head2 Size changes
203
204bn_expand() ensures that B<b> has enough space for a B<bits> bit
205number. bn_wexpand() ensures that B<b> has enough space for an
206B<n> word number. If the number has to be expanded, both macros
207call bn_expand2(), which allocates a new B<d> array and copies the
208data. They return B<NULL> on error, B<b> otherwise.
209
210The bn_fix_top() macro reduces B<a-E<gt>top> to point to the most
211significant non-zero word plus one when B<a> has shrunk.
212
213=head2 Debugging
214
215bn_check_top() verifies that C<((a)-E<gt>top E<gt>= 0 && (a)-E<gt>top
216E<lt>= (a)-E<gt>dmax)>. A violation will cause the program to abort.
217
218bn_print() prints B<a> to stderr. bn_dump() prints B<n> words at B<d>
219(in reverse order, i.e. most significant word first) to stderr.
220
221bn_set_max() makes B<a> a static number with a B<dmax> of its current size.
222This is used by bn_set_low() and bn_set_high() to make B<r> a read-only
223B<BIGNUM> that contains the B<n> low or high words of B<a>.
224
225If B<BN_DEBUG> is not defined, bn_check_top(), bn_print(), bn_dump()
226and bn_set_max() are defined as empty macros.
227
228=head1 SEE ALSO
229
230L<bn(3)>
231
232=head1 COPYRIGHT
233
234Copyright 2000-2016 The OpenSSL Project Authors. All Rights Reserved.
235
236Licensed under the Apache License 2.0 (the "License"). You may not use
237this file except in compliance with the License. You can obtain a copy
238in the file LICENSE in the source distribution or at
239L<https://www.openssl.org/source/license.html>.
240
241=cut
242
