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