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 BN_ULONG bn_mul_words(BN_ULONG *rp, BN_ULONG *ap, int num, BN_ULONG w);
17 BN_ULONG bn_mul_add_words(BN_ULONG *rp, BN_ULONG *ap, int num,
18   BN_ULONG w);
19 void     bn_sqr_words(BN_ULONG *rp, BN_ULONG *ap, int num);
20 BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d);
21 BN_ULONG bn_add_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp,
22   int num);
23 BN_ULONG bn_sub_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp,
24   int num);
25
26 void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
27 void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
28 void bn_sqr_comba4(BN_ULONG *r, BN_ULONG *a);
29 void bn_sqr_comba8(BN_ULONG *r, BN_ULONG *a);
30
31 int bn_cmp_words(BN_ULONG *a, BN_ULONG *b, int n);
32
33 void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b,
34   int nb);
35 void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n);
36 void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
37   int dna,int dnb,BN_ULONG *tmp);
38 void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b,
39   int n, int tna,int tnb, BN_ULONG *tmp);
40 void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b,
41   int n2, BN_ULONG *tmp);
42 void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l,
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
74        {
75        int top;      /* number of words used in d */
76        BN_ULONG *d;  /* pointer to an array containing the integer value */
77        int max;      /* size of the d array */
78        int neg;      /* sign */
79        } BIGNUM;
80
81The integer value is stored in B<d>, a malloc()ed array of words (B<BN_ULONG>),
82least significant word first. A B<BN_ULONG> can be either 16, 32 or 64 bits
83in size, depending on the 'number of bits' (B<BITS2>) specified in
84C<openssl/bn.h>.
85
86B<max> is the size of the B<d> array that has been allocated.  B<top>
87is the number of words being used, so for a value of 4, bn.d[0]=4 and
88bn.top=1.  B<neg> is 1 if the number is negative.  When a B<BIGNUM> is
89B<0>, the B<d> field can be B<NULL> and B<top> == B<0>.
90
91Various routines in this library require the use of temporary
92B<BIGNUM> variables during their execution.  Since dynamic memory
93allocation to create B<BIGNUM>s is rather expensive when used in
94conjunction with repeated subroutine calls, the B<BN_CTX> structure is
95used.  This structure contains B<BN_CTX_NUM> B<BIGNUM>s, see
96L<BN_CTX_start(3)|BN_CTX_start(3)>.
97
98=head2 Low-level arithmetic operations
99
100These functions are implemented in C and for several platforms in
101assembly language:
102
103bn_mul_words(B<rp>, B<ap>, B<num>, B<w>) operates on the B<num> word
104arrays B<rp> and B<ap>.  It computes B<ap> * B<w>, places the result
105in B<rp>, and returns the high word (carry).
106
107bn_mul_add_words(B<rp>, B<ap>, B<num>, B<w>) operates on the B<num>
108word arrays B<rp> and B<ap>.  It computes B<ap> * B<w> + B<rp>, places
109the result in B<rp>, and returns the high word (carry).
110
111bn_sqr_words(B<rp>, B<ap>, B<n>) operates on the B<num> word array
112B<ap> and the 2*B<num> word array B<ap>.  It computes B<ap> * B<ap>
113word-wise, and places the low and high bytes of the result in B<rp>.
114
115bn_div_words(B<h>, B<l>, B<d>) divides the two word number (B<h>,B<l>)
116by B<d> and returns the result.
117
118bn_add_words(B<rp>, B<ap>, B<bp>, B<num>) operates on the B<num> word
119arrays B<ap>, B<bp> and B<rp>.  It computes B<ap> + B<bp>, places the
120result in B<rp>, and returns the high word (carry).
121
122bn_sub_words(B<rp>, B<ap>, B<bp>, B<num>) operates on the B<num> word
123arrays B<ap>, B<bp> and B<rp>.  It computes B<ap> - B<bp>, places the
124result in B<rp>, and returns the carry (1 if B<bp> E<gt> B<ap>, 0
125otherwise).
126
127bn_mul_comba4(B<r>, B<a>, B<b>) operates on the 4 word arrays B<a> and
128B<b> and the 8 word array B<r>.  It computes B<a>*B<b> and places the
129result in B<r>.
130
131bn_mul_comba8(B<r>, B<a>, B<b>) operates on the 8 word arrays B<a> and
132B<b> and the 16 word array B<r>.  It computes B<a>*B<b> and places the
133result in B<r>.
134
135bn_sqr_comba4(B<r>, B<a>, B<b>) operates on the 4 word arrays B<a> and
136B<b> and the 8 word array B<r>.
137
138bn_sqr_comba8(B<r>, B<a>, B<b>) operates on the 8 word arrays B<a> and
139B<b> and the 16 word array B<r>.
140
141The following functions are implemented in C:
142
143bn_cmp_words(B<a>, B<b>, B<n>) operates on the B<n> word arrays B<a>
144and B<b>.  It returns 1, 0 and -1 if B<a> is greater than, equal and
145less than B<b>.
146
147bn_mul_normal(B<r>, B<a>, B<na>, B<b>, B<nb>) operates on the B<na>
148word array B<a>, the B<nb> word array B<b> and the B<na>+B<nb> word
149array B<r>.  It computes B<a>*B<b> and places the result in B<r>.
150
151bn_mul_low_normal(B<r>, B<a>, B<b>, B<n>) operates on the B<n> word
152arrays B<r>, B<a> and B<b>.  It computes the B<n> low words of
153B<a>*B<b> and places the result in B<r>.
154
155bn_mul_recursive(B<r>, B<a>, B<b>, B<n2>, B<dna>, B<dnb>, B<t>) operates
156on the word arrays B<a> and B<b> of length B<n2>+B<dna> and B<n2>+B<dnb>
157(B<dna> and B<dnb> are currently allowed to be 0 or negative) and the 2*B<n2>
158word arrays B<r> and B<t>.  B<n2> must be a power of 2.  It computes
159B<a>*B<b> and places the result in B<r>.
160
161bn_mul_part_recursive(B<r>, B<a>, B<b>, B<n>, B<tna>, B<tnb>, B<tmp>)
162operates on the word arrays B<a> and B<b> of length B<n>+B<tna> and
163B<n>+B<tnb> and the 4*B<n> word arrays B<r> and B<tmp>.
164
165bn_mul_low_recursive(B<r>, B<a>, B<b>, B<n2>, B<tmp>) operates on the
166B<n2> word arrays B<r> and B<tmp> and the B<n2>/2 word arrays B<a>
167and B<b>.
168
169bn_mul_high(B<r>, B<a>, B<b>, B<l>, B<n2>, B<tmp>) operates on the
170B<n2> word arrays B<r>, B<a>, B<b> and B<l> (?) and the 3*B<n2> word
171array B<tmp>.
172
173BN_mul() calls bn_mul_normal(), or an optimized implementation if the
174factors have the same size: bn_mul_comba8() is used if they are 8
175words long, bn_mul_recursive() if they are larger than
176B<BN_MULL_SIZE_NORMAL> and the size is an exact multiple of the word
177size, and bn_mul_part_recursive() for others that are larger than
178B<BN_MULL_SIZE_NORMAL>.
179
180bn_sqr_normal(B<r>, B<a>, B<n>, B<tmp>) operates on the B<n> word array
181B<a> and the 2*B<n> word arrays B<tmp> and B<r>.
182
183The implementations use the following macros which, depending on the
184architecture, may use "long long" C operations or inline assembler.
185They are defined in C<bn_lcl.h>.
186
187mul(B<r>, B<a>, B<w>, B<c>) computes B<w>*B<a>+B<c> and places the
188low word of the result in B<r> and the high word in B<c>.
189
190mul_add(B<r>, B<a>, B<w>, B<c>) computes B<w>*B<a>+B<r>+B<c> and
191places the low word of the result in B<r> and the high word in B<c>.
192
193sqr(B<r0>, B<r1>, B<a>) computes B<a>*B<a> and places the low word
194of the result in B<r0> and the high word in B<r1>.
195
196=head2 Size changes
197
198bn_expand() ensures that B<b> has enough space for a B<bits> bit
199number.  bn_wexpand() ensures that B<b> has enough space for an
200B<n> word number.  If the number has to be expanded, both macros
201call bn_expand2(), which allocates a new B<d> array and copies the
202data.  They return B<NULL> on error, B<b> otherwise.
203
204The bn_fix_top() macro reduces B<a-E<gt>top> to point to the most
205significant non-zero word plus one when B<a> has shrunk.
206
207=head2 Debugging
208
209bn_check_top() verifies that C<((a)-E<gt>top E<gt>= 0 && (a)-E<gt>top
210E<lt>= (a)-E<gt>max)>.  A violation will cause the program to abort.
211
212bn_print() prints B<a> to stderr. bn_dump() prints B<n> words at B<d>
213(in reverse order, i.e. most significant word first) to stderr.
214
215bn_set_max() makes B<a> a static number with a B<max> of its current size.
216This is used by bn_set_low() and bn_set_high() to make B<r> a read-only
217B<BIGNUM> that contains the B<n> low or high words of B<a>.
218
219If B<BN_DEBUG> is not defined, bn_check_top(), bn_print(), bn_dump()
220and bn_set_max() are defined as empty macros.
221
222=head1 SEE ALSO
223
224L<bn(3)|bn(3)>
225
226=cut
227