5 bn_mul_words, bn_mul_add_words, bn_sqr_words, bn_div_words,
6 bn_add_words, bn_sub_words, bn_mul_comba4, bn_mul_comba8,
7 bn_sqr_comba4, bn_sqr_comba8, bn_cmp_words, bn_mul_normal,
8 bn_mul_low_normal, bn_mul_recursive, bn_mul_part_recursive,
9 bn_mul_low_recursive, bn_sqr_normal, bn_sqr_recursive,
10 bn_expand, bn_wexpand, bn_expand2, bn_fix_top, bn_check_top,
11 bn_print, bn_dump, bn_set_max, bn_set_high, bn_set_low - BIGNUM
12 library internal functions
16 #include <openssl/bn.h>
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,
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,
25 BN_ULONG bn_sub_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp,
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);
33 int bn_cmp_words(BN_ULONG *a, BN_ULONG *b, int n);
35 void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b,
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);
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);
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);
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);
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);
66 This page documents the internal functions used by the OpenSSL
67 B<BIGNUM> implementation. They are described here to facilitate
68 debugging and extending the library. They are I<not> to be used by
71 =head2 The BIGNUM structure
73 typedef struct bignum_st BIGNUM;
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 */
86 The integer value is stored in B<d>, a malloc()ed array of words (B<BN_ULONG>),
87 least significant word first. A B<BN_ULONG> can be either 16, 32 or 64 bits
88 in size, depending on the 'number of bits' (B<BITS2>) specified in
91 B<dmax> is the size of the B<d> array that has been allocated. B<top>
92 is the number of words being used, so for a value of 4, bn.d[0]=4 and
93 bn.top=1. B<neg> is 1 if the number is negative. When a B<BIGNUM> is
94 B<0>, the B<d> field can be B<NULL> and B<top> == B<0>.
96 B<flags> is a bit field of flags which are defined in C<openssl/bn.h>. The
97 flags begin with B<BN_FLG_>. The macros BN_set_flags(b, n) and
98 BN_get_flags(b, n) exist to enable or fetch flag(s) B<n> from B<BIGNUM>
101 Various routines in this library require the use of temporary
102 B<BIGNUM> variables during their execution. Since dynamic memory
103 allocation to create B<BIGNUM>s is rather expensive when used in
104 conjunction with repeated subroutine calls, the B<BN_CTX> structure is
105 used. This structure contains B<BN_CTX_NUM> B<BIGNUM>s, see
108 =head2 Low-level arithmetic operations
110 These functions are implemented in C and for several platforms in
113 bn_mul_words(B<rp>, B<ap>, B<num>, B<w>) operates on the B<num> word
114 arrays B<rp> and B<ap>. It computes B<ap> * B<w>, places the result
115 in B<rp>, and returns the high word (carry).
117 bn_mul_add_words(B<rp>, B<ap>, B<num>, B<w>) operates on the B<num>
118 word arrays B<rp> and B<ap>. It computes B<ap> * B<w> + B<rp>, places
119 the result in B<rp>, and returns the high word (carry).
121 bn_sqr_words(B<rp>, B<ap>, B<n>) operates on the B<num> word array
122 B<ap> and the 2*B<num> word array B<ap>. It computes B<ap> * B<ap>
123 word-wise, and places the low and high bytes of the result in B<rp>.
125 bn_div_words(B<h>, B<l>, B<d>) divides the two word number (B<h>, B<l>)
126 by B<d> and returns the result.
128 bn_add_words(B<rp>, B<ap>, B<bp>, B<num>) operates on the B<num> word
129 arrays B<ap>, B<bp> and B<rp>. It computes B<ap> + B<bp>, places the
130 result in B<rp>, and returns the high word (carry).
132 bn_sub_words(B<rp>, B<ap>, B<bp>, B<num>) operates on the B<num> word
133 arrays B<ap>, B<bp> and B<rp>. It computes B<ap> - B<bp>, places the
134 result in B<rp>, and returns the carry (1 if B<bp> E<gt> B<ap>, 0
137 bn_mul_comba4(B<r>, B<a>, B<b>) operates on the 4 word arrays B<a> and
138 B<b> and the 8 word array B<r>. It computes B<a>*B<b> and places the
141 bn_mul_comba8(B<r>, B<a>, B<b>) operates on the 8 word arrays B<a> and
142 B<b> and the 16 word array B<r>. It computes B<a>*B<b> and places the
145 bn_sqr_comba4(B<r>, B<a>, B<b>) operates on the 4 word arrays B<a> and
146 B<b> and the 8 word array B<r>.
148 bn_sqr_comba8(B<r>, B<a>, B<b>) operates on the 8 word arrays B<a> and
149 B<b> and the 16 word array B<r>.
151 The following functions are implemented in C:
153 bn_cmp_words(B<a>, B<b>, B<n>) operates on the B<n> word arrays B<a>
154 and B<b>. It returns 1, 0 and -1 if B<a> is greater than, equal and
157 bn_mul_normal(B<r>, B<a>, B<na>, B<b>, B<nb>) operates on the B<na>
158 word array B<a>, the B<nb> word array B<b> and the B<na>+B<nb> word
159 array B<r>. It computes B<a>*B<b> and places the result in B<r>.
161 bn_mul_low_normal(B<r>, B<a>, B<b>, B<n>) operates on the B<n> word
162 arrays B<r>, B<a> and B<b>. It computes the B<n> low words of
163 B<a>*B<b> and places the result in B<r>.
165 bn_mul_recursive(B<r>, B<a>, B<b>, B<n2>, B<dna>, B<dnb>, B<t>) operates
166 on 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>
168 word arrays B<r> and B<t>. B<n2> must be a power of 2. It computes
169 B<a>*B<b> and places the result in B<r>.
171 bn_mul_part_recursive(B<r>, B<a>, B<b>, B<n>, B<tna>, B<tnb>, B<tmp>)
172 operates on the word arrays B<a> and B<b> of length B<n>+B<tna> and
173 B<n>+B<tnb> and the 4*B<n> word arrays B<r> and B<tmp>.
175 bn_mul_low_recursive(B<r>, B<a>, B<b>, B<n2>, B<tmp>) operates on the
176 B<n2> word arrays B<r> and B<tmp> and the B<n2>/2 word arrays B<a>
179 BN_mul() calls bn_mul_normal(), or an optimized implementation if the
180 factors have the same size: bn_mul_comba8() is used if they are 8
181 words long, bn_mul_recursive() if they are larger than
182 B<BN_MULL_SIZE_NORMAL> and the size is an exact multiple of the word
183 size, and bn_mul_part_recursive() for others that are larger than
184 B<BN_MULL_SIZE_NORMAL>.
186 bn_sqr_normal(B<r>, B<a>, B<n>, B<tmp>) operates on the B<n> word array
187 B<a> and the 2*B<n> word arrays B<tmp> and B<r>.
189 The implementations use the following macros which, depending on the
190 architecture, may use "long long" C operations or inline assembler.
191 They are defined in C<bn_lcl.h>.
193 mul(B<r>, B<a>, B<w>, B<c>) computes B<w>*B<a>+B<c> and places the
194 low word of the result in B<r> and the high word in B<c>.
196 mul_add(B<r>, B<a>, B<w>, B<c>) computes B<w>*B<a>+B<r>+B<c> and
197 places the low word of the result in B<r> and the high word in B<c>.
199 sqr(B<r0>, B<r1>, B<a>) computes B<a>*B<a> and places the low word
200 of the result in B<r0> and the high word in B<r1>.
204 bn_expand() ensures that B<b> has enough space for a B<bits> bit
205 number. bn_wexpand() ensures that B<b> has enough space for an
206 B<n> word number. If the number has to be expanded, both macros
207 call bn_expand2(), which allocates a new B<d> array and copies the
208 data. They return B<NULL> on error, B<b> otherwise.
210 The bn_fix_top() macro reduces B<a-E<gt>top> to point to the most
211 significant non-zero word plus one when B<a> has shrunk.
215 bn_check_top() verifies that C<((a)-E<gt>top E<gt>= 0 && (a)-E<gt>top
216 E<lt>= (a)-E<gt>dmax)>. A violation will cause the program to abort.
218 bn_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.
221 bn_set_max() makes B<a> a static number with a B<dmax> of its current size.
222 This is used by bn_set_low() and bn_set_high() to make B<r> a read-only
223 B<BIGNUM> that contains the B<n> low or high words of B<a>.
225 If B<BN_DEBUG> is not defined, bn_check_top(), bn_print(), bn_dump()
226 and bn_set_max() are defined as empty macros.
234 Copyright 2000-2016 The OpenSSL Project Authors. All Rights Reserved.
236 Licensed under the OpenSSL license (the "License"). You may not use
237 this file except in compliance with the License. You can obtain a copy
238 in the file LICENSE in the source distribution or at
239 L<https://www.openssl.org/source/license.html>.