1/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
2 * All rights reserved.
3 *
4 * This package is an SSL implementation written
5 * by Eric Young (eay@cryptsoft.com).
6 * The implementation was written so as to conform with Netscapes SSL.
7 *
8 * This library is free for commercial and non-commercial use as long as
9 * the following conditions are aheared to. The following conditions
10 * apply to all code found in this distribution, be it the RC4, RSA,
11 * lhash, DES, etc., code; not just the SSL code. The SSL documentation
12 * included with this distribution is covered by the same copyright terms
13 * except that the holder is Tim Hudson (tjh@cryptsoft.com).
14 *
15 * Copyright remains Eric Young's, and as such any Copyright notices in
16 * the code are not to be removed.
17 * If this package is used in a product, Eric Young should be given attribution
18 * as the author of the parts of the library used.
19 * This can be in the form of a textual message at program startup or
20 * in documentation (online or textual) provided with the package.
21 *
22 * Redistribution and use in source and binary forms, with or without
23 * modification, are permitted provided that the following conditions
24 * are met:
25 * 1. Redistributions of source code must retain the copyright
26 * notice, this list of conditions and the following disclaimer.
27 * 2. Redistributions in binary form must reproduce the above copyright
28 * notice, this list of conditions and the following disclaimer in the
29 * documentation and/or other materials provided with the distribution.
30 * 3. All advertising materials mentioning features or use of this software
31 * must display the following acknowledgement:
32 * "This product includes cryptographic software written by
33 * Eric Young (eay@cryptsoft.com)"
34 * The word 'cryptographic' can be left out if the rouines from the library
35 * being used are not cryptographic related :-).
36 * 4. If you include any Windows specific code (or a derivative thereof) from
37 * the apps directory (application code) you must include an acknowledgement:
38 * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
39 *
40 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
41 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
42 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
43 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
44 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
45 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
46 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
47 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
48 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
49 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
50 * SUCH DAMAGE.
51 *
52 * The licence and distribution terms for any publically available version or
53 * derivative of this code cannot be changed. i.e. this code cannot simply be
54 * copied and put under another distribution licence
55 * [including the GNU Public Licence.] */
56
57#include <openssl/bn.h>
58
59#include <string.h>
60
61#include <openssl/err.h>
62#include <openssl/mem.h>
63
64#include "internal.h"
65
66
67int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b) {
68 const BIGNUM *tmp;
69 int a_neg = a->neg, ret;
70
71 // a + b a+b
72 // a + -b a-b
73 // -a + b b-a
74 // -a + -b -(a+b)
75 if (a_neg ^ b->neg) {
76 // only one is negative
77 if (a_neg) {
78 tmp = a;
79 a = b;
80 b = tmp;
81 }
82
83 // we are now a - b
84 if (BN_ucmp(a, b) < 0) {
85 if (!BN_usub(r, b, a)) {
86 return 0;
87 }
88 r->neg = 1;
89 } else {
90 if (!BN_usub(r, a, b)) {
91 return 0;
92 }
93 r->neg = 0;
94 }
95 return 1;
96 }
97
98 ret = BN_uadd(r, a, b);
99 r->neg = a_neg;
100 return ret;
101}
102
103int bn_uadd_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b) {
104 // Widths are public, so we normalize to make |a| the larger one.
105 if (a->width < b->width) {
106 const BIGNUM *tmp = a;
107 a = b;
108 b = tmp;
109 }
110
111 int max = a->width;
112 int min = b->width;
113 if (!bn_wexpand(r, max + 1)) {
114 return 0;
115 }
116 r->width = max + 1;
117
118 BN_ULONG carry = bn_add_words(r->d, a->d, b->d, min);
119 for (int i = min; i < max; i++) {
120 // |r| and |a| may alias, so use a temporary.
121 BN_ULONG tmp = carry + a->d[i];
122 carry = tmp < a->d[i];
123 r->d[i] = tmp;
124 }
125
126 r->d[max] = carry;
127 return 1;
128}
129
130int BN_uadd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b) {
131 if (!bn_uadd_consttime(r, a, b)) {
132 return 0;
133 }
134 bn_set_minimal_width(r);
135 return 1;
136}
137
138int BN_add_word(BIGNUM *a, BN_ULONG w) {
139 BN_ULONG l;
140 int i;
141
142 // degenerate case: w is zero
143 if (!w) {
144 return 1;
145 }
146
147 // degenerate case: a is zero
148 if (BN_is_zero(a)) {
149 return BN_set_word(a, w);
150 }
151
152 // handle 'a' when negative
153 if (a->neg) {
154 a->neg = 0;
155 i = BN_sub_word(a, w);
156 if (!BN_is_zero(a)) {
157 a->neg = !(a->neg);
158 }
159 return i;
160 }
161
162 for (i = 0; w != 0 && i < a->width; i++) {
163 a->d[i] = l = a->d[i] + w;
164 w = (w > l) ? 1 : 0;
165 }
166
167 if (w && i == a->width) {
168 if (!bn_wexpand(a, a->width + 1)) {
169 return 0;
170 }
171 a->width++;
172 a->d[i] = w;
173 }
174
175 return 1;
176}
177
178int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b) {
179 int add = 0, neg = 0;
180 const BIGNUM *tmp;
181
182 // a - b a-b
183 // a - -b a+b
184 // -a - b -(a+b)
185 // -a - -b b-a
186 if (a->neg) {
187 if (b->neg) {
188 tmp = a;
189 a = b;
190 b = tmp;
191 } else {
192 add = 1;
193 neg = 1;
194 }
195 } else {
196 if (b->neg) {
197 add = 1;
198 neg = 0;
199 }
200 }
201
202 if (add) {
203 if (!BN_uadd(r, a, b)) {
204 return 0;
205 }
206
207 r->neg = neg;
208 return 1;
209 }
210
211 if (BN_ucmp(a, b) < 0) {
212 if (!BN_usub(r, b, a)) {
213 return 0;
214 }
215 r->neg = 1;
216 } else {
217 if (!BN_usub(r, a, b)) {
218 return 0;
219 }
220 r->neg = 0;
221 }
222
223 return 1;
224}
225
226int bn_usub_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b) {
227 // |b| may have more words than |a| given non-minimal inputs, but all words
228 // beyond |a->width| must then be zero.
229 int b_width = b->width;
230 if (b_width > a->width) {
231 if (!bn_fits_in_words(b, a->width)) {
232 OPENSSL_PUT_ERROR(BN, BN_R_ARG2_LT_ARG3);
233 return 0;
234 }
235 b_width = a->width;
236 }
237
238 if (!bn_wexpand(r, a->width)) {
239 return 0;
240 }
241
242 BN_ULONG borrow = bn_sub_words(r->d, a->d, b->d, b_width);
243 for (int i = b_width; i < a->width; i++) {
244 // |r| and |a| may alias, so use a temporary.
245 BN_ULONG tmp = a->d[i];
246 r->d[i] = a->d[i] - borrow;
247 borrow = tmp < r->d[i];
248 }
249
250 if (borrow) {
251 OPENSSL_PUT_ERROR(BN, BN_R_ARG2_LT_ARG3);
252 return 0;
253 }
254
255 r->width = a->width;
256 r->neg = 0;
257 return 1;
258}
259
260int BN_usub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b) {
261 if (!bn_usub_consttime(r, a, b)) {
262 return 0;
263 }
264 bn_set_minimal_width(r);
265 return 1;
266}
267
268int BN_sub_word(BIGNUM *a, BN_ULONG w) {
269 int i;
270
271 // degenerate case: w is zero
272 if (!w) {
273 return 1;
274 }
275
276 // degenerate case: a is zero
277 if (BN_is_zero(a)) {
278 i = BN_set_word(a, w);
279 if (i != 0) {
280 BN_set_negative(a, 1);
281 }
282 return i;
283 }
284
285 // handle 'a' when negative
286 if (a->neg) {
287 a->neg = 0;
288 i = BN_add_word(a, w);
289 a->neg = 1;
290 return i;
291 }
292
293 if ((bn_minimal_width(a) == 1) && (a->d[0] < w)) {
294 a->d[0] = w - a->d[0];
295 a->neg = 1;
296 return 1;
297 }
298
299 i = 0;
300 for (;;) {
301 if (a->d[i] >= w) {
302 a->d[i] -= w;
303 break;
304 } else {
305 a->d[i] -= w;
306 i++;
307 w = 1;
308 }
309 }
310
311 if ((a->d[i] == 0) && (i == (a->width - 1))) {
312 a->width--;
313 }
314
315 return 1;
316}
317