1 /* Copyright (C) 1995-1998 Eric Young ([email protected])
2 * All rights reserved.
3 *
4 * This package is an SSL implementation written
5 * by Eric Young ([email protected]).
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 ([email protected]).
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 ([email protected])"
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 ([email protected])"
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
BN_add(BIGNUM * r,const BIGNUM * a,const BIGNUM * b)67 int 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
bn_uadd_consttime(BIGNUM * r,const BIGNUM * a,const BIGNUM * b)103 int 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->d[i] = CRYPTO_addc_w(a->d[i], 0, carry, &carry);
121 }
122
123 r->d[max] = carry;
124 return 1;
125 }
126
BN_uadd(BIGNUM * r,const BIGNUM * a,const BIGNUM * b)127 int BN_uadd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b) {
128 if (!bn_uadd_consttime(r, a, b)) {
129 return 0;
130 }
131 bn_set_minimal_width(r);
132 return 1;
133 }
134
BN_add_word(BIGNUM * a,BN_ULONG w)135 int BN_add_word(BIGNUM *a, BN_ULONG w) {
136 BN_ULONG l;
137 int i;
138
139 // degenerate case: w is zero
140 if (!w) {
141 return 1;
142 }
143
144 // degenerate case: a is zero
145 if (BN_is_zero(a)) {
146 return BN_set_word(a, w);
147 }
148
149 // handle 'a' when negative
150 if (a->neg) {
151 a->neg = 0;
152 i = BN_sub_word(a, w);
153 if (!BN_is_zero(a)) {
154 a->neg = !(a->neg);
155 }
156 return i;
157 }
158
159 for (i = 0; w != 0 && i < a->width; i++) {
160 a->d[i] = l = a->d[i] + w;
161 w = (w > l) ? 1 : 0;
162 }
163
164 if (w && i == a->width) {
165 if (!bn_wexpand(a, a->width + 1)) {
166 return 0;
167 }
168 a->width++;
169 a->d[i] = w;
170 }
171
172 return 1;
173 }
174
BN_sub(BIGNUM * r,const BIGNUM * a,const BIGNUM * b)175 int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b) {
176 int add = 0, neg = 0;
177 const BIGNUM *tmp;
178
179 // a - b a-b
180 // a - -b a+b
181 // -a - b -(a+b)
182 // -a - -b b-a
183 if (a->neg) {
184 if (b->neg) {
185 tmp = a;
186 a = b;
187 b = tmp;
188 } else {
189 add = 1;
190 neg = 1;
191 }
192 } else {
193 if (b->neg) {
194 add = 1;
195 neg = 0;
196 }
197 }
198
199 if (add) {
200 if (!BN_uadd(r, a, b)) {
201 return 0;
202 }
203
204 r->neg = neg;
205 return 1;
206 }
207
208 if (BN_ucmp(a, b) < 0) {
209 if (!BN_usub(r, b, a)) {
210 return 0;
211 }
212 r->neg = 1;
213 } else {
214 if (!BN_usub(r, a, b)) {
215 return 0;
216 }
217 r->neg = 0;
218 }
219
220 return 1;
221 }
222
bn_usub_consttime(BIGNUM * r,const BIGNUM * a,const BIGNUM * b)223 int bn_usub_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b) {
224 // |b| may have more words than |a| given non-minimal inputs, but all words
225 // beyond |a->width| must then be zero.
226 int b_width = b->width;
227 if (b_width > a->width) {
228 if (!bn_fits_in_words(b, a->width)) {
229 OPENSSL_PUT_ERROR(BN, BN_R_ARG2_LT_ARG3);
230 return 0;
231 }
232 b_width = a->width;
233 }
234
235 if (!bn_wexpand(r, a->width)) {
236 return 0;
237 }
238
239 BN_ULONG borrow = bn_sub_words(r->d, a->d, b->d, b_width);
240 for (int i = b_width; i < a->width; i++) {
241 r->d[i] = CRYPTO_subc_w(a->d[i], 0, borrow, &borrow);
242 }
243
244 if (borrow) {
245 OPENSSL_PUT_ERROR(BN, BN_R_ARG2_LT_ARG3);
246 return 0;
247 }
248
249 r->width = a->width;
250 r->neg = 0;
251 return 1;
252 }
253
BN_usub(BIGNUM * r,const BIGNUM * a,const BIGNUM * b)254 int BN_usub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b) {
255 if (!bn_usub_consttime(r, a, b)) {
256 return 0;
257 }
258 bn_set_minimal_width(r);
259 return 1;
260 }
261
BN_sub_word(BIGNUM * a,BN_ULONG w)262 int BN_sub_word(BIGNUM *a, BN_ULONG w) {
263 int i;
264
265 // degenerate case: w is zero
266 if (!w) {
267 return 1;
268 }
269
270 // degenerate case: a is zero
271 if (BN_is_zero(a)) {
272 i = BN_set_word(a, w);
273 if (i != 0) {
274 BN_set_negative(a, 1);
275 }
276 return i;
277 }
278
279 // handle 'a' when negative
280 if (a->neg) {
281 a->neg = 0;
282 i = BN_add_word(a, w);
283 a->neg = 1;
284 return i;
285 }
286
287 if ((bn_minimal_width(a) == 1) && (a->d[0] < w)) {
288 a->d[0] = w - a->d[0];
289 a->neg = 1;
290 return 1;
291 }
292
293 i = 0;
294 for (;;) {
295 if (a->d[i] >= w) {
296 a->d[i] -= w;
297 break;
298 } else {
299 a->d[i] -= w;
300 i++;
301 w = 1;
302 }
303 }
304
305 if ((a->d[i] == 0) && (i == (a->width - 1))) {
306 a->width--;
307 }
308
309 return 1;
310 }
311