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
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(BIGNUM * r,const BIGNUM * a,const BIGNUM * b)103 int BN_uadd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b) {
104 int max, min, dif;
105 BN_ULONG *ap, *bp, *rp, carry, t1, t2;
106 const BIGNUM *tmp;
107
108 if (a->top < b->top) {
109 tmp = a;
110 a = b;
111 b = tmp;
112 }
113 max = a->top;
114 min = b->top;
115 dif = max - min;
116
117 if (!bn_wexpand(r, max + 1)) {
118 return 0;
119 }
120
121 r->top = max;
122
123 ap = a->d;
124 bp = b->d;
125 rp = r->d;
126
127 carry = bn_add_words(rp, ap, bp, min);
128 rp += min;
129 ap += min;
130 bp += min;
131
132 if (carry) {
133 while (dif) {
134 dif--;
135 t1 = *(ap++);
136 t2 = t1 + 1;
137 *(rp++) = t2;
138 if (t2) {
139 carry = 0;
140 break;
141 }
142 }
143 if (carry) {
144 // carry != 0 => dif == 0
145 *rp = 1;
146 r->top++;
147 }
148 }
149
150 if (dif && rp != ap) {
151 while (dif--) {
152 // copy remaining words if ap != rp
153 *(rp++) = *(ap++);
154 }
155 }
156
157 r->neg = 0;
158 return 1;
159 }
160
BN_add_word(BIGNUM * a,BN_ULONG w)161 int BN_add_word(BIGNUM *a, BN_ULONG w) {
162 BN_ULONG l;
163 int i;
164
165 // degenerate case: w is zero
166 if (!w) {
167 return 1;
168 }
169
170 // degenerate case: a is zero
171 if (BN_is_zero(a)) {
172 return BN_set_word(a, w);
173 }
174
175 // handle 'a' when negative
176 if (a->neg) {
177 a->neg = 0;
178 i = BN_sub_word(a, w);
179 if (!BN_is_zero(a)) {
180 a->neg = !(a->neg);
181 }
182 return i;
183 }
184
185 for (i = 0; w != 0 && i < a->top; i++) {
186 a->d[i] = l = a->d[i] + w;
187 w = (w > l) ? 1 : 0;
188 }
189
190 if (w && i == a->top) {
191 if (!bn_wexpand(a, a->top + 1)) {
192 return 0;
193 }
194 a->top++;
195 a->d[i] = w;
196 }
197
198 return 1;
199 }
200
BN_sub(BIGNUM * r,const BIGNUM * a,const BIGNUM * b)201 int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b) {
202 int add = 0, neg = 0;
203 const BIGNUM *tmp;
204
205 // a - b a-b
206 // a - -b a+b
207 // -a - b -(a+b)
208 // -a - -b b-a
209 if (a->neg) {
210 if (b->neg) {
211 tmp = a;
212 a = b;
213 b = tmp;
214 } else {
215 add = 1;
216 neg = 1;
217 }
218 } else {
219 if (b->neg) {
220 add = 1;
221 neg = 0;
222 }
223 }
224
225 if (add) {
226 if (!BN_uadd(r, a, b)) {
227 return 0;
228 }
229
230 r->neg = neg;
231 return 1;
232 }
233
234 if (BN_ucmp(a, b) < 0) {
235 if (!BN_usub(r, b, a)) {
236 return 0;
237 }
238 r->neg = 1;
239 } else {
240 if (!BN_usub(r, a, b)) {
241 return 0;
242 }
243 r->neg = 0;
244 }
245
246 return 1;
247 }
248
BN_usub(BIGNUM * r,const BIGNUM * a,const BIGNUM * b)249 int BN_usub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b) {
250 int max, min, dif;
251 register BN_ULONG t1, t2, *ap, *bp, *rp;
252 int i, carry;
253
254 max = a->top;
255 min = b->top;
256 dif = max - min;
257
258 if (dif < 0) // hmm... should not be happening
259 {
260 OPENSSL_PUT_ERROR(BN, BN_R_ARG2_LT_ARG3);
261 return 0;
262 }
263
264 if (!bn_wexpand(r, max)) {
265 return 0;
266 }
267
268 ap = a->d;
269 bp = b->d;
270 rp = r->d;
271
272 carry = 0;
273 for (i = min; i != 0; i--) {
274 t1 = *(ap++);
275 t2 = *(bp++);
276 if (carry) {
277 carry = (t1 <= t2);
278 t1 -= t2 + 1;
279 } else {
280 carry = (t1 < t2);
281 t1 -= t2;
282 }
283 *(rp++) = t1;
284 }
285
286 if (carry) // subtracted
287 {
288 if (!dif) {
289 // error: a < b
290 return 0;
291 }
292
293 while (dif) {
294 dif--;
295 t1 = *(ap++);
296 t2 = t1 - 1;
297 *(rp++) = t2;
298 if (t1) {
299 break;
300 }
301 }
302 }
303
304 if (dif > 0 && rp != ap) {
305 OPENSSL_memcpy(rp, ap, sizeof(*rp) * dif);
306 }
307
308 r->top = max;
309 r->neg = 0;
310 bn_correct_top(r);
311
312 return 1;
313 }
314
BN_sub_word(BIGNUM * a,BN_ULONG w)315 int BN_sub_word(BIGNUM *a, BN_ULONG w) {
316 int i;
317
318 // degenerate case: w is zero
319 if (!w) {
320 return 1;
321 }
322
323 // degenerate case: a is zero
324 if (BN_is_zero(a)) {
325 i = BN_set_word(a, w);
326 if (i != 0) {
327 BN_set_negative(a, 1);
328 }
329 return i;
330 }
331
332 // handle 'a' when negative
333 if (a->neg) {
334 a->neg = 0;
335 i = BN_add_word(a, w);
336 a->neg = 1;
337 return i;
338 }
339
340 if ((a->top == 1) && (a->d[0] < w)) {
341 a->d[0] = w - a->d[0];
342 a->neg = 1;
343 return 1;
344 }
345
346 i = 0;
347 for (;;) {
348 if (a->d[i] >= w) {
349 a->d[i] -= w;
350 break;
351 } else {
352 a->d[i] -= w;
353 i++;
354 w = 1;
355 }
356 }
357
358 if ((a->d[i] == 0) && (i == (a->top - 1))) {
359 a->top--;
360 }
361
362 return 1;
363 }
364