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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_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| 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 
BN_uadd(BIGNUM * r,const BIGNUM * a,const BIGNUM * b)130 int 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 
BN_add_word(BIGNUM * a,BN_ULONG w)138 int 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 
BN_sub(BIGNUM * r,const BIGNUM * a,const BIGNUM * b)178 int 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 
bn_usub_consttime(BIGNUM * r,const BIGNUM * a,const BIGNUM * b)226 int 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 
BN_usub(BIGNUM * r,const BIGNUM * a,const BIGNUM * b)260 int 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 
BN_sub_word(BIGNUM * a,BN_ULONG w)268 int 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