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/type_check.h>
63
64#include "internal.h"
65
66
67int BN_lshift(BIGNUM *r, const BIGNUM *a, int n) {
68 int i, nw, lb, rb;
69 BN_ULONG *t, *f;
70 BN_ULONG l;
71
72 if (n < 0) {
73 OPENSSL_PUT_ERROR(BN, BN_R_NEGATIVE_NUMBER);
74 return 0;
75 }
76
77 r->neg = a->neg;
78 nw = n / BN_BITS2;
79 if (!bn_wexpand(r, a->width + nw + 1)) {
80 return 0;
81 }
82 lb = n % BN_BITS2;
83 rb = BN_BITS2 - lb;
84 f = a->d;
85 t = r->d;
86 t[a->width + nw] = 0;
87 if (lb == 0) {
88 for (i = a->width - 1; i >= 0; i--) {
89 t[nw + i] = f[i];
90 }
91 } else {
92 for (i = a->width - 1; i >= 0; i--) {
93 l = f[i];
94 t[nw + i + 1] |= l >> rb;
95 t[nw + i] = l << lb;
96 }
97 }
98 OPENSSL_memset(t, 0, nw * sizeof(t[0]));
99 r->width = a->width + nw + 1;
100 bn_set_minimal_width(r);
101
102 return 1;
103}
104
105int BN_lshift1(BIGNUM *r, const BIGNUM *a) {
106 BN_ULONG *ap, *rp, t, c;
107 int i;
108
109 if (r != a) {
110 r->neg = a->neg;
111 if (!bn_wexpand(r, a->width + 1)) {
112 return 0;
113 }
114 r->width = a->width;
115 } else {
116 if (!bn_wexpand(r, a->width + 1)) {
117 return 0;
118 }
119 }
120 ap = a->d;
121 rp = r->d;
122 c = 0;
123 for (i = 0; i < a->width; i++) {
124 t = *(ap++);
125 *(rp++) = (t << 1) | c;
126 c = t >> (BN_BITS2 - 1);
127 }
128 if (c) {
129 *rp = 1;
130 r->width++;
131 }
132
133 return 1;
134}
135
136void bn_rshift_words(BN_ULONG *r, const BN_ULONG *a, unsigned shift,
137 size_t num) {
138 unsigned shift_bits = shift % BN_BITS2;
139 size_t shift_words = shift / BN_BITS2;
140 if (shift_words >= num) {
141 OPENSSL_memset(r, 0, num * sizeof(BN_ULONG));
142 return;
143 }
144 if (shift_bits == 0) {
145 OPENSSL_memmove(r, a + shift_words, (num - shift_words) * sizeof(BN_ULONG));
146 } else {
147 for (size_t i = shift_words; i < num - 1; i++) {
148 r[i - shift_words] =
149 (a[i] >> shift_bits) | (a[i + 1] << (BN_BITS2 - shift_bits));
150 }
151 r[num - 1 - shift_words] = a[num - 1] >> shift_bits;
152 }
153 OPENSSL_memset(r + num - shift_words, 0, shift_words * sizeof(BN_ULONG));
154}
155
156int BN_rshift(BIGNUM *r, const BIGNUM *a, int n) {
157 if (n < 0) {
158 OPENSSL_PUT_ERROR(BN, BN_R_NEGATIVE_NUMBER);
159 return 0;
160 }
161
162 if (!bn_wexpand(r, a->width)) {
163 return 0;
164 }
165 bn_rshift_words(r->d, a->d, n, a->width);
166 r->neg = a->neg;
167 r->width = a->width;
168 bn_set_minimal_width(r);
169 return 1;
170}
171
172int bn_rshift_secret_shift(BIGNUM *r, const BIGNUM *a, unsigned n,
173 BN_CTX *ctx) {
174 int ret = 0;
175 BN_CTX_start(ctx);
176 BIGNUM *tmp = BN_CTX_get(ctx);
177 if (tmp == NULL ||
178 !BN_copy(r, a) ||
179 !bn_wexpand(tmp, r->width)) {
180 goto err;
181 }
182
183 // Shift conditionally by powers of two.
184 unsigned max_bits = BN_BITS2 * r->width;
185 for (unsigned i = 0; (max_bits >> i) != 0; i++) {
186 BN_ULONG mask = (n >> i) & 1;
187 mask = 0 - mask;
188 bn_rshift_words(tmp->d, r->d, 1u << i, r->width);
189 bn_select_words(r->d, mask, tmp->d /* apply shift */,
190 r->d /* ignore shift */, r->width);
191 }
192
193 ret = 1;
194
195err:
196 BN_CTX_end(ctx);
197 return ret;
198}
199
200void bn_rshift1_words(BN_ULONG *r, const BN_ULONG *a, size_t num) {
201 if (num == 0) {
202 return;
203 }
204 for (size_t i = 0; i < num - 1; i++) {
205 r[i] = (a[i] >> 1) | (a[i + 1] << (BN_BITS2 - 1));
206 }
207 r[num - 1] = a[num - 1] >> 1;
208}
209
210int BN_rshift1(BIGNUM *r, const BIGNUM *a) {
211 if (!bn_wexpand(r, a->width)) {
212 return 0;
213 }
214 bn_rshift1_words(r->d, a->d, a->width);
215 r->width = a->width;
216 r->neg = a->neg;
217 bn_set_minimal_width(r);
218 return 1;
219}
220
221int BN_set_bit(BIGNUM *a, int n) {
222 if (n < 0) {
223 return 0;
224 }
225
226 int i = n / BN_BITS2;
227 int j = n % BN_BITS2;
228 if (a->width <= i) {
229 if (!bn_wexpand(a, i + 1)) {
230 return 0;
231 }
232 for (int k = a->width; k < i + 1; k++) {
233 a->d[k] = 0;
234 }
235 a->width = i + 1;
236 }
237
238 a->d[i] |= (((BN_ULONG)1) << j);
239
240 return 1;
241}
242
243int BN_clear_bit(BIGNUM *a, int n) {
244 int i, j;
245
246 if (n < 0) {
247 return 0;
248 }
249
250 i = n / BN_BITS2;
251 j = n % BN_BITS2;
252 if (a->width <= i) {
253 return 0;
254 }
255
256 a->d[i] &= (~(((BN_ULONG)1) << j));
257 bn_set_minimal_width(a);
258 return 1;
259}
260
261int bn_is_bit_set_words(const BN_ULONG *a, size_t num, unsigned bit) {
262 unsigned i = bit / BN_BITS2;
263 unsigned j = bit % BN_BITS2;
264 if (i >= num) {
265 return 0;
266 }
267 return (a[i] >> j) & 1;
268}
269
270int BN_is_bit_set(const BIGNUM *a, int n) {
271 if (n < 0) {
272 return 0;
273 }
274 return bn_is_bit_set_words(a->d, a->width, n);
275}
276
277int BN_mask_bits(BIGNUM *a, int n) {
278 if (n < 0) {
279 return 0;
280 }
281
282 int w = n / BN_BITS2;
283 int b = n % BN_BITS2;
284 if (w >= a->width) {
285 return 1;
286 }
287 if (b == 0) {
288 a->width = w;
289 } else {
290 a->width = w + 1;
291 a->d[w] &= ~(BN_MASK2 << b);
292 }
293
294 bn_set_minimal_width(a);
295 return 1;
296}
297
298static int bn_count_low_zero_bits_word(BN_ULONG l) {
299 OPENSSL_STATIC_ASSERT(sizeof(BN_ULONG) <= sizeof(crypto_word_t),
300 "crypto_word_t is too small");
301 OPENSSL_STATIC_ASSERT(sizeof(int) <= sizeof(crypto_word_t),
302 "crypto_word_t is too small");
303 OPENSSL_STATIC_ASSERT(BN_BITS2 == sizeof(BN_ULONG) * 8,
304 "BN_ULONG has padding bits");
305 // C has very bizarre rules for types smaller than an int.
306 OPENSSL_STATIC_ASSERT(sizeof(BN_ULONG) >= sizeof(int),
307 "BN_ULONG gets promoted to int");
308
309 crypto_word_t mask;
310 int bits = 0;
311
312#if BN_BITS2 > 32
313 // Check if the lower half of |x| are all zero.
314 mask = constant_time_is_zero_w(l << (BN_BITS2 - 32));
315 // If the lower half is all zeros, it is included in the bit count and we
316 // count the upper half. Otherwise, we count the lower half.
317 bits += 32 & mask;
318 l = constant_time_select_w(mask, l >> 32, l);
319#endif
320
321 // The remaining blocks are analogous iterations at lower powers of two.
322 mask = constant_time_is_zero_w(l << (BN_BITS2 - 16));
323 bits += 16 & mask;
324 l = constant_time_select_w(mask, l >> 16, l);
325
326 mask = constant_time_is_zero_w(l << (BN_BITS2 - 8));
327 bits += 8 & mask;
328 l = constant_time_select_w(mask, l >> 8, l);
329
330 mask = constant_time_is_zero_w(l << (BN_BITS2 - 4));
331 bits += 4 & mask;
332 l = constant_time_select_w(mask, l >> 4, l);
333
334 mask = constant_time_is_zero_w(l << (BN_BITS2 - 2));
335 bits += 2 & mask;
336 l = constant_time_select_w(mask, l >> 2, l);
337
338 mask = constant_time_is_zero_w(l << (BN_BITS2 - 1));
339 bits += 1 & mask;
340
341 return bits;
342}
343
344int BN_count_low_zero_bits(const BIGNUM *bn) {
345 OPENSSL_STATIC_ASSERT(sizeof(BN_ULONG) <= sizeof(crypto_word_t),
346 "crypto_word_t is too small");
347 OPENSSL_STATIC_ASSERT(sizeof(int) <= sizeof(crypto_word_t),
348 "crypto_word_t is too small");
349
350 int ret = 0;
351 crypto_word_t saw_nonzero = 0;
352 for (int i = 0; i < bn->width; i++) {
353 crypto_word_t nonzero = ~constant_time_is_zero_w(bn->d[i]);
354 crypto_word_t first_nonzero = ~saw_nonzero & nonzero;
355 saw_nonzero |= nonzero;
356
357 int bits = bn_count_low_zero_bits_word(bn->d[i]);
358 ret |= first_nonzero & (i * BN_BITS2 + bits);
359 }
360
361 // If got to the end of |bn| and saw no non-zero words, |bn| is zero. |ret|
362 // will then remain zero.
363 return ret;
364}
365