Line data Source code
1 : /* crypto/bn/bn_exp.c */
2 : /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
3 : * All rights reserved.
4 : *
5 : * This package is an SSL implementation written
6 : * by Eric Young (eay@cryptsoft.com).
7 : * The implementation was written so as to conform with Netscapes SSL.
8 : *
9 : * This library is free for commercial and non-commercial use as long as
10 : * the following conditions are aheared to. The following conditions
11 : * apply to all code found in this distribution, be it the RC4, RSA,
12 : * lhash, DES, etc., code; not just the SSL code. The SSL documentation
13 : * included with this distribution is covered by the same copyright terms
14 : * except that the holder is Tim Hudson (tjh@cryptsoft.com).
15 : *
16 : * Copyright remains Eric Young's, and as such any Copyright notices in
17 : * the code are not to be removed.
18 : * If this package is used in a product, Eric Young should be given attribution
19 : * as the author of the parts of the library used.
20 : * This can be in the form of a textual message at program startup or
21 : * in documentation (online or textual) provided with the package.
22 : *
23 : * Redistribution and use in source and binary forms, with or without
24 : * modification, are permitted provided that the following conditions
25 : * are met:
26 : * 1. Redistributions of source code must retain the copyright
27 : * notice, this list of conditions and the following disclaimer.
28 : * 2. Redistributions in binary form must reproduce the above copyright
29 : * notice, this list of conditions and the following disclaimer in the
30 : * documentation and/or other materials provided with the distribution.
31 : * 3. All advertising materials mentioning features or use of this software
32 : * must display the following acknowledgement:
33 : * "This product includes cryptographic software written by
34 : * Eric Young (eay@cryptsoft.com)"
35 : * The word 'cryptographic' can be left out if the rouines from the library
36 : * being used are not cryptographic related :-).
37 : * 4. If you include any Windows specific code (or a derivative thereof) from
38 : * the apps directory (application code) you must include an acknowledgement:
39 : * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
40 : *
41 : * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
42 : * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
43 : * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
44 : * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
45 : * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
46 : * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
47 : * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
48 : * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
49 : * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
50 : * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
51 : * SUCH DAMAGE.
52 : *
53 : * The licence and distribution terms for any publically available version or
54 : * derivative of this code cannot be changed. i.e. this code cannot simply be
55 : * copied and put under another distribution licence
56 : * [including the GNU Public Licence.]
57 : */
58 : /* ====================================================================
59 : * Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved.
60 : *
61 : * Redistribution and use in source and binary forms, with or without
62 : * modification, are permitted provided that the following conditions
63 : * are met:
64 : *
65 : * 1. Redistributions of source code must retain the above copyright
66 : * notice, this list of conditions and the following disclaimer.
67 : *
68 : * 2. Redistributions in binary form must reproduce the above copyright
69 : * notice, this list of conditions and the following disclaimer in
70 : * the documentation and/or other materials provided with the
71 : * distribution.
72 : *
73 : * 3. All advertising materials mentioning features or use of this
74 : * software must display the following acknowledgment:
75 : * "This product includes software developed by the OpenSSL Project
76 : * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
77 : *
78 : * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
79 : * endorse or promote products derived from this software without
80 : * prior written permission. For written permission, please contact
81 : * openssl-core@openssl.org.
82 : *
83 : * 5. Products derived from this software may not be called "OpenSSL"
84 : * nor may "OpenSSL" appear in their names without prior written
85 : * permission of the OpenSSL Project.
86 : *
87 : * 6. Redistributions of any form whatsoever must retain the following
88 : * acknowledgment:
89 : * "This product includes software developed by the OpenSSL Project
90 : * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
91 : *
92 : * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
93 : * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
94 : * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
95 : * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
96 : * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
97 : * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
98 : * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
99 : * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
100 : * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
101 : * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
102 : * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
103 : * OF THE POSSIBILITY OF SUCH DAMAGE.
104 : * ====================================================================
105 : *
106 : * This product includes cryptographic software written by Eric Young
107 : * (eay@cryptsoft.com). This product includes software written by Tim
108 : * Hudson (tjh@cryptsoft.com).
109 : *
110 : */
111 :
112 : #include "cryptlib.h"
113 : #include "bn_lcl.h"
114 :
115 : #include <stdlib.h>
116 : #ifdef _WIN32
117 : # include <malloc.h>
118 : # ifndef alloca
119 : # define alloca _alloca
120 : # endif
121 : #elif defined(__GNUC__)
122 : # ifndef alloca
123 : # define alloca(s) __builtin_alloca((s))
124 : # endif
125 : #elif defined(__sun)
126 : # include <alloca.h>
127 : #endif
128 :
129 : #include "rsaz_exp.h"
130 :
131 : #undef SPARC_T4_MONT
132 : #if defined(OPENSSL_BN_ASM_MONT) && (defined(__sparc__) || defined(__sparc))
133 : # include "sparc_arch.h"
134 : extern unsigned int OPENSSL_sparcv9cap_P[];
135 : # define SPARC_T4_MONT
136 : #endif
137 :
138 : /* maximum precomputation table size for *variable* sliding windows */
139 : #define TABLE_SIZE 32
140 :
141 : /* this one works - simple but works */
142 0 : int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
143 : {
144 : int i, bits, ret = 0;
145 : BIGNUM *v, *rr;
146 :
147 0 : if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
148 : /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
149 0 : BNerr(BN_F_BN_EXP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
150 0 : return -1;
151 : }
152 :
153 0 : BN_CTX_start(ctx);
154 0 : if ((r == a) || (r == p))
155 0 : rr = BN_CTX_get(ctx);
156 : else
157 : rr = r;
158 0 : v = BN_CTX_get(ctx);
159 0 : if (rr == NULL || v == NULL)
160 : goto err;
161 :
162 0 : if (BN_copy(v, a) == NULL)
163 : goto err;
164 0 : bits = BN_num_bits(p);
165 :
166 0 : if (BN_is_odd(p)) {
167 0 : if (BN_copy(rr, a) == NULL)
168 : goto err;
169 : } else {
170 0 : if (!BN_one(rr))
171 : goto err;
172 : }
173 :
174 0 : for (i = 1; i < bits; i++) {
175 0 : if (!BN_sqr(v, v, ctx))
176 : goto err;
177 0 : if (BN_is_bit_set(p, i)) {
178 0 : if (!BN_mul(rr, rr, v, ctx))
179 : goto err;
180 : }
181 : }
182 0 : if (r != rr)
183 0 : BN_copy(r, rr);
184 : ret = 1;
185 : err:
186 0 : BN_CTX_end(ctx);
187 : bn_check_top(r);
188 0 : return (ret);
189 : }
190 :
191 345 : int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
192 : BN_CTX *ctx)
193 : {
194 : int ret;
195 :
196 : bn_check_top(a);
197 : bn_check_top(p);
198 : bn_check_top(m);
199 :
200 : /*-
201 : * For even modulus m = 2^k*m_odd, it might make sense to compute
202 : * a^p mod m_odd and a^p mod 2^k separately (with Montgomery
203 : * exponentiation for the odd part), using appropriate exponent
204 : * reductions, and combine the results using the CRT.
205 : *
206 : * For now, we use Montgomery only if the modulus is odd; otherwise,
207 : * exponentiation using the reciprocal-based quick remaindering
208 : * algorithm is used.
209 : *
210 : * (Timing obtained with expspeed.c [computations a^p mod m
211 : * where a, p, m are of the same length: 256, 512, 1024, 2048,
212 : * 4096, 8192 bits], compared to the running time of the
213 : * standard algorithm:
214 : *
215 : * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
216 : * 55 .. 77 % [UltraSparc processor, but
217 : * debug-solaris-sparcv8-gcc conf.]
218 : *
219 : * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
220 : * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
221 : *
222 : * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
223 : * at 2048 and more bits, but at 512 and 1024 bits, it was
224 : * slower even than the standard algorithm!
225 : *
226 : * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
227 : * should be obtained when the new Montgomery reduction code
228 : * has been integrated into OpenSSL.)
229 : */
230 :
231 : #define MONT_MUL_MOD
232 : #define MONT_EXP_WORD
233 : #define RECP_MUL_MOD
234 :
235 : #ifdef MONT_MUL_MOD
236 : /*
237 : * I have finally been able to take out this pre-condition of the top bit
238 : * being set. It was caused by an error in BN_div with negatives. There
239 : * was also another problem when for a^b%m a >= m. eay 07-May-97
240 : */
241 : /* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */
242 :
243 345 : if (BN_is_odd(m)) {
244 : # ifdef MONT_EXP_WORD
245 345 : if (a->top == 1 && !a->neg
246 0 : && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0)) {
247 0 : BN_ULONG A = a->d[0];
248 0 : ret = BN_mod_exp_mont_word(r, A, p, m, ctx, NULL);
249 : } else
250 : # endif
251 345 : ret = BN_mod_exp_mont(r, a, p, m, ctx, NULL);
252 : } else
253 : #endif
254 : #ifdef RECP_MUL_MOD
255 : {
256 0 : ret = BN_mod_exp_recp(r, a, p, m, ctx);
257 : }
258 : #else
259 : {
260 : ret = BN_mod_exp_simple(r, a, p, m, ctx);
261 : }
262 : #endif
263 :
264 : bn_check_top(r);
265 345 : return (ret);
266 : }
267 :
268 0 : int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
269 : const BIGNUM *m, BN_CTX *ctx)
270 : {
271 : int i, j, bits, ret = 0, wstart, wend, window, wvalue;
272 : int start = 1;
273 : BIGNUM *aa;
274 : /* Table of variables obtained from 'ctx' */
275 : BIGNUM *val[TABLE_SIZE];
276 : BN_RECP_CTX recp;
277 :
278 0 : if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
279 : /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
280 0 : BNerr(BN_F_BN_MOD_EXP_RECP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
281 0 : return -1;
282 : }
283 :
284 0 : bits = BN_num_bits(p);
285 :
286 0 : if (bits == 0) {
287 0 : ret = BN_one(r);
288 0 : return ret;
289 : }
290 :
291 0 : BN_CTX_start(ctx);
292 0 : aa = BN_CTX_get(ctx);
293 0 : val[0] = BN_CTX_get(ctx);
294 0 : if (!aa || !val[0])
295 : goto err;
296 :
297 0 : BN_RECP_CTX_init(&recp);
298 0 : if (m->neg) {
299 : /* ignore sign of 'm' */
300 0 : if (!BN_copy(aa, m))
301 : goto err;
302 0 : aa->neg = 0;
303 0 : if (BN_RECP_CTX_set(&recp, aa, ctx) <= 0)
304 : goto err;
305 : } else {
306 0 : if (BN_RECP_CTX_set(&recp, m, ctx) <= 0)
307 : goto err;
308 : }
309 :
310 0 : if (!BN_nnmod(val[0], a, m, ctx))
311 : goto err; /* 1 */
312 0 : if (BN_is_zero(val[0])) {
313 0 : BN_zero(r);
314 : ret = 1;
315 0 : goto err;
316 : }
317 :
318 0 : window = BN_window_bits_for_exponent_size(bits);
319 0 : if (window > 1) {
320 0 : if (!BN_mod_mul_reciprocal(aa, val[0], val[0], &recp, ctx))
321 : goto err; /* 2 */
322 0 : j = 1 << (window - 1);
323 0 : for (i = 1; i < j; i++) {
324 0 : if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
325 0 : !BN_mod_mul_reciprocal(val[i], val[i - 1], aa, &recp, ctx))
326 : goto err;
327 : }
328 : }
329 :
330 : start = 1; /* This is used to avoid multiplication etc
331 : * when there is only the value '1' in the
332 : * buffer. */
333 : wvalue = 0; /* The 'value' of the window */
334 0 : wstart = bits - 1; /* The top bit of the window */
335 : wend = 0; /* The bottom bit of the window */
336 :
337 0 : if (!BN_one(r))
338 : goto err;
339 :
340 : for (;;) {
341 0 : if (BN_is_bit_set(p, wstart) == 0) {
342 0 : if (!start)
343 0 : if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
344 : goto err;
345 0 : if (wstart == 0)
346 : break;
347 0 : wstart--;
348 0 : continue;
349 : }
350 : /*
351 : * We now have wstart on a 'set' bit, we now need to work out how bit
352 : * a window to do. To do this we need to scan forward until the last
353 : * set bit before the end of the window
354 : */
355 : j = wstart;
356 : wvalue = 1;
357 : wend = 0;
358 0 : for (i = 1; i < window; i++) {
359 0 : if (wstart - i < 0)
360 : break;
361 0 : if (BN_is_bit_set(p, wstart - i)) {
362 0 : wvalue <<= (i - wend);
363 0 : wvalue |= 1;
364 : wend = i;
365 : }
366 : }
367 :
368 : /* wend is the size of the current window */
369 : j = wend + 1;
370 : /* add the 'bytes above' */
371 0 : if (!start)
372 0 : for (i = 0; i < j; i++) {
373 0 : if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
374 : goto err;
375 : }
376 :
377 : /* wvalue will be an odd number < 2^window */
378 0 : if (!BN_mod_mul_reciprocal(r, r, val[wvalue >> 1], &recp, ctx))
379 : goto err;
380 :
381 : /* move the 'window' down further */
382 0 : wstart -= wend + 1;
383 : wvalue = 0;
384 : start = 0;
385 0 : if (wstart < 0)
386 : break;
387 : }
388 : ret = 1;
389 : err:
390 0 : BN_CTX_end(ctx);
391 0 : BN_RECP_CTX_free(&recp);
392 : bn_check_top(r);
393 0 : return (ret);
394 : }
395 :
396 2270 : int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
397 : const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
398 : {
399 : int i, j, bits, ret = 0, wstart, wend, window, wvalue;
400 : int start = 1;
401 : BIGNUM *d, *r;
402 : const BIGNUM *aa;
403 : /* Table of variables obtained from 'ctx' */
404 : BIGNUM *val[TABLE_SIZE];
405 : BN_MONT_CTX *mont = NULL;
406 :
407 2270 : if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
408 762 : return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
409 : }
410 :
411 : bn_check_top(a);
412 : bn_check_top(p);
413 : bn_check_top(m);
414 :
415 1508 : if (!BN_is_odd(m)) {
416 0 : BNerr(BN_F_BN_MOD_EXP_MONT, BN_R_CALLED_WITH_EVEN_MODULUS);
417 0 : return (0);
418 : }
419 1508 : bits = BN_num_bits(p);
420 1508 : if (bits == 0) {
421 0 : ret = BN_one(rr);
422 0 : return ret;
423 : }
424 :
425 1508 : BN_CTX_start(ctx);
426 1508 : d = BN_CTX_get(ctx);
427 1508 : r = BN_CTX_get(ctx);
428 1508 : val[0] = BN_CTX_get(ctx);
429 1508 : if (!d || !r || !val[0])
430 : goto err;
431 :
432 : /*
433 : * If this is not done, things will break in the montgomery part
434 : */
435 :
436 1508 : if (in_mont != NULL)
437 : mont = in_mont;
438 : else {
439 345 : if ((mont = BN_MONT_CTX_new()) == NULL)
440 : goto err;
441 345 : if (!BN_MONT_CTX_set(mont, m, ctx))
442 : goto err;
443 : }
444 :
445 1508 : if (a->neg || BN_ucmp(a, m) >= 0) {
446 0 : if (!BN_nnmod(val[0], a, m, ctx))
447 : goto err;
448 : aa = val[0];
449 : } else
450 : aa = a;
451 1508 : if (BN_is_zero(aa)) {
452 0 : BN_zero(rr);
453 : ret = 1;
454 0 : goto err;
455 : }
456 1508 : if (!BN_to_montgomery(val[0], aa, mont, ctx))
457 : goto err; /* 1 */
458 :
459 1508 : window = BN_window_bits_for_exponent_size(bits);
460 1508 : if (window > 1) {
461 36 : if (!BN_mod_mul_montgomery(d, val[0], val[0], mont, ctx))
462 : goto err; /* 2 */
463 36 : j = 1 << (window - 1);
464 576 : for (i = 1; i < j; i++) {
465 1080 : if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
466 540 : !BN_mod_mul_montgomery(val[i], val[i - 1], d, mont, ctx))
467 : goto err;
468 : }
469 : }
470 :
471 : start = 1; /* This is used to avoid multiplication etc
472 : * when there is only the value '1' in the
473 : * buffer. */
474 : wvalue = 0; /* The 'value' of the window */
475 1508 : wstart = bits - 1; /* The top bit of the window */
476 : wend = 0; /* The bottom bit of the window */
477 :
478 : #if 1 /* by Shay Gueron's suggestion */
479 1508 : j = m->top; /* borrow j */
480 1508 : if (m->d[j - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
481 1508 : if (bn_wexpand(r, j) == NULL)
482 : goto err;
483 : /* 2^(top*BN_BITS2) - m */
484 1508 : r->d[0] = (0 - m->d[0]) & BN_MASK2;
485 23840 : for (i = 1; i < j; i++)
486 22332 : r->d[i] = (~m->d[i]) & BN_MASK2;
487 1508 : r->top = j;
488 : /*
489 : * Upper words will be zero if the corresponding words of 'm' were
490 : * 0xfff[...], so decrement r->top accordingly.
491 : */
492 1508 : bn_correct_top(r);
493 : } else
494 : #endif
495 0 : if (!BN_to_montgomery(r, BN_value_one(), mont, ctx))
496 : goto err;
497 : for (;;) {
498 33646 : if (BN_is_bit_set(p, wstart) == 0) {
499 27660 : if (!start) {
500 27660 : if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
501 : goto err;
502 : }
503 27660 : if (wstart == 0)
504 : break;
505 27660 : wstart--;
506 27660 : continue;
507 : }
508 : /*
509 : * We now have wstart on a 'set' bit, we now need to work out how bit
510 : * a window to do. To do this we need to scan forward until the last
511 : * set bit before the end of the window
512 : */
513 : j = wstart;
514 : wvalue = 1;
515 : wend = 0;
516 12024 : for (i = 1; i < window; i++) {
517 12060 : if (wstart - i < 0)
518 : break;
519 12024 : if (BN_is_bit_set(p, wstart - i)) {
520 6282 : wvalue <<= (i - wend);
521 6282 : wvalue |= 1;
522 : wend = i;
523 : }
524 : }
525 :
526 : /* wend is the size of the current window */
527 : j = wend + 1;
528 : /* add the 'bytes above' */
529 5986 : if (!start)
530 14090 : for (i = 0; i < j; i++) {
531 14090 : if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
532 : goto err;
533 : }
534 :
535 : /* wvalue will be an odd number < 2^window */
536 5986 : if (!BN_mod_mul_montgomery(r, r, val[wvalue >> 1], mont, ctx))
537 : goto err;
538 :
539 : /* move the 'window' down further */
540 5986 : wstart -= wend + 1;
541 : wvalue = 0;
542 : start = 0;
543 5986 : if (wstart < 0)
544 : break;
545 : }
546 : #if defined(SPARC_T4_MONT)
547 : if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
548 : j = mont->N.top; /* borrow j */
549 : val[0]->d[0] = 1; /* borrow val[0] */
550 : for (i = 1; i < j; i++)
551 : val[0]->d[i] = 0;
552 : val[0]->top = j;
553 : if (!BN_mod_mul_montgomery(rr, r, val[0], mont, ctx))
554 : goto err;
555 : } else
556 : #endif
557 1508 : if (!BN_from_montgomery(rr, r, mont, ctx))
558 : goto err;
559 : ret = 1;
560 : err:
561 1508 : if ((in_mont == NULL) && (mont != NULL))
562 345 : BN_MONT_CTX_free(mont);
563 1508 : BN_CTX_end(ctx);
564 : bn_check_top(rr);
565 1508 : return (ret);
566 : }
567 :
568 : #if defined(SPARC_T4_MONT)
569 : static BN_ULONG bn_get_bits(const BIGNUM *a, int bitpos)
570 : {
571 : BN_ULONG ret = 0;
572 : int wordpos;
573 :
574 : wordpos = bitpos / BN_BITS2;
575 : bitpos %= BN_BITS2;
576 : if (wordpos >= 0 && wordpos < a->top) {
577 : ret = a->d[wordpos] & BN_MASK2;
578 : if (bitpos) {
579 : ret >>= bitpos;
580 : if (++wordpos < a->top)
581 : ret |= a->d[wordpos] << (BN_BITS2 - bitpos);
582 : }
583 : }
584 :
585 : return ret & BN_MASK2;
586 : }
587 : #endif
588 :
589 : /*
590 : * BN_mod_exp_mont_consttime() stores the precomputed powers in a specific
591 : * layout so that accessing any of these table values shows the same access
592 : * pattern as far as cache lines are concerned. The following functions are
593 : * used to transfer a BIGNUM from/to that table.
594 : */
595 :
596 : static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top,
597 : unsigned char *buf, int idx,
598 : int width)
599 : {
600 : size_t i, j;
601 :
602 24384 : if (top > b->top)
603 : top = b->top; /* this works because 'buf' is explicitly
604 : * zeroed */
605 1582674 : for (i = 0, j = idx; i < top * sizeof b->d[0]; i++, j += width) {
606 1560576 : buf[j] = ((unsigned char *)b->d)[i];
607 : }
608 :
609 : return 1;
610 : }
611 :
612 78113 : static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top,
613 : unsigned char *buf, int idx,
614 : int width)
615 : {
616 : size_t i, j;
617 :
618 78113 : if (bn_wexpand(b, top) == NULL)
619 : return 0;
620 :
621 5077345 : for (i = 0, j = idx; i < top * sizeof b->d[0]; i++, j += width) {
622 4999232 : ((unsigned char *)b->d)[i] = buf[j];
623 : }
624 :
625 78113 : b->top = top;
626 78113 : bn_correct_top(b);
627 : return 1;
628 : }
629 :
630 : /*
631 : * Given a pointer value, compute the next address that is a cache line
632 : * multiple.
633 : */
634 : #define MOD_EXP_CTIME_ALIGN(x_) \
635 : ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
636 :
637 : /*
638 : * This variant of BN_mod_exp_mont() uses fixed windows and the special
639 : * precomputation memory layout to limit data-dependency to a minimum to
640 : * protect secret exponents (cf. the hyper-threading timing attacks pointed
641 : * out by Colin Percival,
642 : * http://www.daemong-consideredperthreading-considered-harmful/)
643 : */
644 762 : int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
645 : const BIGNUM *m, BN_CTX *ctx,
646 : BN_MONT_CTX *in_mont)
647 : {
648 : int i, bits, ret = 0, window, wvalue;
649 : int top;
650 : BN_MONT_CTX *mont = NULL;
651 :
652 : int numPowers;
653 : unsigned char *powerbufFree = NULL;
654 : int powerbufLen = 0;
655 : unsigned char *powerbuf = NULL;
656 : BIGNUM tmp, am;
657 : #if defined(SPARC_T4_MONT)
658 : unsigned int t4 = 0;
659 : #endif
660 :
661 : bn_check_top(a);
662 : bn_check_top(p);
663 : bn_check_top(m);
664 :
665 762 : top = m->top;
666 :
667 762 : if (!(m->d[0] & 1)) {
668 0 : BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME, BN_R_CALLED_WITH_EVEN_MODULUS);
669 0 : return (0);
670 : }
671 762 : bits = BN_num_bits(p);
672 762 : if (bits == 0) {
673 0 : ret = BN_one(rr);
674 0 : return ret;
675 : }
676 :
677 762 : BN_CTX_start(ctx);
678 :
679 : /*
680 : * Allocate a montgomery context if it was not supplied by the caller. If
681 : * this is not done, things will break in the montgomery part.
682 : */
683 762 : if (in_mont != NULL)
684 : mont = in_mont;
685 : else {
686 0 : if ((mont = BN_MONT_CTX_new()) == NULL)
687 : goto err;
688 0 : if (!BN_MONT_CTX_set(mont, m, ctx))
689 : goto err;
690 : }
691 :
692 : #ifdef RSAZ_ENABLED
693 : /*
694 : * If the size of the operands allow it, perform the optimized
695 : * RSAZ exponentiation. For further information see
696 : * crypto/bn/rsaz_exp.c and accompanying assembly modules.
697 : */
698 : if ((16 == a->top) && (16 == p->top) && (BN_num_bits(m) == 1024)
699 : && rsaz_avx2_eligible()) {
700 : if (NULL == bn_wexpand(rr, 16))
701 : goto err;
702 : RSAZ_1024_mod_exp_avx2(rr->d, a->d, p->d, m->d, mont->RR.d,
703 : mont->n0[0]);
704 : rr->top = 16;
705 : rr->neg = 0;
706 : bn_correct_top(rr);
707 : ret = 1;
708 : goto err;
709 : } else if ((8 == a->top) && (8 == p->top) && (BN_num_bits(m) == 512)) {
710 : if (NULL == bn_wexpand(rr, 8))
711 : goto err;
712 : RSAZ_512_mod_exp(rr->d, a->d, p->d, m->d, mont->n0[0], mont->RR.d);
713 : rr->top = 8;
714 : rr->neg = 0;
715 : bn_correct_top(rr);
716 : ret = 1;
717 : goto err;
718 : }
719 : #endif
720 :
721 : /* Get the window size to use with size of p. */
722 762 : window = BN_window_bits_for_ctime_exponent_size(bits);
723 : #if defined(SPARC_T4_MONT)
724 : if (window >= 5 && (top & 15) == 0 && top <= 64 &&
725 : (OPENSSL_sparcv9cap_P[1] & (CFR_MONTMUL | CFR_MONTSQR)) ==
726 : (CFR_MONTMUL | CFR_MONTSQR) && (t4 = OPENSSL_sparcv9cap_P[0]))
727 : window = 5;
728 : else
729 : #endif
730 : #if defined(OPENSSL_BN_ASM_MONT5)
731 : if (window >= 5) {
732 : window = 5; /* ~5% improvement for RSA2048 sign, and even
733 : * for RSA4096 */
734 : if ((top & 7) == 0)
735 : powerbufLen += 2 * top * sizeof(m->d[0]);
736 : }
737 : #endif
738 : (void)0;
739 :
740 : /*
741 : * Allocate a buffer large enough to hold all of the pre-computed powers
742 : * of am, am itself and tmp.
743 : */
744 762 : numPowers = 1 << window;
745 1524 : powerbufLen += sizeof(m->d[0]) * (top * numPowers +
746 : ((2 * top) >
747 762 : numPowers ? (2 * top) : numPowers));
748 : #ifdef alloca
749 762 : if (powerbufLen < 3072)
750 762 : powerbufFree =
751 762 : alloca(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
752 : else
753 : #endif
754 0 : if ((powerbufFree =
755 0 : (unsigned char *)OPENSSL_malloc(powerbufLen +
756 : MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH))
757 : == NULL)
758 : goto err;
759 :
760 762 : powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
761 762 : memset(powerbuf, 0, powerbufLen);
762 :
763 : #ifdef alloca
764 762 : if (powerbufLen < 3072)
765 : powerbufFree = NULL;
766 : #endif
767 :
768 : /* lay down tmp and am right after powers table */
769 762 : tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers);
770 762 : am.d = tmp.d + top;
771 762 : tmp.top = am.top = 0;
772 762 : tmp.dmax = am.dmax = top;
773 762 : tmp.neg = am.neg = 0;
774 762 : tmp.flags = am.flags = BN_FLG_STATIC_DATA;
775 :
776 : /* prepare a^0 in Montgomery domain */
777 : #if 1 /* by Shay Gueron's suggestion */
778 762 : if (m->d[top - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
779 : /* 2^(top*BN_BITS2) - m */
780 762 : tmp.d[0] = (0 - m->d[0]) & BN_MASK2;
781 6096 : for (i = 1; i < top; i++)
782 5334 : tmp.d[i] = (~m->d[i]) & BN_MASK2;
783 762 : tmp.top = top;
784 : } else
785 : #endif
786 0 : if (!BN_to_montgomery(&tmp, BN_value_one(), mont, ctx))
787 : goto err;
788 :
789 : /* prepare a^1 in Montgomery domain */
790 762 : if (a->neg || BN_ucmp(a, m) >= 0) {
791 0 : if (!BN_mod(&am, a, m, ctx))
792 : goto err;
793 0 : if (!BN_to_montgomery(&am, &am, mont, ctx))
794 : goto err;
795 762 : } else if (!BN_to_montgomery(&am, a, mont, ctx))
796 : goto err;
797 :
798 : #if defined(SPARC_T4_MONT)
799 : if (t4) {
800 : typedef int (*bn_pwr5_mont_f) (BN_ULONG *tp, const BN_ULONG *np,
801 : const BN_ULONG *n0, const void *table,
802 : int power, int bits);
803 : int bn_pwr5_mont_t4_8(BN_ULONG *tp, const BN_ULONG *np,
804 : const BN_ULONG *n0, const void *table,
805 : int power, int bits);
806 : int bn_pwr5_mont_t4_16(BN_ULONG *tp, const BN_ULONG *np,
807 : const BN_ULONG *n0, const void *table,
808 : int power, int bits);
809 : int bn_pwr5_mont_t4_24(BN_ULONG *tp, const BN_ULONG *np,
810 : const BN_ULONG *n0, const void *table,
811 : int power, int bits);
812 : int bn_pwr5_mont_t4_32(BN_ULONG *tp, const BN_ULONG *np,
813 : const BN_ULONG *n0, const void *table,
814 : int power, int bits);
815 : static const bn_pwr5_mont_f pwr5_funcs[4] = {
816 : bn_pwr5_mont_t4_8, bn_pwr5_mont_t4_16,
817 : bn_pwr5_mont_t4_24, bn_pwr5_mont_t4_32
818 : };
819 : bn_pwr5_mont_f pwr5_worker = pwr5_funcs[top / 16 - 1];
820 :
821 : typedef int (*bn_mul_mont_f) (BN_ULONG *rp, const BN_ULONG *ap,
822 : const void *bp, const BN_ULONG *np,
823 : const BN_ULONG *n0);
824 : int bn_mul_mont_t4_8(BN_ULONG *rp, const BN_ULONG *ap, const void *bp,
825 : const BN_ULONG *np, const BN_ULONG *n0);
826 : int bn_mul_mont_t4_16(BN_ULONG *rp, const BN_ULONG *ap,
827 : const void *bp, const BN_ULONG *np,
828 : const BN_ULONG *n0);
829 : int bn_mul_mont_t4_24(BN_ULONG *rp, const BN_ULONG *ap,
830 : const void *bp, const BN_ULONG *np,
831 : const BN_ULONG *n0);
832 : int bn_mul_mont_t4_32(BN_ULONG *rp, const BN_ULONG *ap,
833 : const void *bp, const BN_ULONG *np,
834 : const BN_ULONG *n0);
835 : static const bn_mul_mont_f mul_funcs[4] = {
836 : bn_mul_mont_t4_8, bn_mul_mont_t4_16,
837 : bn_mul_mont_t4_24, bn_mul_mont_t4_32
838 : };
839 : bn_mul_mont_f mul_worker = mul_funcs[top / 16 - 1];
840 :
841 : void bn_mul_mont_vis3(BN_ULONG *rp, const BN_ULONG *ap,
842 : const void *bp, const BN_ULONG *np,
843 : const BN_ULONG *n0, int num);
844 : void bn_mul_mont_t4(BN_ULONG *rp, const BN_ULONG *ap,
845 : const void *bp, const BN_ULONG *np,
846 : const BN_ULONG *n0, int num);
847 : void bn_mul_mont_gather5_t4(BN_ULONG *rp, const BN_ULONG *ap,
848 : const void *table, const BN_ULONG *np,
849 : const BN_ULONG *n0, int num, int power);
850 : void bn_flip_n_scatter5_t4(const BN_ULONG *inp, size_t num,
851 : void *table, size_t power);
852 : void bn_gather5_t4(BN_ULONG *out, size_t num,
853 : void *table, size_t power);
854 : void bn_flip_t4(BN_ULONG *dst, BN_ULONG *src, size_t num);
855 :
856 : BN_ULONG *np = mont->N.d, *n0 = mont->n0;
857 : int stride = 5 * (6 - (top / 16 - 1)); /* multiple of 5, but less
858 : * than 32 */
859 :
860 : /*
861 : * BN_to_montgomery can contaminate words above .top [in
862 : * BN_DEBUG[_DEBUG] build]...
863 : */
864 : for (i = am.top; i < top; i++)
865 : am.d[i] = 0;
866 : for (i = tmp.top; i < top; i++)
867 : tmp.d[i] = 0;
868 :
869 : bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 0);
870 : bn_flip_n_scatter5_t4(am.d, top, powerbuf, 1);
871 : if (!(*mul_worker) (tmp.d, am.d, am.d, np, n0) &&
872 : !(*mul_worker) (tmp.d, am.d, am.d, np, n0))
873 : bn_mul_mont_vis3(tmp.d, am.d, am.d, np, n0, top);
874 : bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 2);
875 :
876 : for (i = 3; i < 32; i++) {
877 : /* Calculate a^i = a^(i-1) * a */
878 : if (!(*mul_worker) (tmp.d, tmp.d, am.d, np, n0) &&
879 : !(*mul_worker) (tmp.d, tmp.d, am.d, np, n0))
880 : bn_mul_mont_vis3(tmp.d, tmp.d, am.d, np, n0, top);
881 : bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, i);
882 : }
883 :
884 : /* switch to 64-bit domain */
885 : np = alloca(top * sizeof(BN_ULONG));
886 : top /= 2;
887 : bn_flip_t4(np, mont->N.d, top);
888 :
889 : bits--;
890 : for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--)
891 : wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
892 : bn_gather5_t4(tmp.d, top, powerbuf, wvalue);
893 :
894 : /*
895 : * Scan the exponent one window at a time starting from the most
896 : * significant bits.
897 : */
898 : while (bits >= 0) {
899 : if (bits < stride)
900 : stride = bits + 1;
901 : bits -= stride;
902 : wvalue = bn_get_bits(p, bits + 1);
903 :
904 : if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride))
905 : continue;
906 : /* retry once and fall back */
907 : if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride))
908 : continue;
909 :
910 : bits += stride - 5;
911 : wvalue >>= stride - 5;
912 : wvalue &= 31;
913 : bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
914 : bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
915 : bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
916 : bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
917 : bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
918 : bn_mul_mont_gather5_t4(tmp.d, tmp.d, powerbuf, np, n0, top,
919 : wvalue);
920 : }
921 :
922 : bn_flip_t4(tmp.d, tmp.d, top);
923 : top *= 2;
924 : /* back to 32-bit domain */
925 : tmp.top = top;
926 : bn_correct_top(&tmp);
927 : OPENSSL_cleanse(np, top * sizeof(BN_ULONG));
928 : } else
929 : #endif
930 : #if defined(OPENSSL_BN_ASM_MONT5)
931 : if (window == 5 && top > 1) {
932 : /*
933 : * This optimization uses ideas from http://eprint.iacr.org/2011/239,
934 : * specifically optimization of cache-timing attack countermeasures
935 : * and pre-computation optimization.
936 : */
937 :
938 : /*
939 : * Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as
940 : * 512-bit RSA is hardly relevant, we omit it to spare size...
941 : */
942 : void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap,
943 : const void *table, const BN_ULONG *np,
944 : const BN_ULONG *n0, int num, int power);
945 : void bn_scatter5(const BN_ULONG *inp, size_t num,
946 : void *table, size_t power);
947 : void bn_gather5(BN_ULONG *out, size_t num, void *table, size_t power);
948 : void bn_power5(BN_ULONG *rp, const BN_ULONG *ap,
949 : const void *table, const BN_ULONG *np,
950 : const BN_ULONG *n0, int num, int power);
951 : int bn_get_bits5(const BN_ULONG *ap, int off);
952 : int bn_from_montgomery(BN_ULONG *rp, const BN_ULONG *ap,
953 : const BN_ULONG *not_used, const BN_ULONG *np,
954 : const BN_ULONG *n0, int num);
955 :
956 : BN_ULONG *np = mont->N.d, *n0 = mont->n0, *np2;
957 :
958 : /*
959 : * BN_to_montgomery can contaminate words above .top [in
960 : * BN_DEBUG[_DEBUG] build]...
961 : */
962 : for (i = am.top; i < top; i++)
963 : am.d[i] = 0;
964 : for (i = tmp.top; i < top; i++)
965 : tmp.d[i] = 0;
966 :
967 : if (top & 7)
968 : np2 = np;
969 : else
970 : for (np2 = am.d + top, i = 0; i < top; i++)
971 : np2[2 * i] = np[i];
972 :
973 : bn_scatter5(tmp.d, top, powerbuf, 0);
974 : bn_scatter5(am.d, am.top, powerbuf, 1);
975 : bn_mul_mont(tmp.d, am.d, am.d, np, n0, top);
976 : bn_scatter5(tmp.d, top, powerbuf, 2);
977 :
978 : # if 0
979 : for (i = 3; i < 32; i++) {
980 : /* Calculate a^i = a^(i-1) * a */
981 : bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np2, n0, top, i - 1);
982 : bn_scatter5(tmp.d, top, powerbuf, i);
983 : }
984 : # else
985 : /* same as above, but uses squaring for 1/2 of operations */
986 : for (i = 4; i < 32; i *= 2) {
987 : bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
988 : bn_scatter5(tmp.d, top, powerbuf, i);
989 : }
990 : for (i = 3; i < 8; i += 2) {
991 : int j;
992 : bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np2, n0, top, i - 1);
993 : bn_scatter5(tmp.d, top, powerbuf, i);
994 : for (j = 2 * i; j < 32; j *= 2) {
995 : bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
996 : bn_scatter5(tmp.d, top, powerbuf, j);
997 : }
998 : }
999 : for (; i < 16; i += 2) {
1000 : bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np2, n0, top, i - 1);
1001 : bn_scatter5(tmp.d, top, powerbuf, i);
1002 : bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1003 : bn_scatter5(tmp.d, top, powerbuf, 2 * i);
1004 : }
1005 : for (; i < 32; i += 2) {
1006 : bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np2, n0, top, i - 1);
1007 : bn_scatter5(tmp.d, top, powerbuf, i);
1008 : }
1009 : # endif
1010 : bits--;
1011 : for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--)
1012 : wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
1013 : bn_gather5(tmp.d, top, powerbuf, wvalue);
1014 :
1015 : /*
1016 : * Scan the exponent one window at a time starting from the most
1017 : * significant bits.
1018 : */
1019 : if (top & 7)
1020 : while (bits >= 0) {
1021 : for (wvalue = 0, i = 0; i < 5; i++, bits--)
1022 : wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
1023 :
1024 : bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1025 : bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1026 : bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1027 : bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1028 : bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1029 : bn_mul_mont_gather5(tmp.d, tmp.d, powerbuf, np, n0, top,
1030 : wvalue);
1031 : } else {
1032 : while (bits >= 0) {
1033 : wvalue = bn_get_bits5(p->d, bits - 4);
1034 : bits -= 5;
1035 : bn_power5(tmp.d, tmp.d, powerbuf, np2, n0, top, wvalue);
1036 : }
1037 : }
1038 :
1039 : ret = bn_from_montgomery(tmp.d, tmp.d, NULL, np2, n0, top);
1040 : tmp.top = top;
1041 : bn_correct_top(&tmp);
1042 : if (ret) {
1043 : if (!BN_copy(rr, &tmp))
1044 : ret = 0;
1045 : goto err; /* non-zero ret means it's not error */
1046 : }
1047 : } else
1048 : #endif
1049 : {
1050 762 : if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, numPowers))
1051 : goto err;
1052 762 : if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, numPowers))
1053 : goto err;
1054 :
1055 : /*
1056 : * If the window size is greater than 1, then calculate
1057 : * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even
1058 : * powers could instead be computed as (a^(i/2))^2 to use the slight
1059 : * performance advantage of sqr over mul).
1060 : */
1061 762 : if (window > 1) {
1062 762 : if (!BN_mod_mul_montgomery(&tmp, &am, &am, mont, ctx))
1063 : goto err;
1064 : if (!MOD_EXP_CTIME_COPY_TO_PREBUF
1065 762 : (&tmp, top, powerbuf, 2, numPowers))
1066 : goto err;
1067 22098 : for (i = 3; i < numPowers; i++) {
1068 : /* Calculate a^i = a^(i-1) * a */
1069 22098 : if (!BN_mod_mul_montgomery(&tmp, &am, &tmp, mont, ctx))
1070 : goto err;
1071 : if (!MOD_EXP_CTIME_COPY_TO_PREBUF
1072 22098 : (&tmp, top, powerbuf, i, numPowers))
1073 : goto err;
1074 : }
1075 : }
1076 :
1077 762 : bits--;
1078 3024 : for (wvalue = 0, i = bits % window; i >= 0; i--, bits--)
1079 2262 : wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
1080 762 : if (!MOD_EXP_CTIME_COPY_FROM_PREBUF
1081 762 : (&tmp, top, powerbuf, wvalue, numPowers))
1082 : goto err;
1083 :
1084 : /*
1085 : * Scan the exponent one window at a time starting from the most
1086 : * significant bits.
1087 : */
1088 78113 : while (bits >= 0) {
1089 : wvalue = 0; /* The 'value' of the window */
1090 :
1091 : /* Scan the window, squaring the result as we go */
1092 386755 : for (i = 0; i < window; i++, bits--) {
1093 386755 : if (!BN_mod_mul_montgomery(&tmp, &tmp, &tmp, mont, ctx))
1094 : goto err;
1095 386755 : wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
1096 : }
1097 :
1098 : /*
1099 : * Fetch the appropriate pre-computed value from the pre-buf
1100 : */
1101 77351 : if (!MOD_EXP_CTIME_COPY_FROM_PREBUF
1102 77351 : (&am, top, powerbuf, wvalue, numPowers))
1103 : goto err;
1104 :
1105 : /* Multiply the result into the intermediate result */
1106 77351 : if (!BN_mod_mul_montgomery(&tmp, &tmp, &am, mont, ctx))
1107 : goto err;
1108 : }
1109 : }
1110 :
1111 : /* Convert the final result from montgomery to standard format */
1112 : #if defined(SPARC_T4_MONT)
1113 : if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
1114 : am.d[0] = 1; /* borrow am */
1115 : for (i = 1; i < top; i++)
1116 : am.d[i] = 0;
1117 : if (!BN_mod_mul_montgomery(rr, &tmp, &am, mont, ctx))
1118 : goto err;
1119 : } else
1120 : #endif
1121 762 : if (!BN_from_montgomery(rr, &tmp, mont, ctx))
1122 : goto err;
1123 : ret = 1;
1124 : err:
1125 762 : if ((in_mont == NULL) && (mont != NULL))
1126 0 : BN_MONT_CTX_free(mont);
1127 762 : if (powerbuf != NULL) {
1128 762 : OPENSSL_cleanse(powerbuf, powerbufLen);
1129 762 : if (powerbufFree)
1130 0 : OPENSSL_free(powerbufFree);
1131 : }
1132 762 : BN_CTX_end(ctx);
1133 762 : return (ret);
1134 : }
1135 :
1136 0 : int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
1137 : const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
1138 : {
1139 : BN_MONT_CTX *mont = NULL;
1140 : int b, bits, ret = 0;
1141 : int r_is_one;
1142 : BN_ULONG w, next_w;
1143 : BIGNUM *d, *r, *t;
1144 : BIGNUM *swap_tmp;
1145 : #define BN_MOD_MUL_WORD(r, w, m) \
1146 : (BN_mul_word(r, (w)) && \
1147 : (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
1148 : (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
1149 : /*
1150 : * BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is
1151 : * probably more overhead than always using BN_mod (which uses BN_copy if
1152 : * a similar test returns true).
1153 : */
1154 : /*
1155 : * We can use BN_mod and do not need BN_nnmod because our accumulator is
1156 : * never negative (the result of BN_mod does not depend on the sign of
1157 : * the modulus).
1158 : */
1159 : #define BN_TO_MONTGOMERY_WORD(r, w, mont) \
1160 : (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
1161 :
1162 0 : if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
1163 : /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1164 0 : BNerr(BN_F_BN_MOD_EXP_MONT_WORD, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1165 0 : return -1;
1166 : }
1167 :
1168 : bn_check_top(p);
1169 : bn_check_top(m);
1170 :
1171 0 : if (!BN_is_odd(m)) {
1172 0 : BNerr(BN_F_BN_MOD_EXP_MONT_WORD, BN_R_CALLED_WITH_EVEN_MODULUS);
1173 0 : return (0);
1174 : }
1175 0 : if (m->top == 1)
1176 0 : a %= m->d[0]; /* make sure that 'a' is reduced */
1177 :
1178 0 : bits = BN_num_bits(p);
1179 0 : if (bits == 0) {
1180 : /* x**0 mod 1 is still zero. */
1181 0 : if (BN_is_one(m)) {
1182 : ret = 1;
1183 0 : BN_zero(rr);
1184 : } else
1185 0 : ret = BN_one(rr);
1186 0 : return ret;
1187 : }
1188 0 : if (a == 0) {
1189 0 : BN_zero(rr);
1190 : ret = 1;
1191 0 : return ret;
1192 : }
1193 :
1194 0 : BN_CTX_start(ctx);
1195 0 : d = BN_CTX_get(ctx);
1196 0 : r = BN_CTX_get(ctx);
1197 0 : t = BN_CTX_get(ctx);
1198 0 : if (d == NULL || r == NULL || t == NULL)
1199 : goto err;
1200 :
1201 0 : if (in_mont != NULL)
1202 : mont = in_mont;
1203 : else {
1204 0 : if ((mont = BN_MONT_CTX_new()) == NULL)
1205 : goto err;
1206 0 : if (!BN_MONT_CTX_set(mont, m, ctx))
1207 : goto err;
1208 : }
1209 :
1210 : r_is_one = 1; /* except for Montgomery factor */
1211 :
1212 : /* bits-1 >= 0 */
1213 :
1214 : /* The result is accumulated in the product r*w. */
1215 : w = a; /* bit 'bits-1' of 'p' is always set */
1216 0 : for (b = bits - 2; b >= 0; b--) {
1217 : /* First, square r*w. */
1218 0 : next_w = w * w;
1219 0 : if ((next_w / w) != w) { /* overflow */
1220 0 : if (r_is_one) {
1221 0 : if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1222 : goto err;
1223 : r_is_one = 0;
1224 : } else {
1225 0 : if (!BN_MOD_MUL_WORD(r, w, m))
1226 : goto err;
1227 : }
1228 : next_w = 1;
1229 : }
1230 : w = next_w;
1231 0 : if (!r_is_one) {
1232 0 : if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
1233 : goto err;
1234 : }
1235 :
1236 : /* Second, multiply r*w by 'a' if exponent bit is set. */
1237 0 : if (BN_is_bit_set(p, b)) {
1238 0 : next_w = w * a;
1239 0 : if ((next_w / a) != w) { /* overflow */
1240 0 : if (r_is_one) {
1241 0 : if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1242 : goto err;
1243 : r_is_one = 0;
1244 : } else {
1245 0 : if (!BN_MOD_MUL_WORD(r, w, m))
1246 : goto err;
1247 : }
1248 : next_w = a;
1249 : }
1250 : w = next_w;
1251 : }
1252 : }
1253 :
1254 : /* Finally, set r:=r*w. */
1255 0 : if (w != 1) {
1256 0 : if (r_is_one) {
1257 0 : if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1258 : goto err;
1259 : r_is_one = 0;
1260 : } else {
1261 0 : if (!BN_MOD_MUL_WORD(r, w, m))
1262 : goto err;
1263 : }
1264 : }
1265 :
1266 0 : if (r_is_one) { /* can happen only if a == 1 */
1267 0 : if (!BN_one(rr))
1268 : goto err;
1269 : } else {
1270 0 : if (!BN_from_montgomery(rr, r, mont, ctx))
1271 : goto err;
1272 : }
1273 : ret = 1;
1274 : err:
1275 0 : if ((in_mont == NULL) && (mont != NULL))
1276 0 : BN_MONT_CTX_free(mont);
1277 0 : BN_CTX_end(ctx);
1278 : bn_check_top(rr);
1279 0 : return (ret);
1280 : }
1281 :
1282 : /* The old fallback, simple version :-) */
1283 0 : int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
1284 : const BIGNUM *m, BN_CTX *ctx)
1285 : {
1286 : int i, j, bits, ret = 0, wstart, wend, window, wvalue;
1287 : int start = 1;
1288 : BIGNUM *d;
1289 : /* Table of variables obtained from 'ctx' */
1290 : BIGNUM *val[TABLE_SIZE];
1291 :
1292 0 : if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
1293 : /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1294 0 : BNerr(BN_F_BN_MOD_EXP_SIMPLE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1295 0 : return -1;
1296 : }
1297 :
1298 0 : bits = BN_num_bits(p);
1299 :
1300 0 : if (bits == 0) {
1301 0 : ret = BN_one(r);
1302 0 : return ret;
1303 : }
1304 :
1305 0 : BN_CTX_start(ctx);
1306 0 : d = BN_CTX_get(ctx);
1307 0 : val[0] = BN_CTX_get(ctx);
1308 0 : if (!d || !val[0])
1309 : goto err;
1310 :
1311 0 : if (!BN_nnmod(val[0], a, m, ctx))
1312 : goto err; /* 1 */
1313 0 : if (BN_is_zero(val[0])) {
1314 0 : BN_zero(r);
1315 : ret = 1;
1316 0 : goto err;
1317 : }
1318 :
1319 0 : window = BN_window_bits_for_exponent_size(bits);
1320 0 : if (window > 1) {
1321 0 : if (!BN_mod_mul(d, val[0], val[0], m, ctx))
1322 : goto err; /* 2 */
1323 0 : j = 1 << (window - 1);
1324 0 : for (i = 1; i < j; i++) {
1325 0 : if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
1326 0 : !BN_mod_mul(val[i], val[i - 1], d, m, ctx))
1327 : goto err;
1328 : }
1329 : }
1330 :
1331 : start = 1; /* This is used to avoid multiplication etc
1332 : * when there is only the value '1' in the
1333 : * buffer. */
1334 : wvalue = 0; /* The 'value' of the window */
1335 0 : wstart = bits - 1; /* The top bit of the window */
1336 : wend = 0; /* The bottom bit of the window */
1337 :
1338 0 : if (!BN_one(r))
1339 : goto err;
1340 :
1341 : for (;;) {
1342 0 : if (BN_is_bit_set(p, wstart) == 0) {
1343 0 : if (!start)
1344 0 : if (!BN_mod_mul(r, r, r, m, ctx))
1345 : goto err;
1346 0 : if (wstart == 0)
1347 : break;
1348 0 : wstart--;
1349 0 : continue;
1350 : }
1351 : /*
1352 : * We now have wstart on a 'set' bit, we now need to work out how bit
1353 : * a window to do. To do this we need to scan forward until the last
1354 : * set bit before the end of the window
1355 : */
1356 : j = wstart;
1357 : wvalue = 1;
1358 : wend = 0;
1359 0 : for (i = 1; i < window; i++) {
1360 0 : if (wstart - i < 0)
1361 : break;
1362 0 : if (BN_is_bit_set(p, wstart - i)) {
1363 0 : wvalue <<= (i - wend);
1364 0 : wvalue |= 1;
1365 : wend = i;
1366 : }
1367 : }
1368 :
1369 : /* wend is the size of the current window */
1370 : j = wend + 1;
1371 : /* add the 'bytes above' */
1372 0 : if (!start)
1373 0 : for (i = 0; i < j; i++) {
1374 0 : if (!BN_mod_mul(r, r, r, m, ctx))
1375 : goto err;
1376 : }
1377 :
1378 : /* wvalue will be an odd number < 2^window */
1379 0 : if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx))
1380 : goto err;
1381 :
1382 : /* move the 'window' down further */
1383 0 : wstart -= wend + 1;
1384 : wvalue = 0;
1385 : start = 0;
1386 0 : if (wstart < 0)
1387 : break;
1388 : }
1389 : ret = 1;
1390 : err:
1391 0 : BN_CTX_end(ctx);
1392 : bn_check_top(r);
1393 0 : return (ret);
1394 : }
|
