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1/* $OpenBSD: bn_exp.c,v 1.23 2015/09/10 15:56:25 jsing Exp $ */
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 <stdlib.h>
113#include <string.h>
114
115#include <openssl/err.h>
116
117#include "bn_lcl.h"
118
119/* maximum precomputation table size for *variable* sliding windows */
120#define TABLE_SIZE 32
121
122/* this one works - simple but works */
123int
124BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
125{
126 int i, bits, ret = 0;
127 BIGNUM *v, *rr;
128
129 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
130 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
131 BNerr(BN_F_BN_EXP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
132 return -1;
133 }
134
135 BN_CTX_start(ctx);
136 if ((r == a) || (r == p))
137 rr = BN_CTX_get(ctx);
138 else
139 rr = r;
140 v = BN_CTX_get(ctx);
141 if (rr == NULL || v == NULL)
142 goto err;
143
144 if (BN_copy(v, a) == NULL)
145 goto err;
146 bits = BN_num_bits(p);
147
148 if (BN_is_odd(p)) {
149 if (BN_copy(rr, a) == NULL)
150 goto err;
151 } else {
152 if (!BN_one(rr))
153 goto err;
154 }
155
156 for (i = 1; i < bits; i++) {
157 if (!BN_sqr(v, v, ctx))
158 goto err;
159 if (BN_is_bit_set(p, i)) {
160 if (!BN_mul(rr, rr, v, ctx))
161 goto err;
162 }
163 }
164 ret = 1;
165
166err:
167 if (r != rr && rr != NULL)
168 BN_copy(r, rr);
169 BN_CTX_end(ctx);
170 bn_check_top(r);
171 return (ret);
172}
173
174int
175BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
176 BN_CTX *ctx)
177{
178 int ret;
179
180 bn_check_top(a);
181 bn_check_top(p);
182 bn_check_top(m);
183
184 /* For even modulus m = 2^k*m_odd, it might make sense to compute
185 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery
186 * exponentiation for the odd part), using appropriate exponent
187 * reductions, and combine the results using the CRT.
188 *
189 * For now, we use Montgomery only if the modulus is odd; otherwise,
190 * exponentiation using the reciprocal-based quick remaindering
191 * algorithm is used.
192 *
193 * (Timing obtained with expspeed.c [computations a^p mod m
194 * where a, p, m are of the same length: 256, 512, 1024, 2048,
195 * 4096, 8192 bits], compared to the running time of the
196 * standard algorithm:
197 *
198 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
199 * 55 .. 77 % [UltraSparc processor, but
200 * debug-solaris-sparcv8-gcc conf.]
201 *
202 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
203 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
204 *
205 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
206 * at 2048 and more bits, but at 512 and 1024 bits, it was
207 * slower even than the standard algorithm!
208 *
209 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
210 * should be obtained when the new Montgomery reduction code
211 * has been integrated into OpenSSL.)
212 */
213
214#define MONT_MUL_MOD
215#define MONT_EXP_WORD
216#define RECP_MUL_MOD
217
218#ifdef MONT_MUL_MOD
219 /* I have finally been able to take out this pre-condition of
220 * the top bit being set. It was caused by an error in BN_div
221 * with negatives. There was also another problem when for a^b%m
222 * a >= m. eay 07-May-97 */
223/* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */
224
225 if (BN_is_odd(m)) {
226# ifdef MONT_EXP_WORD
227 if (a->top == 1 && !a->neg &&
228 (BN_get_flags(p, BN_FLG_CONSTTIME) == 0)) {
229 BN_ULONG A = a->d[0];
230 ret = BN_mod_exp_mont_word(r, A,p, m,ctx, NULL);
231 } else
232# endif
233 ret = BN_mod_exp_mont(r, a,p, m,ctx, NULL);
234 } else
235#endif
236#ifdef RECP_MUL_MOD
237 {
238 ret = BN_mod_exp_recp(r, a,p, m, ctx);
239 }
240#else
241 {
242 ret = BN_mod_exp_simple(r, a,p, m, ctx);
243 }
244#endif
245
246 bn_check_top(r);
247 return (ret);
248}
249
250int
251BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
252 BN_CTX *ctx)
253{
254 int i, j, bits, ret = 0, wstart, wend, window, wvalue;
255 int start = 1;
256 BIGNUM *aa;
257 /* Table of variables obtained from 'ctx' */
258 BIGNUM *val[TABLE_SIZE];
259 BN_RECP_CTX recp;
260
261 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
262 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
263 BNerr(BN_F_BN_MOD_EXP_RECP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
264 return -1;
265 }
266
267 bits = BN_num_bits(p);
268
269 if (bits == 0) {
270 ret = BN_one(r);
271 return ret;
272 }
273
274 BN_CTX_start(ctx);
275 if ((aa = BN_CTX_get(ctx)) == NULL)
276 goto err;
277 if ((val[0] = BN_CTX_get(ctx)) == NULL)
278 goto err;
279
280 BN_RECP_CTX_init(&recp);
281 if (m->neg) {
282 /* ignore sign of 'm' */
283 if (!BN_copy(aa, m))
284 goto err;
285 aa->neg = 0;
286 if (BN_RECP_CTX_set(&recp, aa, ctx) <= 0)
287 goto err;
288 } else {
289 if (BN_RECP_CTX_set(&recp, m, ctx) <= 0)
290 goto err;
291 }
292
293 if (!BN_nnmod(val[0], a, m, ctx))
294 goto err; /* 1 */
295 if (BN_is_zero(val[0])) {
296 BN_zero(r);
297 ret = 1;
298 goto err;
299 }
300
301 window = BN_window_bits_for_exponent_size(bits);
302 if (window > 1) {
303 if (!BN_mod_mul_reciprocal(aa, val[0], val[0], &recp, ctx))
304 goto err; /* 2 */
305 j = 1 << (window - 1);
306 for (i = 1; i < j; i++) {
307 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
308 !BN_mod_mul_reciprocal(val[i], val[i - 1],
309 aa, &recp, ctx))
310 goto err;
311 }
312 }
313
314 start = 1; /* This is used to avoid multiplication etc
315 * when there is only the value '1' in the
316 * buffer. */
317 wvalue = 0; /* The 'value' of the window */
318 wstart = bits - 1; /* The top bit of the window */
319 wend = 0; /* The bottom bit of the window */
320
321 if (!BN_one(r))
322 goto err;
323
324 for (;;) {
325 if (BN_is_bit_set(p, wstart) == 0) {
326 if (!start)
327 if (!BN_mod_mul_reciprocal(r, r,r, &recp, ctx))
328 goto err;
329 if (wstart == 0)
330 break;
331 wstart--;
332 continue;
333 }
334 /* We now have wstart on a 'set' bit, we now need to work out
335 * how bit a window to do. To do this we need to scan
336 * forward until the last set bit before the end of the
337 * window */
338 j = wstart;
339 wvalue = 1;
340 wend = 0;
341 for (i = 1; i < window; i++) {
342 if (wstart - i < 0)
343 break;
344 if (BN_is_bit_set(p, wstart - i)) {
345 wvalue <<= (i - wend);
346 wvalue |= 1;
347 wend = i;
348 }
349 }
350
351 /* wend is the size of the current window */
352 j = wend + 1;
353 /* add the 'bytes above' */
354 if (!start)
355 for (i = 0; i < j; i++) {
356 if (!BN_mod_mul_reciprocal(r, r,r, &recp, ctx))
357 goto err;
358 }
359
360 /* wvalue will be an odd number < 2^window */
361 if (!BN_mod_mul_reciprocal(r, r,val[wvalue >> 1], &recp, ctx))
362 goto err;
363
364 /* move the 'window' down further */
365 wstart -= wend + 1;
366 wvalue = 0;
367 start = 0;
368 if (wstart < 0)
369 break;
370 }
371 ret = 1;
372
373err:
374 BN_CTX_end(ctx);
375 BN_RECP_CTX_free(&recp);
376 bn_check_top(r);
377 return (ret);
378}
379
380int
381BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
382 BN_CTX *ctx, BN_MONT_CTX *in_mont)
383{
384 int i, j, bits, ret = 0, wstart, wend, window, wvalue;
385 int start = 1;
386 BIGNUM *d, *r;
387 const BIGNUM *aa;
388 /* Table of variables obtained from 'ctx' */
389 BIGNUM *val[TABLE_SIZE];
390 BN_MONT_CTX *mont = NULL;
391
392 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
393 return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
394 }
395
396 bn_check_top(a);
397 bn_check_top(p);
398 bn_check_top(m);
399
400 if (!BN_is_odd(m)) {
401 BNerr(BN_F_BN_MOD_EXP_MONT, BN_R_CALLED_WITH_EVEN_MODULUS);
402 return (0);
403 }
404 bits = BN_num_bits(p);
405 if (bits == 0) {
406 ret = BN_one(rr);
407 return ret;
408 }
409
410 BN_CTX_start(ctx);
411 if ((d = BN_CTX_get(ctx)) == NULL)
412 goto err;
413 if ((r = BN_CTX_get(ctx)) == NULL)
414 goto err;
415 if ((val[0] = BN_CTX_get(ctx)) == NULL)
416 goto err;
417
418 /* If this is not done, things will break in the montgomery
419 * part */
420
421 if (in_mont != NULL)
422 mont = in_mont;
423 else {
424 if ((mont = BN_MONT_CTX_new()) == NULL)
425 goto err;
426 if (!BN_MONT_CTX_set(mont, m, ctx))
427 goto err;
428 }
429
430 if (a->neg || BN_ucmp(a, m) >= 0) {
431 if (!BN_nnmod(val[0], a,m, ctx))
432 goto err;
433 aa = val[0];
434 } else
435 aa = a;
436 if (BN_is_zero(aa)) {
437 BN_zero(rr);
438 ret = 1;
439 goto err;
440 }
441 if (!BN_to_montgomery(val[0], aa, mont, ctx))
442 goto err; /* 1 */
443
444 window = BN_window_bits_for_exponent_size(bits);
445 if (window > 1) {
446 if (!BN_mod_mul_montgomery(d, val[0], val[0], mont, ctx))
447 goto err; /* 2 */
448 j = 1 << (window - 1);
449 for (i = 1; i < j; i++) {
450 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
451 !BN_mod_mul_montgomery(val[i], val[i - 1],
452 d, mont, ctx))
453 goto err;
454 }
455 }
456
457 start = 1; /* This is used to avoid multiplication etc
458 * when there is only the value '1' in the
459 * buffer. */
460 wvalue = 0; /* The 'value' of the window */
461 wstart = bits - 1; /* The top bit of the window */
462 wend = 0; /* The bottom bit of the window */
463
464 if (!BN_to_montgomery(r, BN_value_one(), mont, ctx))
465 goto err;
466 for (;;) {
467 if (BN_is_bit_set(p, wstart) == 0) {
468 if (!start) {
469 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
470 goto err;
471 }
472 if (wstart == 0)
473 break;
474 wstart--;
475 continue;
476 }
477 /* We now have wstart on a 'set' bit, we now need to work out
478 * how bit a window to do. To do this we need to scan
479 * forward until the last set bit before the end of the
480 * window */
481 j = wstart;
482 wvalue = 1;
483 wend = 0;
484 for (i = 1; i < window; i++) {
485 if (wstart - i < 0)
486 break;
487 if (BN_is_bit_set(p, wstart - i)) {
488 wvalue <<= (i - wend);
489 wvalue |= 1;
490 wend = i;
491 }
492 }
493
494 /* wend is the size of the current window */
495 j = wend + 1;
496 /* add the 'bytes above' */
497 if (!start)
498 for (i = 0; i < j; i++) {
499 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
500 goto err;
501 }
502
503 /* wvalue will be an odd number < 2^window */
504 if (!BN_mod_mul_montgomery(r, r, val[wvalue >> 1], mont, ctx))
505 goto err;
506
507 /* move the 'window' down further */
508 wstart -= wend + 1;
509 wvalue = 0;
510 start = 0;
511 if (wstart < 0)
512 break;
513 }
514 if (!BN_from_montgomery(rr, r,mont, ctx))
515 goto err;
516 ret = 1;
517
518err:
519 if ((in_mont == NULL) && (mont != NULL))
520 BN_MONT_CTX_free(mont);
521 BN_CTX_end(ctx);
522 bn_check_top(rr);
523 return (ret);
524}
525
526
527/* BN_mod_exp_mont_consttime() stores the precomputed powers in a specific layout
528 * so that accessing any of these table values shows the same access pattern as far
529 * as cache lines are concerned. The following functions are used to transfer a BIGNUM
530 * from/to that table. */
531
532static int
533MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top, unsigned char *buf,
534 int idx, int width)
535{
536 size_t i, j;
537
538 if (top > b->top)
539 top = b->top; /* this works because 'buf' is explicitly zeroed */
540 for (i = 0, j = idx; i < top * sizeof b->d[0]; i++, j += width) {
541 buf[j] = ((unsigned char*)b->d)[i];
542 }
543
544 return 1;
545}
546
547static int
548MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top, unsigned char *buf, int idx,
549 int width)
550{
551 size_t i, j;
552
553 if (bn_wexpand(b, top) == NULL)
554 return 0;
555
556 for (i = 0, j = idx; i < top * sizeof b->d[0]; i++, j += width) {
557 ((unsigned char*)b->d)[i] = buf[j];
558 }
559
560 b->top = top;
561 bn_correct_top(b);
562 return 1;
563}
564
565/* Given a pointer value, compute the next address that is a cache line multiple. */
566#define MOD_EXP_CTIME_ALIGN(x_) \
567 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
568
569/* This variant of BN_mod_exp_mont() uses fixed windows and the special
570 * precomputation memory layout to limit data-dependency to a minimum
571 * to protect secret exponents (cf. the hyper-threading timing attacks
572 * pointed out by Colin Percival,
573 * http://www.daemonology.net/hyperthreading-considered-harmful/)
574 */
575int
576BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
577 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
578{
579 int i, bits, ret = 0, window, wvalue;
580 int top;
581 BN_MONT_CTX *mont = NULL;
582 int numPowers;
583 unsigned char *powerbufFree = NULL;
584 int powerbufLen = 0;
585 unsigned char *powerbuf = NULL;
586 BIGNUM tmp, am;
587
588 bn_check_top(a);
589 bn_check_top(p);
590 bn_check_top(m);
591
592 top = m->top;
593
594 if (!(m->d[0] & 1)) {
595 BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME,
596 BN_R_CALLED_WITH_EVEN_MODULUS);
597 return (0);
598 }
599 bits = BN_num_bits(p);
600 if (bits == 0) {
601 ret = BN_one(rr);
602 return ret;
603 }
604
605 BN_CTX_start(ctx);
606
607 /* Allocate a montgomery context if it was not supplied by the caller.
608 * If this is not done, things will break in the montgomery part.
609 */
610 if (in_mont != NULL)
611 mont = in_mont;
612 else {
613 if ((mont = BN_MONT_CTX_new()) == NULL)
614 goto err;
615 if (!BN_MONT_CTX_set(mont, m, ctx))
616 goto err;
617 }
618
619 /* Get the window size to use with size of p. */
620 window = BN_window_bits_for_ctime_exponent_size(bits);
621#if defined(OPENSSL_BN_ASM_MONT5)
622 if (window == 6 && bits <= 1024)
623 window = 5; /* ~5% improvement of 2048-bit RSA sign */
624#endif
625
626 /* Allocate a buffer large enough to hold all of the pre-computed
627 * powers of am, am itself and tmp.
628 */
629 numPowers = 1 << window;
630 powerbufLen = sizeof(m->d[0]) * (top * numPowers +
631 ((2*top) > numPowers ? (2*top) : numPowers));
632 if ((powerbufFree = malloc(powerbufLen +
633 MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH)) == NULL)
634 goto err;
635
636 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
637 memset(powerbuf, 0, powerbufLen);
638
639 /* lay down tmp and am right after powers table */
640 tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers);
641 am.d = tmp.d + top;
642 tmp.top = am.top = 0;
643 tmp.dmax = am.dmax = top;
644 tmp.neg = am.neg = 0;
645 tmp.flags = am.flags = BN_FLG_STATIC_DATA;
646
647 /* prepare a^0 in Montgomery domain */
648#if 1
649 if (!BN_to_montgomery(&tmp, BN_value_one(), mont, ctx))
650 goto err;
651#else
652 tmp.d[0] = (0 - m - >d[0]) & BN_MASK2; /* 2^(top*BN_BITS2) - m */
653 for (i = 1; i < top; i++)
654 tmp.d[i] = (~m->d[i]) & BN_MASK2;
655 tmp.top = top;
656#endif
657
658 /* prepare a^1 in Montgomery domain */
659 if (a->neg || BN_ucmp(a, m) >= 0) {
660 if (!BN_mod(&am, a,m, ctx))
661 goto err;
662 if (!BN_to_montgomery(&am, &am, mont, ctx))
663 goto err;
664 } else if (!BN_to_montgomery(&am, a,mont, ctx))
665 goto err;
666
667#if defined(OPENSSL_BN_ASM_MONT5)
668 /* This optimization uses ideas from http://eprint.iacr.org/2011/239,
669 * specifically optimization of cache-timing attack countermeasures
670 * and pre-computation optimization. */
671
672 /* Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as
673 * 512-bit RSA is hardly relevant, we omit it to spare size... */
674 if (window == 5 && top > 1) {
675 void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap,
676 const void *table, const BN_ULONG *np,
677 const BN_ULONG *n0, int num, int power);
678 void bn_scatter5(const BN_ULONG *inp, size_t num,
679 void *table, size_t power);
680 void bn_gather5(BN_ULONG *out, size_t num,
681 void *table, size_t power);
682
683 BN_ULONG *np = mont->N.d, *n0 = mont->n0;
684
685 /* BN_to_montgomery can contaminate words above .top
686 * [in BN_DEBUG[_DEBUG] build]... */
687 for (i = am.top; i < top; i++)
688 am.d[i] = 0;
689 for (i = tmp.top; i < top; i++)
690 tmp.d[i] = 0;
691
692 bn_scatter5(tmp.d, top, powerbuf, 0);
693 bn_scatter5(am.d, am.top, powerbuf, 1);
694 bn_mul_mont(tmp.d, am.d, am.d, np, n0, top);
695 bn_scatter5(tmp.d, top, powerbuf, 2);
696
697#if 0
698 for (i = 3; i < 32; i++) {
699 /* Calculate a^i = a^(i-1) * a */
700 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np,
701 n0, top, i - 1);
702 bn_scatter5(tmp.d, top, powerbuf, i);
703 }
704#else
705 /* same as above, but uses squaring for 1/2 of operations */
706 for (i = 4; i < 32; i*=2) {
707 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
708 bn_scatter5(tmp.d, top, powerbuf, i);
709 }
710 for (i = 3; i < 8; i += 2) {
711 int j;
712 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np,
713 n0, top, i - 1);
714 bn_scatter5(tmp.d, top, powerbuf, i);
715 for (j = 2 * i; j < 32; j *= 2) {
716 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
717 bn_scatter5(tmp.d, top, powerbuf, j);
718 }
719 }
720 for (; i < 16; i += 2) {
721 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np,
722 n0, top, i - 1);
723 bn_scatter5(tmp.d, top, powerbuf, i);
724 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
725 bn_scatter5(tmp.d, top, powerbuf, 2*i);
726 }
727 for (; i < 32; i += 2) {
728 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np,
729 n0, top, i - 1);
730 bn_scatter5(tmp.d, top, powerbuf, i);
731 }
732#endif
733 bits--;
734 for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--)
735 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
736 bn_gather5(tmp.d, top, powerbuf, wvalue);
737
738 /* Scan the exponent one window at a time starting from the most
739 * significant bits.
740 */
741 while (bits >= 0) {
742 for (wvalue = 0, i = 0; i < 5; i++, bits--)
743 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
744
745 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
746 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
747 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
748 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
749 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
750 bn_mul_mont_gather5(tmp.d, tmp.d, powerbuf, np, n0, top, wvalue);
751 }
752
753 tmp.top = top;
754 bn_correct_top(&tmp);
755 } else
756#endif
757 {
758 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0,
759 numPowers))
760 goto err;
761 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1,
762 numPowers))
763 goto err;
764
765 /* If the window size is greater than 1, then calculate
766 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1)
767 * (even powers could instead be computed as (a^(i/2))^2
768 * to use the slight performance advantage of sqr over mul).
769 */
770 if (window > 1) {
771 if (!BN_mod_mul_montgomery(&tmp, &am, &am, mont, ctx))
772 goto err;
773 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf,
774 2, numPowers))
775 goto err;
776 for (i = 3; i < numPowers; i++) {
777 /* Calculate a^i = a^(i-1) * a */
778 if (!BN_mod_mul_montgomery(&tmp, &am, &tmp,
779 mont, ctx))
780 goto err;
781 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top,
782 powerbuf, i, numPowers))
783 goto err;
784 }
785 }
786
787 bits--;
788 for (wvalue = 0, i = bits % window; i >= 0; i--, bits--)
789 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
790 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp, top, powerbuf,
791 wvalue, numPowers))
792 goto err;
793
794 /* Scan the exponent one window at a time starting from the most
795 * significant bits.
796 */
797 while (bits >= 0) {
798 wvalue = 0; /* The 'value' of the window */
799
800 /* Scan the window, squaring the result as we go */
801 for (i = 0; i < window; i++, bits--) {
802 if (!BN_mod_mul_montgomery(&tmp, &tmp, &tmp,
803 mont, ctx))
804 goto err;
805 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
806 }
807
808 /* Fetch the appropriate pre-computed value from the pre-buf */
809 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf,
810 wvalue, numPowers))
811 goto err;
812
813 /* Multiply the result into the intermediate result */
814 if (!BN_mod_mul_montgomery(&tmp, &tmp, &am, mont, ctx))
815 goto err;
816 }
817 }
818
819 /* Convert the final result from montgomery to standard format */
820 if (!BN_from_montgomery(rr, &tmp, mont, ctx))
821 goto err;
822 ret = 1;
823
824err:
825 if ((in_mont == NULL) && (mont != NULL))
826 BN_MONT_CTX_free(mont);
827 if (powerbuf != NULL) {
828 explicit_bzero(powerbuf, powerbufLen);
829 free(powerbufFree);
830 }
831 BN_CTX_end(ctx);
832 return (ret);
833}
834
835int
836BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p, const BIGNUM *m,
837 BN_CTX *ctx, BN_MONT_CTX *in_mont)
838{
839 BN_MONT_CTX *mont = NULL;
840 int b, bits, ret = 0;
841 int r_is_one;
842 BN_ULONG w, next_w;
843 BIGNUM *d, *r, *t;
844 BIGNUM *swap_tmp;
845
846#define BN_MOD_MUL_WORD(r, w, m) \
847 (BN_mul_word(r, (w)) && \
848 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
849 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
850 /* BN_MOD_MUL_WORD is only used with 'w' large,
851 * so the BN_ucmp test is probably more overhead
852 * than always using BN_mod (which uses BN_copy if
853 * a similar test returns true). */
854 /* We can use BN_mod and do not need BN_nnmod because our
855 * accumulator is never negative (the result of BN_mod does
856 * not depend on the sign of the modulus).
857 */
858#define BN_TO_MONTGOMERY_WORD(r, w, mont) \
859 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
860
861 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
862 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
863 BNerr(BN_F_BN_MOD_EXP_MONT_WORD,
864 ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
865 return -1;
866 }
867
868 bn_check_top(p);
869 bn_check_top(m);
870
871 if (!BN_is_odd(m)) {
872 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, BN_R_CALLED_WITH_EVEN_MODULUS);
873 return (0);
874 }
875 if (m->top == 1)
876 a %= m->d[0]; /* make sure that 'a' is reduced */
877
878 bits = BN_num_bits(p);
879 if (bits == 0) {
880 ret = BN_one(rr);
881 return ret;
882 }
883 if (a == 0) {
884 BN_zero(rr);
885 ret = 1;
886 return ret;
887 }
888
889 BN_CTX_start(ctx);
890 if ((d = BN_CTX_get(ctx)) == NULL)
891 goto err;
892 if ((r = BN_CTX_get(ctx)) == NULL)
893 goto err;
894 if ((t = BN_CTX_get(ctx)) == NULL)
895 goto err;
896
897 if (in_mont != NULL)
898 mont = in_mont;
899 else {
900 if ((mont = BN_MONT_CTX_new()) == NULL)
901 goto err;
902 if (!BN_MONT_CTX_set(mont, m, ctx))
903 goto err;
904 }
905
906 r_is_one = 1; /* except for Montgomery factor */
907
908 /* bits-1 >= 0 */
909
910 /* The result is accumulated in the product r*w. */
911 w = a; /* bit 'bits-1' of 'p' is always set */
912 for (b = bits - 2; b >= 0; b--) {
913 /* First, square r*w. */
914 next_w = w * w;
915 if ((next_w / w) != w) /* overflow */
916 {
917 if (r_is_one) {
918 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
919 goto err;
920 r_is_one = 0;
921 } else {
922 if (!BN_MOD_MUL_WORD(r, w, m))
923 goto err;
924 }
925 next_w = 1;
926 }
927 w = next_w;
928 if (!r_is_one) {
929 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
930 goto err;
931 }
932
933 /* Second, multiply r*w by 'a' if exponent bit is set. */
934 if (BN_is_bit_set(p, b)) {
935 next_w = w * a;
936 if ((next_w / a) != w) /* overflow */
937 {
938 if (r_is_one) {
939 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
940 goto err;
941 r_is_one = 0;
942 } else {
943 if (!BN_MOD_MUL_WORD(r, w, m))
944 goto err;
945 }
946 next_w = a;
947 }
948 w = next_w;
949 }
950 }
951
952 /* Finally, set r:=r*w. */
953 if (w != 1) {
954 if (r_is_one) {
955 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
956 goto err;
957 r_is_one = 0;
958 } else {
959 if (!BN_MOD_MUL_WORD(r, w, m))
960 goto err;
961 }
962 }
963
964 if (r_is_one) /* can happen only if a == 1*/
965 {
966 if (!BN_one(rr))
967 goto err;
968 } else {
969 if (!BN_from_montgomery(rr, r, mont, ctx))
970 goto err;
971 }
972 ret = 1;
973
974err:
975 if ((in_mont == NULL) && (mont != NULL))
976 BN_MONT_CTX_free(mont);
977 BN_CTX_end(ctx);
978 bn_check_top(rr);
979 return (ret);
980}
981
982
983/* The old fallback, simple version :-) */
984int
985BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
986 BN_CTX *ctx)
987{
988 int i, j,bits, ret = 0, wstart, wend, window, wvalue;
989 int start = 1;
990 BIGNUM *d;
991 /* Table of variables obtained from 'ctx' */
992 BIGNUM *val[TABLE_SIZE];
993
994 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
995 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
996 BNerr(BN_F_BN_MOD_EXP_SIMPLE,
997 ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
998 return -1;
999 }
1000
1001 bits = BN_num_bits(p);
1002
1003 if (bits == 0) {
1004 ret = BN_one(r);
1005 return ret;
1006 }
1007
1008 BN_CTX_start(ctx);
1009 if ((d = BN_CTX_get(ctx)) == NULL)
1010 goto err;
1011 if ((val[0] = BN_CTX_get(ctx)) == NULL)
1012 goto err;
1013
1014 if (!BN_nnmod(val[0],a,m,ctx))
1015 goto err; /* 1 */
1016 if (BN_is_zero(val[0])) {
1017 BN_zero(r);
1018 ret = 1;
1019 goto err;
1020 }
1021
1022 window = BN_window_bits_for_exponent_size(bits);
1023 if (window > 1) {
1024 if (!BN_mod_mul(d, val[0], val[0], m, ctx))
1025 goto err; /* 2 */
1026 j = 1 << (window - 1);
1027 for (i = 1; i < j; i++) {
1028 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
1029 !BN_mod_mul(val[i], val[i - 1], d,m, ctx))
1030 goto err;
1031 }
1032 }
1033
1034 start = 1; /* This is used to avoid multiplication etc
1035 * when there is only the value '1' in the
1036 * buffer. */
1037 wvalue = 0; /* The 'value' of the window */
1038 wstart = bits - 1; /* The top bit of the window */
1039 wend = 0; /* The bottom bit of the window */
1040
1041 if (!BN_one(r))
1042 goto err;
1043
1044 for (;;) {
1045 if (BN_is_bit_set(p, wstart) == 0) {
1046 if (!start)
1047 if (!BN_mod_mul(r, r, r, m, ctx))
1048 goto err;
1049 if (wstart == 0)
1050 break;
1051 wstart--;
1052 continue;
1053 }
1054 /* We now have wstart on a 'set' bit, we now need to work out
1055 * how bit a window to do. To do this we need to scan
1056 * forward until the last set bit before the end of the
1057 * window */
1058 j = wstart;
1059 wvalue = 1;
1060 wend = 0;
1061 for (i = 1; i < window; i++) {
1062 if (wstart - i < 0)
1063 break;
1064 if (BN_is_bit_set(p, wstart - i)) {
1065 wvalue <<= (i - wend);
1066 wvalue |= 1;
1067 wend = i;
1068 }
1069 }
1070
1071 /* wend is the size of the current window */
1072 j = wend + 1;
1073 /* add the 'bytes above' */
1074 if (!start)
1075 for (i = 0; i < j; i++) {
1076 if (!BN_mod_mul(r, r, r, m, ctx))
1077 goto err;
1078 }
1079
1080 /* wvalue will be an odd number < 2^window */
1081 if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx))
1082 goto err;
1083
1084 /* move the 'window' down further */
1085 wstart -= wend + 1;
1086 wvalue = 0;
1087 start = 0;
1088 if (wstart < 0)
1089 break;
1090 }
1091 ret = 1;
1092
1093err:
1094 BN_CTX_end(ctx);
1095 bn_check_top(r);
1096 return (ret);
1097}
generated by cgit v1.2.3-55-g6feb (git 2.39.1) at 2025-05-08 00:44:06 +0000