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 __SSP__
123 # ifndef alloca
124 # define alloca(s) __builtin_alloca((s))
125 # endif
126 # else
127 # undef alloca
128 # endif
129 #endif
130
131 /* maximum precomputation table size for *variable* sliding windows */
132 #define TABLE_SIZE 32
133
134 /* this one works - simple but works */
BN_exp(BIGNUM * r,const BIGNUM * a,const BIGNUM * p,BN_CTX * ctx)135 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
136 {
137 int i, bits, ret = 0;
138 BIGNUM *v, *rr;
139
140 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
141 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
142 BNerr(BN_F_BN_EXP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
143 return -1;
144 }
145
146 BN_CTX_start(ctx);
147 if ((r == a) || (r == p))
148 rr = BN_CTX_get(ctx);
149 else
150 rr = r;
151 v = BN_CTX_get(ctx);
152 if (rr == NULL || v == NULL)
153 goto err;
154
155 if (BN_copy(v, a) == NULL)
156 goto err;
157 bits = BN_num_bits(p);
158
159 if (BN_is_odd(p)) {
160 if (BN_copy(rr, a) == NULL)
161 goto err;
162 } else {
163 if (!BN_one(rr))
164 goto err;
165 }
166
167 for (i = 1; i < bits; i++) {
168 if (!BN_sqr(v, v, ctx))
169 goto err;
170 if (BN_is_bit_set(p, i)) {
171 if (!BN_mul(rr, rr, v, ctx))
172 goto err;
173 }
174 }
175 if (r != rr)
176 BN_copy(r, rr);
177 ret = 1;
178 err:
179 BN_CTX_end(ctx);
180 bn_check_top(r);
181 return (ret);
182 }
183
BN_mod_exp(BIGNUM * r,const BIGNUM * a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx)184 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
185 BN_CTX *ctx)
186 {
187 int ret;
188
189 bn_check_top(a);
190 bn_check_top(p);
191 bn_check_top(m);
192
193 /*-
194 * For even modulus m = 2^k*m_odd, it might make sense to compute
195 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery
196 * exponentiation for the odd part), using appropriate exponent
197 * reductions, and combine the results using the CRT.
198 *
199 * For now, we use Montgomery only if the modulus is odd; otherwise,
200 * exponentiation using the reciprocal-based quick remaindering
201 * algorithm is used.
202 *
203 * (Timing obtained with expspeed.c [computations a^p mod m
204 * where a, p, m are of the same length: 256, 512, 1024, 2048,
205 * 4096, 8192 bits], compared to the running time of the
206 * standard algorithm:
207 *
208 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
209 * 55 .. 77 % [UltraSparc processor, but
210 * debug-solaris-sparcv8-gcc conf.]
211 *
212 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
213 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
214 *
215 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
216 * at 2048 and more bits, but at 512 and 1024 bits, it was
217 * slower even than the standard algorithm!
218 *
219 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
220 * should be obtained when the new Montgomery reduction code
221 * has been integrated into OpenSSL.)
222 */
223
224 #define MONT_MUL_MOD
225 #define MONT_EXP_WORD
226 #define RECP_MUL_MOD
227
228 #ifdef MONT_MUL_MOD
229 /*
230 * I have finally been able to take out this pre-condition of the top bit
231 * being set. It was caused by an error in BN_div with negatives. There
232 * was also another problem when for a^b%m a >= m. eay 07-May-97
233 */
234 /* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */
235
236 if (BN_is_odd(m)) {
237 # ifdef MONT_EXP_WORD
238 if (a->top == 1 && !a->neg
239 && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0)) {
240 BN_ULONG A = a->d[0];
241 ret = BN_mod_exp_mont_word(r, A, p, m, ctx, NULL);
242 } else
243 # endif
244 ret = BN_mod_exp_mont(r, a, p, m, ctx, NULL);
245 } else
246 #endif
247 #ifdef RECP_MUL_MOD
248 {
249 ret = BN_mod_exp_recp(r, a, p, m, ctx);
250 }
251 #else
252 {
253 ret = BN_mod_exp_simple(r, a, p, m, ctx);
254 }
255 #endif
256
257 bn_check_top(r);
258 return (ret);
259 }
260
BN_mod_exp_recp(BIGNUM * r,const BIGNUM * a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx)261 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
262 const BIGNUM *m, BN_CTX *ctx)
263 {
264 int i, j, bits, ret = 0, wstart, wend, window, wvalue;
265 int start = 1;
266 BIGNUM *aa;
267 /* Table of variables obtained from 'ctx' */
268 BIGNUM *val[TABLE_SIZE];
269 BN_RECP_CTX recp;
270
271 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
272 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
273 BNerr(BN_F_BN_MOD_EXP_RECP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
274 return -1;
275 }
276
277 bits = BN_num_bits(p);
278
279 if (bits == 0) {
280 ret = BN_one(r);
281 return ret;
282 }
283
284 BN_CTX_start(ctx);
285 aa = BN_CTX_get(ctx);
286 val[0] = BN_CTX_get(ctx);
287 if (!aa || !val[0])
288 goto err;
289
290 BN_RECP_CTX_init(&recp);
291 if (m->neg) {
292 /* ignore sign of 'm' */
293 if (!BN_copy(aa, m))
294 goto err;
295 aa->neg = 0;
296 if (BN_RECP_CTX_set(&recp, aa, ctx) <= 0)
297 goto err;
298 } else {
299 if (BN_RECP_CTX_set(&recp, m, ctx) <= 0)
300 goto err;
301 }
302
303 if (!BN_nnmod(val[0], a, m, ctx))
304 goto err; /* 1 */
305 if (BN_is_zero(val[0])) {
306 BN_zero(r);
307 ret = 1;
308 goto err;
309 }
310
311 window = BN_window_bits_for_exponent_size(bits);
312 if (window > 1) {
313 if (!BN_mod_mul_reciprocal(aa, val[0], val[0], &recp, ctx))
314 goto err; /* 2 */
315 j = 1 << (window - 1);
316 for (i = 1; i < j; i++) {
317 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
318 !BN_mod_mul_reciprocal(val[i], val[i - 1], aa, &recp, ctx))
319 goto err;
320 }
321 }
322
323 start = 1; /* This is used to avoid multiplication etc
324 * when there is only the value '1' in the
325 * buffer. */
326 wvalue = 0; /* The 'value' of the window */
327 wstart = bits - 1; /* The top bit of the window */
328 wend = 0; /* The bottom bit of the window */
329
330 if (!BN_one(r))
331 goto err;
332
333 for (;;) {
334 if (BN_is_bit_set(p, wstart) == 0) {
335 if (!start)
336 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
337 goto err;
338 if (wstart == 0)
339 break;
340 wstart--;
341 continue;
342 }
343 /*
344 * We now have wstart on a 'set' bit, we now need to work out how bit
345 * a window to do. To do this we need to scan forward until the last
346 * set bit before the end of the window
347 */
348 j = wstart;
349 wvalue = 1;
350 wend = 0;
351 for (i = 1; i < window; i++) {
352 if (wstart - i < 0)
353 break;
354 if (BN_is_bit_set(p, wstart - i)) {
355 wvalue <<= (i - wend);
356 wvalue |= 1;
357 wend = i;
358 }
359 }
360
361 /* wend is the size of the current window */
362 j = wend + 1;
363 /* add the 'bytes above' */
364 if (!start)
365 for (i = 0; i < j; i++) {
366 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
367 goto err;
368 }
369
370 /* wvalue will be an odd number < 2^window */
371 if (!BN_mod_mul_reciprocal(r, r, val[wvalue >> 1], &recp, ctx))
372 goto err;
373
374 /* move the 'window' down further */
375 wstart -= wend + 1;
376 wvalue = 0;
377 start = 0;
378 if (wstart < 0)
379 break;
380 }
381 ret = 1;
382 err:
383 BN_CTX_end(ctx);
384 BN_RECP_CTX_free(&recp);
385 bn_check_top(r);
386 return (ret);
387 }
388
BN_mod_exp_mont(BIGNUM * rr,const BIGNUM * a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx,BN_MONT_CTX * in_mont)389 int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
390 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
391 {
392 int i, j, bits, ret = 0, wstart, wend, window, wvalue;
393 int start = 1;
394 BIGNUM *d, *r;
395 const BIGNUM *aa;
396 /* Table of variables obtained from 'ctx' */
397 BIGNUM *val[TABLE_SIZE];
398 BN_MONT_CTX *mont = NULL;
399
400 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
401 return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
402 }
403
404 bn_check_top(a);
405 bn_check_top(p);
406 bn_check_top(m);
407
408 if (!BN_is_odd(m)) {
409 BNerr(BN_F_BN_MOD_EXP_MONT, BN_R_CALLED_WITH_EVEN_MODULUS);
410 return (0);
411 }
412 bits = BN_num_bits(p);
413 if (bits == 0) {
414 ret = BN_one(rr);
415 return ret;
416 }
417
418 BN_CTX_start(ctx);
419 d = BN_CTX_get(ctx);
420 r = BN_CTX_get(ctx);
421 val[0] = BN_CTX_get(ctx);
422 if (!d || !r || !val[0])
423 goto err;
424
425 /*
426 * If this is not done, things will break in the montgomery part
427 */
428
429 if (in_mont != NULL)
430 mont = in_mont;
431 else {
432 if ((mont = BN_MONT_CTX_new()) == NULL)
433 goto err;
434 if (!BN_MONT_CTX_set(mont, m, ctx))
435 goto err;
436 }
437
438 if (a->neg || BN_ucmp(a, m) >= 0) {
439 if (!BN_nnmod(val[0], a, m, ctx))
440 goto err;
441 aa = val[0];
442 } else
443 aa = a;
444 if (BN_is_zero(aa)) {
445 BN_zero(rr);
446 ret = 1;
447 goto err;
448 }
449 if (!BN_to_montgomery(val[0], aa, mont, ctx))
450 goto err; /* 1 */
451
452 window = BN_window_bits_for_exponent_size(bits);
453 if (window > 1) {
454 if (!BN_mod_mul_montgomery(d, val[0], val[0], mont, ctx))
455 goto err; /* 2 */
456 j = 1 << (window - 1);
457 for (i = 1; i < j; i++) {
458 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
459 !BN_mod_mul_montgomery(val[i], val[i - 1], d, mont, ctx))
460 goto err;
461 }
462 }
463
464 start = 1; /* This is used to avoid multiplication etc
465 * when there is only the value '1' in the
466 * buffer. */
467 wvalue = 0; /* The 'value' of the window */
468 wstart = bits - 1; /* The top bit of the window */
469 wend = 0; /* The bottom bit of the window */
470
471 if (!BN_to_montgomery(r, BN_value_one(), mont, ctx))
472 goto err;
473 for (;;) {
474 if (BN_is_bit_set(p, wstart) == 0) {
475 if (!start) {
476 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
477 goto err;
478 }
479 if (wstart == 0)
480 break;
481 wstart--;
482 continue;
483 }
484 /*
485 * We now have wstart on a 'set' bit, we now need to work out how bit
486 * a window to do. To do this we need to scan forward until the last
487 * set bit before the end of the window
488 */
489 j = wstart;
490 wvalue = 1;
491 wend = 0;
492 for (i = 1; i < window; i++) {
493 if (wstart - i < 0)
494 break;
495 if (BN_is_bit_set(p, wstart - i)) {
496 wvalue <<= (i - wend);
497 wvalue |= 1;
498 wend = i;
499 }
500 }
501
502 /* wend is the size of the current window */
503 j = wend + 1;
504 /* add the 'bytes above' */
505 if (!start)
506 for (i = 0; i < j; i++) {
507 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
508 goto err;
509 }
510
511 /* wvalue will be an odd number < 2^window */
512 if (!BN_mod_mul_montgomery(r, r, val[wvalue >> 1], mont, ctx))
513 goto err;
514
515 /* move the 'window' down further */
516 wstart -= wend + 1;
517 wvalue = 0;
518 start = 0;
519 if (wstart < 0)
520 break;
521 }
522 if (!BN_from_montgomery(rr, r, mont, ctx))
523 goto err;
524 ret = 1;
525 err:
526 if ((in_mont == NULL) && (mont != NULL))
527 BN_MONT_CTX_free(mont);
528 BN_CTX_end(ctx);
529 bn_check_top(rr);
530 return (ret);
531 }
532
533 /*
534 * BN_mod_exp_mont_consttime() stores the precomputed powers in a specific
535 * layout so that accessing any of these table values shows the same access
536 * pattern as far as cache lines are concerned. The following functions are
537 * used to transfer a BIGNUM from/to that table.
538 */
539
MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM * b,int top,unsigned char * buf,int idx,int width)540 static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top,
541 unsigned char *buf, int idx,
542 int width)
543 {
544 size_t i, j;
545
546 if (top > b->top)
547 top = b->top; /* this works because 'buf' is explicitly
548 * zeroed */
549 for (i = 0, j = idx; i < top * sizeof b->d[0]; i++, j += width) {
550 buf[j] = ((unsigned char *)b->d)[i];
551 }
552
553 return 1;
554 }
555
MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM * b,int top,unsigned char * buf,int idx,int width)556 static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top,
557 unsigned char *buf, int idx,
558 int width)
559 {
560 size_t i, j;
561
562 if (bn_wexpand(b, top) == NULL)
563 return 0;
564
565 for (i = 0, j = idx; i < top * sizeof b->d[0]; i++, j += width) {
566 ((unsigned char *)b->d)[i] = buf[j];
567 }
568
569 b->top = top;
570 bn_correct_top(b);
571 return 1;
572 }
573
574 /*
575 * Given a pointer value, compute the next address that is a cache line
576 * multiple.
577 */
578 #define MOD_EXP_CTIME_ALIGN(x_) \
579 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
580
581 /*
582 * This variant of BN_mod_exp_mont() uses fixed windows and the special
583 * precomputation memory layout to limit data-dependency to a minimum to
584 * protect secret exponents (cf. the hyper-threading timing attacks pointed
585 * out by Colin Percival,
586 * http://www.daemong-consideredperthreading-considered-harmful/)
587 */
BN_mod_exp_mont_consttime(BIGNUM * rr,const BIGNUM * a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx,BN_MONT_CTX * in_mont)588 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
589 const BIGNUM *m, BN_CTX *ctx,
590 BN_MONT_CTX *in_mont)
591 {
592 int i, bits, ret = 0, window, wvalue;
593 int top;
594 BN_MONT_CTX *mont = NULL;
595
596 int numPowers;
597 unsigned char *powerbufFree = NULL;
598 int powerbufLen = 0;
599 unsigned char *powerbuf = NULL;
600 BIGNUM tmp, am;
601
602 bn_check_top(a);
603 bn_check_top(p);
604 bn_check_top(m);
605
606 top = m->top;
607
608 if (!(m->d[0] & 1)) {
609 BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME, BN_R_CALLED_WITH_EVEN_MODULUS);
610 return (0);
611 }
612 bits = BN_num_bits(p);
613 if (bits == 0) {
614 ret = BN_one(rr);
615 return ret;
616 }
617
618 BN_CTX_start(ctx);
619
620 /*
621 * Allocate a montgomery context if it was not supplied by the caller. If
622 * this is not done, things will break in the montgomery part.
623 */
624 if (in_mont != NULL)
625 mont = in_mont;
626 else {
627 if ((mont = BN_MONT_CTX_new()) == NULL)
628 goto err;
629 if (!BN_MONT_CTX_set(mont, m, ctx))
630 goto err;
631 }
632
633 /* Get the window size to use with size of p. */
634 window = BN_window_bits_for_ctime_exponent_size(bits);
635 #if defined(OPENSSL_BN_ASM_MONT5)
636 if (window == 6 && bits <= 1024)
637 window = 5; /* ~5% improvement of 2048-bit RSA sign */
638 #endif
639
640 /*
641 * Allocate a buffer large enough to hold all of the pre-computed powers
642 * of am, am itself and tmp.
643 */
644 numPowers = 1 << window;
645 powerbufLen = sizeof(m->d[0]) * (top * numPowers +
646 ((2 * top) >
647 numPowers ? (2 * top) : numPowers));
648 #ifdef alloca
649 if (powerbufLen < 3072)
650 powerbufFree =
651 alloca(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
652 else
653 #endif
654 if ((powerbufFree =
655 (unsigned char *)OPENSSL_malloc(powerbufLen +
656 MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH))
657 == NULL)
658 goto err;
659
660 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
661 memset(powerbuf, 0, powerbufLen);
662
663 #ifdef alloca
664 if (powerbufLen < 3072)
665 powerbufFree = NULL;
666 #endif
667
668 /* lay down tmp and am right after powers table */
669 tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers);
670 am.d = tmp.d + top;
671 tmp.top = am.top = 0;
672 tmp.dmax = am.dmax = top;
673 tmp.neg = am.neg = 0;
674 tmp.flags = am.flags = BN_FLG_STATIC_DATA;
675
676 /* prepare a^0 in Montgomery domain */
677 #if 1
678 if (!BN_to_montgomery(&tmp, BN_value_one(), mont, ctx))
679 goto err;
680 #else
681 tmp.d[0] = (0 - m->d[0]) & BN_MASK2; /* 2^(top*BN_BITS2) - m */
682 for (i = 1; i < top; i++)
683 tmp.d[i] = (~m->d[i]) & BN_MASK2;
684 tmp.top = top;
685 #endif
686
687 /* prepare a^1 in Montgomery domain */
688 if (a->neg || BN_ucmp(a, m) >= 0) {
689 if (!BN_mod(&am, a, m, ctx))
690 goto err;
691 if (!BN_to_montgomery(&am, &am, mont, ctx))
692 goto err;
693 } else if (!BN_to_montgomery(&am, a, mont, ctx))
694 goto err;
695
696 #if defined(OPENSSL_BN_ASM_MONT5)
697 if (window == 5 && top > 1) {
698 /*
699 * This optimization uses ideas from http://eprint.iacr.org/2011/239,
700 * specifically optimization of cache-timing attack countermeasures
701 * and pre-computation optimization.
702 */
703
704 /*
705 * Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as
706 * 512-bit RSA is hardly relevant, we omit it to spare size...
707 */
708 void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap,
709 const void *table, const BN_ULONG *np,
710 const BN_ULONG *n0, int num, int power);
711 void bn_scatter5(const BN_ULONG *inp, size_t num,
712 void *table, size_t power);
713 void bn_gather5(BN_ULONG *out, size_t num, void *table, size_t power);
714
715 BN_ULONG *np = mont->N.d, *n0 = mont->n0;
716
717 /*
718 * BN_to_montgomery can contaminate words above .top [in
719 * BN_DEBUG[_DEBUG] build]...
720 */
721 for (i = am.top; i < top; i++)
722 am.d[i] = 0;
723 for (i = tmp.top; i < top; i++)
724 tmp.d[i] = 0;
725
726 bn_scatter5(tmp.d, top, powerbuf, 0);
727 bn_scatter5(am.d, am.top, powerbuf, 1);
728 bn_mul_mont(tmp.d, am.d, am.d, np, n0, top);
729 bn_scatter5(tmp.d, top, powerbuf, 2);
730
731 # if 0
732 for (i = 3; i < 32; i++) {
733 /* Calculate a^i = a^(i-1) * a */
734 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
735 bn_scatter5(tmp.d, top, powerbuf, i);
736 }
737 # else
738 /* same as above, but uses squaring for 1/2 of operations */
739 for (i = 4; i < 32; i *= 2) {
740 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
741 bn_scatter5(tmp.d, top, powerbuf, i);
742 }
743 for (i = 3; i < 8; i += 2) {
744 int j;
745 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
746 bn_scatter5(tmp.d, top, powerbuf, i);
747 for (j = 2 * i; j < 32; j *= 2) {
748 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
749 bn_scatter5(tmp.d, top, powerbuf, j);
750 }
751 }
752 for (; i < 16; i += 2) {
753 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
754 bn_scatter5(tmp.d, top, powerbuf, i);
755 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
756 bn_scatter5(tmp.d, top, powerbuf, 2 * i);
757 }
758 for (; i < 32; i += 2) {
759 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
760 bn_scatter5(tmp.d, top, powerbuf, i);
761 }
762 # endif
763 bits--;
764 for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--)
765 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
766 bn_gather5(tmp.d, top, powerbuf, wvalue);
767
768 /*
769 * Scan the exponent one window at a time starting from the most
770 * significant bits.
771 */
772 while (bits >= 0) {
773 for (wvalue = 0, i = 0; i < 5; i++, bits--)
774 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
775
776 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
777 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
778 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
779 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
780 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
781 bn_mul_mont_gather5(tmp.d, tmp.d, powerbuf, np, n0, top, wvalue);
782 }
783
784 tmp.top = top;
785 bn_correct_top(&tmp);
786 } else
787 #endif
788 {
789 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, numPowers))
790 goto err;
791 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, numPowers))
792 goto err;
793
794 /*
795 * If the window size is greater than 1, then calculate
796 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even
797 * powers could instead be computed as (a^(i/2))^2 to use the slight
798 * performance advantage of sqr over mul).
799 */
800 if (window > 1) {
801 if (!BN_mod_mul_montgomery(&tmp, &am, &am, mont, ctx))
802 goto err;
803 if (!MOD_EXP_CTIME_COPY_TO_PREBUF
804 (&tmp, top, powerbuf, 2, numPowers))
805 goto err;
806 for (i = 3; i < numPowers; i++) {
807 /* Calculate a^i = a^(i-1) * a */
808 if (!BN_mod_mul_montgomery(&tmp, &am, &tmp, mont, ctx))
809 goto err;
810 if (!MOD_EXP_CTIME_COPY_TO_PREBUF
811 (&tmp, top, powerbuf, i, numPowers))
812 goto err;
813 }
814 }
815
816 bits--;
817 for (wvalue = 0, i = bits % window; i >= 0; i--, bits--)
818 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
819 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF
820 (&tmp, top, powerbuf, wvalue, numPowers))
821 goto err;
822
823 /*
824 * Scan the exponent one window at a time starting from the most
825 * significant bits.
826 */
827 while (bits >= 0) {
828 wvalue = 0; /* The 'value' of the window */
829
830 /* Scan the window, squaring the result as we go */
831 for (i = 0; i < window; i++, bits--) {
832 if (!BN_mod_mul_montgomery(&tmp, &tmp, &tmp, mont, ctx))
833 goto err;
834 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
835 }
836
837 /*
838 * Fetch the appropriate pre-computed value from the pre-buf
839 */
840 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF
841 (&am, top, powerbuf, wvalue, numPowers))
842 goto err;
843
844 /* Multiply the result into the intermediate result */
845 if (!BN_mod_mul_montgomery(&tmp, &tmp, &am, mont, ctx))
846 goto err;
847 }
848 }
849
850 /* Convert the final result from montgomery to standard format */
851 if (!BN_from_montgomery(rr, &tmp, mont, ctx))
852 goto err;
853 ret = 1;
854 err:
855 if ((in_mont == NULL) && (mont != NULL))
856 BN_MONT_CTX_free(mont);
857 if (powerbuf != NULL) {
858 OPENSSL_cleanse(powerbuf, powerbufLen);
859 if (powerbufFree)
860 OPENSSL_free(powerbufFree);
861 }
862 BN_CTX_end(ctx);
863 return (ret);
864 }
865
BN_mod_exp_mont_word(BIGNUM * rr,BN_ULONG a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx,BN_MONT_CTX * in_mont)866 int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
867 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
868 {
869 BN_MONT_CTX *mont = NULL;
870 int b, bits, ret = 0;
871 int r_is_one;
872 BN_ULONG w, next_w;
873 BIGNUM *d, *r, *t;
874 BIGNUM *swap_tmp;
875 #define BN_MOD_MUL_WORD(r, w, m) \
876 (BN_mul_word(r, (w)) && \
877 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
878 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
879 /*
880 * BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is
881 * probably more overhead than always using BN_mod (which uses BN_copy if
882 * a similar test returns true).
883 */
884 /*
885 * We can use BN_mod and do not need BN_nnmod because our accumulator is
886 * never negative (the result of BN_mod does not depend on the sign of
887 * the modulus).
888 */
889 #define BN_TO_MONTGOMERY_WORD(r, w, mont) \
890 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
891
892 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
893 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
894 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
895 return -1;
896 }
897
898 bn_check_top(p);
899 bn_check_top(m);
900
901 if (!BN_is_odd(m)) {
902 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, BN_R_CALLED_WITH_EVEN_MODULUS);
903 return (0);
904 }
905 if (m->top == 1)
906 a %= m->d[0]; /* make sure that 'a' is reduced */
907
908 bits = BN_num_bits(p);
909 if (bits == 0) {
910 /* x**0 mod 1 is still zero. */
911 if (BN_is_one(m)) {
912 ret = 1;
913 BN_zero(rr);
914 } else
915 ret = BN_one(rr);
916 return ret;
917 }
918 if (a == 0) {
919 BN_zero(rr);
920 ret = 1;
921 return ret;
922 }
923
924 BN_CTX_start(ctx);
925 d = BN_CTX_get(ctx);
926 r = BN_CTX_get(ctx);
927 t = BN_CTX_get(ctx);
928 if (d == NULL || r == NULL || t == NULL)
929 goto err;
930
931 if (in_mont != NULL)
932 mont = in_mont;
933 else {
934 if ((mont = BN_MONT_CTX_new()) == NULL)
935 goto err;
936 if (!BN_MONT_CTX_set(mont, m, ctx))
937 goto err;
938 }
939
940 r_is_one = 1; /* except for Montgomery factor */
941
942 /* bits-1 >= 0 */
943
944 /* The result is accumulated in the product r*w. */
945 w = a; /* bit 'bits-1' of 'p' is always set */
946 for (b = bits - 2; b >= 0; b--) {
947 /* First, square r*w. */
948 next_w = w * w;
949 if ((next_w / w) != w) { /* overflow */
950 if (r_is_one) {
951 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
952 goto err;
953 r_is_one = 0;
954 } else {
955 if (!BN_MOD_MUL_WORD(r, w, m))
956 goto err;
957 }
958 next_w = 1;
959 }
960 w = next_w;
961 if (!r_is_one) {
962 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
963 goto err;
964 }
965
966 /* Second, multiply r*w by 'a' if exponent bit is set. */
967 if (BN_is_bit_set(p, b)) {
968 next_w = w * a;
969 if ((next_w / a) != w) { /* overflow */
970 if (r_is_one) {
971 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
972 goto err;
973 r_is_one = 0;
974 } else {
975 if (!BN_MOD_MUL_WORD(r, w, m))
976 goto err;
977 }
978 next_w = a;
979 }
980 w = next_w;
981 }
982 }
983
984 /* Finally, set r:=r*w. */
985 if (w != 1) {
986 if (r_is_one) {
987 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
988 goto err;
989 r_is_one = 0;
990 } else {
991 if (!BN_MOD_MUL_WORD(r, w, m))
992 goto err;
993 }
994 }
995
996 if (r_is_one) { /* can happen only if a == 1 */
997 if (!BN_one(rr))
998 goto err;
999 } else {
1000 if (!BN_from_montgomery(rr, r, mont, ctx))
1001 goto err;
1002 }
1003 ret = 1;
1004 err:
1005 if ((in_mont == NULL) && (mont != NULL))
1006 BN_MONT_CTX_free(mont);
1007 BN_CTX_end(ctx);
1008 bn_check_top(rr);
1009 return (ret);
1010 }
1011
1012 /* The old fallback, simple version :-) */
BN_mod_exp_simple(BIGNUM * r,const BIGNUM * a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx)1013 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
1014 const BIGNUM *m, BN_CTX *ctx)
1015 {
1016 int i, j, bits, ret = 0, wstart, wend, window, wvalue;
1017 int start = 1;
1018 BIGNUM *d;
1019 /* Table of variables obtained from 'ctx' */
1020 BIGNUM *val[TABLE_SIZE];
1021
1022 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
1023 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1024 BNerr(BN_F_BN_MOD_EXP_SIMPLE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1025 return -1;
1026 }
1027
1028 bits = BN_num_bits(p);
1029
1030 if (bits == 0) {
1031 ret = BN_one(r);
1032 return ret;
1033 }
1034
1035 BN_CTX_start(ctx);
1036 d = BN_CTX_get(ctx);
1037 val[0] = BN_CTX_get(ctx);
1038 if (!d || !val[0])
1039 goto err;
1040
1041 if (!BN_nnmod(val[0], a, m, ctx))
1042 goto err; /* 1 */
1043 if (BN_is_zero(val[0])) {
1044 BN_zero(r);
1045 ret = 1;
1046 goto err;
1047 }
1048
1049 window = BN_window_bits_for_exponent_size(bits);
1050 if (window > 1) {
1051 if (!BN_mod_mul(d, val[0], val[0], m, ctx))
1052 goto err; /* 2 */
1053 j = 1 << (window - 1);
1054 for (i = 1; i < j; i++) {
1055 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
1056 !BN_mod_mul(val[i], val[i - 1], d, m, ctx))
1057 goto err;
1058 }
1059 }
1060
1061 start = 1; /* This is used to avoid multiplication etc
1062 * when there is only the value '1' in the
1063 * buffer. */
1064 wvalue = 0; /* The 'value' of the window */
1065 wstart = bits - 1; /* The top bit of the window */
1066 wend = 0; /* The bottom bit of the window */
1067
1068 if (!BN_one(r))
1069 goto err;
1070
1071 for (;;) {
1072 if (BN_is_bit_set(p, wstart) == 0) {
1073 if (!start)
1074 if (!BN_mod_mul(r, r, r, m, ctx))
1075 goto err;
1076 if (wstart == 0)
1077 break;
1078 wstart--;
1079 continue;
1080 }
1081 /*
1082 * We now have wstart on a 'set' bit, we now need to work out how bit
1083 * a window to do. To do this we need to scan forward until the last
1084 * set bit before the end of the window
1085 */
1086 j = wstart;
1087 wvalue = 1;
1088 wend = 0;
1089 for (i = 1; i < window; i++) {
1090 if (wstart - i < 0)
1091 break;
1092 if (BN_is_bit_set(p, wstart - i)) {
1093 wvalue <<= (i - wend);
1094 wvalue |= 1;
1095 wend = i;
1096 }
1097 }
1098
1099 /* wend is the size of the current window */
1100 j = wend + 1;
1101 /* add the 'bytes above' */
1102 if (!start)
1103 for (i = 0; i < j; i++) {
1104 if (!BN_mod_mul(r, r, r, m, ctx))
1105 goto err;
1106 }
1107
1108 /* wvalue will be an odd number < 2^window */
1109 if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx))
1110 goto err;
1111
1112 /* move the 'window' down further */
1113 wstart -= wend + 1;
1114 wvalue = 0;
1115 start = 0;
1116 if (wstart < 0)
1117 break;
1118 }
1119 ret = 1;
1120 err:
1121 BN_CTX_end(ctx);
1122 bn_check_top(r);
1123 return (ret);
1124 }
1125