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 "constant_time_locl.h"
114 #include "bn_lcl.h"
115
116 #include <stdlib.h>
117 #ifdef _WIN32
118 # include <malloc.h>
119 # ifndef alloca
120 # define alloca _alloca
121 # endif
122 #elif defined(__GNUC__)
123 # ifndef alloca
124 # define alloca(s) __builtin_alloca((s))
125 # endif
126 #endif
127
128 /* maximum precomputation table size for *variable* sliding windows */
129 #define TABLE_SIZE 32
130
131 /* this one works - simple but works */
BN_exp(BIGNUM * r,const BIGNUM * a,const BIGNUM * p,BN_CTX * ctx)132 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
133 {
134 int i, bits, ret = 0;
135 BIGNUM *v, *rr;
136
137 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
138 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
139 BNerr(BN_F_BN_EXP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
140 return -1;
141 }
142
143 BN_CTX_start(ctx);
144 if ((r == a) || (r == p))
145 rr = BN_CTX_get(ctx);
146 else
147 rr = r;
148 v = BN_CTX_get(ctx);
149 if (rr == NULL || v == NULL)
150 goto err;
151
152 if (BN_copy(v, a) == NULL)
153 goto err;
154 bits = BN_num_bits(p);
155
156 if (BN_is_odd(p)) {
157 if (BN_copy(rr, a) == NULL)
158 goto err;
159 } else {
160 if (!BN_one(rr))
161 goto err;
162 }
163
164 for (i = 1; i < bits; i++) {
165 if (!BN_sqr(v, v, ctx))
166 goto err;
167 if (BN_is_bit_set(p, i)) {
168 if (!BN_mul(rr, rr, v, ctx))
169 goto err;
170 }
171 }
172 if (r != rr)
173 BN_copy(r, rr);
174 ret = 1;
175 err:
176 BN_CTX_end(ctx);
177 bn_check_top(r);
178 return (ret);
179 }
180
BN_mod_exp(BIGNUM * r,const BIGNUM * a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx)181 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
182 BN_CTX *ctx)
183 {
184 int ret;
185
186 bn_check_top(a);
187 bn_check_top(p);
188 bn_check_top(m);
189
190 /*-
191 * For even modulus m = 2^k*m_odd, it might make sense to compute
192 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery
193 * exponentiation for the odd part), using appropriate exponent
194 * reductions, and combine the results using the CRT.
195 *
196 * For now, we use Montgomery only if the modulus is odd; otherwise,
197 * exponentiation using the reciprocal-based quick remaindering
198 * algorithm is used.
199 *
200 * (Timing obtained with expspeed.c [computations a^p mod m
201 * where a, p, m are of the same length: 256, 512, 1024, 2048,
202 * 4096, 8192 bits], compared to the running time of the
203 * standard algorithm:
204 *
205 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
206 * 55 .. 77 % [UltraSparc processor, but
207 * debug-solaris-sparcv8-gcc conf.]
208 *
209 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
210 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
211 *
212 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
213 * at 2048 and more bits, but at 512 and 1024 bits, it was
214 * slower even than the standard algorithm!
215 *
216 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
217 * should be obtained when the new Montgomery reduction code
218 * has been integrated into OpenSSL.)
219 */
220
221 #define MONT_MUL_MOD
222 #define MONT_EXP_WORD
223 #define RECP_MUL_MOD
224
225 #ifdef MONT_MUL_MOD
226 /*
227 * I have finally been able to take out this pre-condition of the top bit
228 * being set. It was caused by an error in BN_div with negatives. There
229 * was also another problem when for a^b%m a >= m. eay 07-May-97
230 */
231 /* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */
232
233 if (BN_is_odd(m)) {
234 # ifdef MONT_EXP_WORD
235 if (a->top == 1 && !a->neg
236 && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0)) {
237 BN_ULONG A = a->d[0];
238 ret = BN_mod_exp_mont_word(r, A, p, m, ctx, NULL);
239 } else
240 # endif
241 ret = BN_mod_exp_mont(r, a, p, m, ctx, NULL);
242 } else
243 #endif
244 #ifdef RECP_MUL_MOD
245 {
246 ret = BN_mod_exp_recp(r, a, p, m, ctx);
247 }
248 #else
249 {
250 ret = BN_mod_exp_simple(r, a, p, m, ctx);
251 }
252 #endif
253
254 bn_check_top(r);
255 return (ret);
256 }
257
BN_mod_exp_recp(BIGNUM * r,const BIGNUM * a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx)258 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
259 const BIGNUM *m, BN_CTX *ctx)
260 {
261 int i, j, bits, ret = 0, wstart, wend, window, wvalue;
262 int start = 1;
263 BIGNUM *aa;
264 /* Table of variables obtained from 'ctx' */
265 BIGNUM *val[TABLE_SIZE];
266 BN_RECP_CTX recp;
267
268 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
269 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
270 BNerr(BN_F_BN_MOD_EXP_RECP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
271 return -1;
272 }
273
274 bits = BN_num_bits(p);
275 if (bits == 0) {
276 /* x**0 mod 1 is still zero. */
277 if (BN_is_one(m)) {
278 ret = 1;
279 BN_zero(r);
280 } else {
281 ret = BN_one(r);
282 }
283 return ret;
284 }
285
286 BN_CTX_start(ctx);
287 aa = BN_CTX_get(ctx);
288 val[0] = BN_CTX_get(ctx);
289 if (!aa || !val[0])
290 goto err;
291
292 BN_RECP_CTX_init(&recp);
293 if (m->neg) {
294 /* ignore sign of 'm' */
295 if (!BN_copy(aa, m))
296 goto err;
297 aa->neg = 0;
298 if (BN_RECP_CTX_set(&recp, aa, ctx) <= 0)
299 goto err;
300 } else {
301 if (BN_RECP_CTX_set(&recp, m, ctx) <= 0)
302 goto err;
303 }
304
305 if (!BN_nnmod(val[0], a, m, ctx))
306 goto err; /* 1 */
307 if (BN_is_zero(val[0])) {
308 BN_zero(r);
309 ret = 1;
310 goto err;
311 }
312
313 window = BN_window_bits_for_exponent_size(bits);
314 if (window > 1) {
315 if (!BN_mod_mul_reciprocal(aa, val[0], val[0], &recp, ctx))
316 goto err; /* 2 */
317 j = 1 << (window - 1);
318 for (i = 1; i < j; i++) {
319 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
320 !BN_mod_mul_reciprocal(val[i], val[i - 1], aa, &recp, ctx))
321 goto err;
322 }
323 }
324
325 start = 1; /* This is used to avoid multiplication etc
326 * when there is only the value '1' in the
327 * buffer. */
328 wvalue = 0; /* The 'value' of the window */
329 wstart = bits - 1; /* The top bit of the window */
330 wend = 0; /* The bottom bit of the window */
331
332 if (!BN_one(r))
333 goto err;
334
335 for (;;) {
336 if (BN_is_bit_set(p, wstart) == 0) {
337 if (!start)
338 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
339 goto err;
340 if (wstart == 0)
341 break;
342 wstart--;
343 continue;
344 }
345 /*
346 * We now have wstart on a 'set' bit, we now need to work out how bit
347 * a window to do. To do this we need to scan forward until the last
348 * set bit before the end of the window
349 */
350 j = wstart;
351 wvalue = 1;
352 wend = 0;
353 for (i = 1; i < window; i++) {
354 if (wstart - i < 0)
355 break;
356 if (BN_is_bit_set(p, wstart - i)) {
357 wvalue <<= (i - wend);
358 wvalue |= 1;
359 wend = i;
360 }
361 }
362
363 /* wend is the size of the current window */
364 j = wend + 1;
365 /* add the 'bytes above' */
366 if (!start)
367 for (i = 0; i < j; i++) {
368 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
369 goto err;
370 }
371
372 /* wvalue will be an odd number < 2^window */
373 if (!BN_mod_mul_reciprocal(r, r, val[wvalue >> 1], &recp, ctx))
374 goto err;
375
376 /* move the 'window' down further */
377 wstart -= wend + 1;
378 wvalue = 0;
379 start = 0;
380 if (wstart < 0)
381 break;
382 }
383 ret = 1;
384 err:
385 BN_CTX_end(ctx);
386 BN_RECP_CTX_free(&recp);
387 bn_check_top(r);
388 return (ret);
389 }
390
BN_mod_exp_mont(BIGNUM * rr,const BIGNUM * a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx,BN_MONT_CTX * in_mont)391 int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
392 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
393 {
394 int i, j, bits, ret = 0, wstart, wend, window, wvalue;
395 int start = 1;
396 BIGNUM *d, *r;
397 const BIGNUM *aa;
398 /* Table of variables obtained from 'ctx' */
399 BIGNUM *val[TABLE_SIZE];
400 BN_MONT_CTX *mont = NULL;
401
402 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
403 return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
404 }
405
406 bn_check_top(a);
407 bn_check_top(p);
408 bn_check_top(m);
409
410 if (!BN_is_odd(m)) {
411 BNerr(BN_F_BN_MOD_EXP_MONT, BN_R_CALLED_WITH_EVEN_MODULUS);
412 return (0);
413 }
414 bits = BN_num_bits(p);
415 if (bits == 0) {
416 /* x**0 mod 1 is still zero. */
417 if (BN_is_one(m)) {
418 ret = 1;
419 BN_zero(rr);
420 } else {
421 ret = BN_one(rr);
422 }
423 return ret;
424 }
425
426 BN_CTX_start(ctx);
427 d = BN_CTX_get(ctx);
428 r = BN_CTX_get(ctx);
429 val[0] = BN_CTX_get(ctx);
430 if (!d || !r || !val[0])
431 goto err;
432
433 /*
434 * If this is not done, things will break in the montgomery part
435 */
436
437 if (in_mont != NULL)
438 mont = in_mont;
439 else {
440 if ((mont = BN_MONT_CTX_new()) == NULL)
441 goto err;
442 if (!BN_MONT_CTX_set(mont, m, ctx))
443 goto err;
444 }
445
446 if (a->neg || BN_ucmp(a, m) >= 0) {
447 if (!BN_nnmod(val[0], a, m, ctx))
448 goto err;
449 aa = val[0];
450 } else
451 aa = a;
452 if (BN_is_zero(aa)) {
453 BN_zero(rr);
454 ret = 1;
455 goto err;
456 }
457 if (!BN_to_montgomery(val[0], aa, mont, ctx))
458 goto err; /* 1 */
459
460 window = BN_window_bits_for_exponent_size(bits);
461 if (window > 1) {
462 if (!BN_mod_mul_montgomery(d, val[0], val[0], mont, ctx))
463 goto err; /* 2 */
464 j = 1 << (window - 1);
465 for (i = 1; i < j; i++) {
466 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
467 !BN_mod_mul_montgomery(val[i], val[i - 1], d, mont, ctx))
468 goto err;
469 }
470 }
471
472 start = 1; /* This is used to avoid multiplication etc
473 * when there is only the value '1' in the
474 * buffer. */
475 wvalue = 0; /* The 'value' of the window */
476 wstart = bits - 1; /* The top bit of the window */
477 wend = 0; /* The bottom bit of the window */
478
479 if (!BN_to_montgomery(r, BN_value_one(), mont, ctx))
480 goto err;
481 for (;;) {
482 if (BN_is_bit_set(p, wstart) == 0) {
483 if (!start) {
484 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
485 goto err;
486 }
487 if (wstart == 0)
488 break;
489 wstart--;
490 continue;
491 }
492 /*
493 * We now have wstart on a 'set' bit, we now need to work out how bit
494 * a window to do. To do this we need to scan forward until the last
495 * set bit before the end of the window
496 */
497 j = wstart;
498 wvalue = 1;
499 wend = 0;
500 for (i = 1; i < window; i++) {
501 if (wstart - i < 0)
502 break;
503 if (BN_is_bit_set(p, wstart - i)) {
504 wvalue <<= (i - wend);
505 wvalue |= 1;
506 wend = i;
507 }
508 }
509
510 /* wend is the size of the current window */
511 j = wend + 1;
512 /* add the 'bytes above' */
513 if (!start)
514 for (i = 0; i < j; i++) {
515 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
516 goto err;
517 }
518
519 /* wvalue will be an odd number < 2^window */
520 if (!BN_mod_mul_montgomery(r, r, val[wvalue >> 1], mont, ctx))
521 goto err;
522
523 /* move the 'window' down further */
524 wstart -= wend + 1;
525 wvalue = 0;
526 start = 0;
527 if (wstart < 0)
528 break;
529 }
530 if (!BN_from_montgomery(rr, r, mont, ctx))
531 goto err;
532 ret = 1;
533 err:
534 if ((in_mont == NULL) && (mont != NULL))
535 BN_MONT_CTX_free(mont);
536 BN_CTX_end(ctx);
537 bn_check_top(rr);
538 return (ret);
539 }
540
541 /*
542 * BN_mod_exp_mont_consttime() stores the precomputed powers in a specific
543 * layout so that accessing any of these table values shows the same access
544 * pattern as far as cache lines are concerned. The following functions are
545 * used to transfer a BIGNUM from/to that table.
546 */
547
MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM * b,int top,unsigned char * buf,int idx,int window)548 static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top,
549 unsigned char *buf, int idx,
550 int window)
551 {
552 int i, j;
553 int width = 1 << window;
554 BN_ULONG *table = (BN_ULONG *)buf;
555
556 if (top > b->top)
557 top = b->top; /* this works because 'buf' is explicitly
558 * zeroed */
559 for (i = 0, j = idx; i < top; i++, j += width) {
560 table[j] = b->d[i];
561 }
562
563 return 1;
564 }
565
MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM * b,int top,unsigned char * buf,int idx,int window)566 static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top,
567 unsigned char *buf, int idx,
568 int window)
569 {
570 int i, j;
571 int width = 1 << window;
572 volatile BN_ULONG *table = (volatile BN_ULONG *)buf;
573
574 if (bn_wexpand(b, top) == NULL)
575 return 0;
576
577 if (window <= 3) {
578 for (i = 0; i < top; i++, table += width) {
579 BN_ULONG acc = 0;
580
581 for (j = 0; j < width; j++) {
582 acc |= table[j] &
583 ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1));
584 }
585
586 b->d[i] = acc;
587 }
588 } else {
589 int xstride = 1 << (window - 2);
590 BN_ULONG y0, y1, y2, y3;
591
592 i = idx >> (window - 2); /* equivalent of idx / xstride */
593 idx &= xstride - 1; /* equivalent of idx % xstride */
594
595 y0 = (BN_ULONG)0 - (constant_time_eq_int(i,0)&1);
596 y1 = (BN_ULONG)0 - (constant_time_eq_int(i,1)&1);
597 y2 = (BN_ULONG)0 - (constant_time_eq_int(i,2)&1);
598 y3 = (BN_ULONG)0 - (constant_time_eq_int(i,3)&1);
599
600 for (i = 0; i < top; i++, table += width) {
601 BN_ULONG acc = 0;
602
603 for (j = 0; j < xstride; j++) {
604 acc |= ( (table[j + 0 * xstride] & y0) |
605 (table[j + 1 * xstride] & y1) |
606 (table[j + 2 * xstride] & y2) |
607 (table[j + 3 * xstride] & y3) )
608 & ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1));
609 }
610
611 b->d[i] = acc;
612 }
613 }
614
615 b->top = top;
616 bn_correct_top(b);
617 return 1;
618 }
619
620 /*
621 * Given a pointer value, compute the next address that is a cache line
622 * multiple.
623 */
624 #define MOD_EXP_CTIME_ALIGN(x_) \
625 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
626
627 /*
628 * This variant of BN_mod_exp_mont() uses fixed windows and the special
629 * precomputation memory layout to limit data-dependency to a minimum to
630 * protect secret exponents (cf. the hyper-threading timing attacks pointed
631 * out by Colin Percival,
632 * http://www.daemonology.net/hyperthreading-considered-harmful/)
633 */
BN_mod_exp_mont_consttime(BIGNUM * rr,const BIGNUM * a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx,BN_MONT_CTX * in_mont)634 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
635 const BIGNUM *m, BN_CTX *ctx,
636 BN_MONT_CTX *in_mont)
637 {
638 int i, bits, ret = 0, window, wvalue;
639 int top;
640 BN_MONT_CTX *mont = NULL;
641
642 int numPowers;
643 unsigned char *powerbufFree = NULL;
644 int powerbufLen = 0;
645 unsigned char *powerbuf = NULL;
646 BIGNUM tmp, am;
647
648 bn_check_top(a);
649 bn_check_top(p);
650 bn_check_top(m);
651
652 if (!BN_is_odd(m)) {
653 BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME, BN_R_CALLED_WITH_EVEN_MODULUS);
654 return (0);
655 }
656
657 top = m->top;
658
659 bits = BN_num_bits(p);
660 if (bits == 0) {
661 /* x**0 mod 1 is still zero. */
662 if (BN_is_one(m)) {
663 ret = 1;
664 BN_zero(rr);
665 } else {
666 ret = BN_one(rr);
667 }
668 return ret;
669 }
670
671 BN_CTX_start(ctx);
672
673 /*
674 * Allocate a montgomery context if it was not supplied by the caller. If
675 * this is not done, things will break in the montgomery part.
676 */
677 if (in_mont != NULL)
678 mont = in_mont;
679 else {
680 if ((mont = BN_MONT_CTX_new()) == NULL)
681 goto err;
682 if (!BN_MONT_CTX_set(mont, m, ctx))
683 goto err;
684 }
685
686 /* Get the window size to use with size of p. */
687 window = BN_window_bits_for_ctime_exponent_size(bits);
688 #if defined(OPENSSL_BN_ASM_MONT5)
689 if (window == 6 && bits <= 1024)
690 window = 5; /* ~5% improvement of 2048-bit RSA sign */
691 #endif
692
693 /*
694 * Allocate a buffer large enough to hold all of the pre-computed powers
695 * of am, am itself and tmp.
696 */
697 numPowers = 1 << window;
698 powerbufLen = sizeof(m->d[0]) * (top * numPowers +
699 ((2 * top) >
700 numPowers ? (2 * top) : numPowers));
701 #ifdef alloca
702 if (powerbufLen < 3072)
703 powerbufFree =
704 alloca(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
705 else
706 #endif
707 if ((powerbufFree =
708 (unsigned char *)OPENSSL_malloc(powerbufLen +
709 MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH))
710 == NULL)
711 goto err;
712
713 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
714 memset(powerbuf, 0, powerbufLen);
715
716 #ifdef alloca
717 if (powerbufLen < 3072)
718 powerbufFree = NULL;
719 #endif
720
721 /* lay down tmp and am right after powers table */
722 tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers);
723 am.d = tmp.d + top;
724 tmp.top = am.top = 0;
725 tmp.dmax = am.dmax = top;
726 tmp.neg = am.neg = 0;
727 tmp.flags = am.flags = BN_FLG_STATIC_DATA;
728
729 /* prepare a^0 in Montgomery domain */
730 #if 1
731 if (!BN_to_montgomery(&tmp, BN_value_one(), mont, ctx))
732 goto err;
733 #else
734 tmp.d[0] = (0 - m->d[0]) & BN_MASK2; /* 2^(top*BN_BITS2) - m */
735 for (i = 1; i < top; i++)
736 tmp.d[i] = (~m->d[i]) & BN_MASK2;
737 tmp.top = top;
738 #endif
739
740 /* prepare a^1 in Montgomery domain */
741 if (a->neg || BN_ucmp(a, m) >= 0) {
742 if (!BN_mod(&am, a, m, ctx))
743 goto err;
744 if (!BN_to_montgomery(&am, &am, mont, ctx))
745 goto err;
746 } else if (!BN_to_montgomery(&am, a, mont, ctx))
747 goto err;
748
749 #if defined(OPENSSL_BN_ASM_MONT5)
750 if (window == 5 && top > 1) {
751 /*
752 * This optimization uses ideas from http://eprint.iacr.org/2011/239,
753 * specifically optimization of cache-timing attack countermeasures
754 * and pre-computation optimization.
755 */
756
757 /*
758 * Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as
759 * 512-bit RSA is hardly relevant, we omit it to spare size...
760 */
761 void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap,
762 const void *table, const BN_ULONG *np,
763 const BN_ULONG *n0, int num, int power);
764 void bn_scatter5(const BN_ULONG *inp, size_t num,
765 void *table, size_t power);
766 void bn_gather5(BN_ULONG *out, size_t num, void *table, size_t power);
767
768 BN_ULONG *np = mont->N.d, *n0 = mont->n0;
769
770 /*
771 * BN_to_montgomery can contaminate words above .top [in
772 * BN_DEBUG[_DEBUG] build]...
773 */
774 for (i = am.top; i < top; i++)
775 am.d[i] = 0;
776 for (i = tmp.top; i < top; i++)
777 tmp.d[i] = 0;
778
779 bn_scatter5(tmp.d, top, powerbuf, 0);
780 bn_scatter5(am.d, am.top, powerbuf, 1);
781 bn_mul_mont(tmp.d, am.d, am.d, np, n0, top);
782 bn_scatter5(tmp.d, top, powerbuf, 2);
783
784 # if 0
785 for (i = 3; i < 32; i++) {
786 /* Calculate a^i = a^(i-1) * a */
787 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
788 bn_scatter5(tmp.d, top, powerbuf, i);
789 }
790 # else
791 /* same as above, but uses squaring for 1/2 of operations */
792 for (i = 4; i < 32; i *= 2) {
793 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
794 bn_scatter5(tmp.d, top, powerbuf, i);
795 }
796 for (i = 3; i < 8; i += 2) {
797 int j;
798 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
799 bn_scatter5(tmp.d, top, powerbuf, i);
800 for (j = 2 * i; j < 32; j *= 2) {
801 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
802 bn_scatter5(tmp.d, top, powerbuf, j);
803 }
804 }
805 for (; i < 16; i += 2) {
806 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
807 bn_scatter5(tmp.d, top, powerbuf, i);
808 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
809 bn_scatter5(tmp.d, top, powerbuf, 2 * i);
810 }
811 for (; i < 32; i += 2) {
812 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
813 bn_scatter5(tmp.d, top, powerbuf, i);
814 }
815 # endif
816 bits--;
817 for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--)
818 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
819 bn_gather5(tmp.d, top, powerbuf, wvalue);
820
821 /*
822 * Scan the exponent one window at a time starting from the most
823 * significant bits.
824 */
825 while (bits >= 0) {
826 for (wvalue = 0, i = 0; i < 5; i++, bits--)
827 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
828
829 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
830 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
831 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
832 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
833 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
834 bn_mul_mont_gather5(tmp.d, tmp.d, powerbuf, np, n0, top, wvalue);
835 }
836
837 tmp.top = top;
838 bn_correct_top(&tmp);
839 } else
840 #endif
841 {
842 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, window))
843 goto err;
844 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, window))
845 goto err;
846
847 /*
848 * If the window size is greater than 1, then calculate
849 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even
850 * powers could instead be computed as (a^(i/2))^2 to use the slight
851 * performance advantage of sqr over mul).
852 */
853 if (window > 1) {
854 if (!BN_mod_mul_montgomery(&tmp, &am, &am, mont, ctx))
855 goto err;
856 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2,
857 window))
858 goto err;
859 for (i = 3; i < numPowers; i++) {
860 /* Calculate a^i = a^(i-1) * a */
861 if (!BN_mod_mul_montgomery(&tmp, &am, &tmp, mont, ctx))
862 goto err;
863 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i,
864 window))
865 goto err;
866 }
867 }
868
869 bits--;
870 for (wvalue = 0, i = bits % window; i >= 0; i--, bits--)
871 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
872 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp, top, powerbuf, wvalue,
873 window))
874 goto err;
875
876 /*
877 * Scan the exponent one window at a time starting from the most
878 * significant bits.
879 */
880 while (bits >= 0) {
881 wvalue = 0; /* The 'value' of the window */
882
883 /* Scan the window, squaring the result as we go */
884 for (i = 0; i < window; i++, bits--) {
885 if (!BN_mod_mul_montgomery(&tmp, &tmp, &tmp, mont, ctx))
886 goto err;
887 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
888 }
889
890 /*
891 * Fetch the appropriate pre-computed value from the pre-buf
892 */
893 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue,
894 window))
895 goto err;
896
897 /* Multiply the result into the intermediate result */
898 if (!BN_mod_mul_montgomery(&tmp, &tmp, &am, mont, ctx))
899 goto err;
900 }
901 }
902
903 /* Convert the final result from montgomery to standard format */
904 if (!BN_from_montgomery(rr, &tmp, mont, ctx))
905 goto err;
906 ret = 1;
907 err:
908 if ((in_mont == NULL) && (mont != NULL))
909 BN_MONT_CTX_free(mont);
910 if (powerbuf != NULL) {
911 OPENSSL_cleanse(powerbuf, powerbufLen);
912 if (powerbufFree)
913 OPENSSL_free(powerbufFree);
914 }
915 BN_CTX_end(ctx);
916 return (ret);
917 }
918
BN_mod_exp_mont_word(BIGNUM * rr,BN_ULONG a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx,BN_MONT_CTX * in_mont)919 int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
920 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
921 {
922 BN_MONT_CTX *mont = NULL;
923 int b, bits, ret = 0;
924 int r_is_one;
925 BN_ULONG w, next_w;
926 BIGNUM *d, *r, *t;
927 BIGNUM *swap_tmp;
928 #define BN_MOD_MUL_WORD(r, w, m) \
929 (BN_mul_word(r, (w)) && \
930 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
931 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
932 /*
933 * BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is
934 * probably more overhead than always using BN_mod (which uses BN_copy if
935 * a similar test returns true).
936 */
937 /*
938 * We can use BN_mod and do not need BN_nnmod because our accumulator is
939 * never negative (the result of BN_mod does not depend on the sign of
940 * the modulus).
941 */
942 #define BN_TO_MONTGOMERY_WORD(r, w, mont) \
943 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
944
945 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
946 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
947 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
948 return -1;
949 }
950
951 bn_check_top(p);
952 bn_check_top(m);
953
954 if (!BN_is_odd(m)) {
955 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, BN_R_CALLED_WITH_EVEN_MODULUS);
956 return (0);
957 }
958 if (m->top == 1)
959 a %= m->d[0]; /* make sure that 'a' is reduced */
960
961 bits = BN_num_bits(p);
962 if (bits == 0) {
963 /* x**0 mod 1 is still zero. */
964 if (BN_is_one(m)) {
965 ret = 1;
966 BN_zero(rr);
967 } else {
968 ret = BN_one(rr);
969 }
970 return ret;
971 }
972 if (a == 0) {
973 BN_zero(rr);
974 ret = 1;
975 return ret;
976 }
977
978 BN_CTX_start(ctx);
979 d = BN_CTX_get(ctx);
980 r = BN_CTX_get(ctx);
981 t = BN_CTX_get(ctx);
982 if (d == NULL || r == NULL || t == NULL)
983 goto err;
984
985 if (in_mont != NULL)
986 mont = in_mont;
987 else {
988 if ((mont = BN_MONT_CTX_new()) == NULL)
989 goto err;
990 if (!BN_MONT_CTX_set(mont, m, ctx))
991 goto err;
992 }
993
994 r_is_one = 1; /* except for Montgomery factor */
995
996 /* bits-1 >= 0 */
997
998 /* The result is accumulated in the product r*w. */
999 w = a; /* bit 'bits-1' of 'p' is always set */
1000 for (b = bits - 2; b >= 0; b--) {
1001 /* First, square r*w. */
1002 next_w = w * w;
1003 if ((next_w / w) != w) { /* overflow */
1004 if (r_is_one) {
1005 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1006 goto err;
1007 r_is_one = 0;
1008 } else {
1009 if (!BN_MOD_MUL_WORD(r, w, m))
1010 goto err;
1011 }
1012 next_w = 1;
1013 }
1014 w = next_w;
1015 if (!r_is_one) {
1016 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
1017 goto err;
1018 }
1019
1020 /* Second, multiply r*w by 'a' if exponent bit is set. */
1021 if (BN_is_bit_set(p, b)) {
1022 next_w = w * a;
1023 if ((next_w / a) != w) { /* overflow */
1024 if (r_is_one) {
1025 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1026 goto err;
1027 r_is_one = 0;
1028 } else {
1029 if (!BN_MOD_MUL_WORD(r, w, m))
1030 goto err;
1031 }
1032 next_w = a;
1033 }
1034 w = next_w;
1035 }
1036 }
1037
1038 /* Finally, set r:=r*w. */
1039 if (w != 1) {
1040 if (r_is_one) {
1041 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1042 goto err;
1043 r_is_one = 0;
1044 } else {
1045 if (!BN_MOD_MUL_WORD(r, w, m))
1046 goto err;
1047 }
1048 }
1049
1050 if (r_is_one) { /* can happen only if a == 1 */
1051 if (!BN_one(rr))
1052 goto err;
1053 } else {
1054 if (!BN_from_montgomery(rr, r, mont, ctx))
1055 goto err;
1056 }
1057 ret = 1;
1058 err:
1059 if ((in_mont == NULL) && (mont != NULL))
1060 BN_MONT_CTX_free(mont);
1061 BN_CTX_end(ctx);
1062 bn_check_top(rr);
1063 return (ret);
1064 }
1065
1066 /* The old fallback, simple version :-) */
BN_mod_exp_simple(BIGNUM * r,const BIGNUM * a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx)1067 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
1068 const BIGNUM *m, BN_CTX *ctx)
1069 {
1070 int i, j, bits, ret = 0, wstart, wend, window, wvalue;
1071 int start = 1;
1072 BIGNUM *d;
1073 /* Table of variables obtained from 'ctx' */
1074 BIGNUM *val[TABLE_SIZE];
1075
1076 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
1077 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1078 BNerr(BN_F_BN_MOD_EXP_SIMPLE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1079 return -1;
1080 }
1081
1082 bits = BN_num_bits(p);
1083 if (bits == 0) {
1084 /* x**0 mod 1 is still zero. */
1085 if (BN_is_one(m)) {
1086 ret = 1;
1087 BN_zero(r);
1088 } else {
1089 ret = BN_one(r);
1090 }
1091 return ret;
1092 }
1093
1094 BN_CTX_start(ctx);
1095 d = BN_CTX_get(ctx);
1096 val[0] = BN_CTX_get(ctx);
1097 if (!d || !val[0])
1098 goto err;
1099
1100 if (!BN_nnmod(val[0], a, m, ctx))
1101 goto err; /* 1 */
1102 if (BN_is_zero(val[0])) {
1103 BN_zero(r);
1104 ret = 1;
1105 goto err;
1106 }
1107
1108 window = BN_window_bits_for_exponent_size(bits);
1109 if (window > 1) {
1110 if (!BN_mod_mul(d, val[0], val[0], m, ctx))
1111 goto err; /* 2 */
1112 j = 1 << (window - 1);
1113 for (i = 1; i < j; i++) {
1114 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
1115 !BN_mod_mul(val[i], val[i - 1], d, m, ctx))
1116 goto err;
1117 }
1118 }
1119
1120 start = 1; /* This is used to avoid multiplication etc
1121 * when there is only the value '1' in the
1122 * buffer. */
1123 wvalue = 0; /* The 'value' of the window */
1124 wstart = bits - 1; /* The top bit of the window */
1125 wend = 0; /* The bottom bit of the window */
1126
1127 if (!BN_one(r))
1128 goto err;
1129
1130 for (;;) {
1131 if (BN_is_bit_set(p, wstart) == 0) {
1132 if (!start)
1133 if (!BN_mod_mul(r, r, r, m, ctx))
1134 goto err;
1135 if (wstart == 0)
1136 break;
1137 wstart--;
1138 continue;
1139 }
1140 /*
1141 * We now have wstart on a 'set' bit, we now need to work out how bit
1142 * a window to do. To do this we need to scan forward until the last
1143 * set bit before the end of the window
1144 */
1145 j = wstart;
1146 wvalue = 1;
1147 wend = 0;
1148 for (i = 1; i < window; i++) {
1149 if (wstart - i < 0)
1150 break;
1151 if (BN_is_bit_set(p, wstart - i)) {
1152 wvalue <<= (i - wend);
1153 wvalue |= 1;
1154 wend = i;
1155 }
1156 }
1157
1158 /* wend is the size of the current window */
1159 j = wend + 1;
1160 /* add the 'bytes above' */
1161 if (!start)
1162 for (i = 0; i < j; i++) {
1163 if (!BN_mod_mul(r, r, r, m, ctx))
1164 goto err;
1165 }
1166
1167 /* wvalue will be an odd number < 2^window */
1168 if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx))
1169 goto err;
1170
1171 /* move the 'window' down further */
1172 wstart -= wend + 1;
1173 wvalue = 0;
1174 start = 0;
1175 if (wstart < 0)
1176 break;
1177 }
1178 ret = 1;
1179 err:
1180 BN_CTX_end(ctx);
1181 bn_check_top(r);
1182 return (ret);
1183 }
1184