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