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