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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
113#include "cryptlib.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 */
132int 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 {
139 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
140 BNerr(BN_F_BN_EXP,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
141 return -1;
142 }
143
144 BN_CTX_start(ctx);
145 if ((r == a) || (r == p))
146 rr = BN_CTX_get(ctx);
147 else
148 rr = r;
149 v = BN_CTX_get(ctx);
150 if (rr == NULL || v == NULL) goto err;
151
152 if (BN_copy(v,a) == NULL) goto err;
153 bits=BN_num_bits(p);
154
155 if (BN_is_odd(p))
156 { if (BN_copy(rr,a) == NULL) goto err; }
157 else { if (!BN_one(rr)) goto err; }
158
159 for (i=1; i<bits; i++)
160 {
161 if (!BN_sqr(v,v,ctx)) goto err;
162 if (BN_is_bit_set(p,i))
163 {
164 if (!BN_mul(rr,rr,v,ctx)) goto err;
165 }
166 }
167 ret=1;
168err:
169 if (r != rr) BN_copy(r,rr);
170 BN_CTX_end(ctx);
171 bn_check_top(r);
172 return(ret);
173 }
174
175
176int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
177 BN_CTX *ctx)
178 {
179 int ret;
180
181 bn_check_top(a);
182 bn_check_top(p);
183 bn_check_top(m);
184
185 /* For even modulus m = 2^k*m_odd, it might make sense to compute
186 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery
187 * exponentiation for the odd part), using appropriate exponent
188 * reductions, and combine the results using the CRT.
189 *
190 * For now, we use Montgomery only if the modulus is odd; otherwise,
191 * exponentiation using the reciprocal-based quick remaindering
192 * algorithm is used.
193 *
194 * (Timing obtained with expspeed.c [computations a^p mod m
195 * where a, p, m are of the same length: 256, 512, 1024, 2048,
196 * 4096, 8192 bits], compared to the running time of the
197 * standard algorithm:
198 *
199 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
200 * 55 .. 77 % [UltraSparc processor, but
201 * debug-solaris-sparcv8-gcc conf.]
202 *
203 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
204 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
205 *
206 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
207 * at 2048 and more bits, but at 512 and 1024 bits, it was
208 * slower even than the standard algorithm!
209 *
210 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
211 * should be obtained when the new Montgomery reduction code
212 * has been integrated into OpenSSL.)
213 */
214
215#define MONT_MUL_MOD
216#define MONT_EXP_WORD
217#define RECP_MUL_MOD
218
219#ifdef MONT_MUL_MOD
220 /* I have finally been able to take out this pre-condition of
221 * the top bit being set. It was caused by an error in BN_div
222 * with negatives. There was also another problem when for a^b%m
223 * a >= m. eay 07-May-97 */
224/* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */
225
226 if (BN_is_odd(m))
227 {
228# ifdef MONT_EXP_WORD
229 if (a->top == 1 && !a->neg && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0))
230 {
231 BN_ULONG A = a->d[0];
232 ret=BN_mod_exp_mont_word(r,A,p,m,ctx,NULL);
233 }
234 else
235# endif
236 ret=BN_mod_exp_mont(r,a,p,m,ctx,NULL);
237 }
238 else
239#endif
240#ifdef RECP_MUL_MOD
241 { ret=BN_mod_exp_recp(r,a,p,m,ctx); }
242#else
243 { ret=BN_mod_exp_simple(r,a,p,m,ctx); }
244#endif
245
246 bn_check_top(r);
247 return(ret);
248 }
249
250
251int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
252 const BIGNUM *m, BN_CTX *ctx)
253 {
254 int i,j,bits,ret=0,wstart,wend,window,wvalue;
255 int start=1;
256 BIGNUM *aa;
257 /* Table of variables obtained from 'ctx' */
258 BIGNUM *val[TABLE_SIZE];
259 BN_RECP_CTX recp;
260
261 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
262 {
263 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
264 BNerr(BN_F_BN_MOD_EXP_RECP,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
265 return -1;
266 }
267
268 bits=BN_num_bits(p);
269
270 if (bits == 0)
271 {
272 ret = BN_one(r);
273 return ret;
274 }
275
276 BN_CTX_start(ctx);
277 aa = BN_CTX_get(ctx);
278 val[0] = BN_CTX_get(ctx);
279 if(!aa || !val[0]) goto err;
280
281 BN_RECP_CTX_init(&recp);
282 if (m->neg)
283 {
284 /* ignore sign of 'm' */
285 if (!BN_copy(aa, m)) goto err;
286 aa->neg = 0;
287 if (BN_RECP_CTX_set(&recp,aa,ctx) <= 0) goto err;
288 }
289 else
290 {
291 if (BN_RECP_CTX_set(&recp,m,ctx) <= 0) goto err;
292 }
293
294 if (!BN_nnmod(val[0],a,m,ctx)) goto err; /* 1 */
295 if (BN_is_zero(val[0]))
296 {
297 BN_zero(r);
298 ret = 1;
299 goto err;
300 }
301
302 window = BN_window_bits_for_exponent_size(bits);
303 if (window > 1)
304 {
305 if (!BN_mod_mul_reciprocal(aa,val[0],val[0],&recp,ctx))
306 goto err; /* 2 */
307 j=1<<(window-1);
308 for (i=1; i<j; i++)
309 {
310 if(((val[i] = BN_CTX_get(ctx)) == NULL) ||
311 !BN_mod_mul_reciprocal(val[i],val[i-1],
312 aa,&recp,ctx))
313 goto err;
314 }
315 }
316
317 start=1; /* This is used to avoid multiplication etc
318 * when there is only the value '1' in the
319 * buffer. */
320 wvalue=0; /* The 'value' of the window */
321 wstart=bits-1; /* The top bit of the window */
322 wend=0; /* The bottom bit of the window */
323
324 if (!BN_one(r)) goto err;
325
326 for (;;)
327 {
328 if (BN_is_bit_set(p,wstart) == 0)
329 {
330 if (!start)
331 if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
332 goto err;
333 if (wstart == 0) break;
334 wstart--;
335 continue;
336 }
337 /* We now have wstart on a 'set' bit, we now need to work out
338 * how bit a window to do. To do this we need to scan
339 * forward until the last set bit before the end of the
340 * window */
341 j=wstart;
342 wvalue=1;
343 wend=0;
344 for (i=1; i<window; i++)
345 {
346 if (wstart-i < 0) break;
347 if (BN_is_bit_set(p,wstart-i))
348 {
349 wvalue<<=(i-wend);
350 wvalue|=1;
351 wend=i;
352 }
353 }
354
355 /* wend is the size of the current window */
356 j=wend+1;
357 /* add the 'bytes above' */
358 if (!start)
359 for (i=0; i<j; i++)
360 {
361 if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
362 goto err;
363 }
364
365 /* wvalue will be an odd number < 2^window */
366 if (!BN_mod_mul_reciprocal(r,r,val[wvalue>>1],&recp,ctx))
367 goto err;
368
369 /* move the 'window' down further */
370 wstart-=wend+1;
371 wvalue=0;
372 start=0;
373 if (wstart < 0) break;
374 }
375 ret=1;
376err:
377 BN_CTX_end(ctx);
378 BN_RECP_CTX_free(&recp);
379 bn_check_top(r);
380 return(ret);
381 }
382
383
384int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
385 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
386 {
387 int i,j,bits,ret=0,wstart,wend,window,wvalue;
388 int start=1;
389 BIGNUM *d,*r;
390 const BIGNUM *aa;
391 /* Table of variables obtained from 'ctx' */
392 BIGNUM *val[TABLE_SIZE];
393 BN_MONT_CTX *mont=NULL;
394
395 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
396 {
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 {
406 BNerr(BN_F_BN_MOD_EXP_MONT,BN_R_CALLED_WITH_EVEN_MODULUS);
407 return(0);
408 }
409 bits=BN_num_bits(p);
410 if (bits == 0)
411 {
412 ret = BN_one(rr);
413 return ret;
414 }
415
416 BN_CTX_start(ctx);
417 d = BN_CTX_get(ctx);
418 r = BN_CTX_get(ctx);
419 val[0] = BN_CTX_get(ctx);
420 if (!d || !r || !val[0]) goto err;
421
422 /* If this is not done, things will break in the montgomery
423 * part */
424
425 if (in_mont != NULL)
426 mont=in_mont;
427 else
428 {
429 if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
430 if (!BN_MONT_CTX_set(mont,m,ctx)) goto err;
431 }
432
433 if (a->neg || BN_ucmp(a,m) >= 0)
434 {
435 if (!BN_nnmod(val[0],a,m,ctx))
436 goto err;
437 aa= val[0];
438 }
439 else
440 aa=a;
441 if (BN_is_zero(aa))
442 {
443 BN_zero(rr);
444 ret = 1;
445 goto err;
446 }
447 if (!BN_to_montgomery(val[0],aa,mont,ctx)) goto err; /* 1 */
448
449 window = BN_window_bits_for_exponent_size(bits);
450 if (window > 1)
451 {
452 if (!BN_mod_mul_montgomery(d,val[0],val[0],mont,ctx)) goto err; /* 2 */
453 j=1<<(window-1);
454 for (i=1; i<j; i++)
455 {
456 if(((val[i] = BN_CTX_get(ctx)) == NULL) ||
457 !BN_mod_mul_montgomery(val[i],val[i-1],
458 d,mont,ctx))
459 goto err;
460 }
461 }
462
463 start=1; /* This is used to avoid multiplication etc
464 * when there is only the value '1' in the
465 * buffer. */
466 wvalue=0; /* The 'value' of the window */
467 wstart=bits-1; /* The top bit of the window */
468 wend=0; /* The bottom bit of the window */
469
470 if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err;
471 for (;;)
472 {
473 if (BN_is_bit_set(p,wstart) == 0)
474 {
475 if (!start)
476 {
477 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
478 goto err;
479 }
480 if (wstart == 0) break;
481 wstart--;
482 continue;
483 }
484 /* We now have wstart on a 'set' bit, we now need to work out
485 * how bit a window to do. To do this we need to scan
486 * forward until the last set bit before the end of the
487 * window */
488 j=wstart;
489 wvalue=1;
490 wend=0;
491 for (i=1; i<window; i++)
492 {
493 if (wstart-i < 0) break;
494 if (BN_is_bit_set(p,wstart-i))
495 {
496 wvalue<<=(i-wend);
497 wvalue|=1;
498 wend=i;
499 }
500 }
501
502 /* wend is the size of the current window */
503 j=wend+1;
504 /* add the 'bytes above' */
505 if (!start)
506 for (i=0; i<j; i++)
507 {
508 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
509 goto err;
510 }
511
512 /* wvalue will be an odd number < 2^window */
513 if (!BN_mod_mul_montgomery(r,r,val[wvalue>>1],mont,ctx))
514 goto err;
515
516 /* move the 'window' down further */
517 wstart-=wend+1;
518 wvalue=0;
519 start=0;
520 if (wstart < 0) break;
521 }
522 if (!BN_from_montgomery(rr,r,mont,ctx)) goto err;
523 ret=1;
524err:
525 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
526 BN_CTX_end(ctx);
527 bn_check_top(rr);
528 return(ret);
529 }
530
531
532/* BN_mod_exp_mont_consttime() stores the precomputed powers in a specific layout
533 * so that accessing any of these table values shows the same access pattern as far
534 * as cache lines are concerned. The following functions are used to transfer a BIGNUM
535 * from/to that table. */
536
537static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top, unsigned char *buf, int idx, int width)
538 {
539 size_t i, j;
540
541 if (top > b->top)
542 top = b->top; /* this works because 'buf' is explicitly zeroed */
543 for (i = 0, j=idx; i < top * sizeof b->d[0]; i++, j+=width)
544 {
545 buf[j] = ((unsigned char*)b->d)[i];
546 }
547
548 return 1;
549 }
550
551static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top, unsigned char *buf, int idx, int width)
552 {
553 size_t i, j;
554
555 if (bn_wexpand(b, top) == NULL)
556 return 0;
557
558 for (i=0, j=idx; i < top * sizeof b->d[0]; i++, j+=width)
559 {
560 ((unsigned char*)b->d)[i] = buf[j];
561 }
562
563 b->top = top;
564 bn_correct_top(b);
565 return 1;
566 }
567
568/* Given a pointer value, compute the next address that is a cache line multiple. */
569#define MOD_EXP_CTIME_ALIGN(x_) \
570 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
571
572/* This variant of BN_mod_exp_mont() uses fixed windows and the special
573 * precomputation memory layout to limit data-dependency to a minimum
574 * to protect secret exponents (cf. the hyper-threading timing attacks
575 * pointed out by Colin Percival,
576 * http://www.daemonology.net/hyperthreading-considered-harmful/)
577 */
578int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
579 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
580 {
581 int i,bits,ret=0,window,wvalue;
582 int top;
583 BN_MONT_CTX *mont=NULL;
584
585 int numPowers;
586 unsigned char *powerbufFree=NULL;
587 int powerbufLen = 0;
588 unsigned char *powerbuf=NULL;
589 BIGNUM tmp, am;
590
591 bn_check_top(a);
592 bn_check_top(p);
593 bn_check_top(m);
594
595 top = m->top;
596
597 if (!(m->d[0] & 1))
598 {
599 BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME,BN_R_CALLED_WITH_EVEN_MODULUS);
600 return(0);
601 }
602 bits=BN_num_bits(p);
603 if (bits == 0)
604 {
605 ret = BN_one(rr);
606 return ret;
607 }
608
609 BN_CTX_start(ctx);
610
611 /* Allocate a montgomery context if it was not supplied by the caller.
612 * If this is not done, things will break in the montgomery part.
613 */
614 if (in_mont != NULL)
615 mont=in_mont;
616 else
617 {
618 if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
619 if (!BN_MONT_CTX_set(mont,m,ctx)) goto err;
620 }
621
622 /* Get the window size to use with size of p. */
623 window = BN_window_bits_for_ctime_exponent_size(bits);
624#if defined(OPENSSL_BN_ASM_MONT5)
625 if (window==6 && bits<=1024) window=5; /* ~5% improvement of 2048-bit RSA sign */
626#endif
627
628 /* Allocate a buffer large enough to hold all of the pre-computed
629 * powers of am, am itself and tmp.
630 */
631 numPowers = 1 << window;
632 powerbufLen = sizeof(m->d[0])*(top*numPowers +
633 ((2*top)>numPowers?(2*top):numPowers));
634#ifdef alloca
635 if (powerbufLen < 3072)
636 powerbufFree = alloca(powerbufLen+MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
637 else
638#endif
639 if ((powerbufFree=(unsigned char*)OPENSSL_malloc(powerbufLen+MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH)) == NULL)
640 goto err;
641
642 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
643 memset(powerbuf, 0, powerbufLen);
644
645#ifdef alloca
646 if (powerbufLen < 3072)
647 powerbufFree = NULL;
648#endif
649
650 /* lay down tmp and am right after powers table */
651 tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0])*top*numPowers);
652 am.d = tmp.d + top;
653 tmp.top = am.top = 0;
654 tmp.dmax = am.dmax = top;
655 tmp.neg = am.neg = 0;
656 tmp.flags = am.flags = BN_FLG_STATIC_DATA;
657
658 /* prepare a^0 in Montgomery domain */
659#if 1
660 if (!BN_to_montgomery(&tmp,BN_value_one(),mont,ctx)) goto err;
661#else
662 tmp.d[0] = (0-m->d[0])&BN_MASK2; /* 2^(top*BN_BITS2) - m */
663 for (i=1;i<top;i++)
664 tmp.d[i] = (~m->d[i])&BN_MASK2;
665 tmp.top = top;
666#endif
667
668 /* prepare a^1 in Montgomery domain */
669 if (a->neg || BN_ucmp(a,m) >= 0)
670 {
671 if (!BN_mod(&am,a,m,ctx)) goto err;
672 if (!BN_to_montgomery(&am,&am,mont,ctx)) goto err;
673 }
674 else if (!BN_to_montgomery(&am,a,mont,ctx)) goto err;
675
676#if defined(OPENSSL_BN_ASM_MONT5)
677 /* This optimization uses ideas from http://eprint.iacr.org/2011/239,
678 * specifically optimization of cache-timing attack countermeasures
679 * and pre-computation optimization. */
680
681 /* Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as
682 * 512-bit RSA is hardly relevant, we omit it to spare size... */
683 if (window==5)
684 {
685 void bn_mul_mont_gather5(BN_ULONG *rp,const BN_ULONG *ap,
686 const void *table,const BN_ULONG *np,
687 const BN_ULONG *n0,int num,int power);
688 void bn_scatter5(const BN_ULONG *inp,size_t num,
689 void *table,size_t power);
690 void bn_gather5(BN_ULONG *out,size_t num,
691 void *table,size_t power);
692
693 BN_ULONG *np=mont->N.d, *n0=mont->n0;
694
695 /* BN_to_montgomery can contaminate words above .top
696 * [in BN_DEBUG[_DEBUG] build]... */
697 for (i=am.top; i<top; i++) am.d[i]=0;
698 for (i=tmp.top; i<top; i++) tmp.d[i]=0;
699
700 bn_scatter5(tmp.d,top,powerbuf,0);
701 bn_scatter5(am.d,am.top,powerbuf,1);
702 bn_mul_mont(tmp.d,am.d,am.d,np,n0,top);
703 bn_scatter5(tmp.d,top,powerbuf,2);
704
705#if 0
706 for (i=3; i<32; i++)
707 {
708 /* Calculate a^i = a^(i-1) * a */
709 bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1);
710 bn_scatter5(tmp.d,top,powerbuf,i);
711 }
712#else
713 /* same as above, but uses squaring for 1/2 of operations */
714 for (i=4; i<32; i*=2)
715 {
716 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
717 bn_scatter5(tmp.d,top,powerbuf,i);
718 }
719 for (i=3; i<8; i+=2)
720 {
721 int j;
722 bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1);
723 bn_scatter5(tmp.d,top,powerbuf,i);
724 for (j=2*i; j<32; j*=2)
725 {
726 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
727 bn_scatter5(tmp.d,top,powerbuf,j);
728 }
729 }
730 for (; i<16; i+=2)
731 {
732 bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1);
733 bn_scatter5(tmp.d,top,powerbuf,i);
734 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
735 bn_scatter5(tmp.d,top,powerbuf,2*i);
736 }
737 for (; i<32; i+=2)
738 {
739 bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1);
740 bn_scatter5(tmp.d,top,powerbuf,i);
741 }
742#endif
743 bits--;
744 for (wvalue=0, i=bits%5; i>=0; i--,bits--)
745 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
746 bn_gather5(tmp.d,top,powerbuf,wvalue);
747
748 /* Scan the exponent one window at a time starting from the most
749 * significant bits.
750 */
751 while (bits >= 0)
752 {
753 for (wvalue=0, i=0; i<5; i++,bits--)
754 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
755
756 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
757 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
758 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
759 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
760 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
761 bn_mul_mont_gather5(tmp.d,tmp.d,powerbuf,np,n0,top,wvalue);
762 }
763
764 tmp.top=top;
765 bn_correct_top(&tmp);
766 }
767 else
768#endif
769 {
770 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, numPowers)) goto err;
771 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, numPowers)) goto err;
772
773 /* If the window size is greater than 1, then calculate
774 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1)
775 * (even powers could instead be computed as (a^(i/2))^2
776 * to use the slight performance advantage of sqr over mul).
777 */
778 if (window > 1)
779 {
780 if (!BN_mod_mul_montgomery(&tmp,&am,&am,mont,ctx)) goto err;
781 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2, numPowers)) goto err;
782 for (i=3; i<numPowers; i++)
783 {
784 /* Calculate a^i = a^(i-1) * a */
785 if (!BN_mod_mul_montgomery(&tmp,&am,&tmp,mont,ctx))
786 goto err;
787 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i, numPowers)) goto err;
788 }
789 }
790
791 bits--;
792 for (wvalue=0, i=bits%window; i>=0; i--,bits--)
793 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
794 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp,top,powerbuf,wvalue,numPowers)) goto err;
795
796 /* Scan the exponent one window at a time starting from the most
797 * significant bits.
798 */
799 while (bits >= 0)
800 {
801 wvalue=0; /* The 'value' of the window */
802
803 /* Scan the window, squaring the result as we go */
804 for (i=0; i<window; i++,bits--)
805 {
806 if (!BN_mod_mul_montgomery(&tmp,&tmp,&tmp,mont,ctx)) goto err;
807 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
808 }
809
810 /* Fetch the appropriate pre-computed value from the pre-buf */
811 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue, numPowers)) goto err;
812
813 /* Multiply the result into the intermediate result */
814 if (!BN_mod_mul_montgomery(&tmp,&tmp,&am,mont,ctx)) goto err;
815 }
816 }
817
818 /* Convert the final result from montgomery to standard format */
819 if (!BN_from_montgomery(rr,&tmp,mont,ctx)) goto err;
820 ret=1;
821err:
822 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
823 if (powerbuf!=NULL)
824 {
825 OPENSSL_cleanse(powerbuf,powerbufLen);
826 if (powerbufFree) OPENSSL_free(powerbufFree);
827 }
828 BN_CTX_end(ctx);
829 return(ret);
830 }
831
832int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
833 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
834 {
835 BN_MONT_CTX *mont = NULL;
836 int b, bits, ret=0;
837 int r_is_one;
838 BN_ULONG w, next_w;
839 BIGNUM *d, *r, *t;
840 BIGNUM *swap_tmp;
841#define BN_MOD_MUL_WORD(r, w, m) \
842 (BN_mul_word(r, (w)) && \
843 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
844 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
845 /* BN_MOD_MUL_WORD is only used with 'w' large,
846 * so the BN_ucmp test is probably more overhead
847 * than always using BN_mod (which uses BN_copy if
848 * a similar test returns true). */
849 /* We can use BN_mod and do not need BN_nnmod because our
850 * accumulator is never negative (the result of BN_mod does
851 * not depend on the sign of the modulus).
852 */
853#define BN_TO_MONTGOMERY_WORD(r, w, mont) \
854 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
855
856 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
857 {
858 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
859 BNerr(BN_F_BN_MOD_EXP_MONT_WORD,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
860 return -1;
861 }
862
863 bn_check_top(p);
864 bn_check_top(m);
865
866 if (!BN_is_odd(m))
867 {
868 BNerr(BN_F_BN_MOD_EXP_MONT_WORD,BN_R_CALLED_WITH_EVEN_MODULUS);
869 return(0);
870 }
871 if (m->top == 1)
872 a %= m->d[0]; /* make sure that 'a' is reduced */
873
874 bits = BN_num_bits(p);
875 if (bits == 0)
876 {
877 ret = BN_one(rr);
878 return ret;
879 }
880 if (a == 0)
881 {
882 BN_zero(rr);
883 ret = 1;
884 return ret;
885 }
886
887 BN_CTX_start(ctx);
888 d = BN_CTX_get(ctx);
889 r = BN_CTX_get(ctx);
890 t = BN_CTX_get(ctx);
891 if (d == NULL || r == NULL || t == NULL) goto err;
892
893 if (in_mont != NULL)
894 mont=in_mont;
895 else
896 {
897 if ((mont = BN_MONT_CTX_new()) == NULL) goto err;
898 if (!BN_MONT_CTX_set(mont, m, ctx)) goto err;
899 }
900
901 r_is_one = 1; /* except for Montgomery factor */
902
903 /* bits-1 >= 0 */
904
905 /* The result is accumulated in the product r*w. */
906 w = a; /* bit 'bits-1' of 'p' is always set */
907 for (b = bits-2; b >= 0; b--)
908 {
909 /* First, square r*w. */
910 next_w = w*w;
911 if ((next_w/w) != w) /* overflow */
912 {
913 if (r_is_one)
914 {
915 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
916 r_is_one = 0;
917 }
918 else
919 {
920 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
921 }
922 next_w = 1;
923 }
924 w = next_w;
925 if (!r_is_one)
926 {
927 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) goto err;
928 }
929
930 /* Second, multiply r*w by 'a' if exponent bit is set. */
931 if (BN_is_bit_set(p, b))
932 {
933 next_w = w*a;
934 if ((next_w/a) != w) /* overflow */
935 {
936 if (r_is_one)
937 {
938 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
939 r_is_one = 0;
940 }
941 else
942 {
943 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
944 }
945 next_w = a;
946 }
947 w = next_w;
948 }
949 }
950
951 /* Finally, set r:=r*w. */
952 if (w != 1)
953 {
954 if (r_is_one)
955 {
956 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
957 r_is_one = 0;
958 }
959 else
960 {
961 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
962 }
963 }
964
965 if (r_is_one) /* can happen only if a == 1*/
966 {
967 if (!BN_one(rr)) goto err;
968 }
969 else
970 {
971 if (!BN_from_montgomery(rr, r, mont, ctx)) goto err;
972 }
973 ret = 1;
974err:
975 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
976 BN_CTX_end(ctx);
977 bn_check_top(rr);
978 return(ret);
979 }
980
981
982/* The old fallback, simple version :-) */
983int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
984 const BIGNUM *m, BN_CTX *ctx)
985 {
986 int i,j,bits,ret=0,wstart,wend,window,wvalue;
987 int start=1;
988 BIGNUM *d;
989 /* Table of variables obtained from 'ctx' */
990 BIGNUM *val[TABLE_SIZE];
991
992 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
993 {
994 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
995 BNerr(BN_F_BN_MOD_EXP_SIMPLE,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
996 return -1;
997 }
998
999 bits=BN_num_bits(p);
1000
1001 if (bits == 0)
1002 {
1003 ret = BN_one(r);
1004 return ret;
1005 }
1006
1007 BN_CTX_start(ctx);
1008 d = BN_CTX_get(ctx);
1009 val[0] = BN_CTX_get(ctx);
1010 if(!d || !val[0]) goto err;
1011
1012 if (!BN_nnmod(val[0],a,m,ctx)) goto err; /* 1 */
1013 if (BN_is_zero(val[0]))
1014 {
1015 BN_zero(r);
1016 ret = 1;
1017 goto err;
1018 }
1019
1020 window = BN_window_bits_for_exponent_size(bits);
1021 if (window > 1)
1022 {
1023 if (!BN_mod_mul(d,val[0],val[0],m,ctx))
1024 goto err; /* 2 */
1025 j=1<<(window-1);
1026 for (i=1; i<j; i++)
1027 {
1028 if(((val[i] = BN_CTX_get(ctx)) == NULL) ||
1029 !BN_mod_mul(val[i],val[i-1],d,m,ctx))
1030 goto err;
1031 }
1032 }
1033
1034 start=1; /* This is used to avoid multiplication etc
1035 * when there is only the value '1' in the
1036 * buffer. */
1037 wvalue=0; /* The 'value' of the window */
1038 wstart=bits-1; /* The top bit of the window */
1039 wend=0; /* The bottom bit of the window */
1040
1041 if (!BN_one(r)) goto err;
1042
1043 for (;;)
1044 {
1045 if (BN_is_bit_set(p,wstart) == 0)
1046 {
1047 if (!start)
1048 if (!BN_mod_mul(r,r,r,m,ctx))
1049 goto err;
1050 if (wstart == 0) break;
1051 wstart--;
1052 continue;
1053 }
1054 /* We now have wstart on a 'set' bit, we now need to work out
1055 * how bit a window to do. To do this we need to scan
1056 * forward until the last set bit before the end of the
1057 * window */
1058 j=wstart;
1059 wvalue=1;
1060 wend=0;
1061 for (i=1; i<window; i++)
1062 {
1063 if (wstart-i < 0) break;
1064 if (BN_is_bit_set(p,wstart-i))
1065 {
1066 wvalue<<=(i-wend);
1067 wvalue|=1;
1068 wend=i;
1069 }
1070 }
1071
1072 /* wend is the size of the current window */
1073 j=wend+1;
1074 /* add the 'bytes above' */
1075 if (!start)
1076 for (i=0; i<j; i++)
1077 {
1078 if (!BN_mod_mul(r,r,r,m,ctx))
1079 goto err;
1080 }
1081
1082 /* wvalue will be an odd number < 2^window */
1083 if (!BN_mod_mul(r,r,val[wvalue>>1],m,ctx))
1084 goto err;
1085
1086 /* move the 'window' down further */
1087 wstart-=wend+1;
1088 wvalue=0;
1089 start=0;
1090 if (wstart < 0) break;
1091 }
1092 ret=1;
1093err:
1094 BN_CTX_end(ctx);
1095 bn_check_top(r);
1096 return(ret);
1097 }
generated by cgit v1.2.3-55-g6feb (git 2.39.1) at 2025-12-13 13:12:04 +0000