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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/* maximum precomputation table size for *variable* sliding windows */
117#define TABLE_SIZE 32
118
119/* this one works - simple but works */
120int 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 {
127 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
128 BNerr(BN_F_BN_EXP,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
129 return -1;
130 }
131
132 BN_CTX_start(ctx);
133 if ((r == a) || (r == p))
134 rr = BN_CTX_get(ctx);
135 else
136 rr = r;
137 v = BN_CTX_get(ctx);
138 if (rr == NULL || v == NULL) goto err;
139
140 if (BN_copy(v,a) == NULL) goto err;
141 bits=BN_num_bits(p);
142
143 if (BN_is_odd(p))
144 { if (BN_copy(rr,a) == NULL) goto err; }
145 else { if (!BN_one(rr)) goto err; }
146
147 for (i=1; i<bits; i++)
148 {
149 if (!BN_sqr(v,v,ctx)) goto err;
150 if (BN_is_bit_set(p,i))
151 {
152 if (!BN_mul(rr,rr,v,ctx)) goto err;
153 }
154 }
155 ret=1;
156err:
157 if (r != rr) BN_copy(r,rr);
158 BN_CTX_end(ctx);
159 bn_check_top(r);
160 return(ret);
161 }
162
163
164int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
165 BN_CTX *ctx)
166 {
167 int ret;
168
169 bn_check_top(a);
170 bn_check_top(p);
171 bn_check_top(m);
172
173 /* For even modulus m = 2^k*m_odd, it might make sense to compute
174 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery
175 * exponentiation for the odd part), using appropriate exponent
176 * reductions, and combine the results using the CRT.
177 *
178 * For now, we use Montgomery only if the modulus is odd; otherwise,
179 * exponentiation using the reciprocal-based quick remaindering
180 * algorithm is used.
181 *
182 * (Timing obtained with expspeed.c [computations a^p mod m
183 * where a, p, m are of the same length: 256, 512, 1024, 2048,
184 * 4096, 8192 bits], compared to the running time of the
185 * standard algorithm:
186 *
187 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
188 * 55 .. 77 % [UltraSparc processor, but
189 * debug-solaris-sparcv8-gcc conf.]
190 *
191 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
192 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
193 *
194 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
195 * at 2048 and more bits, but at 512 and 1024 bits, it was
196 * slower even than the standard algorithm!
197 *
198 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
199 * should be obtained when the new Montgomery reduction code
200 * has been integrated into OpenSSL.)
201 */
202
203#define MONT_MUL_MOD
204#define MONT_EXP_WORD
205#define RECP_MUL_MOD
206
207#ifdef MONT_MUL_MOD
208 /* I have finally been able to take out this pre-condition of
209 * the top bit being set. It was caused by an error in BN_div
210 * with negatives. There was also another problem when for a^b%m
211 * a >= m. eay 07-May-97 */
212/* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */
213
214 if (BN_is_odd(m))
215 {
216# ifdef MONT_EXP_WORD
217 if (a->top == 1 && !a->neg && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0))
218 {
219 BN_ULONG A = a->d[0];
220 ret=BN_mod_exp_mont_word(r,A,p,m,ctx,NULL);
221 }
222 else
223# endif
224 ret=BN_mod_exp_mont(r,a,p,m,ctx,NULL);
225 }
226 else
227#endif
228#ifdef RECP_MUL_MOD
229 { ret=BN_mod_exp_recp(r,a,p,m,ctx); }
230#else
231 { ret=BN_mod_exp_simple(r,a,p,m,ctx); }
232#endif
233
234 bn_check_top(r);
235 return(ret);
236 }
237
238
239int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
240 const BIGNUM *m, BN_CTX *ctx)
241 {
242 int i,j,bits,ret=0,wstart,wend,window,wvalue;
243 int start=1;
244 BIGNUM *aa;
245 /* Table of variables obtained from 'ctx' */
246 BIGNUM *val[TABLE_SIZE];
247 BN_RECP_CTX recp;
248
249 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
250 {
251 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
252 BNerr(BN_F_BN_MOD_EXP_RECP,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
253 return -1;
254 }
255
256 bits=BN_num_bits(p);
257
258 if (bits == 0)
259 {
260 ret = BN_one(r);
261 return ret;
262 }
263
264 BN_CTX_start(ctx);
265 aa = BN_CTX_get(ctx);
266 val[0] = BN_CTX_get(ctx);
267 if(!aa || !val[0]) goto err;
268
269 BN_RECP_CTX_init(&recp);
270 if (m->neg)
271 {
272 /* ignore sign of 'm' */
273 if (!BN_copy(aa, m)) goto err;
274 aa->neg = 0;
275 if (BN_RECP_CTX_set(&recp,aa,ctx) <= 0) goto err;
276 }
277 else
278 {
279 if (BN_RECP_CTX_set(&recp,m,ctx) <= 0) goto err;
280 }
281
282 if (!BN_nnmod(val[0],a,m,ctx)) goto err; /* 1 */
283 if (BN_is_zero(val[0]))
284 {
285 BN_zero(r);
286 ret = 1;
287 goto err;
288 }
289
290 window = BN_window_bits_for_exponent_size(bits);
291 if (window > 1)
292 {
293 if (!BN_mod_mul_reciprocal(aa,val[0],val[0],&recp,ctx))
294 goto err; /* 2 */
295 j=1<<(window-1);
296 for (i=1; i<j; i++)
297 {
298 if(((val[i] = BN_CTX_get(ctx)) == NULL) ||
299 !BN_mod_mul_reciprocal(val[i],val[i-1],
300 aa,&recp,ctx))
301 goto err;
302 }
303 }
304
305 start=1; /* This is used to avoid multiplication etc
306 * when there is only the value '1' in the
307 * buffer. */
308 wvalue=0; /* The 'value' of the window */
309 wstart=bits-1; /* The top bit of the window */
310 wend=0; /* The bottom bit of the window */
311
312 if (!BN_one(r)) goto err;
313
314 for (;;)
315 {
316 if (BN_is_bit_set(p,wstart) == 0)
317 {
318 if (!start)
319 if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
320 goto err;
321 if (wstart == 0) break;
322 wstart--;
323 continue;
324 }
325 /* We now have wstart on a 'set' bit, we now need to work out
326 * how bit a window to do. To do this we need to scan
327 * forward until the last set bit before the end of the
328 * window */
329 j=wstart;
330 wvalue=1;
331 wend=0;
332 for (i=1; i<window; i++)
333 {
334 if (wstart-i < 0) break;
335 if (BN_is_bit_set(p,wstart-i))
336 {
337 wvalue<<=(i-wend);
338 wvalue|=1;
339 wend=i;
340 }
341 }
342
343 /* wend is the size of the current window */
344 j=wend+1;
345 /* add the 'bytes above' */
346 if (!start)
347 for (i=0; i<j; i++)
348 {
349 if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
350 goto err;
351 }
352
353 /* wvalue will be an odd number < 2^window */
354 if (!BN_mod_mul_reciprocal(r,r,val[wvalue>>1],&recp,ctx))
355 goto err;
356
357 /* move the 'window' down further */
358 wstart-=wend+1;
359 wvalue=0;
360 start=0;
361 if (wstart < 0) break;
362 }
363 ret=1;
364err:
365 BN_CTX_end(ctx);
366 BN_RECP_CTX_free(&recp);
367 bn_check_top(r);
368 return(ret);
369 }
370
371
372int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
373 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
374 {
375 int i,j,bits,ret=0,wstart,wend,window,wvalue;
376 int start=1;
377 BIGNUM *d,*r;
378 const BIGNUM *aa;
379 /* Table of variables obtained from 'ctx' */
380 BIGNUM *val[TABLE_SIZE];
381 BN_MONT_CTX *mont=NULL;
382
383 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
384 {
385 return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
386 }
387
388 bn_check_top(a);
389 bn_check_top(p);
390 bn_check_top(m);
391
392 if (!BN_is_odd(m))
393 {
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 {
400 ret = BN_one(rr);
401 return ret;
402 }
403
404 BN_CTX_start(ctx);
405 d = BN_CTX_get(ctx);
406 r = BN_CTX_get(ctx);
407 val[0] = BN_CTX_get(ctx);
408 if (!d || !r || !val[0]) goto err;
409
410 /* If this is not done, things will break in the montgomery
411 * part */
412
413 if (in_mont != NULL)
414 mont=in_mont;
415 else
416 {
417 if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
418 if (!BN_MONT_CTX_set(mont,m,ctx)) goto err;
419 }
420
421 if (a->neg || BN_ucmp(a,m) >= 0)
422 {
423 if (!BN_nnmod(val[0],a,m,ctx))
424 goto err;
425 aa= val[0];
426 }
427 else
428 aa=a;
429 if (BN_is_zero(aa))
430 {
431 BN_zero(rr);
432 ret = 1;
433 goto err;
434 }
435 if (!BN_to_montgomery(val[0],aa,mont,ctx)) goto err; /* 1 */
436
437 window = BN_window_bits_for_exponent_size(bits);
438 if (window > 1)
439 {
440 if (!BN_mod_mul_montgomery(d,val[0],val[0],mont,ctx)) goto err; /* 2 */
441 j=1<<(window-1);
442 for (i=1; i<j; i++)
443 {
444 if(((val[i] = BN_CTX_get(ctx)) == NULL) ||
445 !BN_mod_mul_montgomery(val[i],val[i-1],
446 d,mont,ctx))
447 goto err;
448 }
449 }
450
451 start=1; /* This is used to avoid multiplication etc
452 * when there is only the value '1' in the
453 * buffer. */
454 wvalue=0; /* The 'value' of the window */
455 wstart=bits-1; /* The top bit of the window */
456 wend=0; /* The bottom bit of the window */
457
458 if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err;
459 for (;;)
460 {
461 if (BN_is_bit_set(p,wstart) == 0)
462 {
463 if (!start)
464 {
465 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
466 goto err;
467 }
468 if (wstart == 0) break;
469 wstart--;
470 continue;
471 }
472 /* We now have wstart on a 'set' bit, we now need to work out
473 * how bit a window to do. To do this we need to scan
474 * forward until the last set bit before the end of the
475 * window */
476 j=wstart;
477 wvalue=1;
478 wend=0;
479 for (i=1; i<window; i++)
480 {
481 if (wstart-i < 0) break;
482 if (BN_is_bit_set(p,wstart-i))
483 {
484 wvalue<<=(i-wend);
485 wvalue|=1;
486 wend=i;
487 }
488 }
489
490 /* wend is the size of the current window */
491 j=wend+1;
492 /* add the 'bytes above' */
493 if (!start)
494 for (i=0; i<j; i++)
495 {
496 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
497 goto err;
498 }
499
500 /* wvalue will be an odd number < 2^window */
501 if (!BN_mod_mul_montgomery(r,r,val[wvalue>>1],mont,ctx))
502 goto err;
503
504 /* move the 'window' down further */
505 wstart-=wend+1;
506 wvalue=0;
507 start=0;
508 if (wstart < 0) break;
509 }
510 if (!BN_from_montgomery(rr,r,mont,ctx)) goto err;
511 ret=1;
512err:
513 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
514 BN_CTX_end(ctx);
515 bn_check_top(rr);
516 return(ret);
517 }
518
519
520/* BN_mod_exp_mont_consttime() stores the precomputed powers in a specific layout
521 * so that accessing any of these table values shows the same access pattern as far
522 * as cache lines are concerned. The following functions are used to transfer a BIGNUM
523 * from/to that table. */
524
525static int MOD_EXP_CTIME_COPY_TO_PREBUF(BIGNUM *b, int top, unsigned char *buf, int idx, int width)
526 {
527 size_t i, j;
528
529 if (bn_wexpand(b, top) == NULL)
530 return 0;
531 while (b->top < top)
532 {
533 b->d[b->top++] = 0;
534 }
535
536 for (i = 0, j=idx; i < top * sizeof b->d[0]; i++, j+=width)
537 {
538 buf[j] = ((unsigned char*)b->d)[i];
539 }
540
541 bn_correct_top(b);
542 return 1;
543 }
544
545static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top, unsigned char *buf, int idx, int width)
546 {
547 size_t i, j;
548
549 if (bn_wexpand(b, top) == NULL)
550 return 0;
551
552 for (i=0, j=idx; i < top * sizeof b->d[0]; i++, j+=width)
553 {
554 ((unsigned char*)b->d)[i] = buf[j];
555 }
556
557 b->top = top;
558 bn_correct_top(b);
559 return 1;
560 }
561
562/* Given a pointer value, compute the next address that is a cache line multiple. */
563#define MOD_EXP_CTIME_ALIGN(x_) \
564 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((BN_ULONG)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
565
566/* This variant of BN_mod_exp_mont() uses fixed windows and the special
567 * precomputation memory layout to limit data-dependency to a minimum
568 * to protect secret exponents (cf. the hyper-threading timing attacks
569 * pointed out by Colin Percival,
570 * http://www.daemonology.net/hyperthreading-considered-harmful/)
571 */
572int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
573 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
574 {
575 int i,bits,ret=0,idx,window,wvalue;
576 int top;
577 BIGNUM *r;
578 const BIGNUM *aa;
579 BN_MONT_CTX *mont=NULL;
580
581 int numPowers;
582 unsigned char *powerbufFree=NULL;
583 int powerbufLen = 0;
584 unsigned char *powerbuf=NULL;
585 BIGNUM *computeTemp=NULL, *am=NULL;
586
587 bn_check_top(a);
588 bn_check_top(p);
589 bn_check_top(m);
590
591 top = m->top;
592
593 if (!(m->d[0] & 1))
594 {
595 BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME,BN_R_CALLED_WITH_EVEN_MODULUS);
596 return(0);
597 }
598 bits=BN_num_bits(p);
599 if (bits == 0)
600 {
601 ret = BN_one(rr);
602 return ret;
603 }
604
605 /* Initialize BIGNUM context and allocate intermediate result */
606 BN_CTX_start(ctx);
607 r = BN_CTX_get(ctx);
608 if (r == NULL) goto err;
609
610 /* Allocate a montgomery context if it was not supplied by the caller.
611 * If this is not done, things will break in the montgomery part.
612 */
613 if (in_mont != NULL)
614 mont=in_mont;
615 else
616 {
617 if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
618 if (!BN_MONT_CTX_set(mont,m,ctx)) goto err;
619 }
620
621 /* Get the window size to use with size of p. */
622 window = BN_window_bits_for_ctime_exponent_size(bits);
623
624 /* Allocate a buffer large enough to hold all of the pre-computed
625 * powers of a.
626 */
627 numPowers = 1 << window;
628 powerbufLen = sizeof(m->d[0])*top*numPowers;
629 if ((powerbufFree=(unsigned char*)OPENSSL_malloc(powerbufLen+MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH)) == NULL)
630 goto err;
631
632 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
633 memset(powerbuf, 0, powerbufLen);
634
635 /* Initialize the intermediate result. Do this early to save double conversion,
636 * once each for a^0 and intermediate result.
637 */
638 if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err;
639 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(r, top, powerbuf, 0, numPowers)) goto err;
640
641 /* Initialize computeTemp as a^1 with montgomery precalcs */
642 computeTemp = BN_CTX_get(ctx);
643 am = BN_CTX_get(ctx);
644 if (computeTemp==NULL || am==NULL) goto err;
645
646 if (a->neg || BN_ucmp(a,m) >= 0)
647 {
648 if (!BN_mod(am,a,m,ctx))
649 goto err;
650 aa= am;
651 }
652 else
653 aa=a;
654 if (!BN_to_montgomery(am,aa,mont,ctx)) goto err;
655 if (!BN_copy(computeTemp, am)) goto err;
656 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(am, top, powerbuf, 1, numPowers)) goto err;
657
658 /* If the window size is greater than 1, then calculate
659 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1)
660 * (even powers could instead be computed as (a^(i/2))^2
661 * to use the slight performance advantage of sqr over mul).
662 */
663 if (window > 1)
664 {
665 for (i=2; i<numPowers; i++)
666 {
667 /* Calculate a^i = a^(i-1) * a */
668 if (!BN_mod_mul_montgomery(computeTemp,am,computeTemp,mont,ctx))
669 goto err;
670 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(computeTemp, top, powerbuf, i, numPowers)) goto err;
671 }
672 }
673
674 /* Adjust the number of bits up to a multiple of the window size.
675 * If the exponent length is not a multiple of the window size, then
676 * this pads the most significant bits with zeros to normalize the
677 * scanning loop to there's no special cases.
678 *
679 * * NOTE: Making the window size a power of two less than the native
680 * * word size ensures that the padded bits won't go past the last
681 * * word in the internal BIGNUM structure. Going past the end will
682 * * still produce the correct result, but causes a different branch
683 * * to be taken in the BN_is_bit_set function.
684 */
685 bits = ((bits+window-1)/window)*window;
686 idx=bits-1; /* The top bit of the window */
687
688 /* Scan the exponent one window at a time starting from the most
689 * significant bits.
690 */
691 while (idx >= 0)
692 {
693 wvalue=0; /* The 'value' of the window */
694
695 /* Scan the window, squaring the result as we go */
696 for (i=0; i<window; i++,idx--)
697 {
698 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx)) goto err;
699 wvalue = (wvalue<<1)+BN_is_bit_set(p,idx);
700 }
701
702 /* Fetch the appropriate pre-computed value from the pre-buf */
703 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(computeTemp, top, powerbuf, wvalue, numPowers)) goto err;
704
705 /* Multiply the result into the intermediate result */
706 if (!BN_mod_mul_montgomery(r,r,computeTemp,mont,ctx)) goto err;
707 }
708
709 /* Convert the final result from montgomery to standard format */
710 if (!BN_from_montgomery(rr,r,mont,ctx)) goto err;
711 ret=1;
712err:
713 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
714 if (powerbuf!=NULL)
715 {
716 OPENSSL_cleanse(powerbuf,powerbufLen);
717 OPENSSL_free(powerbufFree);
718 }
719 if (am!=NULL) BN_clear(am);
720 if (computeTemp!=NULL) BN_clear(computeTemp);
721 BN_CTX_end(ctx);
722 return(ret);
723 }
724
725int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
726 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
727 {
728 BN_MONT_CTX *mont = NULL;
729 int b, bits, ret=0;
730 int r_is_one;
731 BN_ULONG w, next_w;
732 BIGNUM *d, *r, *t;
733 BIGNUM *swap_tmp;
734#define BN_MOD_MUL_WORD(r, w, m) \
735 (BN_mul_word(r, (w)) && \
736 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
737 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
738 /* BN_MOD_MUL_WORD is only used with 'w' large,
739 * so the BN_ucmp test is probably more overhead
740 * than always using BN_mod (which uses BN_copy if
741 * a similar test returns true). */
742 /* We can use BN_mod and do not need BN_nnmod because our
743 * accumulator is never negative (the result of BN_mod does
744 * not depend on the sign of the modulus).
745 */
746#define BN_TO_MONTGOMERY_WORD(r, w, mont) \
747 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
748
749 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
750 {
751 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
752 BNerr(BN_F_BN_MOD_EXP_MONT_WORD,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
753 return -1;
754 }
755
756 bn_check_top(p);
757 bn_check_top(m);
758
759 if (!BN_is_odd(m))
760 {
761 BNerr(BN_F_BN_MOD_EXP_MONT_WORD,BN_R_CALLED_WITH_EVEN_MODULUS);
762 return(0);
763 }
764 if (m->top == 1)
765 a %= m->d[0]; /* make sure that 'a' is reduced */
766
767 bits = BN_num_bits(p);
768 if (bits == 0)
769 {
770 ret = BN_one(rr);
771 return ret;
772 }
773 if (a == 0)
774 {
775 BN_zero(rr);
776 ret = 1;
777 return ret;
778 }
779
780 BN_CTX_start(ctx);
781 d = BN_CTX_get(ctx);
782 r = BN_CTX_get(ctx);
783 t = BN_CTX_get(ctx);
784 if (d == NULL || r == NULL || t == NULL) goto err;
785
786 if (in_mont != NULL)
787 mont=in_mont;
788 else
789 {
790 if ((mont = BN_MONT_CTX_new()) == NULL) goto err;
791 if (!BN_MONT_CTX_set(mont, m, ctx)) goto err;
792 }
793
794 r_is_one = 1; /* except for Montgomery factor */
795
796 /* bits-1 >= 0 */
797
798 /* The result is accumulated in the product r*w. */
799 w = a; /* bit 'bits-1' of 'p' is always set */
800 for (b = bits-2; b >= 0; b--)
801 {
802 /* First, square r*w. */
803 next_w = w*w;
804 if ((next_w/w) != w) /* overflow */
805 {
806 if (r_is_one)
807 {
808 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
809 r_is_one = 0;
810 }
811 else
812 {
813 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
814 }
815 next_w = 1;
816 }
817 w = next_w;
818 if (!r_is_one)
819 {
820 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) goto err;
821 }
822
823 /* Second, multiply r*w by 'a' if exponent bit is set. */
824 if (BN_is_bit_set(p, b))
825 {
826 next_w = w*a;
827 if ((next_w/a) != w) /* overflow */
828 {
829 if (r_is_one)
830 {
831 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
832 r_is_one = 0;
833 }
834 else
835 {
836 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
837 }
838 next_w = a;
839 }
840 w = next_w;
841 }
842 }
843
844 /* Finally, set r:=r*w. */
845 if (w != 1)
846 {
847 if (r_is_one)
848 {
849 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
850 r_is_one = 0;
851 }
852 else
853 {
854 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
855 }
856 }
857
858 if (r_is_one) /* can happen only if a == 1*/
859 {
860 if (!BN_one(rr)) goto err;
861 }
862 else
863 {
864 if (!BN_from_montgomery(rr, r, mont, ctx)) goto err;
865 }
866 ret = 1;
867err:
868 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
869 BN_CTX_end(ctx);
870 bn_check_top(rr);
871 return(ret);
872 }
873
874
875/* The old fallback, simple version :-) */
876int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
877 const BIGNUM *m, BN_CTX *ctx)
878 {
879 int i,j,bits,ret=0,wstart,wend,window,wvalue;
880 int start=1;
881 BIGNUM *d;
882 /* Table of variables obtained from 'ctx' */
883 BIGNUM *val[TABLE_SIZE];
884
885 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
886 {
887 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
888 BNerr(BN_F_BN_MOD_EXP_SIMPLE,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
889 return -1;
890 }
891
892 bits=BN_num_bits(p);
893
894 if (bits == 0)
895 {
896 ret = BN_one(r);
897 return ret;
898 }
899
900 BN_CTX_start(ctx);
901 d = BN_CTX_get(ctx);
902 val[0] = BN_CTX_get(ctx);
903 if(!d || !val[0]) goto err;
904
905 if (!BN_nnmod(val[0],a,m,ctx)) goto err; /* 1 */
906 if (BN_is_zero(val[0]))
907 {
908 BN_zero(r);
909 ret = 1;
910 goto err;
911 }
912
913 window = BN_window_bits_for_exponent_size(bits);
914 if (window > 1)
915 {
916 if (!BN_mod_mul(d,val[0],val[0],m,ctx))
917 goto err; /* 2 */
918 j=1<<(window-1);
919 for (i=1; i<j; i++)
920 {
921 if(((val[i] = BN_CTX_get(ctx)) == NULL) ||
922 !BN_mod_mul(val[i],val[i-1],d,m,ctx))
923 goto err;
924 }
925 }
926
927 start=1; /* This is used to avoid multiplication etc
928 * when there is only the value '1' in the
929 * buffer. */
930 wvalue=0; /* The 'value' of the window */
931 wstart=bits-1; /* The top bit of the window */
932 wend=0; /* The bottom bit of the window */
933
934 if (!BN_one(r)) goto err;
935
936 for (;;)
937 {
938 if (BN_is_bit_set(p,wstart) == 0)
939 {
940 if (!start)
941 if (!BN_mod_mul(r,r,r,m,ctx))
942 goto err;
943 if (wstart == 0) break;
944 wstart--;
945 continue;
946 }
947 /* We now have wstart on a 'set' bit, we now need to work out
948 * how bit a window to do. To do this we need to scan
949 * forward until the last set bit before the end of the
950 * window */
951 j=wstart;
952 wvalue=1;
953 wend=0;
954 for (i=1; i<window; i++)
955 {
956 if (wstart-i < 0) break;
957 if (BN_is_bit_set(p,wstart-i))
958 {
959 wvalue<<=(i-wend);
960 wvalue|=1;
961 wend=i;
962 }
963 }
964
965 /* wend is the size of the current window */
966 j=wend+1;
967 /* add the 'bytes above' */
968 if (!start)
969 for (i=0; i<j; i++)
970 {
971 if (!BN_mod_mul(r,r,r,m,ctx))
972 goto err;
973 }
974
975 /* wvalue will be an odd number < 2^window */
976 if (!BN_mod_mul(r,r,val[wvalue>>1],m,ctx))
977 goto err;
978
979 /* move the 'window' down further */
980 wstart-=wend+1;
981 wvalue=0;
982 start=0;
983 if (wstart < 0) break;
984 }
985 ret=1;
986err:
987 BN_CTX_end(ctx);
988 bn_check_top(r);
989 return(ret);
990 }
991
generated by cgit v1.2.3-55-g6feb (git 2.39.1) at 2025-03-21 08:18:37 +0000