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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_EXP_CONSTTIME) != 0)
126 {
127 /* BN_FLG_EXP_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 if ((v = BN_CTX_get(ctx)) == NULL) goto err;
138
139 if (BN_copy(v,a) == NULL) goto err;
140 bits=BN_num_bits(p);
141
142 if (BN_is_odd(p))
143 { if (BN_copy(rr,a) == NULL) goto err; }
144 else { if (!BN_one(rr)) goto err; }
145
146 for (i=1; i<bits; i++)
147 {
148 if (!BN_sqr(v,v,ctx)) goto err;
149 if (BN_is_bit_set(p,i))
150 {
151 if (!BN_mul(rr,rr,v,ctx)) goto err;
152 }
153 }
154 ret=1;
155err:
156 if (r != rr) BN_copy(r,rr);
157 BN_CTX_end(ctx);
158 return(ret);
159 }
160
161
162int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
163 BN_CTX *ctx)
164 {
165 int ret;
166
167 bn_check_top(a);
168 bn_check_top(p);
169 bn_check_top(m);
170
171 /* For even modulus m = 2^k*m_odd, it might make sense to compute
172 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery
173 * exponentiation for the odd part), using appropriate exponent
174 * reductions, and combine the results using the CRT.
175 *
176 * For now, we use Montgomery only if the modulus is odd; otherwise,
177 * exponentiation using the reciprocal-based quick remaindering
178 * algorithm is used.
179 *
180 * (Timing obtained with expspeed.c [computations a^p mod m
181 * where a, p, m are of the same length: 256, 512, 1024, 2048,
182 * 4096, 8192 bits], compared to the running time of the
183 * standard algorithm:
184 *
185 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
186 * 55 .. 77 % [UltraSparc processor, but
187 * debug-solaris-sparcv8-gcc conf.]
188 *
189 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
190 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
191 *
192 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
193 * at 2048 and more bits, but at 512 and 1024 bits, it was
194 * slower even than the standard algorithm!
195 *
196 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
197 * should be obtained when the new Montgomery reduction code
198 * has been integrated into OpenSSL.)
199 */
200
201#define MONT_MUL_MOD
202#define MONT_EXP_WORD
203#define RECP_MUL_MOD
204
205#ifdef MONT_MUL_MOD
206 /* I have finally been able to take out this pre-condition of
207 * the top bit being set. It was caused by an error in BN_div
208 * with negatives. There was also another problem when for a^b%m
209 * a >= m. eay 07-May-97 */
210/* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */
211
212 if (BN_is_odd(m))
213 {
214# ifdef MONT_EXP_WORD
215 if (a->top == 1 && !a->neg && (BN_get_flags(p, BN_FLG_EXP_CONSTTIME) == 0))
216 {
217 BN_ULONG A = a->d[0];
218 ret=BN_mod_exp_mont_word(r,A,p,m,ctx,NULL);
219 }
220 else
221# endif
222 ret=BN_mod_exp_mont(r,a,p,m,ctx,NULL);
223 }
224 else
225#endif
226#ifdef RECP_MUL_MOD
227 { ret=BN_mod_exp_recp(r,a,p,m,ctx); }
228#else
229 { ret=BN_mod_exp_simple(r,a,p,m,ctx); }
230#endif
231
232 return(ret);
233 }
234
235
236int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
237 const BIGNUM *m, BN_CTX *ctx)
238 {
239 int i,j,bits,ret=0,wstart,wend,window,wvalue;
240 int start=1,ts=0;
241 BIGNUM *aa;
242 BIGNUM val[TABLE_SIZE];
243 BN_RECP_CTX recp;
244
245 if (BN_get_flags(p, BN_FLG_EXP_CONSTTIME) != 0)
246 {
247 /* BN_FLG_EXP_CONSTTIME only supported by BN_mod_exp_mont() */
248 BNerr(BN_F_BN_MOD_EXP_RECP,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
249 return -1;
250 }
251
252 bits=BN_num_bits(p);
253
254 if (bits == 0)
255 {
256 ret = BN_one(r);
257 return ret;
258 }
259
260 BN_CTX_start(ctx);
261 if ((aa = BN_CTX_get(ctx)) == NULL) goto err;
262
263 BN_RECP_CTX_init(&recp);
264 if (m->neg)
265 {
266 /* ignore sign of 'm' */
267 if (!BN_copy(aa, m)) goto err;
268 aa->neg = 0;
269 if (BN_RECP_CTX_set(&recp,aa,ctx) <= 0) goto err;
270 }
271 else
272 {
273 if (BN_RECP_CTX_set(&recp,m,ctx) <= 0) goto err;
274 }
275
276 BN_init(&(val[0]));
277 ts=1;
278
279 if (!BN_nnmod(&(val[0]),a,m,ctx)) goto err; /* 1 */
280 if (BN_is_zero(&(val[0])))
281 {
282 ret = BN_zero(r);
283 goto err;
284 }
285
286 window = BN_window_bits_for_exponent_size(bits);
287 if (window > 1)
288 {
289 if (!BN_mod_mul_reciprocal(aa,&(val[0]),&(val[0]),&recp,ctx))
290 goto err; /* 2 */
291 j=1<<(window-1);
292 for (i=1; i<j; i++)
293 {
294 BN_init(&val[i]);
295 if (!BN_mod_mul_reciprocal(&(val[i]),&(val[i-1]),aa,&recp,ctx))
296 goto err;
297 }
298 ts=i;
299 }
300
301 start=1; /* This is used to avoid multiplication etc
302 * when there is only the value '1' in the
303 * buffer. */
304 wvalue=0; /* The 'value' of the window */
305 wstart=bits-1; /* The top bit of the window */
306 wend=0; /* The bottom bit of the window */
307
308 if (!BN_one(r)) goto err;
309
310 for (;;)
311 {
312 if (BN_is_bit_set(p,wstart) == 0)
313 {
314 if (!start)
315 if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
316 goto err;
317 if (wstart == 0) break;
318 wstart--;
319 continue;
320 }
321 /* We now have wstart on a 'set' bit, we now need to work out
322 * how bit a window to do. To do this we need to scan
323 * forward until the last set bit before the end of the
324 * window */
325 j=wstart;
326 wvalue=1;
327 wend=0;
328 for (i=1; i<window; i++)
329 {
330 if (wstart-i < 0) break;
331 if (BN_is_bit_set(p,wstart-i))
332 {
333 wvalue<<=(i-wend);
334 wvalue|=1;
335 wend=i;
336 }
337 }
338
339 /* wend is the size of the current window */
340 j=wend+1;
341 /* add the 'bytes above' */
342 if (!start)
343 for (i=0; i<j; i++)
344 {
345 if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
346 goto err;
347 }
348
349 /* wvalue will be an odd number < 2^window */
350 if (!BN_mod_mul_reciprocal(r,r,&(val[wvalue>>1]),&recp,ctx))
351 goto err;
352
353 /* move the 'window' down further */
354 wstart-=wend+1;
355 wvalue=0;
356 start=0;
357 if (wstart < 0) break;
358 }
359 ret=1;
360err:
361 BN_CTX_end(ctx);
362 for (i=0; i<ts; i++)
363 BN_clear_free(&(val[i]));
364 BN_RECP_CTX_free(&recp);
365 return(ret);
366 }
367
368
369int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
370 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
371 {
372 int i,j,bits,ret=0,wstart,wend,window,wvalue;
373 int start=1,ts=0;
374 BIGNUM *d,*r;
375 const BIGNUM *aa;
376 BIGNUM val[TABLE_SIZE];
377 BN_MONT_CTX *mont=NULL;
378
379 if (BN_get_flags(p, BN_FLG_EXP_CONSTTIME) != 0)
380 {
381 return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
382 }
383
384 bn_check_top(a);
385 bn_check_top(p);
386 bn_check_top(m);
387
388 if (!(m->d[0] & 1))
389 {
390 BNerr(BN_F_BN_MOD_EXP_MONT,BN_R_CALLED_WITH_EVEN_MODULUS);
391 return(0);
392 }
393 bits=BN_num_bits(p);
394 if (bits == 0)
395 {
396 ret = BN_one(rr);
397 return ret;
398 }
399
400 BN_CTX_start(ctx);
401 d = BN_CTX_get(ctx);
402 r = BN_CTX_get(ctx);
403 if (d == NULL || r == NULL) goto err;
404
405 /* If this is not done, things will break in the montgomery
406 * part */
407
408 if (in_mont != NULL)
409 mont=in_mont;
410 else
411 {
412 if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
413 if (!BN_MONT_CTX_set(mont,m,ctx)) goto err;
414 }
415
416 BN_init(&val[0]);
417 ts=1;
418 if (a->neg || BN_ucmp(a,m) >= 0)
419 {
420 if (!BN_nnmod(&(val[0]),a,m,ctx))
421 goto err;
422 aa= &(val[0]);
423 }
424 else
425 aa=a;
426 if (BN_is_zero(aa))
427 {
428 ret = BN_zero(rr);
429 goto err;
430 }
431 if (!BN_to_montgomery(&(val[0]),aa,mont,ctx)) goto err; /* 1 */
432
433 window = BN_window_bits_for_exponent_size(bits);
434 if (window > 1)
435 {
436 if (!BN_mod_mul_montgomery(d,&(val[0]),&(val[0]),mont,ctx)) goto err; /* 2 */
437 j=1<<(window-1);
438 for (i=1; i<j; i++)
439 {
440 BN_init(&(val[i]));
441 if (!BN_mod_mul_montgomery(&(val[i]),&(val[i-1]),d,mont,ctx))
442 goto err;
443 }
444 ts=i;
445 }
446
447 start=1; /* This is used to avoid multiplication etc
448 * when there is only the value '1' in the
449 * buffer. */
450 wvalue=0; /* The 'value' of the window */
451 wstart=bits-1; /* The top bit of the window */
452 wend=0; /* The bottom bit of the window */
453
454 if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err;
455 for (;;)
456 {
457 if (BN_is_bit_set(p,wstart) == 0)
458 {
459 if (!start)
460 {
461 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
462 goto err;
463 }
464 if (wstart == 0) break;
465 wstart--;
466 continue;
467 }
468 /* We now have wstart on a 'set' bit, we now need to work out
469 * how bit a window to do. To do this we need to scan
470 * forward until the last set bit before the end of the
471 * window */
472 j=wstart;
473 wvalue=1;
474 wend=0;
475 for (i=1; i<window; i++)
476 {
477 if (wstart-i < 0) break;
478 if (BN_is_bit_set(p,wstart-i))
479 {
480 wvalue<<=(i-wend);
481 wvalue|=1;
482 wend=i;
483 }
484 }
485
486 /* wend is the size of the current window */
487 j=wend+1;
488 /* add the 'bytes above' */
489 if (!start)
490 for (i=0; i<j; i++)
491 {
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) break;
505 }
506 if (!BN_from_montgomery(rr,r,mont,ctx)) goto err;
507 ret=1;
508err:
509 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
510 BN_CTX_end(ctx);
511 for (i=0; i<ts; i++)
512 BN_clear_free(&(val[i]));
513 return(ret);
514 }
515
516
517/* BN_mod_exp_mont_consttime() stores the precomputed powers in a specific layout
518 * so that accessing any of these table values shows the same access pattern as far
519 * as cache lines are concerned. The following functions are used to transfer a BIGNUM
520 * from/to that table. */
521
522static int MOD_EXP_CTIME_COPY_TO_PREBUF(BIGNUM *b, int top, unsigned char *buf, int idx, int width)
523 {
524 size_t i, j;
525
526 if (bn_wexpand(b, top) == NULL)
527 return 0;
528 while (b->top < top)
529 {
530 b->d[b->top++] = 0;
531 }
532
533 for (i = 0, j=idx; i < top * sizeof b->d[0]; i++, j+=width)
534 {
535 buf[j] = ((unsigned char*)b->d)[i];
536 }
537
538 bn_fix_top(b);
539 return 1;
540 }
541
542static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top, unsigned char *buf, int idx, int width)
543 {
544 size_t i, j;
545
546 if (bn_wexpand(b, top) == NULL)
547 return 0;
548
549 for (i=0, j=idx; i < top * sizeof b->d[0]; i++, j+=width)
550 {
551 ((unsigned char*)b->d)[i] = buf[j];
552 }
553
554 b->top = top;
555 bn_fix_top(b);
556 return 1;
557 }
558
559/* Given a pointer value, compute the next address that is a cache line multiple. */
560#define MOD_EXP_CTIME_ALIGN(x_) \
561 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((BN_ULONG)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
562
563/* This variant of BN_mod_exp_mont() uses fixed windows and the special
564 * precomputation memory layout to limit data-dependency to a minimum
565 * to protect secret exponents (cf. the hyper-threading timing attacks
566 * pointed out by Colin Percival,
567 * http://www.daemonology.net/hyperthreading-considered-harmful/)
568 */
569int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
570 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
571 {
572 int i,bits,ret=0,idx,window,wvalue;
573 int top;
574 BIGNUM *r;
575 const BIGNUM *aa;
576 BN_MONT_CTX *mont=NULL;
577
578 int numPowers;
579 unsigned char *powerbufFree=NULL;
580 int powerbufLen = 0;
581 unsigned char *powerbuf=NULL;
582 BIGNUM *computeTemp=NULL, *am=NULL;
583
584 bn_check_top(a);
585 bn_check_top(p);
586 bn_check_top(m);
587
588 top = m->top;
589
590 if (!(m->d[0] & 1))
591 {
592 BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME,BN_R_CALLED_WITH_EVEN_MODULUS);
593 return(0);
594 }
595 bits=BN_num_bits(p);
596 if (bits == 0)
597 {
598 ret = BN_one(rr);
599 return ret;
600 }
601
602 /* Initialize BIGNUM context and allocate intermediate result */
603 BN_CTX_start(ctx);
604 r = BN_CTX_get(ctx);
605 if (r == NULL) goto err;
606
607 /* Allocate a montgomery context if it was not supplied by the caller.
608 * If this is not done, things will break in the montgomery part.
609 */
610 if (in_mont != NULL)
611 mont=in_mont;
612 else
613 {
614 if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
615 if (!BN_MONT_CTX_set(mont,m,ctx)) goto err;
616 }
617
618 /* Get the window size to use with size of p. */
619 window = BN_window_bits_for_ctime_exponent_size(bits);
620
621 /* Allocate a buffer large enough to hold all of the pre-computed
622 * powers of a.
623 */
624 numPowers = 1 << window;
625 powerbufLen = sizeof(m->d[0])*top*numPowers;
626 if ((powerbufFree=(unsigned char*)OPENSSL_malloc(powerbufLen+MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH)) == NULL)
627 goto err;
628
629 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
630 memset(powerbuf, 0, powerbufLen);
631
632 /* Initialize the intermediate result. Do this early to save double conversion,
633 * once each for a^0 and intermediate result.
634 */
635 if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err;
636 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(r, top, powerbuf, 0, numPowers)) goto err;
637
638 /* Initialize computeTemp as a^1 with montgomery precalcs */
639 computeTemp = BN_CTX_get(ctx);
640 am = BN_CTX_get(ctx);
641 if (computeTemp==NULL || am==NULL) goto err;
642
643 if (a->neg || BN_ucmp(a,m) >= 0)
644 {
645 if (!BN_mod(am,a,m,ctx))
646 goto err;
647 aa= am;
648 }
649 else
650 aa=a;
651 if (!BN_to_montgomery(am,aa,mont,ctx)) goto err;
652 if (!BN_copy(computeTemp, am)) goto err;
653 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(am, top, powerbuf, 1, numPowers)) goto err;
654
655 /* If the window size is greater than 1, then calculate
656 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1)
657 * (even powers could instead be computed as (a^(i/2))^2
658 * to use the slight performance advantage of sqr over mul).
659 */
660 if (window > 1)
661 {
662 for (i=2; i<numPowers; i++)
663 {
664 /* Calculate a^i = a^(i-1) * a */
665 if (!BN_mod_mul_montgomery(computeTemp,am,computeTemp,mont,ctx))
666 goto err;
667 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(computeTemp, top, powerbuf, i, numPowers)) goto err;
668 }
669 }
670
671 /* Adjust the number of bits up to a multiple of the window size.
672 * If the exponent length is not a multiple of the window size, then
673 * this pads the most significant bits with zeros to normalize the
674 * scanning loop to there's no special cases.
675 *
676 * * NOTE: Making the window size a power of two less than the native
677 * * word size ensures that the padded bits won't go past the last
678 * * word in the internal BIGNUM structure. Going past the end will
679 * * still produce the correct result, but causes a different branch
680 * * to be taken in the BN_is_bit_set function.
681 */
682 bits = ((bits+window-1)/window)*window;
683 idx=bits-1; /* The top bit of the window */
684
685 /* Scan the exponent one window at a time starting from the most
686 * significant bits.
687 */
688 while (idx >= 0)
689 {
690 wvalue=0; /* The 'value' of the window */
691
692 /* Scan the window, squaring the result as we go */
693 for (i=0; i<window; i++,idx--)
694 {
695 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx)) goto err;
696 wvalue = (wvalue<<1)+BN_is_bit_set(p,idx);
697 }
698
699 /* Fetch the appropriate pre-computed value from the pre-buf */
700 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(computeTemp, top, powerbuf, wvalue, numPowers)) goto err;
701
702 /* Multiply the result into the intermediate result */
703 if (!BN_mod_mul_montgomery(r,r,computeTemp,mont,ctx)) goto err;
704 }
705
706 /* Convert the final result from montgomery to standard format */
707 if (!BN_from_montgomery(rr,r,mont,ctx)) goto err;
708 ret=1;
709err:
710 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
711 if (powerbuf!=NULL)
712 {
713 OPENSSL_cleanse(powerbuf,powerbufLen);
714 OPENSSL_free(powerbufFree);
715 }
716 if (am!=NULL) BN_clear(am);
717 if (computeTemp!=NULL) BN_clear(computeTemp);
718 BN_CTX_end(ctx);
719 return(ret);
720 }
721
722int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
723 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
724 {
725 BN_MONT_CTX *mont = NULL;
726 int b, bits, ret=0;
727 int r_is_one;
728 BN_ULONG w, next_w;
729 BIGNUM *d, *r, *t;
730 BIGNUM *swap_tmp;
731#define BN_MOD_MUL_WORD(r, w, m) \
732 (BN_mul_word(r, (w)) && \
733 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
734 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
735 /* BN_MOD_MUL_WORD is only used with 'w' large,
736 * so the BN_ucmp test is probably more overhead
737 * than always using BN_mod (which uses BN_copy if
738 * a similar test returns true). */
739 /* We can use BN_mod and do not need BN_nnmod because our
740 * accumulator is never negative (the result of BN_mod does
741 * not depend on the sign of the modulus).
742 */
743#define BN_TO_MONTGOMERY_WORD(r, w, mont) \
744 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
745
746 if (BN_get_flags(p, BN_FLG_EXP_CONSTTIME) != 0)
747 {
748 /* BN_FLG_EXP_CONSTTIME only supported by BN_mod_exp_mont() */
749 BNerr(BN_F_BN_MOD_EXP_MONT_WORD,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
750 return -1;
751 }
752
753 bn_check_top(p);
754 bn_check_top(m);
755
756 if (m->top == 0 || !(m->d[0] & 1))
757 {
758 BNerr(BN_F_BN_MOD_EXP_MONT_WORD,BN_R_CALLED_WITH_EVEN_MODULUS);
759 return(0);
760 }
761 if (m->top == 1)
762 a %= m->d[0]; /* make sure that 'a' is reduced */
763
764 bits = BN_num_bits(p);
765 if (bits == 0)
766 {
767 ret = BN_one(rr);
768 return ret;
769 }
770 if (a == 0)
771 {
772 ret = BN_zero(rr);
773 return ret;
774 }
775
776 BN_CTX_start(ctx);
777 d = BN_CTX_get(ctx);
778 r = BN_CTX_get(ctx);
779 t = BN_CTX_get(ctx);
780 if (d == NULL || r == NULL || t == NULL) goto err;
781
782 if (in_mont != NULL)
783 mont=in_mont;
784 else
785 {
786 if ((mont = BN_MONT_CTX_new()) == NULL) goto err;
787 if (!BN_MONT_CTX_set(mont, m, ctx)) goto err;
788 }
789
790 r_is_one = 1; /* except for Montgomery factor */
791
792 /* bits-1 >= 0 */
793
794 /* The result is accumulated in the product r*w. */
795 w = a; /* bit 'bits-1' of 'p' is always set */
796 for (b = bits-2; b >= 0; b--)
797 {
798 /* First, square r*w. */
799 next_w = w*w;
800 if ((next_w/w) != w) /* overflow */
801 {
802 if (r_is_one)
803 {
804 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
805 r_is_one = 0;
806 }
807 else
808 {
809 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
810 }
811 next_w = 1;
812 }
813 w = next_w;
814 if (!r_is_one)
815 {
816 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) goto err;
817 }
818
819 /* Second, multiply r*w by 'a' if exponent bit is set. */
820 if (BN_is_bit_set(p, b))
821 {
822 next_w = w*a;
823 if ((next_w/a) != w) /* overflow */
824 {
825 if (r_is_one)
826 {
827 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
828 r_is_one = 0;
829 }
830 else
831 {
832 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
833 }
834 next_w = a;
835 }
836 w = next_w;
837 }
838 }
839
840 /* Finally, set r:=r*w. */
841 if (w != 1)
842 {
843 if (r_is_one)
844 {
845 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
846 r_is_one = 0;
847 }
848 else
849 {
850 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
851 }
852 }
853
854 if (r_is_one) /* can happen only if a == 1*/
855 {
856 if (!BN_one(rr)) goto err;
857 }
858 else
859 {
860 if (!BN_from_montgomery(rr, r, mont, ctx)) goto err;
861 }
862 ret = 1;
863err:
864 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
865 BN_CTX_end(ctx);
866 return(ret);
867 }
868
869
870/* The old fallback, simple version :-) */
871int BN_mod_exp_simple(BIGNUM *r,
872 const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
873 BN_CTX *ctx)
874 {
875 int i,j,bits,ret=0,wstart,wend,window,wvalue,ts=0;
876 int start=1;
877 BIGNUM *d;
878 BIGNUM val[TABLE_SIZE];
879
880 if (BN_get_flags(p, BN_FLG_EXP_CONSTTIME) != 0)
881 {
882 /* BN_FLG_EXP_CONSTTIME only supported by BN_mod_exp_mont() */
883 BNerr(BN_F_BN_MOD_EXP_SIMPLE,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
884 return -1;
885 }
886
887 bits=BN_num_bits(p);
888
889 if (bits == 0)
890 {
891 ret = BN_one(r);
892 return ret;
893 }
894
895 BN_CTX_start(ctx);
896 if ((d = BN_CTX_get(ctx)) == NULL) goto err;
897
898 BN_init(&(val[0]));
899 ts=1;
900 if (!BN_nnmod(&(val[0]),a,m,ctx)) goto err; /* 1 */
901 if (BN_is_zero(&(val[0])))
902 {
903 ret = BN_zero(r);
904 goto err;
905 }
906
907 window = BN_window_bits_for_exponent_size(bits);
908 if (window > 1)
909 {
910 if (!BN_mod_mul(d,&(val[0]),&(val[0]),m,ctx))
911 goto err; /* 2 */
912 j=1<<(window-1);
913 for (i=1; i<j; i++)
914 {
915 BN_init(&(val[i]));
916 if (!BN_mod_mul(&(val[i]),&(val[i-1]),d,m,ctx))
917 goto err;
918 }
919 ts=i;
920 }
921
922 start=1; /* This is used to avoid multiplication etc
923 * when there is only the value '1' in the
924 * buffer. */
925 wvalue=0; /* The 'value' of the window */
926 wstart=bits-1; /* The top bit of the window */
927 wend=0; /* The bottom bit of the window */
928
929 if (!BN_one(r)) goto err;
930
931 for (;;)
932 {
933 if (BN_is_bit_set(p,wstart) == 0)
934 {
935 if (!start)
936 if (!BN_mod_mul(r,r,r,m,ctx))
937 goto err;
938 if (wstart == 0) break;
939 wstart--;
940 continue;
941 }
942 /* We now have wstart on a 'set' bit, we now need to work out
943 * how bit a window to do. To do this we need to scan
944 * forward until the last set bit before the end of the
945 * window */
946 j=wstart;
947 wvalue=1;
948 wend=0;
949 for (i=1; i<window; i++)
950 {
951 if (wstart-i < 0) break;
952 if (BN_is_bit_set(p,wstart-i))
953 {
954 wvalue<<=(i-wend);
955 wvalue|=1;
956 wend=i;
957 }
958 }
959
960 /* wend is the size of the current window */
961 j=wend+1;
962 /* add the 'bytes above' */
963 if (!start)
964 for (i=0; i<j; i++)
965 {
966 if (!BN_mod_mul(r,r,r,m,ctx))
967 goto err;
968 }
969
970 /* wvalue will be an odd number < 2^window */
971 if (!BN_mod_mul(r,r,&(val[wvalue>>1]),m,ctx))
972 goto err;
973
974 /* move the 'window' down further */
975 wstart-=wend+1;
976 wvalue=0;
977 start=0;
978 if (wstart < 0) break;
979 }
980 ret=1;
981err:
982 BN_CTX_end(ctx);
983 for (i=0; i<ts; i++)
984 BN_clear_free(&(val[i]));
985 return(ret);
986 }
987
generated by cgit v1.2.3-55-g6feb (git 2.39.1) at 2025-03-21 23:30:18 +0000