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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 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 bn_check_top(r);
159 return(ret);
160 }
161
162
163int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
164 BN_CTX *ctx)
165 {
166 int ret;
167
168 bn_check_top(a);
169 bn_check_top(p);
170 bn_check_top(m);
171
172 /* For even modulus m = 2^k*m_odd, it might make sense to compute
173 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery
174 * exponentiation for the odd part), using appropriate exponent
175 * reductions, and combine the results using the CRT.
176 *
177 * For now, we use Montgomery only if the modulus is odd; otherwise,
178 * exponentiation using the reciprocal-based quick remaindering
179 * algorithm is used.
180 *
181 * (Timing obtained with expspeed.c [computations a^p mod m
182 * where a, p, m are of the same length: 256, 512, 1024, 2048,
183 * 4096, 8192 bits], compared to the running time of the
184 * standard algorithm:
185 *
186 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
187 * 55 .. 77 % [UltraSparc processor, but
188 * debug-solaris-sparcv8-gcc conf.]
189 *
190 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
191 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
192 *
193 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
194 * at 2048 and more bits, but at 512 and 1024 bits, it was
195 * slower even than the standard algorithm!
196 *
197 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
198 * should be obtained when the new Montgomery reduction code
199 * has been integrated into OpenSSL.)
200 */
201
202#define MONT_MUL_MOD
203#define MONT_EXP_WORD
204#define RECP_MUL_MOD
205
206#ifdef MONT_MUL_MOD
207 /* I have finally been able to take out this pre-condition of
208 * the top bit being set. It was caused by an error in BN_div
209 * with negatives. There was also another problem when for a^b%m
210 * a >= m. eay 07-May-97 */
211/* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */
212
213 if (BN_is_odd(m))
214 {
215# ifdef MONT_EXP_WORD
216 if (a->top == 1 && !a->neg && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0))
217 {
218 BN_ULONG A = a->d[0];
219 ret=BN_mod_exp_mont_word(r,A,p,m,ctx,NULL);
220 }
221 else
222# endif
223 ret=BN_mod_exp_mont(r,a,p,m,ctx,NULL);
224 }
225 else
226#endif
227#ifdef RECP_MUL_MOD
228 { ret=BN_mod_exp_recp(r,a,p,m,ctx); }
229#else
230 { ret=BN_mod_exp_simple(r,a,p,m,ctx); }
231#endif
232
233 bn_check_top(r);
234 return(ret);
235 }
236
237
238int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
239 const BIGNUM *m, BN_CTX *ctx)
240 {
241 int i,j,bits,ret=0,wstart,wend,window,wvalue;
242 int start=1;
243 BIGNUM *aa;
244 /* Table of variables obtained from 'ctx' */
245 BIGNUM *val[TABLE_SIZE];
246 BN_RECP_CTX recp;
247
248 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
249 {
250 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
251 BNerr(BN_F_BN_MOD_EXP_RECP,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
252 return -1;
253 }
254
255 bits=BN_num_bits(p);
256
257 if (bits == 0)
258 {
259 ret = BN_one(r);
260 return ret;
261 }
262
263 BN_CTX_start(ctx);
264 aa = BN_CTX_get(ctx);
265 val[0] = BN_CTX_get(ctx);
266 if(!aa || !val[0]) goto err;
267
268 BN_RECP_CTX_init(&recp);
269 if (m->neg)
270 {
271 /* ignore sign of 'm' */
272 if (!BN_copy(aa, m)) goto err;
273 aa->neg = 0;
274 if (BN_RECP_CTX_set(&recp,aa,ctx) <= 0) goto err;
275 }
276 else
277 {
278 if (BN_RECP_CTX_set(&recp,m,ctx) <= 0) goto err;
279 }
280
281 if (!BN_nnmod(val[0],a,m,ctx)) goto err; /* 1 */
282 if (BN_is_zero(val[0]))
283 {
284 BN_zero(r);
285 ret = 1;
286 goto err;
287 }
288
289 window = BN_window_bits_for_exponent_size(bits);
290 if (window > 1)
291 {
292 if (!BN_mod_mul_reciprocal(aa,val[0],val[0],&recp,ctx))
293 goto err; /* 2 */
294 j=1<<(window-1);
295 for (i=1; i<j; i++)
296 {
297 if(((val[i] = BN_CTX_get(ctx)) == NULL) ||
298 !BN_mod_mul_reciprocal(val[i],val[i-1],
299 aa,&recp,ctx))
300 goto err;
301 }
302 }
303
304 start=1; /* This is used to avoid multiplication etc
305 * when there is only the value '1' in the
306 * buffer. */
307 wvalue=0; /* The 'value' of the window */
308 wstart=bits-1; /* The top bit of the window */
309 wend=0; /* The bottom bit of the window */
310
311 if (!BN_one(r)) goto err;
312
313 for (;;)
314 {
315 if (BN_is_bit_set(p,wstart) == 0)
316 {
317 if (!start)
318 if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
319 goto err;
320 if (wstart == 0) break;
321 wstart--;
322 continue;
323 }
324 /* We now have wstart on a 'set' bit, we now need to work out
325 * how bit a window to do. To do this we need to scan
326 * forward until the last set bit before the end of the
327 * window */
328 j=wstart;
329 wvalue=1;
330 wend=0;
331 for (i=1; i<window; i++)
332 {
333 if (wstart-i < 0) break;
334 if (BN_is_bit_set(p,wstart-i))
335 {
336 wvalue<<=(i-wend);
337 wvalue|=1;
338 wend=i;
339 }
340 }
341
342 /* wend is the size of the current window */
343 j=wend+1;
344 /* add the 'bytes above' */
345 if (!start)
346 for (i=0; i<j; i++)
347 {
348 if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
349 goto err;
350 }
351
352 /* wvalue will be an odd number < 2^window */
353 if (!BN_mod_mul_reciprocal(r,r,val[wvalue>>1],&recp,ctx))
354 goto err;
355
356 /* move the 'window' down further */
357 wstart-=wend+1;
358 wvalue=0;
359 start=0;
360 if (wstart < 0) break;
361 }
362 ret=1;
363err:
364 BN_CTX_end(ctx);
365 BN_RECP_CTX_free(&recp);
366 bn_check_top(r);
367 return(ret);
368 }
369
370
371int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
372 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
373 {
374 int i,j,bits,ret=0,wstart,wend,window,wvalue;
375 int start=1;
376 BIGNUM *d,*r;
377 const BIGNUM *aa;
378 /* Table of variables obtained from 'ctx' */
379 BIGNUM *val[TABLE_SIZE];
380 BN_MONT_CTX *mont=NULL;
381
382 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
383 {
384 return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
385 }
386
387 bn_check_top(a);
388 bn_check_top(p);
389 bn_check_top(m);
390
391 if (!BN_is_odd(m))
392 {
393 BNerr(BN_F_BN_MOD_EXP_MONT,BN_R_CALLED_WITH_EVEN_MODULUS);
394 return(0);
395 }
396 bits=BN_num_bits(p);
397 if (bits == 0)
398 {
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]) goto err;
408
409 /* If this is not done, things will break in the montgomery
410 * part */
411
412 if (in_mont != NULL)
413 mont=in_mont;
414 else
415 {
416 if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
417 if (!BN_MONT_CTX_set(mont,m,ctx)) goto err;
418 }
419
420 if (a->neg || BN_ucmp(a,m) >= 0)
421 {
422 if (!BN_nnmod(val[0],a,m,ctx))
423 goto err;
424 aa= val[0];
425 }
426 else
427 aa=a;
428 if (BN_is_zero(aa))
429 {
430 BN_zero(rr);
431 ret = 1;
432 goto err;
433 }
434 if (!BN_to_montgomery(val[0],aa,mont,ctx)) goto err; /* 1 */
435
436 window = BN_window_bits_for_exponent_size(bits);
437 if (window > 1)
438 {
439 if (!BN_mod_mul_montgomery(d,val[0],val[0],mont,ctx)) goto err; /* 2 */
440 j=1<<(window-1);
441 for (i=1; i<j; i++)
442 {
443 if(((val[i] = BN_CTX_get(ctx)) == NULL) ||
444 !BN_mod_mul_montgomery(val[i],val[i-1],
445 d,mont,ctx))
446 goto err;
447 }
448 }
449
450 start=1; /* This is used to avoid multiplication etc
451 * when there is only the value '1' in the
452 * buffer. */
453 wvalue=0; /* The 'value' of the window */
454 wstart=bits-1; /* The top bit of the window */
455 wend=0; /* The bottom bit of the window */
456
457 if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err;
458 for (;;)
459 {
460 if (BN_is_bit_set(p,wstart) == 0)
461 {
462 if (!start)
463 {
464 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
465 goto err;
466 }
467 if (wstart == 0) break;
468 wstart--;
469 continue;
470 }
471 /* We now have wstart on a 'set' bit, we now need to work out
472 * how bit a window to do. To do this we need to scan
473 * forward until the last set bit before the end of the
474 * window */
475 j=wstart;
476 wvalue=1;
477 wend=0;
478 for (i=1; i<window; i++)
479 {
480 if (wstart-i < 0) break;
481 if (BN_is_bit_set(p,wstart-i))
482 {
483 wvalue<<=(i-wend);
484 wvalue|=1;
485 wend=i;
486 }
487 }
488
489 /* wend is the size of the current window */
490 j=wend+1;
491 /* add the 'bytes above' */
492 if (!start)
493 for (i=0; i<j; i++)
494 {
495 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
496 goto err;
497 }
498
499 /* wvalue will be an odd number < 2^window */
500 if (!BN_mod_mul_montgomery(r,r,val[wvalue>>1],mont,ctx))
501 goto err;
502
503 /* move the 'window' down further */
504 wstart-=wend+1;
505 wvalue=0;
506 start=0;
507 if (wstart < 0) break;
508 }
509 if (!BN_from_montgomery(rr,r,mont,ctx)) goto err;
510 ret=1;
511err:
512 if ((in_mont == NULL) && (mont != NULL)) 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 layout
520 * so that accessing any of these table values shows the same access pattern as far
521 * as cache lines are concerned. The following functions are used to transfer a BIGNUM
522 * from/to that table. */
523
524static int MOD_EXP_CTIME_COPY_TO_PREBUF(BIGNUM *b, int top, unsigned char *buf, int idx, int width)
525 {
526 size_t i, j;
527
528 if (bn_wexpand(b, top) == NULL)
529 return 0;
530 while (b->top < top)
531 {
532 b->d[b->top++] = 0;
533 }
534
535 for (i = 0, j=idx; i < top * sizeof b->d[0]; i++, j+=width)
536 {
537 buf[j] = ((unsigned char*)b->d)[i];
538 }
539
540 bn_correct_top(b);
541 return 1;
542 }
543
544static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top, unsigned char *buf, int idx, int width)
545 {
546 size_t i, j;
547
548 if (bn_wexpand(b, top) == NULL)
549 return 0;
550
551 for (i=0, j=idx; i < top * sizeof b->d[0]; i++, j+=width)
552 {
553 ((unsigned char*)b->d)[i] = buf[j];
554 }
555
556 b->top = top;
557 bn_correct_top(b);
558 return 1;
559 }
560
561/* Given a pointer value, compute the next address that is a cache line multiple. */
562#define MOD_EXP_CTIME_ALIGN(x_) \
563 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((BN_ULONG)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
564
565/* This variant of BN_mod_exp_mont() uses fixed windows and the special
566 * precomputation memory layout to limit data-dependency to a minimum
567 * to protect secret exponents (cf. the hyper-threading timing attacks
568 * pointed out by Colin Percival,
569 * http://www.daemonology.net/hyperthreading-considered-harmful/)
570 */
571int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
572 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
573 {
574 int i,bits,ret=0,idx,window,wvalue;
575 int top;
576 BIGNUM *r;
577 const BIGNUM *aa;
578 BN_MONT_CTX *mont=NULL;
579
580 int numPowers;
581 unsigned char *powerbufFree=NULL;
582 int powerbufLen = 0;
583 unsigned char *powerbuf=NULL;
584 BIGNUM *computeTemp=NULL, *am=NULL;
585
586 bn_check_top(a);
587 bn_check_top(p);
588 bn_check_top(m);
589
590 top = m->top;
591
592 if (!(m->d[0] & 1))
593 {
594 BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME,BN_R_CALLED_WITH_EVEN_MODULUS);
595 return(0);
596 }
597 bits=BN_num_bits(p);
598 if (bits == 0)
599 {
600 ret = BN_one(rr);
601 return ret;
602 }
603
604 /* Initialize BIGNUM context and allocate intermediate result */
605 BN_CTX_start(ctx);
606 r = BN_CTX_get(ctx);
607 if (r == NULL) goto err;
608
609 /* Allocate a montgomery context if it was not supplied by the caller.
610 * If this is not done, things will break in the montgomery part.
611 */
612 if (in_mont != NULL)
613 mont=in_mont;
614 else
615 {
616 if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
617 if (!BN_MONT_CTX_set(mont,m,ctx)) goto err;
618 }
619
620 /* Get the window size to use with size of p. */
621 window = BN_window_bits_for_ctime_exponent_size(bits);
622
623 /* Allocate a buffer large enough to hold all of the pre-computed
624 * powers of a.
625 */
626 numPowers = 1 << window;
627 powerbufLen = sizeof(m->d[0])*top*numPowers;
628 if ((powerbufFree=(unsigned char*)OPENSSL_malloc(powerbufLen+MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH)) == NULL)
629 goto err;
630
631 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
632 memset(powerbuf, 0, powerbufLen);
633
634 /* Initialize the intermediate result. Do this early to save double conversion,
635 * once each for a^0 and intermediate result.
636 */
637 if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err;
638 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(r, top, powerbuf, 0, numPowers)) goto err;
639
640 /* Initialize computeTemp as a^1 with montgomery precalcs */
641 computeTemp = BN_CTX_get(ctx);
642 am = BN_CTX_get(ctx);
643 if (computeTemp==NULL || am==NULL) goto err;
644
645 if (a->neg || BN_ucmp(a,m) >= 0)
646 {
647 if (!BN_mod(am,a,m,ctx))
648 goto err;
649 aa= am;
650 }
651 else
652 aa=a;
653 if (!BN_to_montgomery(am,aa,mont,ctx)) goto err;
654 if (!BN_copy(computeTemp, am)) goto err;
655 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(am, top, powerbuf, 1, numPowers)) goto err;
656
657 /* If the window size is greater than 1, then calculate
658 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1)
659 * (even powers could instead be computed as (a^(i/2))^2
660 * to use the slight performance advantage of sqr over mul).
661 */
662 if (window > 1)
663 {
664 for (i=2; i<numPowers; i++)
665 {
666 /* Calculate a^i = a^(i-1) * a */
667 if (!BN_mod_mul_montgomery(computeTemp,am,computeTemp,mont,ctx))
668 goto err;
669 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(computeTemp, top, powerbuf, i, numPowers)) goto err;
670 }
671 }
672
673 /* Adjust the number of bits up to a multiple of the window size.
674 * If the exponent length is not a multiple of the window size, then
675 * this pads the most significant bits with zeros to normalize the
676 * scanning loop to there's no special cases.
677 *
678 * * NOTE: Making the window size a power of two less than the native
679 * * word size ensures that the padded bits won't go past the last
680 * * word in the internal BIGNUM structure. Going past the end will
681 * * still produce the correct result, but causes a different branch
682 * * to be taken in the BN_is_bit_set function.
683 */
684 bits = ((bits+window-1)/window)*window;
685 idx=bits-1; /* The top bit of the window */
686
687 /* Scan the exponent one window at a time starting from the most
688 * significant bits.
689 */
690 while (idx >= 0)
691 {
692 wvalue=0; /* The 'value' of the window */
693
694 /* Scan the window, squaring the result as we go */
695 for (i=0; i<window; i++,idx--)
696 {
697 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx)) goto err;
698 wvalue = (wvalue<<1)+BN_is_bit_set(p,idx);
699 }
700
701 /* Fetch the appropriate pre-computed value from the pre-buf */
702 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(computeTemp, top, powerbuf, wvalue, numPowers)) goto err;
703
704 /* Multiply the result into the intermediate result */
705 if (!BN_mod_mul_montgomery(r,r,computeTemp,mont,ctx)) goto err;
706 }
707
708 /* Convert the final result from montgomery to standard format */
709 if (!BN_from_montgomery(rr,r,mont,ctx)) goto err;
710 ret=1;
711err:
712 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
713 if (powerbuf!=NULL)
714 {
715 OPENSSL_cleanse(powerbuf,powerbufLen);
716 OPENSSL_free(powerbufFree);
717 }
718 if (am!=NULL) BN_clear(am);
719 if (computeTemp!=NULL) BN_clear(computeTemp);
720 BN_CTX_end(ctx);
721 return(ret);
722 }
723
724int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
725 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
726 {
727 BN_MONT_CTX *mont = NULL;
728 int b, bits, ret=0;
729 int r_is_one;
730 BN_ULONG w, next_w;
731 BIGNUM *d, *r, *t;
732 BIGNUM *swap_tmp;
733#define BN_MOD_MUL_WORD(r, w, m) \
734 (BN_mul_word(r, (w)) && \
735 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
736 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
737 /* BN_MOD_MUL_WORD is only used with 'w' large,
738 * so the BN_ucmp test is probably more overhead
739 * than always using BN_mod (which uses BN_copy if
740 * a similar test returns true). */
741 /* We can use BN_mod and do not need BN_nnmod because our
742 * accumulator is never negative (the result of BN_mod does
743 * not depend on the sign of the modulus).
744 */
745#define BN_TO_MONTGOMERY_WORD(r, w, mont) \
746 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
747
748 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
749 {
750 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
751 BNerr(BN_F_BN_MOD_EXP_MONT_WORD,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
752 return -1;
753 }
754
755 bn_check_top(p);
756 bn_check_top(m);
757
758 if (!BN_is_odd(m))
759 {
760 BNerr(BN_F_BN_MOD_EXP_MONT_WORD,BN_R_CALLED_WITH_EVEN_MODULUS);
761 return(0);
762 }
763 if (m->top == 1)
764 a %= m->d[0]; /* make sure that 'a' is reduced */
765
766 bits = BN_num_bits(p);
767 if (bits == 0)
768 {
769 ret = BN_one(rr);
770 return ret;
771 }
772 if (a == 0)
773 {
774 BN_zero(rr);
775 ret = 1;
776 return ret;
777 }
778
779 BN_CTX_start(ctx);
780 d = BN_CTX_get(ctx);
781 r = BN_CTX_get(ctx);
782 t = BN_CTX_get(ctx);
783 if (d == NULL || r == NULL || t == NULL) goto err;
784
785 if (in_mont != NULL)
786 mont=in_mont;
787 else
788 {
789 if ((mont = BN_MONT_CTX_new()) == NULL) goto err;
790 if (!BN_MONT_CTX_set(mont, m, ctx)) goto err;
791 }
792
793 r_is_one = 1; /* except for Montgomery factor */
794
795 /* bits-1 >= 0 */
796
797 /* The result is accumulated in the product r*w. */
798 w = a; /* bit 'bits-1' of 'p' is always set */
799 for (b = bits-2; b >= 0; b--)
800 {
801 /* First, square r*w. */
802 next_w = w*w;
803 if ((next_w/w) != w) /* overflow */
804 {
805 if (r_is_one)
806 {
807 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
808 r_is_one = 0;
809 }
810 else
811 {
812 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
813 }
814 next_w = 1;
815 }
816 w = next_w;
817 if (!r_is_one)
818 {
819 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) goto err;
820 }
821
822 /* Second, multiply r*w by 'a' if exponent bit is set. */
823 if (BN_is_bit_set(p, b))
824 {
825 next_w = w*a;
826 if ((next_w/a) != w) /* overflow */
827 {
828 if (r_is_one)
829 {
830 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
831 r_is_one = 0;
832 }
833 else
834 {
835 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
836 }
837 next_w = a;
838 }
839 w = next_w;
840 }
841 }
842
843 /* Finally, set r:=r*w. */
844 if (w != 1)
845 {
846 if (r_is_one)
847 {
848 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
849 r_is_one = 0;
850 }
851 else
852 {
853 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
854 }
855 }
856
857 if (r_is_one) /* can happen only if a == 1*/
858 {
859 if (!BN_one(rr)) goto err;
860 }
861 else
862 {
863 if (!BN_from_montgomery(rr, r, mont, ctx)) goto err;
864 }
865 ret = 1;
866err:
867 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
868 BN_CTX_end(ctx);
869 bn_check_top(rr);
870 return(ret);
871 }
872
873
874/* The old fallback, simple version :-) */
875int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
876 const BIGNUM *m, BN_CTX *ctx)
877 {
878 int i,j,bits,ret=0,wstart,wend,window,wvalue;
879 int start=1;
880 BIGNUM *d;
881 /* Table of variables obtained from 'ctx' */
882 BIGNUM *val[TABLE_SIZE];
883
884 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
885 {
886 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
887 BNerr(BN_F_BN_MOD_EXP_SIMPLE,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
888 return -1;
889 }
890
891 bits=BN_num_bits(p);
892
893 if (bits == 0)
894 {
895 ret = BN_one(r);
896 return ret;
897 }
898
899 BN_CTX_start(ctx);
900 d = BN_CTX_get(ctx);
901 val[0] = BN_CTX_get(ctx);
902 if(!d || !val[0]) goto err;
903
904 if (!BN_nnmod(val[0],a,m,ctx)) goto err; /* 1 */
905 if (BN_is_zero(val[0]))
906 {
907 BN_zero(r);
908 ret = 1;
909 goto err;
910 }
911
912 window = BN_window_bits_for_exponent_size(bits);
913 if (window > 1)
914 {
915 if (!BN_mod_mul(d,val[0],val[0],m,ctx))
916 goto err; /* 2 */
917 j=1<<(window-1);
918 for (i=1; i<j; i++)
919 {
920 if(((val[i] = BN_CTX_get(ctx)) == NULL) ||
921 !BN_mod_mul(val[i],val[i-1],d,m,ctx))
922 goto err;
923 }
924 }
925
926 start=1; /* This is used to avoid multiplication etc
927 * when there is only the value '1' in the
928 * buffer. */
929 wvalue=0; /* The 'value' of the window */
930 wstart=bits-1; /* The top bit of the window */
931 wend=0; /* The bottom bit of the window */
932
933 if (!BN_one(r)) goto err;
934
935 for (;;)
936 {
937 if (BN_is_bit_set(p,wstart) == 0)
938 {
939 if (!start)
940 if (!BN_mod_mul(r,r,r,m,ctx))
941 goto err;
942 if (wstart == 0) break;
943 wstart--;
944 continue;
945 }
946 /* We now have wstart on a 'set' bit, we now need to work out
947 * how bit a window to do. To do this we need to scan
948 * forward until the last set bit before the end of the
949 * window */
950 j=wstart;
951 wvalue=1;
952 wend=0;
953 for (i=1; i<window; i++)
954 {
955 if (wstart-i < 0) break;
956 if (BN_is_bit_set(p,wstart-i))
957 {
958 wvalue<<=(i-wend);
959 wvalue|=1;
960 wend=i;
961 }
962 }
963
964 /* wend is the size of the current window */
965 j=wend+1;
966 /* add the 'bytes above' */
967 if (!start)
968 for (i=0; i<j; i++)
969 {
970 if (!BN_mod_mul(r,r,r,m,ctx))
971 goto err;
972 }
973
974 /* wvalue will be an odd number < 2^window */
975 if (!BN_mod_mul(r,r,val[wvalue>>1],m,ctx))
976 goto err;
977
978 /* move the 'window' down further */
979 wstart-=wend+1;
980 wvalue=0;
981 start=0;
982 if (wstart < 0) break;
983 }
984 ret=1;
985err:
986 BN_CTX_end(ctx);
987 bn_check_top(r);
988 return(ret);
989 }
990
generated by cgit v1.2.3-55-g6feb (git 2.39.1) at 2025-04-04 08:48:43 +0000