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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) 1998-2000 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#define TABLE_SIZE 32
117
118/* this one works - simple but works */
119int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
120 {
121 int i,bits,ret=0;
122 BIGNUM *v,*rr;
123
124 BN_CTX_start(ctx);
125 if ((r == a) || (r == p))
126 rr = BN_CTX_get(ctx);
127 else
128 rr = r;
129 if ((v = BN_CTX_get(ctx)) == NULL) goto err;
130
131 if (BN_copy(v,a) == NULL) goto err;
132 bits=BN_num_bits(p);
133
134 if (BN_is_odd(p))
135 { if (BN_copy(rr,a) == NULL) goto err; }
136 else { if (!BN_one(rr)) goto err; }
137
138 for (i=1; i<bits; i++)
139 {
140 if (!BN_sqr(v,v,ctx)) goto err;
141 if (BN_is_bit_set(p,i))
142 {
143 if (!BN_mul(rr,rr,v,ctx)) goto err;
144 }
145 }
146 ret=1;
147err:
148 if (r != rr) BN_copy(r,rr);
149 BN_CTX_end(ctx);
150 return(ret);
151 }
152
153
154int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
155 BN_CTX *ctx)
156 {
157 int ret;
158
159 bn_check_top(a);
160 bn_check_top(p);
161 bn_check_top(m);
162
163 /* For even modulus m = 2^k*m_odd, it might make sense to compute
164 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery
165 * exponentiation for the odd part), using appropriate exponent
166 * reductions, and combine the results using the CRT.
167 *
168 * For now, we use Montgomery only if the modulus is odd; otherwise,
169 * exponentiation using the reciprocal-based quick remaindering
170 * algorithm is used.
171 *
172 * (Timing obtained with expspeed.c [computations a^p mod m
173 * where a, p, m are of the same length: 256, 512, 1024, 2048,
174 * 4096, 8192 bits], compared to the running time of the
175 * standard algorithm:
176 *
177 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
178 * 55 .. 77 % [UltraSparc processor, but
179 * debug-solaris-sparcv8-gcc conf.]
180 *
181 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
182 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
183 *
184 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
185 * at 2048 and more bits, but at 512 and 1024 bits, it was
186 * slower even than the standard algorithm!
187 *
188 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
189 * should be obtained when the new Montgomery reduction code
190 * has been integrated into OpenSSL.)
191 */
192
193#define MONT_MUL_MOD
194#define MONT_EXP_WORD
195#define RECP_MUL_MOD
196
197#ifdef MONT_MUL_MOD
198 /* I have finally been able to take out this pre-condition of
199 * the top bit being set. It was caused by an error in BN_div
200 * with negatives. There was also another problem when for a^b%m
201 * a >= m. eay 07-May-97 */
202/* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */
203
204 if (BN_is_odd(m))
205 {
206# ifdef MONT_EXP_WORD
207 if (a->top == 1 && !a->neg)
208 {
209 BN_ULONG A = a->d[0];
210 ret=BN_mod_exp_mont_word(r,A,p,m,ctx,NULL);
211 }
212 else
213# endif
214 ret=BN_mod_exp_mont(r,a,p,m,ctx,NULL);
215 }
216 else
217#endif
218#ifdef RECP_MUL_MOD
219 { ret=BN_mod_exp_recp(r,a,p,m,ctx); }
220#else
221 { ret=BN_mod_exp_simple(r,a,p,m,ctx); }
222#endif
223
224 return(ret);
225 }
226
227
228int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
229 const BIGNUM *m, BN_CTX *ctx)
230 {
231 int i,j,bits,ret=0,wstart,wend,window,wvalue;
232 int start=1,ts=0;
233 BIGNUM *aa;
234 BIGNUM val[TABLE_SIZE];
235 BN_RECP_CTX recp;
236
237 bits=BN_num_bits(p);
238
239 if (bits == 0)
240 {
241 ret = BN_one(r);
242 return ret;
243 }
244
245 BN_CTX_start(ctx);
246 if ((aa = BN_CTX_get(ctx)) == NULL) goto err;
247
248 BN_RECP_CTX_init(&recp);
249 if (m->neg)
250 {
251 /* ignore sign of 'm' */
252 if (!BN_copy(aa, m)) goto err;
253 aa->neg = 0;
254 if (BN_RECP_CTX_set(&recp,aa,ctx) <= 0) goto err;
255 }
256 else
257 {
258 if (BN_RECP_CTX_set(&recp,m,ctx) <= 0) goto err;
259 }
260
261 BN_init(&(val[0]));
262 ts=1;
263
264 if (!BN_nnmod(&(val[0]),a,m,ctx)) goto err; /* 1 */
265 if (BN_is_zero(&(val[0])))
266 {
267 ret = BN_zero(r);
268 goto err;
269 }
270
271 window = BN_window_bits_for_exponent_size(bits);
272 if (window > 1)
273 {
274 if (!BN_mod_mul_reciprocal(aa,&(val[0]),&(val[0]),&recp,ctx))
275 goto err; /* 2 */
276 j=1<<(window-1);
277 for (i=1; i<j; i++)
278 {
279 BN_init(&val[i]);
280 if (!BN_mod_mul_reciprocal(&(val[i]),&(val[i-1]),aa,&recp,ctx))
281 goto err;
282 }
283 ts=i;
284 }
285
286 start=1; /* This is used to avoid multiplication etc
287 * when there is only the value '1' in the
288 * buffer. */
289 wvalue=0; /* The 'value' of the window */
290 wstart=bits-1; /* The top bit of the window */
291 wend=0; /* The bottom bit of the window */
292
293 if (!BN_one(r)) goto err;
294
295 for (;;)
296 {
297 if (BN_is_bit_set(p,wstart) == 0)
298 {
299 if (!start)
300 if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
301 goto err;
302 if (wstart == 0) break;
303 wstart--;
304 continue;
305 }
306 /* We now have wstart on a 'set' bit, we now need to work out
307 * how bit a window to do. To do this we need to scan
308 * forward until the last set bit before the end of the
309 * window */
310 j=wstart;
311 wvalue=1;
312 wend=0;
313 for (i=1; i<window; i++)
314 {
315 if (wstart-i < 0) break;
316 if (BN_is_bit_set(p,wstart-i))
317 {
318 wvalue<<=(i-wend);
319 wvalue|=1;
320 wend=i;
321 }
322 }
323
324 /* wend is the size of the current window */
325 j=wend+1;
326 /* add the 'bytes above' */
327 if (!start)
328 for (i=0; i<j; i++)
329 {
330 if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
331 goto err;
332 }
333
334 /* wvalue will be an odd number < 2^window */
335 if (!BN_mod_mul_reciprocal(r,r,&(val[wvalue>>1]),&recp,ctx))
336 goto err;
337
338 /* move the 'window' down further */
339 wstart-=wend+1;
340 wvalue=0;
341 start=0;
342 if (wstart < 0) break;
343 }
344 ret=1;
345err:
346 BN_CTX_end(ctx);
347 for (i=0; i<ts; i++)
348 BN_clear_free(&(val[i]));
349 BN_RECP_CTX_free(&recp);
350 return(ret);
351 }
352
353
354int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
355 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
356 {
357 int i,j,bits,ret=0,wstart,wend,window,wvalue;
358 int start=1,ts=0;
359 BIGNUM *d,*r;
360 const BIGNUM *aa;
361 BIGNUM val[TABLE_SIZE];
362 BN_MONT_CTX *mont=NULL;
363
364 bn_check_top(a);
365 bn_check_top(p);
366 bn_check_top(m);
367
368 if (!(m->d[0] & 1))
369 {
370 BNerr(BN_F_BN_MOD_EXP_MONT,BN_R_CALLED_WITH_EVEN_MODULUS);
371 return(0);
372 }
373 bits=BN_num_bits(p);
374 if (bits == 0)
375 {
376 ret = BN_one(rr);
377 return ret;
378 }
379
380 BN_CTX_start(ctx);
381 d = BN_CTX_get(ctx);
382 r = BN_CTX_get(ctx);
383 if (d == NULL || r == NULL) goto err;
384
385 /* If this is not done, things will break in the montgomery
386 * part */
387
388 if (in_mont != NULL)
389 mont=in_mont;
390 else
391 {
392 if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
393 if (!BN_MONT_CTX_set(mont,m,ctx)) goto err;
394 }
395
396 BN_init(&val[0]);
397 ts=1;
398 if (a->neg || BN_ucmp(a,m) >= 0)
399 {
400 if (!BN_nnmod(&(val[0]),a,m,ctx))
401 goto err;
402 aa= &(val[0]);
403 }
404 else
405 aa=a;
406 if (BN_is_zero(aa))
407 {
408 ret = BN_zero(rr);
409 goto err;
410 }
411 if (!BN_to_montgomery(&(val[0]),aa,mont,ctx)) goto err; /* 1 */
412
413 window = BN_window_bits_for_exponent_size(bits);
414 if (window > 1)
415 {
416 if (!BN_mod_mul_montgomery(d,&(val[0]),&(val[0]),mont,ctx)) goto err; /* 2 */
417 j=1<<(window-1);
418 for (i=1; i<j; i++)
419 {
420 BN_init(&(val[i]));
421 if (!BN_mod_mul_montgomery(&(val[i]),&(val[i-1]),d,mont,ctx))
422 goto err;
423 }
424 ts=i;
425 }
426
427 start=1; /* This is used to avoid multiplication etc
428 * when there is only the value '1' in the
429 * buffer. */
430 wvalue=0; /* The 'value' of the window */
431 wstart=bits-1; /* The top bit of the window */
432 wend=0; /* The bottom bit of the window */
433
434 if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err;
435 for (;;)
436 {
437 if (BN_is_bit_set(p,wstart) == 0)
438 {
439 if (!start)
440 {
441 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
442 goto err;
443 }
444 if (wstart == 0) break;
445 wstart--;
446 continue;
447 }
448 /* We now have wstart on a 'set' bit, we now need to work out
449 * how bit a window to do. To do this we need to scan
450 * forward until the last set bit before the end of the
451 * window */
452 j=wstart;
453 wvalue=1;
454 wend=0;
455 for (i=1; i<window; i++)
456 {
457 if (wstart-i < 0) break;
458 if (BN_is_bit_set(p,wstart-i))
459 {
460 wvalue<<=(i-wend);
461 wvalue|=1;
462 wend=i;
463 }
464 }
465
466 /* wend is the size of the current window */
467 j=wend+1;
468 /* add the 'bytes above' */
469 if (!start)
470 for (i=0; i<j; i++)
471 {
472 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
473 goto err;
474 }
475
476 /* wvalue will be an odd number < 2^window */
477 if (!BN_mod_mul_montgomery(r,r,&(val[wvalue>>1]),mont,ctx))
478 goto err;
479
480 /* move the 'window' down further */
481 wstart-=wend+1;
482 wvalue=0;
483 start=0;
484 if (wstart < 0) break;
485 }
486 if (!BN_from_montgomery(rr,r,mont,ctx)) goto err;
487 ret=1;
488err:
489 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
490 BN_CTX_end(ctx);
491 for (i=0; i<ts; i++)
492 BN_clear_free(&(val[i]));
493 return(ret);
494 }
495
496int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
497 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
498 {
499 BN_MONT_CTX *mont = NULL;
500 int b, bits, ret=0;
501 int r_is_one;
502 BN_ULONG w, next_w;
503 BIGNUM *d, *r, *t;
504 BIGNUM *swap_tmp;
505#define BN_MOD_MUL_WORD(r, w, m) \
506 (BN_mul_word(r, (w)) && \
507 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
508 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
509 /* BN_MOD_MUL_WORD is only used with 'w' large,
510 * so the BN_ucmp test is probably more overhead
511 * than always using BN_mod (which uses BN_copy if
512 * a similar test returns true). */
513 /* We can use BN_mod and do not need BN_nnmod because our
514 * accumulator is never negative (the result of BN_mod does
515 * not depend on the sign of the modulus).
516 */
517#define BN_TO_MONTGOMERY_WORD(r, w, mont) \
518 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
519
520 bn_check_top(p);
521 bn_check_top(m);
522
523 if (m->top == 0 || !(m->d[0] & 1))
524 {
525 BNerr(BN_F_BN_MOD_EXP_MONT_WORD,BN_R_CALLED_WITH_EVEN_MODULUS);
526 return(0);
527 }
528 if (m->top == 1)
529 a %= m->d[0]; /* make sure that 'a' is reduced */
530
531 bits = BN_num_bits(p);
532 if (bits == 0)
533 {
534 ret = BN_one(rr);
535 return ret;
536 }
537 if (a == 0)
538 {
539 ret = BN_zero(rr);
540 return ret;
541 }
542
543 BN_CTX_start(ctx);
544 d = BN_CTX_get(ctx);
545 r = BN_CTX_get(ctx);
546 t = BN_CTX_get(ctx);
547 if (d == NULL || r == NULL || t == NULL) goto err;
548
549 if (in_mont != NULL)
550 mont=in_mont;
551 else
552 {
553 if ((mont = BN_MONT_CTX_new()) == NULL) goto err;
554 if (!BN_MONT_CTX_set(mont, m, ctx)) goto err;
555 }
556
557 r_is_one = 1; /* except for Montgomery factor */
558
559 /* bits-1 >= 0 */
560
561 /* The result is accumulated in the product r*w. */
562 w = a; /* bit 'bits-1' of 'p' is always set */
563 for (b = bits-2; b >= 0; b--)
564 {
565 /* First, square r*w. */
566 next_w = w*w;
567 if ((next_w/w) != w) /* overflow */
568 {
569 if (r_is_one)
570 {
571 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
572 r_is_one = 0;
573 }
574 else
575 {
576 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
577 }
578 next_w = 1;
579 }
580 w = next_w;
581 if (!r_is_one)
582 {
583 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) goto err;
584 }
585
586 /* Second, multiply r*w by 'a' if exponent bit is set. */
587 if (BN_is_bit_set(p, b))
588 {
589 next_w = w*a;
590 if ((next_w/a) != w) /* overflow */
591 {
592 if (r_is_one)
593 {
594 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
595 r_is_one = 0;
596 }
597 else
598 {
599 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
600 }
601 next_w = a;
602 }
603 w = next_w;
604 }
605 }
606
607 /* Finally, set r:=r*w. */
608 if (w != 1)
609 {
610 if (r_is_one)
611 {
612 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
613 r_is_one = 0;
614 }
615 else
616 {
617 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
618 }
619 }
620
621 if (r_is_one) /* can happen only if a == 1*/
622 {
623 if (!BN_one(rr)) goto err;
624 }
625 else
626 {
627 if (!BN_from_montgomery(rr, r, mont, ctx)) goto err;
628 }
629 ret = 1;
630err:
631 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
632 BN_CTX_end(ctx);
633 return(ret);
634 }
635
636
637/* The old fallback, simple version :-) */
638int BN_mod_exp_simple(BIGNUM *r,
639 const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
640 BN_CTX *ctx)
641 {
642 int i,j,bits,ret=0,wstart,wend,window,wvalue,ts=0;
643 int start=1;
644 BIGNUM *d;
645 BIGNUM val[TABLE_SIZE];
646
647 bits=BN_num_bits(p);
648
649 if (bits == 0)
650 {
651 ret = BN_one(r);
652 return ret;
653 }
654
655 BN_CTX_start(ctx);
656 if ((d = BN_CTX_get(ctx)) == NULL) goto err;
657
658 BN_init(&(val[0]));
659 ts=1;
660 if (!BN_nnmod(&(val[0]),a,m,ctx)) goto err; /* 1 */
661 if (BN_is_zero(&(val[0])))
662 {
663 ret = BN_zero(r);
664 goto err;
665 }
666
667 window = BN_window_bits_for_exponent_size(bits);
668 if (window > 1)
669 {
670 if (!BN_mod_mul(d,&(val[0]),&(val[0]),m,ctx))
671 goto err; /* 2 */
672 j=1<<(window-1);
673 for (i=1; i<j; i++)
674 {
675 BN_init(&(val[i]));
676 if (!BN_mod_mul(&(val[i]),&(val[i-1]),d,m,ctx))
677 goto err;
678 }
679 ts=i;
680 }
681
682 start=1; /* This is used to avoid multiplication etc
683 * when there is only the value '1' in the
684 * buffer. */
685 wvalue=0; /* The 'value' of the window */
686 wstart=bits-1; /* The top bit of the window */
687 wend=0; /* The bottom bit of the window */
688
689 if (!BN_one(r)) goto err;
690
691 for (;;)
692 {
693 if (BN_is_bit_set(p,wstart) == 0)
694 {
695 if (!start)
696 if (!BN_mod_mul(r,r,r,m,ctx))
697 goto err;
698 if (wstart == 0) break;
699 wstart--;
700 continue;
701 }
702 /* We now have wstart on a 'set' bit, we now need to work out
703 * how bit a window to do. To do this we need to scan
704 * forward until the last set bit before the end of the
705 * window */
706 j=wstart;
707 wvalue=1;
708 wend=0;
709 for (i=1; i<window; i++)
710 {
711 if (wstart-i < 0) break;
712 if (BN_is_bit_set(p,wstart-i))
713 {
714 wvalue<<=(i-wend);
715 wvalue|=1;
716 wend=i;
717 }
718 }
719
720 /* wend is the size of the current window */
721 j=wend+1;
722 /* add the 'bytes above' */
723 if (!start)
724 for (i=0; i<j; i++)
725 {
726 if (!BN_mod_mul(r,r,r,m,ctx))
727 goto err;
728 }
729
730 /* wvalue will be an odd number < 2^window */
731 if (!BN_mod_mul(r,r,&(val[wvalue>>1]),m,ctx))
732 goto err;
733
734 /* move the 'window' down further */
735 wstart-=wend+1;
736 wvalue=0;
737 start=0;
738 if (wstart < 0) break;
739 }
740 ret=1;
741err:
742 BN_CTX_end(ctx);
743 for (i=0; i<ts; i++)
744 BN_clear_free(&(val[i]));
745 return(ret);
746 }
747
generated by cgit v1.2.3-55-g6feb (git 2.39.1) at 2025-12-09 02:22:43 +0000