source: EcnlProtoTool/trunk/openssl-1.1.0e/crypto/bn/bn_exp.c@ 331

Last change on this file since 331 was 331, checked in by coas-nagasima, 6 years ago

prototoolに関連するプロジェクトをnewlibからmuslを使うよう変更・更新
ntshellをnewlibの下位の実装から、muslのsyscallの実装に変更・更新
以下のOSSをアップデート
・mruby-1.3.0
・musl-1.1.18
・onigmo-6.1.3
・tcc-0.9.27
以下のOSSを追加
・openssl-1.1.0e
・curl-7.57.0
・zlib-1.2.11
以下のmrbgemsを追加
・iij/mruby-digest
・iij/mruby-env
・iij/mruby-errno
・iij/mruby-iijson
・iij/mruby-ipaddr
・iij/mruby-mock
・iij/mruby-require
・iij/mruby-tls-openssl
  • Property svn:eol-style set to native
  • Property svn:mime-type set to text/x-csrc
File size: 42.6 KB
Line 
1/*
2 * Copyright 1995-2016 The OpenSSL Project Authors. All Rights Reserved.
3 *
4 * Licensed under the OpenSSL license (the "License"). You may not use
5 * this file except in compliance with the License. You can obtain a copy
6 * in the file LICENSE in the source distribution or at
7 * https://www.openssl.org/source/license.html
8 */
9
10#include "internal/cryptlib.h"
11#include "internal/constant_time_locl.h"
12#include "bn_lcl.h"
13
14#include <stdlib.h>
15#ifdef _WIN32
16# include <malloc.h>
17# ifndef alloca
18# define alloca _alloca
19# endif
20#elif defined(__GNUC__)
21# ifndef alloca
22# define alloca(s) __builtin_alloca((s))
23# endif
24#elif defined(__sun)
25# include <alloca.h>
26#endif
27
28#include "rsaz_exp.h"
29
30#undef SPARC_T4_MONT
31#if defined(OPENSSL_BN_ASM_MONT) && (defined(__sparc__) || defined(__sparc))
32# include "sparc_arch.h"
33extern unsigned int OPENSSL_sparcv9cap_P[];
34# define SPARC_T4_MONT
35#endif
36
37/* maximum precomputation table size for *variable* sliding windows */
38#define TABLE_SIZE 32
39
40/* this one works - simple but works */
41int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
42{
43 int i, bits, ret = 0;
44 BIGNUM *v, *rr;
45
46 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
47 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
48 BNerr(BN_F_BN_EXP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
49 return 0;
50 }
51
52 BN_CTX_start(ctx);
53 if ((r == a) || (r == p))
54 rr = BN_CTX_get(ctx);
55 else
56 rr = r;
57 v = BN_CTX_get(ctx);
58 if (rr == NULL || v == NULL)
59 goto err;
60
61 if (BN_copy(v, a) == NULL)
62 goto err;
63 bits = BN_num_bits(p);
64
65 if (BN_is_odd(p)) {
66 if (BN_copy(rr, a) == NULL)
67 goto err;
68 } else {
69 if (!BN_one(rr))
70 goto err;
71 }
72
73 for (i = 1; i < bits; i++) {
74 if (!BN_sqr(v, v, ctx))
75 goto err;
76 if (BN_is_bit_set(p, i)) {
77 if (!BN_mul(rr, rr, v, ctx))
78 goto err;
79 }
80 }
81 if (r != rr && BN_copy(r, rr) == NULL)
82 goto err;
83
84 ret = 1;
85 err:
86 BN_CTX_end(ctx);
87 bn_check_top(r);
88 return (ret);
89}
90
91int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
92 BN_CTX *ctx)
93{
94 int ret;
95
96 bn_check_top(a);
97 bn_check_top(p);
98 bn_check_top(m);
99
100 /*-
101 * For even modulus m = 2^k*m_odd, it might make sense to compute
102 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery
103 * exponentiation for the odd part), using appropriate exponent
104 * reductions, and combine the results using the CRT.
105 *
106 * For now, we use Montgomery only if the modulus is odd; otherwise,
107 * exponentiation using the reciprocal-based quick remaindering
108 * algorithm is used.
109 *
110 * (Timing obtained with expspeed.c [computations a^p mod m
111 * where a, p, m are of the same length: 256, 512, 1024, 2048,
112 * 4096, 8192 bits], compared to the running time of the
113 * standard algorithm:
114 *
115 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
116 * 55 .. 77 % [UltraSparc processor, but
117 * debug-solaris-sparcv8-gcc conf.]
118 *
119 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
120 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
121 *
122 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
123 * at 2048 and more bits, but at 512 and 1024 bits, it was
124 * slower even than the standard algorithm!
125 *
126 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
127 * should be obtained when the new Montgomery reduction code
128 * has been integrated into OpenSSL.)
129 */
130
131#define MONT_MUL_MOD
132#define MONT_EXP_WORD
133#define RECP_MUL_MOD
134
135#ifdef MONT_MUL_MOD
136 /*
137 * I have finally been able to take out this pre-condition of the top bit
138 * being set. It was caused by an error in BN_div with negatives. There
139 * was also another problem when for a^b%m a >= m. eay 07-May-97
140 */
141 /* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */
142
143 if (BN_is_odd(m)) {
144# ifdef MONT_EXP_WORD
145 if (a->top == 1 && !a->neg
146 && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0)) {
147 BN_ULONG A = a->d[0];
148 ret = BN_mod_exp_mont_word(r, A, p, m, ctx, NULL);
149 } else
150# endif
151 ret = BN_mod_exp_mont(r, a, p, m, ctx, NULL);
152 } else
153#endif
154#ifdef RECP_MUL_MOD
155 {
156 ret = BN_mod_exp_recp(r, a, p, m, ctx);
157 }
158#else
159 {
160 ret = BN_mod_exp_simple(r, a, p, m, ctx);
161 }
162#endif
163
164 bn_check_top(r);
165 return (ret);
166}
167
168int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
169 const BIGNUM *m, BN_CTX *ctx)
170{
171 int i, j, bits, ret = 0, wstart, wend, window, wvalue;
172 int start = 1;
173 BIGNUM *aa;
174 /* Table of variables obtained from 'ctx' */
175 BIGNUM *val[TABLE_SIZE];
176 BN_RECP_CTX recp;
177
178 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
179 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
180 BNerr(BN_F_BN_MOD_EXP_RECP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
181 return 0;
182 }
183
184 bits = BN_num_bits(p);
185 if (bits == 0) {
186 /* x**0 mod 1 is still zero. */
187 if (BN_is_one(m)) {
188 ret = 1;
189 BN_zero(r);
190 } else {
191 ret = BN_one(r);
192 }
193 return ret;
194 }
195
196 BN_CTX_start(ctx);
197 aa = BN_CTX_get(ctx);
198 val[0] = BN_CTX_get(ctx);
199 if (!aa || !val[0])
200 goto err;
201
202 BN_RECP_CTX_init(&recp);
203 if (m->neg) {
204 /* ignore sign of 'm' */
205 if (!BN_copy(aa, m))
206 goto err;
207 aa->neg = 0;
208 if (BN_RECP_CTX_set(&recp, aa, ctx) <= 0)
209 goto err;
210 } else {
211 if (BN_RECP_CTX_set(&recp, m, ctx) <= 0)
212 goto err;
213 }
214
215 if (!BN_nnmod(val[0], a, m, ctx))
216 goto err; /* 1 */
217 if (BN_is_zero(val[0])) {
218 BN_zero(r);
219 ret = 1;
220 goto err;
221 }
222
223 window = BN_window_bits_for_exponent_size(bits);
224 if (window > 1) {
225 if (!BN_mod_mul_reciprocal(aa, val[0], val[0], &recp, ctx))
226 goto err; /* 2 */
227 j = 1 << (window - 1);
228 for (i = 1; i < j; i++) {
229 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
230 !BN_mod_mul_reciprocal(val[i], val[i - 1], aa, &recp, ctx))
231 goto err;
232 }
233 }
234
235 start = 1; /* This is used to avoid multiplication etc
236 * when there is only the value '1' in the
237 * buffer. */
238 wvalue = 0; /* The 'value' of the window */
239 wstart = bits - 1; /* The top bit of the window */
240 wend = 0; /* The bottom bit of the window */
241
242 if (!BN_one(r))
243 goto err;
244
245 for (;;) {
246 if (BN_is_bit_set(p, wstart) == 0) {
247 if (!start)
248 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
249 goto err;
250 if (wstart == 0)
251 break;
252 wstart--;
253 continue;
254 }
255 /*
256 * We now have wstart on a 'set' bit, we now need to work out how bit
257 * a window to do. To do this we need to scan forward until the last
258 * set bit before the end of the window
259 */
260 j = wstart;
261 wvalue = 1;
262 wend = 0;
263 for (i = 1; i < window; i++) {
264 if (wstart - i < 0)
265 break;
266 if (BN_is_bit_set(p, wstart - i)) {
267 wvalue <<= (i - wend);
268 wvalue |= 1;
269 wend = i;
270 }
271 }
272
273 /* wend is the size of the current window */
274 j = wend + 1;
275 /* add the 'bytes above' */
276 if (!start)
277 for (i = 0; i < j; i++) {
278 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
279 goto err;
280 }
281
282 /* wvalue will be an odd number < 2^window */
283 if (!BN_mod_mul_reciprocal(r, r, val[wvalue >> 1], &recp, ctx))
284 goto err;
285
286 /* move the 'window' down further */
287 wstart -= wend + 1;
288 wvalue = 0;
289 start = 0;
290 if (wstart < 0)
291 break;
292 }
293 ret = 1;
294 err:
295 BN_CTX_end(ctx);
296 BN_RECP_CTX_free(&recp);
297 bn_check_top(r);
298 return (ret);
299}
300
301int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
302 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
303{
304 int i, j, bits, ret = 0, wstart, wend, window, wvalue;
305 int start = 1;
306 BIGNUM *d, *r;
307 const BIGNUM *aa;
308 /* Table of variables obtained from 'ctx' */
309 BIGNUM *val[TABLE_SIZE];
310 BN_MONT_CTX *mont = NULL;
311
312 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
313 return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
314 }
315
316 bn_check_top(a);
317 bn_check_top(p);
318 bn_check_top(m);
319
320 if (!BN_is_odd(m)) {
321 BNerr(BN_F_BN_MOD_EXP_MONT, BN_R_CALLED_WITH_EVEN_MODULUS);
322 return (0);
323 }
324 bits = BN_num_bits(p);
325 if (bits == 0) {
326 /* x**0 mod 1 is still zero. */
327 if (BN_is_one(m)) {
328 ret = 1;
329 BN_zero(rr);
330 } else {
331 ret = BN_one(rr);
332 }
333 return ret;
334 }
335
336 BN_CTX_start(ctx);
337 d = BN_CTX_get(ctx);
338 r = BN_CTX_get(ctx);
339 val[0] = BN_CTX_get(ctx);
340 if (!d || !r || !val[0])
341 goto err;
342
343 /*
344 * If this is not done, things will break in the montgomery part
345 */
346
347 if (in_mont != NULL)
348 mont = in_mont;
349 else {
350 if ((mont = BN_MONT_CTX_new()) == NULL)
351 goto err;
352 if (!BN_MONT_CTX_set(mont, m, ctx))
353 goto err;
354 }
355
356 if (a->neg || BN_ucmp(a, m) >= 0) {
357 if (!BN_nnmod(val[0], a, m, ctx))
358 goto err;
359 aa = val[0];
360 } else
361 aa = a;
362 if (BN_is_zero(aa)) {
363 BN_zero(rr);
364 ret = 1;
365 goto err;
366 }
367 if (!BN_to_montgomery(val[0], aa, mont, ctx))
368 goto err; /* 1 */
369
370 window = BN_window_bits_for_exponent_size(bits);
371 if (window > 1) {
372 if (!BN_mod_mul_montgomery(d, val[0], val[0], mont, ctx))
373 goto err; /* 2 */
374 j = 1 << (window - 1);
375 for (i = 1; i < j; i++) {
376 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
377 !BN_mod_mul_montgomery(val[i], val[i - 1], d, mont, ctx))
378 goto err;
379 }
380 }
381
382 start = 1; /* This is used to avoid multiplication etc
383 * when there is only the value '1' in the
384 * buffer. */
385 wvalue = 0; /* The 'value' of the window */
386 wstart = bits - 1; /* The top bit of the window */
387 wend = 0; /* The bottom bit of the window */
388
389#if 1 /* by Shay Gueron's suggestion */
390 j = m->top; /* borrow j */
391 if (m->d[j - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
392 if (bn_wexpand(r, j) == NULL)
393 goto err;
394 /* 2^(top*BN_BITS2) - m */
395 r->d[0] = (0 - m->d[0]) & BN_MASK2;
396 for (i = 1; i < j; i++)
397 r->d[i] = (~m->d[i]) & BN_MASK2;
398 r->top = j;
399 /*
400 * Upper words will be zero if the corresponding words of 'm' were
401 * 0xfff[...], so decrement r->top accordingly.
402 */
403 bn_correct_top(r);
404 } else
405#endif
406 if (!BN_to_montgomery(r, BN_value_one(), mont, ctx))
407 goto err;
408 for (;;) {
409 if (BN_is_bit_set(p, wstart) == 0) {
410 if (!start) {
411 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
412 goto err;
413 }
414 if (wstart == 0)
415 break;
416 wstart--;
417 continue;
418 }
419 /*
420 * We now have wstart on a 'set' bit, we now need to work out how bit
421 * a window to do. To do this we need to scan forward until the last
422 * set bit before the end of the window
423 */
424 j = wstart;
425 wvalue = 1;
426 wend = 0;
427 for (i = 1; i < window; i++) {
428 if (wstart - i < 0)
429 break;
430 if (BN_is_bit_set(p, wstart - i)) {
431 wvalue <<= (i - wend);
432 wvalue |= 1;
433 wend = i;
434 }
435 }
436
437 /* wend is the size of the current window */
438 j = wend + 1;
439 /* add the 'bytes above' */
440 if (!start)
441 for (i = 0; i < j; i++) {
442 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
443 goto err;
444 }
445
446 /* wvalue will be an odd number < 2^window */
447 if (!BN_mod_mul_montgomery(r, r, val[wvalue >> 1], mont, ctx))
448 goto err;
449
450 /* move the 'window' down further */
451 wstart -= wend + 1;
452 wvalue = 0;
453 start = 0;
454 if (wstart < 0)
455 break;
456 }
457#if defined(SPARC_T4_MONT)
458 if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
459 j = mont->N.top; /* borrow j */
460 val[0]->d[0] = 1; /* borrow val[0] */
461 for (i = 1; i < j; i++)
462 val[0]->d[i] = 0;
463 val[0]->top = j;
464 if (!BN_mod_mul_montgomery(rr, r, val[0], mont, ctx))
465 goto err;
466 } else
467#endif
468 if (!BN_from_montgomery(rr, r, mont, ctx))
469 goto err;
470 ret = 1;
471 err:
472 if (in_mont == NULL)
473 BN_MONT_CTX_free(mont);
474 BN_CTX_end(ctx);
475 bn_check_top(rr);
476 return (ret);
477}
478
479#if defined(SPARC_T4_MONT)
480static BN_ULONG bn_get_bits(const BIGNUM *a, int bitpos)
481{
482 BN_ULONG ret = 0;
483 int wordpos;
484
485 wordpos = bitpos / BN_BITS2;
486 bitpos %= BN_BITS2;
487 if (wordpos >= 0 && wordpos < a->top) {
488 ret = a->d[wordpos] & BN_MASK2;
489 if (bitpos) {
490 ret >>= bitpos;
491 if (++wordpos < a->top)
492 ret |= a->d[wordpos] << (BN_BITS2 - bitpos);
493 }
494 }
495
496 return ret & BN_MASK2;
497}
498#endif
499
500/*
501 * BN_mod_exp_mont_consttime() stores the precomputed powers in a specific
502 * layout so that accessing any of these table values shows the same access
503 * pattern as far as cache lines are concerned. The following functions are
504 * used to transfer a BIGNUM from/to that table.
505 */
506
507static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top,
508 unsigned char *buf, int idx,
509 int window)
510{
511 int i, j;
512 int width = 1 << window;
513 BN_ULONG *table = (BN_ULONG *)buf;
514
515 if (top > b->top)
516 top = b->top; /* this works because 'buf' is explicitly
517 * zeroed */
518 for (i = 0, j = idx; i < top; i++, j += width) {
519 table[j] = b->d[i];
520 }
521
522 return 1;
523}
524
525static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top,
526 unsigned char *buf, int idx,
527 int window)
528{
529 int i, j;
530 int width = 1 << window;
531 /*
532 * We declare table 'volatile' in order to discourage compiler
533 * from reordering loads from the table. Concern is that if
534 * reordered in specific manner loads might give away the
535 * information we are trying to conceal. Some would argue that
536 * compiler can reorder them anyway, but it can as well be
537 * argued that doing so would be violation of standard...
538 */
539 volatile BN_ULONG *table = (volatile BN_ULONG *)buf;
540
541 if (bn_wexpand(b, top) == NULL)
542 return 0;
543
544 if (window <= 3) {
545 for (i = 0; i < top; i++, table += width) {
546 BN_ULONG acc = 0;
547
548 for (j = 0; j < width; j++) {
549 acc |= table[j] &
550 ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1));
551 }
552
553 b->d[i] = acc;
554 }
555 } else {
556 int xstride = 1 << (window - 2);
557 BN_ULONG y0, y1, y2, y3;
558
559 i = idx >> (window - 2); /* equivalent of idx / xstride */
560 idx &= xstride - 1; /* equivalent of idx % xstride */
561
562 y0 = (BN_ULONG)0 - (constant_time_eq_int(i,0)&1);
563 y1 = (BN_ULONG)0 - (constant_time_eq_int(i,1)&1);
564 y2 = (BN_ULONG)0 - (constant_time_eq_int(i,2)&1);
565 y3 = (BN_ULONG)0 - (constant_time_eq_int(i,3)&1);
566
567 for (i = 0; i < top; i++, table += width) {
568 BN_ULONG acc = 0;
569
570 for (j = 0; j < xstride; j++) {
571 acc |= ( (table[j + 0 * xstride] & y0) |
572 (table[j + 1 * xstride] & y1) |
573 (table[j + 2 * xstride] & y2) |
574 (table[j + 3 * xstride] & y3) )
575 & ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1));
576 }
577
578 b->d[i] = acc;
579 }
580 }
581
582 b->top = top;
583 bn_correct_top(b);
584 return 1;
585}
586
587/*
588 * Given a pointer value, compute the next address that is a cache line
589 * multiple.
590 */
591#define MOD_EXP_CTIME_ALIGN(x_) \
592 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
593
594/*
595 * This variant of BN_mod_exp_mont() uses fixed windows and the special
596 * precomputation memory layout to limit data-dependency to a minimum to
597 * protect secret exponents (cf. the hyper-threading timing attacks pointed
598 * out by Colin Percival,
599 * http://www.daemonology.net/hyperthreading-considered-harmful/)
600 */
601int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
602 const BIGNUM *m, BN_CTX *ctx,
603 BN_MONT_CTX *in_mont)
604{
605 int i, bits, ret = 0, window, wvalue;
606 int top;
607 BN_MONT_CTX *mont = NULL;
608
609 int numPowers;
610 unsigned char *powerbufFree = NULL;
611 int powerbufLen = 0;
612 unsigned char *powerbuf = NULL;
613 BIGNUM tmp, am;
614#if defined(SPARC_T4_MONT)
615 unsigned int t4 = 0;
616#endif
617
618 bn_check_top(a);
619 bn_check_top(p);
620 bn_check_top(m);
621
622 if (!BN_is_odd(m)) {
623 BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME, BN_R_CALLED_WITH_EVEN_MODULUS);
624 return (0);
625 }
626
627 top = m->top;
628
629 bits = BN_num_bits(p);
630 if (bits == 0) {
631 /* x**0 mod 1 is still zero. */
632 if (BN_is_one(m)) {
633 ret = 1;
634 BN_zero(rr);
635 } else {
636 ret = BN_one(rr);
637 }
638 return ret;
639 }
640
641 BN_CTX_start(ctx);
642
643 /*
644 * Allocate a montgomery context if it was not supplied by the caller. If
645 * this is not done, things will break in the montgomery part.
646 */
647 if (in_mont != NULL)
648 mont = in_mont;
649 else {
650 if ((mont = BN_MONT_CTX_new()) == NULL)
651 goto err;
652 if (!BN_MONT_CTX_set(mont, m, ctx))
653 goto err;
654 }
655
656#ifdef RSAZ_ENABLED
657 /*
658 * If the size of the operands allow it, perform the optimized
659 * RSAZ exponentiation. For further information see
660 * crypto/bn/rsaz_exp.c and accompanying assembly modules.
661 */
662 if ((16 == a->top) && (16 == p->top) && (BN_num_bits(m) == 1024)
663 && rsaz_avx2_eligible()) {
664 if (NULL == bn_wexpand(rr, 16))
665 goto err;
666 RSAZ_1024_mod_exp_avx2(rr->d, a->d, p->d, m->d, mont->RR.d,
667 mont->n0[0]);
668 rr->top = 16;
669 rr->neg = 0;
670 bn_correct_top(rr);
671 ret = 1;
672 goto err;
673 } else if ((8 == a->top) && (8 == p->top) && (BN_num_bits(m) == 512)) {
674 if (NULL == bn_wexpand(rr, 8))
675 goto err;
676 RSAZ_512_mod_exp(rr->d, a->d, p->d, m->d, mont->n0[0], mont->RR.d);
677 rr->top = 8;
678 rr->neg = 0;
679 bn_correct_top(rr);
680 ret = 1;
681 goto err;
682 }
683#endif
684
685 /* Get the window size to use with size of p. */
686 window = BN_window_bits_for_ctime_exponent_size(bits);
687#if defined(SPARC_T4_MONT)
688 if (window >= 5 && (top & 15) == 0 && top <= 64 &&
689 (OPENSSL_sparcv9cap_P[1] & (CFR_MONTMUL | CFR_MONTSQR)) ==
690 (CFR_MONTMUL | CFR_MONTSQR) && (t4 = OPENSSL_sparcv9cap_P[0]))
691 window = 5;
692 else
693#endif
694#if defined(OPENSSL_BN_ASM_MONT5)
695 if (window >= 5) {
696 window = 5; /* ~5% improvement for RSA2048 sign, and even
697 * for RSA4096 */
698 /* reserve space for mont->N.d[] copy */
699 powerbufLen += top * sizeof(mont->N.d[0]);
700 }
701#endif
702 (void)0;
703
704 /*
705 * Allocate a buffer large enough to hold all of the pre-computed powers
706 * of am, am itself and tmp.
707 */
708 numPowers = 1 << window;
709 powerbufLen += sizeof(m->d[0]) * (top * numPowers +
710 ((2 * top) >
711 numPowers ? (2 * top) : numPowers));
712#ifdef alloca
713 if (powerbufLen < 3072)
714 powerbufFree =
715 alloca(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
716 else
717#endif
718 if ((powerbufFree =
719 OPENSSL_malloc(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH))
720 == NULL)
721 goto err;
722
723 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
724 memset(powerbuf, 0, powerbufLen);
725
726#ifdef alloca
727 if (powerbufLen < 3072)
728 powerbufFree = NULL;
729#endif
730
731 /* lay down tmp and am right after powers table */
732 tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers);
733 am.d = tmp.d + top;
734 tmp.top = am.top = 0;
735 tmp.dmax = am.dmax = top;
736 tmp.neg = am.neg = 0;
737 tmp.flags = am.flags = BN_FLG_STATIC_DATA;
738
739 /* prepare a^0 in Montgomery domain */
740#if 1 /* by Shay Gueron's suggestion */
741 if (m->d[top - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
742 /* 2^(top*BN_BITS2) - m */
743 tmp.d[0] = (0 - m->d[0]) & BN_MASK2;
744 for (i = 1; i < top; i++)
745 tmp.d[i] = (~m->d[i]) & BN_MASK2;
746 tmp.top = top;
747 } else
748#endif
749 if (!BN_to_montgomery(&tmp, BN_value_one(), mont, ctx))
750 goto err;
751
752 /* prepare a^1 in Montgomery domain */
753 if (a->neg || BN_ucmp(a, m) >= 0) {
754 if (!BN_mod(&am, a, m, ctx))
755 goto err;
756 if (!BN_to_montgomery(&am, &am, mont, ctx))
757 goto err;
758 } else if (!BN_to_montgomery(&am, a, mont, ctx))
759 goto err;
760
761#if defined(SPARC_T4_MONT)
762 if (t4) {
763 typedef int (*bn_pwr5_mont_f) (BN_ULONG *tp, const BN_ULONG *np,
764 const BN_ULONG *n0, const void *table,
765 int power, int bits);
766 int bn_pwr5_mont_t4_8(BN_ULONG *tp, const BN_ULONG *np,
767 const BN_ULONG *n0, const void *table,
768 int power, int bits);
769 int bn_pwr5_mont_t4_16(BN_ULONG *tp, const BN_ULONG *np,
770 const BN_ULONG *n0, const void *table,
771 int power, int bits);
772 int bn_pwr5_mont_t4_24(BN_ULONG *tp, const BN_ULONG *np,
773 const BN_ULONG *n0, const void *table,
774 int power, int bits);
775 int bn_pwr5_mont_t4_32(BN_ULONG *tp, const BN_ULONG *np,
776 const BN_ULONG *n0, const void *table,
777 int power, int bits);
778 static const bn_pwr5_mont_f pwr5_funcs[4] = {
779 bn_pwr5_mont_t4_8, bn_pwr5_mont_t4_16,
780 bn_pwr5_mont_t4_24, bn_pwr5_mont_t4_32
781 };
782 bn_pwr5_mont_f pwr5_worker = pwr5_funcs[top / 16 - 1];
783
784 typedef int (*bn_mul_mont_f) (BN_ULONG *rp, const BN_ULONG *ap,
785 const void *bp, const BN_ULONG *np,
786 const BN_ULONG *n0);
787 int bn_mul_mont_t4_8(BN_ULONG *rp, const BN_ULONG *ap, const void *bp,
788 const BN_ULONG *np, const BN_ULONG *n0);
789 int bn_mul_mont_t4_16(BN_ULONG *rp, const BN_ULONG *ap,
790 const void *bp, const BN_ULONG *np,
791 const BN_ULONG *n0);
792 int bn_mul_mont_t4_24(BN_ULONG *rp, const BN_ULONG *ap,
793 const void *bp, const BN_ULONG *np,
794 const BN_ULONG *n0);
795 int bn_mul_mont_t4_32(BN_ULONG *rp, const BN_ULONG *ap,
796 const void *bp, const BN_ULONG *np,
797 const BN_ULONG *n0);
798 static const bn_mul_mont_f mul_funcs[4] = {
799 bn_mul_mont_t4_8, bn_mul_mont_t4_16,
800 bn_mul_mont_t4_24, bn_mul_mont_t4_32
801 };
802 bn_mul_mont_f mul_worker = mul_funcs[top / 16 - 1];
803
804 void bn_mul_mont_vis3(BN_ULONG *rp, const BN_ULONG *ap,
805 const void *bp, const BN_ULONG *np,
806 const BN_ULONG *n0, int num);
807 void bn_mul_mont_t4(BN_ULONG *rp, const BN_ULONG *ap,
808 const void *bp, const BN_ULONG *np,
809 const BN_ULONG *n0, int num);
810 void bn_mul_mont_gather5_t4(BN_ULONG *rp, const BN_ULONG *ap,
811 const void *table, const BN_ULONG *np,
812 const BN_ULONG *n0, int num, int power);
813 void bn_flip_n_scatter5_t4(const BN_ULONG *inp, size_t num,
814 void *table, size_t power);
815 void bn_gather5_t4(BN_ULONG *out, size_t num,
816 void *table, size_t power);
817 void bn_flip_t4(BN_ULONG *dst, BN_ULONG *src, size_t num);
818
819 BN_ULONG *np = mont->N.d, *n0 = mont->n0;
820 int stride = 5 * (6 - (top / 16 - 1)); /* multiple of 5, but less
821 * than 32 */
822
823 /*
824 * BN_to_montgomery can contaminate words above .top [in
825 * BN_DEBUG[_DEBUG] build]...
826 */
827 for (i = am.top; i < top; i++)
828 am.d[i] = 0;
829 for (i = tmp.top; i < top; i++)
830 tmp.d[i] = 0;
831
832 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 0);
833 bn_flip_n_scatter5_t4(am.d, top, powerbuf, 1);
834 if (!(*mul_worker) (tmp.d, am.d, am.d, np, n0) &&
835 !(*mul_worker) (tmp.d, am.d, am.d, np, n0))
836 bn_mul_mont_vis3(tmp.d, am.d, am.d, np, n0, top);
837 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 2);
838
839 for (i = 3; i < 32; i++) {
840 /* Calculate a^i = a^(i-1) * a */
841 if (!(*mul_worker) (tmp.d, tmp.d, am.d, np, n0) &&
842 !(*mul_worker) (tmp.d, tmp.d, am.d, np, n0))
843 bn_mul_mont_vis3(tmp.d, tmp.d, am.d, np, n0, top);
844 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, i);
845 }
846
847 /* switch to 64-bit domain */
848 np = alloca(top * sizeof(BN_ULONG));
849 top /= 2;
850 bn_flip_t4(np, mont->N.d, top);
851
852 bits--;
853 for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--)
854 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
855 bn_gather5_t4(tmp.d, top, powerbuf, wvalue);
856
857 /*
858 * Scan the exponent one window at a time starting from the most
859 * significant bits.
860 */
861 while (bits >= 0) {
862 if (bits < stride)
863 stride = bits + 1;
864 bits -= stride;
865 wvalue = bn_get_bits(p, bits + 1);
866
867 if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride))
868 continue;
869 /* retry once and fall back */
870 if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride))
871 continue;
872
873 bits += stride - 5;
874 wvalue >>= stride - 5;
875 wvalue &= 31;
876 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
877 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
878 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
879 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
880 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
881 bn_mul_mont_gather5_t4(tmp.d, tmp.d, powerbuf, np, n0, top,
882 wvalue);
883 }
884
885 bn_flip_t4(tmp.d, tmp.d, top);
886 top *= 2;
887 /* back to 32-bit domain */
888 tmp.top = top;
889 bn_correct_top(&tmp);
890 OPENSSL_cleanse(np, top * sizeof(BN_ULONG));
891 } else
892#endif
893#if defined(OPENSSL_BN_ASM_MONT5)
894 if (window == 5 && top > 1) {
895 /*
896 * This optimization uses ideas from http://eprint.iacr.org/2011/239,
897 * specifically optimization of cache-timing attack countermeasures
898 * and pre-computation optimization.
899 */
900
901 /*
902 * Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as
903 * 512-bit RSA is hardly relevant, we omit it to spare size...
904 */
905 void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap,
906 const void *table, const BN_ULONG *np,
907 const BN_ULONG *n0, int num, int power);
908 void bn_scatter5(const BN_ULONG *inp, size_t num,
909 void *table, size_t power);
910 void bn_gather5(BN_ULONG *out, size_t num, void *table, size_t power);
911 void bn_power5(BN_ULONG *rp, const BN_ULONG *ap,
912 const void *table, const BN_ULONG *np,
913 const BN_ULONG *n0, int num, int power);
914 int bn_get_bits5(const BN_ULONG *ap, int off);
915 int bn_from_montgomery(BN_ULONG *rp, const BN_ULONG *ap,
916 const BN_ULONG *not_used, const BN_ULONG *np,
917 const BN_ULONG *n0, int num);
918
919 BN_ULONG *n0 = mont->n0, *np;
920
921 /*
922 * BN_to_montgomery can contaminate words above .top [in
923 * BN_DEBUG[_DEBUG] build]...
924 */
925 for (i = am.top; i < top; i++)
926 am.d[i] = 0;
927 for (i = tmp.top; i < top; i++)
928 tmp.d[i] = 0;
929
930 /*
931 * copy mont->N.d[] to improve cache locality
932 */
933 for (np = am.d + top, i = 0; i < top; i++)
934 np[i] = mont->N.d[i];
935
936 bn_scatter5(tmp.d, top, powerbuf, 0);
937 bn_scatter5(am.d, am.top, powerbuf, 1);
938 bn_mul_mont(tmp.d, am.d, am.d, np, n0, top);
939 bn_scatter5(tmp.d, top, powerbuf, 2);
940
941# if 0
942 for (i = 3; i < 32; i++) {
943 /* Calculate a^i = a^(i-1) * a */
944 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
945 bn_scatter5(tmp.d, top, powerbuf, i);
946 }
947# else
948 /* same as above, but uses squaring for 1/2 of operations */
949 for (i = 4; i < 32; i *= 2) {
950 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
951 bn_scatter5(tmp.d, top, powerbuf, i);
952 }
953 for (i = 3; i < 8; i += 2) {
954 int j;
955 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
956 bn_scatter5(tmp.d, top, powerbuf, i);
957 for (j = 2 * i; j < 32; j *= 2) {
958 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
959 bn_scatter5(tmp.d, top, powerbuf, j);
960 }
961 }
962 for (; i < 16; i += 2) {
963 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
964 bn_scatter5(tmp.d, top, powerbuf, i);
965 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
966 bn_scatter5(tmp.d, top, powerbuf, 2 * i);
967 }
968 for (; i < 32; i += 2) {
969 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
970 bn_scatter5(tmp.d, top, powerbuf, i);
971 }
972# endif
973 bits--;
974 for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--)
975 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
976 bn_gather5(tmp.d, top, powerbuf, wvalue);
977
978 /*
979 * Scan the exponent one window at a time starting from the most
980 * significant bits.
981 */
982 if (top & 7)
983 while (bits >= 0) {
984 for (wvalue = 0, i = 0; i < 5; i++, bits--)
985 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
986
987 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
988 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
989 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
990 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
991 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
992 bn_mul_mont_gather5(tmp.d, tmp.d, powerbuf, np, n0, top,
993 wvalue);
994 } else {
995 while (bits >= 0) {
996 wvalue = bn_get_bits5(p->d, bits - 4);
997 bits -= 5;
998 bn_power5(tmp.d, tmp.d, powerbuf, np, n0, top, wvalue);
999 }
1000 }
1001
1002 ret = bn_from_montgomery(tmp.d, tmp.d, NULL, np, n0, top);
1003 tmp.top = top;
1004 bn_correct_top(&tmp);
1005 if (ret) {
1006 if (!BN_copy(rr, &tmp))
1007 ret = 0;
1008 goto err; /* non-zero ret means it's not error */
1009 }
1010 } else
1011#endif
1012 {
1013 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, window))
1014 goto err;
1015 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, window))
1016 goto err;
1017
1018 /*
1019 * If the window size is greater than 1, then calculate
1020 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even
1021 * powers could instead be computed as (a^(i/2))^2 to use the slight
1022 * performance advantage of sqr over mul).
1023 */
1024 if (window > 1) {
1025 if (!BN_mod_mul_montgomery(&tmp, &am, &am, mont, ctx))
1026 goto err;
1027 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2,
1028 window))
1029 goto err;
1030 for (i = 3; i < numPowers; i++) {
1031 /* Calculate a^i = a^(i-1) * a */
1032 if (!BN_mod_mul_montgomery(&tmp, &am, &tmp, mont, ctx))
1033 goto err;
1034 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i,
1035 window))
1036 goto err;
1037 }
1038 }
1039
1040 bits--;
1041 for (wvalue = 0, i = bits % window; i >= 0; i--, bits--)
1042 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
1043 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp, top, powerbuf, wvalue,
1044 window))
1045 goto err;
1046
1047 /*
1048 * Scan the exponent one window at a time starting from the most
1049 * significant bits.
1050 */
1051 while (bits >= 0) {
1052 wvalue = 0; /* The 'value' of the window */
1053
1054 /* Scan the window, squaring the result as we go */
1055 for (i = 0; i < window; i++, bits--) {
1056 if (!BN_mod_mul_montgomery(&tmp, &tmp, &tmp, mont, ctx))
1057 goto err;
1058 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
1059 }
1060
1061 /*
1062 * Fetch the appropriate pre-computed value from the pre-buf
1063 */
1064 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue,
1065 window))
1066 goto err;
1067
1068 /* Multiply the result into the intermediate result */
1069 if (!BN_mod_mul_montgomery(&tmp, &tmp, &am, mont, ctx))
1070 goto err;
1071 }
1072 }
1073
1074 /* Convert the final result from montgomery to standard format */
1075#if defined(SPARC_T4_MONT)
1076 if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
1077 am.d[0] = 1; /* borrow am */
1078 for (i = 1; i < top; i++)
1079 am.d[i] = 0;
1080 if (!BN_mod_mul_montgomery(rr, &tmp, &am, mont, ctx))
1081 goto err;
1082 } else
1083#endif
1084 if (!BN_from_montgomery(rr, &tmp, mont, ctx))
1085 goto err;
1086 ret = 1;
1087 err:
1088 if (in_mont == NULL)
1089 BN_MONT_CTX_free(mont);
1090 if (powerbuf != NULL) {
1091 OPENSSL_cleanse(powerbuf, powerbufLen);
1092 OPENSSL_free(powerbufFree);
1093 }
1094 BN_CTX_end(ctx);
1095 return (ret);
1096}
1097
1098int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
1099 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
1100{
1101 BN_MONT_CTX *mont = NULL;
1102 int b, bits, ret = 0;
1103 int r_is_one;
1104 BN_ULONG w, next_w;
1105 BIGNUM *d, *r, *t;
1106 BIGNUM *swap_tmp;
1107#define BN_MOD_MUL_WORD(r, w, m) \
1108 (BN_mul_word(r, (w)) && \
1109 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
1110 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
1111 /*
1112 * BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is
1113 * probably more overhead than always using BN_mod (which uses BN_copy if
1114 * a similar test returns true).
1115 */
1116 /*
1117 * We can use BN_mod and do not need BN_nnmod because our accumulator is
1118 * never negative (the result of BN_mod does not depend on the sign of
1119 * the modulus).
1120 */
1121#define BN_TO_MONTGOMERY_WORD(r, w, mont) \
1122 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
1123
1124 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
1125 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1126 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1127 return 0;
1128 }
1129
1130 bn_check_top(p);
1131 bn_check_top(m);
1132
1133 if (!BN_is_odd(m)) {
1134 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, BN_R_CALLED_WITH_EVEN_MODULUS);
1135 return (0);
1136 }
1137 if (m->top == 1)
1138 a %= m->d[0]; /* make sure that 'a' is reduced */
1139
1140 bits = BN_num_bits(p);
1141 if (bits == 0) {
1142 /* x**0 mod 1 is still zero. */
1143 if (BN_is_one(m)) {
1144 ret = 1;
1145 BN_zero(rr);
1146 } else {
1147 ret = BN_one(rr);
1148 }
1149 return ret;
1150 }
1151 if (a == 0) {
1152 BN_zero(rr);
1153 ret = 1;
1154 return ret;
1155 }
1156
1157 BN_CTX_start(ctx);
1158 d = BN_CTX_get(ctx);
1159 r = BN_CTX_get(ctx);
1160 t = BN_CTX_get(ctx);
1161 if (d == NULL || r == NULL || t == NULL)
1162 goto err;
1163
1164 if (in_mont != NULL)
1165 mont = in_mont;
1166 else {
1167 if ((mont = BN_MONT_CTX_new()) == NULL)
1168 goto err;
1169 if (!BN_MONT_CTX_set(mont, m, ctx))
1170 goto err;
1171 }
1172
1173 r_is_one = 1; /* except for Montgomery factor */
1174
1175 /* bits-1 >= 0 */
1176
1177 /* The result is accumulated in the product r*w. */
1178 w = a; /* bit 'bits-1' of 'p' is always set */
1179 for (b = bits - 2; b >= 0; b--) {
1180 /* First, square r*w. */
1181 next_w = w * w;
1182 if ((next_w / w) != w) { /* overflow */
1183 if (r_is_one) {
1184 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1185 goto err;
1186 r_is_one = 0;
1187 } else {
1188 if (!BN_MOD_MUL_WORD(r, w, m))
1189 goto err;
1190 }
1191 next_w = 1;
1192 }
1193 w = next_w;
1194 if (!r_is_one) {
1195 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
1196 goto err;
1197 }
1198
1199 /* Second, multiply r*w by 'a' if exponent bit is set. */
1200 if (BN_is_bit_set(p, b)) {
1201 next_w = w * a;
1202 if ((next_w / a) != w) { /* overflow */
1203 if (r_is_one) {
1204 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1205 goto err;
1206 r_is_one = 0;
1207 } else {
1208 if (!BN_MOD_MUL_WORD(r, w, m))
1209 goto err;
1210 }
1211 next_w = a;
1212 }
1213 w = next_w;
1214 }
1215 }
1216
1217 /* Finally, set r:=r*w. */
1218 if (w != 1) {
1219 if (r_is_one) {
1220 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1221 goto err;
1222 r_is_one = 0;
1223 } else {
1224 if (!BN_MOD_MUL_WORD(r, w, m))
1225 goto err;
1226 }
1227 }
1228
1229 if (r_is_one) { /* can happen only if a == 1 */
1230 if (!BN_one(rr))
1231 goto err;
1232 } else {
1233 if (!BN_from_montgomery(rr, r, mont, ctx))
1234 goto err;
1235 }
1236 ret = 1;
1237 err:
1238 if (in_mont == NULL)
1239 BN_MONT_CTX_free(mont);
1240 BN_CTX_end(ctx);
1241 bn_check_top(rr);
1242 return (ret);
1243}
1244
1245/* The old fallback, simple version :-) */
1246int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
1247 const BIGNUM *m, BN_CTX *ctx)
1248{
1249 int i, j, bits, ret = 0, wstart, wend, window, wvalue;
1250 int start = 1;
1251 BIGNUM *d;
1252 /* Table of variables obtained from 'ctx' */
1253 BIGNUM *val[TABLE_SIZE];
1254
1255 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
1256 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1257 BNerr(BN_F_BN_MOD_EXP_SIMPLE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1258 return 0;
1259 }
1260
1261 bits = BN_num_bits(p);
1262 if (bits == 0) {
1263 /* x**0 mod 1 is still zero. */
1264 if (BN_is_one(m)) {
1265 ret = 1;
1266 BN_zero(r);
1267 } else {
1268 ret = BN_one(r);
1269 }
1270 return ret;
1271 }
1272
1273 BN_CTX_start(ctx);
1274 d = BN_CTX_get(ctx);
1275 val[0] = BN_CTX_get(ctx);
1276 if (!d || !val[0])
1277 goto err;
1278
1279 if (!BN_nnmod(val[0], a, m, ctx))
1280 goto err; /* 1 */
1281 if (BN_is_zero(val[0])) {
1282 BN_zero(r);
1283 ret = 1;
1284 goto err;
1285 }
1286
1287 window = BN_window_bits_for_exponent_size(bits);
1288 if (window > 1) {
1289 if (!BN_mod_mul(d, val[0], val[0], m, ctx))
1290 goto err; /* 2 */
1291 j = 1 << (window - 1);
1292 for (i = 1; i < j; i++) {
1293 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
1294 !BN_mod_mul(val[i], val[i - 1], d, m, ctx))
1295 goto err;
1296 }
1297 }
1298
1299 start = 1; /* This is used to avoid multiplication etc
1300 * when there is only the value '1' in the
1301 * buffer. */
1302 wvalue = 0; /* The 'value' of the window */
1303 wstart = bits - 1; /* The top bit of the window */
1304 wend = 0; /* The bottom bit of the window */
1305
1306 if (!BN_one(r))
1307 goto err;
1308
1309 for (;;) {
1310 if (BN_is_bit_set(p, wstart) == 0) {
1311 if (!start)
1312 if (!BN_mod_mul(r, r, r, m, ctx))
1313 goto err;
1314 if (wstart == 0)
1315 break;
1316 wstart--;
1317 continue;
1318 }
1319 /*
1320 * We now have wstart on a 'set' bit, we now need to work out how bit
1321 * a window to do. To do this we need to scan forward until the last
1322 * set bit before the end of the window
1323 */
1324 j = wstart;
1325 wvalue = 1;
1326 wend = 0;
1327 for (i = 1; i < window; i++) {
1328 if (wstart - i < 0)
1329 break;
1330 if (BN_is_bit_set(p, wstart - i)) {
1331 wvalue <<= (i - wend);
1332 wvalue |= 1;
1333 wend = i;
1334 }
1335 }
1336
1337 /* wend is the size of the current window */
1338 j = wend + 1;
1339 /* add the 'bytes above' */
1340 if (!start)
1341 for (i = 0; i < j; i++) {
1342 if (!BN_mod_mul(r, r, r, m, ctx))
1343 goto err;
1344 }
1345
1346 /* wvalue will be an odd number < 2^window */
1347 if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx))
1348 goto err;
1349
1350 /* move the 'window' down further */
1351 wstart -= wend + 1;
1352 wvalue = 0;
1353 start = 0;
1354 if (wstart < 0)
1355 break;
1356 }
1357 ret = 1;
1358 err:
1359 BN_CTX_end(ctx);
1360 bn_check_top(r);
1361 return (ret);
1362}
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