1 /*
2 * Copyright 1995-2023 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.h"
12 #include "bn_local.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"
33 extern 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 /*
41 * Beyond this limit the constant time code is disabled due to
42 * the possible overflow in the computation of powerbufLen in
43 * BN_mod_exp_mont_consttime.
44 * When this limit is exceeded, the computation will be done using
45 * non-constant time code, but it will take very long.
46 */
47 #define BN_CONSTTIME_SIZE_LIMIT (INT_MAX / BN_BYTES / 256)
48
49 /* this one works - simple but works */
BN_exp(BIGNUM * r,const BIGNUM * a,const BIGNUM * p,BN_CTX * ctx)50 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
51 {
52 int i, bits, ret = 0;
53 BIGNUM *v, *rr;
54
55 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
56 || BN_get_flags(a, BN_FLG_CONSTTIME) != 0) {
57 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
58 BNerr(BN_F_BN_EXP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
59 return 0;
60 }
61
62 BN_CTX_start(ctx);
63 rr = ((r == a) || (r == p)) ? BN_CTX_get(ctx) : r;
64 v = BN_CTX_get(ctx);
65 if (rr == NULL || v == NULL)
66 goto err;
67
68 if (BN_copy(v, a) == NULL)
69 goto err;
70 bits = BN_num_bits(p);
71
72 if (BN_is_odd(p)) {
73 if (BN_copy(rr, a) == NULL)
74 goto err;
75 } else {
76 if (!BN_one(rr))
77 goto err;
78 }
79
80 for (i = 1; i < bits; i++) {
81 if (!BN_sqr(v, v, ctx))
82 goto err;
83 if (BN_is_bit_set(p, i)) {
84 if (!BN_mul(rr, rr, v, ctx))
85 goto err;
86 }
87 }
88 if (r != rr && BN_copy(r, rr) == NULL)
89 goto err;
90
91 ret = 1;
92 err:
93 BN_CTX_end(ctx);
94 bn_check_top(r);
95 return ret;
96 }
97
BN_mod_exp(BIGNUM * r,const BIGNUM * a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx)98 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
99 BN_CTX *ctx)
100 {
101 int ret;
102
103 bn_check_top(a);
104 bn_check_top(p);
105 bn_check_top(m);
106
107 /*-
108 * For even modulus m = 2^k*m_odd, it might make sense to compute
109 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery
110 * exponentiation for the odd part), using appropriate exponent
111 * reductions, and combine the results using the CRT.
112 *
113 * For now, we use Montgomery only if the modulus is odd; otherwise,
114 * exponentiation using the reciprocal-based quick remaindering
115 * algorithm is used.
116 *
117 * (Timing obtained with expspeed.c [computations a^p mod m
118 * where a, p, m are of the same length: 256, 512, 1024, 2048,
119 * 4096, 8192 bits], compared to the running time of the
120 * standard algorithm:
121 *
122 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
123 * 55 .. 77 % [UltraSparc processor, but
124 * debug-solaris-sparcv8-gcc conf.]
125 *
126 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
127 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
128 *
129 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
130 * at 2048 and more bits, but at 512 and 1024 bits, it was
131 * slower even than the standard algorithm!
132 *
133 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
134 * should be obtained when the new Montgomery reduction code
135 * has been integrated into OpenSSL.)
136 */
137
138 #define MONT_MUL_MOD
139 #define MONT_EXP_WORD
140 #define RECP_MUL_MOD
141
142 #ifdef MONT_MUL_MOD
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_get_flags(a, BN_FLG_CONSTTIME) == 0)
148 && (BN_get_flags(m, BN_FLG_CONSTTIME) == 0)) {
149 BN_ULONG A = a->d[0];
150 ret = BN_mod_exp_mont_word(r, A, p, m, ctx, NULL);
151 } else
152 # endif
153 ret = BN_mod_exp_mont(r, a, p, m, ctx, NULL);
154 } else
155 #endif
156 #ifdef RECP_MUL_MOD
157 {
158 ret = BN_mod_exp_recp(r, a, p, m, ctx);
159 }
160 #else
161 {
162 ret = BN_mod_exp_simple(r, a, p, m, ctx);
163 }
164 #endif
165
166 bn_check_top(r);
167 return ret;
168 }
169
BN_mod_exp_recp(BIGNUM * r,const BIGNUM * a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx)170 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
171 const BIGNUM *m, BN_CTX *ctx)
172 {
173 int i, j, bits, ret = 0, wstart, wend, window, wvalue;
174 int start = 1;
175 BIGNUM *aa;
176 /* Table of variables obtained from 'ctx' */
177 BIGNUM *val[TABLE_SIZE];
178 BN_RECP_CTX recp;
179
180 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
181 || BN_get_flags(a, BN_FLG_CONSTTIME) != 0
182 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) {
183 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
184 BNerr(BN_F_BN_MOD_EXP_RECP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
185 return 0;
186 }
187
188 bits = BN_num_bits(p);
189 if (bits == 0) {
190 /* x**0 mod 1, or x**0 mod -1 is still zero. */
191 if (BN_abs_is_word(m, 1)) {
192 ret = 1;
193 BN_zero(r);
194 } else {
195 ret = BN_one(r);
196 }
197 return ret;
198 }
199
200 BN_RECP_CTX_init(&recp);
201
202 BN_CTX_start(ctx);
203 aa = BN_CTX_get(ctx);
204 val[0] = BN_CTX_get(ctx);
205 if (val[0] == NULL)
206 goto err;
207
208 if (m->neg) {
209 /* ignore sign of 'm' */
210 if (!BN_copy(aa, m))
211 goto err;
212 aa->neg = 0;
213 if (BN_RECP_CTX_set(&recp, aa, ctx) <= 0)
214 goto err;
215 } else {
216 if (BN_RECP_CTX_set(&recp, m, ctx) <= 0)
217 goto err;
218 }
219
220 if (!BN_nnmod(val[0], a, m, ctx))
221 goto err; /* 1 */
222 if (BN_is_zero(val[0])) {
223 BN_zero(r);
224 ret = 1;
225 goto err;
226 }
227
228 window = BN_window_bits_for_exponent_size(bits);
229 if (window > 1) {
230 if (!BN_mod_mul_reciprocal(aa, val[0], val[0], &recp, ctx))
231 goto err; /* 2 */
232 j = 1 << (window - 1);
233 for (i = 1; i < j; i++) {
234 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
235 !BN_mod_mul_reciprocal(val[i], val[i - 1], aa, &recp, ctx))
236 goto err;
237 }
238 }
239
240 start = 1; /* This is used to avoid multiplication etc
241 * when there is only the value '1' in the
242 * buffer. */
243 wvalue = 0; /* The 'value' of the window */
244 wstart = bits - 1; /* The top bit of the window */
245 wend = 0; /* The bottom bit of the window */
246
247 if (!BN_one(r))
248 goto err;
249
250 for (;;) {
251 if (BN_is_bit_set(p, wstart) == 0) {
252 if (!start)
253 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
254 goto err;
255 if (wstart == 0)
256 break;
257 wstart--;
258 continue;
259 }
260 /*
261 * We now have wstart on a 'set' bit, we now need to work out how bit
262 * a window to do. To do this we need to scan forward until the last
263 * set bit before the end of the window
264 */
265 j = wstart;
266 wvalue = 1;
267 wend = 0;
268 for (i = 1; i < window; i++) {
269 if (wstart - i < 0)
270 break;
271 if (BN_is_bit_set(p, wstart - i)) {
272 wvalue <<= (i - wend);
273 wvalue |= 1;
274 wend = i;
275 }
276 }
277
278 /* wend is the size of the current window */
279 j = wend + 1;
280 /* add the 'bytes above' */
281 if (!start)
282 for (i = 0; i < j; i++) {
283 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
284 goto err;
285 }
286
287 /* wvalue will be an odd number < 2^window */
288 if (!BN_mod_mul_reciprocal(r, r, val[wvalue >> 1], &recp, ctx))
289 goto err;
290
291 /* move the 'window' down further */
292 wstart -= wend + 1;
293 wvalue = 0;
294 start = 0;
295 if (wstart < 0)
296 break;
297 }
298 ret = 1;
299 err:
300 BN_CTX_end(ctx);
301 BN_RECP_CTX_free(&recp);
302 bn_check_top(r);
303 return ret;
304 }
305
BN_mod_exp_mont(BIGNUM * rr,const BIGNUM * a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx,BN_MONT_CTX * in_mont)306 int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
307 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
308 {
309 int i, j, bits, ret = 0, wstart, wend, window, wvalue;
310 int start = 1;
311 BIGNUM *d, *r;
312 const BIGNUM *aa;
313 /* Table of variables obtained from 'ctx' */
314 BIGNUM *val[TABLE_SIZE];
315 BN_MONT_CTX *mont = NULL;
316
317 bn_check_top(a);
318 bn_check_top(p);
319 bn_check_top(m);
320
321 if (!BN_is_odd(m)) {
322 BNerr(BN_F_BN_MOD_EXP_MONT, BN_R_CALLED_WITH_EVEN_MODULUS);
323 return 0;
324 }
325
326 if (m->top <= BN_CONSTTIME_SIZE_LIMIT
327 && (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
328 || BN_get_flags(a, BN_FLG_CONSTTIME) != 0
329 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0)) {
330 return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
331 }
332
333 bits = BN_num_bits(p);
334 if (bits == 0) {
335 /* x**0 mod 1, or x**0 mod -1 is still zero. */
336 if (BN_abs_is_word(m, 1)) {
337 ret = 1;
338 BN_zero(rr);
339 } else {
340 ret = BN_one(rr);
341 }
342 return ret;
343 }
344
345 BN_CTX_start(ctx);
346 d = BN_CTX_get(ctx);
347 r = BN_CTX_get(ctx);
348 val[0] = BN_CTX_get(ctx);
349 if (val[0] == NULL)
350 goto err;
351
352 /*
353 * If this is not done, things will break in the montgomery part
354 */
355
356 if (in_mont != NULL)
357 mont = in_mont;
358 else {
359 if ((mont = BN_MONT_CTX_new()) == NULL)
360 goto err;
361 if (!BN_MONT_CTX_set(mont, m, ctx))
362 goto err;
363 }
364
365 if (a->neg || BN_ucmp(a, m) >= 0) {
366 if (!BN_nnmod(val[0], a, m, ctx))
367 goto err;
368 aa = val[0];
369 } else
370 aa = a;
371 if (!bn_to_mont_fixed_top(val[0], aa, mont, ctx))
372 goto err; /* 1 */
373
374 window = BN_window_bits_for_exponent_size(bits);
375 if (window > 1) {
376 if (!bn_mul_mont_fixed_top(d, val[0], val[0], mont, ctx))
377 goto err; /* 2 */
378 j = 1 << (window - 1);
379 for (i = 1; i < j; i++) {
380 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
381 !bn_mul_mont_fixed_top(val[i], val[i - 1], d, mont, ctx))
382 goto err;
383 }
384 }
385
386 start = 1; /* This is used to avoid multiplication etc
387 * when there is only the value '1' in the
388 * buffer. */
389 wvalue = 0; /* The 'value' of the window */
390 wstart = bits - 1; /* The top bit of the window */
391 wend = 0; /* The bottom bit of the window */
392
393 #if 1 /* by Shay Gueron's suggestion */
394 j = m->top; /* borrow j */
395 if (m->d[j - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
396 if (bn_wexpand(r, j) == NULL)
397 goto err;
398 /* 2^(top*BN_BITS2) - m */
399 r->d[0] = (0 - m->d[0]) & BN_MASK2;
400 for (i = 1; i < j; i++)
401 r->d[i] = (~m->d[i]) & BN_MASK2;
402 r->top = j;
403 r->flags |= BN_FLG_FIXED_TOP;
404 } else
405 #endif
406 if (!bn_to_mont_fixed_top(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_mul_mont_fixed_top(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_mul_mont_fixed_top(r, r, r, mont, ctx))
443 goto err;
444 }
445
446 /* wvalue will be an odd number < 2^window */
447 if (!bn_mul_mont_fixed_top(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 /*
458 * Done with zero-padded intermediate BIGNUMs. Final BN_from_montgomery
459 * removes padding [if any] and makes return value suitable for public
460 * API consumer.
461 */
462 #if defined(SPARC_T4_MONT)
463 if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
464 j = mont->N.top; /* borrow j */
465 val[0]->d[0] = 1; /* borrow val[0] */
466 for (i = 1; i < j; i++)
467 val[0]->d[i] = 0;
468 val[0]->top = j;
469 if (!BN_mod_mul_montgomery(rr, r, val[0], mont, ctx))
470 goto err;
471 } else
472 #endif
473 if (!BN_from_montgomery(rr, r, mont, ctx))
474 goto err;
475 ret = 1;
476 err:
477 if (in_mont == NULL)
478 BN_MONT_CTX_free(mont);
479 BN_CTX_end(ctx);
480 bn_check_top(rr);
481 return ret;
482 }
483
bn_get_bits(const BIGNUM * a,int bitpos)484 static BN_ULONG bn_get_bits(const BIGNUM *a, int bitpos)
485 {
486 BN_ULONG ret = 0;
487 int wordpos;
488
489 wordpos = bitpos / BN_BITS2;
490 bitpos %= BN_BITS2;
491 if (wordpos >= 0 && wordpos < a->top) {
492 ret = a->d[wordpos] & BN_MASK2;
493 if (bitpos) {
494 ret >>= bitpos;
495 if (++wordpos < a->top)
496 ret |= a->d[wordpos] << (BN_BITS2 - bitpos);
497 }
498 }
499
500 return ret & BN_MASK2;
501 }
502
503 /*
504 * BN_mod_exp_mont_consttime() stores the precomputed powers in a specific
505 * layout so that accessing any of these table values shows the same access
506 * pattern as far as cache lines are concerned. The following functions are
507 * used to transfer a BIGNUM from/to that table.
508 */
509
MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM * b,int top,unsigned char * buf,int idx,int window)510 static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top,
511 unsigned char *buf, int idx,
512 int window)
513 {
514 int i, j;
515 int width = 1 << window;
516 BN_ULONG *table = (BN_ULONG *)buf;
517
518 if (top > b->top)
519 top = b->top; /* this works because 'buf' is explicitly
520 * zeroed */
521 for (i = 0, j = idx; i < top; i++, j += width) {
522 table[j] = b->d[i];
523 }
524
525 return 1;
526 }
527
MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM * b,int top,unsigned char * buf,int idx,int window)528 static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top,
529 unsigned char *buf, int idx,
530 int window)
531 {
532 int i, j;
533 int width = 1 << window;
534 /*
535 * We declare table 'volatile' in order to discourage compiler
536 * from reordering loads from the table. Concern is that if
537 * reordered in specific manner loads might give away the
538 * information we are trying to conceal. Some would argue that
539 * compiler can reorder them anyway, but it can as well be
540 * argued that doing so would be violation of standard...
541 */
542 volatile BN_ULONG *table = (volatile BN_ULONG *)buf;
543
544 if (bn_wexpand(b, top) == NULL)
545 return 0;
546
547 if (window <= 3) {
548 for (i = 0; i < top; i++, table += width) {
549 BN_ULONG acc = 0;
550
551 for (j = 0; j < width; j++) {
552 acc |= table[j] &
553 ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1));
554 }
555
556 b->d[i] = acc;
557 }
558 } else {
559 int xstride = 1 << (window - 2);
560 BN_ULONG y0, y1, y2, y3;
561
562 i = idx >> (window - 2); /* equivalent of idx / xstride */
563 idx &= xstride - 1; /* equivalent of idx % xstride */
564
565 y0 = (BN_ULONG)0 - (constant_time_eq_int(i,0)&1);
566 y1 = (BN_ULONG)0 - (constant_time_eq_int(i,1)&1);
567 y2 = (BN_ULONG)0 - (constant_time_eq_int(i,2)&1);
568 y3 = (BN_ULONG)0 - (constant_time_eq_int(i,3)&1);
569
570 for (i = 0; i < top; i++, table += width) {
571 BN_ULONG acc = 0;
572
573 for (j = 0; j < xstride; j++) {
574 acc |= ( (table[j + 0 * xstride] & y0) |
575 (table[j + 1 * xstride] & y1) |
576 (table[j + 2 * xstride] & y2) |
577 (table[j + 3 * xstride] & y3) )
578 & ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1));
579 }
580
581 b->d[i] = acc;
582 }
583 }
584
585 b->top = top;
586 b->flags |= BN_FLG_FIXED_TOP;
587 return 1;
588 }
589
590 /*
591 * Given a pointer value, compute the next address that is a cache line
592 * multiple.
593 */
594 #define MOD_EXP_CTIME_ALIGN(x_) \
595 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
596
597 /*
598 * This variant of BN_mod_exp_mont() uses fixed windows and the special
599 * precomputation memory layout to limit data-dependency to a minimum to
600 * protect secret exponents (cf. the hyper-threading timing attacks pointed
601 * out by Colin Percival,
602 * http://www.daemonology.net/hyperthreading-considered-harmful/)
603 */
BN_mod_exp_mont_consttime(BIGNUM * rr,const BIGNUM * a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx,BN_MONT_CTX * in_mont)604 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
605 const BIGNUM *m, BN_CTX *ctx,
606 BN_MONT_CTX *in_mont)
607 {
608 int i, bits, ret = 0, window, wvalue, wmask, window0;
609 int top;
610 BN_MONT_CTX *mont = NULL;
611
612 int numPowers;
613 unsigned char *powerbufFree = NULL;
614 int powerbufLen = 0;
615 unsigned char *powerbuf = NULL;
616 BIGNUM tmp, am;
617 #if defined(SPARC_T4_MONT)
618 unsigned int t4 = 0;
619 #endif
620
621 bn_check_top(a);
622 bn_check_top(p);
623 bn_check_top(m);
624
625 if (!BN_is_odd(m)) {
626 BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME, BN_R_CALLED_WITH_EVEN_MODULUS);
627 return 0;
628 }
629
630 top = m->top;
631
632 if (top > BN_CONSTTIME_SIZE_LIMIT) {
633 /* Prevent overflowing the powerbufLen computation below */
634 return BN_mod_exp_mont(rr, a, p, m, ctx, in_mont);
635 }
636
637 /*
638 * Use all bits stored in |p|, rather than |BN_num_bits|, so we do not leak
639 * whether the top bits are zero.
640 */
641 bits = p->top * BN_BITS2;
642 if (bits == 0) {
643 /* x**0 mod 1, or x**0 mod -1 is still zero. */
644 if (BN_abs_is_word(m, 1)) {
645 ret = 1;
646 BN_zero(rr);
647 } else {
648 ret = BN_one(rr);
649 }
650 return ret;
651 }
652
653 BN_CTX_start(ctx);
654
655 /*
656 * Allocate a montgomery context if it was not supplied by the caller. If
657 * this is not done, things will break in the montgomery part.
658 */
659 if (in_mont != NULL)
660 mont = in_mont;
661 else {
662 if ((mont = BN_MONT_CTX_new()) == NULL)
663 goto err;
664 if (!BN_MONT_CTX_set(mont, m, ctx))
665 goto err;
666 }
667
668 if (a->neg || BN_ucmp(a, m) >= 0) {
669 BIGNUM *reduced = BN_CTX_get(ctx);
670 if (reduced == NULL
671 || !BN_nnmod(reduced, a, m, ctx)) {
672 goto err;
673 }
674 a = reduced;
675 }
676
677 #ifdef RSAZ_ENABLED
678 /*
679 * If the size of the operands allow it, perform the optimized
680 * RSAZ exponentiation. For further information see
681 * crypto/bn/rsaz_exp.c and accompanying assembly modules.
682 */
683 if ((16 == a->top) && (16 == p->top) && (BN_num_bits(m) == 1024)
684 && rsaz_avx2_eligible()) {
685 if (NULL == bn_wexpand(rr, 16))
686 goto err;
687 RSAZ_1024_mod_exp_avx2(rr->d, a->d, p->d, m->d, mont->RR.d,
688 mont->n0[0]);
689 rr->top = 16;
690 rr->neg = 0;
691 bn_correct_top(rr);
692 ret = 1;
693 goto err;
694 } else if ((8 == a->top) && (8 == p->top) && (BN_num_bits(m) == 512)) {
695 if (NULL == bn_wexpand(rr, 8))
696 goto err;
697 RSAZ_512_mod_exp(rr->d, a->d, p->d, m->d, mont->n0[0], mont->RR.d);
698 rr->top = 8;
699 rr->neg = 0;
700 bn_correct_top(rr);
701 ret = 1;
702 goto err;
703 }
704 #endif
705
706 /* Get the window size to use with size of p. */
707 window = BN_window_bits_for_ctime_exponent_size(bits);
708 #if defined(SPARC_T4_MONT)
709 if (window >= 5 && (top & 15) == 0 && top <= 64 &&
710 (OPENSSL_sparcv9cap_P[1] & (CFR_MONTMUL | CFR_MONTSQR)) ==
711 (CFR_MONTMUL | CFR_MONTSQR) && (t4 = OPENSSL_sparcv9cap_P[0]))
712 window = 5;
713 else
714 #endif
715 #if defined(OPENSSL_BN_ASM_MONT5)
716 if (window >= 5 && top <= BN_SOFT_LIMIT) {
717 window = 5; /* ~5% improvement for RSA2048 sign, and even
718 * for RSA4096 */
719 /* reserve space for mont->N.d[] copy */
720 powerbufLen += top * sizeof(mont->N.d[0]);
721 }
722 #endif
723 (void)0;
724
725 /*
726 * Allocate a buffer large enough to hold all of the pre-computed powers
727 * of am, am itself and tmp.
728 */
729 numPowers = 1 << window;
730 powerbufLen += sizeof(m->d[0]) * (top * numPowers +
731 ((2 * top) >
732 numPowers ? (2 * top) : numPowers));
733 #ifdef alloca
734 if (powerbufLen < 3072)
735 powerbufFree =
736 alloca(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
737 else
738 #endif
739 if ((powerbufFree =
740 OPENSSL_malloc(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH))
741 == NULL)
742 goto err;
743
744 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
745 memset(powerbuf, 0, powerbufLen);
746
747 #ifdef alloca
748 if (powerbufLen < 3072)
749 powerbufFree = NULL;
750 #endif
751
752 /* lay down tmp and am right after powers table */
753 tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers);
754 am.d = tmp.d + top;
755 tmp.top = am.top = 0;
756 tmp.dmax = am.dmax = top;
757 tmp.neg = am.neg = 0;
758 tmp.flags = am.flags = BN_FLG_STATIC_DATA;
759
760 /* prepare a^0 in Montgomery domain */
761 #if 1 /* by Shay Gueron's suggestion */
762 if (m->d[top - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
763 /* 2^(top*BN_BITS2) - m */
764 tmp.d[0] = (0 - m->d[0]) & BN_MASK2;
765 for (i = 1; i < top; i++)
766 tmp.d[i] = (~m->d[i]) & BN_MASK2;
767 tmp.top = top;
768 } else
769 #endif
770 if (!bn_to_mont_fixed_top(&tmp, BN_value_one(), mont, ctx))
771 goto err;
772
773 /* prepare a^1 in Montgomery domain */
774 if (!bn_to_mont_fixed_top(&am, a, mont, ctx))
775 goto err;
776
777 if (top > BN_SOFT_LIMIT)
778 goto fallback;
779
780 #if defined(SPARC_T4_MONT)
781 if (t4) {
782 typedef int (*bn_pwr5_mont_f) (BN_ULONG *tp, const BN_ULONG *np,
783 const BN_ULONG *n0, const void *table,
784 int power, int bits);
785 int bn_pwr5_mont_t4_8(BN_ULONG *tp, const BN_ULONG *np,
786 const BN_ULONG *n0, const void *table,
787 int power, int bits);
788 int bn_pwr5_mont_t4_16(BN_ULONG *tp, const BN_ULONG *np,
789 const BN_ULONG *n0, const void *table,
790 int power, int bits);
791 int bn_pwr5_mont_t4_24(BN_ULONG *tp, const BN_ULONG *np,
792 const BN_ULONG *n0, const void *table,
793 int power, int bits);
794 int bn_pwr5_mont_t4_32(BN_ULONG *tp, const BN_ULONG *np,
795 const BN_ULONG *n0, const void *table,
796 int power, int bits);
797 static const bn_pwr5_mont_f pwr5_funcs[4] = {
798 bn_pwr5_mont_t4_8, bn_pwr5_mont_t4_16,
799 bn_pwr5_mont_t4_24, bn_pwr5_mont_t4_32
800 };
801 bn_pwr5_mont_f pwr5_worker = pwr5_funcs[top / 16 - 1];
802
803 typedef int (*bn_mul_mont_f) (BN_ULONG *rp, const BN_ULONG *ap,
804 const void *bp, const BN_ULONG *np,
805 const BN_ULONG *n0);
806 int bn_mul_mont_t4_8(BN_ULONG *rp, const BN_ULONG *ap, const void *bp,
807 const BN_ULONG *np, const BN_ULONG *n0);
808 int bn_mul_mont_t4_16(BN_ULONG *rp, const BN_ULONG *ap,
809 const void *bp, const BN_ULONG *np,
810 const BN_ULONG *n0);
811 int bn_mul_mont_t4_24(BN_ULONG *rp, const BN_ULONG *ap,
812 const void *bp, const BN_ULONG *np,
813 const BN_ULONG *n0);
814 int bn_mul_mont_t4_32(BN_ULONG *rp, const BN_ULONG *ap,
815 const void *bp, const BN_ULONG *np,
816 const BN_ULONG *n0);
817 static const bn_mul_mont_f mul_funcs[4] = {
818 bn_mul_mont_t4_8, bn_mul_mont_t4_16,
819 bn_mul_mont_t4_24, bn_mul_mont_t4_32
820 };
821 bn_mul_mont_f mul_worker = mul_funcs[top / 16 - 1];
822
823 void bn_mul_mont_vis3(BN_ULONG *rp, const BN_ULONG *ap,
824 const void *bp, const BN_ULONG *np,
825 const BN_ULONG *n0, int num);
826 void bn_mul_mont_t4(BN_ULONG *rp, const BN_ULONG *ap,
827 const void *bp, const BN_ULONG *np,
828 const BN_ULONG *n0, int num);
829 void bn_mul_mont_gather5_t4(BN_ULONG *rp, const BN_ULONG *ap,
830 const void *table, const BN_ULONG *np,
831 const BN_ULONG *n0, int num, int power);
832 void bn_flip_n_scatter5_t4(const BN_ULONG *inp, size_t num,
833 void *table, size_t power);
834 void bn_gather5_t4(BN_ULONG *out, size_t num,
835 void *table, size_t power);
836 void bn_flip_t4(BN_ULONG *dst, BN_ULONG *src, size_t num);
837
838 BN_ULONG *np = mont->N.d, *n0 = mont->n0;
839 int stride = 5 * (6 - (top / 16 - 1)); /* multiple of 5, but less
840 * than 32 */
841
842 /*
843 * BN_to_montgomery can contaminate words above .top [in
844 * BN_DEBUG[_DEBUG] build]...
845 */
846 for (i = am.top; i < top; i++)
847 am.d[i] = 0;
848 for (i = tmp.top; i < top; i++)
849 tmp.d[i] = 0;
850
851 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 0);
852 bn_flip_n_scatter5_t4(am.d, top, powerbuf, 1);
853 if (!(*mul_worker) (tmp.d, am.d, am.d, np, n0) &&
854 !(*mul_worker) (tmp.d, am.d, am.d, np, n0))
855 bn_mul_mont_vis3(tmp.d, am.d, am.d, np, n0, top);
856 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 2);
857
858 for (i = 3; i < 32; i++) {
859 /* Calculate a^i = a^(i-1) * a */
860 if (!(*mul_worker) (tmp.d, tmp.d, am.d, np, n0) &&
861 !(*mul_worker) (tmp.d, tmp.d, am.d, np, n0))
862 bn_mul_mont_vis3(tmp.d, tmp.d, am.d, np, n0, top);
863 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, i);
864 }
865
866 /* switch to 64-bit domain */
867 np = alloca(top * sizeof(BN_ULONG));
868 top /= 2;
869 bn_flip_t4(np, mont->N.d, top);
870
871 /*
872 * The exponent may not have a whole number of fixed-size windows.
873 * To simplify the main loop, the initial window has between 1 and
874 * full-window-size bits such that what remains is always a whole
875 * number of windows
876 */
877 window0 = (bits - 1) % 5 + 1;
878 wmask = (1 << window0) - 1;
879 bits -= window0;
880 wvalue = bn_get_bits(p, bits) & wmask;
881 bn_gather5_t4(tmp.d, top, powerbuf, wvalue);
882
883 /*
884 * Scan the exponent one window at a time starting from the most
885 * significant bits.
886 */
887 while (bits > 0) {
888 if (bits < stride)
889 stride = bits;
890 bits -= stride;
891 wvalue = bn_get_bits(p, bits);
892
893 if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride))
894 continue;
895 /* retry once and fall back */
896 if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride))
897 continue;
898
899 bits += stride - 5;
900 wvalue >>= stride - 5;
901 wvalue &= 31;
902 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
903 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
904 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
905 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
906 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
907 bn_mul_mont_gather5_t4(tmp.d, tmp.d, powerbuf, np, n0, top,
908 wvalue);
909 }
910
911 bn_flip_t4(tmp.d, tmp.d, top);
912 top *= 2;
913 /* back to 32-bit domain */
914 tmp.top = top;
915 bn_correct_top(&tmp);
916 OPENSSL_cleanse(np, top * sizeof(BN_ULONG));
917 } else
918 #endif
919 #if defined(OPENSSL_BN_ASM_MONT5)
920 if (window == 5 && top > 1) {
921 /*
922 * This optimization uses ideas from https://eprint.iacr.org/2011/239,
923 * specifically optimization of cache-timing attack countermeasures,
924 * pre-computation optimization, and Almost Montgomery Multiplication.
925 *
926 * The paper discusses a 4-bit window to optimize 512-bit modular
927 * exponentiation, used in RSA-1024 with CRT, but RSA-1024 is no longer
928 * important.
929 *
930 * |bn_mul_mont_gather5| and |bn_power5| implement the "almost"
931 * reduction variant, so the values here may not be fully reduced.
932 * They are bounded by R (i.e. they fit in |top| words), not |m|.
933 * Additionally, we pass these "almost" reduced inputs into
934 * |bn_mul_mont|, which implements the normal reduction variant.
935 * Given those inputs, |bn_mul_mont| may not give reduced
936 * output, but it will still produce "almost" reduced output.
937 */
938 void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap,
939 const void *table, const BN_ULONG *np,
940 const BN_ULONG *n0, int num, int power);
941 void bn_scatter5(const BN_ULONG *inp, size_t num,
942 void *table, size_t power);
943 void bn_gather5(BN_ULONG *out, size_t num, void *table, size_t power);
944 void bn_power5(BN_ULONG *rp, const BN_ULONG *ap,
945 const void *table, const BN_ULONG *np,
946 const BN_ULONG *n0, int num, int power);
947 int bn_get_bits5(const BN_ULONG *ap, int off);
948
949 BN_ULONG *n0 = mont->n0, *np;
950
951 /*
952 * BN_to_montgomery can contaminate words above .top [in
953 * BN_DEBUG[_DEBUG] build]...
954 */
955 for (i = am.top; i < top; i++)
956 am.d[i] = 0;
957 for (i = tmp.top; i < top; i++)
958 tmp.d[i] = 0;
959
960 /*
961 * copy mont->N.d[] to improve cache locality
962 */
963 for (np = am.d + top, i = 0; i < top; i++)
964 np[i] = mont->N.d[i];
965
966 bn_scatter5(tmp.d, top, powerbuf, 0);
967 bn_scatter5(am.d, am.top, powerbuf, 1);
968 bn_mul_mont(tmp.d, am.d, am.d, np, n0, top);
969 bn_scatter5(tmp.d, top, powerbuf, 2);
970
971 # if 0
972 for (i = 3; i < 32; i++) {
973 /* Calculate a^i = a^(i-1) * a */
974 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
975 bn_scatter5(tmp.d, top, powerbuf, i);
976 }
977 # else
978 /* same as above, but uses squaring for 1/2 of operations */
979 for (i = 4; i < 32; i *= 2) {
980 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
981 bn_scatter5(tmp.d, top, powerbuf, i);
982 }
983 for (i = 3; i < 8; i += 2) {
984 int j;
985 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
986 bn_scatter5(tmp.d, top, powerbuf, i);
987 for (j = 2 * i; j < 32; j *= 2) {
988 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
989 bn_scatter5(tmp.d, top, powerbuf, j);
990 }
991 }
992 for (; i < 16; i += 2) {
993 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
994 bn_scatter5(tmp.d, top, powerbuf, i);
995 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
996 bn_scatter5(tmp.d, top, powerbuf, 2 * i);
997 }
998 for (; i < 32; i += 2) {
999 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
1000 bn_scatter5(tmp.d, top, powerbuf, i);
1001 }
1002 # endif
1003 /*
1004 * The exponent may not have a whole number of fixed-size windows.
1005 * To simplify the main loop, the initial window has between 1 and
1006 * full-window-size bits such that what remains is always a whole
1007 * number of windows
1008 */
1009 window0 = (bits - 1) % 5 + 1;
1010 wmask = (1 << window0) - 1;
1011 bits -= window0;
1012 wvalue = bn_get_bits(p, bits) & wmask;
1013 bn_gather5(tmp.d, top, powerbuf, wvalue);
1014
1015 /*
1016 * Scan the exponent one window at a time starting from the most
1017 * significant bits.
1018 */
1019 if (top & 7) {
1020 while (bits > 0) {
1021 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1022 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1023 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1024 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1025 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1026 bn_mul_mont_gather5(tmp.d, tmp.d, powerbuf, np, n0, top,
1027 bn_get_bits5(p->d, bits -= 5));
1028 }
1029 } else {
1030 while (bits > 0) {
1031 bn_power5(tmp.d, tmp.d, powerbuf, np, n0, top,
1032 bn_get_bits5(p->d, bits -= 5));
1033 }
1034 }
1035
1036 tmp.top = top;
1037 /*
1038 * The result is now in |tmp| in Montgomery form, but it may not be
1039 * fully reduced. This is within bounds for |BN_from_montgomery|
1040 * (tmp < R <= m*R) so it will, when converting from Montgomery form,
1041 * produce a fully reduced result.
1042 *
1043 * This differs from Figure 2 of the paper, which uses AMM(h, 1) to
1044 * convert from Montgomery form with unreduced output, followed by an
1045 * extra reduction step. In the paper's terminology, we replace
1046 * steps 9 and 10 with MM(h, 1).
1047 */
1048 } else
1049 #endif
1050 {
1051 fallback:
1052 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, window))
1053 goto err;
1054 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, window))
1055 goto err;
1056
1057 /*
1058 * If the window size is greater than 1, then calculate
1059 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even
1060 * powers could instead be computed as (a^(i/2))^2 to use the slight
1061 * performance advantage of sqr over mul).
1062 */
1063 if (window > 1) {
1064 if (!bn_mul_mont_fixed_top(&tmp, &am, &am, mont, ctx))
1065 goto err;
1066 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2,
1067 window))
1068 goto err;
1069 for (i = 3; i < numPowers; i++) {
1070 /* Calculate a^i = a^(i-1) * a */
1071 if (!bn_mul_mont_fixed_top(&tmp, &am, &tmp, mont, ctx))
1072 goto err;
1073 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i,
1074 window))
1075 goto err;
1076 }
1077 }
1078
1079 /*
1080 * The exponent may not have a whole number of fixed-size windows.
1081 * To simplify the main loop, the initial window has between 1 and
1082 * full-window-size bits such that what remains is always a whole
1083 * number of windows
1084 */
1085 window0 = (bits - 1) % window + 1;
1086 wmask = (1 << window0) - 1;
1087 bits -= window0;
1088 wvalue = bn_get_bits(p, bits) & wmask;
1089 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp, top, powerbuf, wvalue,
1090 window))
1091 goto err;
1092
1093 wmask = (1 << window) - 1;
1094 /*
1095 * Scan the exponent one window at a time starting from the most
1096 * significant bits.
1097 */
1098 while (bits > 0) {
1099
1100 /* Square the result window-size times */
1101 for (i = 0; i < window; i++)
1102 if (!bn_mul_mont_fixed_top(&tmp, &tmp, &tmp, mont, ctx))
1103 goto err;
1104
1105 /*
1106 * Get a window's worth of bits from the exponent
1107 * This avoids calling BN_is_bit_set for each bit, which
1108 * is not only slower but also makes each bit vulnerable to
1109 * EM (and likely other) side-channel attacks like One&Done
1110 * (for details see "One&Done: A Single-Decryption EM-Based
1111 * Attack on OpenSSL's Constant-Time Blinded RSA" by M. Alam,
1112 * H. Khan, M. Dey, N. Sinha, R. Callan, A. Zajic, and
1113 * M. Prvulovic, in USENIX Security'18)
1114 */
1115 bits -= window;
1116 wvalue = bn_get_bits(p, bits) & wmask;
1117 /*
1118 * Fetch the appropriate pre-computed value from the pre-buf
1119 */
1120 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue,
1121 window))
1122 goto err;
1123
1124 /* Multiply the result into the intermediate result */
1125 if (!bn_mul_mont_fixed_top(&tmp, &tmp, &am, mont, ctx))
1126 goto err;
1127 }
1128 }
1129
1130 /*
1131 * Done with zero-padded intermediate BIGNUMs. Final BN_from_montgomery
1132 * removes padding [if any] and makes return value suitable for public
1133 * API consumer.
1134 */
1135 #if defined(SPARC_T4_MONT)
1136 if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
1137 am.d[0] = 1; /* borrow am */
1138 for (i = 1; i < top; i++)
1139 am.d[i] = 0;
1140 if (!BN_mod_mul_montgomery(rr, &tmp, &am, mont, ctx))
1141 goto err;
1142 } else
1143 #endif
1144 if (!BN_from_montgomery(rr, &tmp, mont, ctx))
1145 goto err;
1146 ret = 1;
1147 err:
1148 if (in_mont == NULL)
1149 BN_MONT_CTX_free(mont);
1150 if (powerbuf != NULL) {
1151 OPENSSL_cleanse(powerbuf, powerbufLen);
1152 OPENSSL_free(powerbufFree);
1153 }
1154 BN_CTX_end(ctx);
1155 return ret;
1156 }
1157
BN_mod_exp_mont_word(BIGNUM * rr,BN_ULONG a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx,BN_MONT_CTX * in_mont)1158 int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
1159 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
1160 {
1161 BN_MONT_CTX *mont = NULL;
1162 int b, bits, ret = 0;
1163 int r_is_one;
1164 BN_ULONG w, next_w;
1165 BIGNUM *r, *t;
1166 BIGNUM *swap_tmp;
1167 #define BN_MOD_MUL_WORD(r, w, m) \
1168 (BN_mul_word(r, (w)) && \
1169 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
1170 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
1171 /*
1172 * BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is
1173 * probably more overhead than always using BN_mod (which uses BN_copy if
1174 * a similar test returns true).
1175 */
1176 /*
1177 * We can use BN_mod and do not need BN_nnmod because our accumulator is
1178 * never negative (the result of BN_mod does not depend on the sign of
1179 * the modulus).
1180 */
1181 #define BN_TO_MONTGOMERY_WORD(r, w, mont) \
1182 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
1183
1184 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
1185 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) {
1186 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1187 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1188 return 0;
1189 }
1190
1191 bn_check_top(p);
1192 bn_check_top(m);
1193
1194 if (!BN_is_odd(m)) {
1195 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, BN_R_CALLED_WITH_EVEN_MODULUS);
1196 return 0;
1197 }
1198 if (m->top == 1)
1199 a %= m->d[0]; /* make sure that 'a' is reduced */
1200
1201 bits = BN_num_bits(p);
1202 if (bits == 0) {
1203 /* x**0 mod 1, or x**0 mod -1 is still zero. */
1204 if (BN_abs_is_word(m, 1)) {
1205 ret = 1;
1206 BN_zero(rr);
1207 } else {
1208 ret = BN_one(rr);
1209 }
1210 return ret;
1211 }
1212 if (a == 0) {
1213 BN_zero(rr);
1214 ret = 1;
1215 return ret;
1216 }
1217
1218 BN_CTX_start(ctx);
1219 r = BN_CTX_get(ctx);
1220 t = BN_CTX_get(ctx);
1221 if (t == NULL)
1222 goto err;
1223
1224 if (in_mont != NULL)
1225 mont = in_mont;
1226 else {
1227 if ((mont = BN_MONT_CTX_new()) == NULL)
1228 goto err;
1229 if (!BN_MONT_CTX_set(mont, m, ctx))
1230 goto err;
1231 }
1232
1233 r_is_one = 1; /* except for Montgomery factor */
1234
1235 /* bits-1 >= 0 */
1236
1237 /* The result is accumulated in the product r*w. */
1238 w = a; /* bit 'bits-1' of 'p' is always set */
1239 for (b = bits - 2; b >= 0; b--) {
1240 /* First, square r*w. */
1241 next_w = w * w;
1242 if ((next_w / w) != w) { /* overflow */
1243 if (r_is_one) {
1244 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1245 goto err;
1246 r_is_one = 0;
1247 } else {
1248 if (!BN_MOD_MUL_WORD(r, w, m))
1249 goto err;
1250 }
1251 next_w = 1;
1252 }
1253 w = next_w;
1254 if (!r_is_one) {
1255 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
1256 goto err;
1257 }
1258
1259 /* Second, multiply r*w by 'a' if exponent bit is set. */
1260 if (BN_is_bit_set(p, b)) {
1261 next_w = w * a;
1262 if ((next_w / a) != w) { /* overflow */
1263 if (r_is_one) {
1264 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1265 goto err;
1266 r_is_one = 0;
1267 } else {
1268 if (!BN_MOD_MUL_WORD(r, w, m))
1269 goto err;
1270 }
1271 next_w = a;
1272 }
1273 w = next_w;
1274 }
1275 }
1276
1277 /* Finally, set r:=r*w. */
1278 if (w != 1) {
1279 if (r_is_one) {
1280 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1281 goto err;
1282 r_is_one = 0;
1283 } else {
1284 if (!BN_MOD_MUL_WORD(r, w, m))
1285 goto err;
1286 }
1287 }
1288
1289 if (r_is_one) { /* can happen only if a == 1 */
1290 if (!BN_one(rr))
1291 goto err;
1292 } else {
1293 if (!BN_from_montgomery(rr, r, mont, ctx))
1294 goto err;
1295 }
1296 ret = 1;
1297 err:
1298 if (in_mont == NULL)
1299 BN_MONT_CTX_free(mont);
1300 BN_CTX_end(ctx);
1301 bn_check_top(rr);
1302 return ret;
1303 }
1304
1305 /* The old fallback, simple version :-) */
BN_mod_exp_simple(BIGNUM * r,const BIGNUM * a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx)1306 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
1307 const BIGNUM *m, BN_CTX *ctx)
1308 {
1309 int i, j, bits, ret = 0, wstart, wend, window, wvalue;
1310 int start = 1;
1311 BIGNUM *d;
1312 /* Table of variables obtained from 'ctx' */
1313 BIGNUM *val[TABLE_SIZE];
1314
1315 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
1316 || BN_get_flags(a, BN_FLG_CONSTTIME) != 0
1317 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) {
1318 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1319 BNerr(BN_F_BN_MOD_EXP_SIMPLE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1320 return 0;
1321 }
1322
1323 bits = BN_num_bits(p);
1324 if (bits == 0) {
1325 /* x**0 mod 1, or x**0 mod -1 is still zero. */
1326 if (BN_abs_is_word(m, 1)) {
1327 ret = 1;
1328 BN_zero(r);
1329 } else {
1330 ret = BN_one(r);
1331 }
1332 return ret;
1333 }
1334
1335 BN_CTX_start(ctx);
1336 d = BN_CTX_get(ctx);
1337 val[0] = BN_CTX_get(ctx);
1338 if (val[0] == NULL)
1339 goto err;
1340
1341 if (!BN_nnmod(val[0], a, m, ctx))
1342 goto err; /* 1 */
1343 if (BN_is_zero(val[0])) {
1344 BN_zero(r);
1345 ret = 1;
1346 goto err;
1347 }
1348
1349 window = BN_window_bits_for_exponent_size(bits);
1350 if (window > 1) {
1351 if (!BN_mod_mul(d, val[0], val[0], m, ctx))
1352 goto err; /* 2 */
1353 j = 1 << (window - 1);
1354 for (i = 1; i < j; i++) {
1355 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
1356 !BN_mod_mul(val[i], val[i - 1], d, m, ctx))
1357 goto err;
1358 }
1359 }
1360
1361 start = 1; /* This is used to avoid multiplication etc
1362 * when there is only the value '1' in the
1363 * buffer. */
1364 wvalue = 0; /* The 'value' of the window */
1365 wstart = bits - 1; /* The top bit of the window */
1366 wend = 0; /* The bottom bit of the window */
1367
1368 if (!BN_one(r))
1369 goto err;
1370
1371 for (;;) {
1372 if (BN_is_bit_set(p, wstart) == 0) {
1373 if (!start)
1374 if (!BN_mod_mul(r, r, r, m, ctx))
1375 goto err;
1376 if (wstart == 0)
1377 break;
1378 wstart--;
1379 continue;
1380 }
1381 /*
1382 * We now have wstart on a 'set' bit, we now need to work out how bit
1383 * a window to do. To do this we need to scan forward until the last
1384 * set bit before the end of the window
1385 */
1386 j = wstart;
1387 wvalue = 1;
1388 wend = 0;
1389 for (i = 1; i < window; i++) {
1390 if (wstart - i < 0)
1391 break;
1392 if (BN_is_bit_set(p, wstart - i)) {
1393 wvalue <<= (i - wend);
1394 wvalue |= 1;
1395 wend = i;
1396 }
1397 }
1398
1399 /* wend is the size of the current window */
1400 j = wend + 1;
1401 /* add the 'bytes above' */
1402 if (!start)
1403 for (i = 0; i < j; i++) {
1404 if (!BN_mod_mul(r, r, r, m, ctx))
1405 goto err;
1406 }
1407
1408 /* wvalue will be an odd number < 2^window */
1409 if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx))
1410 goto err;
1411
1412 /* move the 'window' down further */
1413 wstart -= wend + 1;
1414 wvalue = 0;
1415 start = 0;
1416 if (wstart < 0)
1417 break;
1418 }
1419 ret = 1;
1420 err:
1421 BN_CTX_end(ctx);
1422 bn_check_top(r);
1423 return ret;
1424 }
1425