1 /*
2 * Copyright 1995-2026 The OpenSSL Project Authors. All Rights Reserved.
3 *
4 * Licensed under the Apache License 2.0 (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 "crypto/sparc_arch.h"
33 #define SPARC_T4_MONT
34 #endif
35
36 /* maximum precomputation table size for *variable* sliding windows */
37 #define TABLE_SIZE 32
38
39 /*
40 * Beyond this limit the constant time code is disabled due to
41 * the possible overflow in the computation of powerbufLen in
42 * BN_mod_exp_mont_consttime.
43 * When this limit is exceeded, the computation will be done using
44 * non-constant time code, but it will take very long.
45 */
46 #define BN_CONSTTIME_SIZE_LIMIT (INT_MAX / BN_BYTES / 256)
47
48 /* this one works - simple but works */
BN_exp(BIGNUM * r,const BIGNUM * a,const BIGNUM * p,BN_CTX * ctx)49 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
50 {
51 int i, bits, ret = 0;
52 BIGNUM *v, *rr;
53
54 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
55 || BN_get_flags(a, BN_FLG_CONSTTIME) != 0) {
56 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
57 ERR_raise(ERR_LIB_BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
58 return 0;
59 }
60
61 BN_CTX_start(ctx);
62 rr = ((r == a) || (r == p)) ? BN_CTX_get(ctx) : r;
63 v = BN_CTX_get(ctx);
64 if (rr == NULL || v == NULL)
65 goto err;
66
67 if (BN_copy(v, a) == NULL)
68 goto err;
69 bits = BN_num_bits(p);
70
71 if (BN_is_odd(p)) {
72 if (BN_copy(rr, a) == NULL)
73 goto err;
74 } else {
75 if (!BN_one(rr))
76 goto err;
77 }
78
79 for (i = 1; i < bits; i++) {
80 if (!BN_sqr(v, v, ctx))
81 goto err;
82 if (BN_is_bit_set(p, i)) {
83 if (!BN_mul(rr, rr, v, ctx))
84 goto err;
85 }
86 }
87 if (r != rr && BN_copy(r, rr) == NULL)
88 goto err;
89
90 ret = 1;
91 err:
92 BN_CTX_end(ctx);
93 bn_check_top(r);
94 return ret;
95 }
96
BN_mod_exp(BIGNUM * r,const BIGNUM * a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx)97 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
98 BN_CTX *ctx)
99 {
100 int ret;
101
102 bn_check_top(a);
103 bn_check_top(p);
104 bn_check_top(m);
105
106 /*-
107 * For even modulus m = 2^k*m_odd, it might make sense to compute
108 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery
109 * exponentiation for the odd part), using appropriate exponent
110 * reductions, and combine the results using the CRT.
111 *
112 * For now, we use Montgomery only if the modulus is odd; otherwise,
113 * exponentiation using the reciprocal-based quick remaindering
114 * algorithm is used.
115 *
116 * (Timing obtained with expspeed.c [computations a^p mod m
117 * where a, p, m are of the same length: 256, 512, 1024, 2048,
118 * 4096, 8192 bits], compared to the running time of the
119 * standard algorithm:
120 *
121 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
122 * 55 .. 77 % [UltraSparc processor, but
123 * debug-solaris-sparcv8-gcc conf.]
124 *
125 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
126 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
127 *
128 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
129 * at 2048 and more bits, but at 512 and 1024 bits, it was
130 * slower even than the standard algorithm!
131 *
132 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
133 * should be obtained when the new Montgomery reduction code
134 * has been integrated into OpenSSL.)
135 */
136
137 #define MONT_MUL_MOD
138 #define MONT_EXP_WORD
139 #define RECP_MUL_MOD
140
141 #ifdef MONT_MUL_MOD
142 if (BN_is_odd(m)) {
143 #ifdef MONT_EXP_WORD
144 if (a->top == 1 && !a->neg
145 && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0)
146 && (BN_get_flags(a, BN_FLG_CONSTTIME) == 0)
147 && (BN_get_flags(m, BN_FLG_CONSTTIME) == 0)) {
148 BN_ULONG A = a->d[0];
149 ret = BN_mod_exp_mont_word(r, A, p, m, ctx, NULL);
150 } else
151 #endif
152 ret = BN_mod_exp_mont(r, a, p, m, ctx, NULL);
153 } else
154 #endif
155 #ifdef RECP_MUL_MOD
156 {
157 ret = BN_mod_exp_recp(r, a, p, m, ctx);
158 }
159 #else
160 {
161 ret = BN_mod_exp_simple(r, a, p, m, ctx);
162 }
163 #endif
164
165 bn_check_top(r);
166 return ret;
167 }
168
BN_mod_exp_recp(BIGNUM * r,const BIGNUM * a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx)169 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
170 const BIGNUM *m, BN_CTX *ctx)
171 {
172 int i, j, bits, ret = 0, wstart, wend, window;
173 int start = 1;
174 BIGNUM *aa;
175 /* Table of variables obtained from 'ctx' */
176 BIGNUM *val[TABLE_SIZE];
177 BN_RECP_CTX recp;
178
179 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
180 || BN_get_flags(a, BN_FLG_CONSTTIME) != 0
181 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) {
182 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
183 ERR_raise(ERR_LIB_BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
184 return 0;
185 }
186
187 bits = BN_num_bits(p);
188 if (bits == 0) {
189 /* x**0 mod 1, or x**0 mod -1 is still zero. */
190 if (BN_abs_is_word(m, 1)) {
191 ret = 1;
192 BN_zero(r);
193 } else {
194 ret = BN_one(r);
195 }
196 return ret;
197 }
198
199 BN_RECP_CTX_init(&recp);
200
201 BN_CTX_start(ctx);
202 aa = BN_CTX_get(ctx);
203 val[0] = BN_CTX_get(ctx);
204 if (val[0] == NULL)
205 goto err;
206
207 if (m->neg) {
208 /* ignore sign of 'm' */
209 if (!BN_copy(aa, m))
210 goto err;
211 aa->neg = 0;
212 if (BN_RECP_CTX_set(&recp, aa, ctx) <= 0)
213 goto err;
214 } else {
215 if (BN_RECP_CTX_set(&recp, m, ctx) <= 0)
216 goto err;
217 }
218
219 if (!BN_nnmod(val[0], a, m, ctx))
220 goto err; /* 1 */
221 if (BN_is_zero(val[0])) {
222 BN_zero(r);
223 ret = 1;
224 goto err;
225 }
226
227 window = BN_window_bits_for_exponent_size(bits);
228 if (window > 1) {
229 if (!BN_mod_mul_reciprocal(aa, val[0], val[0], &recp, ctx))
230 goto err; /* 2 */
231 j = 1 << (window - 1);
232 for (i = 1; i < j; i++) {
233 if (((val[i] = BN_CTX_get(ctx)) == NULL) || !BN_mod_mul_reciprocal(val[i], val[i - 1], aa, &recp, ctx))
234 goto err;
235 }
236 }
237
238 start = 1; /* This is used to avoid multiplication etc
239 * when there is only the value '1' in the
240 * buffer. */
241 wstart = bits - 1; /* The top bit of the window */
242 wend = 0; /* The bottom bit of the window */
243
244 if (r == p) {
245 BIGNUM *p_dup = BN_CTX_get(ctx);
246
247 if (p_dup == NULL || BN_copy(p_dup, p) == NULL)
248 goto err;
249 p = p_dup;
250 }
251
252 if (!BN_one(r))
253 goto err;
254
255 for (;;) {
256 int wvalue; /* The 'value' of the window */
257
258 if (BN_is_bit_set(p, wstart) == 0) {
259 if (!start)
260 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
261 goto err;
262 if (wstart == 0)
263 break;
264 wstart--;
265 continue;
266 }
267 /*
268 * We now have wstart on a 'set' bit, we now need to work out how bit
269 * a window to do. To do this we need to scan forward until the last
270 * set bit before the end of the window
271 */
272 wvalue = 1;
273 wend = 0;
274 for (i = 1; i < window; i++) {
275 if (wstart - i < 0)
276 break;
277 if (BN_is_bit_set(p, wstart - i)) {
278 wvalue <<= (i - wend);
279 wvalue |= 1;
280 wend = i;
281 }
282 }
283
284 /* wend is the size of the current window */
285 j = wend + 1;
286 /* add the 'bytes above' */
287 if (!start)
288 for (i = 0; i < j; i++) {
289 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
290 goto err;
291 }
292
293 /* wvalue will be an odd number < 2^window */
294 if (!BN_mod_mul_reciprocal(r, r, val[wvalue >> 1], &recp, ctx))
295 goto err;
296
297 /* move the 'window' down further */
298 wstart -= wend + 1;
299 start = 0;
300 if (wstart < 0)
301 break;
302 }
303 ret = 1;
304 err:
305 BN_CTX_end(ctx);
306 BN_RECP_CTX_free(&recp);
307 bn_check_top(r);
308 return ret;
309 }
310
BN_mod_exp_mont(BIGNUM * rr,const BIGNUM * a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx,BN_MONT_CTX * in_mont)311 int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
312 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
313 {
314 int i, j, bits, ret = 0, wstart, wend, window;
315 int start = 1;
316 BIGNUM *d, *r;
317 const BIGNUM *aa;
318 /* Table of variables obtained from 'ctx' */
319 BIGNUM *val[TABLE_SIZE];
320 BN_MONT_CTX *mont = NULL;
321
322 bn_check_top(a);
323 bn_check_top(p);
324 bn_check_top(m);
325
326 if (!BN_is_odd(m)) {
327 ERR_raise(ERR_LIB_BN, BN_R_CALLED_WITH_EVEN_MODULUS);
328 return 0;
329 }
330
331 if (m->top <= BN_CONSTTIME_SIZE_LIMIT
332 && (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
333 || BN_get_flags(a, BN_FLG_CONSTTIME) != 0
334 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0)) {
335 return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
336 }
337
338 bits = BN_num_bits(p);
339 if (bits == 0) {
340 /* x**0 mod 1, or x**0 mod -1 is still zero. */
341 if (BN_abs_is_word(m, 1)) {
342 ret = 1;
343 BN_zero(rr);
344 } else {
345 ret = BN_one(rr);
346 }
347 return ret;
348 }
349
350 BN_CTX_start(ctx);
351 d = BN_CTX_get(ctx);
352 r = BN_CTX_get(ctx);
353 val[0] = BN_CTX_get(ctx);
354 if (val[0] == NULL)
355 goto err;
356
357 /*
358 * If this is not done, things will break in the montgomery part
359 */
360
361 if (in_mont != NULL)
362 mont = in_mont;
363 else {
364 if ((mont = BN_MONT_CTX_new()) == NULL)
365 goto err;
366 if (!BN_MONT_CTX_set(mont, m, ctx))
367 goto err;
368 }
369
370 if (a->neg || BN_ucmp(a, m) >= 0) {
371 if (!BN_nnmod(val[0], a, m, ctx))
372 goto err;
373 aa = val[0];
374 } else
375 aa = a;
376 if (!bn_to_mont_fixed_top(val[0], aa, mont, ctx))
377 goto err; /* 1 */
378
379 window = BN_window_bits_for_exponent_size(bits);
380 if (window > 1) {
381 if (!bn_mul_mont_fixed_top(d, val[0], val[0], mont, ctx))
382 goto err; /* 2 */
383 j = 1 << (window - 1);
384 for (i = 1; i < j; i++) {
385 if (((val[i] = BN_CTX_get(ctx)) == NULL) || !bn_mul_mont_fixed_top(val[i], val[i - 1], d, mont, ctx))
386 goto err;
387 }
388 }
389
390 start = 1; /* This is used to avoid multiplication etc
391 * when there is only the value '1' in the
392 * buffer. */
393 wstart = bits - 1; /* The top bit of the window */
394 wend = 0; /* The bottom bit of the window */
395
396 #if 1 /* by Shay Gueron's suggestion */
397 j = m->top; /* borrow j */
398 if (m->d[j - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
399 if (bn_wexpand(r, j) == NULL)
400 goto err;
401 /* 2^(top*BN_BITS2) - m */
402 r->d[0] = (0 - m->d[0]) & BN_MASK2;
403 for (i = 1; i < j; i++)
404 r->d[i] = (~m->d[i]) & BN_MASK2;
405 r->top = j;
406 r->flags |= BN_FLG_FIXED_TOP;
407 } else
408 #endif
409 if (!bn_to_mont_fixed_top(r, BN_value_one(), mont, ctx))
410 goto err;
411 for (;;) {
412 int wvalue; /* The 'value' of the window */
413
414 if (BN_is_bit_set(p, wstart) == 0) {
415 if (!start) {
416 if (!bn_mul_mont_fixed_top(r, r, r, mont, ctx))
417 goto err;
418 }
419 if (wstart == 0)
420 break;
421 wstart--;
422 continue;
423 }
424 /*
425 * We now have wstart on a 'set' bit, we now need to work out how bit
426 * a window to do. To do this we need to scan forward until the last
427 * set bit before the end of the window
428 */
429 wvalue = 1;
430 wend = 0;
431 for (i = 1; i < window; i++) {
432 if (wstart - i < 0)
433 break;
434 if (BN_is_bit_set(p, wstart - i)) {
435 wvalue <<= (i - wend);
436 wvalue |= 1;
437 wend = i;
438 }
439 }
440
441 /* wend is the size of the current window */
442 j = wend + 1;
443 /* add the 'bytes above' */
444 if (!start)
445 for (i = 0; i < j; i++) {
446 if (!bn_mul_mont_fixed_top(r, r, r, mont, ctx))
447 goto err;
448 }
449
450 /* wvalue will be an odd number < 2^window */
451 if (!bn_mul_mont_fixed_top(r, r, val[wvalue >> 1], mont, ctx))
452 goto err;
453
454 /* move the 'window' down further */
455 wstart -= wend + 1;
456 start = 0;
457 if (wstart < 0)
458 break;
459 }
460 /*
461 * Done with zero-padded intermediate BIGNUMs. Final BN_from_montgomery
462 * removes padding [if any] and makes return value suitable for public
463 * API consumer.
464 */
465 #if defined(SPARC_T4_MONT)
466 if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
467 j = mont->N.top; /* borrow j */
468 val[0]->d[0] = 1; /* borrow val[0] */
469 for (i = 1; i < j; i++)
470 val[0]->d[i] = 0;
471 val[0]->top = j;
472 if (!BN_mod_mul_montgomery(rr, r, val[0], mont, ctx))
473 goto err;
474 } else
475 #endif
476 if (!BN_from_montgomery(rr, r, mont, ctx))
477 goto err;
478 ret = 1;
479 err:
480 if (in_mont == NULL)
481 BN_MONT_CTX_free(mont);
482 BN_CTX_end(ctx);
483 bn_check_top(rr);
484 return ret;
485 }
486
bn_get_bits(const BIGNUM * a,int bitpos)487 static BN_ULONG bn_get_bits(const BIGNUM *a, int bitpos)
488 {
489 BN_ULONG ret = 0;
490 int wordpos;
491
492 wordpos = bitpos / BN_BITS2;
493 bitpos %= BN_BITS2;
494 if (wordpos >= 0 && wordpos < a->top) {
495 ret = a->d[wordpos] & BN_MASK2;
496 if (bitpos) {
497 ret >>= bitpos;
498 if (++wordpos < a->top)
499 ret |= a->d[wordpos] << (BN_BITS2 - bitpos);
500 }
501 }
502
503 return ret & BN_MASK2;
504 }
505
506 /*
507 * BN_mod_exp_mont_consttime() stores the precomputed powers in a specific
508 * layout so that accessing any of these table values shows the same access
509 * pattern as far as cache lines are concerned. The following functions are
510 * used to transfer a BIGNUM from/to that table.
511 */
512
MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM * b,int top,unsigned char * buf,int idx,int window)513 static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top,
514 unsigned char *buf, int idx,
515 int window)
516 {
517 int i, j;
518 int width = 1 << window;
519 BN_ULONG *table = (BN_ULONG *)buf;
520
521 if (top > b->top)
522 top = b->top; /* this works because 'buf' is explicitly
523 * zeroed */
524 for (i = 0, j = idx; i < top; i++, j += width) {
525 table[j] = b->d[i];
526 }
527
528 return 1;
529 }
530
MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM * b,int top,unsigned char * buf,int idx,int window)531 static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top,
532 unsigned char *buf, int idx,
533 int window)
534 {
535 int i, j;
536 int width = 1 << window;
537 /*
538 * We declare table 'volatile' in order to discourage compiler
539 * from reordering loads from the table. Concern is that if
540 * reordered in specific manner loads might give away the
541 * information we are trying to conceal. Some would argue that
542 * compiler can reorder them anyway, but it can as well be
543 * argued that doing so would be violation of standard...
544 */
545 volatile BN_ULONG *table = (volatile BN_ULONG *)buf;
546
547 if (bn_wexpand(b, top) == NULL)
548 return 0;
549
550 if (window <= 3) {
551 for (i = 0; i < top; i++, table += width) {
552 BN_ULONG acc = 0;
553
554 for (j = 0; j < width; j++) {
555 acc |= table[j] & value_barrier_bn((BN_ULONG)0 - (constant_time_eq_int(j, idx) & 1));
556 }
557
558 b->d[i] = acc;
559 }
560 } else {
561 int xstride = 1 << (window - 2);
562 BN_ULONG y0, y1, y2, y3;
563
564 i = idx >> (window - 2); /* equivalent of idx / xstride */
565 idx &= xstride - 1; /* equivalent of idx % xstride */
566
567 y0 = (BN_ULONG)0 - (constant_time_eq_int(i, 0) & 1);
568 y1 = (BN_ULONG)0 - (constant_time_eq_int(i, 1) & 1);
569 y2 = (BN_ULONG)0 - (constant_time_eq_int(i, 2) & 1);
570 y3 = (BN_ULONG)0 - (constant_time_eq_int(i, 3) & 1);
571
572 for (i = 0; i < top; i++, table += width) {
573 BN_ULONG acc = 0;
574
575 for (j = 0; j < xstride; j++) {
576 acc |= ((table[j + 0 * xstride] & value_barrier_bn(y0)) | (table[j + 1 * xstride] & value_barrier_bn(y1))
577 | (table[j + 2 * xstride] & value_barrier_bn(y2)) | (table[j + 3 * xstride] & value_barrier_bn(y3)))
578 & value_barrier_bn((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_fixed_top(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_fixed_top(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 if (!BN_is_odd(m)) {
622 ERR_raise(ERR_LIB_BN, BN_R_CALLED_WITH_EVEN_MODULUS);
623 return 0;
624 }
625
626 top = m->top;
627
628 if (top > BN_CONSTTIME_SIZE_LIMIT) {
629 /* Prevent overflowing the powerbufLen computation below */
630 return BN_mod_exp_mont(rr, a, p, m, ctx, in_mont);
631 }
632
633 /*
634 * Use all bits stored in |p|, rather than |BN_num_bits|, so we do not leak
635 * whether the top bits are zero.
636 */
637 bits = p->top * BN_BITS2;
638 if (bits == 0) {
639 /* x**0 mod 1, or x**0 mod -1 is still zero. */
640 if (BN_abs_is_word(m, 1)) {
641 ret = 1;
642 BN_zero(rr);
643 } else {
644 ret = BN_one(rr);
645 }
646 return ret;
647 }
648
649 BN_CTX_start(ctx);
650
651 /*
652 * Allocate a montgomery context if it was not supplied by the caller. If
653 * this is not done, things will break in the montgomery part.
654 */
655 if (in_mont != NULL)
656 mont = in_mont;
657 else {
658 if ((mont = BN_MONT_CTX_new()) == NULL)
659 goto err;
660 if (!BN_MONT_CTX_set(mont, m, ctx))
661 goto err;
662 }
663
664 if (a->neg || BN_ucmp(a, m) >= 0) {
665 BIGNUM *reduced = BN_CTX_get(ctx);
666 if (reduced == NULL
667 || !BN_nnmod(reduced, a, m, ctx)) {
668 goto err;
669 }
670 a = reduced;
671 }
672
673 #ifdef RSAZ_ENABLED
674 /*
675 * If the size of the operands allow it, perform the optimized
676 * RSAZ exponentiation. For further information see
677 * crypto/bn/rsaz_exp.c and accompanying assembly modules.
678 */
679 if ((16 == a->top) && (16 == p->top) && (BN_num_bits(m) == 1024)
680 && rsaz_avx2_eligible()) {
681 if (NULL == bn_wexpand(rr, 16))
682 goto err;
683 RSAZ_1024_mod_exp_avx2(rr->d, a->d, p->d, m->d, mont->RR.d,
684 mont->n0[0]);
685 rr->top = 16;
686 rr->neg = 0;
687 bn_correct_top(rr);
688 ret = 1;
689 goto err;
690 } else if ((8 == a->top) && (8 == p->top) && (BN_num_bits(m) == 512)) {
691 if (NULL == bn_wexpand(rr, 8))
692 goto err;
693 RSAZ_512_mod_exp(rr->d, a->d, p->d, m->d, mont->n0[0], mont->RR.d);
694 rr->top = 8;
695 rr->neg = 0;
696 bn_correct_top(rr);
697 ret = 1;
698 goto err;
699 }
700 #endif
701
702 /* Get the window size to use with size of p. */
703 window = BN_window_bits_for_ctime_exponent_size(bits);
704 #if defined(SPARC_T4_MONT)
705 if (window >= 5 && (top & 15) == 0 && top <= 64 && (OPENSSL_sparcv9cap_P[1] & (CFR_MONTMUL | CFR_MONTSQR)) == (CFR_MONTMUL | CFR_MONTSQR) && (t4 = OPENSSL_sparcv9cap_P[0]))
706 window = 5;
707 else
708 #endif
709 #if defined(OPENSSL_BN_ASM_MONT5)
710 if (window >= 5 && top <= BN_SOFT_LIMIT) {
711 window = 5; /* ~5% improvement for RSA2048 sign, and even
712 * for RSA4096 */
713 /* reserve space for mont->N.d[] copy */
714 powerbufLen += top * sizeof(mont->N.d[0]);
715 }
716 #endif
717 (void)0;
718
719 /*
720 * Allocate a buffer large enough to hold all of the pre-computed powers
721 * of am, am itself and tmp.
722 */
723 numPowers = 1 << window;
724 powerbufLen += sizeof(m->d[0]) * (top * numPowers + ((2 * top) > numPowers ? (2 * top) : numPowers));
725 #ifdef alloca
726 if (powerbufLen < 3072)
727 powerbufFree = alloca(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
728 else
729 #endif
730 if ((powerbufFree = OPENSSL_malloc(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH))
731 == NULL)
732 goto err;
733
734 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
735 memset(powerbuf, 0, powerbufLen);
736
737 #ifdef alloca
738 if (powerbufLen < 3072)
739 powerbufFree = NULL;
740 #endif
741
742 /* lay down tmp and am right after powers table */
743 tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers);
744 am.d = tmp.d + top;
745 tmp.top = am.top = 0;
746 tmp.dmax = am.dmax = top;
747 tmp.neg = am.neg = 0;
748 tmp.flags = am.flags = BN_FLG_STATIC_DATA;
749
750 /* prepare a^0 in Montgomery domain */
751 #if 1 /* by Shay Gueron's suggestion */
752 if (m->d[top - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
753 /* 2^(top*BN_BITS2) - m */
754 tmp.d[0] = (0 - m->d[0]) & BN_MASK2;
755 for (i = 1; i < top; i++)
756 tmp.d[i] = (~m->d[i]) & BN_MASK2;
757 tmp.top = top;
758 } else
759 #endif
760 if (!bn_to_mont_fixed_top(&tmp, BN_value_one(), mont, ctx))
761 goto err;
762
763 /* prepare a^1 in Montgomery domain */
764 if (!bn_to_mont_fixed_top(&am, a, mont, ctx))
765 goto err;
766
767 if (top > BN_SOFT_LIMIT)
768 goto fallback;
769
770 #if defined(SPARC_T4_MONT)
771 if (t4) {
772 typedef int (*bn_pwr5_mont_f)(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_8(BN_ULONG *tp, const BN_ULONG *np,
776 const BN_ULONG *n0, const void *table,
777 int power, int bits);
778 int bn_pwr5_mont_t4_16(BN_ULONG *tp, const BN_ULONG *np,
779 const BN_ULONG *n0, const void *table,
780 int power, int bits);
781 int bn_pwr5_mont_t4_24(BN_ULONG *tp, const BN_ULONG *np,
782 const BN_ULONG *n0, const void *table,
783 int power, int bits);
784 int bn_pwr5_mont_t4_32(BN_ULONG *tp, const BN_ULONG *np,
785 const BN_ULONG *n0, const void *table,
786 int power, int bits);
787 static const bn_pwr5_mont_f pwr5_funcs[4] = {
788 bn_pwr5_mont_t4_8, bn_pwr5_mont_t4_16,
789 bn_pwr5_mont_t4_24, bn_pwr5_mont_t4_32
790 };
791 bn_pwr5_mont_f pwr5_worker = pwr5_funcs[top / 16 - 1];
792
793 typedef int (*bn_mul_mont_f)(BN_ULONG *rp, const BN_ULONG *ap,
794 const void *bp, const BN_ULONG *np,
795 const BN_ULONG *n0);
796 int bn_mul_mont_t4_8(BN_ULONG *rp, const BN_ULONG *ap, const void *bp,
797 const BN_ULONG *np, const BN_ULONG *n0);
798 int bn_mul_mont_t4_16(BN_ULONG *rp, const BN_ULONG *ap,
799 const void *bp, const BN_ULONG *np,
800 const BN_ULONG *n0);
801 int bn_mul_mont_t4_24(BN_ULONG *rp, const BN_ULONG *ap,
802 const void *bp, const BN_ULONG *np,
803 const BN_ULONG *n0);
804 int bn_mul_mont_t4_32(BN_ULONG *rp, const BN_ULONG *ap,
805 const void *bp, const BN_ULONG *np,
806 const BN_ULONG *n0);
807 static const bn_mul_mont_f mul_funcs[4] = {
808 bn_mul_mont_t4_8, bn_mul_mont_t4_16,
809 bn_mul_mont_t4_24, bn_mul_mont_t4_32
810 };
811 bn_mul_mont_f mul_worker = mul_funcs[top / 16 - 1];
812
813 void bn_mul_mont_vis3(BN_ULONG *rp, const BN_ULONG *ap,
814 const void *bp, const BN_ULONG *np,
815 const BN_ULONG *n0, int num);
816 void bn_mul_mont_t4(BN_ULONG *rp, const BN_ULONG *ap,
817 const void *bp, const BN_ULONG *np,
818 const BN_ULONG *n0, int num);
819 void bn_mul_mont_gather5_t4(BN_ULONG *rp, const BN_ULONG *ap,
820 const void *table, const BN_ULONG *np,
821 const BN_ULONG *n0, int num, int power);
822 void bn_flip_n_scatter5_t4(const BN_ULONG *inp, size_t num,
823 void *table, size_t power);
824 void bn_gather5_t4(BN_ULONG *out, size_t num,
825 void *table, size_t power);
826 void bn_flip_t4(BN_ULONG *dst, BN_ULONG *src, size_t num);
827
828 BN_ULONG *np = mont->N.d, *n0 = mont->n0;
829 int stride = 5 * (6 - (top / 16 - 1)); /* multiple of 5, but less
830 * than 32 */
831
832 /*
833 * BN_to_montgomery can contaminate words above .top [in
834 * BN_DEBUG build...
835 */
836 for (i = am.top; i < top; i++)
837 am.d[i] = 0;
838 for (i = tmp.top; i < top; i++)
839 tmp.d[i] = 0;
840
841 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 0);
842 bn_flip_n_scatter5_t4(am.d, top, powerbuf, 1);
843 if (!(*mul_worker)(tmp.d, am.d, am.d, np, n0) && !(*mul_worker)(tmp.d, am.d, am.d, np, n0))
844 bn_mul_mont_vis3(tmp.d, am.d, am.d, np, n0, top);
845 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 2);
846
847 for (i = 3; i < 32; i++) {
848 /* Calculate a^i = a^(i-1) * a */
849 if (!(*mul_worker)(tmp.d, tmp.d, am.d, np, n0) && !(*mul_worker)(tmp.d, tmp.d, am.d, np, n0))
850 bn_mul_mont_vis3(tmp.d, tmp.d, am.d, np, n0, top);
851 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, i);
852 }
853
854 /* switch to 64-bit domain */
855 np = alloca(top * sizeof(BN_ULONG));
856 top /= 2;
857 bn_flip_t4(np, mont->N.d, top);
858
859 /*
860 * The exponent may not have a whole number of fixed-size windows.
861 * To simplify the main loop, the initial window has between 1 and
862 * full-window-size bits such that what remains is always a whole
863 * number of windows
864 */
865 window0 = (bits - 1) % 5 + 1;
866 wmask = (1 << window0) - 1;
867 bits -= window0;
868 wvalue = bn_get_bits(p, bits) & wmask;
869 bn_gather5_t4(tmp.d, top, powerbuf, wvalue);
870
871 /*
872 * Scan the exponent one window at a time starting from the most
873 * significant bits.
874 */
875 while (bits > 0) {
876 if (bits < stride)
877 stride = bits;
878 bits -= stride;
879 wvalue = bn_get_bits(p, bits);
880
881 if ((*pwr5_worker)(tmp.d, np, n0, powerbuf, wvalue, stride))
882 continue;
883 /* retry once and fall back */
884 if ((*pwr5_worker)(tmp.d, np, n0, powerbuf, wvalue, stride))
885 continue;
886
887 bits += stride - 5;
888 wvalue >>= stride - 5;
889 wvalue &= 31;
890 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
891 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
892 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
893 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
894 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
895 bn_mul_mont_gather5_t4(tmp.d, tmp.d, powerbuf, np, n0, top,
896 wvalue);
897 }
898
899 bn_flip_t4(tmp.d, tmp.d, top);
900 top *= 2;
901 /* back to 32-bit domain */
902 tmp.top = top;
903 bn_correct_top(&tmp);
904 OPENSSL_cleanse(np, top * sizeof(BN_ULONG));
905 } else
906 #endif
907 #if defined(OPENSSL_BN_ASM_MONT5)
908 if (window == 5 && top > 1) {
909 /*
910 * This optimization uses ideas from https://eprint.iacr.org/2011/239,
911 * specifically optimization of cache-timing attack countermeasures,
912 * pre-computation optimization, and Almost Montgomery Multiplication.
913 *
914 * The paper discusses a 4-bit window to optimize 512-bit modular
915 * exponentiation, used in RSA-1024 with CRT, but RSA-1024 is no longer
916 * important.
917 *
918 * |bn_mul_mont_gather5| and |bn_power5| implement the "almost"
919 * reduction variant, so the values here may not be fully reduced.
920 * They are bounded by R (i.e. they fit in |top| words), not |m|.
921 * Additionally, we pass these "almost" reduced inputs into
922 * |bn_mul_mont|, which implements the normal reduction variant.
923 * Given those inputs, |bn_mul_mont| may not give reduced
924 * output, but it will still produce "almost" reduced output.
925 */
926 void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap,
927 const void *table, const BN_ULONG *np,
928 const BN_ULONG *n0, int num, int power);
929 void bn_scatter5(const BN_ULONG *inp, size_t num,
930 void *table, size_t power);
931 void bn_gather5(BN_ULONG *out, size_t num, void *table, size_t power);
932 void bn_power5(BN_ULONG *rp, const BN_ULONG *ap,
933 const void *table, const BN_ULONG *np,
934 const BN_ULONG *n0, int num, int power);
935 int bn_get_bits5(const BN_ULONG *ap, int off);
936
937 BN_ULONG *n0 = mont->n0, *np;
938
939 /*
940 * BN_to_montgomery can contaminate words above .top [in
941 * BN_DEBUG build...
942 */
943 for (i = am.top; i < top; i++)
944 am.d[i] = 0;
945 for (i = tmp.top; i < top; i++)
946 tmp.d[i] = 0;
947
948 /*
949 * copy mont->N.d[] to improve cache locality
950 */
951 for (np = am.d + top, i = 0; i < top; i++)
952 np[i] = mont->N.d[i];
953
954 bn_scatter5(tmp.d, top, powerbuf, 0);
955 bn_scatter5(am.d, am.top, powerbuf, 1);
956 bn_mul_mont(tmp.d, am.d, am.d, np, n0, top);
957 bn_scatter5(tmp.d, top, powerbuf, 2);
958
959 #if 0
960 for (i = 3; i < 32; i++) {
961 /* Calculate a^i = a^(i-1) * a */
962 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
963 bn_scatter5(tmp.d, top, powerbuf, i);
964 }
965 #else
966 /* same as above, but uses squaring for 1/2 of operations */
967 for (i = 4; i < 32; i *= 2) {
968 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
969 bn_scatter5(tmp.d, top, powerbuf, i);
970 }
971 for (i = 3; i < 8; i += 2) {
972 int j;
973 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
974 bn_scatter5(tmp.d, top, powerbuf, i);
975 for (j = 2 * i; j < 32; j *= 2) {
976 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
977 bn_scatter5(tmp.d, top, powerbuf, j);
978 }
979 }
980 for (; i < 16; i += 2) {
981 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
982 bn_scatter5(tmp.d, top, powerbuf, i);
983 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
984 bn_scatter5(tmp.d, top, powerbuf, 2 * i);
985 }
986 for (; i < 32; i += 2) {
987 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
988 bn_scatter5(tmp.d, top, powerbuf, i);
989 }
990 #endif
991 /*
992 * The exponent may not have a whole number of fixed-size windows.
993 * To simplify the main loop, the initial window has between 1 and
994 * full-window-size bits such that what remains is always a whole
995 * number of windows
996 */
997 window0 = (bits - 1) % 5 + 1;
998 wmask = (1 << window0) - 1;
999 bits -= window0;
1000 wvalue = bn_get_bits(p, bits) & wmask;
1001 bn_gather5(tmp.d, top, powerbuf, wvalue);
1002
1003 /*
1004 * Scan the exponent one window at a time starting from the most
1005 * significant bits.
1006 */
1007 if (top & 7) {
1008 while (bits > 0) {
1009 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1010 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1011 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1012 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1013 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1014 bn_mul_mont_gather5(tmp.d, tmp.d, powerbuf, np, n0, top,
1015 bn_get_bits5(p->d, bits -= 5));
1016 }
1017 } else {
1018 while (bits > 0) {
1019 bn_power5(tmp.d, tmp.d, powerbuf, np, n0, top,
1020 bn_get_bits5(p->d, bits -= 5));
1021 }
1022 }
1023
1024 tmp.top = top;
1025 /*
1026 * The result is now in |tmp| in Montgomery form, but it may not be
1027 * fully reduced. This is within bounds for |BN_from_montgomery|
1028 * (tmp < R <= m*R) so it will, when converting from Montgomery form,
1029 * produce a fully reduced result.
1030 *
1031 * This differs from Figure 2 of the paper, which uses AMM(h, 1) to
1032 * convert from Montgomery form with unreduced output, followed by an
1033 * extra reduction step. In the paper's terminology, we replace
1034 * steps 9 and 10 with MM(h, 1).
1035 */
1036 } else
1037 #endif
1038 {
1039 fallback:
1040 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, window))
1041 goto err;
1042 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, window))
1043 goto err;
1044
1045 /*
1046 * If the window size is greater than 1, then calculate
1047 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even
1048 * powers could instead be computed as (a^(i/2))^2 to use the slight
1049 * performance advantage of sqr over mul).
1050 */
1051 if (window > 1) {
1052 if (!bn_mul_mont_fixed_top(&tmp, &am, &am, mont, ctx))
1053 goto err;
1054 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2,
1055 window))
1056 goto err;
1057 for (i = 3; i < numPowers; i++) {
1058 /* Calculate a^i = a^(i-1) * a */
1059 if (!bn_mul_mont_fixed_top(&tmp, &am, &tmp, mont, ctx))
1060 goto err;
1061 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i,
1062 window))
1063 goto err;
1064 }
1065 }
1066
1067 /*
1068 * The exponent may not have a whole number of fixed-size windows.
1069 * To simplify the main loop, the initial window has between 1 and
1070 * full-window-size bits such that what remains is always a whole
1071 * number of windows
1072 */
1073 window0 = (bits - 1) % window + 1;
1074 wmask = (1 << window0) - 1;
1075 bits -= window0;
1076 wvalue = bn_get_bits(p, bits) & wmask;
1077 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp, top, powerbuf, wvalue,
1078 window))
1079 goto err;
1080
1081 wmask = (1 << window) - 1;
1082 /*
1083 * Scan the exponent one window at a time starting from the most
1084 * significant bits.
1085 */
1086 while (bits > 0) {
1087
1088 /* Square the result window-size times */
1089 for (i = 0; i < window; i++)
1090 if (!bn_mul_mont_fixed_top(&tmp, &tmp, &tmp, mont, ctx))
1091 goto err;
1092
1093 /*
1094 * Get a window's worth of bits from the exponent
1095 * This avoids calling BN_is_bit_set for each bit, which
1096 * is not only slower but also makes each bit vulnerable to
1097 * EM (and likely other) side-channel attacks like One&Done
1098 * (for details see "One&Done: A Single-Decryption EM-Based
1099 * Attack on OpenSSL's Constant-Time Blinded RSA" by M. Alam,
1100 * H. Khan, M. Dey, N. Sinha, R. Callan, A. Zajic, and
1101 * M. Prvulovic, in USENIX Security'18)
1102 */
1103 bits -= window;
1104 wvalue = bn_get_bits(p, bits) & wmask;
1105 /*
1106 * Fetch the appropriate pre-computed value from the pre-buf
1107 */
1108 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue,
1109 window))
1110 goto err;
1111
1112 /* Multiply the result into the intermediate result */
1113 if (!bn_mul_mont_fixed_top(&tmp, &tmp, &am, mont, ctx))
1114 goto err;
1115 }
1116 }
1117
1118 /*
1119 * Done with zero-padded intermediate BIGNUMs. Final BN_from_montgomery
1120 * removes padding [if any] and makes return value suitable for public
1121 * API consumer.
1122 */
1123 #if defined(SPARC_T4_MONT)
1124 if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
1125 am.d[0] = 1; /* borrow am */
1126 for (i = 1; i < top; i++)
1127 am.d[i] = 0;
1128 if (!BN_mod_mul_montgomery(rr, &tmp, &am, mont, ctx))
1129 goto err;
1130 } else
1131 #endif
1132 if (!bn_from_mont_fixed_top(rr, &tmp, mont, ctx))
1133 goto err;
1134 ret = 1;
1135 err:
1136 if (in_mont == NULL)
1137 BN_MONT_CTX_free(mont);
1138 if (powerbuf != NULL) {
1139 OPENSSL_cleanse(powerbuf, powerbufLen);
1140 OPENSSL_free(powerbufFree);
1141 }
1142 BN_CTX_end(ctx);
1143 return ret;
1144 }
1145
BN_mod_exp_mont_consttime(BIGNUM * rr,const BIGNUM * a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx,BN_MONT_CTX * in_mont)1146 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
1147 const BIGNUM *m, BN_CTX *ctx,
1148 BN_MONT_CTX *in_mont)
1149 {
1150 bn_check_top(a);
1151 bn_check_top(p);
1152 bn_check_top(m);
1153 if (!bn_mod_exp_mont_fixed_top(rr, a, p, m, ctx, in_mont))
1154 return 0;
1155 bn_correct_top(rr);
1156 return 1;
1157 }
1158
BN_mod_exp_mont_word(BIGNUM * rr,BN_ULONG a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx,BN_MONT_CTX * in_mont)1159 int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
1160 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
1161 {
1162 BN_MONT_CTX *mont = NULL;
1163 int b, bits, ret = 0;
1164 int r_is_one;
1165 BN_ULONG w, next_w;
1166 BIGNUM *r, *t;
1167 BIGNUM *swap_tmp;
1168 #define BN_MOD_MUL_WORD(r, w, m) \
1169 (BN_mul_word(r, (w)) && (/* 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 ERR_raise(ERR_LIB_BN, 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 ERR_raise(ERR_LIB_BN, 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;
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 ERR_raise(ERR_LIB_BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1320 return 0;
1321 }
1322
1323 if (r == m) {
1324 ERR_raise(ERR_LIB_BN, ERR_R_PASSED_INVALID_ARGUMENT);
1325 return 0;
1326 }
1327
1328 bits = BN_num_bits(p);
1329 if (bits == 0) {
1330 /* x**0 mod 1, or x**0 mod -1 is still zero. */
1331 if (BN_abs_is_word(m, 1)) {
1332 ret = 1;
1333 BN_zero(r);
1334 } else {
1335 ret = BN_one(r);
1336 }
1337 return ret;
1338 }
1339
1340 BN_CTX_start(ctx);
1341 d = BN_CTX_get(ctx);
1342 val[0] = BN_CTX_get(ctx);
1343 if (val[0] == NULL)
1344 goto err;
1345
1346 if (!BN_nnmod(val[0], a, m, ctx))
1347 goto err; /* 1 */
1348 if (BN_is_zero(val[0])) {
1349 BN_zero(r);
1350 ret = 1;
1351 goto err;
1352 }
1353
1354 window = BN_window_bits_for_exponent_size(bits);
1355 if (window > 1) {
1356 if (!BN_mod_mul(d, val[0], val[0], m, ctx))
1357 goto err; /* 2 */
1358 j = 1 << (window - 1);
1359 for (i = 1; i < j; i++) {
1360 if (((val[i] = BN_CTX_get(ctx)) == NULL) || !BN_mod_mul(val[i], val[i - 1], d, m, ctx))
1361 goto err;
1362 }
1363 }
1364
1365 start = 1; /* This is used to avoid multiplication etc
1366 * when there is only the value '1' in the
1367 * buffer. */
1368 wstart = bits - 1; /* The top bit of the window */
1369 wend = 0; /* The bottom bit of the window */
1370
1371 if (r == p) {
1372 BIGNUM *p_dup = BN_CTX_get(ctx);
1373
1374 if (p_dup == NULL || BN_copy(p_dup, p) == NULL)
1375 goto err;
1376 p = p_dup;
1377 }
1378
1379 if (!BN_one(r))
1380 goto err;
1381
1382 for (;;) {
1383 int wvalue; /* The 'value' of the window */
1384
1385 if (BN_is_bit_set(p, wstart) == 0) {
1386 if (!start)
1387 if (!BN_mod_mul(r, r, r, m, ctx))
1388 goto err;
1389 if (wstart == 0)
1390 break;
1391 wstart--;
1392 continue;
1393 }
1394 /*
1395 * We now have wstart on a 'set' bit, we now need to work out how bit
1396 * a window to do. To do this we need to scan forward until the last
1397 * set bit before the end of the window
1398 */
1399 wvalue = 1;
1400 wend = 0;
1401 for (i = 1; i < window; i++) {
1402 if (wstart - i < 0)
1403 break;
1404 if (BN_is_bit_set(p, wstart - i)) {
1405 wvalue <<= (i - wend);
1406 wvalue |= 1;
1407 wend = i;
1408 }
1409 }
1410
1411 /* wend is the size of the current window */
1412 j = wend + 1;
1413 /* add the 'bytes above' */
1414 if (!start)
1415 for (i = 0; i < j; i++) {
1416 if (!BN_mod_mul(r, r, r, m, ctx))
1417 goto err;
1418 }
1419
1420 /* wvalue will be an odd number < 2^window */
1421 if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx))
1422 goto err;
1423
1424 /* move the 'window' down further */
1425 wstart -= wend + 1;
1426 start = 0;
1427 if (wstart < 0)
1428 break;
1429 }
1430 ret = 1;
1431 err:
1432 BN_CTX_end(ctx);
1433 bn_check_top(r);
1434 return ret;
1435 }
1436
1437 /*
1438 * This is a variant of modular exponentiation optimization that does
1439 * parallel 2-primes exponentiation using 256-bit (AVX512VL) AVX512_IFMA ISA
1440 * or AVX_IFMA ISA in 52-bit binary redundant representation.
1441 * If such instructions are not available, or input data size is not supported,
1442 * it falls back to two BN_mod_exp_mont_consttime() calls.
1443 */
BN_mod_exp_mont_consttime_x2(BIGNUM * rr1,const BIGNUM * a1,const BIGNUM * p1,const BIGNUM * m1,BN_MONT_CTX * in_mont1,BIGNUM * rr2,const BIGNUM * a2,const BIGNUM * p2,const BIGNUM * m2,BN_MONT_CTX * in_mont2,BN_CTX * ctx)1444 int BN_mod_exp_mont_consttime_x2(BIGNUM *rr1, const BIGNUM *a1, const BIGNUM *p1,
1445 const BIGNUM *m1, BN_MONT_CTX *in_mont1,
1446 BIGNUM *rr2, const BIGNUM *a2, const BIGNUM *p2,
1447 const BIGNUM *m2, BN_MONT_CTX *in_mont2,
1448 BN_CTX *ctx)
1449 {
1450 int ret = 0;
1451
1452 #ifdef RSAZ_ENABLED
1453 BN_MONT_CTX *mont1 = NULL;
1454 BN_MONT_CTX *mont2 = NULL;
1455
1456 if ((ossl_rsaz_avx512ifma_eligible() || ossl_rsaz_avxifma_eligible()) && (((a1->top == 16) && (p1->top == 16) && (BN_num_bits(m1) == 1024) && (a2->top == 16) && (p2->top == 16) && (BN_num_bits(m2) == 1024)) || ((a1->top == 24) && (p1->top == 24) && (BN_num_bits(m1) == 1536) && (a2->top == 24) && (p2->top == 24) && (BN_num_bits(m2) == 1536)) || ((a1->top == 32) && (p1->top == 32) && (BN_num_bits(m1) == 2048) && (a2->top == 32) && (p2->top == 32) && (BN_num_bits(m2) == 2048)))) {
1457
1458 int topn = a1->top;
1459 /* Modulus bits of |m1| and |m2| are equal */
1460 int mod_bits = BN_num_bits(m1);
1461
1462 if (bn_wexpand(rr1, topn) == NULL)
1463 goto err;
1464 if (bn_wexpand(rr2, topn) == NULL)
1465 goto err;
1466
1467 /* Ensure that montgomery contexts are initialized */
1468 if (in_mont1 != NULL) {
1469 mont1 = in_mont1;
1470 } else {
1471 if ((mont1 = BN_MONT_CTX_new()) == NULL)
1472 goto err;
1473 if (!BN_MONT_CTX_set(mont1, m1, ctx))
1474 goto err;
1475 }
1476 if (in_mont2 != NULL) {
1477 mont2 = in_mont2;
1478 } else {
1479 if ((mont2 = BN_MONT_CTX_new()) == NULL)
1480 goto err;
1481 if (!BN_MONT_CTX_set(mont2, m2, ctx))
1482 goto err;
1483 }
1484
1485 ret = ossl_rsaz_mod_exp_avx512_x2(rr1->d, a1->d, p1->d, m1->d,
1486 mont1->RR.d, mont1->n0[0],
1487 rr2->d, a2->d, p2->d, m2->d,
1488 mont2->RR.d, mont2->n0[0],
1489 mod_bits);
1490
1491 rr1->top = topn;
1492 rr1->neg = 0;
1493 bn_correct_top(rr1);
1494 bn_check_top(rr1);
1495
1496 rr2->top = topn;
1497 rr2->neg = 0;
1498 bn_correct_top(rr2);
1499 bn_check_top(rr2);
1500
1501 goto err;
1502 }
1503 #endif
1504
1505 /* rr1 = a1^p1 mod m1 */
1506 ret = BN_mod_exp_mont_consttime(rr1, a1, p1, m1, ctx, in_mont1);
1507 /* rr2 = a2^p2 mod m2 */
1508 ret &= BN_mod_exp_mont_consttime(rr2, a2, p2, m2, ctx, in_mont2);
1509
1510 #ifdef RSAZ_ENABLED
1511 err:
1512 if (in_mont2 == NULL)
1513 BN_MONT_CTX_free(mont2);
1514 if (in_mont1 == NULL)
1515 BN_MONT_CTX_free(mont1);
1516 #endif
1517
1518 return ret;
1519 }
1520