1 /*
2 * Copyright 1995-2025 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] & ((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] & y0) | (table[j + 1 * xstride] & y1) | (table[j + 2 * xstride] & y2) | (table[j + 3 * xstride] & y3))
577 & ((BN_ULONG)0 - (constant_time_eq_int(j, idx) & 1));
578 }
579
580 b->d[i] = acc;
581 }
582 }
583
584 b->top = top;
585 b->flags |= BN_FLG_FIXED_TOP;
586 return 1;
587 }
588
589 /*
590 * Given a pointer value, compute the next address that is a cache line
591 * multiple.
592 */
593 #define MOD_EXP_CTIME_ALIGN(x_) \
594 ((unsigned char *)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
595
596 /*
597 * This variant of BN_mod_exp_mont() uses fixed windows and the special
598 * precomputation memory layout to limit data-dependency to a minimum to
599 * protect secret exponents (cf. the hyper-threading timing attacks pointed
600 * out by Colin Percival,
601 * http://www.daemonology.net/hyperthreading-considered-harmful/)
602 */
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)603 int bn_mod_exp_mont_fixed_top(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
604 const BIGNUM *m, BN_CTX *ctx,
605 BN_MONT_CTX *in_mont)
606 {
607 int i, bits, ret = 0, window, wvalue, wmask, window0;
608 int top;
609 BN_MONT_CTX *mont = NULL;
610
611 int numPowers;
612 unsigned char *powerbufFree = NULL;
613 int powerbufLen = 0;
614 unsigned char *powerbuf = NULL;
615 BIGNUM tmp, am;
616 #if defined(SPARC_T4_MONT)
617 unsigned int t4 = 0;
618 #endif
619
620 if (!BN_is_odd(m)) {
621 ERR_raise(ERR_LIB_BN, BN_R_CALLED_WITH_EVEN_MODULUS);
622 return 0;
623 }
624
625 top = m->top;
626
627 if (top > BN_CONSTTIME_SIZE_LIMIT) {
628 /* Prevent overflowing the powerbufLen computation below */
629 return BN_mod_exp_mont(rr, a, p, m, ctx, in_mont);
630 }
631
632 /*
633 * Use all bits stored in |p|, rather than |BN_num_bits|, so we do not leak
634 * whether the top bits are zero.
635 */
636 bits = p->top * BN_BITS2;
637 if (bits == 0) {
638 /* x**0 mod 1, or x**0 mod -1 is still zero. */
639 if (BN_abs_is_word(m, 1)) {
640 ret = 1;
641 BN_zero(rr);
642 } else {
643 ret = BN_one(rr);
644 }
645 return ret;
646 }
647
648 BN_CTX_start(ctx);
649
650 /*
651 * Allocate a montgomery context if it was not supplied by the caller. If
652 * this is not done, things will break in the montgomery part.
653 */
654 if (in_mont != NULL)
655 mont = in_mont;
656 else {
657 if ((mont = BN_MONT_CTX_new()) == NULL)
658 goto err;
659 if (!BN_MONT_CTX_set(mont, m, ctx))
660 goto err;
661 }
662
663 if (a->neg || BN_ucmp(a, m) >= 0) {
664 BIGNUM *reduced = BN_CTX_get(ctx);
665 if (reduced == NULL
666 || !BN_nnmod(reduced, a, m, ctx)) {
667 goto err;
668 }
669 a = reduced;
670 }
671
672 #ifdef RSAZ_ENABLED
673 /*
674 * If the size of the operands allow it, perform the optimized
675 * RSAZ exponentiation. For further information see
676 * crypto/bn/rsaz_exp.c and accompanying assembly modules.
677 */
678 if ((16 == a->top) && (16 == p->top) && (BN_num_bits(m) == 1024)
679 && rsaz_avx2_eligible()) {
680 if (NULL == bn_wexpand(rr, 16))
681 goto err;
682 RSAZ_1024_mod_exp_avx2(rr->d, a->d, p->d, m->d, mont->RR.d,
683 mont->n0[0]);
684 rr->top = 16;
685 rr->neg = 0;
686 bn_correct_top(rr);
687 ret = 1;
688 goto err;
689 } else if ((8 == a->top) && (8 == p->top) && (BN_num_bits(m) == 512)) {
690 if (NULL == bn_wexpand(rr, 8))
691 goto err;
692 RSAZ_512_mod_exp(rr->d, a->d, p->d, m->d, mont->n0[0], mont->RR.d);
693 rr->top = 8;
694 rr->neg = 0;
695 bn_correct_top(rr);
696 ret = 1;
697 goto err;
698 }
699 #endif
700
701 /* Get the window size to use with size of p. */
702 window = BN_window_bits_for_ctime_exponent_size(bits);
703 #if defined(SPARC_T4_MONT)
704 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]))
705 window = 5;
706 else
707 #endif
708 #if defined(OPENSSL_BN_ASM_MONT5)
709 if (window >= 5 && top <= BN_SOFT_LIMIT) {
710 window = 5; /* ~5% improvement for RSA2048 sign, and even
711 * for RSA4096 */
712 /* reserve space for mont->N.d[] copy */
713 powerbufLen += top * sizeof(mont->N.d[0]);
714 }
715 #endif
716 (void)0;
717
718 /*
719 * Allocate a buffer large enough to hold all of the pre-computed powers
720 * of am, am itself and tmp.
721 */
722 numPowers = 1 << window;
723 powerbufLen += sizeof(m->d[0]) * (top * numPowers + ((2 * top) > numPowers ? (2 * top) : numPowers));
724 #ifdef alloca
725 if (powerbufLen < 3072)
726 powerbufFree = alloca(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
727 else
728 #endif
729 if ((powerbufFree = OPENSSL_malloc(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH))
730 == NULL)
731 goto err;
732
733 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
734 memset(powerbuf, 0, powerbufLen);
735
736 #ifdef alloca
737 if (powerbufLen < 3072)
738 powerbufFree = NULL;
739 #endif
740
741 /* lay down tmp and am right after powers table */
742 tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers);
743 am.d = tmp.d + top;
744 tmp.top = am.top = 0;
745 tmp.dmax = am.dmax = top;
746 tmp.neg = am.neg = 0;
747 tmp.flags = am.flags = BN_FLG_STATIC_DATA;
748
749 /* prepare a^0 in Montgomery domain */
750 #if 1 /* by Shay Gueron's suggestion */
751 if (m->d[top - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
752 /* 2^(top*BN_BITS2) - m */
753 tmp.d[0] = (0 - m->d[0]) & BN_MASK2;
754 for (i = 1; i < top; i++)
755 tmp.d[i] = (~m->d[i]) & BN_MASK2;
756 tmp.top = top;
757 } else
758 #endif
759 if (!bn_to_mont_fixed_top(&tmp, BN_value_one(), mont, ctx))
760 goto err;
761
762 /* prepare a^1 in Montgomery domain */
763 if (!bn_to_mont_fixed_top(&am, a, mont, ctx))
764 goto err;
765
766 if (top > BN_SOFT_LIMIT)
767 goto fallback;
768
769 #if defined(SPARC_T4_MONT)
770 if (t4) {
771 typedef int (*bn_pwr5_mont_f)(BN_ULONG *tp, const BN_ULONG *np,
772 const BN_ULONG *n0, const void *table,
773 int power, int bits);
774 int bn_pwr5_mont_t4_8(BN_ULONG * tp, const BN_ULONG *np,
775 const BN_ULONG *n0, const void *table,
776 int power, int bits);
777 int bn_pwr5_mont_t4_16(BN_ULONG * tp, const BN_ULONG *np,
778 const BN_ULONG *n0, const void *table,
779 int power, int bits);
780 int bn_pwr5_mont_t4_24(BN_ULONG * tp, const BN_ULONG *np,
781 const BN_ULONG *n0, const void *table,
782 int power, int bits);
783 int bn_pwr5_mont_t4_32(BN_ULONG * tp, const BN_ULONG *np,
784 const BN_ULONG *n0, const void *table,
785 int power, int bits);
786 static const bn_pwr5_mont_f pwr5_funcs[4] = {
787 bn_pwr5_mont_t4_8, bn_pwr5_mont_t4_16,
788 bn_pwr5_mont_t4_24, bn_pwr5_mont_t4_32
789 };
790 bn_pwr5_mont_f pwr5_worker = pwr5_funcs[top / 16 - 1];
791
792 typedef int (*bn_mul_mont_f)(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_8(BN_ULONG * rp, const BN_ULONG *ap, const void *bp,
796 const BN_ULONG *np, const BN_ULONG *n0);
797 int bn_mul_mont_t4_16(BN_ULONG * rp, const BN_ULONG *ap,
798 const void *bp, const BN_ULONG *np,
799 const BN_ULONG *n0);
800 int bn_mul_mont_t4_24(BN_ULONG * rp, const BN_ULONG *ap,
801 const void *bp, const BN_ULONG *np,
802 const BN_ULONG *n0);
803 int bn_mul_mont_t4_32(BN_ULONG * rp, const BN_ULONG *ap,
804 const void *bp, const BN_ULONG *np,
805 const BN_ULONG *n0);
806 static const bn_mul_mont_f mul_funcs[4] = {
807 bn_mul_mont_t4_8, bn_mul_mont_t4_16,
808 bn_mul_mont_t4_24, bn_mul_mont_t4_32
809 };
810 bn_mul_mont_f mul_worker = mul_funcs[top / 16 - 1];
811
812 void bn_mul_mont_vis3(BN_ULONG * rp, const BN_ULONG *ap,
813 const void *bp, const BN_ULONG *np,
814 const BN_ULONG *n0, int num);
815 void bn_mul_mont_t4(BN_ULONG * rp, const BN_ULONG *ap,
816 const void *bp, const BN_ULONG *np,
817 const BN_ULONG *n0, int num);
818 void bn_mul_mont_gather5_t4(BN_ULONG * rp, const BN_ULONG *ap,
819 const void *table, const BN_ULONG *np,
820 const BN_ULONG *n0, int num, int power);
821 void bn_flip_n_scatter5_t4(const BN_ULONG *inp, size_t num,
822 void *table, size_t power);
823 void bn_gather5_t4(BN_ULONG * out, size_t num,
824 void *table, size_t power);
825 void bn_flip_t4(BN_ULONG * dst, BN_ULONG * src, size_t num);
826
827 BN_ULONG *np = mont->N.d, *n0 = mont->n0;
828 int stride = 5 * (6 - (top / 16 - 1)); /* multiple of 5, but less
829 * than 32 */
830
831 /*
832 * BN_to_montgomery can contaminate words above .top [in
833 * BN_DEBUG build...
834 */
835 for (i = am.top; i < top; i++)
836 am.d[i] = 0;
837 for (i = tmp.top; i < top; i++)
838 tmp.d[i] = 0;
839
840 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 0);
841 bn_flip_n_scatter5_t4(am.d, top, powerbuf, 1);
842 if (!(*mul_worker)(tmp.d, am.d, am.d, np, n0) && !(*mul_worker)(tmp.d, am.d, am.d, np, n0))
843 bn_mul_mont_vis3(tmp.d, am.d, am.d, np, n0, top);
844 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 2);
845
846 for (i = 3; i < 32; i++) {
847 /* Calculate a^i = a^(i-1) * a */
848 if (!(*mul_worker)(tmp.d, tmp.d, am.d, np, n0) && !(*mul_worker)(tmp.d, tmp.d, am.d, np, n0))
849 bn_mul_mont_vis3(tmp.d, tmp.d, am.d, np, n0, top);
850 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, i);
851 }
852
853 /* switch to 64-bit domain */
854 np = alloca(top * sizeof(BN_ULONG));
855 top /= 2;
856 bn_flip_t4(np, mont->N.d, top);
857
858 /*
859 * The exponent may not have a whole number of fixed-size windows.
860 * To simplify the main loop, the initial window has between 1 and
861 * full-window-size bits such that what remains is always a whole
862 * number of windows
863 */
864 window0 = (bits - 1) % 5 + 1;
865 wmask = (1 << window0) - 1;
866 bits -= window0;
867 wvalue = bn_get_bits(p, bits) & wmask;
868 bn_gather5_t4(tmp.d, top, powerbuf, wvalue);
869
870 /*
871 * Scan the exponent one window at a time starting from the most
872 * significant bits.
873 */
874 while (bits > 0) {
875 if (bits < stride)
876 stride = bits;
877 bits -= stride;
878 wvalue = bn_get_bits(p, bits);
879
880 if ((*pwr5_worker)(tmp.d, np, n0, powerbuf, wvalue, stride))
881 continue;
882 /* retry once and fall back */
883 if ((*pwr5_worker)(tmp.d, np, n0, powerbuf, wvalue, stride))
884 continue;
885
886 bits += stride - 5;
887 wvalue >>= stride - 5;
888 wvalue &= 31;
889 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
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_gather5_t4(tmp.d, tmp.d, powerbuf, np, n0, top,
895 wvalue);
896 }
897
898 bn_flip_t4(tmp.d, tmp.d, top);
899 top *= 2;
900 /* back to 32-bit domain */
901 tmp.top = top;
902 bn_correct_top(&tmp);
903 OPENSSL_cleanse(np, top * sizeof(BN_ULONG));
904 } else
905 #endif
906 #if defined(OPENSSL_BN_ASM_MONT5)
907 if (window == 5 && top > 1) {
908 /*
909 * This optimization uses ideas from https://eprint.iacr.org/2011/239,
910 * specifically optimization of cache-timing attack countermeasures,
911 * pre-computation optimization, and Almost Montgomery Multiplication.
912 *
913 * The paper discusses a 4-bit window to optimize 512-bit modular
914 * exponentiation, used in RSA-1024 with CRT, but RSA-1024 is no longer
915 * important.
916 *
917 * |bn_mul_mont_gather5| and |bn_power5| implement the "almost"
918 * reduction variant, so the values here may not be fully reduced.
919 * They are bounded by R (i.e. they fit in |top| words), not |m|.
920 * Additionally, we pass these "almost" reduced inputs into
921 * |bn_mul_mont|, which implements the normal reduction variant.
922 * Given those inputs, |bn_mul_mont| may not give reduced
923 * output, but it will still produce "almost" reduced output.
924 */
925 void bn_mul_mont_gather5(BN_ULONG * rp, const BN_ULONG *ap,
926 const void *table, const BN_ULONG *np,
927 const BN_ULONG *n0, int num, int power);
928 void bn_scatter5(const BN_ULONG *inp, size_t num,
929 void *table, size_t power);
930 void bn_gather5(BN_ULONG * out, size_t num, void *table, size_t power);
931 void bn_power5(BN_ULONG * rp, const BN_ULONG *ap,
932 const void *table, const BN_ULONG *np,
933 const BN_ULONG *n0, int num, int power);
934 int bn_get_bits5(const BN_ULONG *ap, int off);
935
936 BN_ULONG *n0 = mont->n0, *np;
937
938 /*
939 * BN_to_montgomery can contaminate words above .top [in
940 * BN_DEBUG build...
941 */
942 for (i = am.top; i < top; i++)
943 am.d[i] = 0;
944 for (i = tmp.top; i < top; i++)
945 tmp.d[i] = 0;
946
947 /*
948 * copy mont->N.d[] to improve cache locality
949 */
950 for (np = am.d + top, i = 0; i < top; i++)
951 np[i] = mont->N.d[i];
952
953 bn_scatter5(tmp.d, top, powerbuf, 0);
954 bn_scatter5(am.d, am.top, powerbuf, 1);
955 bn_mul_mont(tmp.d, am.d, am.d, np, n0, top);
956 bn_scatter5(tmp.d, top, powerbuf, 2);
957
958 #if 0
959 for (i = 3; i < 32; i++) {
960 /* Calculate a^i = a^(i-1) * a */
961 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
962 bn_scatter5(tmp.d, top, powerbuf, i);
963 }
964 #else
965 /* same as above, but uses squaring for 1/2 of operations */
966 for (i = 4; i < 32; i *= 2) {
967 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
968 bn_scatter5(tmp.d, top, powerbuf, i);
969 }
970 for (i = 3; i < 8; i += 2) {
971 int j;
972 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
973 bn_scatter5(tmp.d, top, powerbuf, i);
974 for (j = 2 * i; j < 32; j *= 2) {
975 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
976 bn_scatter5(tmp.d, top, powerbuf, j);
977 }
978 }
979 for (; i < 16; i += 2) {
980 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
981 bn_scatter5(tmp.d, top, powerbuf, i);
982 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
983 bn_scatter5(tmp.d, top, powerbuf, 2 * i);
984 }
985 for (; i < 32; i += 2) {
986 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
987 bn_scatter5(tmp.d, top, powerbuf, i);
988 }
989 #endif
990 /*
991 * The exponent may not have a whole number of fixed-size windows.
992 * To simplify the main loop, the initial window has between 1 and
993 * full-window-size bits such that what remains is always a whole
994 * number of windows
995 */
996 window0 = (bits - 1) % 5 + 1;
997 wmask = (1 << window0) - 1;
998 bits -= window0;
999 wvalue = bn_get_bits(p, bits) & wmask;
1000 bn_gather5(tmp.d, top, powerbuf, wvalue);
1001
1002 /*
1003 * Scan the exponent one window at a time starting from the most
1004 * significant bits.
1005 */
1006 if (top & 7) {
1007 while (bits > 0) {
1008 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
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_gather5(tmp.d, tmp.d, powerbuf, np, n0, top,
1014 bn_get_bits5(p->d, bits -= 5));
1015 }
1016 } else {
1017 while (bits > 0) {
1018 bn_power5(tmp.d, tmp.d, powerbuf, np, n0, top,
1019 bn_get_bits5(p->d, bits -= 5));
1020 }
1021 }
1022
1023 tmp.top = top;
1024 /*
1025 * The result is now in |tmp| in Montgomery form, but it may not be
1026 * fully reduced. This is within bounds for |BN_from_montgomery|
1027 * (tmp < R <= m*R) so it will, when converting from Montgomery form,
1028 * produce a fully reduced result.
1029 *
1030 * This differs from Figure 2 of the paper, which uses AMM(h, 1) to
1031 * convert from Montgomery form with unreduced output, followed by an
1032 * extra reduction step. In the paper's terminology, we replace
1033 * steps 9 and 10 with MM(h, 1).
1034 */
1035 } else
1036 #endif
1037 {
1038 fallback:
1039 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, window))
1040 goto err;
1041 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, window))
1042 goto err;
1043
1044 /*
1045 * If the window size is greater than 1, then calculate
1046 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even
1047 * powers could instead be computed as (a^(i/2))^2 to use the slight
1048 * performance advantage of sqr over mul).
1049 */
1050 if (window > 1) {
1051 if (!bn_mul_mont_fixed_top(&tmp, &am, &am, mont, ctx))
1052 goto err;
1053 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2,
1054 window))
1055 goto err;
1056 for (i = 3; i < numPowers; i++) {
1057 /* Calculate a^i = a^(i-1) * a */
1058 if (!bn_mul_mont_fixed_top(&tmp, &am, &tmp, mont, ctx))
1059 goto err;
1060 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i,
1061 window))
1062 goto err;
1063 }
1064 }
1065
1066 /*
1067 * The exponent may not have a whole number of fixed-size windows.
1068 * To simplify the main loop, the initial window has between 1 and
1069 * full-window-size bits such that what remains is always a whole
1070 * number of windows
1071 */
1072 window0 = (bits - 1) % window + 1;
1073 wmask = (1 << window0) - 1;
1074 bits -= window0;
1075 wvalue = bn_get_bits(p, bits) & wmask;
1076 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp, top, powerbuf, wvalue,
1077 window))
1078 goto err;
1079
1080 wmask = (1 << window) - 1;
1081 /*
1082 * Scan the exponent one window at a time starting from the most
1083 * significant bits.
1084 */
1085 while (bits > 0) {
1086
1087 /* Square the result window-size times */
1088 for (i = 0; i < window; i++)
1089 if (!bn_mul_mont_fixed_top(&tmp, &tmp, &tmp, mont, ctx))
1090 goto err;
1091
1092 /*
1093 * Get a window's worth of bits from the exponent
1094 * This avoids calling BN_is_bit_set for each bit, which
1095 * is not only slower but also makes each bit vulnerable to
1096 * EM (and likely other) side-channel attacks like One&Done
1097 * (for details see "One&Done: A Single-Decryption EM-Based
1098 * Attack on OpenSSL's Constant-Time Blinded RSA" by M. Alam,
1099 * H. Khan, M. Dey, N. Sinha, R. Callan, A. Zajic, and
1100 * M. Prvulovic, in USENIX Security'18)
1101 */
1102 bits -= window;
1103 wvalue = bn_get_bits(p, bits) & wmask;
1104 /*
1105 * Fetch the appropriate pre-computed value from the pre-buf
1106 */
1107 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue,
1108 window))
1109 goto err;
1110
1111 /* Multiply the result into the intermediate result */
1112 if (!bn_mul_mont_fixed_top(&tmp, &tmp, &am, mont, ctx))
1113 goto err;
1114 }
1115 }
1116
1117 /*
1118 * Done with zero-padded intermediate BIGNUMs. Final BN_from_montgomery
1119 * removes padding [if any] and makes return value suitable for public
1120 * API consumer.
1121 */
1122 #if defined(SPARC_T4_MONT)
1123 if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
1124 am.d[0] = 1; /* borrow am */
1125 for (i = 1; i < top; i++)
1126 am.d[i] = 0;
1127 if (!BN_mod_mul_montgomery(rr, &tmp, &am, mont, ctx))
1128 goto err;
1129 } else
1130 #endif
1131 if (!bn_from_mont_fixed_top(rr, &tmp, mont, ctx))
1132 goto err;
1133 ret = 1;
1134 err:
1135 if (in_mont == NULL)
1136 BN_MONT_CTX_free(mont);
1137 if (powerbuf != NULL) {
1138 OPENSSL_cleanse(powerbuf, powerbufLen);
1139 OPENSSL_free(powerbufFree);
1140 }
1141 BN_CTX_end(ctx);
1142 return ret;
1143 }
1144
BN_mod_exp_mont_consttime(BIGNUM * rr,const BIGNUM * a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx,BN_MONT_CTX * in_mont)1145 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
1146 const BIGNUM *m, BN_CTX *ctx,
1147 BN_MONT_CTX *in_mont)
1148 {
1149 bn_check_top(a);
1150 bn_check_top(p);
1151 bn_check_top(m);
1152 if (!bn_mod_exp_mont_fixed_top(rr, a, p, m, ctx, in_mont))
1153 return 0;
1154 bn_correct_top(rr);
1155 return 1;
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)) && (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
1169 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
1170 /*
1171 * BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is
1172 * probably more overhead than always using BN_mod (which uses BN_copy if
1173 * a similar test returns true).
1174 */
1175 /*
1176 * We can use BN_mod and do not need BN_nnmod because our accumulator is
1177 * never negative (the result of BN_mod does not depend on the sign of
1178 * the modulus).
1179 */
1180 #define BN_TO_MONTGOMERY_WORD(r, w, mont) \
1181 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
1182
1183 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
1184 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) {
1185 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1186 ERR_raise(ERR_LIB_BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1187 return 0;
1188 }
1189
1190 bn_check_top(p);
1191 bn_check_top(m);
1192
1193 if (!BN_is_odd(m)) {
1194 ERR_raise(ERR_LIB_BN, BN_R_CALLED_WITH_EVEN_MODULUS);
1195 return 0;
1196 }
1197 if (m->top == 1)
1198 a %= m->d[0]; /* make sure that 'a' is reduced */
1199
1200 bits = BN_num_bits(p);
1201 if (bits == 0) {
1202 /* x**0 mod 1, or x**0 mod -1 is still zero. */
1203 if (BN_abs_is_word(m, 1)) {
1204 ret = 1;
1205 BN_zero(rr);
1206 } else {
1207 ret = BN_one(rr);
1208 }
1209 return ret;
1210 }
1211 if (a == 0) {
1212 BN_zero(rr);
1213 ret = 1;
1214 return ret;
1215 }
1216
1217 BN_CTX_start(ctx);
1218 r = BN_CTX_get(ctx);
1219 t = BN_CTX_get(ctx);
1220 if (t == NULL)
1221 goto err;
1222
1223 if (in_mont != NULL)
1224 mont = in_mont;
1225 else {
1226 if ((mont = BN_MONT_CTX_new()) == NULL)
1227 goto err;
1228 if (!BN_MONT_CTX_set(mont, m, ctx))
1229 goto err;
1230 }
1231
1232 r_is_one = 1; /* except for Montgomery factor */
1233
1234 /* bits-1 >= 0 */
1235
1236 /* The result is accumulated in the product r*w. */
1237 w = a; /* bit 'bits-1' of 'p' is always set */
1238 for (b = bits - 2; b >= 0; b--) {
1239 /* First, square r*w. */
1240 next_w = w * w;
1241 if ((next_w / w) != w) { /* overflow */
1242 if (r_is_one) {
1243 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1244 goto err;
1245 r_is_one = 0;
1246 } else {
1247 if (!BN_MOD_MUL_WORD(r, w, m))
1248 goto err;
1249 }
1250 next_w = 1;
1251 }
1252 w = next_w;
1253 if (!r_is_one) {
1254 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
1255 goto err;
1256 }
1257
1258 /* Second, multiply r*w by 'a' if exponent bit is set. */
1259 if (BN_is_bit_set(p, b)) {
1260 next_w = w * a;
1261 if ((next_w / a) != w) { /* overflow */
1262 if (r_is_one) {
1263 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1264 goto err;
1265 r_is_one = 0;
1266 } else {
1267 if (!BN_MOD_MUL_WORD(r, w, m))
1268 goto err;
1269 }
1270 next_w = a;
1271 }
1272 w = next_w;
1273 }
1274 }
1275
1276 /* Finally, set r:=r*w. */
1277 if (w != 1) {
1278 if (r_is_one) {
1279 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1280 goto err;
1281 r_is_one = 0;
1282 } else {
1283 if (!BN_MOD_MUL_WORD(r, w, m))
1284 goto err;
1285 }
1286 }
1287
1288 if (r_is_one) { /* can happen only if a == 1 */
1289 if (!BN_one(rr))
1290 goto err;
1291 } else {
1292 if (!BN_from_montgomery(rr, r, mont, ctx))
1293 goto err;
1294 }
1295 ret = 1;
1296 err:
1297 if (in_mont == NULL)
1298 BN_MONT_CTX_free(mont);
1299 BN_CTX_end(ctx);
1300 bn_check_top(rr);
1301 return ret;
1302 }
1303
1304 /* The old fallback, simple version :-) */
BN_mod_exp_simple(BIGNUM * r,const BIGNUM * a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx)1305 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
1306 const BIGNUM *m, BN_CTX *ctx)
1307 {
1308 int i, j, bits, ret = 0, wstart, wend, window;
1309 int start = 1;
1310 BIGNUM *d;
1311 /* Table of variables obtained from 'ctx' */
1312 BIGNUM *val[TABLE_SIZE];
1313
1314 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
1315 || BN_get_flags(a, BN_FLG_CONSTTIME) != 0
1316 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) {
1317 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1318 ERR_raise(ERR_LIB_BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1319 return 0;
1320 }
1321
1322 if (r == m) {
1323 ERR_raise(ERR_LIB_BN, ERR_R_PASSED_INVALID_ARGUMENT);
1324 return 0;
1325 }
1326
1327 bits = BN_num_bits(p);
1328 if (bits == 0) {
1329 /* x**0 mod 1, or x**0 mod -1 is still zero. */
1330 if (BN_abs_is_word(m, 1)) {
1331 ret = 1;
1332 BN_zero(r);
1333 } else {
1334 ret = BN_one(r);
1335 }
1336 return ret;
1337 }
1338
1339 BN_CTX_start(ctx);
1340 d = BN_CTX_get(ctx);
1341 val[0] = BN_CTX_get(ctx);
1342 if (val[0] == NULL)
1343 goto err;
1344
1345 if (!BN_nnmod(val[0], a, m, ctx))
1346 goto err; /* 1 */
1347 if (BN_is_zero(val[0])) {
1348 BN_zero(r);
1349 ret = 1;
1350 goto err;
1351 }
1352
1353 window = BN_window_bits_for_exponent_size(bits);
1354 if (window > 1) {
1355 if (!BN_mod_mul(d, val[0], val[0], m, ctx))
1356 goto err; /* 2 */
1357 j = 1 << (window - 1);
1358 for (i = 1; i < j; i++) {
1359 if (((val[i] = BN_CTX_get(ctx)) == NULL) || !BN_mod_mul(val[i], val[i - 1], d, m, ctx))
1360 goto err;
1361 }
1362 }
1363
1364 start = 1; /* This is used to avoid multiplication etc
1365 * when there is only the value '1' in the
1366 * buffer. */
1367 wstart = bits - 1; /* The top bit of the window */
1368 wend = 0; /* The bottom bit of the window */
1369
1370 if (r == p) {
1371 BIGNUM *p_dup = BN_CTX_get(ctx);
1372
1373 if (p_dup == NULL || BN_copy(p_dup, p) == NULL)
1374 goto err;
1375 p = p_dup;
1376 }
1377
1378 if (!BN_one(r))
1379 goto err;
1380
1381 for (;;) {
1382 int wvalue; /* The 'value' of the window */
1383
1384 if (BN_is_bit_set(p, wstart) == 0) {
1385 if (!start)
1386 if (!BN_mod_mul(r, r, r, m, ctx))
1387 goto err;
1388 if (wstart == 0)
1389 break;
1390 wstart--;
1391 continue;
1392 }
1393 /*
1394 * We now have wstart on a 'set' bit, we now need to work out how bit
1395 * a window to do. To do this we need to scan forward until the last
1396 * set bit before the end of the window
1397 */
1398 wvalue = 1;
1399 wend = 0;
1400 for (i = 1; i < window; i++) {
1401 if (wstart - i < 0)
1402 break;
1403 if (BN_is_bit_set(p, wstart - i)) {
1404 wvalue <<= (i - wend);
1405 wvalue |= 1;
1406 wend = i;
1407 }
1408 }
1409
1410 /* wend is the size of the current window */
1411 j = wend + 1;
1412 /* add the 'bytes above' */
1413 if (!start)
1414 for (i = 0; i < j; i++) {
1415 if (!BN_mod_mul(r, r, r, m, ctx))
1416 goto err;
1417 }
1418
1419 /* wvalue will be an odd number < 2^window */
1420 if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx))
1421 goto err;
1422
1423 /* move the 'window' down further */
1424 wstart -= wend + 1;
1425 start = 0;
1426 if (wstart < 0)
1427 break;
1428 }
1429 ret = 1;
1430 err:
1431 BN_CTX_end(ctx);
1432 bn_check_top(r);
1433 return ret;
1434 }
1435
1436 /*
1437 * This is a variant of modular exponentiation optimization that does
1438 * parallel 2-primes exponentiation using 256-bit (AVX512VL) AVX512_IFMA ISA
1439 * or AVX_IFMA ISA in 52-bit binary redundant representation.
1440 * If such instructions are not available, or input data size is not supported,
1441 * it falls back to two BN_mod_exp_mont_consttime() calls.
1442 */
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)1443 int BN_mod_exp_mont_consttime_x2(BIGNUM *rr1, const BIGNUM *a1, const BIGNUM *p1,
1444 const BIGNUM *m1, BN_MONT_CTX *in_mont1,
1445 BIGNUM *rr2, const BIGNUM *a2, const BIGNUM *p2,
1446 const BIGNUM *m2, BN_MONT_CTX *in_mont2,
1447 BN_CTX *ctx)
1448 {
1449 int ret = 0;
1450
1451 #ifdef RSAZ_ENABLED
1452 BN_MONT_CTX *mont1 = NULL;
1453 BN_MONT_CTX *mont2 = NULL;
1454
1455 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)))) {
1456
1457 int topn = a1->top;
1458 /* Modulus bits of |m1| and |m2| are equal */
1459 int mod_bits = BN_num_bits(m1);
1460
1461 if (bn_wexpand(rr1, topn) == NULL)
1462 goto err;
1463 if (bn_wexpand(rr2, topn) == NULL)
1464 goto err;
1465
1466 /* Ensure that montgomery contexts are initialized */
1467 if (in_mont1 != NULL) {
1468 mont1 = in_mont1;
1469 } else {
1470 if ((mont1 = BN_MONT_CTX_new()) == NULL)
1471 goto err;
1472 if (!BN_MONT_CTX_set(mont1, m1, ctx))
1473 goto err;
1474 }
1475 if (in_mont2 != NULL) {
1476 mont2 = in_mont2;
1477 } else {
1478 if ((mont2 = BN_MONT_CTX_new()) == NULL)
1479 goto err;
1480 if (!BN_MONT_CTX_set(mont2, m2, ctx))
1481 goto err;
1482 }
1483
1484 ret = ossl_rsaz_mod_exp_avx512_x2(rr1->d, a1->d, p1->d, m1->d,
1485 mont1->RR.d, mont1->n0[0],
1486 rr2->d, a2->d, p2->d, m2->d,
1487 mont2->RR.d, mont2->n0[0],
1488 mod_bits);
1489
1490 rr1->top = topn;
1491 rr1->neg = 0;
1492 bn_correct_top(rr1);
1493 bn_check_top(rr1);
1494
1495 rr2->top = topn;
1496 rr2->neg = 0;
1497 bn_correct_top(rr2);
1498 bn_check_top(rr2);
1499
1500 goto err;
1501 }
1502 #endif
1503
1504 /* rr1 = a1^p1 mod m1 */
1505 ret = BN_mod_exp_mont_consttime(rr1, a1, p1, m1, ctx, in_mont1);
1506 /* rr2 = a2^p2 mod m2 */
1507 ret &= BN_mod_exp_mont_consttime(rr2, a2, p2, m2, ctx, in_mont2);
1508
1509 #ifdef RSAZ_ENABLED
1510 err:
1511 if (in_mont2 == NULL)
1512 BN_MONT_CTX_free(mont2);
1513 if (in_mont1 == NULL)
1514 BN_MONT_CTX_free(mont1);
1515 #endif
1516
1517 return ret;
1518 }
1519