1 | /* |
2 | * Copyright 1995-2018 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 "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 | /* this one works - simple but works */ |
41 | int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx) |
42 | { |
43 | int i, bits, ret = 0; |
44 | BIGNUM *v, *rr; |
45 | |
46 | if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0 |
47 | || BN_get_flags(a, BN_FLG_CONSTTIME) != 0) { |
48 | /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ |
49 | BNerr(BN_F_BN_EXP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); |
50 | return 0; |
51 | } |
52 | |
53 | BN_CTX_start(ctx); |
54 | rr = ((r == a) || (r == p)) ? BN_CTX_get(ctx) : r; |
55 | v = BN_CTX_get(ctx); |
56 | if (rr == NULL || v == NULL) |
57 | goto err; |
58 | |
59 | if (BN_copy(v, a) == NULL) |
60 | goto err; |
61 | bits = BN_num_bits(p); |
62 | |
63 | if (BN_is_odd(p)) { |
64 | if (BN_copy(rr, a) == NULL) |
65 | goto err; |
66 | } else { |
67 | if (!BN_one(rr)) |
68 | goto err; |
69 | } |
70 | |
71 | for (i = 1; i < bits; i++) { |
72 | if (!BN_sqr(v, v, ctx)) |
73 | goto err; |
74 | if (BN_is_bit_set(p, i)) { |
75 | if (!BN_mul(rr, rr, v, ctx)) |
76 | goto err; |
77 | } |
78 | } |
79 | if (r != rr && BN_copy(r, rr) == NULL) |
80 | goto err; |
81 | |
82 | ret = 1; |
83 | err: |
84 | BN_CTX_end(ctx); |
85 | bn_check_top(r); |
86 | return ret; |
87 | } |
88 | |
89 | int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m, |
90 | BN_CTX *ctx) |
91 | { |
92 | int ret; |
93 | |
94 | bn_check_top(a); |
95 | bn_check_top(p); |
96 | bn_check_top(m); |
97 | |
98 | /*- |
99 | * For even modulus m = 2^k*m_odd, it might make sense to compute |
100 | * a^p mod m_odd and a^p mod 2^k separately (with Montgomery |
101 | * exponentiation for the odd part), using appropriate exponent |
102 | * reductions, and combine the results using the CRT. |
103 | * |
104 | * For now, we use Montgomery only if the modulus is odd; otherwise, |
105 | * exponentiation using the reciprocal-based quick remaindering |
106 | * algorithm is used. |
107 | * |
108 | * (Timing obtained with expspeed.c [computations a^p mod m |
109 | * where a, p, m are of the same length: 256, 512, 1024, 2048, |
110 | * 4096, 8192 bits], compared to the running time of the |
111 | * standard algorithm: |
112 | * |
113 | * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration] |
114 | * 55 .. 77 % [UltraSparc processor, but |
115 | * debug-solaris-sparcv8-gcc conf.] |
116 | * |
117 | * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration] |
118 | * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc] |
119 | * |
120 | * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont |
121 | * at 2048 and more bits, but at 512 and 1024 bits, it was |
122 | * slower even than the standard algorithm! |
123 | * |
124 | * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations] |
125 | * should be obtained when the new Montgomery reduction code |
126 | * has been integrated into OpenSSL.) |
127 | */ |
128 | |
129 | #define MONT_MUL_MOD |
130 | #define MONT_EXP_WORD |
131 | #define RECP_MUL_MOD |
132 | |
133 | #ifdef MONT_MUL_MOD |
134 | if (BN_is_odd(m)) { |
135 | # ifdef MONT_EXP_WORD |
136 | if (a->top == 1 && !a->neg |
137 | && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0) |
138 | && (BN_get_flags(a, BN_FLG_CONSTTIME) == 0) |
139 | && (BN_get_flags(m, BN_FLG_CONSTTIME) == 0)) { |
140 | BN_ULONG A = a->d[0]; |
141 | ret = BN_mod_exp_mont_word(r, A, p, m, ctx, NULL); |
142 | } else |
143 | # endif |
144 | ret = BN_mod_exp_mont(r, a, p, m, ctx, NULL); |
145 | } else |
146 | #endif |
147 | #ifdef RECP_MUL_MOD |
148 | { |
149 | ret = BN_mod_exp_recp(r, a, p, m, ctx); |
150 | } |
151 | #else |
152 | { |
153 | ret = BN_mod_exp_simple(r, a, p, m, ctx); |
154 | } |
155 | #endif |
156 | |
157 | bn_check_top(r); |
158 | return ret; |
159 | } |
160 | |
161 | int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, |
162 | const BIGNUM *m, BN_CTX *ctx) |
163 | { |
164 | int i, j, bits, ret = 0, wstart, wend, window, wvalue; |
165 | int start = 1; |
166 | BIGNUM *aa; |
167 | /* Table of variables obtained from 'ctx' */ |
168 | BIGNUM *val[TABLE_SIZE]; |
169 | BN_RECP_CTX recp; |
170 | |
171 | if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0 |
172 | || BN_get_flags(a, BN_FLG_CONSTTIME) != 0 |
173 | || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) { |
174 | /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ |
175 | BNerr(BN_F_BN_MOD_EXP_RECP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); |
176 | return 0; |
177 | } |
178 | |
179 | bits = BN_num_bits(p); |
180 | if (bits == 0) { |
181 | /* x**0 mod 1, or x**0 mod -1 is still zero. */ |
182 | if (BN_abs_is_word(m, 1)) { |
183 | ret = 1; |
184 | BN_zero(r); |
185 | } else { |
186 | ret = BN_one(r); |
187 | } |
188 | return ret; |
189 | } |
190 | |
191 | BN_CTX_start(ctx); |
192 | aa = BN_CTX_get(ctx); |
193 | val[0] = BN_CTX_get(ctx); |
194 | if (val[0] == NULL) |
195 | goto err; |
196 | |
197 | BN_RECP_CTX_init(&recp); |
198 | if (m->neg) { |
199 | /* ignore sign of 'm' */ |
200 | if (!BN_copy(aa, m)) |
201 | goto err; |
202 | aa->neg = 0; |
203 | if (BN_RECP_CTX_set(&recp, aa, ctx) <= 0) |
204 | goto err; |
205 | } else { |
206 | if (BN_RECP_CTX_set(&recp, m, ctx) <= 0) |
207 | goto err; |
208 | } |
209 | |
210 | if (!BN_nnmod(val[0], a, m, ctx)) |
211 | goto err; /* 1 */ |
212 | if (BN_is_zero(val[0])) { |
213 | BN_zero(r); |
214 | ret = 1; |
215 | goto err; |
216 | } |
217 | |
218 | window = BN_window_bits_for_exponent_size(bits); |
219 | if (window > 1) { |
220 | if (!BN_mod_mul_reciprocal(aa, val[0], val[0], &recp, ctx)) |
221 | goto err; /* 2 */ |
222 | j = 1 << (window - 1); |
223 | for (i = 1; i < j; i++) { |
224 | if (((val[i] = BN_CTX_get(ctx)) == NULL) || |
225 | !BN_mod_mul_reciprocal(val[i], val[i - 1], aa, &recp, ctx)) |
226 | goto err; |
227 | } |
228 | } |
229 | |
230 | start = 1; /* This is used to avoid multiplication etc |
231 | * when there is only the value '1' in the |
232 | * buffer. */ |
233 | wvalue = 0; /* The 'value' of the window */ |
234 | wstart = bits - 1; /* The top bit of the window */ |
235 | wend = 0; /* The bottom bit of the window */ |
236 | |
237 | if (!BN_one(r)) |
238 | goto err; |
239 | |
240 | for (;;) { |
241 | if (BN_is_bit_set(p, wstart) == 0) { |
242 | if (!start) |
243 | if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx)) |
244 | goto err; |
245 | if (wstart == 0) |
246 | break; |
247 | wstart--; |
248 | continue; |
249 | } |
250 | /* |
251 | * We now have wstart on a 'set' bit, we now need to work out how bit |
252 | * a window to do. To do this we need to scan forward until the last |
253 | * set bit before the end of the window |
254 | */ |
255 | j = wstart; |
256 | wvalue = 1; |
257 | wend = 0; |
258 | for (i = 1; i < window; i++) { |
259 | if (wstart - i < 0) |
260 | break; |
261 | if (BN_is_bit_set(p, wstart - i)) { |
262 | wvalue <<= (i - wend); |
263 | wvalue |= 1; |
264 | wend = i; |
265 | } |
266 | } |
267 | |
268 | /* wend is the size of the current window */ |
269 | j = wend + 1; |
270 | /* add the 'bytes above' */ |
271 | if (!start) |
272 | for (i = 0; i < j; i++) { |
273 | if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx)) |
274 | goto err; |
275 | } |
276 | |
277 | /* wvalue will be an odd number < 2^window */ |
278 | if (!BN_mod_mul_reciprocal(r, r, val[wvalue >> 1], &recp, ctx)) |
279 | goto err; |
280 | |
281 | /* move the 'window' down further */ |
282 | wstart -= wend + 1; |
283 | wvalue = 0; |
284 | start = 0; |
285 | if (wstart < 0) |
286 | break; |
287 | } |
288 | ret = 1; |
289 | err: |
290 | BN_CTX_end(ctx); |
291 | BN_RECP_CTX_free(&recp); |
292 | bn_check_top(r); |
293 | return ret; |
294 | } |
295 | |
296 | int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, |
297 | const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont) |
298 | { |
299 | int i, j, bits, ret = 0, wstart, wend, window, wvalue; |
300 | int start = 1; |
301 | BIGNUM *d, *r; |
302 | const BIGNUM *aa; |
303 | /* Table of variables obtained from 'ctx' */ |
304 | BIGNUM *val[TABLE_SIZE]; |
305 | BN_MONT_CTX *mont = NULL; |
306 | |
307 | if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0 |
308 | || BN_get_flags(a, BN_FLG_CONSTTIME) != 0 |
309 | || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) { |
310 | return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont); |
311 | } |
312 | |
313 | bn_check_top(a); |
314 | bn_check_top(p); |
315 | bn_check_top(m); |
316 | |
317 | if (!BN_is_odd(m)) { |
318 | BNerr(BN_F_BN_MOD_EXP_MONT, BN_R_CALLED_WITH_EVEN_MODULUS); |
319 | return 0; |
320 | } |
321 | bits = BN_num_bits(p); |
322 | if (bits == 0) { |
323 | /* x**0 mod 1, or x**0 mod -1 is still zero. */ |
324 | if (BN_abs_is_word(m, 1)) { |
325 | ret = 1; |
326 | BN_zero(rr); |
327 | } else { |
328 | ret = BN_one(rr); |
329 | } |
330 | return ret; |
331 | } |
332 | |
333 | BN_CTX_start(ctx); |
334 | d = BN_CTX_get(ctx); |
335 | r = BN_CTX_get(ctx); |
336 | val[0] = BN_CTX_get(ctx); |
337 | if (val[0] == NULL) |
338 | goto err; |
339 | |
340 | /* |
341 | * If this is not done, things will break in the montgomery part |
342 | */ |
343 | |
344 | if (in_mont != NULL) |
345 | mont = in_mont; |
346 | else { |
347 | if ((mont = BN_MONT_CTX_new()) == NULL) |
348 | goto err; |
349 | if (!BN_MONT_CTX_set(mont, m, ctx)) |
350 | goto err; |
351 | } |
352 | |
353 | if (a->neg || BN_ucmp(a, m) >= 0) { |
354 | if (!BN_nnmod(val[0], a, m, ctx)) |
355 | goto err; |
356 | aa = val[0]; |
357 | } else |
358 | aa = a; |
359 | if (!bn_to_mont_fixed_top(val[0], aa, mont, ctx)) |
360 | goto err; /* 1 */ |
361 | |
362 | window = BN_window_bits_for_exponent_size(bits); |
363 | if (window > 1) { |
364 | if (!bn_mul_mont_fixed_top(d, val[0], val[0], mont, ctx)) |
365 | goto err; /* 2 */ |
366 | j = 1 << (window - 1); |
367 | for (i = 1; i < j; i++) { |
368 | if (((val[i] = BN_CTX_get(ctx)) == NULL) || |
369 | !bn_mul_mont_fixed_top(val[i], val[i - 1], d, mont, ctx)) |
370 | goto err; |
371 | } |
372 | } |
373 | |
374 | start = 1; /* This is used to avoid multiplication etc |
375 | * when there is only the value '1' in the |
376 | * buffer. */ |
377 | wvalue = 0; /* The 'value' of the window */ |
378 | wstart = bits - 1; /* The top bit of the window */ |
379 | wend = 0; /* The bottom bit of the window */ |
380 | |
381 | #if 1 /* by Shay Gueron's suggestion */ |
382 | j = m->top; /* borrow j */ |
383 | if (m->d[j - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) { |
384 | if (bn_wexpand(r, j) == NULL) |
385 | goto err; |
386 | /* 2^(top*BN_BITS2) - m */ |
387 | r->d[0] = (0 - m->d[0]) & BN_MASK2; |
388 | for (i = 1; i < j; i++) |
389 | r->d[i] = (~m->d[i]) & BN_MASK2; |
390 | r->top = j; |
391 | r->flags |= BN_FLG_FIXED_TOP; |
392 | } else |
393 | #endif |
394 | if (!bn_to_mont_fixed_top(r, BN_value_one(), mont, ctx)) |
395 | goto err; |
396 | for (;;) { |
397 | if (BN_is_bit_set(p, wstart) == 0) { |
398 | if (!start) { |
399 | if (!bn_mul_mont_fixed_top(r, r, r, mont, ctx)) |
400 | goto err; |
401 | } |
402 | if (wstart == 0) |
403 | break; |
404 | wstart--; |
405 | continue; |
406 | } |
407 | /* |
408 | * We now have wstart on a 'set' bit, we now need to work out how bit |
409 | * a window to do. To do this we need to scan forward until the last |
410 | * set bit before the end of the window |
411 | */ |
412 | j = wstart; |
413 | wvalue = 1; |
414 | wend = 0; |
415 | for (i = 1; i < window; i++) { |
416 | if (wstart - i < 0) |
417 | break; |
418 | if (BN_is_bit_set(p, wstart - i)) { |
419 | wvalue <<= (i - wend); |
420 | wvalue |= 1; |
421 | wend = i; |
422 | } |
423 | } |
424 | |
425 | /* wend is the size of the current window */ |
426 | j = wend + 1; |
427 | /* add the 'bytes above' */ |
428 | if (!start) |
429 | for (i = 0; i < j; i++) { |
430 | if (!bn_mul_mont_fixed_top(r, r, r, mont, ctx)) |
431 | goto err; |
432 | } |
433 | |
434 | /* wvalue will be an odd number < 2^window */ |
435 | if (!bn_mul_mont_fixed_top(r, r, val[wvalue >> 1], mont, ctx)) |
436 | goto err; |
437 | |
438 | /* move the 'window' down further */ |
439 | wstart -= wend + 1; |
440 | wvalue = 0; |
441 | start = 0; |
442 | if (wstart < 0) |
443 | break; |
444 | } |
445 | /* |
446 | * Done with zero-padded intermediate BIGNUMs. Final BN_from_montgomery |
447 | * removes padding [if any] and makes return value suitable for public |
448 | * API consumer. |
449 | */ |
450 | #if defined(SPARC_T4_MONT) |
451 | if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) { |
452 | j = mont->N.top; /* borrow j */ |
453 | val[0]->d[0] = 1; /* borrow val[0] */ |
454 | for (i = 1; i < j; i++) |
455 | val[0]->d[i] = 0; |
456 | val[0]->top = j; |
457 | if (!BN_mod_mul_montgomery(rr, r, val[0], mont, ctx)) |
458 | goto err; |
459 | } else |
460 | #endif |
461 | if (!BN_from_montgomery(rr, r, mont, ctx)) |
462 | goto err; |
463 | ret = 1; |
464 | err: |
465 | if (in_mont == NULL) |
466 | BN_MONT_CTX_free(mont); |
467 | BN_CTX_end(ctx); |
468 | bn_check_top(rr); |
469 | return ret; |
470 | } |
471 | |
472 | static BN_ULONG bn_get_bits(const BIGNUM *a, int bitpos) |
473 | { |
474 | BN_ULONG ret = 0; |
475 | int wordpos; |
476 | |
477 | wordpos = bitpos / BN_BITS2; |
478 | bitpos %= BN_BITS2; |
479 | if (wordpos >= 0 && wordpos < a->top) { |
480 | ret = a->d[wordpos] & BN_MASK2; |
481 | if (bitpos) { |
482 | ret >>= bitpos; |
483 | if (++wordpos < a->top) |
484 | ret |= a->d[wordpos] << (BN_BITS2 - bitpos); |
485 | } |
486 | } |
487 | |
488 | return ret & BN_MASK2; |
489 | } |
490 | |
491 | /* |
492 | * BN_mod_exp_mont_consttime() stores the precomputed powers in a specific |
493 | * layout so that accessing any of these table values shows the same access |
494 | * pattern as far as cache lines are concerned. The following functions are |
495 | * used to transfer a BIGNUM from/to that table. |
496 | */ |
497 | |
498 | static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top, |
499 | unsigned char *buf, int idx, |
500 | int window) |
501 | { |
502 | int i, j; |
503 | int width = 1 << window; |
504 | BN_ULONG *table = (BN_ULONG *)buf; |
505 | |
506 | if (top > b->top) |
507 | top = b->top; /* this works because 'buf' is explicitly |
508 | * zeroed */ |
509 | for (i = 0, j = idx; i < top; i++, j += width) { |
510 | table[j] = b->d[i]; |
511 | } |
512 | |
513 | return 1; |
514 | } |
515 | |
516 | static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top, |
517 | unsigned char *buf, int idx, |
518 | int window) |
519 | { |
520 | int i, j; |
521 | int width = 1 << window; |
522 | /* |
523 | * We declare table 'volatile' in order to discourage compiler |
524 | * from reordering loads from the table. Concern is that if |
525 | * reordered in specific manner loads might give away the |
526 | * information we are trying to conceal. Some would argue that |
527 | * compiler can reorder them anyway, but it can as well be |
528 | * argued that doing so would be violation of standard... |
529 | */ |
530 | volatile BN_ULONG *table = (volatile BN_ULONG *)buf; |
531 | |
532 | if (bn_wexpand(b, top) == NULL) |
533 | return 0; |
534 | |
535 | if (window <= 3) { |
536 | for (i = 0; i < top; i++, table += width) { |
537 | BN_ULONG acc = 0; |
538 | |
539 | for (j = 0; j < width; j++) { |
540 | acc |= table[j] & |
541 | ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1)); |
542 | } |
543 | |
544 | b->d[i] = acc; |
545 | } |
546 | } else { |
547 | int xstride = 1 << (window - 2); |
548 | BN_ULONG y0, y1, y2, y3; |
549 | |
550 | i = idx >> (window - 2); /* equivalent of idx / xstride */ |
551 | idx &= xstride - 1; /* equivalent of idx % xstride */ |
552 | |
553 | y0 = (BN_ULONG)0 - (constant_time_eq_int(i,0)&1); |
554 | y1 = (BN_ULONG)0 - (constant_time_eq_int(i,1)&1); |
555 | y2 = (BN_ULONG)0 - (constant_time_eq_int(i,2)&1); |
556 | y3 = (BN_ULONG)0 - (constant_time_eq_int(i,3)&1); |
557 | |
558 | for (i = 0; i < top; i++, table += width) { |
559 | BN_ULONG acc = 0; |
560 | |
561 | for (j = 0; j < xstride; j++) { |
562 | acc |= ( (table[j + 0 * xstride] & y0) | |
563 | (table[j + 1 * xstride] & y1) | |
564 | (table[j + 2 * xstride] & y2) | |
565 | (table[j + 3 * xstride] & y3) ) |
566 | & ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1)); |
567 | } |
568 | |
569 | b->d[i] = acc; |
570 | } |
571 | } |
572 | |
573 | b->top = top; |
574 | b->flags |= BN_FLG_FIXED_TOP; |
575 | return 1; |
576 | } |
577 | |
578 | /* |
579 | * Given a pointer value, compute the next address that is a cache line |
580 | * multiple. |
581 | */ |
582 | #define MOD_EXP_CTIME_ALIGN(x_) \ |
583 | ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK)))) |
584 | |
585 | /* |
586 | * This variant of BN_mod_exp_mont() uses fixed windows and the special |
587 | * precomputation memory layout to limit data-dependency to a minimum to |
588 | * protect secret exponents (cf. the hyper-threading timing attacks pointed |
589 | * out by Colin Percival, |
590 | * http://www.daemonology.net/hyperthreading-considered-harmful/) |
591 | */ |
592 | int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, |
593 | const BIGNUM *m, BN_CTX *ctx, |
594 | BN_MONT_CTX *in_mont) |
595 | { |
596 | int i, bits, ret = 0, window, wvalue, wmask, window0; |
597 | int top; |
598 | BN_MONT_CTX *mont = NULL; |
599 | |
600 | int numPowers; |
601 | unsigned char *powerbufFree = NULL; |
602 | int powerbufLen = 0; |
603 | unsigned char *powerbuf = NULL; |
604 | BIGNUM tmp, am; |
605 | #if defined(SPARC_T4_MONT) |
606 | unsigned int t4 = 0; |
607 | #endif |
608 | |
609 | bn_check_top(a); |
610 | bn_check_top(p); |
611 | bn_check_top(m); |
612 | |
613 | if (!BN_is_odd(m)) { |
614 | BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME, BN_R_CALLED_WITH_EVEN_MODULUS); |
615 | return 0; |
616 | } |
617 | |
618 | top = m->top; |
619 | |
620 | /* |
621 | * Use all bits stored in |p|, rather than |BN_num_bits|, so we do not leak |
622 | * whether the top bits are zero. |
623 | */ |
624 | bits = p->top * BN_BITS2; |
625 | if (bits == 0) { |
626 | /* x**0 mod 1, or x**0 mod -1 is still zero. */ |
627 | if (BN_abs_is_word(m, 1)) { |
628 | ret = 1; |
629 | BN_zero(rr); |
630 | } else { |
631 | ret = BN_one(rr); |
632 | } |
633 | return ret; |
634 | } |
635 | |
636 | BN_CTX_start(ctx); |
637 | |
638 | /* |
639 | * Allocate a montgomery context if it was not supplied by the caller. If |
640 | * this is not done, things will break in the montgomery part. |
641 | */ |
642 | if (in_mont != NULL) |
643 | mont = in_mont; |
644 | else { |
645 | if ((mont = BN_MONT_CTX_new()) == NULL) |
646 | goto err; |
647 | if (!BN_MONT_CTX_set(mont, m, ctx)) |
648 | goto err; |
649 | } |
650 | |
651 | if (a->neg || BN_ucmp(a, m) >= 0) { |
652 | BIGNUM *reduced = BN_CTX_get(ctx); |
653 | if (reduced == NULL |
654 | || !BN_nnmod(reduced, a, m, ctx)) { |
655 | goto err; |
656 | } |
657 | a = reduced; |
658 | } |
659 | |
660 | #ifdef RSAZ_ENABLED |
661 | /* |
662 | * If the size of the operands allow it, perform the optimized |
663 | * RSAZ exponentiation. For further information see |
664 | * crypto/bn/rsaz_exp.c and accompanying assembly modules. |
665 | */ |
666 | if ((16 == a->top) && (16 == p->top) && (BN_num_bits(m) == 1024) |
667 | && rsaz_avx2_eligible()) { |
668 | if (NULL == bn_wexpand(rr, 16)) |
669 | goto err; |
670 | RSAZ_1024_mod_exp_avx2(rr->d, a->d, p->d, m->d, mont->RR.d, |
671 | mont->n0[0]); |
672 | rr->top = 16; |
673 | rr->neg = 0; |
674 | bn_correct_top(rr); |
675 | ret = 1; |
676 | goto err; |
677 | } else if ((8 == a->top) && (8 == p->top) && (BN_num_bits(m) == 512)) { |
678 | if (NULL == bn_wexpand(rr, 8)) |
679 | goto err; |
680 | RSAZ_512_mod_exp(rr->d, a->d, p->d, m->d, mont->n0[0], mont->RR.d); |
681 | rr->top = 8; |
682 | rr->neg = 0; |
683 | bn_correct_top(rr); |
684 | ret = 1; |
685 | goto err; |
686 | } |
687 | #endif |
688 | |
689 | /* Get the window size to use with size of p. */ |
690 | window = BN_window_bits_for_ctime_exponent_size(bits); |
691 | #if defined(SPARC_T4_MONT) |
692 | if (window >= 5 && (top & 15) == 0 && top <= 64 && |
693 | (OPENSSL_sparcv9cap_P[1] & (CFR_MONTMUL | CFR_MONTSQR)) == |
694 | (CFR_MONTMUL | CFR_MONTSQR) && (t4 = OPENSSL_sparcv9cap_P[0])) |
695 | window = 5; |
696 | else |
697 | #endif |
698 | #if defined(OPENSSL_BN_ASM_MONT5) |
699 | if (window >= 5) { |
700 | window = 5; /* ~5% improvement for RSA2048 sign, and even |
701 | * for RSA4096 */ |
702 | /* reserve space for mont->N.d[] copy */ |
703 | powerbufLen += top * sizeof(mont->N.d[0]); |
704 | } |
705 | #endif |
706 | (void)0; |
707 | |
708 | /* |
709 | * Allocate a buffer large enough to hold all of the pre-computed powers |
710 | * of am, am itself and tmp. |
711 | */ |
712 | numPowers = 1 << window; |
713 | powerbufLen += sizeof(m->d[0]) * (top * numPowers + |
714 | ((2 * top) > |
715 | numPowers ? (2 * top) : numPowers)); |
716 | #ifdef alloca |
717 | if (powerbufLen < 3072) |
718 | powerbufFree = |
719 | alloca(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH); |
720 | else |
721 | #endif |
722 | if ((powerbufFree = |
723 | OPENSSL_malloc(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH)) |
724 | == NULL) |
725 | goto err; |
726 | |
727 | powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree); |
728 | memset(powerbuf, 0, powerbufLen); |
729 | |
730 | #ifdef alloca |
731 | if (powerbufLen < 3072) |
732 | powerbufFree = NULL; |
733 | #endif |
734 | |
735 | /* lay down tmp and am right after powers table */ |
736 | tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers); |
737 | am.d = tmp.d + top; |
738 | tmp.top = am.top = 0; |
739 | tmp.dmax = am.dmax = top; |
740 | tmp.neg = am.neg = 0; |
741 | tmp.flags = am.flags = BN_FLG_STATIC_DATA; |
742 | |
743 | /* prepare a^0 in Montgomery domain */ |
744 | #if 1 /* by Shay Gueron's suggestion */ |
745 | if (m->d[top - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) { |
746 | /* 2^(top*BN_BITS2) - m */ |
747 | tmp.d[0] = (0 - m->d[0]) & BN_MASK2; |
748 | for (i = 1; i < top; i++) |
749 | tmp.d[i] = (~m->d[i]) & BN_MASK2; |
750 | tmp.top = top; |
751 | } else |
752 | #endif |
753 | if (!bn_to_mont_fixed_top(&tmp, BN_value_one(), mont, ctx)) |
754 | goto err; |
755 | |
756 | /* prepare a^1 in Montgomery domain */ |
757 | if (!bn_to_mont_fixed_top(&am, a, mont, ctx)) |
758 | goto err; |
759 | |
760 | #if defined(SPARC_T4_MONT) |
761 | if (t4) { |
762 | typedef int (*bn_pwr5_mont_f) (BN_ULONG *tp, const BN_ULONG *np, |
763 | const BN_ULONG *n0, const void *table, |
764 | int power, int bits); |
765 | int bn_pwr5_mont_t4_8(BN_ULONG *tp, const BN_ULONG *np, |
766 | const BN_ULONG *n0, const void *table, |
767 | int power, int bits); |
768 | int bn_pwr5_mont_t4_16(BN_ULONG *tp, const BN_ULONG *np, |
769 | const BN_ULONG *n0, const void *table, |
770 | int power, int bits); |
771 | int bn_pwr5_mont_t4_24(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_32(BN_ULONG *tp, const BN_ULONG *np, |
775 | const BN_ULONG *n0, const void *table, |
776 | int power, int bits); |
777 | static const bn_pwr5_mont_f pwr5_funcs[4] = { |
778 | bn_pwr5_mont_t4_8, bn_pwr5_mont_t4_16, |
779 | bn_pwr5_mont_t4_24, bn_pwr5_mont_t4_32 |
780 | }; |
781 | bn_pwr5_mont_f pwr5_worker = pwr5_funcs[top / 16 - 1]; |
782 | |
783 | typedef int (*bn_mul_mont_f) (BN_ULONG *rp, const BN_ULONG *ap, |
784 | const void *bp, const BN_ULONG *np, |
785 | const BN_ULONG *n0); |
786 | int bn_mul_mont_t4_8(BN_ULONG *rp, const BN_ULONG *ap, const void *bp, |
787 | const BN_ULONG *np, const BN_ULONG *n0); |
788 | int bn_mul_mont_t4_16(BN_ULONG *rp, const BN_ULONG *ap, |
789 | const void *bp, const BN_ULONG *np, |
790 | const BN_ULONG *n0); |
791 | int bn_mul_mont_t4_24(BN_ULONG *rp, const BN_ULONG *ap, |
792 | const void *bp, const BN_ULONG *np, |
793 | const BN_ULONG *n0); |
794 | int bn_mul_mont_t4_32(BN_ULONG *rp, const BN_ULONG *ap, |
795 | const void *bp, const BN_ULONG *np, |
796 | const BN_ULONG *n0); |
797 | static const bn_mul_mont_f mul_funcs[4] = { |
798 | bn_mul_mont_t4_8, bn_mul_mont_t4_16, |
799 | bn_mul_mont_t4_24, bn_mul_mont_t4_32 |
800 | }; |
801 | bn_mul_mont_f mul_worker = mul_funcs[top / 16 - 1]; |
802 | |
803 | void bn_mul_mont_vis3(BN_ULONG *rp, const BN_ULONG *ap, |
804 | const void *bp, const BN_ULONG *np, |
805 | const BN_ULONG *n0, int num); |
806 | void bn_mul_mont_t4(BN_ULONG *rp, const BN_ULONG *ap, |
807 | const void *bp, const BN_ULONG *np, |
808 | const BN_ULONG *n0, int num); |
809 | void bn_mul_mont_gather5_t4(BN_ULONG *rp, const BN_ULONG *ap, |
810 | const void *table, const BN_ULONG *np, |
811 | const BN_ULONG *n0, int num, int power); |
812 | void bn_flip_n_scatter5_t4(const BN_ULONG *inp, size_t num, |
813 | void *table, size_t power); |
814 | void bn_gather5_t4(BN_ULONG *out, size_t num, |
815 | void *table, size_t power); |
816 | void bn_flip_t4(BN_ULONG *dst, BN_ULONG *src, size_t num); |
817 | |
818 | BN_ULONG *np = mont->N.d, *n0 = mont->n0; |
819 | int stride = 5 * (6 - (top / 16 - 1)); /* multiple of 5, but less |
820 | * than 32 */ |
821 | |
822 | /* |
823 | * BN_to_montgomery can contaminate words above .top [in |
824 | * BN_DEBUG[_DEBUG] build]... |
825 | */ |
826 | for (i = am.top; i < top; i++) |
827 | am.d[i] = 0; |
828 | for (i = tmp.top; i < top; i++) |
829 | tmp.d[i] = 0; |
830 | |
831 | bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 0); |
832 | bn_flip_n_scatter5_t4(am.d, top, powerbuf, 1); |
833 | if (!(*mul_worker) (tmp.d, am.d, am.d, np, n0) && |
834 | !(*mul_worker) (tmp.d, am.d, am.d, np, n0)) |
835 | bn_mul_mont_vis3(tmp.d, am.d, am.d, np, n0, top); |
836 | bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 2); |
837 | |
838 | for (i = 3; i < 32; i++) { |
839 | /* Calculate a^i = a^(i-1) * a */ |
840 | if (!(*mul_worker) (tmp.d, tmp.d, am.d, np, n0) && |
841 | !(*mul_worker) (tmp.d, tmp.d, am.d, np, n0)) |
842 | bn_mul_mont_vis3(tmp.d, tmp.d, am.d, np, n0, top); |
843 | bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, i); |
844 | } |
845 | |
846 | /* switch to 64-bit domain */ |
847 | np = alloca(top * sizeof(BN_ULONG)); |
848 | top /= 2; |
849 | bn_flip_t4(np, mont->N.d, top); |
850 | |
851 | /* |
852 | * The exponent may not have a whole number of fixed-size windows. |
853 | * To simplify the main loop, the initial window has between 1 and |
854 | * full-window-size bits such that what remains is always a whole |
855 | * number of windows |
856 | */ |
857 | window0 = (bits - 1) % 5 + 1; |
858 | wmask = (1 << window0) - 1; |
859 | bits -= window0; |
860 | wvalue = bn_get_bits(p, bits) & wmask; |
861 | bn_gather5_t4(tmp.d, top, powerbuf, wvalue); |
862 | |
863 | /* |
864 | * Scan the exponent one window at a time starting from the most |
865 | * significant bits. |
866 | */ |
867 | while (bits > 0) { |
868 | if (bits < stride) |
869 | stride = bits; |
870 | bits -= stride; |
871 | wvalue = bn_get_bits(p, bits); |
872 | |
873 | if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride)) |
874 | continue; |
875 | /* retry once and fall back */ |
876 | if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride)) |
877 | continue; |
878 | |
879 | bits += stride - 5; |
880 | wvalue >>= stride - 5; |
881 | wvalue &= 31; |
882 | bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); |
883 | bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); |
884 | bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); |
885 | bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); |
886 | bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); |
887 | bn_mul_mont_gather5_t4(tmp.d, tmp.d, powerbuf, np, n0, top, |
888 | wvalue); |
889 | } |
890 | |
891 | bn_flip_t4(tmp.d, tmp.d, top); |
892 | top *= 2; |
893 | /* back to 32-bit domain */ |
894 | tmp.top = top; |
895 | bn_correct_top(&tmp); |
896 | OPENSSL_cleanse(np, top * sizeof(BN_ULONG)); |
897 | } else |
898 | #endif |
899 | #if defined(OPENSSL_BN_ASM_MONT5) |
900 | if (window == 5 && top > 1) { |
901 | /* |
902 | * This optimization uses ideas from http://eprint.iacr.org/2011/239, |
903 | * specifically optimization of cache-timing attack countermeasures |
904 | * and pre-computation optimization. |
905 | */ |
906 | |
907 | /* |
908 | * Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as |
909 | * 512-bit RSA is hardly relevant, we omit it to spare size... |
910 | */ |
911 | void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap, |
912 | const void *table, const BN_ULONG *np, |
913 | const BN_ULONG *n0, int num, int power); |
914 | void bn_scatter5(const BN_ULONG *inp, size_t num, |
915 | void *table, size_t power); |
916 | void bn_gather5(BN_ULONG *out, size_t num, void *table, size_t power); |
917 | void bn_power5(BN_ULONG *rp, const BN_ULONG *ap, |
918 | const void *table, const BN_ULONG *np, |
919 | const BN_ULONG *n0, int num, int power); |
920 | int bn_get_bits5(const BN_ULONG *ap, int off); |
921 | int bn_from_montgomery(BN_ULONG *rp, const BN_ULONG *ap, |
922 | const BN_ULONG *not_used, const BN_ULONG *np, |
923 | const BN_ULONG *n0, int num); |
924 | |
925 | BN_ULONG *n0 = mont->n0, *np; |
926 | |
927 | /* |
928 | * BN_to_montgomery can contaminate words above .top [in |
929 | * BN_DEBUG[_DEBUG] build]... |
930 | */ |
931 | for (i = am.top; i < top; i++) |
932 | am.d[i] = 0; |
933 | for (i = tmp.top; i < top; i++) |
934 | tmp.d[i] = 0; |
935 | |
936 | /* |
937 | * copy mont->N.d[] to improve cache locality |
938 | */ |
939 | for (np = am.d + top, i = 0; i < top; i++) |
940 | np[i] = mont->N.d[i]; |
941 | |
942 | bn_scatter5(tmp.d, top, powerbuf, 0); |
943 | bn_scatter5(am.d, am.top, powerbuf, 1); |
944 | bn_mul_mont(tmp.d, am.d, am.d, np, n0, top); |
945 | bn_scatter5(tmp.d, top, powerbuf, 2); |
946 | |
947 | # if 0 |
948 | for (i = 3; i < 32; i++) { |
949 | /* Calculate a^i = a^(i-1) * a */ |
950 | bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); |
951 | bn_scatter5(tmp.d, top, powerbuf, i); |
952 | } |
953 | # else |
954 | /* same as above, but uses squaring for 1/2 of operations */ |
955 | for (i = 4; i < 32; i *= 2) { |
956 | bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); |
957 | bn_scatter5(tmp.d, top, powerbuf, i); |
958 | } |
959 | for (i = 3; i < 8; i += 2) { |
960 | int j; |
961 | bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); |
962 | bn_scatter5(tmp.d, top, powerbuf, i); |
963 | for (j = 2 * i; j < 32; j *= 2) { |
964 | bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); |
965 | bn_scatter5(tmp.d, top, powerbuf, j); |
966 | } |
967 | } |
968 | for (; i < 16; i += 2) { |
969 | bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); |
970 | bn_scatter5(tmp.d, top, powerbuf, i); |
971 | bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); |
972 | bn_scatter5(tmp.d, top, powerbuf, 2 * i); |
973 | } |
974 | for (; i < 32; i += 2) { |
975 | bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); |
976 | bn_scatter5(tmp.d, top, powerbuf, i); |
977 | } |
978 | # endif |
979 | /* |
980 | * The exponent may not have a whole number of fixed-size windows. |
981 | * To simplify the main loop, the initial window has between 1 and |
982 | * full-window-size bits such that what remains is always a whole |
983 | * number of windows |
984 | */ |
985 | window0 = (bits - 1) % 5 + 1; |
986 | wmask = (1 << window0) - 1; |
987 | bits -= window0; |
988 | wvalue = bn_get_bits(p, bits) & wmask; |
989 | bn_gather5(tmp.d, top, powerbuf, wvalue); |
990 | |
991 | /* |
992 | * Scan the exponent one window at a time starting from the most |
993 | * significant bits. |
994 | */ |
995 | if (top & 7) { |
996 | while (bits > 0) { |
997 | bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); |
998 | bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); |
999 | bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); |
1000 | bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); |
1001 | bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); |
1002 | bn_mul_mont_gather5(tmp.d, tmp.d, powerbuf, np, n0, top, |
1003 | bn_get_bits5(p->d, bits -= 5)); |
1004 | } |
1005 | } else { |
1006 | while (bits > 0) { |
1007 | bn_power5(tmp.d, tmp.d, powerbuf, np, n0, top, |
1008 | bn_get_bits5(p->d, bits -= 5)); |
1009 | } |
1010 | } |
1011 | |
1012 | ret = bn_from_montgomery(tmp.d, tmp.d, NULL, np, n0, top); |
1013 | tmp.top = top; |
1014 | bn_correct_top(&tmp); |
1015 | if (ret) { |
1016 | if (!BN_copy(rr, &tmp)) |
1017 | ret = 0; |
1018 | goto err; /* non-zero ret means it's not error */ |
1019 | } |
1020 | } else |
1021 | #endif |
1022 | { |
1023 | if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, window)) |
1024 | goto err; |
1025 | if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, window)) |
1026 | goto err; |
1027 | |
1028 | /* |
1029 | * If the window size is greater than 1, then calculate |
1030 | * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even |
1031 | * powers could instead be computed as (a^(i/2))^2 to use the slight |
1032 | * performance advantage of sqr over mul). |
1033 | */ |
1034 | if (window > 1) { |
1035 | if (!bn_mul_mont_fixed_top(&tmp, &am, &am, mont, ctx)) |
1036 | goto err; |
1037 | if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2, |
1038 | window)) |
1039 | goto err; |
1040 | for (i = 3; i < numPowers; i++) { |
1041 | /* Calculate a^i = a^(i-1) * a */ |
1042 | if (!bn_mul_mont_fixed_top(&tmp, &am, &tmp, mont, ctx)) |
1043 | goto err; |
1044 | if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i, |
1045 | window)) |
1046 | goto err; |
1047 | } |
1048 | } |
1049 | |
1050 | /* |
1051 | * The exponent may not have a whole number of fixed-size windows. |
1052 | * To simplify the main loop, the initial window has between 1 and |
1053 | * full-window-size bits such that what remains is always a whole |
1054 | * number of windows |
1055 | */ |
1056 | window0 = (bits - 1) % window + 1; |
1057 | wmask = (1 << window0) - 1; |
1058 | bits -= window0; |
1059 | wvalue = bn_get_bits(p, bits) & wmask; |
1060 | if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp, top, powerbuf, wvalue, |
1061 | window)) |
1062 | goto err; |
1063 | |
1064 | wmask = (1 << window) - 1; |
1065 | /* |
1066 | * Scan the exponent one window at a time starting from the most |
1067 | * significant bits. |
1068 | */ |
1069 | while (bits > 0) { |
1070 | |
1071 | /* Square the result window-size times */ |
1072 | for (i = 0; i < window; i++) |
1073 | if (!bn_mul_mont_fixed_top(&tmp, &tmp, &tmp, mont, ctx)) |
1074 | goto err; |
1075 | |
1076 | /* |
1077 | * Get a window's worth of bits from the exponent |
1078 | * This avoids calling BN_is_bit_set for each bit, which |
1079 | * is not only slower but also makes each bit vulnerable to |
1080 | * EM (and likely other) side-channel attacks like One&Done |
1081 | * (for details see "One&Done: A Single-Decryption EM-Based |
1082 | * Attack on OpenSSL's Constant-Time Blinded RSA" by M. Alam, |
1083 | * H. Khan, M. Dey, N. Sinha, R. Callan, A. Zajic, and |
1084 | * M. Prvulovic, in USENIX Security'18) |
1085 | */ |
1086 | bits -= window; |
1087 | wvalue = bn_get_bits(p, bits) & wmask; |
1088 | /* |
1089 | * Fetch the appropriate pre-computed value from the pre-buf |
1090 | */ |
1091 | if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue, |
1092 | window)) |
1093 | goto err; |
1094 | |
1095 | /* Multiply the result into the intermediate result */ |
1096 | if (!bn_mul_mont_fixed_top(&tmp, &tmp, &am, mont, ctx)) |
1097 | goto err; |
1098 | } |
1099 | } |
1100 | |
1101 | /* |
1102 | * Done with zero-padded intermediate BIGNUMs. Final BN_from_montgomery |
1103 | * removes padding [if any] and makes return value suitable for public |
1104 | * API consumer. |
1105 | */ |
1106 | #if defined(SPARC_T4_MONT) |
1107 | if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) { |
1108 | am.d[0] = 1; /* borrow am */ |
1109 | for (i = 1; i < top; i++) |
1110 | am.d[i] = 0; |
1111 | if (!BN_mod_mul_montgomery(rr, &tmp, &am, mont, ctx)) |
1112 | goto err; |
1113 | } else |
1114 | #endif |
1115 | if (!BN_from_montgomery(rr, &tmp, mont, ctx)) |
1116 | goto err; |
1117 | ret = 1; |
1118 | err: |
1119 | if (in_mont == NULL) |
1120 | BN_MONT_CTX_free(mont); |
1121 | if (powerbuf != NULL) { |
1122 | OPENSSL_cleanse(powerbuf, powerbufLen); |
1123 | OPENSSL_free(powerbufFree); |
1124 | } |
1125 | BN_CTX_end(ctx); |
1126 | return ret; |
1127 | } |
1128 | |
1129 | int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p, |
1130 | const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont) |
1131 | { |
1132 | BN_MONT_CTX *mont = NULL; |
1133 | int b, bits, ret = 0; |
1134 | int r_is_one; |
1135 | BN_ULONG w, next_w; |
1136 | BIGNUM *r, *t; |
1137 | BIGNUM *swap_tmp; |
1138 | #define BN_MOD_MUL_WORD(r, w, m) \ |
1139 | (BN_mul_word(r, (w)) && \ |
1140 | (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \ |
1141 | (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1)))) |
1142 | /* |
1143 | * BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is |
1144 | * probably more overhead than always using BN_mod (which uses BN_copy if |
1145 | * a similar test returns true). |
1146 | */ |
1147 | /* |
1148 | * We can use BN_mod and do not need BN_nnmod because our accumulator is |
1149 | * never negative (the result of BN_mod does not depend on the sign of |
1150 | * the modulus). |
1151 | */ |
1152 | #define BN_TO_MONTGOMERY_WORD(r, w, mont) \ |
1153 | (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx)) |
1154 | |
1155 | if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0 |
1156 | || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) { |
1157 | /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ |
1158 | BNerr(BN_F_BN_MOD_EXP_MONT_WORD, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); |
1159 | return 0; |
1160 | } |
1161 | |
1162 | bn_check_top(p); |
1163 | bn_check_top(m); |
1164 | |
1165 | if (!BN_is_odd(m)) { |
1166 | BNerr(BN_F_BN_MOD_EXP_MONT_WORD, BN_R_CALLED_WITH_EVEN_MODULUS); |
1167 | return 0; |
1168 | } |
1169 | if (m->top == 1) |
1170 | a %= m->d[0]; /* make sure that 'a' is reduced */ |
1171 | |
1172 | bits = BN_num_bits(p); |
1173 | if (bits == 0) { |
1174 | /* x**0 mod 1, or x**0 mod -1 is still zero. */ |
1175 | if (BN_abs_is_word(m, 1)) { |
1176 | ret = 1; |
1177 | BN_zero(rr); |
1178 | } else { |
1179 | ret = BN_one(rr); |
1180 | } |
1181 | return ret; |
1182 | } |
1183 | if (a == 0) { |
1184 | BN_zero(rr); |
1185 | ret = 1; |
1186 | return ret; |
1187 | } |
1188 | |
1189 | BN_CTX_start(ctx); |
1190 | r = BN_CTX_get(ctx); |
1191 | t = BN_CTX_get(ctx); |
1192 | if (t == NULL) |
1193 | goto err; |
1194 | |
1195 | if (in_mont != NULL) |
1196 | mont = in_mont; |
1197 | else { |
1198 | if ((mont = BN_MONT_CTX_new()) == NULL) |
1199 | goto err; |
1200 | if (!BN_MONT_CTX_set(mont, m, ctx)) |
1201 | goto err; |
1202 | } |
1203 | |
1204 | r_is_one = 1; /* except for Montgomery factor */ |
1205 | |
1206 | /* bits-1 >= 0 */ |
1207 | |
1208 | /* The result is accumulated in the product r*w. */ |
1209 | w = a; /* bit 'bits-1' of 'p' is always set */ |
1210 | for (b = bits - 2; b >= 0; b--) { |
1211 | /* First, square r*w. */ |
1212 | next_w = w * w; |
1213 | if ((next_w / w) != w) { /* overflow */ |
1214 | if (r_is_one) { |
1215 | if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) |
1216 | goto err; |
1217 | r_is_one = 0; |
1218 | } else { |
1219 | if (!BN_MOD_MUL_WORD(r, w, m)) |
1220 | goto err; |
1221 | } |
1222 | next_w = 1; |
1223 | } |
1224 | w = next_w; |
1225 | if (!r_is_one) { |
1226 | if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) |
1227 | goto err; |
1228 | } |
1229 | |
1230 | /* Second, multiply r*w by 'a' if exponent bit is set. */ |
1231 | if (BN_is_bit_set(p, b)) { |
1232 | next_w = w * a; |
1233 | if ((next_w / a) != w) { /* overflow */ |
1234 | if (r_is_one) { |
1235 | if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) |
1236 | goto err; |
1237 | r_is_one = 0; |
1238 | } else { |
1239 | if (!BN_MOD_MUL_WORD(r, w, m)) |
1240 | goto err; |
1241 | } |
1242 | next_w = a; |
1243 | } |
1244 | w = next_w; |
1245 | } |
1246 | } |
1247 | |
1248 | /* Finally, set r:=r*w. */ |
1249 | if (w != 1) { |
1250 | if (r_is_one) { |
1251 | if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) |
1252 | goto err; |
1253 | r_is_one = 0; |
1254 | } else { |
1255 | if (!BN_MOD_MUL_WORD(r, w, m)) |
1256 | goto err; |
1257 | } |
1258 | } |
1259 | |
1260 | if (r_is_one) { /* can happen only if a == 1 */ |
1261 | if (!BN_one(rr)) |
1262 | goto err; |
1263 | } else { |
1264 | if (!BN_from_montgomery(rr, r, mont, ctx)) |
1265 | goto err; |
1266 | } |
1267 | ret = 1; |
1268 | err: |
1269 | if (in_mont == NULL) |
1270 | BN_MONT_CTX_free(mont); |
1271 | BN_CTX_end(ctx); |
1272 | bn_check_top(rr); |
1273 | return ret; |
1274 | } |
1275 | |
1276 | /* The old fallback, simple version :-) */ |
1277 | int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, |
1278 | const BIGNUM *m, BN_CTX *ctx) |
1279 | { |
1280 | int i, j, bits, ret = 0, wstart, wend, window, wvalue; |
1281 | int start = 1; |
1282 | BIGNUM *d; |
1283 | /* Table of variables obtained from 'ctx' */ |
1284 | BIGNUM *val[TABLE_SIZE]; |
1285 | |
1286 | if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0 |
1287 | || BN_get_flags(a, BN_FLG_CONSTTIME) != 0 |
1288 | || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) { |
1289 | /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ |
1290 | BNerr(BN_F_BN_MOD_EXP_SIMPLE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); |
1291 | return 0; |
1292 | } |
1293 | |
1294 | bits = BN_num_bits(p); |
1295 | if (bits == 0) { |
1296 | /* x**0 mod 1, or x**0 mod -1 is still zero. */ |
1297 | if (BN_abs_is_word(m, 1)) { |
1298 | ret = 1; |
1299 | BN_zero(r); |
1300 | } else { |
1301 | ret = BN_one(r); |
1302 | } |
1303 | return ret; |
1304 | } |
1305 | |
1306 | BN_CTX_start(ctx); |
1307 | d = BN_CTX_get(ctx); |
1308 | val[0] = BN_CTX_get(ctx); |
1309 | if (val[0] == NULL) |
1310 | goto err; |
1311 | |
1312 | if (!BN_nnmod(val[0], a, m, ctx)) |
1313 | goto err; /* 1 */ |
1314 | if (BN_is_zero(val[0])) { |
1315 | BN_zero(r); |
1316 | ret = 1; |
1317 | goto err; |
1318 | } |
1319 | |
1320 | window = BN_window_bits_for_exponent_size(bits); |
1321 | if (window > 1) { |
1322 | if (!BN_mod_mul(d, val[0], val[0], m, ctx)) |
1323 | goto err; /* 2 */ |
1324 | j = 1 << (window - 1); |
1325 | for (i = 1; i < j; i++) { |
1326 | if (((val[i] = BN_CTX_get(ctx)) == NULL) || |
1327 | !BN_mod_mul(val[i], val[i - 1], d, m, ctx)) |
1328 | goto err; |
1329 | } |
1330 | } |
1331 | |
1332 | start = 1; /* This is used to avoid multiplication etc |
1333 | * when there is only the value '1' in the |
1334 | * buffer. */ |
1335 | wvalue = 0; /* The 'value' of the window */ |
1336 | wstart = bits - 1; /* The top bit of the window */ |
1337 | wend = 0; /* The bottom bit of the window */ |
1338 | |
1339 | if (!BN_one(r)) |
1340 | goto err; |
1341 | |
1342 | for (;;) { |
1343 | if (BN_is_bit_set(p, wstart) == 0) { |
1344 | if (!start) |
1345 | if (!BN_mod_mul(r, r, r, m, ctx)) |
1346 | goto err; |
1347 | if (wstart == 0) |
1348 | break; |
1349 | wstart--; |
1350 | continue; |
1351 | } |
1352 | /* |
1353 | * We now have wstart on a 'set' bit, we now need to work out how bit |
1354 | * a window to do. To do this we need to scan forward until the last |
1355 | * set bit before the end of the window |
1356 | */ |
1357 | j = wstart; |
1358 | wvalue = 1; |
1359 | wend = 0; |
1360 | for (i = 1; i < window; i++) { |
1361 | if (wstart - i < 0) |
1362 | break; |
1363 | if (BN_is_bit_set(p, wstart - i)) { |
1364 | wvalue <<= (i - wend); |
1365 | wvalue |= 1; |
1366 | wend = i; |
1367 | } |
1368 | } |
1369 | |
1370 | /* wend is the size of the current window */ |
1371 | j = wend + 1; |
1372 | /* add the 'bytes above' */ |
1373 | if (!start) |
1374 | for (i = 0; i < j; i++) { |
1375 | if (!BN_mod_mul(r, r, r, m, ctx)) |
1376 | goto err; |
1377 | } |
1378 | |
1379 | /* wvalue will be an odd number < 2^window */ |
1380 | if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx)) |
1381 | goto err; |
1382 | |
1383 | /* move the 'window' down further */ |
1384 | wstart -= wend + 1; |
1385 | wvalue = 0; |
1386 | start = 0; |
1387 | if (wstart < 0) |
1388 | break; |
1389 | } |
1390 | ret = 1; |
1391 | err: |
1392 | BN_CTX_end(ctx); |
1393 | bn_check_top(r); |
1394 | return ret; |
1395 | } |
1396 | |