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d02b48c6 | 1 | /* crypto/bn/bn_exp.c */ |
58964a49 | 2 | /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com) |
d02b48c6 RE |
3 | * All rights reserved. |
4 | * | |
5 | * This package is an SSL implementation written | |
6 | * by Eric Young (eay@cryptsoft.com). | |
7 | * The implementation was written so as to conform with Netscapes SSL. | |
0f113f3e | 8 | * |
d02b48c6 RE |
9 | * This library is free for commercial and non-commercial use as long as |
10 | * the following conditions are aheared to. The following conditions | |
11 | * apply to all code found in this distribution, be it the RC4, RSA, | |
12 | * lhash, DES, etc., code; not just the SSL code. The SSL documentation | |
13 | * included with this distribution is covered by the same copyright terms | |
14 | * except that the holder is Tim Hudson (tjh@cryptsoft.com). | |
0f113f3e | 15 | * |
d02b48c6 RE |
16 | * Copyright remains Eric Young's, and as such any Copyright notices in |
17 | * the code are not to be removed. | |
18 | * If this package is used in a product, Eric Young should be given attribution | |
19 | * as the author of the parts of the library used. | |
20 | * This can be in the form of a textual message at program startup or | |
21 | * in documentation (online or textual) provided with the package. | |
0f113f3e | 22 | * |
d02b48c6 RE |
23 | * Redistribution and use in source and binary forms, with or without |
24 | * modification, are permitted provided that the following conditions | |
25 | * are met: | |
26 | * 1. Redistributions of source code must retain the copyright | |
27 | * notice, this list of conditions and the following disclaimer. | |
28 | * 2. Redistributions in binary form must reproduce the above copyright | |
29 | * notice, this list of conditions and the following disclaimer in the | |
30 | * documentation and/or other materials provided with the distribution. | |
31 | * 3. All advertising materials mentioning features or use of this software | |
32 | * must display the following acknowledgement: | |
33 | * "This product includes cryptographic software written by | |
34 | * Eric Young (eay@cryptsoft.com)" | |
35 | * The word 'cryptographic' can be left out if the rouines from the library | |
36 | * being used are not cryptographic related :-). | |
0f113f3e | 37 | * 4. If you include any Windows specific code (or a derivative thereof) from |
d02b48c6 RE |
38 | * the apps directory (application code) you must include an acknowledgement: |
39 | * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)" | |
0f113f3e | 40 | * |
d02b48c6 RE |
41 | * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND |
42 | * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE | |
43 | * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE | |
44 | * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE | |
45 | * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL | |
46 | * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS | |
47 | * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) | |
48 | * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT | |
49 | * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY | |
50 | * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF | |
51 | * SUCH DAMAGE. | |
0f113f3e | 52 | * |
d02b48c6 RE |
53 | * The licence and distribution terms for any publically available version or |
54 | * derivative of this code cannot be changed. i.e. this code cannot simply be | |
55 | * copied and put under another distribution licence | |
56 | * [including the GNU Public Licence.] | |
57 | */ | |
f8989a21 | 58 | /* ==================================================================== |
46a64376 | 59 | * Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved. |
f8989a21 BM |
60 | * |
61 | * Redistribution and use in source and binary forms, with or without | |
62 | * modification, are permitted provided that the following conditions | |
63 | * are met: | |
64 | * | |
65 | * 1. Redistributions of source code must retain the above copyright | |
0f113f3e | 66 | * notice, this list of conditions and the following disclaimer. |
f8989a21 BM |
67 | * |
68 | * 2. Redistributions in binary form must reproduce the above copyright | |
69 | * notice, this list of conditions and the following disclaimer in | |
70 | * the documentation and/or other materials provided with the | |
71 | * distribution. | |
72 | * | |
73 | * 3. All advertising materials mentioning features or use of this | |
74 | * software must display the following acknowledgment: | |
75 | * "This product includes software developed by the OpenSSL Project | |
76 | * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" | |
77 | * | |
78 | * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to | |
79 | * endorse or promote products derived from this software without | |
80 | * prior written permission. For written permission, please contact | |
81 | * openssl-core@openssl.org. | |
82 | * | |
83 | * 5. Products derived from this software may not be called "OpenSSL" | |
84 | * nor may "OpenSSL" appear in their names without prior written | |
85 | * permission of the OpenSSL Project. | |
86 | * | |
87 | * 6. Redistributions of any form whatsoever must retain the following | |
88 | * acknowledgment: | |
89 | * "This product includes software developed by the OpenSSL Project | |
90 | * for use in the OpenSSL Toolkit (http://www.openssl.org/)" | |
91 | * | |
92 | * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY | |
93 | * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE | |
94 | * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR | |
95 | * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR | |
96 | * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, | |
97 | * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT | |
98 | * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; | |
99 | * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) | |
100 | * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, | |
101 | * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) | |
102 | * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED | |
103 | * OF THE POSSIBILITY OF SUCH DAMAGE. | |
104 | * ==================================================================== | |
105 | * | |
106 | * This product includes cryptographic software written by Eric Young | |
107 | * (eay@cryptsoft.com). This product includes software written by Tim | |
108 | * Hudson (tjh@cryptsoft.com). | |
109 | * | |
110 | */ | |
111 | ||
b39fc560 | 112 | #include "internal/cryptlib.h" |
d02b48c6 | 113 | #include "bn_lcl.h" |
6dad7bd6 | 114 | |
361512da AP |
115 | #include <stdlib.h> |
116 | #ifdef _WIN32 | |
117 | # include <malloc.h> | |
118 | # ifndef alloca | |
119 | # define alloca _alloca | |
120 | # endif | |
121 | #elif defined(__GNUC__) | |
122 | # ifndef alloca | |
123 | # define alloca(s) __builtin_alloca((s)) | |
124 | # endif | |
b74ce8d9 AP |
125 | #elif defined(__sun) |
126 | # include <alloca.h> | |
361512da AP |
127 | #endif |
128 | ||
ed45f3c2 | 129 | #include "rsaz_exp.h" |
ca48ace5 | 130 | |
cbce8c46 | 131 | #undef SPARC_T4_MONT |
b69437e1 | 132 | #if defined(OPENSSL_BN_ASM_MONT) && (defined(__sparc__) || defined(__sparc)) |
68c06bf6 AP |
133 | # include "sparc_arch.h" |
134 | extern unsigned int OPENSSL_sparcv9cap_P[]; | |
cbce8c46 | 135 | # define SPARC_T4_MONT |
68c06bf6 AP |
136 | #endif |
137 | ||
46a64376 | 138 | /* maximum precomputation table size for *variable* sliding windows */ |
0f113f3e | 139 | #define TABLE_SIZE 32 |
dfeab068 | 140 | |
58964a49 | 141 | /* this one works - simple but works */ |
020fc820 | 142 | int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx) |
0f113f3e MC |
143 | { |
144 | int i, bits, ret = 0; | |
145 | BIGNUM *v, *rr; | |
146 | ||
147 | if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) { | |
148 | /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ | |
149 | BNerr(BN_F_BN_EXP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); | |
150 | return -1; | |
151 | } | |
152 | ||
153 | BN_CTX_start(ctx); | |
154 | if ((r == a) || (r == p)) | |
155 | rr = BN_CTX_get(ctx); | |
156 | else | |
157 | rr = r; | |
158 | v = BN_CTX_get(ctx); | |
159 | if (rr == NULL || v == NULL) | |
160 | goto err; | |
161 | ||
162 | if (BN_copy(v, a) == NULL) | |
163 | goto err; | |
164 | bits = BN_num_bits(p); | |
165 | ||
166 | if (BN_is_odd(p)) { | |
167 | if (BN_copy(rr, a) == NULL) | |
168 | goto err; | |
169 | } else { | |
170 | if (!BN_one(rr)) | |
171 | goto err; | |
172 | } | |
173 | ||
174 | for (i = 1; i < bits; i++) { | |
175 | if (!BN_sqr(v, v, ctx)) | |
176 | goto err; | |
177 | if (BN_is_bit_set(p, i)) { | |
178 | if (!BN_mul(rr, rr, v, ctx)) | |
179 | goto err; | |
180 | } | |
181 | } | |
0f113f3e MC |
182 | if (r != rr) |
183 | BN_copy(r, rr); | |
8c5a7b33 MC |
184 | ret = 1; |
185 | err: | |
0f113f3e MC |
186 | BN_CTX_end(ctx); |
187 | bn_check_top(r); | |
188 | return (ret); | |
189 | } | |
6dad7bd6 | 190 | |
020fc820 | 191 | int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m, |
0f113f3e MC |
192 | BN_CTX *ctx) |
193 | { | |
194 | int ret; | |
195 | ||
196 | bn_check_top(a); | |
197 | bn_check_top(p); | |
198 | bn_check_top(m); | |
199 | ||
50e735f9 MC |
200 | /*- |
201 | * For even modulus m = 2^k*m_odd, it might make sense to compute | |
202 | * a^p mod m_odd and a^p mod 2^k separately (with Montgomery | |
203 | * exponentiation for the odd part), using appropriate exponent | |
204 | * reductions, and combine the results using the CRT. | |
205 | * | |
206 | * For now, we use Montgomery only if the modulus is odd; otherwise, | |
207 | * exponentiation using the reciprocal-based quick remaindering | |
208 | * algorithm is used. | |
209 | * | |
210 | * (Timing obtained with expspeed.c [computations a^p mod m | |
211 | * where a, p, m are of the same length: 256, 512, 1024, 2048, | |
212 | * 4096, 8192 bits], compared to the running time of the | |
213 | * standard algorithm: | |
214 | * | |
215 | * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration] | |
216 | * 55 .. 77 % [UltraSparc processor, but | |
217 | * debug-solaris-sparcv8-gcc conf.] | |
218 | * | |
219 | * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration] | |
220 | * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc] | |
221 | * | |
222 | * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont | |
223 | * at 2048 and more bits, but at 512 and 1024 bits, it was | |
224 | * slower even than the standard algorithm! | |
225 | * | |
226 | * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations] | |
227 | * should be obtained when the new Montgomery reduction code | |
228 | * has been integrated into OpenSSL.) | |
229 | */ | |
78a0c1f1 BM |
230 | |
231 | #define MONT_MUL_MOD | |
25439b76 | 232 | #define MONT_EXP_WORD |
78a0c1f1 BM |
233 | #define RECP_MUL_MOD |
234 | ||
d02b48c6 | 235 | #ifdef MONT_MUL_MOD |
0f113f3e MC |
236 | /* |
237 | * I have finally been able to take out this pre-condition of the top bit | |
238 | * being set. It was caused by an error in BN_div with negatives. There | |
239 | * was also another problem when for a^b%m a >= m. eay 07-May-97 | |
240 | */ | |
241 | /* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */ | |
242 | ||
243 | if (BN_is_odd(m)) { | |
244 | # ifdef MONT_EXP_WORD | |
245 | if (a->top == 1 && !a->neg | |
246 | && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0)) { | |
247 | BN_ULONG A = a->d[0]; | |
248 | ret = BN_mod_exp_mont_word(r, A, p, m, ctx, NULL); | |
249 | } else | |
250 | # endif | |
251 | ret = BN_mod_exp_mont(r, a, p, m, ctx, NULL); | |
252 | } else | |
d02b48c6 RE |
253 | #endif |
254 | #ifdef RECP_MUL_MOD | |
0f113f3e MC |
255 | { |
256 | ret = BN_mod_exp_recp(r, a, p, m, ctx); | |
257 | } | |
d02b48c6 | 258 | #else |
0f113f3e MC |
259 | { |
260 | ret = BN_mod_exp_simple(r, a, p, m, ctx); | |
261 | } | |
d02b48c6 RE |
262 | #endif |
263 | ||
0f113f3e MC |
264 | bn_check_top(r); |
265 | return (ret); | |
266 | } | |
6dad7bd6 | 267 | |
84c15db5 | 268 | int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, |
0f113f3e MC |
269 | const BIGNUM *m, BN_CTX *ctx) |
270 | { | |
271 | int i, j, bits, ret = 0, wstart, wend, window, wvalue; | |
272 | int start = 1; | |
273 | BIGNUM *aa; | |
274 | /* Table of variables obtained from 'ctx' */ | |
275 | BIGNUM *val[TABLE_SIZE]; | |
276 | BN_RECP_CTX recp; | |
277 | ||
278 | if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) { | |
279 | /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ | |
280 | BNerr(BN_F_BN_MOD_EXP_RECP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); | |
281 | return -1; | |
282 | } | |
283 | ||
284 | bits = BN_num_bits(p); | |
285 | ||
286 | if (bits == 0) { | |
287 | ret = BN_one(r); | |
288 | return ret; | |
289 | } | |
290 | ||
291 | BN_CTX_start(ctx); | |
292 | aa = BN_CTX_get(ctx); | |
293 | val[0] = BN_CTX_get(ctx); | |
294 | if (!aa || !val[0]) | |
295 | goto err; | |
296 | ||
297 | BN_RECP_CTX_init(&recp); | |
298 | if (m->neg) { | |
299 | /* ignore sign of 'm' */ | |
300 | if (!BN_copy(aa, m)) | |
301 | goto err; | |
302 | aa->neg = 0; | |
303 | if (BN_RECP_CTX_set(&recp, aa, ctx) <= 0) | |
304 | goto err; | |
305 | } else { | |
306 | if (BN_RECP_CTX_set(&recp, m, ctx) <= 0) | |
307 | goto err; | |
308 | } | |
309 | ||
310 | if (!BN_nnmod(val[0], a, m, ctx)) | |
311 | goto err; /* 1 */ | |
312 | if (BN_is_zero(val[0])) { | |
313 | BN_zero(r); | |
314 | ret = 1; | |
315 | goto err; | |
316 | } | |
317 | ||
318 | window = BN_window_bits_for_exponent_size(bits); | |
319 | if (window > 1) { | |
320 | if (!BN_mod_mul_reciprocal(aa, val[0], val[0], &recp, ctx)) | |
321 | goto err; /* 2 */ | |
322 | j = 1 << (window - 1); | |
323 | for (i = 1; i < j; i++) { | |
324 | if (((val[i] = BN_CTX_get(ctx)) == NULL) || | |
325 | !BN_mod_mul_reciprocal(val[i], val[i - 1], aa, &recp, ctx)) | |
326 | goto err; | |
327 | } | |
328 | } | |
329 | ||
330 | start = 1; /* This is used to avoid multiplication etc | |
331 | * when there is only the value '1' in the | |
332 | * buffer. */ | |
333 | wvalue = 0; /* The 'value' of the window */ | |
334 | wstart = bits - 1; /* The top bit of the window */ | |
335 | wend = 0; /* The bottom bit of the window */ | |
336 | ||
337 | if (!BN_one(r)) | |
338 | goto err; | |
339 | ||
340 | for (;;) { | |
341 | if (BN_is_bit_set(p, wstart) == 0) { | |
342 | if (!start) | |
343 | if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx)) | |
344 | goto err; | |
345 | if (wstart == 0) | |
346 | break; | |
347 | wstart--; | |
348 | continue; | |
349 | } | |
350 | /* | |
351 | * We now have wstart on a 'set' bit, we now need to work out how bit | |
352 | * a window to do. To do this we need to scan forward until the last | |
353 | * set bit before the end of the window | |
354 | */ | |
355 | j = wstart; | |
356 | wvalue = 1; | |
357 | wend = 0; | |
358 | for (i = 1; i < window; i++) { | |
359 | if (wstart - i < 0) | |
360 | break; | |
361 | if (BN_is_bit_set(p, wstart - i)) { | |
362 | wvalue <<= (i - wend); | |
363 | wvalue |= 1; | |
364 | wend = i; | |
365 | } | |
366 | } | |
367 | ||
368 | /* wend is the size of the current window */ | |
369 | j = wend + 1; | |
370 | /* add the 'bytes above' */ | |
371 | if (!start) | |
372 | for (i = 0; i < j; i++) { | |
373 | if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx)) | |
374 | goto err; | |
375 | } | |
376 | ||
377 | /* wvalue will be an odd number < 2^window */ | |
378 | if (!BN_mod_mul_reciprocal(r, r, val[wvalue >> 1], &recp, ctx)) | |
379 | goto err; | |
380 | ||
381 | /* move the 'window' down further */ | |
382 | wstart -= wend + 1; | |
383 | wvalue = 0; | |
384 | start = 0; | |
385 | if (wstart < 0) | |
386 | break; | |
387 | } | |
388 | ret = 1; | |
389 | err: | |
390 | BN_CTX_end(ctx); | |
391 | BN_RECP_CTX_free(&recp); | |
392 | bn_check_top(r); | |
393 | return (ret); | |
394 | } | |
6dad7bd6 | 395 | |
020fc820 | 396 | int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, |
0f113f3e MC |
397 | const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont) |
398 | { | |
399 | int i, j, bits, ret = 0, wstart, wend, window, wvalue; | |
400 | int start = 1; | |
401 | BIGNUM *d, *r; | |
402 | const BIGNUM *aa; | |
403 | /* Table of variables obtained from 'ctx' */ | |
404 | BIGNUM *val[TABLE_SIZE]; | |
405 | BN_MONT_CTX *mont = NULL; | |
406 | ||
407 | if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) { | |
408 | return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont); | |
409 | } | |
410 | ||
411 | bn_check_top(a); | |
412 | bn_check_top(p); | |
413 | bn_check_top(m); | |
414 | ||
415 | if (!BN_is_odd(m)) { | |
416 | BNerr(BN_F_BN_MOD_EXP_MONT, BN_R_CALLED_WITH_EVEN_MODULUS); | |
417 | return (0); | |
418 | } | |
419 | bits = BN_num_bits(p); | |
420 | if (bits == 0) { | |
421 | ret = BN_one(rr); | |
422 | return ret; | |
423 | } | |
424 | ||
425 | BN_CTX_start(ctx); | |
426 | d = BN_CTX_get(ctx); | |
427 | r = BN_CTX_get(ctx); | |
428 | val[0] = BN_CTX_get(ctx); | |
429 | if (!d || !r || !val[0]) | |
430 | goto err; | |
431 | ||
432 | /* | |
433 | * If this is not done, things will break in the montgomery part | |
434 | */ | |
435 | ||
436 | if (in_mont != NULL) | |
437 | mont = in_mont; | |
438 | else { | |
439 | if ((mont = BN_MONT_CTX_new()) == NULL) | |
440 | goto err; | |
441 | if (!BN_MONT_CTX_set(mont, m, ctx)) | |
442 | goto err; | |
443 | } | |
444 | ||
445 | if (a->neg || BN_ucmp(a, m) >= 0) { | |
446 | if (!BN_nnmod(val[0], a, m, ctx)) | |
447 | goto err; | |
448 | aa = val[0]; | |
449 | } else | |
450 | aa = a; | |
451 | if (BN_is_zero(aa)) { | |
452 | BN_zero(rr); | |
453 | ret = 1; | |
454 | goto err; | |
455 | } | |
456 | if (!BN_to_montgomery(val[0], aa, mont, ctx)) | |
457 | goto err; /* 1 */ | |
458 | ||
459 | window = BN_window_bits_for_exponent_size(bits); | |
460 | if (window > 1) { | |
461 | if (!BN_mod_mul_montgomery(d, val[0], val[0], mont, ctx)) | |
462 | goto err; /* 2 */ | |
463 | j = 1 << (window - 1); | |
464 | for (i = 1; i < j; i++) { | |
465 | if (((val[i] = BN_CTX_get(ctx)) == NULL) || | |
466 | !BN_mod_mul_montgomery(val[i], val[i - 1], d, mont, ctx)) | |
467 | goto err; | |
468 | } | |
469 | } | |
470 | ||
471 | start = 1; /* This is used to avoid multiplication etc | |
472 | * when there is only the value '1' in the | |
473 | * buffer. */ | |
474 | wvalue = 0; /* The 'value' of the window */ | |
475 | wstart = bits - 1; /* The top bit of the window */ | |
476 | wend = 0; /* The bottom bit of the window */ | |
477 | ||
478 | #if 1 /* by Shay Gueron's suggestion */ | |
479 | j = m->top; /* borrow j */ | |
480 | if (m->d[j - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) { | |
481 | if (bn_wexpand(r, j) == NULL) | |
482 | goto err; | |
483 | /* 2^(top*BN_BITS2) - m */ | |
484 | r->d[0] = (0 - m->d[0]) & BN_MASK2; | |
485 | for (i = 1; i < j; i++) | |
486 | r->d[i] = (~m->d[i]) & BN_MASK2; | |
487 | r->top = j; | |
488 | /* | |
489 | * Upper words will be zero if the corresponding words of 'm' were | |
490 | * 0xfff[...], so decrement r->top accordingly. | |
491 | */ | |
492 | bn_correct_top(r); | |
493 | } else | |
4ddacd99 | 494 | #endif |
0f113f3e MC |
495 | if (!BN_to_montgomery(r, BN_value_one(), mont, ctx)) |
496 | goto err; | |
497 | for (;;) { | |
498 | if (BN_is_bit_set(p, wstart) == 0) { | |
499 | if (!start) { | |
500 | if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) | |
501 | goto err; | |
502 | } | |
503 | if (wstart == 0) | |
504 | break; | |
505 | wstart--; | |
506 | continue; | |
507 | } | |
508 | /* | |
509 | * We now have wstart on a 'set' bit, we now need to work out how bit | |
510 | * a window to do. To do this we need to scan forward until the last | |
511 | * set bit before the end of the window | |
512 | */ | |
513 | j = wstart; | |
514 | wvalue = 1; | |
515 | wend = 0; | |
516 | for (i = 1; i < window; i++) { | |
517 | if (wstart - i < 0) | |
518 | break; | |
519 | if (BN_is_bit_set(p, wstart - i)) { | |
520 | wvalue <<= (i - wend); | |
521 | wvalue |= 1; | |
522 | wend = i; | |
523 | } | |
524 | } | |
525 | ||
526 | /* wend is the size of the current window */ | |
527 | j = wend + 1; | |
528 | /* add the 'bytes above' */ | |
529 | if (!start) | |
530 | for (i = 0; i < j; i++) { | |
531 | if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) | |
532 | goto err; | |
533 | } | |
534 | ||
535 | /* wvalue will be an odd number < 2^window */ | |
536 | if (!BN_mod_mul_montgomery(r, r, val[wvalue >> 1], mont, ctx)) | |
537 | goto err; | |
538 | ||
539 | /* move the 'window' down further */ | |
540 | wstart -= wend + 1; | |
541 | wvalue = 0; | |
542 | start = 0; | |
543 | if (wstart < 0) | |
544 | break; | |
545 | } | |
cbce8c46 | 546 | #if defined(SPARC_T4_MONT) |
0f113f3e MC |
547 | if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) { |
548 | j = mont->N.top; /* borrow j */ | |
549 | val[0]->d[0] = 1; /* borrow val[0] */ | |
550 | for (i = 1; i < j; i++) | |
551 | val[0]->d[i] = 0; | |
552 | val[0]->top = j; | |
553 | if (!BN_mod_mul_montgomery(rr, r, val[0], mont, ctx)) | |
554 | goto err; | |
555 | } else | |
4ddacd99 | 556 | #endif |
0f113f3e MC |
557 | if (!BN_from_montgomery(rr, r, mont, ctx)) |
558 | goto err; | |
559 | ret = 1; | |
560 | err: | |
23a1d5e9 | 561 | if (in_mont == NULL) |
0f113f3e MC |
562 | BN_MONT_CTX_free(mont); |
563 | BN_CTX_end(ctx); | |
564 | bn_check_top(rr); | |
565 | return (ret); | |
566 | } | |
6dad7bd6 | 567 | |
cbce8c46 | 568 | #if defined(SPARC_T4_MONT) |
4ddacd99 | 569 | static BN_ULONG bn_get_bits(const BIGNUM *a, int bitpos) |
0f113f3e MC |
570 | { |
571 | BN_ULONG ret = 0; | |
572 | int wordpos; | |
573 | ||
574 | wordpos = bitpos / BN_BITS2; | |
575 | bitpos %= BN_BITS2; | |
576 | if (wordpos >= 0 && wordpos < a->top) { | |
577 | ret = a->d[wordpos] & BN_MASK2; | |
578 | if (bitpos) { | |
579 | ret >>= bitpos; | |
580 | if (++wordpos < a->top) | |
581 | ret |= a->d[wordpos] << (BN_BITS2 - bitpos); | |
582 | } | |
583 | } | |
584 | ||
585 | return ret & BN_MASK2; | |
4ddacd99 AP |
586 | } |
587 | #endif | |
46a64376 | 588 | |
0f113f3e MC |
589 | /* |
590 | * BN_mod_exp_mont_consttime() stores the precomputed powers in a specific | |
591 | * layout so that accessing any of these table values shows the same access | |
592 | * pattern as far as cache lines are concerned. The following functions are | |
593 | * used to transfer a BIGNUM from/to that table. | |
594 | */ | |
46a64376 | 595 | |
0f113f3e MC |
596 | static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top, |
597 | unsigned char *buf, int idx, | |
598 | int width) | |
599 | { | |
600 | size_t i, j; | |
46a64376 | 601 | |
0f113f3e MC |
602 | if (top > b->top) |
603 | top = b->top; /* this works because 'buf' is explicitly | |
604 | * zeroed */ | |
605 | for (i = 0, j = idx; i < top * sizeof b->d[0]; i++, j += width) { | |
606 | buf[j] = ((unsigned char *)b->d)[i]; | |
607 | } | |
46a64376 | 608 | |
0f113f3e MC |
609 | return 1; |
610 | } | |
46a64376 | 611 | |
0f113f3e MC |
612 | static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top, |
613 | unsigned char *buf, int idx, | |
614 | int width) | |
615 | { | |
616 | size_t i, j; | |
46a64376 | 617 | |
0f113f3e MC |
618 | if (bn_wexpand(b, top) == NULL) |
619 | return 0; | |
46a64376 | 620 | |
0f113f3e MC |
621 | for (i = 0, j = idx; i < top * sizeof b->d[0]; i++, j += width) { |
622 | ((unsigned char *)b->d)[i] = buf[j]; | |
623 | } | |
46a64376 | 624 | |
0f113f3e MC |
625 | b->top = top; |
626 | bn_correct_top(b); | |
627 | return 1; | |
628 | } | |
46a64376 | 629 | |
0f113f3e MC |
630 | /* |
631 | * Given a pointer value, compute the next address that is a cache line | |
632 | * multiple. | |
633 | */ | |
46a64376 | 634 | #define MOD_EXP_CTIME_ALIGN(x_) \ |
0f113f3e MC |
635 | ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK)))) |
636 | ||
637 | /* | |
638 | * This variant of BN_mod_exp_mont() uses fixed windows and the special | |
639 | * precomputation memory layout to limit data-dependency to a minimum to | |
640 | * protect secret exponents (cf. the hyper-threading timing attacks pointed | |
641 | * out by Colin Percival, | |
642 | * http://www.daemong-consideredperthreading-considered-harmful/) | |
46a64376 BM |
643 | */ |
644 | int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, | |
0f113f3e MC |
645 | const BIGNUM *m, BN_CTX *ctx, |
646 | BN_MONT_CTX *in_mont) | |
647 | { | |
648 | int i, bits, ret = 0, window, wvalue; | |
649 | int top; | |
650 | BN_MONT_CTX *mont = NULL; | |
651 | ||
652 | int numPowers; | |
653 | unsigned char *powerbufFree = NULL; | |
654 | int powerbufLen = 0; | |
655 | unsigned char *powerbuf = NULL; | |
656 | BIGNUM tmp, am; | |
cbce8c46 | 657 | #if defined(SPARC_T4_MONT) |
0f113f3e | 658 | unsigned int t4 = 0; |
68c06bf6 | 659 | #endif |
46a64376 | 660 | |
0f113f3e MC |
661 | bn_check_top(a); |
662 | bn_check_top(p); | |
663 | bn_check_top(m); | |
664 | ||
a9009e51 | 665 | if (!BN_is_odd(m)) { |
0f113f3e MC |
666 | BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME, BN_R_CALLED_WITH_EVEN_MODULUS); |
667 | return (0); | |
668 | } | |
a9009e51 EK |
669 | |
670 | top = m->top; | |
671 | ||
0f113f3e MC |
672 | bits = BN_num_bits(p); |
673 | if (bits == 0) { | |
674 | ret = BN_one(rr); | |
675 | return ret; | |
676 | } | |
677 | ||
678 | BN_CTX_start(ctx); | |
679 | ||
680 | /* | |
681 | * Allocate a montgomery context if it was not supplied by the caller. If | |
682 | * this is not done, things will break in the montgomery part. | |
683 | */ | |
684 | if (in_mont != NULL) | |
685 | mont = in_mont; | |
686 | else { | |
687 | if ((mont = BN_MONT_CTX_new()) == NULL) | |
688 | goto err; | |
689 | if (!BN_MONT_CTX_set(mont, m, ctx)) | |
690 | goto err; | |
691 | } | |
46a64376 | 692 | |
ca48ace5 | 693 | #ifdef RSAZ_ENABLED |
0f113f3e MC |
694 | /* |
695 | * If the size of the operands allow it, perform the optimized | |
696 | * RSAZ exponentiation. For further information see | |
697 | * crypto/bn/rsaz_exp.c and accompanying assembly modules. | |
698 | */ | |
699 | if ((16 == a->top) && (16 == p->top) && (BN_num_bits(m) == 1024) | |
700 | && rsaz_avx2_eligible()) { | |
701 | if (NULL == bn_wexpand(rr, 16)) | |
702 | goto err; | |
703 | RSAZ_1024_mod_exp_avx2(rr->d, a->d, p->d, m->d, mont->RR.d, | |
704 | mont->n0[0]); | |
705 | rr->top = 16; | |
706 | rr->neg = 0; | |
707 | bn_correct_top(rr); | |
708 | ret = 1; | |
709 | goto err; | |
710 | } else if ((8 == a->top) && (8 == p->top) && (BN_num_bits(m) == 512)) { | |
711 | if (NULL == bn_wexpand(rr, 8)) | |
712 | goto err; | |
713 | RSAZ_512_mod_exp(rr->d, a->d, p->d, m->d, mont->n0[0], mont->RR.d); | |
714 | rr->top = 8; | |
715 | rr->neg = 0; | |
716 | bn_correct_top(rr); | |
717 | ret = 1; | |
718 | goto err; | |
719 | } | |
ca48ace5 AP |
720 | #endif |
721 | ||
0f113f3e MC |
722 | /* Get the window size to use with size of p. */ |
723 | window = BN_window_bits_for_ctime_exponent_size(bits); | |
cbce8c46 | 724 | #if defined(SPARC_T4_MONT) |
0f113f3e MC |
725 | if (window >= 5 && (top & 15) == 0 && top <= 64 && |
726 | (OPENSSL_sparcv9cap_P[1] & (CFR_MONTMUL | CFR_MONTSQR)) == | |
727 | (CFR_MONTMUL | CFR_MONTSQR) && (t4 = OPENSSL_sparcv9cap_P[0])) | |
728 | window = 5; | |
729 | else | |
68c06bf6 | 730 | #endif |
361512da | 731 | #if defined(OPENSSL_BN_ASM_MONT5) |
0f113f3e MC |
732 | if (window >= 5) { |
733 | window = 5; /* ~5% improvement for RSA2048 sign, and even | |
734 | * for RSA4096 */ | |
735 | if ((top & 7) == 0) | |
736 | powerbufLen += 2 * top * sizeof(m->d[0]); | |
737 | } | |
361512da | 738 | #endif |
0f113f3e MC |
739 | (void)0; |
740 | ||
741 | /* | |
742 | * Allocate a buffer large enough to hold all of the pre-computed powers | |
743 | * of am, am itself and tmp. | |
744 | */ | |
745 | numPowers = 1 << window; | |
746 | powerbufLen += sizeof(m->d[0]) * (top * numPowers + | |
747 | ((2 * top) > | |
748 | numPowers ? (2 * top) : numPowers)); | |
cfdbff23 | 749 | #ifdef alloca |
0f113f3e MC |
750 | if (powerbufLen < 3072) |
751 | powerbufFree = | |
752 | alloca(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH); | |
753 | else | |
cfdbff23 | 754 | #endif |
0f113f3e | 755 | if ((powerbufFree = |
b196e7d9 | 756 | OPENSSL_malloc(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH)) |
0f113f3e MC |
757 | == NULL) |
758 | goto err; | |
759 | ||
760 | powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree); | |
761 | memset(powerbuf, 0, powerbufLen); | |
46a64376 | 762 | |
cfdbff23 | 763 | #ifdef alloca |
0f113f3e MC |
764 | if (powerbufLen < 3072) |
765 | powerbufFree = NULL; | |
cfdbff23 | 766 | #endif |
361512da | 767 | |
0f113f3e MC |
768 | /* lay down tmp and am right after powers table */ |
769 | tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers); | |
770 | am.d = tmp.d + top; | |
771 | tmp.top = am.top = 0; | |
772 | tmp.dmax = am.dmax = top; | |
773 | tmp.neg = am.neg = 0; | |
774 | tmp.flags = am.flags = BN_FLG_STATIC_DATA; | |
775 | ||
776 | /* prepare a^0 in Montgomery domain */ | |
777 | #if 1 /* by Shay Gueron's suggestion */ | |
778 | if (m->d[top - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) { | |
779 | /* 2^(top*BN_BITS2) - m */ | |
780 | tmp.d[0] = (0 - m->d[0]) & BN_MASK2; | |
781 | for (i = 1; i < top; i++) | |
782 | tmp.d[i] = (~m->d[i]) & BN_MASK2; | |
783 | tmp.top = top; | |
784 | } else | |
8329e2e7 | 785 | #endif |
0f113f3e MC |
786 | if (!BN_to_montgomery(&tmp, BN_value_one(), mont, ctx)) |
787 | goto err; | |
788 | ||
789 | /* prepare a^1 in Montgomery domain */ | |
790 | if (a->neg || BN_ucmp(a, m) >= 0) { | |
791 | if (!BN_mod(&am, a, m, ctx)) | |
792 | goto err; | |
793 | if (!BN_to_montgomery(&am, &am, mont, ctx)) | |
794 | goto err; | |
795 | } else if (!BN_to_montgomery(&am, a, mont, ctx)) | |
796 | goto err; | |
361512da | 797 | |
cbce8c46 | 798 | #if defined(SPARC_T4_MONT) |
0f113f3e MC |
799 | if (t4) { |
800 | typedef int (*bn_pwr5_mont_f) (BN_ULONG *tp, const BN_ULONG *np, | |
801 | const BN_ULONG *n0, const void *table, | |
802 | int power, int bits); | |
803 | int bn_pwr5_mont_t4_8(BN_ULONG *tp, const BN_ULONG *np, | |
804 | const BN_ULONG *n0, const void *table, | |
805 | int power, int bits); | |
806 | int bn_pwr5_mont_t4_16(BN_ULONG *tp, const BN_ULONG *np, | |
807 | const BN_ULONG *n0, const void *table, | |
808 | int power, int bits); | |
809 | int bn_pwr5_mont_t4_24(BN_ULONG *tp, const BN_ULONG *np, | |
810 | const BN_ULONG *n0, const void *table, | |
811 | int power, int bits); | |
812 | int bn_pwr5_mont_t4_32(BN_ULONG *tp, const BN_ULONG *np, | |
813 | const BN_ULONG *n0, const void *table, | |
814 | int power, int bits); | |
815 | static const bn_pwr5_mont_f pwr5_funcs[4] = { | |
816 | bn_pwr5_mont_t4_8, bn_pwr5_mont_t4_16, | |
817 | bn_pwr5_mont_t4_24, bn_pwr5_mont_t4_32 | |
818 | }; | |
819 | bn_pwr5_mont_f pwr5_worker = pwr5_funcs[top / 16 - 1]; | |
820 | ||
821 | typedef int (*bn_mul_mont_f) (BN_ULONG *rp, const BN_ULONG *ap, | |
822 | const void *bp, const BN_ULONG *np, | |
823 | const BN_ULONG *n0); | |
824 | int bn_mul_mont_t4_8(BN_ULONG *rp, const BN_ULONG *ap, const void *bp, | |
825 | const BN_ULONG *np, const BN_ULONG *n0); | |
826 | int bn_mul_mont_t4_16(BN_ULONG *rp, const BN_ULONG *ap, | |
827 | const void *bp, const BN_ULONG *np, | |
828 | const BN_ULONG *n0); | |
829 | int bn_mul_mont_t4_24(BN_ULONG *rp, const BN_ULONG *ap, | |
830 | const void *bp, const BN_ULONG *np, | |
831 | const BN_ULONG *n0); | |
832 | int bn_mul_mont_t4_32(BN_ULONG *rp, const BN_ULONG *ap, | |
833 | const void *bp, const BN_ULONG *np, | |
834 | const BN_ULONG *n0); | |
835 | static const bn_mul_mont_f mul_funcs[4] = { | |
836 | bn_mul_mont_t4_8, bn_mul_mont_t4_16, | |
837 | bn_mul_mont_t4_24, bn_mul_mont_t4_32 | |
838 | }; | |
839 | bn_mul_mont_f mul_worker = mul_funcs[top / 16 - 1]; | |
840 | ||
841 | void bn_mul_mont_vis3(BN_ULONG *rp, const BN_ULONG *ap, | |
842 | const void *bp, const BN_ULONG *np, | |
843 | const BN_ULONG *n0, int num); | |
844 | void bn_mul_mont_t4(BN_ULONG *rp, const BN_ULONG *ap, | |
845 | const void *bp, const BN_ULONG *np, | |
846 | const BN_ULONG *n0, int num); | |
847 | void bn_mul_mont_gather5_t4(BN_ULONG *rp, const BN_ULONG *ap, | |
848 | const void *table, const BN_ULONG *np, | |
849 | const BN_ULONG *n0, int num, int power); | |
850 | void bn_flip_n_scatter5_t4(const BN_ULONG *inp, size_t num, | |
851 | void *table, size_t power); | |
852 | void bn_gather5_t4(BN_ULONG *out, size_t num, | |
853 | void *table, size_t power); | |
854 | void bn_flip_t4(BN_ULONG *dst, BN_ULONG *src, size_t num); | |
855 | ||
856 | BN_ULONG *np = mont->N.d, *n0 = mont->n0; | |
857 | int stride = 5 * (6 - (top / 16 - 1)); /* multiple of 5, but less | |
858 | * than 32 */ | |
859 | ||
860 | /* | |
861 | * BN_to_montgomery can contaminate words above .top [in | |
862 | * BN_DEBUG[_DEBUG] build]... | |
863 | */ | |
864 | for (i = am.top; i < top; i++) | |
865 | am.d[i] = 0; | |
866 | for (i = tmp.top; i < top; i++) | |
867 | tmp.d[i] = 0; | |
868 | ||
869 | bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 0); | |
870 | bn_flip_n_scatter5_t4(am.d, top, powerbuf, 1); | |
871 | if (!(*mul_worker) (tmp.d, am.d, am.d, np, n0) && | |
872 | !(*mul_worker) (tmp.d, am.d, am.d, np, n0)) | |
873 | bn_mul_mont_vis3(tmp.d, am.d, am.d, np, n0, top); | |
874 | bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 2); | |
875 | ||
876 | for (i = 3; i < 32; i++) { | |
877 | /* Calculate a^i = a^(i-1) * a */ | |
878 | if (!(*mul_worker) (tmp.d, tmp.d, am.d, np, n0) && | |
879 | !(*mul_worker) (tmp.d, tmp.d, am.d, np, n0)) | |
880 | bn_mul_mont_vis3(tmp.d, tmp.d, am.d, np, n0, top); | |
881 | bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, i); | |
882 | } | |
883 | ||
884 | /* switch to 64-bit domain */ | |
885 | np = alloca(top * sizeof(BN_ULONG)); | |
886 | top /= 2; | |
887 | bn_flip_t4(np, mont->N.d, top); | |
888 | ||
889 | bits--; | |
890 | for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--) | |
891 | wvalue = (wvalue << 1) + BN_is_bit_set(p, bits); | |
892 | bn_gather5_t4(tmp.d, top, powerbuf, wvalue); | |
893 | ||
894 | /* | |
895 | * Scan the exponent one window at a time starting from the most | |
896 | * significant bits. | |
897 | */ | |
898 | while (bits >= 0) { | |
899 | if (bits < stride) | |
900 | stride = bits + 1; | |
901 | bits -= stride; | |
902 | wvalue = bn_get_bits(p, bits + 1); | |
903 | ||
904 | if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride)) | |
905 | continue; | |
906 | /* retry once and fall back */ | |
907 | if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride)) | |
908 | continue; | |
909 | ||
910 | bits += stride - 5; | |
911 | wvalue >>= stride - 5; | |
912 | wvalue &= 31; | |
913 | bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); | |
914 | bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); | |
915 | bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); | |
916 | bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); | |
917 | bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); | |
918 | bn_mul_mont_gather5_t4(tmp.d, tmp.d, powerbuf, np, n0, top, | |
919 | wvalue); | |
920 | } | |
921 | ||
922 | bn_flip_t4(tmp.d, tmp.d, top); | |
923 | top *= 2; | |
924 | /* back to 32-bit domain */ | |
925 | tmp.top = top; | |
926 | bn_correct_top(&tmp); | |
927 | OPENSSL_cleanse(np, top * sizeof(BN_ULONG)); | |
928 | } else | |
68c06bf6 | 929 | #endif |
361512da | 930 | #if defined(OPENSSL_BN_ASM_MONT5) |
0f113f3e MC |
931 | if (window == 5 && top > 1) { |
932 | /* | |
933 | * This optimization uses ideas from http://eprint.iacr.org/2011/239, | |
934 | * specifically optimization of cache-timing attack countermeasures | |
935 | * and pre-computation optimization. | |
936 | */ | |
937 | ||
938 | /* | |
939 | * Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as | |
940 | * 512-bit RSA is hardly relevant, we omit it to spare size... | |
941 | */ | |
942 | void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap, | |
943 | const void *table, const BN_ULONG *np, | |
944 | const BN_ULONG *n0, int num, int power); | |
945 | void bn_scatter5(const BN_ULONG *inp, size_t num, | |
946 | void *table, size_t power); | |
947 | void bn_gather5(BN_ULONG *out, size_t num, void *table, size_t power); | |
948 | void bn_power5(BN_ULONG *rp, const BN_ULONG *ap, | |
949 | const void *table, const BN_ULONG *np, | |
950 | const BN_ULONG *n0, int num, int power); | |
951 | int bn_get_bits5(const BN_ULONG *ap, int off); | |
952 | int bn_from_montgomery(BN_ULONG *rp, const BN_ULONG *ap, | |
953 | const BN_ULONG *not_used, const BN_ULONG *np, | |
954 | const BN_ULONG *n0, int num); | |
955 | ||
956 | BN_ULONG *np = mont->N.d, *n0 = mont->n0, *np2; | |
957 | ||
958 | /* | |
959 | * BN_to_montgomery can contaminate words above .top [in | |
960 | * BN_DEBUG[_DEBUG] build]... | |
961 | */ | |
962 | for (i = am.top; i < top; i++) | |
963 | am.d[i] = 0; | |
964 | for (i = tmp.top; i < top; i++) | |
965 | tmp.d[i] = 0; | |
966 | ||
967 | if (top & 7) | |
968 | np2 = np; | |
969 | else | |
970 | for (np2 = am.d + top, i = 0; i < top; i++) | |
971 | np2[2 * i] = np[i]; | |
972 | ||
973 | bn_scatter5(tmp.d, top, powerbuf, 0); | |
974 | bn_scatter5(am.d, am.top, powerbuf, 1); | |
975 | bn_mul_mont(tmp.d, am.d, am.d, np, n0, top); | |
976 | bn_scatter5(tmp.d, top, powerbuf, 2); | |
977 | ||
978 | # if 0 | |
979 | for (i = 3; i < 32; i++) { | |
980 | /* Calculate a^i = a^(i-1) * a */ | |
981 | bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np2, n0, top, i - 1); | |
982 | bn_scatter5(tmp.d, top, powerbuf, i); | |
983 | } | |
984 | # else | |
985 | /* same as above, but uses squaring for 1/2 of operations */ | |
986 | for (i = 4; i < 32; i *= 2) { | |
987 | bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); | |
988 | bn_scatter5(tmp.d, top, powerbuf, i); | |
989 | } | |
990 | for (i = 3; i < 8; i += 2) { | |
991 | int j; | |
992 | bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np2, n0, top, i - 1); | |
993 | bn_scatter5(tmp.d, top, powerbuf, i); | |
994 | for (j = 2 * i; j < 32; j *= 2) { | |
995 | bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); | |
996 | bn_scatter5(tmp.d, top, powerbuf, j); | |
997 | } | |
998 | } | |
999 | for (; i < 16; i += 2) { | |
1000 | bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np2, n0, top, i - 1); | |
1001 | bn_scatter5(tmp.d, top, powerbuf, i); | |
1002 | bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); | |
1003 | bn_scatter5(tmp.d, top, powerbuf, 2 * i); | |
1004 | } | |
1005 | for (; i < 32; i += 2) { | |
1006 | bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np2, n0, top, i - 1); | |
1007 | bn_scatter5(tmp.d, top, powerbuf, i); | |
1008 | } | |
1009 | # endif | |
1010 | bits--; | |
1011 | for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--) | |
1012 | wvalue = (wvalue << 1) + BN_is_bit_set(p, bits); | |
1013 | bn_gather5(tmp.d, top, powerbuf, wvalue); | |
1014 | ||
1015 | /* | |
1016 | * Scan the exponent one window at a time starting from the most | |
1017 | * significant bits. | |
1018 | */ | |
1019 | if (top & 7) | |
1020 | while (bits >= 0) { | |
1021 | for (wvalue = 0, i = 0; i < 5; i++, bits--) | |
1022 | wvalue = (wvalue << 1) + BN_is_bit_set(p, bits); | |
1023 | ||
1024 | bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); | |
1025 | bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); | |
1026 | bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); | |
1027 | bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); | |
1028 | bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); | |
1029 | bn_mul_mont_gather5(tmp.d, tmp.d, powerbuf, np, n0, top, | |
1030 | wvalue); | |
1031 | } else { | |
1032 | while (bits >= 0) { | |
1033 | wvalue = bn_get_bits5(p->d, bits - 4); | |
1034 | bits -= 5; | |
1035 | bn_power5(tmp.d, tmp.d, powerbuf, np2, n0, top, wvalue); | |
1036 | } | |
1037 | } | |
1038 | ||
1039 | ret = bn_from_montgomery(tmp.d, tmp.d, NULL, np2, n0, top); | |
1040 | tmp.top = top; | |
1041 | bn_correct_top(&tmp); | |
1042 | if (ret) { | |
1043 | if (!BN_copy(rr, &tmp)) | |
1044 | ret = 0; | |
1045 | goto err; /* non-zero ret means it's not error */ | |
1046 | } | |
1047 | } else | |
361512da | 1048 | #endif |
0f113f3e MC |
1049 | { |
1050 | if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, numPowers)) | |
1051 | goto err; | |
1052 | if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, numPowers)) | |
1053 | goto err; | |
1054 | ||
1055 | /* | |
1056 | * If the window size is greater than 1, then calculate | |
1057 | * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even | |
1058 | * powers could instead be computed as (a^(i/2))^2 to use the slight | |
1059 | * performance advantage of sqr over mul). | |
1060 | */ | |
1061 | if (window > 1) { | |
1062 | if (!BN_mod_mul_montgomery(&tmp, &am, &am, mont, ctx)) | |
1063 | goto err; | |
1064 | if (!MOD_EXP_CTIME_COPY_TO_PREBUF | |
1065 | (&tmp, top, powerbuf, 2, numPowers)) | |
1066 | goto err; | |
1067 | for (i = 3; i < numPowers; i++) { | |
1068 | /* Calculate a^i = a^(i-1) * a */ | |
1069 | if (!BN_mod_mul_montgomery(&tmp, &am, &tmp, mont, ctx)) | |
1070 | goto err; | |
1071 | if (!MOD_EXP_CTIME_COPY_TO_PREBUF | |
1072 | (&tmp, top, powerbuf, i, numPowers)) | |
1073 | goto err; | |
1074 | } | |
1075 | } | |
1076 | ||
1077 | bits--; | |
1078 | for (wvalue = 0, i = bits % window; i >= 0; i--, bits--) | |
1079 | wvalue = (wvalue << 1) + BN_is_bit_set(p, bits); | |
1080 | if (!MOD_EXP_CTIME_COPY_FROM_PREBUF | |
1081 | (&tmp, top, powerbuf, wvalue, numPowers)) | |
1082 | goto err; | |
1083 | ||
1084 | /* | |
1085 | * Scan the exponent one window at a time starting from the most | |
1086 | * significant bits. | |
1087 | */ | |
1088 | while (bits >= 0) { | |
1089 | wvalue = 0; /* The 'value' of the window */ | |
1090 | ||
1091 | /* Scan the window, squaring the result as we go */ | |
1092 | for (i = 0; i < window; i++, bits--) { | |
1093 | if (!BN_mod_mul_montgomery(&tmp, &tmp, &tmp, mont, ctx)) | |
1094 | goto err; | |
1095 | wvalue = (wvalue << 1) + BN_is_bit_set(p, bits); | |
1096 | } | |
1097 | ||
1098 | /* | |
1099 | * Fetch the appropriate pre-computed value from the pre-buf | |
1100 | */ | |
1101 | if (!MOD_EXP_CTIME_COPY_FROM_PREBUF | |
1102 | (&am, top, powerbuf, wvalue, numPowers)) | |
1103 | goto err; | |
1104 | ||
1105 | /* Multiply the result into the intermediate result */ | |
1106 | if (!BN_mod_mul_montgomery(&tmp, &tmp, &am, mont, ctx)) | |
1107 | goto err; | |
1108 | } | |
1109 | } | |
1110 | ||
1111 | /* Convert the final result from montgomery to standard format */ | |
cbce8c46 | 1112 | #if defined(SPARC_T4_MONT) |
0f113f3e MC |
1113 | if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) { |
1114 | am.d[0] = 1; /* borrow am */ | |
1115 | for (i = 1; i < top; i++) | |
1116 | am.d[i] = 0; | |
1117 | if (!BN_mod_mul_montgomery(rr, &tmp, &am, mont, ctx)) | |
1118 | goto err; | |
1119 | } else | |
4ddacd99 | 1120 | #endif |
0f113f3e MC |
1121 | if (!BN_from_montgomery(rr, &tmp, mont, ctx)) |
1122 | goto err; | |
1123 | ret = 1; | |
1124 | err: | |
23a1d5e9 | 1125 | if (in_mont == NULL) |
0f113f3e MC |
1126 | BN_MONT_CTX_free(mont); |
1127 | if (powerbuf != NULL) { | |
1128 | OPENSSL_cleanse(powerbuf, powerbufLen); | |
b548a1f1 | 1129 | OPENSSL_free(powerbufFree); |
0f113f3e MC |
1130 | } |
1131 | BN_CTX_end(ctx); | |
1132 | return (ret); | |
1133 | } | |
46a64376 | 1134 | |
6dad7bd6 BM |
1135 | int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p, |
1136 | const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont) | |
0f113f3e MC |
1137 | { |
1138 | BN_MONT_CTX *mont = NULL; | |
1139 | int b, bits, ret = 0; | |
1140 | int r_is_one; | |
1141 | BN_ULONG w, next_w; | |
1142 | BIGNUM *d, *r, *t; | |
1143 | BIGNUM *swap_tmp; | |
f8989a21 | 1144 | #define BN_MOD_MUL_WORD(r, w, m) \ |
0f113f3e MC |
1145 | (BN_mul_word(r, (w)) && \ |
1146 | (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \ | |
1147 | (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1)))) | |
1148 | /* | |
1149 | * BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is | |
1150 | * probably more overhead than always using BN_mod (which uses BN_copy if | |
1151 | * a similar test returns true). | |
1152 | */ | |
1153 | /* | |
1154 | * We can use BN_mod and do not need BN_nnmod because our accumulator is | |
1155 | * never negative (the result of BN_mod does not depend on the sign of | |
1156 | * the modulus). | |
1157 | */ | |
e958c5af | 1158 | #define BN_TO_MONTGOMERY_WORD(r, w, mont) \ |
0f113f3e MC |
1159 | (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx)) |
1160 | ||
1161 | if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) { | |
1162 | /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ | |
1163 | BNerr(BN_F_BN_MOD_EXP_MONT_WORD, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); | |
1164 | return -1; | |
1165 | } | |
1166 | ||
1167 | bn_check_top(p); | |
1168 | bn_check_top(m); | |
1169 | ||
1170 | if (!BN_is_odd(m)) { | |
1171 | BNerr(BN_F_BN_MOD_EXP_MONT_WORD, BN_R_CALLED_WITH_EVEN_MODULUS); | |
1172 | return (0); | |
1173 | } | |
1174 | if (m->top == 1) | |
1175 | a %= m->d[0]; /* make sure that 'a' is reduced */ | |
1176 | ||
1177 | bits = BN_num_bits(p); | |
1178 | if (bits == 0) { | |
1179 | /* x**0 mod 1 is still zero. */ | |
1180 | if (BN_is_one(m)) { | |
1181 | ret = 1; | |
1182 | BN_zero(rr); | |
1183 | } else | |
1184 | ret = BN_one(rr); | |
1185 | return ret; | |
1186 | } | |
1187 | if (a == 0) { | |
1188 | BN_zero(rr); | |
1189 | ret = 1; | |
1190 | return ret; | |
1191 | } | |
1192 | ||
1193 | BN_CTX_start(ctx); | |
1194 | d = BN_CTX_get(ctx); | |
1195 | r = BN_CTX_get(ctx); | |
1196 | t = BN_CTX_get(ctx); | |
1197 | if (d == NULL || r == NULL || t == NULL) | |
1198 | goto err; | |
1199 | ||
1200 | if (in_mont != NULL) | |
1201 | mont = in_mont; | |
1202 | else { | |
1203 | if ((mont = BN_MONT_CTX_new()) == NULL) | |
1204 | goto err; | |
1205 | if (!BN_MONT_CTX_set(mont, m, ctx)) | |
1206 | goto err; | |
1207 | } | |
1208 | ||
1209 | r_is_one = 1; /* except for Montgomery factor */ | |
1210 | ||
1211 | /* bits-1 >= 0 */ | |
1212 | ||
1213 | /* The result is accumulated in the product r*w. */ | |
1214 | w = a; /* bit 'bits-1' of 'p' is always set */ | |
1215 | for (b = bits - 2; b >= 0; b--) { | |
1216 | /* First, square r*w. */ | |
1217 | next_w = w * w; | |
1218 | if ((next_w / w) != w) { /* overflow */ | |
1219 | if (r_is_one) { | |
1220 | if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) | |
1221 | goto err; | |
1222 | r_is_one = 0; | |
1223 | } else { | |
1224 | if (!BN_MOD_MUL_WORD(r, w, m)) | |
1225 | goto err; | |
1226 | } | |
1227 | next_w = 1; | |
1228 | } | |
1229 | w = next_w; | |
1230 | if (!r_is_one) { | |
1231 | if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) | |
1232 | goto err; | |
1233 | } | |
1234 | ||
1235 | /* Second, multiply r*w by 'a' if exponent bit is set. */ | |
1236 | if (BN_is_bit_set(p, b)) { | |
1237 | next_w = w * a; | |
1238 | if ((next_w / a) != w) { /* overflow */ | |
1239 | if (r_is_one) { | |
1240 | if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) | |
1241 | goto err; | |
1242 | r_is_one = 0; | |
1243 | } else { | |
1244 | if (!BN_MOD_MUL_WORD(r, w, m)) | |
1245 | goto err; | |
1246 | } | |
1247 | next_w = a; | |
1248 | } | |
1249 | w = next_w; | |
1250 | } | |
1251 | } | |
1252 | ||
1253 | /* Finally, set r:=r*w. */ | |
1254 | if (w != 1) { | |
1255 | if (r_is_one) { | |
1256 | if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) | |
1257 | goto err; | |
1258 | r_is_one = 0; | |
1259 | } else { | |
1260 | if (!BN_MOD_MUL_WORD(r, w, m)) | |
1261 | goto err; | |
1262 | } | |
1263 | } | |
1264 | ||
1265 | if (r_is_one) { /* can happen only if a == 1 */ | |
1266 | if (!BN_one(rr)) | |
1267 | goto err; | |
1268 | } else { | |
1269 | if (!BN_from_montgomery(rr, r, mont, ctx)) | |
1270 | goto err; | |
1271 | } | |
1272 | ret = 1; | |
1273 | err: | |
23a1d5e9 | 1274 | if (in_mont == NULL) |
0f113f3e MC |
1275 | BN_MONT_CTX_free(mont); |
1276 | BN_CTX_end(ctx); | |
1277 | bn_check_top(rr); | |
1278 | return (ret); | |
1279 | } | |
d02b48c6 RE |
1280 | |
1281 | /* The old fallback, simple version :-) */ | |
82b2f57e | 1282 | int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, |
0f113f3e MC |
1283 | const BIGNUM *m, BN_CTX *ctx) |
1284 | { | |
1285 | int i, j, bits, ret = 0, wstart, wend, window, wvalue; | |
1286 | int start = 1; | |
1287 | BIGNUM *d; | |
1288 | /* Table of variables obtained from 'ctx' */ | |
1289 | BIGNUM *val[TABLE_SIZE]; | |
1290 | ||
1291 | if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) { | |
1292 | /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ | |
1293 | BNerr(BN_F_BN_MOD_EXP_SIMPLE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); | |
1294 | return -1; | |
1295 | } | |
1296 | ||
1297 | bits = BN_num_bits(p); | |
1298 | ||
1299 | if (bits == 0) { | |
1300 | ret = BN_one(r); | |
1301 | return ret; | |
1302 | } | |
1303 | ||
1304 | BN_CTX_start(ctx); | |
1305 | d = BN_CTX_get(ctx); | |
1306 | val[0] = BN_CTX_get(ctx); | |
1307 | if (!d || !val[0]) | |
1308 | goto err; | |
1309 | ||
1310 | if (!BN_nnmod(val[0], a, m, ctx)) | |
1311 | goto err; /* 1 */ | |
1312 | if (BN_is_zero(val[0])) { | |
1313 | BN_zero(r); | |
1314 | ret = 1; | |
1315 | goto err; | |
1316 | } | |
1317 | ||
1318 | window = BN_window_bits_for_exponent_size(bits); | |
1319 | if (window > 1) { | |
1320 | if (!BN_mod_mul(d, val[0], val[0], m, ctx)) | |
1321 | goto err; /* 2 */ | |
1322 | j = 1 << (window - 1); | |
1323 | for (i = 1; i < j; i++) { | |
1324 | if (((val[i] = BN_CTX_get(ctx)) == NULL) || | |
1325 | !BN_mod_mul(val[i], val[i - 1], d, m, ctx)) | |
1326 | goto err; | |
1327 | } | |
1328 | } | |
1329 | ||
1330 | start = 1; /* This is used to avoid multiplication etc | |
1331 | * when there is only the value '1' in the | |
1332 | * buffer. */ | |
1333 | wvalue = 0; /* The 'value' of the window */ | |
1334 | wstart = bits - 1; /* The top bit of the window */ | |
1335 | wend = 0; /* The bottom bit of the window */ | |
1336 | ||
1337 | if (!BN_one(r)) | |
1338 | goto err; | |
1339 | ||
1340 | for (;;) { | |
1341 | if (BN_is_bit_set(p, wstart) == 0) { | |
1342 | if (!start) | |
1343 | if (!BN_mod_mul(r, r, r, m, ctx)) | |
1344 | goto err; | |
1345 | if (wstart == 0) | |
1346 | break; | |
1347 | wstart--; | |
1348 | continue; | |
1349 | } | |
1350 | /* | |
1351 | * We now have wstart on a 'set' bit, we now need to work out how bit | |
1352 | * a window to do. To do this we need to scan forward until the last | |
1353 | * set bit before the end of the window | |
1354 | */ | |
1355 | j = wstart; | |
1356 | wvalue = 1; | |
1357 | wend = 0; | |
1358 | for (i = 1; i < window; i++) { | |
1359 | if (wstart - i < 0) | |
1360 | break; | |
1361 | if (BN_is_bit_set(p, wstart - i)) { | |
1362 | wvalue <<= (i - wend); | |
1363 | wvalue |= 1; | |
1364 | wend = i; | |
1365 | } | |
1366 | } | |
1367 | ||
1368 | /* wend is the size of the current window */ | |
1369 | j = wend + 1; | |
1370 | /* add the 'bytes above' */ | |
1371 | if (!start) | |
1372 | for (i = 0; i < j; i++) { | |
1373 | if (!BN_mod_mul(r, r, r, m, ctx)) | |
1374 | goto err; | |
1375 | } | |
1376 | ||
1377 | /* wvalue will be an odd number < 2^window */ | |
1378 | if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx)) | |
1379 | goto err; | |
1380 | ||
1381 | /* move the 'window' down further */ | |
1382 | wstart -= wend + 1; | |
1383 | wvalue = 0; | |
1384 | start = 0; | |
1385 | if (wstart < 0) | |
1386 | break; | |
1387 | } | |
1388 | ret = 1; | |
1389 | err: | |
1390 | BN_CTX_end(ctx); | |
1391 | bn_check_top(r); | |
1392 | return (ret); | |
1393 | } |