1 | /*
|
---|
2 | * Copyright 1995-2016 The OpenSSL Project Authors. All Rights Reserved.
|
---|
3 | *
|
---|
4 | * Licensed under the OpenSSL license (the "License"). You may not use
|
---|
5 | * this file except in compliance with the License. You can obtain a copy
|
---|
6 | * in the file LICENSE in the source distribution or at
|
---|
7 | * https://www.openssl.org/source/license.html
|
---|
8 | */
|
---|
9 |
|
---|
10 | #include "internal/cryptlib.h"
|
---|
11 | #include "internal/constant_time_locl.h"
|
---|
12 | #include "bn_lcl.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_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
|
---|
48 | BNerr(BN_F_BN_EXP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
|
---|
49 | return 0;
|
---|
50 | }
|
---|
51 |
|
---|
52 | BN_CTX_start(ctx);
|
---|
53 | if ((r == a) || (r == p))
|
---|
54 | rr = BN_CTX_get(ctx);
|
---|
55 | else
|
---|
56 | rr = r;
|
---|
57 | v = BN_CTX_get(ctx);
|
---|
58 | if (rr == NULL || v == NULL)
|
---|
59 | goto err;
|
---|
60 |
|
---|
61 | if (BN_copy(v, a) == NULL)
|
---|
62 | goto err;
|
---|
63 | bits = BN_num_bits(p);
|
---|
64 |
|
---|
65 | if (BN_is_odd(p)) {
|
---|
66 | if (BN_copy(rr, a) == NULL)
|
---|
67 | goto err;
|
---|
68 | } else {
|
---|
69 | if (!BN_one(rr))
|
---|
70 | goto err;
|
---|
71 | }
|
---|
72 |
|
---|
73 | for (i = 1; i < bits; i++) {
|
---|
74 | if (!BN_sqr(v, v, ctx))
|
---|
75 | goto err;
|
---|
76 | if (BN_is_bit_set(p, i)) {
|
---|
77 | if (!BN_mul(rr, rr, v, ctx))
|
---|
78 | goto err;
|
---|
79 | }
|
---|
80 | }
|
---|
81 | if (r != rr && BN_copy(r, rr) == NULL)
|
---|
82 | goto err;
|
---|
83 |
|
---|
84 | ret = 1;
|
---|
85 | err:
|
---|
86 | BN_CTX_end(ctx);
|
---|
87 | bn_check_top(r);
|
---|
88 | return (ret);
|
---|
89 | }
|
---|
90 |
|
---|
91 | int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
|
---|
92 | BN_CTX *ctx)
|
---|
93 | {
|
---|
94 | int ret;
|
---|
95 |
|
---|
96 | bn_check_top(a);
|
---|
97 | bn_check_top(p);
|
---|
98 | bn_check_top(m);
|
---|
99 |
|
---|
100 | /*-
|
---|
101 | * For even modulus m = 2^k*m_odd, it might make sense to compute
|
---|
102 | * a^p mod m_odd and a^p mod 2^k separately (with Montgomery
|
---|
103 | * exponentiation for the odd part), using appropriate exponent
|
---|
104 | * reductions, and combine the results using the CRT.
|
---|
105 | *
|
---|
106 | * For now, we use Montgomery only if the modulus is odd; otherwise,
|
---|
107 | * exponentiation using the reciprocal-based quick remaindering
|
---|
108 | * algorithm is used.
|
---|
109 | *
|
---|
110 | * (Timing obtained with expspeed.c [computations a^p mod m
|
---|
111 | * where a, p, m are of the same length: 256, 512, 1024, 2048,
|
---|
112 | * 4096, 8192 bits], compared to the running time of the
|
---|
113 | * standard algorithm:
|
---|
114 | *
|
---|
115 | * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
|
---|
116 | * 55 .. 77 % [UltraSparc processor, but
|
---|
117 | * debug-solaris-sparcv8-gcc conf.]
|
---|
118 | *
|
---|
119 | * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
|
---|
120 | * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
|
---|
121 | *
|
---|
122 | * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
|
---|
123 | * at 2048 and more bits, but at 512 and 1024 bits, it was
|
---|
124 | * slower even than the standard algorithm!
|
---|
125 | *
|
---|
126 | * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
|
---|
127 | * should be obtained when the new Montgomery reduction code
|
---|
128 | * has been integrated into OpenSSL.)
|
---|
129 | */
|
---|
130 |
|
---|
131 | #define MONT_MUL_MOD
|
---|
132 | #define MONT_EXP_WORD
|
---|
133 | #define RECP_MUL_MOD
|
---|
134 |
|
---|
135 | #ifdef MONT_MUL_MOD
|
---|
136 | /*
|
---|
137 | * I have finally been able to take out this pre-condition of the top bit
|
---|
138 | * being set. It was caused by an error in BN_div with negatives. There
|
---|
139 | * was also another problem when for a^b%m a >= m. eay 07-May-97
|
---|
140 | */
|
---|
141 | /* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */
|
---|
142 |
|
---|
143 | if (BN_is_odd(m)) {
|
---|
144 | # ifdef MONT_EXP_WORD
|
---|
145 | if (a->top == 1 && !a->neg
|
---|
146 | && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0)) {
|
---|
147 | BN_ULONG A = a->d[0];
|
---|
148 | ret = BN_mod_exp_mont_word(r, A, p, m, ctx, NULL);
|
---|
149 | } else
|
---|
150 | # endif
|
---|
151 | ret = BN_mod_exp_mont(r, a, p, m, ctx, NULL);
|
---|
152 | } else
|
---|
153 | #endif
|
---|
154 | #ifdef RECP_MUL_MOD
|
---|
155 | {
|
---|
156 | ret = BN_mod_exp_recp(r, a, p, m, ctx);
|
---|
157 | }
|
---|
158 | #else
|
---|
159 | {
|
---|
160 | ret = BN_mod_exp_simple(r, a, p, m, ctx);
|
---|
161 | }
|
---|
162 | #endif
|
---|
163 |
|
---|
164 | bn_check_top(r);
|
---|
165 | return (ret);
|
---|
166 | }
|
---|
167 |
|
---|
168 | int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
|
---|
169 | const BIGNUM *m, BN_CTX *ctx)
|
---|
170 | {
|
---|
171 | int i, j, bits, ret = 0, wstart, wend, window, wvalue;
|
---|
172 | int start = 1;
|
---|
173 | BIGNUM *aa;
|
---|
174 | /* Table of variables obtained from 'ctx' */
|
---|
175 | BIGNUM *val[TABLE_SIZE];
|
---|
176 | BN_RECP_CTX recp;
|
---|
177 |
|
---|
178 | if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
|
---|
179 | /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
|
---|
180 | BNerr(BN_F_BN_MOD_EXP_RECP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
|
---|
181 | return 0;
|
---|
182 | }
|
---|
183 |
|
---|
184 | bits = BN_num_bits(p);
|
---|
185 | if (bits == 0) {
|
---|
186 | /* x**0 mod 1 is still zero. */
|
---|
187 | if (BN_is_one(m)) {
|
---|
188 | ret = 1;
|
---|
189 | BN_zero(r);
|
---|
190 | } else {
|
---|
191 | ret = BN_one(r);
|
---|
192 | }
|
---|
193 | return ret;
|
---|
194 | }
|
---|
195 |
|
---|
196 | BN_CTX_start(ctx);
|
---|
197 | aa = BN_CTX_get(ctx);
|
---|
198 | val[0] = BN_CTX_get(ctx);
|
---|
199 | if (!aa || !val[0])
|
---|
200 | goto err;
|
---|
201 |
|
---|
202 | BN_RECP_CTX_init(&recp);
|
---|
203 | if (m->neg) {
|
---|
204 | /* ignore sign of 'm' */
|
---|
205 | if (!BN_copy(aa, m))
|
---|
206 | goto err;
|
---|
207 | aa->neg = 0;
|
---|
208 | if (BN_RECP_CTX_set(&recp, aa, ctx) <= 0)
|
---|
209 | goto err;
|
---|
210 | } else {
|
---|
211 | if (BN_RECP_CTX_set(&recp, m, ctx) <= 0)
|
---|
212 | goto err;
|
---|
213 | }
|
---|
214 |
|
---|
215 | if (!BN_nnmod(val[0], a, m, ctx))
|
---|
216 | goto err; /* 1 */
|
---|
217 | if (BN_is_zero(val[0])) {
|
---|
218 | BN_zero(r);
|
---|
219 | ret = 1;
|
---|
220 | goto err;
|
---|
221 | }
|
---|
222 |
|
---|
223 | window = BN_window_bits_for_exponent_size(bits);
|
---|
224 | if (window > 1) {
|
---|
225 | if (!BN_mod_mul_reciprocal(aa, val[0], val[0], &recp, ctx))
|
---|
226 | goto err; /* 2 */
|
---|
227 | j = 1 << (window - 1);
|
---|
228 | for (i = 1; i < j; i++) {
|
---|
229 | if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
|
---|
230 | !BN_mod_mul_reciprocal(val[i], val[i - 1], aa, &recp, ctx))
|
---|
231 | goto err;
|
---|
232 | }
|
---|
233 | }
|
---|
234 |
|
---|
235 | start = 1; /* This is used to avoid multiplication etc
|
---|
236 | * when there is only the value '1' in the
|
---|
237 | * buffer. */
|
---|
238 | wvalue = 0; /* The 'value' of the window */
|
---|
239 | wstart = bits - 1; /* The top bit of the window */
|
---|
240 | wend = 0; /* The bottom bit of the window */
|
---|
241 |
|
---|
242 | if (!BN_one(r))
|
---|
243 | goto err;
|
---|
244 |
|
---|
245 | for (;;) {
|
---|
246 | if (BN_is_bit_set(p, wstart) == 0) {
|
---|
247 | if (!start)
|
---|
248 | if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
|
---|
249 | goto err;
|
---|
250 | if (wstart == 0)
|
---|
251 | break;
|
---|
252 | wstart--;
|
---|
253 | continue;
|
---|
254 | }
|
---|
255 | /*
|
---|
256 | * We now have wstart on a 'set' bit, we now need to work out how bit
|
---|
257 | * a window to do. To do this we need to scan forward until the last
|
---|
258 | * set bit before the end of the window
|
---|
259 | */
|
---|
260 | j = wstart;
|
---|
261 | wvalue = 1;
|
---|
262 | wend = 0;
|
---|
263 | for (i = 1; i < window; i++) {
|
---|
264 | if (wstart - i < 0)
|
---|
265 | break;
|
---|
266 | if (BN_is_bit_set(p, wstart - i)) {
|
---|
267 | wvalue <<= (i - wend);
|
---|
268 | wvalue |= 1;
|
---|
269 | wend = i;
|
---|
270 | }
|
---|
271 | }
|
---|
272 |
|
---|
273 | /* wend is the size of the current window */
|
---|
274 | j = wend + 1;
|
---|
275 | /* add the 'bytes above' */
|
---|
276 | if (!start)
|
---|
277 | for (i = 0; i < j; i++) {
|
---|
278 | if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
|
---|
279 | goto err;
|
---|
280 | }
|
---|
281 |
|
---|
282 | /* wvalue will be an odd number < 2^window */
|
---|
283 | if (!BN_mod_mul_reciprocal(r, r, val[wvalue >> 1], &recp, ctx))
|
---|
284 | goto err;
|
---|
285 |
|
---|
286 | /* move the 'window' down further */
|
---|
287 | wstart -= wend + 1;
|
---|
288 | wvalue = 0;
|
---|
289 | start = 0;
|
---|
290 | if (wstart < 0)
|
---|
291 | break;
|
---|
292 | }
|
---|
293 | ret = 1;
|
---|
294 | err:
|
---|
295 | BN_CTX_end(ctx);
|
---|
296 | BN_RECP_CTX_free(&recp);
|
---|
297 | bn_check_top(r);
|
---|
298 | return (ret);
|
---|
299 | }
|
---|
300 |
|
---|
301 | int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
|
---|
302 | const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
|
---|
303 | {
|
---|
304 | int i, j, bits, ret = 0, wstart, wend, window, wvalue;
|
---|
305 | int start = 1;
|
---|
306 | BIGNUM *d, *r;
|
---|
307 | const BIGNUM *aa;
|
---|
308 | /* Table of variables obtained from 'ctx' */
|
---|
309 | BIGNUM *val[TABLE_SIZE];
|
---|
310 | BN_MONT_CTX *mont = NULL;
|
---|
311 |
|
---|
312 | if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
|
---|
313 | return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
|
---|
314 | }
|
---|
315 |
|
---|
316 | bn_check_top(a);
|
---|
317 | bn_check_top(p);
|
---|
318 | bn_check_top(m);
|
---|
319 |
|
---|
320 | if (!BN_is_odd(m)) {
|
---|
321 | BNerr(BN_F_BN_MOD_EXP_MONT, BN_R_CALLED_WITH_EVEN_MODULUS);
|
---|
322 | return (0);
|
---|
323 | }
|
---|
324 | bits = BN_num_bits(p);
|
---|
325 | if (bits == 0) {
|
---|
326 | /* x**0 mod 1 is still zero. */
|
---|
327 | if (BN_is_one(m)) {
|
---|
328 | ret = 1;
|
---|
329 | BN_zero(rr);
|
---|
330 | } else {
|
---|
331 | ret = BN_one(rr);
|
---|
332 | }
|
---|
333 | return ret;
|
---|
334 | }
|
---|
335 |
|
---|
336 | BN_CTX_start(ctx);
|
---|
337 | d = BN_CTX_get(ctx);
|
---|
338 | r = BN_CTX_get(ctx);
|
---|
339 | val[0] = BN_CTX_get(ctx);
|
---|
340 | if (!d || !r || !val[0])
|
---|
341 | goto err;
|
---|
342 |
|
---|
343 | /*
|
---|
344 | * If this is not done, things will break in the montgomery part
|
---|
345 | */
|
---|
346 |
|
---|
347 | if (in_mont != NULL)
|
---|
348 | mont = in_mont;
|
---|
349 | else {
|
---|
350 | if ((mont = BN_MONT_CTX_new()) == NULL)
|
---|
351 | goto err;
|
---|
352 | if (!BN_MONT_CTX_set(mont, m, ctx))
|
---|
353 | goto err;
|
---|
354 | }
|
---|
355 |
|
---|
356 | if (a->neg || BN_ucmp(a, m) >= 0) {
|
---|
357 | if (!BN_nnmod(val[0], a, m, ctx))
|
---|
358 | goto err;
|
---|
359 | aa = val[0];
|
---|
360 | } else
|
---|
361 | aa = a;
|
---|
362 | if (BN_is_zero(aa)) {
|
---|
363 | BN_zero(rr);
|
---|
364 | ret = 1;
|
---|
365 | goto err;
|
---|
366 | }
|
---|
367 | if (!BN_to_montgomery(val[0], aa, mont, ctx))
|
---|
368 | goto err; /* 1 */
|
---|
369 |
|
---|
370 | window = BN_window_bits_for_exponent_size(bits);
|
---|
371 | if (window > 1) {
|
---|
372 | if (!BN_mod_mul_montgomery(d, val[0], val[0], mont, ctx))
|
---|
373 | goto err; /* 2 */
|
---|
374 | j = 1 << (window - 1);
|
---|
375 | for (i = 1; i < j; i++) {
|
---|
376 | if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
|
---|
377 | !BN_mod_mul_montgomery(val[i], val[i - 1], d, mont, ctx))
|
---|
378 | goto err;
|
---|
379 | }
|
---|
380 | }
|
---|
381 |
|
---|
382 | start = 1; /* This is used to avoid multiplication etc
|
---|
383 | * when there is only the value '1' in the
|
---|
384 | * buffer. */
|
---|
385 | wvalue = 0; /* The 'value' of the window */
|
---|
386 | wstart = bits - 1; /* The top bit of the window */
|
---|
387 | wend = 0; /* The bottom bit of the window */
|
---|
388 |
|
---|
389 | #if 1 /* by Shay Gueron's suggestion */
|
---|
390 | j = m->top; /* borrow j */
|
---|
391 | if (m->d[j - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
|
---|
392 | if (bn_wexpand(r, j) == NULL)
|
---|
393 | goto err;
|
---|
394 | /* 2^(top*BN_BITS2) - m */
|
---|
395 | r->d[0] = (0 - m->d[0]) & BN_MASK2;
|
---|
396 | for (i = 1; i < j; i++)
|
---|
397 | r->d[i] = (~m->d[i]) & BN_MASK2;
|
---|
398 | r->top = j;
|
---|
399 | /*
|
---|
400 | * Upper words will be zero if the corresponding words of 'm' were
|
---|
401 | * 0xfff[...], so decrement r->top accordingly.
|
---|
402 | */
|
---|
403 | bn_correct_top(r);
|
---|
404 | } else
|
---|
405 | #endif
|
---|
406 | if (!BN_to_montgomery(r, BN_value_one(), mont, ctx))
|
---|
407 | goto err;
|
---|
408 | for (;;) {
|
---|
409 | if (BN_is_bit_set(p, wstart) == 0) {
|
---|
410 | if (!start) {
|
---|
411 | if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
|
---|
412 | goto err;
|
---|
413 | }
|
---|
414 | if (wstart == 0)
|
---|
415 | break;
|
---|
416 | wstart--;
|
---|
417 | continue;
|
---|
418 | }
|
---|
419 | /*
|
---|
420 | * We now have wstart on a 'set' bit, we now need to work out how bit
|
---|
421 | * a window to do. To do this we need to scan forward until the last
|
---|
422 | * set bit before the end of the window
|
---|
423 | */
|
---|
424 | j = wstart;
|
---|
425 | wvalue = 1;
|
---|
426 | wend = 0;
|
---|
427 | for (i = 1; i < window; i++) {
|
---|
428 | if (wstart - i < 0)
|
---|
429 | break;
|
---|
430 | if (BN_is_bit_set(p, wstart - i)) {
|
---|
431 | wvalue <<= (i - wend);
|
---|
432 | wvalue |= 1;
|
---|
433 | wend = i;
|
---|
434 | }
|
---|
435 | }
|
---|
436 |
|
---|
437 | /* wend is the size of the current window */
|
---|
438 | j = wend + 1;
|
---|
439 | /* add the 'bytes above' */
|
---|
440 | if (!start)
|
---|
441 | for (i = 0; i < j; i++) {
|
---|
442 | if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
|
---|
443 | goto err;
|
---|
444 | }
|
---|
445 |
|
---|
446 | /* wvalue will be an odd number < 2^window */
|
---|
447 | if (!BN_mod_mul_montgomery(r, r, val[wvalue >> 1], mont, ctx))
|
---|
448 | goto err;
|
---|
449 |
|
---|
450 | /* move the 'window' down further */
|
---|
451 | wstart -= wend + 1;
|
---|
452 | wvalue = 0;
|
---|
453 | start = 0;
|
---|
454 | if (wstart < 0)
|
---|
455 | break;
|
---|
456 | }
|
---|
457 | #if defined(SPARC_T4_MONT)
|
---|
458 | if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
|
---|
459 | j = mont->N.top; /* borrow j */
|
---|
460 | val[0]->d[0] = 1; /* borrow val[0] */
|
---|
461 | for (i = 1; i < j; i++)
|
---|
462 | val[0]->d[i] = 0;
|
---|
463 | val[0]->top = j;
|
---|
464 | if (!BN_mod_mul_montgomery(rr, r, val[0], mont, ctx))
|
---|
465 | goto err;
|
---|
466 | } else
|
---|
467 | #endif
|
---|
468 | if (!BN_from_montgomery(rr, r, mont, ctx))
|
---|
469 | goto err;
|
---|
470 | ret = 1;
|
---|
471 | err:
|
---|
472 | if (in_mont == NULL)
|
---|
473 | BN_MONT_CTX_free(mont);
|
---|
474 | BN_CTX_end(ctx);
|
---|
475 | bn_check_top(rr);
|
---|
476 | return (ret);
|
---|
477 | }
|
---|
478 |
|
---|
479 | #if defined(SPARC_T4_MONT)
|
---|
480 | static BN_ULONG bn_get_bits(const BIGNUM *a, int bitpos)
|
---|
481 | {
|
---|
482 | BN_ULONG ret = 0;
|
---|
483 | int wordpos;
|
---|
484 |
|
---|
485 | wordpos = bitpos / BN_BITS2;
|
---|
486 | bitpos %= BN_BITS2;
|
---|
487 | if (wordpos >= 0 && wordpos < a->top) {
|
---|
488 | ret = a->d[wordpos] & BN_MASK2;
|
---|
489 | if (bitpos) {
|
---|
490 | ret >>= bitpos;
|
---|
491 | if (++wordpos < a->top)
|
---|
492 | ret |= a->d[wordpos] << (BN_BITS2 - bitpos);
|
---|
493 | }
|
---|
494 | }
|
---|
495 |
|
---|
496 | return ret & BN_MASK2;
|
---|
497 | }
|
---|
498 | #endif
|
---|
499 |
|
---|
500 | /*
|
---|
501 | * BN_mod_exp_mont_consttime() stores the precomputed powers in a specific
|
---|
502 | * layout so that accessing any of these table values shows the same access
|
---|
503 | * pattern as far as cache lines are concerned. The following functions are
|
---|
504 | * used to transfer a BIGNUM from/to that table.
|
---|
505 | */
|
---|
506 |
|
---|
507 | static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top,
|
---|
508 | unsigned char *buf, int idx,
|
---|
509 | int window)
|
---|
510 | {
|
---|
511 | int i, j;
|
---|
512 | int width = 1 << window;
|
---|
513 | BN_ULONG *table = (BN_ULONG *)buf;
|
---|
514 |
|
---|
515 | if (top > b->top)
|
---|
516 | top = b->top; /* this works because 'buf' is explicitly
|
---|
517 | * zeroed */
|
---|
518 | for (i = 0, j = idx; i < top; i++, j += width) {
|
---|
519 | table[j] = b->d[i];
|
---|
520 | }
|
---|
521 |
|
---|
522 | return 1;
|
---|
523 | }
|
---|
524 |
|
---|
525 | static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top,
|
---|
526 | unsigned char *buf, int idx,
|
---|
527 | int window)
|
---|
528 | {
|
---|
529 | int i, j;
|
---|
530 | int width = 1 << window;
|
---|
531 | /*
|
---|
532 | * We declare table 'volatile' in order to discourage compiler
|
---|
533 | * from reordering loads from the table. Concern is that if
|
---|
534 | * reordered in specific manner loads might give away the
|
---|
535 | * information we are trying to conceal. Some would argue that
|
---|
536 | * compiler can reorder them anyway, but it can as well be
|
---|
537 | * argued that doing so would be violation of standard...
|
---|
538 | */
|
---|
539 | volatile BN_ULONG *table = (volatile BN_ULONG *)buf;
|
---|
540 |
|
---|
541 | if (bn_wexpand(b, top) == NULL)
|
---|
542 | return 0;
|
---|
543 |
|
---|
544 | if (window <= 3) {
|
---|
545 | for (i = 0; i < top; i++, table += width) {
|
---|
546 | BN_ULONG acc = 0;
|
---|
547 |
|
---|
548 | for (j = 0; j < width; j++) {
|
---|
549 | acc |= table[j] &
|
---|
550 | ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1));
|
---|
551 | }
|
---|
552 |
|
---|
553 | b->d[i] = acc;
|
---|
554 | }
|
---|
555 | } else {
|
---|
556 | int xstride = 1 << (window - 2);
|
---|
557 | BN_ULONG y0, y1, y2, y3;
|
---|
558 |
|
---|
559 | i = idx >> (window - 2); /* equivalent of idx / xstride */
|
---|
560 | idx &= xstride - 1; /* equivalent of idx % xstride */
|
---|
561 |
|
---|
562 | y0 = (BN_ULONG)0 - (constant_time_eq_int(i,0)&1);
|
---|
563 | y1 = (BN_ULONG)0 - (constant_time_eq_int(i,1)&1);
|
---|
564 | y2 = (BN_ULONG)0 - (constant_time_eq_int(i,2)&1);
|
---|
565 | y3 = (BN_ULONG)0 - (constant_time_eq_int(i,3)&1);
|
---|
566 |
|
---|
567 | for (i = 0; i < top; i++, table += width) {
|
---|
568 | BN_ULONG acc = 0;
|
---|
569 |
|
---|
570 | for (j = 0; j < xstride; j++) {
|
---|
571 | acc |= ( (table[j + 0 * xstride] & y0) |
|
---|
572 | (table[j + 1 * xstride] & y1) |
|
---|
573 | (table[j + 2 * xstride] & y2) |
|
---|
574 | (table[j + 3 * xstride] & y3) )
|
---|
575 | & ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1));
|
---|
576 | }
|
---|
577 |
|
---|
578 | b->d[i] = acc;
|
---|
579 | }
|
---|
580 | }
|
---|
581 |
|
---|
582 | b->top = top;
|
---|
583 | bn_correct_top(b);
|
---|
584 | return 1;
|
---|
585 | }
|
---|
586 |
|
---|
587 | /*
|
---|
588 | * Given a pointer value, compute the next address that is a cache line
|
---|
589 | * multiple.
|
---|
590 | */
|
---|
591 | #define MOD_EXP_CTIME_ALIGN(x_) \
|
---|
592 | ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
|
---|
593 |
|
---|
594 | /*
|
---|
595 | * This variant of BN_mod_exp_mont() uses fixed windows and the special
|
---|
596 | * precomputation memory layout to limit data-dependency to a minimum to
|
---|
597 | * protect secret exponents (cf. the hyper-threading timing attacks pointed
|
---|
598 | * out by Colin Percival,
|
---|
599 | * http://www.daemonology.net/hyperthreading-considered-harmful/)
|
---|
600 | */
|
---|
601 | int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
|
---|
602 | const BIGNUM *m, BN_CTX *ctx,
|
---|
603 | BN_MONT_CTX *in_mont)
|
---|
604 | {
|
---|
605 | int i, bits, ret = 0, window, wvalue;
|
---|
606 | int top;
|
---|
607 | BN_MONT_CTX *mont = NULL;
|
---|
608 |
|
---|
609 | int numPowers;
|
---|
610 | unsigned char *powerbufFree = NULL;
|
---|
611 | int powerbufLen = 0;
|
---|
612 | unsigned char *powerbuf = NULL;
|
---|
613 | BIGNUM tmp, am;
|
---|
614 | #if defined(SPARC_T4_MONT)
|
---|
615 | unsigned int t4 = 0;
|
---|
616 | #endif
|
---|
617 |
|
---|
618 | bn_check_top(a);
|
---|
619 | bn_check_top(p);
|
---|
620 | bn_check_top(m);
|
---|
621 |
|
---|
622 | if (!BN_is_odd(m)) {
|
---|
623 | BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME, BN_R_CALLED_WITH_EVEN_MODULUS);
|
---|
624 | return (0);
|
---|
625 | }
|
---|
626 |
|
---|
627 | top = m->top;
|
---|
628 |
|
---|
629 | bits = BN_num_bits(p);
|
---|
630 | if (bits == 0) {
|
---|
631 | /* x**0 mod 1 is still zero. */
|
---|
632 | if (BN_is_one(m)) {
|
---|
633 | ret = 1;
|
---|
634 | BN_zero(rr);
|
---|
635 | } else {
|
---|
636 | ret = BN_one(rr);
|
---|
637 | }
|
---|
638 | return ret;
|
---|
639 | }
|
---|
640 |
|
---|
641 | BN_CTX_start(ctx);
|
---|
642 |
|
---|
643 | /*
|
---|
644 | * Allocate a montgomery context if it was not supplied by the caller. If
|
---|
645 | * this is not done, things will break in the montgomery part.
|
---|
646 | */
|
---|
647 | if (in_mont != NULL)
|
---|
648 | mont = in_mont;
|
---|
649 | else {
|
---|
650 | if ((mont = BN_MONT_CTX_new()) == NULL)
|
---|
651 | goto err;
|
---|
652 | if (!BN_MONT_CTX_set(mont, m, ctx))
|
---|
653 | goto err;
|
---|
654 | }
|
---|
655 |
|
---|
656 | #ifdef RSAZ_ENABLED
|
---|
657 | /*
|
---|
658 | * If the size of the operands allow it, perform the optimized
|
---|
659 | * RSAZ exponentiation. For further information see
|
---|
660 | * crypto/bn/rsaz_exp.c and accompanying assembly modules.
|
---|
661 | */
|
---|
662 | if ((16 == a->top) && (16 == p->top) && (BN_num_bits(m) == 1024)
|
---|
663 | && rsaz_avx2_eligible()) {
|
---|
664 | if (NULL == bn_wexpand(rr, 16))
|
---|
665 | goto err;
|
---|
666 | RSAZ_1024_mod_exp_avx2(rr->d, a->d, p->d, m->d, mont->RR.d,
|
---|
667 | mont->n0[0]);
|
---|
668 | rr->top = 16;
|
---|
669 | rr->neg = 0;
|
---|
670 | bn_correct_top(rr);
|
---|
671 | ret = 1;
|
---|
672 | goto err;
|
---|
673 | } else if ((8 == a->top) && (8 == p->top) && (BN_num_bits(m) == 512)) {
|
---|
674 | if (NULL == bn_wexpand(rr, 8))
|
---|
675 | goto err;
|
---|
676 | RSAZ_512_mod_exp(rr->d, a->d, p->d, m->d, mont->n0[0], mont->RR.d);
|
---|
677 | rr->top = 8;
|
---|
678 | rr->neg = 0;
|
---|
679 | bn_correct_top(rr);
|
---|
680 | ret = 1;
|
---|
681 | goto err;
|
---|
682 | }
|
---|
683 | #endif
|
---|
684 |
|
---|
685 | /* Get the window size to use with size of p. */
|
---|
686 | window = BN_window_bits_for_ctime_exponent_size(bits);
|
---|
687 | #if defined(SPARC_T4_MONT)
|
---|
688 | if (window >= 5 && (top & 15) == 0 && top <= 64 &&
|
---|
689 | (OPENSSL_sparcv9cap_P[1] & (CFR_MONTMUL | CFR_MONTSQR)) ==
|
---|
690 | (CFR_MONTMUL | CFR_MONTSQR) && (t4 = OPENSSL_sparcv9cap_P[0]))
|
---|
691 | window = 5;
|
---|
692 | else
|
---|
693 | #endif
|
---|
694 | #if defined(OPENSSL_BN_ASM_MONT5)
|
---|
695 | if (window >= 5) {
|
---|
696 | window = 5; /* ~5% improvement for RSA2048 sign, and even
|
---|
697 | * for RSA4096 */
|
---|
698 | /* reserve space for mont->N.d[] copy */
|
---|
699 | powerbufLen += top * sizeof(mont->N.d[0]);
|
---|
700 | }
|
---|
701 | #endif
|
---|
702 | (void)0;
|
---|
703 |
|
---|
704 | /*
|
---|
705 | * Allocate a buffer large enough to hold all of the pre-computed powers
|
---|
706 | * of am, am itself and tmp.
|
---|
707 | */
|
---|
708 | numPowers = 1 << window;
|
---|
709 | powerbufLen += sizeof(m->d[0]) * (top * numPowers +
|
---|
710 | ((2 * top) >
|
---|
711 | numPowers ? (2 * top) : numPowers));
|
---|
712 | #ifdef alloca
|
---|
713 | if (powerbufLen < 3072)
|
---|
714 | powerbufFree =
|
---|
715 | alloca(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
|
---|
716 | else
|
---|
717 | #endif
|
---|
718 | if ((powerbufFree =
|
---|
719 | OPENSSL_malloc(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH))
|
---|
720 | == NULL)
|
---|
721 | goto err;
|
---|
722 |
|
---|
723 | powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
|
---|
724 | memset(powerbuf, 0, powerbufLen);
|
---|
725 |
|
---|
726 | #ifdef alloca
|
---|
727 | if (powerbufLen < 3072)
|
---|
728 | powerbufFree = NULL;
|
---|
729 | #endif
|
---|
730 |
|
---|
731 | /* lay down tmp and am right after powers table */
|
---|
732 | tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers);
|
---|
733 | am.d = tmp.d + top;
|
---|
734 | tmp.top = am.top = 0;
|
---|
735 | tmp.dmax = am.dmax = top;
|
---|
736 | tmp.neg = am.neg = 0;
|
---|
737 | tmp.flags = am.flags = BN_FLG_STATIC_DATA;
|
---|
738 |
|
---|
739 | /* prepare a^0 in Montgomery domain */
|
---|
740 | #if 1 /* by Shay Gueron's suggestion */
|
---|
741 | if (m->d[top - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
|
---|
742 | /* 2^(top*BN_BITS2) - m */
|
---|
743 | tmp.d[0] = (0 - m->d[0]) & BN_MASK2;
|
---|
744 | for (i = 1; i < top; i++)
|
---|
745 | tmp.d[i] = (~m->d[i]) & BN_MASK2;
|
---|
746 | tmp.top = top;
|
---|
747 | } else
|
---|
748 | #endif
|
---|
749 | if (!BN_to_montgomery(&tmp, BN_value_one(), mont, ctx))
|
---|
750 | goto err;
|
---|
751 |
|
---|
752 | /* prepare a^1 in Montgomery domain */
|
---|
753 | if (a->neg || BN_ucmp(a, m) >= 0) {
|
---|
754 | if (!BN_mod(&am, a, m, ctx))
|
---|
755 | goto err;
|
---|
756 | if (!BN_to_montgomery(&am, &am, mont, ctx))
|
---|
757 | goto err;
|
---|
758 | } else if (!BN_to_montgomery(&am, a, mont, ctx))
|
---|
759 | goto err;
|
---|
760 |
|
---|
761 | #if defined(SPARC_T4_MONT)
|
---|
762 | if (t4) {
|
---|
763 | typedef int (*bn_pwr5_mont_f) (BN_ULONG *tp, const BN_ULONG *np,
|
---|
764 | const BN_ULONG *n0, const void *table,
|
---|
765 | int power, int bits);
|
---|
766 | int bn_pwr5_mont_t4_8(BN_ULONG *tp, const BN_ULONG *np,
|
---|
767 | const BN_ULONG *n0, const void *table,
|
---|
768 | int power, int bits);
|
---|
769 | int bn_pwr5_mont_t4_16(BN_ULONG *tp, const BN_ULONG *np,
|
---|
770 | const BN_ULONG *n0, const void *table,
|
---|
771 | int power, int bits);
|
---|
772 | int bn_pwr5_mont_t4_24(BN_ULONG *tp, const BN_ULONG *np,
|
---|
773 | const BN_ULONG *n0, const void *table,
|
---|
774 | int power, int bits);
|
---|
775 | int bn_pwr5_mont_t4_32(BN_ULONG *tp, const BN_ULONG *np,
|
---|
776 | const BN_ULONG *n0, const void *table,
|
---|
777 | int power, int bits);
|
---|
778 | static const bn_pwr5_mont_f pwr5_funcs[4] = {
|
---|
779 | bn_pwr5_mont_t4_8, bn_pwr5_mont_t4_16,
|
---|
780 | bn_pwr5_mont_t4_24, bn_pwr5_mont_t4_32
|
---|
781 | };
|
---|
782 | bn_pwr5_mont_f pwr5_worker = pwr5_funcs[top / 16 - 1];
|
---|
783 |
|
---|
784 | typedef int (*bn_mul_mont_f) (BN_ULONG *rp, const BN_ULONG *ap,
|
---|
785 | const void *bp, const BN_ULONG *np,
|
---|
786 | const BN_ULONG *n0);
|
---|
787 | int bn_mul_mont_t4_8(BN_ULONG *rp, const BN_ULONG *ap, const void *bp,
|
---|
788 | const BN_ULONG *np, const BN_ULONG *n0);
|
---|
789 | int bn_mul_mont_t4_16(BN_ULONG *rp, const BN_ULONG *ap,
|
---|
790 | const void *bp, const BN_ULONG *np,
|
---|
791 | const BN_ULONG *n0);
|
---|
792 | int bn_mul_mont_t4_24(BN_ULONG *rp, const BN_ULONG *ap,
|
---|
793 | const void *bp, const BN_ULONG *np,
|
---|
794 | const BN_ULONG *n0);
|
---|
795 | int bn_mul_mont_t4_32(BN_ULONG *rp, const BN_ULONG *ap,
|
---|
796 | const void *bp, const BN_ULONG *np,
|
---|
797 | const BN_ULONG *n0);
|
---|
798 | static const bn_mul_mont_f mul_funcs[4] = {
|
---|
799 | bn_mul_mont_t4_8, bn_mul_mont_t4_16,
|
---|
800 | bn_mul_mont_t4_24, bn_mul_mont_t4_32
|
---|
801 | };
|
---|
802 | bn_mul_mont_f mul_worker = mul_funcs[top / 16 - 1];
|
---|
803 |
|
---|
804 | void bn_mul_mont_vis3(BN_ULONG *rp, const BN_ULONG *ap,
|
---|
805 | const void *bp, const BN_ULONG *np,
|
---|
806 | const BN_ULONG *n0, int num);
|
---|
807 | void bn_mul_mont_t4(BN_ULONG *rp, const BN_ULONG *ap,
|
---|
808 | const void *bp, const BN_ULONG *np,
|
---|
809 | const BN_ULONG *n0, int num);
|
---|
810 | void bn_mul_mont_gather5_t4(BN_ULONG *rp, const BN_ULONG *ap,
|
---|
811 | const void *table, const BN_ULONG *np,
|
---|
812 | const BN_ULONG *n0, int num, int power);
|
---|
813 | void bn_flip_n_scatter5_t4(const BN_ULONG *inp, size_t num,
|
---|
814 | void *table, size_t power);
|
---|
815 | void bn_gather5_t4(BN_ULONG *out, size_t num,
|
---|
816 | void *table, size_t power);
|
---|
817 | void bn_flip_t4(BN_ULONG *dst, BN_ULONG *src, size_t num);
|
---|
818 |
|
---|
819 | BN_ULONG *np = mont->N.d, *n0 = mont->n0;
|
---|
820 | int stride = 5 * (6 - (top / 16 - 1)); /* multiple of 5, but less
|
---|
821 | * than 32 */
|
---|
822 |
|
---|
823 | /*
|
---|
824 | * BN_to_montgomery can contaminate words above .top [in
|
---|
825 | * BN_DEBUG[_DEBUG] build]...
|
---|
826 | */
|
---|
827 | for (i = am.top; i < top; i++)
|
---|
828 | am.d[i] = 0;
|
---|
829 | for (i = tmp.top; i < top; i++)
|
---|
830 | tmp.d[i] = 0;
|
---|
831 |
|
---|
832 | bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 0);
|
---|
833 | bn_flip_n_scatter5_t4(am.d, top, powerbuf, 1);
|
---|
834 | if (!(*mul_worker) (tmp.d, am.d, am.d, np, n0) &&
|
---|
835 | !(*mul_worker) (tmp.d, am.d, am.d, np, n0))
|
---|
836 | bn_mul_mont_vis3(tmp.d, am.d, am.d, np, n0, top);
|
---|
837 | bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 2);
|
---|
838 |
|
---|
839 | for (i = 3; i < 32; i++) {
|
---|
840 | /* Calculate a^i = a^(i-1) * a */
|
---|
841 | if (!(*mul_worker) (tmp.d, tmp.d, am.d, np, n0) &&
|
---|
842 | !(*mul_worker) (tmp.d, tmp.d, am.d, np, n0))
|
---|
843 | bn_mul_mont_vis3(tmp.d, tmp.d, am.d, np, n0, top);
|
---|
844 | bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, i);
|
---|
845 | }
|
---|
846 |
|
---|
847 | /* switch to 64-bit domain */
|
---|
848 | np = alloca(top * sizeof(BN_ULONG));
|
---|
849 | top /= 2;
|
---|
850 | bn_flip_t4(np, mont->N.d, top);
|
---|
851 |
|
---|
852 | bits--;
|
---|
853 | for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--)
|
---|
854 | wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
|
---|
855 | bn_gather5_t4(tmp.d, top, powerbuf, wvalue);
|
---|
856 |
|
---|
857 | /*
|
---|
858 | * Scan the exponent one window at a time starting from the most
|
---|
859 | * significant bits.
|
---|
860 | */
|
---|
861 | while (bits >= 0) {
|
---|
862 | if (bits < stride)
|
---|
863 | stride = bits + 1;
|
---|
864 | bits -= stride;
|
---|
865 | wvalue = bn_get_bits(p, bits + 1);
|
---|
866 |
|
---|
867 | if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride))
|
---|
868 | continue;
|
---|
869 | /* retry once and fall back */
|
---|
870 | if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride))
|
---|
871 | continue;
|
---|
872 |
|
---|
873 | bits += stride - 5;
|
---|
874 | wvalue >>= stride - 5;
|
---|
875 | wvalue &= 31;
|
---|
876 | bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
|
---|
877 | bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
|
---|
878 | bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
|
---|
879 | bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
|
---|
880 | bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
|
---|
881 | bn_mul_mont_gather5_t4(tmp.d, tmp.d, powerbuf, np, n0, top,
|
---|
882 | wvalue);
|
---|
883 | }
|
---|
884 |
|
---|
885 | bn_flip_t4(tmp.d, tmp.d, top);
|
---|
886 | top *= 2;
|
---|
887 | /* back to 32-bit domain */
|
---|
888 | tmp.top = top;
|
---|
889 | bn_correct_top(&tmp);
|
---|
890 | OPENSSL_cleanse(np, top * sizeof(BN_ULONG));
|
---|
891 | } else
|
---|
892 | #endif
|
---|
893 | #if defined(OPENSSL_BN_ASM_MONT5)
|
---|
894 | if (window == 5 && top > 1) {
|
---|
895 | /*
|
---|
896 | * This optimization uses ideas from http://eprint.iacr.org/2011/239,
|
---|
897 | * specifically optimization of cache-timing attack countermeasures
|
---|
898 | * and pre-computation optimization.
|
---|
899 | */
|
---|
900 |
|
---|
901 | /*
|
---|
902 | * Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as
|
---|
903 | * 512-bit RSA is hardly relevant, we omit it to spare size...
|
---|
904 | */
|
---|
905 | void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap,
|
---|
906 | const void *table, const BN_ULONG *np,
|
---|
907 | const BN_ULONG *n0, int num, int power);
|
---|
908 | void bn_scatter5(const BN_ULONG *inp, size_t num,
|
---|
909 | void *table, size_t power);
|
---|
910 | void bn_gather5(BN_ULONG *out, size_t num, void *table, size_t power);
|
---|
911 | void bn_power5(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 | int bn_get_bits5(const BN_ULONG *ap, int off);
|
---|
915 | int bn_from_montgomery(BN_ULONG *rp, const BN_ULONG *ap,
|
---|
916 | const BN_ULONG *not_used, const BN_ULONG *np,
|
---|
917 | const BN_ULONG *n0, int num);
|
---|
918 |
|
---|
919 | BN_ULONG *n0 = mont->n0, *np;
|
---|
920 |
|
---|
921 | /*
|
---|
922 | * BN_to_montgomery can contaminate words above .top [in
|
---|
923 | * BN_DEBUG[_DEBUG] build]...
|
---|
924 | */
|
---|
925 | for (i = am.top; i < top; i++)
|
---|
926 | am.d[i] = 0;
|
---|
927 | for (i = tmp.top; i < top; i++)
|
---|
928 | tmp.d[i] = 0;
|
---|
929 |
|
---|
930 | /*
|
---|
931 | * copy mont->N.d[] to improve cache locality
|
---|
932 | */
|
---|
933 | for (np = am.d + top, i = 0; i < top; i++)
|
---|
934 | np[i] = mont->N.d[i];
|
---|
935 |
|
---|
936 | bn_scatter5(tmp.d, top, powerbuf, 0);
|
---|
937 | bn_scatter5(am.d, am.top, powerbuf, 1);
|
---|
938 | bn_mul_mont(tmp.d, am.d, am.d, np, n0, top);
|
---|
939 | bn_scatter5(tmp.d, top, powerbuf, 2);
|
---|
940 |
|
---|
941 | # if 0
|
---|
942 | for (i = 3; i < 32; i++) {
|
---|
943 | /* Calculate a^i = a^(i-1) * a */
|
---|
944 | bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
|
---|
945 | bn_scatter5(tmp.d, top, powerbuf, i);
|
---|
946 | }
|
---|
947 | # else
|
---|
948 | /* same as above, but uses squaring for 1/2 of operations */
|
---|
949 | for (i = 4; i < 32; i *= 2) {
|
---|
950 | bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
|
---|
951 | bn_scatter5(tmp.d, top, powerbuf, i);
|
---|
952 | }
|
---|
953 | for (i = 3; i < 8; i += 2) {
|
---|
954 | int j;
|
---|
955 | bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
|
---|
956 | bn_scatter5(tmp.d, top, powerbuf, i);
|
---|
957 | for (j = 2 * i; j < 32; j *= 2) {
|
---|
958 | bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
|
---|
959 | bn_scatter5(tmp.d, top, powerbuf, j);
|
---|
960 | }
|
---|
961 | }
|
---|
962 | for (; i < 16; i += 2) {
|
---|
963 | bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
|
---|
964 | bn_scatter5(tmp.d, top, powerbuf, i);
|
---|
965 | bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
|
---|
966 | bn_scatter5(tmp.d, top, powerbuf, 2 * i);
|
---|
967 | }
|
---|
968 | for (; i < 32; 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 | }
|
---|
972 | # endif
|
---|
973 | bits--;
|
---|
974 | for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--)
|
---|
975 | wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
|
---|
976 | bn_gather5(tmp.d, top, powerbuf, wvalue);
|
---|
977 |
|
---|
978 | /*
|
---|
979 | * Scan the exponent one window at a time starting from the most
|
---|
980 | * significant bits.
|
---|
981 | */
|
---|
982 | if (top & 7)
|
---|
983 | while (bits >= 0) {
|
---|
984 | for (wvalue = 0, i = 0; i < 5; i++, bits--)
|
---|
985 | wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
|
---|
986 |
|
---|
987 | bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
|
---|
988 | bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
|
---|
989 | bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
|
---|
990 | bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
|
---|
991 | bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
|
---|
992 | bn_mul_mont_gather5(tmp.d, tmp.d, powerbuf, np, n0, top,
|
---|
993 | wvalue);
|
---|
994 | } else {
|
---|
995 | while (bits >= 0) {
|
---|
996 | wvalue = bn_get_bits5(p->d, bits - 4);
|
---|
997 | bits -= 5;
|
---|
998 | bn_power5(tmp.d, tmp.d, powerbuf, np, n0, top, wvalue);
|
---|
999 | }
|
---|
1000 | }
|
---|
1001 |
|
---|
1002 | ret = bn_from_montgomery(tmp.d, tmp.d, NULL, np, n0, top);
|
---|
1003 | tmp.top = top;
|
---|
1004 | bn_correct_top(&tmp);
|
---|
1005 | if (ret) {
|
---|
1006 | if (!BN_copy(rr, &tmp))
|
---|
1007 | ret = 0;
|
---|
1008 | goto err; /* non-zero ret means it's not error */
|
---|
1009 | }
|
---|
1010 | } else
|
---|
1011 | #endif
|
---|
1012 | {
|
---|
1013 | if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, window))
|
---|
1014 | goto err;
|
---|
1015 | if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, window))
|
---|
1016 | goto err;
|
---|
1017 |
|
---|
1018 | /*
|
---|
1019 | * If the window size is greater than 1, then calculate
|
---|
1020 | * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even
|
---|
1021 | * powers could instead be computed as (a^(i/2))^2 to use the slight
|
---|
1022 | * performance advantage of sqr over mul).
|
---|
1023 | */
|
---|
1024 | if (window > 1) {
|
---|
1025 | if (!BN_mod_mul_montgomery(&tmp, &am, &am, mont, ctx))
|
---|
1026 | goto err;
|
---|
1027 | if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2,
|
---|
1028 | window))
|
---|
1029 | goto err;
|
---|
1030 | for (i = 3; i < numPowers; i++) {
|
---|
1031 | /* Calculate a^i = a^(i-1) * a */
|
---|
1032 | if (!BN_mod_mul_montgomery(&tmp, &am, &tmp, mont, ctx))
|
---|
1033 | goto err;
|
---|
1034 | if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i,
|
---|
1035 | window))
|
---|
1036 | goto err;
|
---|
1037 | }
|
---|
1038 | }
|
---|
1039 |
|
---|
1040 | bits--;
|
---|
1041 | for (wvalue = 0, i = bits % window; i >= 0; i--, bits--)
|
---|
1042 | wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
|
---|
1043 | if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp, top, powerbuf, wvalue,
|
---|
1044 | window))
|
---|
1045 | goto err;
|
---|
1046 |
|
---|
1047 | /*
|
---|
1048 | * Scan the exponent one window at a time starting from the most
|
---|
1049 | * significant bits.
|
---|
1050 | */
|
---|
1051 | while (bits >= 0) {
|
---|
1052 | wvalue = 0; /* The 'value' of the window */
|
---|
1053 |
|
---|
1054 | /* Scan the window, squaring the result as we go */
|
---|
1055 | for (i = 0; i < window; i++, bits--) {
|
---|
1056 | if (!BN_mod_mul_montgomery(&tmp, &tmp, &tmp, mont, ctx))
|
---|
1057 | goto err;
|
---|
1058 | wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
|
---|
1059 | }
|
---|
1060 |
|
---|
1061 | /*
|
---|
1062 | * Fetch the appropriate pre-computed value from the pre-buf
|
---|
1063 | */
|
---|
1064 | if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue,
|
---|
1065 | window))
|
---|
1066 | goto err;
|
---|
1067 |
|
---|
1068 | /* Multiply the result into the intermediate result */
|
---|
1069 | if (!BN_mod_mul_montgomery(&tmp, &tmp, &am, mont, ctx))
|
---|
1070 | goto err;
|
---|
1071 | }
|
---|
1072 | }
|
---|
1073 |
|
---|
1074 | /* Convert the final result from montgomery to standard format */
|
---|
1075 | #if defined(SPARC_T4_MONT)
|
---|
1076 | if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
|
---|
1077 | am.d[0] = 1; /* borrow am */
|
---|
1078 | for (i = 1; i < top; i++)
|
---|
1079 | am.d[i] = 0;
|
---|
1080 | if (!BN_mod_mul_montgomery(rr, &tmp, &am, mont, ctx))
|
---|
1081 | goto err;
|
---|
1082 | } else
|
---|
1083 | #endif
|
---|
1084 | if (!BN_from_montgomery(rr, &tmp, mont, ctx))
|
---|
1085 | goto err;
|
---|
1086 | ret = 1;
|
---|
1087 | err:
|
---|
1088 | if (in_mont == NULL)
|
---|
1089 | BN_MONT_CTX_free(mont);
|
---|
1090 | if (powerbuf != NULL) {
|
---|
1091 | OPENSSL_cleanse(powerbuf, powerbufLen);
|
---|
1092 | OPENSSL_free(powerbufFree);
|
---|
1093 | }
|
---|
1094 | BN_CTX_end(ctx);
|
---|
1095 | return (ret);
|
---|
1096 | }
|
---|
1097 |
|
---|
1098 | int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
|
---|
1099 | const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
|
---|
1100 | {
|
---|
1101 | BN_MONT_CTX *mont = NULL;
|
---|
1102 | int b, bits, ret = 0;
|
---|
1103 | int r_is_one;
|
---|
1104 | BN_ULONG w, next_w;
|
---|
1105 | BIGNUM *d, *r, *t;
|
---|
1106 | BIGNUM *swap_tmp;
|
---|
1107 | #define BN_MOD_MUL_WORD(r, w, m) \
|
---|
1108 | (BN_mul_word(r, (w)) && \
|
---|
1109 | (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
|
---|
1110 | (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
|
---|
1111 | /*
|
---|
1112 | * BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is
|
---|
1113 | * probably more overhead than always using BN_mod (which uses BN_copy if
|
---|
1114 | * a similar test returns true).
|
---|
1115 | */
|
---|
1116 | /*
|
---|
1117 | * We can use BN_mod and do not need BN_nnmod because our accumulator is
|
---|
1118 | * never negative (the result of BN_mod does not depend on the sign of
|
---|
1119 | * the modulus).
|
---|
1120 | */
|
---|
1121 | #define BN_TO_MONTGOMERY_WORD(r, w, mont) \
|
---|
1122 | (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
|
---|
1123 |
|
---|
1124 | if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
|
---|
1125 | /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
|
---|
1126 | BNerr(BN_F_BN_MOD_EXP_MONT_WORD, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
|
---|
1127 | return 0;
|
---|
1128 | }
|
---|
1129 |
|
---|
1130 | bn_check_top(p);
|
---|
1131 | bn_check_top(m);
|
---|
1132 |
|
---|
1133 | if (!BN_is_odd(m)) {
|
---|
1134 | BNerr(BN_F_BN_MOD_EXP_MONT_WORD, BN_R_CALLED_WITH_EVEN_MODULUS);
|
---|
1135 | return (0);
|
---|
1136 | }
|
---|
1137 | if (m->top == 1)
|
---|
1138 | a %= m->d[0]; /* make sure that 'a' is reduced */
|
---|
1139 |
|
---|
1140 | bits = BN_num_bits(p);
|
---|
1141 | if (bits == 0) {
|
---|
1142 | /* x**0 mod 1 is still zero. */
|
---|
1143 | if (BN_is_one(m)) {
|
---|
1144 | ret = 1;
|
---|
1145 | BN_zero(rr);
|
---|
1146 | } else {
|
---|
1147 | ret = BN_one(rr);
|
---|
1148 | }
|
---|
1149 | return ret;
|
---|
1150 | }
|
---|
1151 | if (a == 0) {
|
---|
1152 | BN_zero(rr);
|
---|
1153 | ret = 1;
|
---|
1154 | return ret;
|
---|
1155 | }
|
---|
1156 |
|
---|
1157 | BN_CTX_start(ctx);
|
---|
1158 | d = BN_CTX_get(ctx);
|
---|
1159 | r = BN_CTX_get(ctx);
|
---|
1160 | t = BN_CTX_get(ctx);
|
---|
1161 | if (d == NULL || r == NULL || t == NULL)
|
---|
1162 | goto err;
|
---|
1163 |
|
---|
1164 | if (in_mont != NULL)
|
---|
1165 | mont = in_mont;
|
---|
1166 | else {
|
---|
1167 | if ((mont = BN_MONT_CTX_new()) == NULL)
|
---|
1168 | goto err;
|
---|
1169 | if (!BN_MONT_CTX_set(mont, m, ctx))
|
---|
1170 | goto err;
|
---|
1171 | }
|
---|
1172 |
|
---|
1173 | r_is_one = 1; /* except for Montgomery factor */
|
---|
1174 |
|
---|
1175 | /* bits-1 >= 0 */
|
---|
1176 |
|
---|
1177 | /* The result is accumulated in the product r*w. */
|
---|
1178 | w = a; /* bit 'bits-1' of 'p' is always set */
|
---|
1179 | for (b = bits - 2; b >= 0; b--) {
|
---|
1180 | /* First, square r*w. */
|
---|
1181 | next_w = w * w;
|
---|
1182 | if ((next_w / w) != w) { /* overflow */
|
---|
1183 | if (r_is_one) {
|
---|
1184 | if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
|
---|
1185 | goto err;
|
---|
1186 | r_is_one = 0;
|
---|
1187 | } else {
|
---|
1188 | if (!BN_MOD_MUL_WORD(r, w, m))
|
---|
1189 | goto err;
|
---|
1190 | }
|
---|
1191 | next_w = 1;
|
---|
1192 | }
|
---|
1193 | w = next_w;
|
---|
1194 | if (!r_is_one) {
|
---|
1195 | if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
|
---|
1196 | goto err;
|
---|
1197 | }
|
---|
1198 |
|
---|
1199 | /* Second, multiply r*w by 'a' if exponent bit is set. */
|
---|
1200 | if (BN_is_bit_set(p, b)) {
|
---|
1201 | next_w = w * a;
|
---|
1202 | if ((next_w / a) != w) { /* overflow */
|
---|
1203 | if (r_is_one) {
|
---|
1204 | if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
|
---|
1205 | goto err;
|
---|
1206 | r_is_one = 0;
|
---|
1207 | } else {
|
---|
1208 | if (!BN_MOD_MUL_WORD(r, w, m))
|
---|
1209 | goto err;
|
---|
1210 | }
|
---|
1211 | next_w = a;
|
---|
1212 | }
|
---|
1213 | w = next_w;
|
---|
1214 | }
|
---|
1215 | }
|
---|
1216 |
|
---|
1217 | /* Finally, set r:=r*w. */
|
---|
1218 | if (w != 1) {
|
---|
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 | }
|
---|
1228 |
|
---|
1229 | if (r_is_one) { /* can happen only if a == 1 */
|
---|
1230 | if (!BN_one(rr))
|
---|
1231 | goto err;
|
---|
1232 | } else {
|
---|
1233 | if (!BN_from_montgomery(rr, r, mont, ctx))
|
---|
1234 | goto err;
|
---|
1235 | }
|
---|
1236 | ret = 1;
|
---|
1237 | err:
|
---|
1238 | if (in_mont == NULL)
|
---|
1239 | BN_MONT_CTX_free(mont);
|
---|
1240 | BN_CTX_end(ctx);
|
---|
1241 | bn_check_top(rr);
|
---|
1242 | return (ret);
|
---|
1243 | }
|
---|
1244 |
|
---|
1245 | /* The old fallback, simple version :-) */
|
---|
1246 | int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
|
---|
1247 | const BIGNUM *m, BN_CTX *ctx)
|
---|
1248 | {
|
---|
1249 | int i, j, bits, ret = 0, wstart, wend, window, wvalue;
|
---|
1250 | int start = 1;
|
---|
1251 | BIGNUM *d;
|
---|
1252 | /* Table of variables obtained from 'ctx' */
|
---|
1253 | BIGNUM *val[TABLE_SIZE];
|
---|
1254 |
|
---|
1255 | if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
|
---|
1256 | /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
|
---|
1257 | BNerr(BN_F_BN_MOD_EXP_SIMPLE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
|
---|
1258 | return 0;
|
---|
1259 | }
|
---|
1260 |
|
---|
1261 | bits = BN_num_bits(p);
|
---|
1262 | if (bits == 0) {
|
---|
1263 | /* x**0 mod 1 is still zero. */
|
---|
1264 | if (BN_is_one(m)) {
|
---|
1265 | ret = 1;
|
---|
1266 | BN_zero(r);
|
---|
1267 | } else {
|
---|
1268 | ret = BN_one(r);
|
---|
1269 | }
|
---|
1270 | return ret;
|
---|
1271 | }
|
---|
1272 |
|
---|
1273 | BN_CTX_start(ctx);
|
---|
1274 | d = BN_CTX_get(ctx);
|
---|
1275 | val[0] = BN_CTX_get(ctx);
|
---|
1276 | if (!d || !val[0])
|
---|
1277 | goto err;
|
---|
1278 |
|
---|
1279 | if (!BN_nnmod(val[0], a, m, ctx))
|
---|
1280 | goto err; /* 1 */
|
---|
1281 | if (BN_is_zero(val[0])) {
|
---|
1282 | BN_zero(r);
|
---|
1283 | ret = 1;
|
---|
1284 | goto err;
|
---|
1285 | }
|
---|
1286 |
|
---|
1287 | window = BN_window_bits_for_exponent_size(bits);
|
---|
1288 | if (window > 1) {
|
---|
1289 | if (!BN_mod_mul(d, val[0], val[0], m, ctx))
|
---|
1290 | goto err; /* 2 */
|
---|
1291 | j = 1 << (window - 1);
|
---|
1292 | for (i = 1; i < j; i++) {
|
---|
1293 | if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
|
---|
1294 | !BN_mod_mul(val[i], val[i - 1], d, m, ctx))
|
---|
1295 | goto err;
|
---|
1296 | }
|
---|
1297 | }
|
---|
1298 |
|
---|
1299 | start = 1; /* This is used to avoid multiplication etc
|
---|
1300 | * when there is only the value '1' in the
|
---|
1301 | * buffer. */
|
---|
1302 | wvalue = 0; /* The 'value' of the window */
|
---|
1303 | wstart = bits - 1; /* The top bit of the window */
|
---|
1304 | wend = 0; /* The bottom bit of the window */
|
---|
1305 |
|
---|
1306 | if (!BN_one(r))
|
---|
1307 | goto err;
|
---|
1308 |
|
---|
1309 | for (;;) {
|
---|
1310 | if (BN_is_bit_set(p, wstart) == 0) {
|
---|
1311 | if (!start)
|
---|
1312 | if (!BN_mod_mul(r, r, r, m, ctx))
|
---|
1313 | goto err;
|
---|
1314 | if (wstart == 0)
|
---|
1315 | break;
|
---|
1316 | wstart--;
|
---|
1317 | continue;
|
---|
1318 | }
|
---|
1319 | /*
|
---|
1320 | * We now have wstart on a 'set' bit, we now need to work out how bit
|
---|
1321 | * a window to do. To do this we need to scan forward until the last
|
---|
1322 | * set bit before the end of the window
|
---|
1323 | */
|
---|
1324 | j = wstart;
|
---|
1325 | wvalue = 1;
|
---|
1326 | wend = 0;
|
---|
1327 | for (i = 1; i < window; i++) {
|
---|
1328 | if (wstart - i < 0)
|
---|
1329 | break;
|
---|
1330 | if (BN_is_bit_set(p, wstart - i)) {
|
---|
1331 | wvalue <<= (i - wend);
|
---|
1332 | wvalue |= 1;
|
---|
1333 | wend = i;
|
---|
1334 | }
|
---|
1335 | }
|
---|
1336 |
|
---|
1337 | /* wend is the size of the current window */
|
---|
1338 | j = wend + 1;
|
---|
1339 | /* add the 'bytes above' */
|
---|
1340 | if (!start)
|
---|
1341 | for (i = 0; i < j; i++) {
|
---|
1342 | if (!BN_mod_mul(r, r, r, m, ctx))
|
---|
1343 | goto err;
|
---|
1344 | }
|
---|
1345 |
|
---|
1346 | /* wvalue will be an odd number < 2^window */
|
---|
1347 | if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx))
|
---|
1348 | goto err;
|
---|
1349 |
|
---|
1350 | /* move the 'window' down further */
|
---|
1351 | wstart -= wend + 1;
|
---|
1352 | wvalue = 0;
|
---|
1353 | start = 0;
|
---|
1354 | if (wstart < 0)
|
---|
1355 | break;
|
---|
1356 | }
|
---|
1357 | ret = 1;
|
---|
1358 | err:
|
---|
1359 | BN_CTX_end(ctx);
|
---|
1360 | bn_check_top(r);
|
---|
1361 | return (ret);
|
---|
1362 | }
|
---|