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Commit | Line | Data |
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4f22f405 | 1 | /* |
edea42c6 | 2 | * Copyright 1995-2017 The OpenSSL Project Authors. All Rights Reserved. |
675f605d | 3 | * |
4f22f405 RS |
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 | |
675f605d | 8 | */ |
d02b48c6 | 9 | |
1b3b0a54 | 10 | /* |
b99b1107 BM |
11 | * Details about Montgomery multiplication algorithms can be found at |
12 | * http://security.ece.orst.edu/publications.html, e.g. | |
13 | * http://security.ece.orst.edu/koc/papers/j37acmon.pdf and | |
14 | * sections 3.8 and 4.2 in http://security.ece.orst.edu/koc/papers/r01rsasw.pdf | |
1b3b0a54 RE |
15 | */ |
16 | ||
b39fc560 | 17 | #include "internal/cryptlib.h" |
d02b48c6 RE |
18 | #include "bn_lcl.h" |
19 | ||
0f113f3e | 20 | #define MONT_WORD /* use the faster word-based algorithm */ |
6535eb17 | 21 | |
9b4eab50 AP |
22 | #ifdef MONT_WORD |
23 | static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont); | |
24 | #endif | |
25 | ||
020fc820 | 26 | int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, |
0f113f3e MC |
27 | BN_MONT_CTX *mont, BN_CTX *ctx) |
28 | { | |
29 | BIGNUM *tmp; | |
30 | int ret = 0; | |
9b4eab50 | 31 | #if defined(OPENSSL_BN_ASM_MONT) && defined(MONT_WORD) |
0f113f3e MC |
32 | int num = mont->N.top; |
33 | ||
34 | if (num > 1 && a->top == num && b->top == num) { | |
35 | if (bn_wexpand(r, num) == NULL) | |
36 | return (0); | |
37 | if (bn_mul_mont(r->d, a->d, b->d, mont->N.d, mont->n0, num)) { | |
38 | r->neg = a->neg ^ b->neg; | |
39 | r->top = num; | |
40 | bn_correct_top(r); | |
41 | return (1); | |
42 | } | |
43 | } | |
e7382805 | 44 | #endif |
dfeab068 | 45 | |
0f113f3e MC |
46 | BN_CTX_start(ctx); |
47 | tmp = BN_CTX_get(ctx); | |
48 | if (tmp == NULL) | |
49 | goto err; | |
50 | ||
51 | bn_check_top(tmp); | |
52 | if (a == b) { | |
53 | if (!BN_sqr(tmp, a, ctx)) | |
54 | goto err; | |
55 | } else { | |
56 | if (!BN_mul(tmp, a, b, ctx)) | |
57 | goto err; | |
58 | } | |
59 | /* reduce from aRR to aR */ | |
9b4eab50 | 60 | #ifdef MONT_WORD |
0f113f3e MC |
61 | if (!BN_from_montgomery_word(r, tmp, mont)) |
62 | goto err; | |
9b4eab50 | 63 | #else |
0f113f3e MC |
64 | if (!BN_from_montgomery(r, tmp, mont, ctx)) |
65 | goto err; | |
9b4eab50 | 66 | #endif |
0f113f3e MC |
67 | bn_check_top(r); |
68 | ret = 1; | |
69 | err: | |
70 | BN_CTX_end(ctx); | |
71 | return (ret); | |
72 | } | |
d02b48c6 | 73 | |
6535eb17 | 74 | #ifdef MONT_WORD |
9b4eab50 | 75 | static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont) |
0f113f3e MC |
76 | { |
77 | BIGNUM *n; | |
78 | BN_ULONG *ap, *np, *rp, n0, v, carry; | |
79 | int nl, max, i; | |
80 | ||
81 | n = &(mont->N); | |
82 | nl = n->top; | |
83 | if (nl == 0) { | |
84 | ret->top = 0; | |
85 | return (1); | |
86 | } | |
87 | ||
88 | max = (2 * nl); /* carry is stored separately */ | |
89 | if (bn_wexpand(r, max) == NULL) | |
90 | return (0); | |
91 | ||
92 | r->neg ^= n->neg; | |
93 | np = n->d; | |
94 | rp = r->d; | |
95 | ||
96 | /* clear the top words of T */ | |
9f040d6d RS |
97 | i = max - r->top; |
98 | if (i) | |
99 | memset(&rp[r->top], 0, sizeof(*rp) * i); | |
0f113f3e MC |
100 | |
101 | r->top = max; | |
102 | n0 = mont->n0[0]; | |
103 | ||
104 | for (carry = 0, i = 0; i < nl; i++, rp++) { | |
105 | v = bn_mul_add_words(rp, np, nl, (rp[0] * n0) & BN_MASK2); | |
106 | v = (v + carry + rp[nl]) & BN_MASK2; | |
107 | carry |= (v != rp[nl]); | |
108 | carry &= (v <= rp[nl]); | |
109 | rp[nl] = v; | |
110 | } | |
111 | ||
112 | if (bn_wexpand(ret, nl) == NULL) | |
113 | return (0); | |
114 | ret->top = nl; | |
115 | ret->neg = r->neg; | |
116 | ||
117 | rp = ret->d; | |
118 | ap = &(r->d[nl]); | |
119 | ||
120 | # define BRANCH_FREE 1 | |
121 | # if BRANCH_FREE | |
122 | { | |
123 | BN_ULONG *nrp; | |
124 | size_t m; | |
125 | ||
126 | v = bn_sub_words(rp, ap, np, nl) - carry; | |
127 | /* | |
128 | * if subtraction result is real, then trick unconditional memcpy | |
129 | * below to perform in-place "refresh" instead of actual copy. | |
130 | */ | |
131 | m = (0 - (size_t)v); | |
132 | nrp = | |
133 | (BN_ULONG *)(((PTR_SIZE_INT) rp & ~m) | ((PTR_SIZE_INT) ap & m)); | |
134 | ||
135 | for (i = 0, nl -= 4; i < nl; i += 4) { | |
136 | BN_ULONG t1, t2, t3, t4; | |
137 | ||
138 | t1 = nrp[i + 0]; | |
139 | t2 = nrp[i + 1]; | |
140 | t3 = nrp[i + 2]; | |
141 | ap[i + 0] = 0; | |
142 | t4 = nrp[i + 3]; | |
143 | ap[i + 1] = 0; | |
144 | rp[i + 0] = t1; | |
145 | ap[i + 2] = 0; | |
146 | rp[i + 1] = t2; | |
147 | ap[i + 3] = 0; | |
148 | rp[i + 2] = t3; | |
149 | rp[i + 3] = t4; | |
150 | } | |
151 | for (nl += 4; i < nl; i++) | |
152 | rp[i] = nrp[i], ap[i] = 0; | |
153 | } | |
154 | # else | |
155 | if (bn_sub_words(rp, ap, np, nl) - carry) | |
156 | memcpy(rp, ap, nl * sizeof(BN_ULONG)); | |
157 | # endif | |
158 | bn_correct_top(r); | |
159 | bn_correct_top(ret); | |
160 | bn_check_top(ret); | |
161 | ||
162 | return (1); | |
163 | } | |
164 | #endif /* MONT_WORD */ | |
9b4eab50 AP |
165 | |
166 | int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont, | |
0f113f3e MC |
167 | BN_CTX *ctx) |
168 | { | |
169 | int retn = 0; | |
9b4eab50 | 170 | #ifdef MONT_WORD |
0f113f3e MC |
171 | BIGNUM *t; |
172 | ||
173 | BN_CTX_start(ctx); | |
174 | if ((t = BN_CTX_get(ctx)) && BN_copy(t, a)) | |
175 | retn = BN_from_montgomery_word(ret, t, mont); | |
176 | BN_CTX_end(ctx); | |
177 | #else /* !MONT_WORD */ | |
178 | BIGNUM *t1, *t2; | |
179 | ||
180 | BN_CTX_start(ctx); | |
181 | t1 = BN_CTX_get(ctx); | |
182 | t2 = BN_CTX_get(ctx); | |
edea42c6 | 183 | if (t2 == NULL) |
0f113f3e MC |
184 | goto err; |
185 | ||
186 | if (!BN_copy(t1, a)) | |
187 | goto err; | |
188 | BN_mask_bits(t1, mont->ri); | |
189 | ||
190 | if (!BN_mul(t2, t1, &mont->Ni, ctx)) | |
191 | goto err; | |
192 | BN_mask_bits(t2, mont->ri); | |
193 | ||
194 | if (!BN_mul(t1, t2, &mont->N, ctx)) | |
195 | goto err; | |
196 | if (!BN_add(t2, a, t1)) | |
197 | goto err; | |
198 | if (!BN_rshift(ret, t2, mont->ri)) | |
199 | goto err; | |
200 | ||
201 | if (BN_ucmp(ret, &(mont->N)) >= 0) { | |
202 | if (!BN_usub(ret, ret, &(mont->N))) | |
203 | goto err; | |
204 | } | |
205 | retn = 1; | |
206 | bn_check_top(ret); | |
e93f9a32 | 207 | err: |
0f113f3e MC |
208 | BN_CTX_end(ctx); |
209 | #endif /* MONT_WORD */ | |
210 | return (retn); | |
211 | } | |
d02b48c6 | 212 | |
6b691a5c | 213 | BN_MONT_CTX *BN_MONT_CTX_new(void) |
0f113f3e MC |
214 | { |
215 | BN_MONT_CTX *ret; | |
d02b48c6 | 216 | |
b4faea50 | 217 | if ((ret = OPENSSL_malloc(sizeof(*ret))) == NULL) |
0f113f3e | 218 | return (NULL); |
dfeab068 | 219 | |
0f113f3e MC |
220 | BN_MONT_CTX_init(ret); |
221 | ret->flags = BN_FLG_MALLOCED; | |
222 | return (ret); | |
223 | } | |
d02b48c6 | 224 | |
6b691a5c | 225 | void BN_MONT_CTX_init(BN_MONT_CTX *ctx) |
0f113f3e MC |
226 | { |
227 | ctx->ri = 0; | |
d59c7c81 RS |
228 | bn_init(&(ctx->RR)); |
229 | bn_init(&(ctx->N)); | |
230 | bn_init(&(ctx->Ni)); | |
0f113f3e MC |
231 | ctx->n0[0] = ctx->n0[1] = 0; |
232 | ctx->flags = 0; | |
233 | } | |
dfeab068 | 234 | |
6b691a5c | 235 | void BN_MONT_CTX_free(BN_MONT_CTX *mont) |
0f113f3e MC |
236 | { |
237 | if (mont == NULL) | |
238 | return; | |
e03ddfae | 239 | |
1a586b39 LV |
240 | BN_clear_free(&(mont->RR)); |
241 | BN_clear_free(&(mont->N)); | |
242 | BN_clear_free(&(mont->Ni)); | |
0f113f3e MC |
243 | if (mont->flags & BN_FLG_MALLOCED) |
244 | OPENSSL_free(mont); | |
245 | } | |
d02b48c6 | 246 | |
84c15db5 | 247 | int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx) |
0f113f3e MC |
248 | { |
249 | int ret = 0; | |
250 | BIGNUM *Ri, *R; | |
251 | ||
6a009812 MC |
252 | if (BN_is_zero(mod)) |
253 | return 0; | |
254 | ||
0f113f3e MC |
255 | BN_CTX_start(ctx); |
256 | if ((Ri = BN_CTX_get(ctx)) == NULL) | |
257 | goto err; | |
258 | R = &(mont->RR); /* grab RR as a temp */ | |
259 | if (!BN_copy(&(mont->N), mod)) | |
260 | goto err; /* Set N */ | |
261 | mont->N.neg = 0; | |
dfeab068 | 262 | |
6535eb17 | 263 | #ifdef MONT_WORD |
0f113f3e MC |
264 | { |
265 | BIGNUM tmod; | |
266 | BN_ULONG buf[2]; | |
267 | ||
d59c7c81 | 268 | bn_init(&tmod); |
0f113f3e MC |
269 | tmod.d = buf; |
270 | tmod.dmax = 2; | |
271 | tmod.neg = 0; | |
272 | ||
273 | mont->ri = (BN_num_bits(mod) + (BN_BITS2 - 1)) / BN_BITS2 * BN_BITS2; | |
274 | ||
275 | # if defined(OPENSSL_BN_ASM_MONT) && (BN_BITS2<=32) | |
276 | /* | |
277 | * Only certain BN_BITS2<=32 platforms actually make use of n0[1], | |
278 | * and we could use the #else case (with a shorter R value) for the | |
279 | * others. However, currently only the assembler files do know which | |
280 | * is which. | |
281 | */ | |
282 | ||
283 | BN_zero(R); | |
284 | if (!(BN_set_bit(R, 2 * BN_BITS2))) | |
285 | goto err; | |
286 | ||
287 | tmod.top = 0; | |
288 | if ((buf[0] = mod->d[0])) | |
289 | tmod.top = 1; | |
290 | if ((buf[1] = mod->top > 1 ? mod->d[1] : 0)) | |
291 | tmod.top = 2; | |
292 | ||
293 | if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL) | |
294 | goto err; | |
295 | if (!BN_lshift(Ri, Ri, 2 * BN_BITS2)) | |
296 | goto err; /* R*Ri */ | |
297 | if (!BN_is_zero(Ri)) { | |
298 | if (!BN_sub_word(Ri, 1)) | |
299 | goto err; | |
300 | } else { /* if N mod word size == 1 */ | |
301 | ||
302 | if (bn_expand(Ri, (int)sizeof(BN_ULONG) * 2) == NULL) | |
303 | goto err; | |
304 | /* Ri-- (mod double word size) */ | |
305 | Ri->neg = 0; | |
306 | Ri->d[0] = BN_MASK2; | |
307 | Ri->d[1] = BN_MASK2; | |
308 | Ri->top = 2; | |
309 | } | |
310 | if (!BN_div(Ri, NULL, Ri, &tmod, ctx)) | |
311 | goto err; | |
312 | /* | |
313 | * Ni = (R*Ri-1)/N, keep only couple of least significant words: | |
314 | */ | |
315 | mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0; | |
316 | mont->n0[1] = (Ri->top > 1) ? Ri->d[1] : 0; | |
317 | # else | |
318 | BN_zero(R); | |
319 | if (!(BN_set_bit(R, BN_BITS2))) | |
320 | goto err; /* R */ | |
321 | ||
322 | buf[0] = mod->d[0]; /* tmod = N mod word size */ | |
323 | buf[1] = 0; | |
324 | tmod.top = buf[0] != 0 ? 1 : 0; | |
325 | /* Ri = R^-1 mod N */ | |
326 | if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL) | |
327 | goto err; | |
328 | if (!BN_lshift(Ri, Ri, BN_BITS2)) | |
329 | goto err; /* R*Ri */ | |
330 | if (!BN_is_zero(Ri)) { | |
331 | if (!BN_sub_word(Ri, 1)) | |
332 | goto err; | |
333 | } else { /* if N mod word size == 1 */ | |
334 | ||
335 | if (!BN_set_word(Ri, BN_MASK2)) | |
336 | goto err; /* Ri-- (mod word size) */ | |
337 | } | |
338 | if (!BN_div(Ri, NULL, Ri, &tmod, ctx)) | |
339 | goto err; | |
340 | /* | |
341 | * Ni = (R*Ri-1)/N, keep only least significant word: | |
342 | */ | |
343 | mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0; | |
344 | mont->n0[1] = 0; | |
345 | # endif | |
346 | } | |
347 | #else /* !MONT_WORD */ | |
348 | { /* bignum version */ | |
349 | mont->ri = BN_num_bits(&mont->N); | |
350 | BN_zero(R); | |
351 | if (!BN_set_bit(R, mont->ri)) | |
352 | goto err; /* R = 2^ri */ | |
353 | /* Ri = R^-1 mod N */ | |
354 | if ((BN_mod_inverse(Ri, R, &mont->N, ctx)) == NULL) | |
355 | goto err; | |
356 | if (!BN_lshift(Ri, Ri, mont->ri)) | |
357 | goto err; /* R*Ri */ | |
358 | if (!BN_sub_word(Ri, 1)) | |
359 | goto err; | |
360 | /* | |
361 | * Ni = (R*Ri-1) / N | |
362 | */ | |
363 | if (!BN_div(&(mont->Ni), NULL, Ri, &mont->N, ctx)) | |
364 | goto err; | |
365 | } | |
d02b48c6 RE |
366 | #endif |
367 | ||
0f113f3e MC |
368 | /* setup RR for conversions */ |
369 | BN_zero(&(mont->RR)); | |
370 | if (!BN_set_bit(&(mont->RR), mont->ri * 2)) | |
371 | goto err; | |
372 | if (!BN_mod(&(mont->RR), &(mont->RR), &(mont->N), ctx)) | |
373 | goto err; | |
d02b48c6 | 374 | |
0f113f3e MC |
375 | ret = 1; |
376 | err: | |
377 | BN_CTX_end(ctx); | |
378 | return ret; | |
379 | } | |
d02b48c6 | 380 | |
6b691a5c | 381 | BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from) |
0f113f3e MC |
382 | { |
383 | if (to == from) | |
384 | return (to); | |
385 | ||
386 | if (!BN_copy(&(to->RR), &(from->RR))) | |
387 | return NULL; | |
388 | if (!BN_copy(&(to->N), &(from->N))) | |
389 | return NULL; | |
390 | if (!BN_copy(&(to->Ni), &(from->Ni))) | |
391 | return NULL; | |
392 | to->ri = from->ri; | |
393 | to->n0[0] = from->n0[0]; | |
394 | to->n0[1] = from->n0[1]; | |
395 | return (to); | |
396 | } | |
dfeab068 | 397 | |
d188a536 | 398 | BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, CRYPTO_RWLOCK *lock, |
0f113f3e MC |
399 | const BIGNUM *mod, BN_CTX *ctx) |
400 | { | |
401 | BN_MONT_CTX *ret; | |
402 | ||
d188a536 | 403 | CRYPTO_THREAD_read_lock(lock); |
0f113f3e | 404 | ret = *pmont; |
d188a536 | 405 | CRYPTO_THREAD_unlock(lock); |
0f113f3e MC |
406 | if (ret) |
407 | return ret; | |
408 | ||
409 | /* | |
410 | * We don't want to serialise globally while doing our lazy-init math in | |
411 | * BN_MONT_CTX_set. That punishes threads that are doing independent | |
412 | * things. Instead, punish the case where more than one thread tries to | |
413 | * lazy-init the same 'pmont', by having each do the lazy-init math work | |
414 | * independently and only use the one from the thread that wins the race | |
415 | * (the losers throw away the work they've done). | |
416 | */ | |
417 | ret = BN_MONT_CTX_new(); | |
90945fa3 | 418 | if (ret == NULL) |
0f113f3e MC |
419 | return NULL; |
420 | if (!BN_MONT_CTX_set(ret, mod, ctx)) { | |
421 | BN_MONT_CTX_free(ret); | |
422 | return NULL; | |
423 | } | |
424 | ||
425 | /* The locked compare-and-set, after the local work is done. */ | |
d188a536 | 426 | CRYPTO_THREAD_write_lock(lock); |
0f113f3e MC |
427 | if (*pmont) { |
428 | BN_MONT_CTX_free(ret); | |
429 | ret = *pmont; | |
430 | } else | |
431 | *pmont = ret; | |
d188a536 | 432 | CRYPTO_THREAD_unlock(lock); |
0f113f3e MC |
433 | return ret; |
434 | } |