1/*
2 * Copyright 1995-2018 The OpenSSL Project Authors. All Rights Reserved.
3 *
4 * Licensed under the Apache License 2.0 (the "License"). You may not use
5 * this file except in compliance with the License. You can obtain a copy
6 * in the file LICENSE in the source distribution or at
7 * https://www.openssl.org/source/license.html
8 */
9
10/*
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
15 */
16
17#include "internal/cryptlib.h"
18#include "bn_local.h"
19
20#define MONT_WORD /* use the faster word-based algorithm */
21
22#ifdef MONT_WORD
23static int bn_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont);
24#endif
25
26int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
27 BN_MONT_CTX *mont, BN_CTX *ctx)
28{
29 int ret = bn_mul_mont_fixed_top(r, a, b, mont, ctx);
30
31 bn_correct_top(r);
32 bn_check_top(r);
33
34 return ret;
35}
36
37int bn_mul_mont_fixed_top(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
38 BN_MONT_CTX *mont, BN_CTX *ctx)
39{
40 BIGNUM *tmp;
41 int ret = 0;
42 int num = mont->N.top;
43
44#if defined(OPENSSL_BN_ASM_MONT) && defined(MONT_WORD)
45 if (num > 1 && a->top == num && b->top == num) {
46 if (bn_wexpand(r, num) == NULL)
47 return 0;
48 if (bn_mul_mont(r->d, a->d, b->d, mont->N.d, mont->n0, num)) {
49 r->neg = a->neg ^ b->neg;
50 r->top = num;
51 r->flags |= BN_FLG_FIXED_TOP;
52 return 1;
53 }
54 }
55#endif
56
57 if ((a->top + b->top) > 2 * num)
58 return 0;
59
60 BN_CTX_start(ctx);
61 tmp = BN_CTX_get(ctx);
62 if (tmp == NULL)
63 goto err;
64
65 bn_check_top(tmp);
66 if (a == b) {
67 if (!bn_sqr_fixed_top(tmp, a, ctx))
68 goto err;
69 } else {
70 if (!bn_mul_fixed_top(tmp, a, b, ctx))
71 goto err;
72 }
73 /* reduce from aRR to aR */
74#ifdef MONT_WORD
75 if (!bn_from_montgomery_word(r, tmp, mont))
76 goto err;
77#else
78 if (!BN_from_montgomery(r, tmp, mont, ctx))
79 goto err;
80#endif
81 ret = 1;
82 err:
83 BN_CTX_end(ctx);
84 return ret;
85}
86
87#ifdef MONT_WORD
88static int bn_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont)
89{
90 BIGNUM *n;
91 BN_ULONG *ap, *np, *rp, n0, v, carry;
92 int nl, max, i;
93 unsigned int rtop;
94
95 n = &(mont->N);
96 nl = n->top;
97 if (nl == 0) {
98 ret->top = 0;
99 return 1;
100 }
101
102 max = (2 * nl); /* carry is stored separately */
103 if (bn_wexpand(r, max) == NULL)
104 return 0;
105
106 r->neg ^= n->neg;
107 np = n->d;
108 rp = r->d;
109
110 /* clear the top words of T */
111 for (rtop = r->top, i = 0; i < max; i++) {
112 v = (BN_ULONG)0 - ((i - rtop) >> (8 * sizeof(rtop) - 1));
113 rp[i] &= v;
114 }
115
116 r->top = max;
117 r->flags |= BN_FLG_FIXED_TOP;
118 n0 = mont->n0[0];
119
120 /*
121 * Add multiples of |n| to |r| until R = 2^(nl * BN_BITS2) divides it. On
122 * input, we had |r| < |n| * R, so now |r| < 2 * |n| * R. Note that |r|
123 * includes |carry| which is stored separately.
124 */
125 for (carry = 0, i = 0; i < nl; i++, rp++) {
126 v = bn_mul_add_words(rp, np, nl, (rp[0] * n0) & BN_MASK2);
127 v = (v + carry + rp[nl]) & BN_MASK2;
128 carry |= (v != rp[nl]);
129 carry &= (v <= rp[nl]);
130 rp[nl] = v;
131 }
132
133 if (bn_wexpand(ret, nl) == NULL)
134 return 0;
135 ret->top = nl;
136 ret->flags |= BN_FLG_FIXED_TOP;
137 ret->neg = r->neg;
138
139 rp = ret->d;
140
141 /*
142 * Shift |nl| words to divide by R. We have |ap| < 2 * |n|. Note that |ap|
143 * includes |carry| which is stored separately.
144 */
145 ap = &(r->d[nl]);
146
147 carry -= bn_sub_words(rp, ap, np, nl);
148 /*
149 * |carry| is -1 if |ap| - |np| underflowed or zero if it did not. Note
150 * |carry| cannot be 1. That would imply the subtraction did not fit in
151 * |nl| words, and we know at most one subtraction is needed.
152 */
153 for (i = 0; i < nl; i++) {
154 rp[i] = (carry & ap[i]) | (~carry & rp[i]);
155 ap[i] = 0;
156 }
157
158 return 1;
159}
160#endif /* MONT_WORD */
161
162int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
163 BN_CTX *ctx)
164{
165 int retn;
166
167 retn = bn_from_mont_fixed_top(ret, a, mont, ctx);
168 bn_correct_top(ret);
169 bn_check_top(ret);
170
171 return retn;
172}
173
174int bn_from_mont_fixed_top(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
175 BN_CTX *ctx)
176{
177 int retn = 0;
178#ifdef MONT_WORD
179 BIGNUM *t;
180
181 BN_CTX_start(ctx);
182 if ((t = BN_CTX_get(ctx)) && BN_copy(t, a)) {
183 retn = bn_from_montgomery_word(ret, t, mont);
184 }
185 BN_CTX_end(ctx);
186#else /* !MONT_WORD */
187 BIGNUM *t1, *t2;
188
189 BN_CTX_start(ctx);
190 t1 = BN_CTX_get(ctx);
191 t2 = BN_CTX_get(ctx);
192 if (t2 == NULL)
193 goto err;
194
195 if (!BN_copy(t1, a))
196 goto err;
197 BN_mask_bits(t1, mont->ri);
198
199 if (!BN_mul(t2, t1, &mont->Ni, ctx))
200 goto err;
201 BN_mask_bits(t2, mont->ri);
202
203 if (!BN_mul(t1, t2, &mont->N, ctx))
204 goto err;
205 if (!BN_add(t2, a, t1))
206 goto err;
207 if (!BN_rshift(ret, t2, mont->ri))
208 goto err;
209
210 if (BN_ucmp(ret, &(mont->N)) >= 0) {
211 if (!BN_usub(ret, ret, &(mont->N)))
212 goto err;
213 }
214 retn = 1;
215 bn_check_top(ret);
216 err:
217 BN_CTX_end(ctx);
218#endif /* MONT_WORD */
219 return retn;
220}
221
222int bn_to_mont_fixed_top(BIGNUM *r, const BIGNUM *a, BN_MONT_CTX *mont,
223 BN_CTX *ctx)
224{
225 return bn_mul_mont_fixed_top(r, a, &(mont->RR), mont, ctx);
226}
227
228BN_MONT_CTX *BN_MONT_CTX_new(void)
229{
230 BN_MONT_CTX *ret;
231
232 if ((ret = OPENSSL_malloc(sizeof(*ret))) == NULL) {
233 BNerr(BN_F_BN_MONT_CTX_NEW, ERR_R_MALLOC_FAILURE);
234 return NULL;
235 }
236
237 BN_MONT_CTX_init(ret);
238 ret->flags = BN_FLG_MALLOCED;
239 return ret;
240}
241
242void BN_MONT_CTX_init(BN_MONT_CTX *ctx)
243{
244 ctx->ri = 0;
245 bn_init(&ctx->RR);
246 bn_init(&ctx->N);
247 bn_init(&ctx->Ni);
248 ctx->n0[0] = ctx->n0[1] = 0;
249 ctx->flags = 0;
250}
251
252void BN_MONT_CTX_free(BN_MONT_CTX *mont)
253{
254 if (mont == NULL)
255 return;
256 BN_clear_free(&mont->RR);
257 BN_clear_free(&mont->N);
258 BN_clear_free(&mont->Ni);
259 if (mont->flags & BN_FLG_MALLOCED)
260 OPENSSL_free(mont);
261}
262
263int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)
264{
265 int i, ret = 0;
266 BIGNUM *Ri, *R;
267
268 if (BN_is_zero(mod))
269 return 0;
270
271 BN_CTX_start(ctx);
272 if ((Ri = BN_CTX_get(ctx)) == NULL)
273 goto err;
274 R = &(mont->RR); /* grab RR as a temp */
275 if (!BN_copy(&(mont->N), mod))
276 goto err; /* Set N */
277 if (BN_get_flags(mod, BN_FLG_CONSTTIME) != 0)
278 BN_set_flags(&(mont->N), BN_FLG_CONSTTIME);
279 mont->N.neg = 0;
280
281#ifdef MONT_WORD
282 {
283 BIGNUM tmod;
284 BN_ULONG buf[2];
285
286 bn_init(&tmod);
287 tmod.d = buf;
288 tmod.dmax = 2;
289 tmod.neg = 0;
290
291 if (BN_get_flags(mod, BN_FLG_CONSTTIME) != 0)
292 BN_set_flags(&tmod, BN_FLG_CONSTTIME);
293
294 mont->ri = (BN_num_bits(mod) + (BN_BITS2 - 1)) / BN_BITS2 * BN_BITS2;
295
296# if defined(OPENSSL_BN_ASM_MONT) && (BN_BITS2<=32)
297 /*
298 * Only certain BN_BITS2<=32 platforms actually make use of n0[1],
299 * and we could use the #else case (with a shorter R value) for the
300 * others. However, currently only the assembler files do know which
301 * is which.
302 */
303
304 BN_zero(R);
305 if (!(BN_set_bit(R, 2 * BN_BITS2)))
306 goto err;
307
308 tmod.top = 0;
309 if ((buf[0] = mod->d[0]))
310 tmod.top = 1;
311 if ((buf[1] = mod->top > 1 ? mod->d[1] : 0))
312 tmod.top = 2;
313
314 if (BN_is_one(&tmod))
315 BN_zero(Ri);
316 else if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL)
317 goto err;
318 if (!BN_lshift(Ri, Ri, 2 * BN_BITS2))
319 goto err; /* R*Ri */
320 if (!BN_is_zero(Ri)) {
321 if (!BN_sub_word(Ri, 1))
322 goto err;
323 } else { /* if N mod word size == 1 */
324
325 if (bn_expand(Ri, (int)sizeof(BN_ULONG) * 2) == NULL)
326 goto err;
327 /* Ri-- (mod double word size) */
328 Ri->neg = 0;
329 Ri->d[0] = BN_MASK2;
330 Ri->d[1] = BN_MASK2;
331 Ri->top = 2;
332 }
333 if (!BN_div(Ri, NULL, Ri, &tmod, ctx))
334 goto err;
335 /*
336 * Ni = (R*Ri-1)/N, keep only couple of least significant words:
337 */
338 mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
339 mont->n0[1] = (Ri->top > 1) ? Ri->d[1] : 0;
340# else
341 BN_zero(R);
342 if (!(BN_set_bit(R, BN_BITS2)))
343 goto err; /* R */
344
345 buf[0] = mod->d[0]; /* tmod = N mod word size */
346 buf[1] = 0;
347 tmod.top = buf[0] != 0 ? 1 : 0;
348 /* Ri = R^-1 mod N */
349 if (BN_is_one(&tmod))
350 BN_zero(Ri);
351 else if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL)
352 goto err;
353 if (!BN_lshift(Ri, Ri, BN_BITS2))
354 goto err; /* R*Ri */
355 if (!BN_is_zero(Ri)) {
356 if (!BN_sub_word(Ri, 1))
357 goto err;
358 } else { /* if N mod word size == 1 */
359
360 if (!BN_set_word(Ri, BN_MASK2))
361 goto err; /* Ri-- (mod word size) */
362 }
363 if (!BN_div(Ri, NULL, Ri, &tmod, ctx))
364 goto err;
365 /*
366 * Ni = (R*Ri-1)/N, keep only least significant word:
367 */
368 mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
369 mont->n0[1] = 0;
370# endif
371 }
372#else /* !MONT_WORD */
373 { /* bignum version */
374 mont->ri = BN_num_bits(&mont->N);
375 BN_zero(R);
376 if (!BN_set_bit(R, mont->ri))
377 goto err; /* R = 2^ri */
378 /* Ri = R^-1 mod N */
379 if ((BN_mod_inverse(Ri, R, &mont->N, ctx)) == NULL)
380 goto err;
381 if (!BN_lshift(Ri, Ri, mont->ri))
382 goto err; /* R*Ri */
383 if (!BN_sub_word(Ri, 1))
384 goto err;
385 /*
386 * Ni = (R*Ri-1) / N
387 */
388 if (!BN_div(&(mont->Ni), NULL, Ri, &mont->N, ctx))
389 goto err;
390 }
391#endif
392
393 /* setup RR for conversions */
394 BN_zero(&(mont->RR));
395 if (!BN_set_bit(&(mont->RR), mont->ri * 2))
396 goto err;
397 if (!BN_mod(&(mont->RR), &(mont->RR), &(mont->N), ctx))
398 goto err;
399
400 for (i = mont->RR.top, ret = mont->N.top; i < ret; i++)
401 mont->RR.d[i] = 0;
402 mont->RR.top = ret;
403 mont->RR.flags |= BN_FLG_FIXED_TOP;
404
405 ret = 1;
406 err:
407 BN_CTX_end(ctx);
408 return ret;
409}
410
411BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from)
412{
413 if (to == from)
414 return to;
415
416 if (!BN_copy(&(to->RR), &(from->RR)))
417 return NULL;
418 if (!BN_copy(&(to->N), &(from->N)))
419 return NULL;
420 if (!BN_copy(&(to->Ni), &(from->Ni)))
421 return NULL;
422 to->ri = from->ri;
423 to->n0[0] = from->n0[0];
424 to->n0[1] = from->n0[1];
425 return to;
426}
427
428BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, CRYPTO_RWLOCK *lock,
429 const BIGNUM *mod, BN_CTX *ctx)
430{
431 BN_MONT_CTX *ret;
432
433 CRYPTO_THREAD_read_lock(lock);
434 ret = *pmont;
435 CRYPTO_THREAD_unlock(lock);
436 if (ret)
437 return ret;
438
439 /*
440 * We don't want to serialise globally while doing our lazy-init math in
441 * BN_MONT_CTX_set. That punishes threads that are doing independent
442 * things. Instead, punish the case where more than one thread tries to
443 * lazy-init the same 'pmont', by having each do the lazy-init math work
444 * independently and only use the one from the thread that wins the race
445 * (the losers throw away the work they've done).
446 */
447 ret = BN_MONT_CTX_new();
448 if (ret == NULL)
449 return NULL;
450 if (!BN_MONT_CTX_set(ret, mod, ctx)) {
451 BN_MONT_CTX_free(ret);
452 return NULL;
453 }
454
455 /* The locked compare-and-set, after the local work is done. */
456 CRYPTO_THREAD_write_lock(lock);
457 if (*pmont) {
458 BN_MONT_CTX_free(ret);
459 ret = *pmont;
460 } else
461 *pmont = ret;
462 CRYPTO_THREAD_unlock(lock);
463 return ret;
464}
465