1/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
2 * All rights reserved.
3 *
4 * This package is an SSL implementation written
5 * by Eric Young (eay@cryptsoft.com).
6 * The implementation was written so as to conform with Netscapes SSL.
7 *
8 * This library is free for commercial and non-commercial use as long as
9 * the following conditions are aheared to. The following conditions
10 * apply to all code found in this distribution, be it the RC4, RSA,
11 * lhash, DES, etc., code; not just the SSL code. The SSL documentation
12 * included with this distribution is covered by the same copyright terms
13 * except that the holder is Tim Hudson (tjh@cryptsoft.com).
14 *
15 * Copyright remains Eric Young's, and as such any Copyright notices in
16 * the code are not to be removed.
17 * If this package is used in a product, Eric Young should be given attribution
18 * as the author of the parts of the library used.
19 * This can be in the form of a textual message at program startup or
20 * in documentation (online or textual) provided with the package.
21 *
22 * Redistribution and use in source and binary forms, with or without
23 * modification, are permitted provided that the following conditions
24 * are met:
25 * 1. Redistributions of source code must retain the copyright
26 * notice, this list of conditions and the following disclaimer.
27 * 2. Redistributions in binary form must reproduce the above copyright
28 * notice, this list of conditions and the following disclaimer in the
29 * documentation and/or other materials provided with the distribution.
30 * 3. All advertising materials mentioning features or use of this software
31 * must display the following acknowledgement:
32 * "This product includes cryptographic software written by
33 * Eric Young (eay@cryptsoft.com)"
34 * The word 'cryptographic' can be left out if the rouines from the library
35 * being used are not cryptographic related :-).
36 * 4. If you include any Windows specific code (or a derivative thereof) from
37 * the apps directory (application code) you must include an acknowledgement:
38 * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
39 *
40 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
41 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
42 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
43 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
44 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
45 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
46 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
47 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
48 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
49 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
50 * SUCH DAMAGE.
51 *
52 * The licence and distribution terms for any publically available version or
53 * derivative of this code cannot be changed. i.e. this code cannot simply be
54 * copied and put under another distribution licence
55 * [including the GNU Public Licence.] */
56
57#include <openssl/bn.h>
58
59#include <assert.h>
60#include <limits.h>
61
62#include <openssl/err.h>
63
64#include "internal.h"
65
66
67#if !defined(BN_CAN_DIVIDE_ULLONG) && !defined(BN_CAN_USE_INLINE_ASM)
68// bn_div_words divides a double-width |h|,|l| by |d| and returns the result,
69// which must fit in a |BN_ULONG|.
70static BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d) {
71 BN_ULONG dh, dl, q, ret = 0, th, tl, t;
72 int i, count = 2;
73
74 if (d == 0) {
75 return BN_MASK2;
76 }
77
78 i = BN_num_bits_word(d);
79 assert((i == BN_BITS2) || (h <= (BN_ULONG)1 << i));
80
81 i = BN_BITS2 - i;
82 if (h >= d) {
83 h -= d;
84 }
85
86 if (i) {
87 d <<= i;
88 h = (h << i) | (l >> (BN_BITS2 - i));
89 l <<= i;
90 }
91 dh = (d & BN_MASK2h) >> BN_BITS4;
92 dl = (d & BN_MASK2l);
93 for (;;) {
94 if ((h >> BN_BITS4) == dh) {
95 q = BN_MASK2l;
96 } else {
97 q = h / dh;
98 }
99
100 th = q * dh;
101 tl = dl * q;
102 for (;;) {
103 t = h - th;
104 if ((t & BN_MASK2h) ||
105 ((tl) <= ((t << BN_BITS4) | ((l & BN_MASK2h) >> BN_BITS4)))) {
106 break;
107 }
108 q--;
109 th -= dh;
110 tl -= dl;
111 }
112 t = (tl >> BN_BITS4);
113 tl = (tl << BN_BITS4) & BN_MASK2h;
114 th += t;
115
116 if (l < tl) {
117 th++;
118 }
119 l -= tl;
120 if (h < th) {
121 h += d;
122 q--;
123 }
124 h -= th;
125
126 if (--count == 0) {
127 break;
128 }
129
130 ret = q << BN_BITS4;
131 h = (h << BN_BITS4) | (l >> BN_BITS4);
132 l = (l & BN_MASK2l) << BN_BITS4;
133 }
134
135 ret |= q;
136 return ret;
137}
138#endif // !defined(BN_CAN_DIVIDE_ULLONG) && !defined(BN_CAN_USE_INLINE_ASM)
139
140static inline void bn_div_rem_words(BN_ULONG *quotient_out, BN_ULONG *rem_out,
141 BN_ULONG n0, BN_ULONG n1, BN_ULONG d0) {
142 // GCC and Clang generate function calls to |__udivdi3| and |__umoddi3| when
143 // the |BN_ULLONG|-based C code is used.
144 //
145 // GCC bugs:
146 // * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=14224
147 // * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=43721
148 // * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=54183
149 // * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=58897
150 // * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=65668
151 //
152 // Clang bugs:
153 // * https://llvm.org/bugs/show_bug.cgi?id=6397
154 // * https://llvm.org/bugs/show_bug.cgi?id=12418
155 //
156 // These issues aren't specific to x86 and x86_64, so it might be worthwhile
157 // to add more assembly language implementations.
158#if defined(BN_CAN_USE_INLINE_ASM) && defined(OPENSSL_X86)
159 __asm__ volatile("divl %4"
160 : "=a"(*quotient_out), "=d"(*rem_out)
161 : "a"(n1), "d"(n0), "rm"(d0)
162 : "cc");
163#elif defined(BN_CAN_USE_INLINE_ASM) && defined(OPENSSL_X86_64)
164 __asm__ volatile("divq %4"
165 : "=a"(*quotient_out), "=d"(*rem_out)
166 : "a"(n1), "d"(n0), "rm"(d0)
167 : "cc");
168#else
169#if defined(BN_CAN_DIVIDE_ULLONG)
170 BN_ULLONG n = (((BN_ULLONG)n0) << BN_BITS2) | n1;
171 *quotient_out = (BN_ULONG)(n / d0);
172#else
173 *quotient_out = bn_div_words(n0, n1, d0);
174#endif
175 *rem_out = n1 - (*quotient_out * d0);
176#endif
177}
178
179// BN_div computes "quotient := numerator / divisor", rounding towards zero,
180// and sets up |rem| such that "quotient * divisor + rem = numerator" holds.
181//
182// Thus:
183//
184// quotient->neg == numerator->neg ^ divisor->neg
185// (unless the result is zero)
186// rem->neg == numerator->neg
187// (unless the remainder is zero)
188//
189// If |quotient| or |rem| is NULL, the respective value is not returned.
190//
191// This was specifically designed to contain fewer branches that may leak
192// sensitive information; see "New Branch Prediction Vulnerabilities in OpenSSL
193// and Necessary Software Countermeasures" by Onur Acıçmez, Shay Gueron, and
194// Jean-Pierre Seifert.
195int BN_div(BIGNUM *quotient, BIGNUM *rem, const BIGNUM *numerator,
196 const BIGNUM *divisor, BN_CTX *ctx) {
197 int norm_shift, loop;
198 BIGNUM wnum;
199 BN_ULONG *resp, *wnump;
200 BN_ULONG d0, d1;
201 int num_n, div_n;
202
203 // This function relies on the historical minimal-width |BIGNUM| invariant.
204 // It is already not constant-time (constant-time reductions should use
205 // Montgomery logic), so we shrink all inputs and intermediate values to
206 // retain the previous behavior.
207
208 // Invalid zero-padding would have particularly bad consequences.
209 int numerator_width = bn_minimal_width(numerator);
210 int divisor_width = bn_minimal_width(divisor);
211 if ((numerator_width > 0 && numerator->d[numerator_width - 1] == 0) ||
212 (divisor_width > 0 && divisor->d[divisor_width - 1] == 0)) {
213 OPENSSL_PUT_ERROR(BN, BN_R_NOT_INITIALIZED);
214 return 0;
215 }
216
217 if (BN_is_zero(divisor)) {
218 OPENSSL_PUT_ERROR(BN, BN_R_DIV_BY_ZERO);
219 return 0;
220 }
221
222 BN_CTX_start(ctx);
223 BIGNUM *tmp = BN_CTX_get(ctx);
224 BIGNUM *snum = BN_CTX_get(ctx);
225 BIGNUM *sdiv = BN_CTX_get(ctx);
226 BIGNUM *res = NULL;
227 if (quotient == NULL) {
228 res = BN_CTX_get(ctx);
229 } else {
230 res = quotient;
231 }
232 if (sdiv == NULL || res == NULL) {
233 goto err;
234 }
235
236 // First we normalise the numbers
237 norm_shift = BN_BITS2 - (BN_num_bits(divisor) % BN_BITS2);
238 if (!BN_lshift(sdiv, divisor, norm_shift)) {
239 goto err;
240 }
241 bn_set_minimal_width(sdiv);
242 sdiv->neg = 0;
243 norm_shift += BN_BITS2;
244 if (!BN_lshift(snum, numerator, norm_shift)) {
245 goto err;
246 }
247 bn_set_minimal_width(snum);
248 snum->neg = 0;
249
250 // Since we don't want to have special-case logic for the case where snum is
251 // larger than sdiv, we pad snum with enough zeroes without changing its
252 // value.
253 if (snum->width <= sdiv->width + 1) {
254 if (!bn_wexpand(snum, sdiv->width + 2)) {
255 goto err;
256 }
257 for (int i = snum->width; i < sdiv->width + 2; i++) {
258 snum->d[i] = 0;
259 }
260 snum->width = sdiv->width + 2;
261 } else {
262 if (!bn_wexpand(snum, snum->width + 1)) {
263 goto err;
264 }
265 snum->d[snum->width] = 0;
266 snum->width++;
267 }
268
269 div_n = sdiv->width;
270 num_n = snum->width;
271 loop = num_n - div_n;
272 // Lets setup a 'window' into snum
273 // This is the part that corresponds to the current
274 // 'area' being divided
275 wnum.neg = 0;
276 wnum.d = &(snum->d[loop]);
277 wnum.width = div_n;
278 // only needed when BN_ucmp messes up the values between width and max
279 wnum.dmax = snum->dmax - loop; // so we don't step out of bounds
280
281 // Get the top 2 words of sdiv
282 // div_n=sdiv->width;
283 d0 = sdiv->d[div_n - 1];
284 d1 = (div_n == 1) ? 0 : sdiv->d[div_n - 2];
285
286 // pointer to the 'top' of snum
287 wnump = &(snum->d[num_n - 1]);
288
289 // Setup to 'res'
290 res->neg = (numerator->neg ^ divisor->neg);
291 if (!bn_wexpand(res, loop + 1)) {
292 goto err;
293 }
294 res->width = loop - 1;
295 resp = &(res->d[loop - 1]);
296
297 // space for temp
298 if (!bn_wexpand(tmp, div_n + 1)) {
299 goto err;
300 }
301
302 // if res->width == 0 then clear the neg value otherwise decrease
303 // the resp pointer
304 if (res->width == 0) {
305 res->neg = 0;
306 } else {
307 resp--;
308 }
309
310 for (int i = 0; i < loop - 1; i++, wnump--, resp--) {
311 BN_ULONG q, l0;
312 // the first part of the loop uses the top two words of snum and sdiv to
313 // calculate a BN_ULONG q such that | wnum - sdiv * q | < sdiv
314 BN_ULONG n0, n1, rm = 0;
315
316 n0 = wnump[0];
317 n1 = wnump[-1];
318 if (n0 == d0) {
319 q = BN_MASK2;
320 } else {
321 // n0 < d0
322 bn_div_rem_words(&q, &rm, n0, n1, d0);
323
324#ifdef BN_ULLONG
325 BN_ULLONG t2 = (BN_ULLONG)d1 * q;
326 for (;;) {
327 if (t2 <= ((((BN_ULLONG)rm) << BN_BITS2) | wnump[-2])) {
328 break;
329 }
330 q--;
331 rm += d0;
332 if (rm < d0) {
333 break; // don't let rm overflow
334 }
335 t2 -= d1;
336 }
337#else // !BN_ULLONG
338 BN_ULONG t2l, t2h;
339 BN_UMULT_LOHI(t2l, t2h, d1, q);
340 for (;;) {
341 if (t2h < rm ||
342 (t2h == rm && t2l <= wnump[-2])) {
343 break;
344 }
345 q--;
346 rm += d0;
347 if (rm < d0) {
348 break; // don't let rm overflow
349 }
350 if (t2l < d1) {
351 t2h--;
352 }
353 t2l -= d1;
354 }
355#endif // !BN_ULLONG
356 }
357
358 l0 = bn_mul_words(tmp->d, sdiv->d, div_n, q);
359 tmp->d[div_n] = l0;
360 wnum.d--;
361 // ingore top values of the bignums just sub the two
362 // BN_ULONG arrays with bn_sub_words
363 if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n + 1)) {
364 // Note: As we have considered only the leading
365 // two BN_ULONGs in the calculation of q, sdiv * q
366 // might be greater than wnum (but then (q-1) * sdiv
367 // is less or equal than wnum)
368 q--;
369 if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n)) {
370 // we can't have an overflow here (assuming
371 // that q != 0, but if q == 0 then tmp is
372 // zero anyway)
373 (*wnump)++;
374 }
375 }
376 // store part of the result
377 *resp = q;
378 }
379
380 bn_set_minimal_width(snum);
381
382 if (rem != NULL) {
383 // Keep a copy of the neg flag in numerator because if |rem| == |numerator|
384 // |BN_rshift| will overwrite it.
385 int neg = numerator->neg;
386 if (!BN_rshift(rem, snum, norm_shift)) {
387 goto err;
388 }
389 if (!BN_is_zero(rem)) {
390 rem->neg = neg;
391 }
392 }
393
394 bn_set_minimal_width(res);
395 BN_CTX_end(ctx);
396 return 1;
397
398err:
399 BN_CTX_end(ctx);
400 return 0;
401}
402
403int BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx) {
404 if (!(BN_mod(r, m, d, ctx))) {
405 return 0;
406 }
407 if (!r->neg) {
408 return 1;
409 }
410
411 // now -|d| < r < 0, so we have to set r := r + |d|.
412 return (d->neg ? BN_sub : BN_add)(r, r, d);
413}
414
415BN_ULONG bn_reduce_once(BN_ULONG *r, const BN_ULONG *a, BN_ULONG carry,
416 const BN_ULONG *m, size_t num) {
417 assert(r != a);
418 // |r| = |a| - |m|. |bn_sub_words| performs the bulk of the subtraction, and
419 // then we apply the borrow to |carry|.
420 carry -= bn_sub_words(r, a, m, num);
421 // We know 0 <= |a| < 2*|m|, so -|m| <= |r| < |m|.
422 //
423 // If 0 <= |r| < |m|, |r| fits in |num| words and |carry| is zero. We then
424 // wish to select |r| as the answer. Otherwise -m <= r < 0 and we wish to
425 // return |r| + |m|, or |a|. |carry| must then be -1 or all ones. In both
426 // cases, |carry| is a suitable input to |bn_select_words|.
427 //
428 // Although |carry| may be one if it was one on input and |bn_sub_words|
429 // returns zero, this would give |r| > |m|, violating our input assumptions.
430 assert(carry == 0 || carry == (BN_ULONG)-1);
431 bn_select_words(r, carry, a /* r < 0 */, r /* r >= 0 */, num);
432 return carry;
433}
434
435BN_ULONG bn_reduce_once_in_place(BN_ULONG *r, BN_ULONG carry, const BN_ULONG *m,
436 BN_ULONG *tmp, size_t num) {
437 // See |bn_reduce_once| for why this logic works.
438 carry -= bn_sub_words(tmp, r, m, num);
439 assert(carry == 0 || carry == (BN_ULONG)-1);
440 bn_select_words(r, carry, r /* tmp < 0 */, tmp /* tmp >= 0 */, num);
441 return carry;
442}
443
444void bn_mod_sub_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
445 const BN_ULONG *m, BN_ULONG *tmp, size_t num) {
446 // r = a - b
447 BN_ULONG borrow = bn_sub_words(r, a, b, num);
448 // tmp = a - b + m
449 bn_add_words(tmp, r, m, num);
450 bn_select_words(r, 0 - borrow, tmp /* r < 0 */, r /* r >= 0 */, num);
451}
452
453void bn_mod_add_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
454 const BN_ULONG *m, BN_ULONG *tmp, size_t num) {
455 BN_ULONG carry = bn_add_words(r, a, b, num);
456 bn_reduce_once_in_place(r, carry, m, tmp, num);
457}
458
459int bn_div_consttime(BIGNUM *quotient, BIGNUM *remainder,
460 const BIGNUM *numerator, const BIGNUM *divisor,
461 BN_CTX *ctx) {
462 if (BN_is_negative(numerator) || BN_is_negative(divisor)) {
463 OPENSSL_PUT_ERROR(BN, BN_R_NEGATIVE_NUMBER);
464 return 0;
465 }
466 if (BN_is_zero(divisor)) {
467 OPENSSL_PUT_ERROR(BN, BN_R_DIV_BY_ZERO);
468 return 0;
469 }
470
471 // This function implements long division in binary. It is not very efficient,
472 // but it is simple, easy to make constant-time, and performant enough for RSA
473 // key generation.
474
475 int ret = 0;
476 BN_CTX_start(ctx);
477 BIGNUM *q = quotient, *r = remainder;
478 if (quotient == NULL || quotient == numerator || quotient == divisor) {
479 q = BN_CTX_get(ctx);
480 }
481 if (remainder == NULL || remainder == numerator || remainder == divisor) {
482 r = BN_CTX_get(ctx);
483 }
484 BIGNUM *tmp = BN_CTX_get(ctx);
485 if (q == NULL || r == NULL || tmp == NULL ||
486 !bn_wexpand(q, numerator->width) ||
487 !bn_wexpand(r, divisor->width) ||
488 !bn_wexpand(tmp, divisor->width)) {
489 goto err;
490 }
491
492 OPENSSL_memset(q->d, 0, numerator->width * sizeof(BN_ULONG));
493 q->width = numerator->width;
494 q->neg = 0;
495
496 OPENSSL_memset(r->d, 0, divisor->width * sizeof(BN_ULONG));
497 r->width = divisor->width;
498 r->neg = 0;
499
500 // Incorporate |numerator| into |r|, one bit at a time, reducing after each
501 // step. At the start of each loop iteration, |r| < |divisor|
502 for (int i = numerator->width - 1; i >= 0; i--) {
503 for (int bit = BN_BITS2 - 1; bit >= 0; bit--) {
504 // Incorporate the next bit of the numerator, by computing
505 // r = 2*r or 2*r + 1. Note the result fits in one more word. We store the
506 // extra word in |carry|.
507 BN_ULONG carry = bn_add_words(r->d, r->d, r->d, divisor->width);
508 r->d[0] |= (numerator->d[i] >> bit) & 1;
509 // |r| was previously fully-reduced, so we know:
510 // 2*0 <= r <= 2*(divisor-1) + 1
511 // 0 <= r <= 2*divisor - 1 < 2*divisor.
512 // Thus |r| satisfies the preconditions for |bn_reduce_once_in_place|.
513 BN_ULONG subtracted = bn_reduce_once_in_place(r->d, carry, divisor->d,
514 tmp->d, divisor->width);
515 // The corresponding bit of the quotient is set iff we needed to subtract.
516 q->d[i] |= (~subtracted & 1) << bit;
517 }
518 }
519
520 if ((quotient != NULL && !BN_copy(quotient, q)) ||
521 (remainder != NULL && !BN_copy(remainder, r))) {
522 goto err;
523 }
524
525 ret = 1;
526
527err:
528 BN_CTX_end(ctx);
529 return ret;
530}
531
532static BIGNUM *bn_scratch_space_from_ctx(size_t width, BN_CTX *ctx) {
533 BIGNUM *ret = BN_CTX_get(ctx);
534 if (ret == NULL ||
535 !bn_wexpand(ret, width)) {
536 return NULL;
537 }
538 ret->neg = 0;
539 ret->width = width;
540 return ret;
541}
542
543// bn_resized_from_ctx returns |bn| with width at least |width| or NULL on
544// error. This is so it may be used with low-level "words" functions. If
545// necessary, it allocates a new |BIGNUM| with a lifetime of the current scope
546// in |ctx|, so the caller does not need to explicitly free it. |bn| must fit in
547// |width| words.
548static const BIGNUM *bn_resized_from_ctx(const BIGNUM *bn, size_t width,
549 BN_CTX *ctx) {
550 if ((size_t)bn->width >= width) {
551 // Any excess words must be zero.
552 assert(bn_fits_in_words(bn, width));
553 return bn;
554 }
555 BIGNUM *ret = bn_scratch_space_from_ctx(width, ctx);
556 if (ret == NULL ||
557 !BN_copy(ret, bn) ||
558 !bn_resize_words(ret, width)) {
559 return NULL;
560 }
561 return ret;
562}
563
564int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
565 BN_CTX *ctx) {
566 if (!BN_add(r, a, b)) {
567 return 0;
568 }
569 return BN_nnmod(r, r, m, ctx);
570}
571
572int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
573 const BIGNUM *m) {
574 BN_CTX *ctx = BN_CTX_new();
575 int ok = ctx != NULL &&
576 bn_mod_add_consttime(r, a, b, m, ctx);
577 BN_CTX_free(ctx);
578 return ok;
579}
580
581int bn_mod_add_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
582 const BIGNUM *m, BN_CTX *ctx) {
583 BN_CTX_start(ctx);
584 a = bn_resized_from_ctx(a, m->width, ctx);
585 b = bn_resized_from_ctx(b, m->width, ctx);
586 BIGNUM *tmp = bn_scratch_space_from_ctx(m->width, ctx);
587 int ok = a != NULL && b != NULL && tmp != NULL &&
588 bn_wexpand(r, m->width);
589 if (ok) {
590 bn_mod_add_words(r->d, a->d, b->d, m->d, tmp->d, m->width);
591 r->width = m->width;
592 r->neg = 0;
593 }
594 BN_CTX_end(ctx);
595 return ok;
596}
597
598int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
599 BN_CTX *ctx) {
600 if (!BN_sub(r, a, b)) {
601 return 0;
602 }
603 return BN_nnmod(r, r, m, ctx);
604}
605
606int bn_mod_sub_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
607 const BIGNUM *m, BN_CTX *ctx) {
608 BN_CTX_start(ctx);
609 a = bn_resized_from_ctx(a, m->width, ctx);
610 b = bn_resized_from_ctx(b, m->width, ctx);
611 BIGNUM *tmp = bn_scratch_space_from_ctx(m->width, ctx);
612 int ok = a != NULL && b != NULL && tmp != NULL &&
613 bn_wexpand(r, m->width);
614 if (ok) {
615 bn_mod_sub_words(r->d, a->d, b->d, m->d, tmp->d, m->width);
616 r->width = m->width;
617 r->neg = 0;
618 }
619 BN_CTX_end(ctx);
620 return ok;
621}
622
623int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
624 const BIGNUM *m) {
625 BN_CTX *ctx = BN_CTX_new();
626 int ok = ctx != NULL &&
627 bn_mod_sub_consttime(r, a, b, m, ctx);
628 BN_CTX_free(ctx);
629 return ok;
630}
631
632int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
633 BN_CTX *ctx) {
634 BIGNUM *t;
635 int ret = 0;
636
637 BN_CTX_start(ctx);
638 t = BN_CTX_get(ctx);
639 if (t == NULL) {
640 goto err;
641 }
642
643 if (a == b) {
644 if (!BN_sqr(t, a, ctx)) {
645 goto err;
646 }
647 } else {
648 if (!BN_mul(t, a, b, ctx)) {
649 goto err;
650 }
651 }
652
653 if (!BN_nnmod(r, t, m, ctx)) {
654 goto err;
655 }
656
657 ret = 1;
658
659err:
660 BN_CTX_end(ctx);
661 return ret;
662}
663
664int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx) {
665 if (!BN_sqr(r, a, ctx)) {
666 return 0;
667 }
668
669 // r->neg == 0, thus we don't need BN_nnmod
670 return BN_mod(r, r, m, ctx);
671}
672
673int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m,
674 BN_CTX *ctx) {
675 BIGNUM *abs_m = NULL;
676 int ret;
677
678 if (!BN_nnmod(r, a, m, ctx)) {
679 return 0;
680 }
681
682 if (m->neg) {
683 abs_m = BN_dup(m);
684 if (abs_m == NULL) {
685 return 0;
686 }
687 abs_m->neg = 0;
688 }
689
690 ret = bn_mod_lshift_consttime(r, r, n, (abs_m ? abs_m : m), ctx);
691
692 BN_free(abs_m);
693 return ret;
694}
695
696int bn_mod_lshift_consttime(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m,
697 BN_CTX *ctx) {
698 if (!BN_copy(r, a)) {
699 return 0;
700 }
701 for (int i = 0; i < n; i++) {
702 if (!bn_mod_lshift1_consttime(r, r, m, ctx)) {
703 return 0;
704 }
705 }
706 return 1;
707}
708
709int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m) {
710 BN_CTX *ctx = BN_CTX_new();
711 int ok = ctx != NULL &&
712 bn_mod_lshift_consttime(r, a, n, m, ctx);
713 BN_CTX_free(ctx);
714 return ok;
715}
716
717int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx) {
718 if (!BN_lshift1(r, a)) {
719 return 0;
720 }
721
722 return BN_nnmod(r, r, m, ctx);
723}
724
725int bn_mod_lshift1_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *m,
726 BN_CTX *ctx) {
727 return bn_mod_add_consttime(r, a, a, m, ctx);
728}
729
730int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *m) {
731 BN_CTX *ctx = BN_CTX_new();
732 int ok = ctx != NULL &&
733 bn_mod_lshift1_consttime(r, a, m, ctx);
734 BN_CTX_free(ctx);
735 return ok;
736}
737
738BN_ULONG BN_div_word(BIGNUM *a, BN_ULONG w) {
739 BN_ULONG ret = 0;
740 int i, j;
741
742 if (!w) {
743 // actually this an error (division by zero)
744 return (BN_ULONG) - 1;
745 }
746
747 if (a->width == 0) {
748 return 0;
749 }
750
751 // normalize input for |bn_div_rem_words|.
752 j = BN_BITS2 - BN_num_bits_word(w);
753 w <<= j;
754 if (!BN_lshift(a, a, j)) {
755 return (BN_ULONG) - 1;
756 }
757
758 for (i = a->width - 1; i >= 0; i--) {
759 BN_ULONG l = a->d[i];
760 BN_ULONG d;
761 BN_ULONG unused_rem;
762 bn_div_rem_words(&d, &unused_rem, ret, l, w);
763 ret = l - (d * w);
764 a->d[i] = d;
765 }
766
767 bn_set_minimal_width(a);
768 ret >>= j;
769 return ret;
770}
771
772BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w) {
773#ifndef BN_CAN_DIVIDE_ULLONG
774 BN_ULONG ret = 0;
775#else
776 BN_ULLONG ret = 0;
777#endif
778 int i;
779
780 if (w == 0) {
781 return (BN_ULONG) -1;
782 }
783
784#ifndef BN_CAN_DIVIDE_ULLONG
785 // If |w| is too long and we don't have |BN_ULLONG| division then we need to
786 // fall back to using |BN_div_word|.
787 if (w > ((BN_ULONG)1 << BN_BITS4)) {
788 BIGNUM *tmp = BN_dup(a);
789 if (tmp == NULL) {
790 return (BN_ULONG)-1;
791 }
792 ret = BN_div_word(tmp, w);
793 BN_free(tmp);
794 return ret;
795 }
796#endif
797
798 for (i = a->width - 1; i >= 0; i--) {
799#ifndef BN_CAN_DIVIDE_ULLONG
800 ret = ((ret << BN_BITS4) | ((a->d[i] >> BN_BITS4) & BN_MASK2l)) % w;
801 ret = ((ret << BN_BITS4) | (a->d[i] & BN_MASK2l)) % w;
802#else
803 ret = (BN_ULLONG)(((ret << (BN_ULLONG)BN_BITS2) | a->d[i]) % (BN_ULLONG)w);
804#endif
805 }
806 return (BN_ULONG)ret;
807}
808
809int BN_mod_pow2(BIGNUM *r, const BIGNUM *a, size_t e) {
810 if (e == 0 || a->width == 0) {
811 BN_zero(r);
812 return 1;
813 }
814
815 size_t num_words = 1 + ((e - 1) / BN_BITS2);
816
817 // If |a| definitely has less than |e| bits, just BN_copy.
818 if ((size_t) a->width < num_words) {
819 return BN_copy(r, a) != NULL;
820 }
821
822 // Otherwise, first make sure we have enough space in |r|.
823 // Note that this will fail if num_words > INT_MAX.
824 if (!bn_wexpand(r, num_words)) {
825 return 0;
826 }
827
828 // Copy the content of |a| into |r|.
829 OPENSSL_memcpy(r->d, a->d, num_words * sizeof(BN_ULONG));
830
831 // If |e| isn't word-aligned, we have to mask off some of our bits.
832 size_t top_word_exponent = e % (sizeof(BN_ULONG) * 8);
833 if (top_word_exponent != 0) {
834 r->d[num_words - 1] &= (((BN_ULONG) 1) << top_word_exponent) - 1;
835 }
836
837 // Fill in the remaining fields of |r|.
838 r->neg = a->neg;
839 r->width = (int) num_words;
840 bn_set_minimal_width(r);
841 return 1;
842}
843
844int BN_nnmod_pow2(BIGNUM *r, const BIGNUM *a, size_t e) {
845 if (!BN_mod_pow2(r, a, e)) {
846 return 0;
847 }
848
849 // If the returned value was non-negative, we're done.
850 if (BN_is_zero(r) || !r->neg) {
851 return 1;
852 }
853
854 size_t num_words = 1 + (e - 1) / BN_BITS2;
855
856 // Expand |r| to the size of our modulus.
857 if (!bn_wexpand(r, num_words)) {
858 return 0;
859 }
860
861 // Clear the upper words of |r|.
862 OPENSSL_memset(&r->d[r->width], 0, (num_words - r->width) * BN_BYTES);
863
864 // Set parameters of |r|.
865 r->neg = 0;
866 r->width = (int) num_words;
867
868 // Now, invert every word. The idea here is that we want to compute 2^e-|x|,
869 // which is actually equivalent to the twos-complement representation of |x|
870 // in |e| bits, which is -x = ~x + 1.
871 for (int i = 0; i < r->width; i++) {
872 r->d[i] = ~r->d[i];
873 }
874
875 // If our exponent doesn't span the top word, we have to mask the rest.
876 size_t top_word_exponent = e % BN_BITS2;
877 if (top_word_exponent != 0) {
878 r->d[r->width - 1] &= (((BN_ULONG) 1) << top_word_exponent) - 1;
879 }
880
881 // Keep the minimal-width invariant for |BIGNUM|.
882 bn_set_minimal_width(r);
883
884 // Finally, add one, for the reason described above.
885 return BN_add(r, r, BN_value_one());
886}
887