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diff --git a/src/lib/libcrypto/bn/bn_gcd.c b/src/lib/libcrypto/bn/bn_gcd.c
deleted file mode 100644
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--- a/src/lib/libcrypto/bn/bn_gcd.c
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1/* $OpenBSD: bn_gcd.c,v 1.10 2015/02/09 15:49:22 jsing Exp $ */
2/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
3 * All rights reserved.
4 *
5 * This package is an SSL implementation written
6 * by Eric Young (eay@cryptsoft.com).
7 * The implementation was written so as to conform with Netscapes SSL.
8 *
9 * This library is free for commercial and non-commercial use as long as
10 * the following conditions are aheared to. The following conditions
11 * apply to all code found in this distribution, be it the RC4, RSA,
12 * lhash, DES, etc., code; not just the SSL code. The SSL documentation
13 * included with this distribution is covered by the same copyright terms
14 * except that the holder is Tim Hudson (tjh@cryptsoft.com).
15 *
16 * Copyright remains Eric Young's, and as such any Copyright notices in
17 * the code are not to be removed.
18 * If this package is used in a product, Eric Young should be given attribution
19 * as the author of the parts of the library used.
20 * This can be in the form of a textual message at program startup or
21 * in documentation (online or textual) provided with the package.
22 *
23 * Redistribution and use in source and binary forms, with or without
24 * modification, are permitted provided that the following conditions
25 * are met:
26 * 1. Redistributions of source code must retain the copyright
27 * notice, this list of conditions and the following disclaimer.
28 * 2. Redistributions in binary form must reproduce the above copyright
29 * notice, this list of conditions and the following disclaimer in the
30 * documentation and/or other materials provided with the distribution.
31 * 3. All advertising materials mentioning features or use of this software
32 * must display the following acknowledgement:
33 * "This product includes cryptographic software written by
34 * Eric Young (eay@cryptsoft.com)"
35 * The word 'cryptographic' can be left out if the rouines from the library
36 * being used are not cryptographic related :-).
37 * 4. If you include any Windows specific code (or a derivative thereof) from
38 * the apps directory (application code) you must include an acknowledgement:
39 * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
40 *
41 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
42 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
43 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
44 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
45 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
46 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
47 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
48 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
49 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
50 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
51 * SUCH DAMAGE.
52 *
53 * The licence and distribution terms for any publically available version or
54 * derivative of this code cannot be changed. i.e. this code cannot simply be
55 * copied and put under another distribution licence
56 * [including the GNU Public Licence.]
57 */
58/* ====================================================================
59 * Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved.
60 *
61 * Redistribution and use in source and binary forms, with or without
62 * modification, are permitted provided that the following conditions
63 * are met:
64 *
65 * 1. Redistributions of source code must retain the above copyright
66 * notice, this list of conditions and the following disclaimer.
67 *
68 * 2. Redistributions in binary form must reproduce the above copyright
69 * notice, this list of conditions and the following disclaimer in
70 * the documentation and/or other materials provided with the
71 * distribution.
72 *
73 * 3. All advertising materials mentioning features or use of this
74 * software must display the following acknowledgment:
75 * "This product includes software developed by the OpenSSL Project
76 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
77 *
78 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
79 * endorse or promote products derived from this software without
80 * prior written permission. For written permission, please contact
81 * openssl-core@openssl.org.
82 *
83 * 5. Products derived from this software may not be called "OpenSSL"
84 * nor may "OpenSSL" appear in their names without prior written
85 * permission of the OpenSSL Project.
86 *
87 * 6. Redistributions of any form whatsoever must retain the following
88 * acknowledgment:
89 * "This product includes software developed by the OpenSSL Project
90 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
91 *
92 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
93 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
94 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
95 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
96 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
97 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
98 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
99 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
100 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
101 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
102 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
103 * OF THE POSSIBILITY OF SUCH DAMAGE.
104 * ====================================================================
105 *
106 * This product includes cryptographic software written by Eric Young
107 * (eay@cryptsoft.com). This product includes software written by Tim
108 * Hudson (tjh@cryptsoft.com).
109 *
110 */
111
112#include <openssl/err.h>
113
114#include "bn_lcl.h"
115
116static BIGNUM *euclid(BIGNUM *a, BIGNUM *b);
117
118int
119BN_gcd(BIGNUM *r, const BIGNUM *in_a, const BIGNUM *in_b, BN_CTX *ctx)
120{
121 BIGNUM *a, *b, *t;
122 int ret = 0;
123
124 bn_check_top(in_a);
125 bn_check_top(in_b);
126
127 BN_CTX_start(ctx);
128 if ((a = BN_CTX_get(ctx)) == NULL)
129 goto err;
130 if ((b = BN_CTX_get(ctx)) == NULL)
131 goto err;
132
133 if (BN_copy(a, in_a) == NULL)
134 goto err;
135 if (BN_copy(b, in_b) == NULL)
136 goto err;
137 a->neg = 0;
138 b->neg = 0;
139
140 if (BN_cmp(a, b) < 0) {
141 t = a;
142 a = b;
143 b = t;
144 }
145 t = euclid(a, b);
146 if (t == NULL)
147 goto err;
148
149 if (BN_copy(r, t) == NULL)
150 goto err;
151 ret = 1;
152
153err:
154 BN_CTX_end(ctx);
155 bn_check_top(r);
156 return (ret);
157}
158
159static BIGNUM *
160euclid(BIGNUM *a, BIGNUM *b)
161{
162 BIGNUM *t;
163 int shifts = 0;
164
165 bn_check_top(a);
166 bn_check_top(b);
167
168 /* 0 <= b <= a */
169 while (!BN_is_zero(b)) {
170 /* 0 < b <= a */
171
172 if (BN_is_odd(a)) {
173 if (BN_is_odd(b)) {
174 if (!BN_sub(a, a, b))
175 goto err;
176 if (!BN_rshift1(a, a))
177 goto err;
178 if (BN_cmp(a, b) < 0) {
179 t = a;
180 a = b;
181 b = t;
182 }
183 }
184 else /* a odd - b even */
185 {
186 if (!BN_rshift1(b, b))
187 goto err;
188 if (BN_cmp(a, b) < 0) {
189 t = a;
190 a = b;
191 b = t;
192 }
193 }
194 }
195 else /* a is even */
196 {
197 if (BN_is_odd(b)) {
198 if (!BN_rshift1(a, a))
199 goto err;
200 if (BN_cmp(a, b) < 0) {
201 t = a;
202 a = b;
203 b = t;
204 }
205 }
206 else /* a even - b even */
207 {
208 if (!BN_rshift1(a, a))
209 goto err;
210 if (!BN_rshift1(b, b))
211 goto err;
212 shifts++;
213 }
214 }
215 /* 0 <= b <= a */
216 }
217
218 if (shifts) {
219 if (!BN_lshift(a, a, shifts))
220 goto err;
221 }
222 bn_check_top(a);
223 return (a);
224
225err:
226 return (NULL);
227}
228
229
230/* solves ax == 1 (mod n) */
231static BIGNUM *BN_mod_inverse_no_branch(BIGNUM *in, const BIGNUM *a,
232 const BIGNUM *n, BN_CTX *ctx);
233
234BIGNUM *
235BN_mod_inverse(BIGNUM *in, const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx)
236{
237 BIGNUM *A, *B, *X, *Y, *M, *D, *T, *R = NULL;
238 BIGNUM *ret = NULL;
239 int sign;
240
241 if ((BN_get_flags(a, BN_FLG_CONSTTIME) != 0) ||
242 (BN_get_flags(n, BN_FLG_CONSTTIME) != 0)) {
243 return BN_mod_inverse_no_branch(in, a, n, ctx);
244 }
245
246 bn_check_top(a);
247 bn_check_top(n);
248
249 BN_CTX_start(ctx);
250 if ((A = BN_CTX_get(ctx)) == NULL)
251 goto err;
252 if ((B = BN_CTX_get(ctx)) == NULL)
253 goto err;
254 if ((X = BN_CTX_get(ctx)) == NULL)
255 goto err;
256 if ((D = BN_CTX_get(ctx)) == NULL)
257 goto err;
258 if ((M = BN_CTX_get(ctx)) == NULL)
259 goto err;
260 if ((Y = BN_CTX_get(ctx)) == NULL)
261 goto err;
262 if ((T = BN_CTX_get(ctx)) == NULL)
263 goto err;
264
265 if (in == NULL)
266 R = BN_new();
267 else
268 R = in;
269 if (R == NULL)
270 goto err;
271
272 BN_one(X);
273 BN_zero(Y);
274 if (BN_copy(B, a) == NULL)
275 goto err;
276 if (BN_copy(A, n) == NULL)
277 goto err;
278 A->neg = 0;
279 if (B->neg || (BN_ucmp(B, A) >= 0)) {
280 if (!BN_nnmod(B, B, A, ctx))
281 goto err;
282 }
283 sign = -1;
284 /* From B = a mod |n|, A = |n| it follows that
285 *
286 * 0 <= B < A,
287 * -sign*X*a == B (mod |n|),
288 * sign*Y*a == A (mod |n|).
289 */
290
291 if (BN_is_odd(n) && (BN_num_bits(n) <= (BN_BITS <= 32 ? 450 : 2048))) {
292 /* Binary inversion algorithm; requires odd modulus.
293 * This is faster than the general algorithm if the modulus
294 * is sufficiently small (about 400 .. 500 bits on 32-bit
295 * sytems, but much more on 64-bit systems) */
296 int shift;
297
298 while (!BN_is_zero(B)) {
299 /*
300 * 0 < B < |n|,
301 * 0 < A <= |n|,
302 * (1) -sign*X*a == B (mod |n|),
303 * (2) sign*Y*a == A (mod |n|)
304 */
305
306 /* Now divide B by the maximum possible power of two in the integers,
307 * and divide X by the same value mod |n|.
308 * When we're done, (1) still holds. */
309 shift = 0;
310 while (!BN_is_bit_set(B, shift)) /* note that 0 < B */
311 {
312 shift++;
313
314 if (BN_is_odd(X)) {
315 if (!BN_uadd(X, X, n))
316 goto err;
317 }
318 /* now X is even, so we can easily divide it by two */
319 if (!BN_rshift1(X, X))
320 goto err;
321 }
322 if (shift > 0) {
323 if (!BN_rshift(B, B, shift))
324 goto err;
325 }
326
327
328 /* Same for A and Y. Afterwards, (2) still holds. */
329 shift = 0;
330 while (!BN_is_bit_set(A, shift)) /* note that 0 < A */
331 {
332 shift++;
333
334 if (BN_is_odd(Y)) {
335 if (!BN_uadd(Y, Y, n))
336 goto err;
337 }
338 /* now Y is even */
339 if (!BN_rshift1(Y, Y))
340 goto err;
341 }
342 if (shift > 0) {
343 if (!BN_rshift(A, A, shift))
344 goto err;
345 }
346
347
348 /* We still have (1) and (2).
349 * Both A and B are odd.
350 * The following computations ensure that
351 *
352 * 0 <= B < |n|,
353 * 0 < A < |n|,
354 * (1) -sign*X*a == B (mod |n|),
355 * (2) sign*Y*a == A (mod |n|),
356 *
357 * and that either A or B is even in the next iteration.
358 */
359 if (BN_ucmp(B, A) >= 0) {
360 /* -sign*(X + Y)*a == B - A (mod |n|) */
361 if (!BN_uadd(X, X, Y))
362 goto err;
363 /* NB: we could use BN_mod_add_quick(X, X, Y, n), but that
364 * actually makes the algorithm slower */
365 if (!BN_usub(B, B, A))
366 goto err;
367 } else {
368 /* sign*(X + Y)*a == A - B (mod |n|) */
369 if (!BN_uadd(Y, Y, X))
370 goto err;
371 /* as above, BN_mod_add_quick(Y, Y, X, n) would slow things down */
372 if (!BN_usub(A, A, B))
373 goto err;
374 }
375 }
376 } else {
377 /* general inversion algorithm */
378
379 while (!BN_is_zero(B)) {
380 BIGNUM *tmp;
381
382 /*
383 * 0 < B < A,
384 * (*) -sign*X*a == B (mod |n|),
385 * sign*Y*a == A (mod |n|)
386 */
387
388 /* (D, M) := (A/B, A%B) ... */
389 if (BN_num_bits(A) == BN_num_bits(B)) {
390 if (!BN_one(D))
391 goto err;
392 if (!BN_sub(M, A, B))
393 goto err;
394 } else if (BN_num_bits(A) == BN_num_bits(B) + 1) {
395 /* A/B is 1, 2, or 3 */
396 if (!BN_lshift1(T, B))
397 goto err;
398 if (BN_ucmp(A, T) < 0) {
399 /* A < 2*B, so D=1 */
400 if (!BN_one(D))
401 goto err;
402 if (!BN_sub(M, A, B))
403 goto err;
404 } else {
405 /* A >= 2*B, so D=2 or D=3 */
406 if (!BN_sub(M, A, T))
407 goto err;
408 if (!BN_add(D,T,B)) goto err; /* use D (:= 3*B) as temp */
409 if (BN_ucmp(A, D) < 0) {
410 /* A < 3*B, so D=2 */
411 if (!BN_set_word(D, 2))
412 goto err;
413 /* M (= A - 2*B) already has the correct value */
414 } else {
415 /* only D=3 remains */
416 if (!BN_set_word(D, 3))
417 goto err;
418 /* currently M = A - 2*B, but we need M = A - 3*B */
419 if (!BN_sub(M, M, B))
420 goto err;
421 }
422 }
423 } else {
424 if (!BN_div(D, M, A, B, ctx))
425 goto err;
426 }
427
428 /* Now
429 * A = D*B + M;
430 * thus we have
431 * (**) sign*Y*a == D*B + M (mod |n|).
432 */
433 tmp = A; /* keep the BIGNUM object, the value does not matter */
434
435 /* (A, B) := (B, A mod B) ... */
436 A = B;
437 B = M;
438 /* ... so we have 0 <= B < A again */
439
440 /* Since the former M is now B and the former B is now A,
441 * (**) translates into
442 * sign*Y*a == D*A + B (mod |n|),
443 * i.e.
444 * sign*Y*a - D*A == B (mod |n|).
445 * Similarly, (*) translates into
446 * -sign*X*a == A (mod |n|).
447 *
448 * Thus,
449 * sign*Y*a + D*sign*X*a == B (mod |n|),
450 * i.e.
451 * sign*(Y + D*X)*a == B (mod |n|).
452 *
453 * So if we set (X, Y, sign) := (Y + D*X, X, -sign), we arrive back at
454 * -sign*X*a == B (mod |n|),
455 * sign*Y*a == A (mod |n|).
456 * Note that X and Y stay non-negative all the time.
457 */
458
459 /* most of the time D is very small, so we can optimize tmp := D*X+Y */
460 if (BN_is_one(D)) {
461 if (!BN_add(tmp, X, Y))
462 goto err;
463 } else {
464 if (BN_is_word(D, 2)) {
465 if (!BN_lshift1(tmp, X))
466 goto err;
467 } else if (BN_is_word(D, 4)) {
468 if (!BN_lshift(tmp, X, 2))
469 goto err;
470 } else if (D->top == 1) {
471 if (!BN_copy(tmp, X))
472 goto err;
473 if (!BN_mul_word(tmp, D->d[0]))
474 goto err;
475 } else {
476 if (!BN_mul(tmp, D,X, ctx))
477 goto err;
478 }
479 if (!BN_add(tmp, tmp, Y))
480 goto err;
481 }
482
483 M = Y; /* keep the BIGNUM object, the value does not matter */
484 Y = X;
485 X = tmp;
486 sign = -sign;
487 }
488 }
489
490 /*
491 * The while loop (Euclid's algorithm) ends when
492 * A == gcd(a,n);
493 * we have
494 * sign*Y*a == A (mod |n|),
495 * where Y is non-negative.
496 */
497
498 if (sign < 0) {
499 if (!BN_sub(Y, n, Y))
500 goto err;
501 }
502 /* Now Y*a == A (mod |n|). */
503
504 if (BN_is_one(A)) {
505 /* Y*a == 1 (mod |n|) */
506 if (!Y->neg && BN_ucmp(Y, n) < 0) {
507 if (!BN_copy(R, Y))
508 goto err;
509 } else {
510 if (!BN_nnmod(R, Y,n, ctx))
511 goto err;
512 }
513 } else {
514 BNerr(BN_F_BN_MOD_INVERSE, BN_R_NO_INVERSE);
515 goto err;
516 }
517 ret = R;
518
519err:
520 if ((ret == NULL) && (in == NULL))
521 BN_free(R);
522 BN_CTX_end(ctx);
523 bn_check_top(ret);
524 return (ret);
525}
526
527
528/* BN_mod_inverse_no_branch is a special version of BN_mod_inverse.
529 * It does not contain branches that may leak sensitive information.
530 */
531static BIGNUM *
532BN_mod_inverse_no_branch(BIGNUM *in, const BIGNUM *a, const BIGNUM *n,
533 BN_CTX *ctx)
534{
535 BIGNUM *A, *B, *X, *Y, *M, *D, *T, *R = NULL;
536 BIGNUM local_A, local_B;
537 BIGNUM *pA, *pB;
538 BIGNUM *ret = NULL;
539 int sign;
540
541 bn_check_top(a);
542 bn_check_top(n);
543
544 BN_CTX_start(ctx);
545 if ((A = BN_CTX_get(ctx)) == NULL)
546 goto err;
547 if ((B = BN_CTX_get(ctx)) == NULL)
548 goto err;
549 if ((X = BN_CTX_get(ctx)) == NULL)
550 goto err;
551 if ((D = BN_CTX_get(ctx)) == NULL)
552 goto err;
553 if ((M = BN_CTX_get(ctx)) == NULL)
554 goto err;
555 if ((Y = BN_CTX_get(ctx)) == NULL)
556 goto err;
557 if ((T = BN_CTX_get(ctx)) == NULL)
558 goto err;
559
560 if (in == NULL)
561 R = BN_new();
562 else
563 R = in;
564 if (R == NULL)
565 goto err;
566
567 BN_one(X);
568 BN_zero(Y);
569 if (BN_copy(B, a) == NULL)
570 goto err;
571 if (BN_copy(A, n) == NULL)
572 goto err;
573 A->neg = 0;
574
575 if (B->neg || (BN_ucmp(B, A) >= 0)) {
576 /* Turn BN_FLG_CONSTTIME flag on, so that when BN_div is invoked,
577 * BN_div_no_branch will be called eventually.
578 */
579 pB = &local_B;
580 BN_with_flags(pB, B, BN_FLG_CONSTTIME);
581 if (!BN_nnmod(B, pB, A, ctx))
582 goto err;
583 }
584 sign = -1;
585 /* From B = a mod |n|, A = |n| it follows that
586 *
587 * 0 <= B < A,
588 * -sign*X*a == B (mod |n|),
589 * sign*Y*a == A (mod |n|).
590 */
591
592 while (!BN_is_zero(B)) {
593 BIGNUM *tmp;
594
595 /*
596 * 0 < B < A,
597 * (*) -sign*X*a == B (mod |n|),
598 * sign*Y*a == A (mod |n|)
599 */
600
601 /* Turn BN_FLG_CONSTTIME flag on, so that when BN_div is invoked,
602 * BN_div_no_branch will be called eventually.
603 */
604 pA = &local_A;
605 BN_with_flags(pA, A, BN_FLG_CONSTTIME);
606
607 /* (D, M) := (A/B, A%B) ... */
608 if (!BN_div(D, M, pA, B, ctx))
609 goto err;
610
611 /* Now
612 * A = D*B + M;
613 * thus we have
614 * (**) sign*Y*a == D*B + M (mod |n|).
615 */
616 tmp = A; /* keep the BIGNUM object, the value does not matter */
617
618 /* (A, B) := (B, A mod B) ... */
619 A = B;
620 B = M;
621 /* ... so we have 0 <= B < A again */
622
623 /* Since the former M is now B and the former B is now A,
624 * (**) translates into
625 * sign*Y*a == D*A + B (mod |n|),
626 * i.e.
627 * sign*Y*a - D*A == B (mod |n|).
628 * Similarly, (*) translates into
629 * -sign*X*a == A (mod |n|).
630 *
631 * Thus,
632 * sign*Y*a + D*sign*X*a == B (mod |n|),
633 * i.e.
634 * sign*(Y + D*X)*a == B (mod |n|).
635 *
636 * So if we set (X, Y, sign) := (Y + D*X, X, -sign), we arrive back at
637 * -sign*X*a == B (mod |n|),
638 * sign*Y*a == A (mod |n|).
639 * Note that X and Y stay non-negative all the time.
640 */
641
642 if (!BN_mul(tmp, D, X, ctx))
643 goto err;
644 if (!BN_add(tmp, tmp, Y))
645 goto err;
646
647 M = Y; /* keep the BIGNUM object, the value does not matter */
648 Y = X;
649 X = tmp;
650 sign = -sign;
651 }
652
653 /*
654 * The while loop (Euclid's algorithm) ends when
655 * A == gcd(a,n);
656 * we have
657 * sign*Y*a == A (mod |n|),
658 * where Y is non-negative.
659 */
660
661 if (sign < 0) {
662 if (!BN_sub(Y, n, Y))
663 goto err;
664 }
665 /* Now Y*a == A (mod |n|). */
666
667 if (BN_is_one(A)) {
668 /* Y*a == 1 (mod |n|) */
669 if (!Y->neg && BN_ucmp(Y, n) < 0) {
670 if (!BN_copy(R, Y))
671 goto err;
672 } else {
673 if (!BN_nnmod(R, Y, n, ctx))
674 goto err;
675 }
676 } else {
677 BNerr(BN_F_BN_MOD_INVERSE_NO_BRANCH, BN_R_NO_INVERSE);
678 goto err;
679 }
680 ret = R;
681
682err:
683 if ((ret == NULL) && (in == NULL))
684 BN_free(R);
685 BN_CTX_end(ctx);
686 bn_check_top(ret);
687 return (ret);
688}
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