]> git.ipfire.org Git - thirdparty/openssl.git/blob - crypto/bn/bn_gcd.c
projects / thirdparty / openssl.git / blob
? search:
summary | shortlog | log | commit | commitdiff | tree
blame | history | raw | HEAD
remove OPENSSL_FIPSAPI
[thirdparty/openssl.git] / crypto / bn / bn_gcd.c
1 /* crypto/bn/bn_gcd.c */
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
113
114 #include "cryptlib.h"
115 #include "bn_lcl.h"
116
117 static BIGNUM *euclid(BIGNUM *a, BIGNUM *b);
118
119 int BN_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 a = BN_CTX_get(ctx);
129 b = BN_CTX_get(ctx);
130 if (a == NULL || b == NULL) goto err;
131
132 if (BN_copy(a,in_a) == NULL) goto err;
133 if (BN_copy(b,in_b) == NULL) goto err;
134 a->neg = 0;
135 b->neg = 0;
136
137 if (BN_cmp(a,b) < 0) { t=a; a=b; b=t; }
138 t=euclid(a,b);
139 if (t == NULL) goto err;
140
141 if (BN_copy(r,t) == NULL) goto err;
142 ret=1;
143 err:
144 BN_CTX_end(ctx);
145 bn_check_top(r);
146 return(ret);
147 }
148
149 static BIGNUM *euclid(BIGNUM *a, BIGNUM *b)
150 {
151 BIGNUM *t;
152 int shifts=0;
153
154 bn_check_top(a);
155 bn_check_top(b);
156
157 /* 0 <= b <= a */
158 while (!BN_is_zero(b))
159 {
160 /* 0 < b <= a */
161
162 if (BN_is_odd(a))
163 {
164 if (BN_is_odd(b))
165 {
166 if (!BN_sub(a,a,b)) goto err;
167 if (!BN_rshift1(a,a)) goto err;
168 if (BN_cmp(a,b) < 0)
169 { t=a; a=b; b=t; }
170 }
171 else /* a odd - b even */
172 {
173 if (!BN_rshift1(b,b)) goto err;
174 if (BN_cmp(a,b) < 0)
175 { t=a; a=b; b=t; }
176 }
177 }
178 else /* a is even */
179 {
180 if (BN_is_odd(b))
181 {
182 if (!BN_rshift1(a,a)) goto err;
183 if (BN_cmp(a,b) < 0)
184 { t=a; a=b; b=t; }
185 }
186 else /* a even - b even */
187 {
188 if (!BN_rshift1(a,a)) goto err;
189 if (!BN_rshift1(b,b)) goto err;
190 shifts++;
191 }
192 }
193 /* 0 <= b <= a */
194 }
195
196 if (shifts)
197 {
198 if (!BN_lshift(a,a,shifts)) goto err;
199 }
200 bn_check_top(a);
201 return(a);
202 err:
203 return(NULL);
204 }
205
206
207 /* solves ax == 1 (mod n) */
208 static BIGNUM *BN_mod_inverse_no_branch(BIGNUM *in,
209 const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx);
210
211 BIGNUM *BN_mod_inverse(BIGNUM *in,
212 const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx)
213 {
214 BIGNUM *rv;
215 int noinv;
216 rv = int_bn_mod_inverse(in, a, n, ctx, &noinv);
217 if (noinv)
218 BNerr(BN_F_BN_MOD_INVERSE,BN_R_NO_INVERSE);
219 return rv;
220 }
221
222 BIGNUM *int_bn_mod_inverse(BIGNUM *in,
223 const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx, int *pnoinv)
224 {
225 BIGNUM *A,*B,*X,*Y,*M,*D,*T,*R=NULL;
226 BIGNUM *ret=NULL;
227 int sign;
228
229 if (pnoinv)
230 *pnoinv = 0;
231
232 if ((BN_get_flags(a, BN_FLG_CONSTTIME) != 0) || (BN_get_flags(n, BN_FLG_CONSTTIME) != 0))
233 {
234 return BN_mod_inverse_no_branch(in, a, n, ctx);
235 }
236
237 bn_check_top(a);
238 bn_check_top(n);
239
240 BN_CTX_start(ctx);
241 A = BN_CTX_get(ctx);
242 B = BN_CTX_get(ctx);
243 X = BN_CTX_get(ctx);
244 D = BN_CTX_get(ctx);
245 M = BN_CTX_get(ctx);
246 Y = BN_CTX_get(ctx);
247 T = BN_CTX_get(ctx);
248 if (T == NULL) goto err;
249
250 if (in == NULL)
251 R=BN_new();
252 else
253 R=in;
254 if (R == NULL) goto err;
255
256 BN_one(X);
257 BN_zero(Y);
258 if (BN_copy(B,a) == NULL) goto err;
259 if (BN_copy(A,n) == NULL) goto err;
260 A->neg = 0;
261 if (B->neg || (BN_ucmp(B, A) >= 0))
262 {
263 if (!BN_nnmod(B, B, A, ctx)) goto err;
264 }
265 sign = -1;
266 /* From B = a mod |n|, A = |n| it follows that
267 *
268 * 0 <= B < A,
269 * -sign*X*a == B (mod |n|),
270 * sign*Y*a == A (mod |n|).
271 */
272
273 if (BN_is_odd(n) && (BN_num_bits(n) <= (BN_BITS <= 32 ? 450 : 2048)))
274 {
275 /* Binary inversion algorithm; requires odd modulus.
276 * This is faster than the general algorithm if the modulus
277 * is sufficiently small (about 400 .. 500 bits on 32-bit
278 * sytems, but much more on 64-bit systems) */
279 int shift;
280
281 while (!BN_is_zero(B))
282 {
283 /*
284 * 0 < B < |n|,
285 * 0 < A <= |n|,
286 * (1) -sign*X*a == B (mod |n|),
287 * (2) sign*Y*a == A (mod |n|)
288 */
289
290 /* Now divide B by the maximum possible power of two in the integers,
291 * and divide X by the same value mod |n|.
292 * When we're done, (1) still holds. */
293 shift = 0;
294 while (!BN_is_bit_set(B, shift)) /* note that 0 < B */
295 {
296 shift++;
297
298 if (BN_is_odd(X))
299 {
300 if (!BN_uadd(X, X, n)) goto err;
301 }
302 /* now X is even, so we can easily divide it by two */
303 if (!BN_rshift1(X, X)) goto err;
304 }
305 if (shift > 0)
306 {
307 if (!BN_rshift(B, B, shift)) goto err;
308 }
309
310
311 /* Same for A and Y. Afterwards, (2) still holds. */
312 shift = 0;
313 while (!BN_is_bit_set(A, shift)) /* note that 0 < A */
314 {
315 shift++;
316
317 if (BN_is_odd(Y))
318 {
319 if (!BN_uadd(Y, Y, n)) goto err;
320 }
321 /* now Y is even */
322 if (!BN_rshift1(Y, Y)) goto err;
323 }
324 if (shift > 0)
325 {
326 if (!BN_rshift(A, A, shift)) goto err;
327 }
328
329
330 /* We still have (1) and (2).
331 * Both A and B are odd.
332 * The following computations ensure that
333 *
334 * 0 <= B < |n|,
335 * 0 < A < |n|,
336 * (1) -sign*X*a == B (mod |n|),
337 * (2) sign*Y*a == A (mod |n|),
338 *
339 * and that either A or B is even in the next iteration.
340 */
341 if (BN_ucmp(B, A) >= 0)
342 {
343 /* -sign*(X + Y)*a == B - A (mod |n|) */
344 if (!BN_uadd(X, X, Y)) goto err;
345 /* NB: we could use BN_mod_add_quick(X, X, Y, n), but that
346 * actually makes the algorithm slower */
347 if (!BN_usub(B, B, A)) goto err;
348 }
349 else
350 {
351 /* sign*(X + Y)*a == A - B (mod |n|) */
352 if (!BN_uadd(Y, Y, X)) goto err;
353 /* as above, BN_mod_add_quick(Y, Y, X, n) would slow things down */
354 if (!BN_usub(A, A, B)) goto err;
355 }
356 }
357 }
358 else
359 {
360 /* general inversion algorithm */
361
362 while (!BN_is_zero(B))
363 {
364 BIGNUM *tmp;
365
366 /*
367 * 0 < B < A,
368 * (*) -sign*X*a == B (mod |n|),
369 * sign*Y*a == A (mod |n|)
370 */
371
372 /* (D, M) := (A/B, A%B) ... */
373 if (BN_num_bits(A) == BN_num_bits(B))
374 {
375 if (!BN_one(D)) goto err;
376 if (!BN_sub(M,A,B)) goto err;
377 }
378 else if (BN_num_bits(A) == BN_num_bits(B) + 1)
379 {
380 /* A/B is 1, 2, or 3 */
381 if (!BN_lshift1(T,B)) goto err;
382 if (BN_ucmp(A,T) < 0)
383 {
384 /* A < 2*B, so D=1 */
385 if (!BN_one(D)) goto err;
386 if (!BN_sub(M,A,B)) goto err;
387 }
388 else
389 {
390 /* A >= 2*B, so D=2 or D=3 */
391 if (!BN_sub(M,A,T)) goto err;
392 if (!BN_add(D,T,B)) goto err; /* use D (:= 3*B) as temp */
393 if (BN_ucmp(A,D) < 0)
394 {
395 /* A < 3*B, so D=2 */
396 if (!BN_set_word(D,2)) goto err;
397 /* M (= A - 2*B) already has the correct value */
398 }
399 else
400 {
401 /* only D=3 remains */
402 if (!BN_set_word(D,3)) goto err;
403 /* currently M = A - 2*B, but we need M = A - 3*B */
404 if (!BN_sub(M,M,B)) goto err;
405 }
406 }
407 }
408 else
409 {
410 if (!BN_div(D,M,A,B,ctx)) goto err;
411 }
412
413 /* Now
414 * A = D*B + M;
415 * thus we have
416 * (**) sign*Y*a == D*B + M (mod |n|).
417 */
418
419 tmp=A; /* keep the BIGNUM object, the value does not matter */
420
421 /* (A, B) := (B, A mod B) ... */
422 A=B;
423 B=M;
424 /* ... so we have 0 <= B < A again */
425
426 /* Since the former M is now B and the former B is now A,
427 * (**) translates into
428 * sign*Y*a == D*A + B (mod |n|),
429 * i.e.
430 * sign*Y*a - D*A == B (mod |n|).
431 * Similarly, (*) translates into
432 * -sign*X*a == A (mod |n|).
433 *
434 * Thus,
435 * sign*Y*a + D*sign*X*a == B (mod |n|),
436 * i.e.
437 * sign*(Y + D*X)*a == B (mod |n|).
438 *
439 * So if we set (X, Y, sign) := (Y + D*X, X, -sign), we arrive back at
440 * -sign*X*a == B (mod |n|),
441 * sign*Y*a == A (mod |n|).
442 * Note that X and Y stay non-negative all the time.
443 */
444
445 /* most of the time D is very small, so we can optimize tmp := D*X+Y */
446 if (BN_is_one(D))
447 {
448 if (!BN_add(tmp,X,Y)) goto err;
449 }
450 else
451 {
452 if (BN_is_word(D,2))
453 {
454 if (!BN_lshift1(tmp,X)) goto err;
455 }
456 else if (BN_is_word(D,4))
457 {
458 if (!BN_lshift(tmp,X,2)) goto err;
459 }
460 else if (D->top == 1)
461 {
462 if (!BN_copy(tmp,X)) goto err;
463 if (!BN_mul_word(tmp,D->d[0])) goto err;
464 }
465 else
466 {
467 if (!BN_mul(tmp,D,X,ctx)) goto err;
468 }
469 if (!BN_add(tmp,tmp,Y)) goto err;
470 }
471
472 M=Y; /* keep the BIGNUM object, the value does not matter */
473 Y=X;
474 X=tmp;
475 sign = -sign;
476 }
477 }
478
479 /*
480 * The while loop (Euclid's algorithm) ends when
481 * A == gcd(a,n);
482 * we have
483 * sign*Y*a == A (mod |n|),
484 * where Y is non-negative.
485 */
486
487 if (sign < 0)
488 {
489 if (!BN_sub(Y,n,Y)) goto err;
490 }
491 /* Now Y*a == A (mod |n|). */
492
493
494 if (BN_is_one(A))
495 {
496 /* Y*a == 1 (mod |n|) */
497 if (!Y->neg && BN_ucmp(Y,n) < 0)
498 {
499 if (!BN_copy(R,Y)) goto err;
500 }
501 else
502 {
503 if (!BN_nnmod(R,Y,n,ctx)) goto err;
504 }
505 }
506 else
507 {
508 if (pnoinv)
509 *pnoinv = 1;
510 goto err;
511 }
512 ret=R;
513 err:
514 if ((ret == NULL) && (in == NULL)) BN_free(R);
515 BN_CTX_end(ctx);
516 bn_check_top(ret);
517 return(ret);
518 }
519
520
521 /* BN_mod_inverse_no_branch is a special version of BN_mod_inverse.
522 * It does not contain branches that may leak sensitive information.
523 */
524 static BIGNUM *BN_mod_inverse_no_branch(BIGNUM *in,
525 const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx)
526 {
527 BIGNUM *A,*B,*X,*Y,*M,*D,*T,*R=NULL;
528 BIGNUM local_A, local_B;
529 BIGNUM *pA, *pB;
530 BIGNUM *ret=NULL;
531 int sign;
532
533 bn_check_top(a);
534 bn_check_top(n);
535
536 BN_CTX_start(ctx);
537 A = BN_CTX_get(ctx);
538 B = BN_CTX_get(ctx);
539 X = BN_CTX_get(ctx);
540 D = BN_CTX_get(ctx);
541 M = BN_CTX_get(ctx);
542 Y = BN_CTX_get(ctx);
543 T = BN_CTX_get(ctx);
544 if (T == NULL) goto err;
545
546 if (in == NULL)
547 R=BN_new();
548 else
549 R=in;
550 if (R == NULL) goto err;
551
552 BN_one(X);
553 BN_zero(Y);
554 if (BN_copy(B,a) == NULL) goto err;
555 if (BN_copy(A,n) == NULL) goto err;
556 A->neg = 0;
557
558 if (B->neg || (BN_ucmp(B, A) >= 0))
559 {
560 /* Turn BN_FLG_CONSTTIME flag on, so that when BN_div is invoked,
561 * BN_div_no_branch will be called eventually.
562 */
563 pB = &local_B;
564 BN_with_flags(pB, B, BN_FLG_CONSTTIME);
565 if (!BN_nnmod(B, pB, A, ctx)) goto err;
566 }
567 sign = -1;
568 /* From B = a mod |n|, A = |n| it follows that
569 *
570 * 0 <= B < A,
571 * -sign*X*a == B (mod |n|),
572 * sign*Y*a == A (mod |n|).
573 */
574
575 while (!BN_is_zero(B))
576 {
577 BIGNUM *tmp;
578
579 /*
580 * 0 < B < A,
581 * (*) -sign*X*a == B (mod |n|),
582 * sign*Y*a == A (mod |n|)
583 */
584
585 /* Turn BN_FLG_CONSTTIME flag on, so that when BN_div is invoked,
586 * BN_div_no_branch will be called eventually.
587 */
588 pA = &local_A;
589 BN_with_flags(pA, A, BN_FLG_CONSTTIME);
590
591 /* (D, M) := (A/B, A%B) ... */
592 if (!BN_div(D,M,pA,B,ctx)) goto err;
593
594 /* Now
595 * A = D*B + M;
596 * thus we have
597 * (**) sign*Y*a == D*B + M (mod |n|).
598 */
599
600 tmp=A; /* keep the BIGNUM object, the value does not matter */
601
602 /* (A, B) := (B, A mod B) ... */
603 A=B;
604 B=M;
605 /* ... so we have 0 <= B < A again */
606
607 /* Since the former M is now B and the former B is now A,
608 * (**) translates into
609 * sign*Y*a == D*A + B (mod |n|),
610 * i.e.
611 * sign*Y*a - D*A == B (mod |n|).
612 * Similarly, (*) translates into
613 * -sign*X*a == A (mod |n|).
614 *
615 * Thus,
616 * sign*Y*a + D*sign*X*a == B (mod |n|),
617 * i.e.
618 * sign*(Y + D*X)*a == B (mod |n|).
619 *
620 * So if we set (X, Y, sign) := (Y + D*X, X, -sign), we arrive back at
621 * -sign*X*a == B (mod |n|),
622 * sign*Y*a == A (mod |n|).
623 * Note that X and Y stay non-negative all the time.
624 */
625
626 if (!BN_mul(tmp,D,X,ctx)) goto err;
627 if (!BN_add(tmp,tmp,Y)) goto err;
628
629 M=Y; /* keep the BIGNUM object, the value does not matter */
630 Y=X;
631 X=tmp;
632 sign = -sign;
633 }
634
635 /*
636 * The while loop (Euclid's algorithm) ends when
637 * A == gcd(a,n);
638 * we have
639 * sign*Y*a == A (mod |n|),
640 * where Y is non-negative.
641 */
642
643 if (sign < 0)
644 {
645 if (!BN_sub(Y,n,Y)) goto err;
646 }
647 /* Now Y*a == A (mod |n|). */
648
649 if (BN_is_one(A))
650 {
651 /* Y*a == 1 (mod |n|) */
652 if (!Y->neg && BN_ucmp(Y,n) < 0)
653 {
654 if (!BN_copy(R,Y)) goto err;
655 }
656 else
657 {
658 if (!BN_nnmod(R,Y,n,ctx)) goto err;
659 }
660 }
661 else
662 {
663 BNerr(BN_F_BN_MOD_INVERSE_NO_BRANCH,BN_R_NO_INVERSE);
664 goto err;
665 }
666 ret=R;
667 err:
668 if ((ret == NULL) && (in == NULL)) BN_free(R);
669 BN_CTX_end(ctx);
670 bn_check_top(ret);
671 return(ret);
672 }
A mirror of the official openssl repository