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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 #include "cryptlib.h"
113 #include "bn_lcl.h"
114 
115 static BIGNUM *euclid(BIGNUM *a, BIGNUM *b);
116 
BN_gcd(BIGNUM * r,const BIGNUM * in_a,const BIGNUM * in_b,BN_CTX * ctx)117 int BN_gcd(BIGNUM *r, const BIGNUM *in_a, const BIGNUM *in_b, BN_CTX *ctx)
118 	{
119 	BIGNUM *a,*b,*t;
120 	int ret=0;
121 
122 	bn_check_top(in_a);
123 	bn_check_top(in_b);
124 
125 	BN_CTX_start(ctx);
126 	a = BN_CTX_get(ctx);
127 	b = BN_CTX_get(ctx);
128 	if (a == NULL || b == NULL) goto err;
129 
130 	if (BN_copy(a,in_a) == NULL) goto err;
131 	if (BN_copy(b,in_b) == NULL) goto err;
132 	a->neg = 0;
133 	b->neg = 0;
134 
135 	if (BN_cmp(a,b) < 0) { t=a; a=b; b=t; }
136 	t=euclid(a,b);
137 	if (t == NULL) goto err;
138 
139 	if (BN_copy(r,t) == NULL) goto err;
140 	ret=1;
141 err:
142 	BN_CTX_end(ctx);
143 	bn_check_top(r);
144 	return(ret);
145 	}
146 
euclid(BIGNUM * a,BIGNUM * b)147 static BIGNUM *euclid(BIGNUM *a, BIGNUM *b)
148 	{
149 	BIGNUM *t;
150 	int shifts=0;
151 
152 	bn_check_top(a);
153 	bn_check_top(b);
154 
155 	/* 0 <= b <= a */
156 	while (!BN_is_zero(b))
157 		{
158 		/* 0 < b <= a */
159 
160 		if (BN_is_odd(a))
161 			{
162 			if (BN_is_odd(b))
163 				{
164 				if (!BN_sub(a,a,b)) goto err;
165 				if (!BN_rshift1(a,a)) goto err;
166 				if (BN_cmp(a,b) < 0)
167 					{ t=a; a=b; b=t; }
168 				}
169 			else		/* a odd - b even */
170 				{
171 				if (!BN_rshift1(b,b)) goto err;
172 				if (BN_cmp(a,b) < 0)
173 					{ t=a; a=b; b=t; }
174 				}
175 			}
176 		else			/* a is even */
177 			{
178 			if (BN_is_odd(b))
179 				{
180 				if (!BN_rshift1(a,a)) goto err;
181 				if (BN_cmp(a,b) < 0)
182 					{ t=a; a=b; b=t; }
183 				}
184 			else		/* a even - b even */
185 				{
186 				if (!BN_rshift1(a,a)) goto err;
187 				if (!BN_rshift1(b,b)) goto err;
188 				shifts++;
189 				}
190 			}
191 		/* 0 <= b <= a */
192 		}
193 
194 	if (shifts)
195 		{
196 		if (!BN_lshift(a,a,shifts)) goto err;
197 		}
198 	bn_check_top(a);
199 	return(a);
200 err:
201 	return(NULL);
202 	}
203 
204 
205 /* solves ax == 1 (mod n) */
206 static BIGNUM *BN_mod_inverse_no_branch(BIGNUM *in,
207         const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx);
208 
BN_mod_inverse(BIGNUM * in,const BIGNUM * a,const BIGNUM * n,BN_CTX * ctx)209 BIGNUM *BN_mod_inverse(BIGNUM *in,
210 	const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx)
211 	{
212 	BIGNUM *A,*B,*X,*Y,*M,*D,*T,*R=NULL;
213 	BIGNUM *ret=NULL;
214 	int sign;
215 
216 	if ((BN_get_flags(a, BN_FLG_CONSTTIME) != 0) || (BN_get_flags(n, BN_FLG_CONSTTIME) != 0))
217 		{
218 		return BN_mod_inverse_no_branch(in, a, n, ctx);
219 		}
220 
221 	bn_check_top(a);
222 	bn_check_top(n);
223 
224 	BN_CTX_start(ctx);
225 	A = BN_CTX_get(ctx);
226 	B = BN_CTX_get(ctx);
227 	X = BN_CTX_get(ctx);
228 	D = BN_CTX_get(ctx);
229 	M = BN_CTX_get(ctx);
230 	Y = BN_CTX_get(ctx);
231 	T = BN_CTX_get(ctx);
232 	if (T == NULL) goto err;
233 
234 	if (in == NULL)
235 		R=BN_new();
236 	else
237 		R=in;
238 	if (R == NULL) goto err;
239 
240 	BN_one(X);
241 	BN_zero(Y);
242 	if (BN_copy(B,a) == NULL) goto err;
243 	if (BN_copy(A,n) == NULL) goto err;
244 	A->neg = 0;
245 	if (B->neg || (BN_ucmp(B, A) >= 0))
246 		{
247 		if (!BN_nnmod(B, B, A, ctx)) goto err;
248 		}
249 	sign = -1;
250 	/* From  B = a mod |n|,  A = |n|  it follows that
251 	 *
252 	 *      0 <= B < A,
253 	 *     -sign*X*a  ==  B   (mod |n|),
254 	 *      sign*Y*a  ==  A   (mod |n|).
255 	 */
256 
257 	if (BN_is_odd(n) && (BN_num_bits(n) <= (BN_BITS <= 32 ? 450 : 2048)))
258 		{
259 		/* Binary inversion algorithm; requires odd modulus.
260 		 * This is faster than the general algorithm if the modulus
261 		 * is sufficiently small (about 400 .. 500 bits on 32-bit
262 		 * sytems, but much more on 64-bit systems) */
263 		int shift;
264 
265 		while (!BN_is_zero(B))
266 			{
267 			/*
268 			 *      0 < B < |n|,
269 			 *      0 < A <= |n|,
270 			 * (1) -sign*X*a  ==  B   (mod |n|),
271 			 * (2)  sign*Y*a  ==  A   (mod |n|)
272 			 */
273 
274 			/* Now divide  B  by the maximum possible power of two in the integers,
275 			 * and divide  X  by the same value mod |n|.
276 			 * When we're done, (1) still holds. */
277 			shift = 0;
278 			while (!BN_is_bit_set(B, shift)) /* note that 0 < B */
279 				{
280 				shift++;
281 
282 				if (BN_is_odd(X))
283 					{
284 					if (!BN_uadd(X, X, n)) goto err;
285 					}
286 				/* now X is even, so we can easily divide it by two */
287 				if (!BN_rshift1(X, X)) goto err;
288 				}
289 			if (shift > 0)
290 				{
291 				if (!BN_rshift(B, B, shift)) goto err;
292 				}
293 
294 
295 			/* Same for  A  and  Y.  Afterwards, (2) still holds. */
296 			shift = 0;
297 			while (!BN_is_bit_set(A, shift)) /* note that 0 < A */
298 				{
299 				shift++;
300 
301 				if (BN_is_odd(Y))
302 					{
303 					if (!BN_uadd(Y, Y, n)) goto err;
304 					}
305 				/* now Y is even */
306 				if (!BN_rshift1(Y, Y)) goto err;
307 				}
308 			if (shift > 0)
309 				{
310 				if (!BN_rshift(A, A, shift)) goto err;
311 				}
312 
313 
314 			/* We still have (1) and (2).
315 			 * Both  A  and  B  are odd.
316 			 * The following computations ensure that
317 			 *
318 			 *     0 <= B < |n|,
319 			 *      0 < A < |n|,
320 			 * (1) -sign*X*a  ==  B   (mod |n|),
321 			 * (2)  sign*Y*a  ==  A   (mod |n|),
322 			 *
323 			 * and that either  A  or  B  is even in the next iteration.
324 			 */
325 			if (BN_ucmp(B, A) >= 0)
326 				{
327 				/* -sign*(X + Y)*a == B - A  (mod |n|) */
328 				if (!BN_uadd(X, X, Y)) goto err;
329 				/* NB: we could use BN_mod_add_quick(X, X, Y, n), but that
330 				 * actually makes the algorithm slower */
331 				if (!BN_usub(B, B, A)) goto err;
332 				}
333 			else
334 				{
335 				/*  sign*(X + Y)*a == A - B  (mod |n|) */
336 				if (!BN_uadd(Y, Y, X)) goto err;
337 				/* as above, BN_mod_add_quick(Y, Y, X, n) would slow things down */
338 				if (!BN_usub(A, A, B)) goto err;
339 				}
340 			}
341 		}
342 	else
343 		{
344 		/* general inversion algorithm */
345 
346 		while (!BN_is_zero(B))
347 			{
348 			BIGNUM *tmp;
349 
350 			/*
351 			 *      0 < B < A,
352 			 * (*) -sign*X*a  ==  B   (mod |n|),
353 			 *      sign*Y*a  ==  A   (mod |n|)
354 			 */
355 
356 			/* (D, M) := (A/B, A%B) ... */
357 			if (BN_num_bits(A) == BN_num_bits(B))
358 				{
359 				if (!BN_one(D)) goto err;
360 				if (!BN_sub(M,A,B)) goto err;
361 				}
362 			else if (BN_num_bits(A) == BN_num_bits(B) + 1)
363 				{
364 				/* A/B is 1, 2, or 3 */
365 				if (!BN_lshift1(T,B)) goto err;
366 				if (BN_ucmp(A,T) < 0)
367 					{
368 					/* A < 2*B, so D=1 */
369 					if (!BN_one(D)) goto err;
370 					if (!BN_sub(M,A,B)) goto err;
371 					}
372 				else
373 					{
374 					/* A >= 2*B, so D=2 or D=3 */
375 					if (!BN_sub(M,A,T)) goto err;
376 					if (!BN_add(D,T,B)) goto err; /* use D (:= 3*B) as temp */
377 					if (BN_ucmp(A,D) < 0)
378 						{
379 						/* A < 3*B, so D=2 */
380 						if (!BN_set_word(D,2)) goto err;
381 						/* M (= A - 2*B) already has the correct value */
382 						}
383 					else
384 						{
385 						/* only D=3 remains */
386 						if (!BN_set_word(D,3)) goto err;
387 						/* currently  M = A - 2*B,  but we need  M = A - 3*B */
388 						if (!BN_sub(M,M,B)) goto err;
389 						}
390 					}
391 				}
392 			else
393 				{
394 				if (!BN_div(D,M,A,B,ctx)) goto err;
395 				}
396 
397 			/* Now
398 			 *      A = D*B + M;
399 			 * thus we have
400 			 * (**)  sign*Y*a  ==  D*B + M   (mod |n|).
401 			 */
402 
403 			tmp=A; /* keep the BIGNUM object, the value does not matter */
404 
405 			/* (A, B) := (B, A mod B) ... */
406 			A=B;
407 			B=M;
408 			/* ... so we have  0 <= B < A  again */
409 
410 			/* Since the former  M  is now  B  and the former  B  is now  A,
411 			 * (**) translates into
412 			 *       sign*Y*a  ==  D*A + B    (mod |n|),
413 			 * i.e.
414 			 *       sign*Y*a - D*A  ==  B    (mod |n|).
415 			 * Similarly, (*) translates into
416 			 *      -sign*X*a  ==  A          (mod |n|).
417 			 *
418 			 * Thus,
419 			 *   sign*Y*a + D*sign*X*a  ==  B  (mod |n|),
420 			 * i.e.
421 			 *        sign*(Y + D*X)*a  ==  B  (mod |n|).
422 			 *
423 			 * So if we set  (X, Y, sign) := (Y + D*X, X, -sign),  we arrive back at
424 			 *      -sign*X*a  ==  B   (mod |n|),
425 			 *       sign*Y*a  ==  A   (mod |n|).
426 			 * Note that  X  and  Y  stay non-negative all the time.
427 			 */
428 
429 			/* most of the time D is very small, so we can optimize tmp := D*X+Y */
430 			if (BN_is_one(D))
431 				{
432 				if (!BN_add(tmp,X,Y)) goto err;
433 				}
434 			else
435 				{
436 				if (BN_is_word(D,2))
437 					{
438 					if (!BN_lshift1(tmp,X)) goto err;
439 					}
440 				else if (BN_is_word(D,4))
441 					{
442 					if (!BN_lshift(tmp,X,2)) goto err;
443 					}
444 				else if (D->top == 1)
445 					{
446 					if (!BN_copy(tmp,X)) goto err;
447 					if (!BN_mul_word(tmp,D->d[0])) goto err;
448 					}
449 				else
450 					{
451 					if (!BN_mul(tmp,D,X,ctx)) goto err;
452 					}
453 				if (!BN_add(tmp,tmp,Y)) goto err;
454 				}
455 
456 			M=Y; /* keep the BIGNUM object, the value does not matter */
457 			Y=X;
458 			X=tmp;
459 			sign = -sign;
460 			}
461 		}
462 
463 	/*
464 	 * The while loop (Euclid's algorithm) ends when
465 	 *      A == gcd(a,n);
466 	 * we have
467 	 *       sign*Y*a  ==  A  (mod |n|),
468 	 * where  Y  is non-negative.
469 	 */
470 
471 	if (sign < 0)
472 		{
473 		if (!BN_sub(Y,n,Y)) goto err;
474 		}
475 	/* Now  Y*a  ==  A  (mod |n|).  */
476 
477 
478 	if (BN_is_one(A))
479 		{
480 		/* Y*a == 1  (mod |n|) */
481 		if (!Y->neg && BN_ucmp(Y,n) < 0)
482 			{
483 			if (!BN_copy(R,Y)) goto err;
484 			}
485 		else
486 			{
487 			if (!BN_nnmod(R,Y,n,ctx)) goto err;
488 			}
489 		}
490 	else
491 		{
492 		BNerr(BN_F_BN_MOD_INVERSE,BN_R_NO_INVERSE);
493 		goto err;
494 		}
495 	ret=R;
496 err:
497 	if ((ret == NULL) && (in == NULL)) BN_free(R);
498 	BN_CTX_end(ctx);
499 	bn_check_top(ret);
500 	return(ret);
501 	}
502 
503 
504 /* BN_mod_inverse_no_branch is a special version of BN_mod_inverse.
505  * It does not contain branches that may leak sensitive information.
506  */
BN_mod_inverse_no_branch(BIGNUM * in,const BIGNUM * a,const BIGNUM * n,BN_CTX * ctx)507 static BIGNUM *BN_mod_inverse_no_branch(BIGNUM *in,
508 	const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx)
509 	{
510 	BIGNUM *A,*B,*X,*Y,*M,*D,*T,*R=NULL;
511 	BIGNUM local_A, local_B;
512 	BIGNUM *pA, *pB;
513 	BIGNUM *ret=NULL;
514 	int sign;
515 
516 	bn_check_top(a);
517 	bn_check_top(n);
518 
519 	BN_CTX_start(ctx);
520 	A = BN_CTX_get(ctx);
521 	B = BN_CTX_get(ctx);
522 	X = BN_CTX_get(ctx);
523 	D = BN_CTX_get(ctx);
524 	M = BN_CTX_get(ctx);
525 	Y = BN_CTX_get(ctx);
526 	T = BN_CTX_get(ctx);
527 	if (T == NULL) goto err;
528 
529 	if (in == NULL)
530 		R=BN_new();
531 	else
532 		R=in;
533 	if (R == NULL) goto err;
534 
535 	BN_one(X);
536 	BN_zero(Y);
537 	if (BN_copy(B,a) == NULL) goto err;
538 	if (BN_copy(A,n) == NULL) goto err;
539 	A->neg = 0;
540 
541 	if (B->neg || (BN_ucmp(B, A) >= 0))
542 		{
543 		/* Turn BN_FLG_CONSTTIME flag on, so that when BN_div is invoked,
544 	 	 * BN_div_no_branch will be called eventually.
545 	 	 */
546 		pB = &local_B;
547 		BN_with_flags(pB, B, BN_FLG_CONSTTIME);
548 		if (!BN_nnmod(B, pB, A, ctx)) goto err;
549 		}
550 	sign = -1;
551 	/* From  B = a mod |n|,  A = |n|  it follows that
552 	 *
553 	 *      0 <= B < A,
554 	 *     -sign*X*a  ==  B   (mod |n|),
555 	 *      sign*Y*a  ==  A   (mod |n|).
556 	 */
557 
558 	while (!BN_is_zero(B))
559 		{
560 		BIGNUM *tmp;
561 
562 		/*
563 		 *      0 < B < A,
564 		 * (*) -sign*X*a  ==  B   (mod |n|),
565 		 *      sign*Y*a  ==  A   (mod |n|)
566 		 */
567 
568 		/* Turn BN_FLG_CONSTTIME flag on, so that when BN_div is invoked,
569 	 	 * BN_div_no_branch will be called eventually.
570 	 	 */
571 		pA = &local_A;
572 		BN_with_flags(pA, A, BN_FLG_CONSTTIME);
573 
574 		/* (D, M) := (A/B, A%B) ... */
575 		if (!BN_div(D,M,pA,B,ctx)) goto err;
576 
577 		/* Now
578 		 *      A = D*B + M;
579 		 * thus we have
580 		 * (**)  sign*Y*a  ==  D*B + M   (mod |n|).
581 		 */
582 
583 		tmp=A; /* keep the BIGNUM object, the value does not matter */
584 
585 		/* (A, B) := (B, A mod B) ... */
586 		A=B;
587 		B=M;
588 		/* ... so we have  0 <= B < A  again */
589 
590 		/* Since the former  M  is now  B  and the former  B  is now  A,
591 		 * (**) translates into
592 		 *       sign*Y*a  ==  D*A + B    (mod |n|),
593 		 * i.e.
594 		 *       sign*Y*a - D*A  ==  B    (mod |n|).
595 		 * Similarly, (*) translates into
596 		 *      -sign*X*a  ==  A          (mod |n|).
597 		 *
598 		 * Thus,
599 		 *   sign*Y*a + D*sign*X*a  ==  B  (mod |n|),
600 		 * i.e.
601 		 *        sign*(Y + D*X)*a  ==  B  (mod |n|).
602 		 *
603 		 * So if we set  (X, Y, sign) := (Y + D*X, X, -sign),  we arrive back at
604 		 *      -sign*X*a  ==  B   (mod |n|),
605 		 *       sign*Y*a  ==  A   (mod |n|).
606 		 * Note that  X  and  Y  stay non-negative all the time.
607 		 */
608 
609 		if (!BN_mul(tmp,D,X,ctx)) goto err;
610 		if (!BN_add(tmp,tmp,Y)) goto err;
611 
612 		M=Y; /* keep the BIGNUM object, the value does not matter */
613 		Y=X;
614 		X=tmp;
615 		sign = -sign;
616 		}
617 
618 	/*
619 	 * The while loop (Euclid's algorithm) ends when
620 	 *      A == gcd(a,n);
621 	 * we have
622 	 *       sign*Y*a  ==  A  (mod |n|),
623 	 * where  Y  is non-negative.
624 	 */
625 
626 	if (sign < 0)
627 		{
628 		if (!BN_sub(Y,n,Y)) goto err;
629 		}
630 	/* Now  Y*a  ==  A  (mod |n|).  */
631 
632 	if (BN_is_one(A))
633 		{
634 		/* Y*a == 1  (mod |n|) */
635 		if (!Y->neg && BN_ucmp(Y,n) < 0)
636 			{
637 			if (!BN_copy(R,Y)) goto err;
638 			}
639 		else
640 			{
641 			if (!BN_nnmod(R,Y,n,ctx)) goto err;
642 			}
643 		}
644 	else
645 		{
646 		BNerr(BN_F_BN_MOD_INVERSE_NO_BRANCH,BN_R_NO_INVERSE);
647 		goto err;
648 		}
649 	ret=R;
650 err:
651 	if ((ret == NULL) && (in == NULL)) BN_free(R);
652 	BN_CTX_end(ctx);
653 	bn_check_top(ret);
654 	return(ret);
655 	}
656