xref: /openbsd-src/lib/libcrypto/bn/bn_lib.c (revision b2ea75c1b17e1a9a339660e7ed45cd24946b230e)
1 /* crypto/bn/bn_lib.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 #ifndef BN_DEBUG
60 # undef NDEBUG /* avoid conflicting definitions */
61 # define NDEBUG
62 #endif
63 
64 #include <assert.h>
65 #include <limits.h>
66 #include <stdio.h>
67 #include "cryptlib.h"
68 #include "bn_lcl.h"
69 
70 const char *BN_version="Big Number" OPENSSL_VERSION_PTEXT;
71 
72 /* For a 32 bit machine
73  * 2 -   4 ==  128
74  * 3 -   8 ==  256
75  * 4 -  16 ==  512
76  * 5 -  32 == 1024
77  * 6 -  64 == 2048
78  * 7 - 128 == 4096
79  * 8 - 256 == 8192
80  */
81 static int bn_limit_bits=0;
82 static int bn_limit_num=8;        /* (1<<bn_limit_bits) */
83 static int bn_limit_bits_low=0;
84 static int bn_limit_num_low=8;    /* (1<<bn_limit_bits_low) */
85 static int bn_limit_bits_high=0;
86 static int bn_limit_num_high=8;   /* (1<<bn_limit_bits_high) */
87 static int bn_limit_bits_mont=0;
88 static int bn_limit_num_mont=8;   /* (1<<bn_limit_bits_mont) */
89 
90 void BN_set_params(int mult, int high, int low, int mont)
91 	{
92 	if (mult >= 0)
93 		{
94 		if (mult > (sizeof(int)*8)-1)
95 			mult=sizeof(int)*8-1;
96 		bn_limit_bits=mult;
97 		bn_limit_num=1<<mult;
98 		}
99 	if (high >= 0)
100 		{
101 		if (high > (sizeof(int)*8)-1)
102 			high=sizeof(int)*8-1;
103 		bn_limit_bits_high=high;
104 		bn_limit_num_high=1<<high;
105 		}
106 	if (low >= 0)
107 		{
108 		if (low > (sizeof(int)*8)-1)
109 			low=sizeof(int)*8-1;
110 		bn_limit_bits_low=low;
111 		bn_limit_num_low=1<<low;
112 		}
113 	if (mont >= 0)
114 		{
115 		if (mont > (sizeof(int)*8)-1)
116 			mont=sizeof(int)*8-1;
117 		bn_limit_bits_mont=mont;
118 		bn_limit_num_mont=1<<mont;
119 		}
120 	}
121 
122 int BN_get_params(int which)
123 	{
124 	if      (which == 0) return(bn_limit_bits);
125 	else if (which == 1) return(bn_limit_bits_high);
126 	else if (which == 2) return(bn_limit_bits_low);
127 	else if (which == 3) return(bn_limit_bits_mont);
128 	else return(0);
129 	}
130 
131 BIGNUM *BN_value_one(void)
132 	{
133 	static BN_ULONG data_one=1L;
134 	static BIGNUM const_one={&data_one,1,1,0};
135 
136 	return(&const_one);
137 	}
138 
139 char *BN_options(void)
140 	{
141 	static int init=0;
142 	static char data[16];
143 
144 	if (!init)
145 		{
146 		init++;
147 #ifdef BN_LLONG
148 		sprintf(data,"bn(%d,%d)",(int)sizeof(BN_ULLONG)*8,
149 			(int)sizeof(BN_ULONG)*8);
150 #else
151 		sprintf(data,"bn(%d,%d)",(int)sizeof(BN_ULONG)*8,
152 			(int)sizeof(BN_ULONG)*8);
153 #endif
154 		}
155 	return(data);
156 	}
157 
158 int BN_num_bits_word(BN_ULONG l)
159 	{
160 	static const char bits[256]={
161 		0,1,2,2,3,3,3,3,4,4,4,4,4,4,4,4,
162 		5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,
163 		6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
164 		6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
165 		7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
166 		7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
167 		7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
168 		7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
169 		8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
170 		8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
171 		8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
172 		8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
173 		8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
174 		8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
175 		8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
176 		8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
177 		};
178 
179 #if defined(SIXTY_FOUR_BIT_LONG)
180 	if (l & 0xffffffff00000000L)
181 		{
182 		if (l & 0xffff000000000000L)
183 			{
184 			if (l & 0xff00000000000000L)
185 				{
186 				return(bits[(int)(l>>56)]+56);
187 				}
188 			else	return(bits[(int)(l>>48)]+48);
189 			}
190 		else
191 			{
192 			if (l & 0x0000ff0000000000L)
193 				{
194 				return(bits[(int)(l>>40)]+40);
195 				}
196 			else	return(bits[(int)(l>>32)]+32);
197 			}
198 		}
199 	else
200 #else
201 #ifdef SIXTY_FOUR_BIT
202 	if (l & 0xffffffff00000000LL)
203 		{
204 		if (l & 0xffff000000000000LL)
205 			{
206 			if (l & 0xff00000000000000LL)
207 				{
208 				return(bits[(int)(l>>56)]+56);
209 				}
210 			else	return(bits[(int)(l>>48)]+48);
211 			}
212 		else
213 			{
214 			if (l & 0x0000ff0000000000LL)
215 				{
216 				return(bits[(int)(l>>40)]+40);
217 				}
218 			else	return(bits[(int)(l>>32)]+32);
219 			}
220 		}
221 	else
222 #endif
223 #endif
224 		{
225 #if defined(THIRTY_TWO_BIT) || defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG)
226 		if (l & 0xffff0000L)
227 			{
228 			if (l & 0xff000000L)
229 				return(bits[(int)(l>>24L)]+24);
230 			else	return(bits[(int)(l>>16L)]+16);
231 			}
232 		else
233 #endif
234 			{
235 #if defined(SIXTEEN_BIT) || defined(THIRTY_TWO_BIT) || defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG)
236 			if (l & 0xff00L)
237 				return(bits[(int)(l>>8)]+8);
238 			else
239 #endif
240 				return(bits[(int)(l   )]  );
241 			}
242 		}
243 	}
244 
245 int BN_num_bits(const BIGNUM *a)
246 	{
247 	BN_ULONG l;
248 	int i;
249 
250 	bn_check_top(a);
251 
252 	if (a->top == 0) return(0);
253 	l=a->d[a->top-1];
254 	assert(l != 0);
255 	i=(a->top-1)*BN_BITS2;
256 	return(i+BN_num_bits_word(l));
257 	}
258 
259 void BN_clear_free(BIGNUM *a)
260 	{
261 	int i;
262 
263 	if (a == NULL) return;
264 	if (a->d != NULL)
265 		{
266 		memset(a->d,0,a->dmax*sizeof(a->d[0]));
267 		if (!(BN_get_flags(a,BN_FLG_STATIC_DATA)))
268 			OPENSSL_free(a->d);
269 		}
270 	i=BN_get_flags(a,BN_FLG_MALLOCED);
271 	memset(a,0,sizeof(BIGNUM));
272 	if (i)
273 		OPENSSL_free(a);
274 	}
275 
276 void BN_free(BIGNUM *a)
277 	{
278 	if (a == NULL) return;
279 	if ((a->d != NULL) && !(BN_get_flags(a,BN_FLG_STATIC_DATA)))
280 		OPENSSL_free(a->d);
281 	a->flags|=BN_FLG_FREE; /* REMOVE? */
282 	if (a->flags & BN_FLG_MALLOCED)
283 		OPENSSL_free(a);
284 	}
285 
286 void BN_init(BIGNUM *a)
287 	{
288 	memset(a,0,sizeof(BIGNUM));
289 	}
290 
291 BIGNUM *BN_new(void)
292 	{
293 	BIGNUM *ret;
294 
295 	if ((ret=(BIGNUM *)OPENSSL_malloc(sizeof(BIGNUM))) == NULL)
296 		{
297 		BNerr(BN_F_BN_NEW,ERR_R_MALLOC_FAILURE);
298 		return(NULL);
299 		}
300 	ret->flags=BN_FLG_MALLOCED;
301 	ret->top=0;
302 	ret->neg=0;
303 	ret->dmax=0;
304 	ret->d=NULL;
305 	return(ret);
306 	}
307 
308 /* This is an internal function that should not be used in applications.
309  * It ensures that 'b' has enough room for a 'words' word number number.
310  * It is mostly used by the various BIGNUM routines. If there is an error,
311  * NULL is returned. If not, 'b' is returned. */
312 
313 BIGNUM *bn_expand2(BIGNUM *b, int words)
314 	{
315 	BN_ULONG *A,*a;
316 	const BN_ULONG *B;
317 	int i;
318 
319 	bn_check_top(b);
320 
321 	if (words > b->dmax)
322 		{
323 		if (words > (INT_MAX/(4*BN_BITS2)))
324 			{
325 			BNerr(BN_F_BN_EXPAND2,BN_R_BIGNUM_TOO_LONG);
326 			return NULL;
327 			}
328 
329 		bn_check_top(b);
330 		if (BN_get_flags(b,BN_FLG_STATIC_DATA))
331 			{
332 			BNerr(BN_F_BN_EXPAND2,BN_R_EXPAND_ON_STATIC_BIGNUM_DATA);
333 			return(NULL);
334 			}
335 		a=A=(BN_ULONG *)OPENSSL_malloc(sizeof(BN_ULONG)*(words+1));
336 		if (A == NULL)
337 			{
338 			BNerr(BN_F_BN_EXPAND2,ERR_R_MALLOC_FAILURE);
339 			return(NULL);
340 			}
341 #if 1
342 		B=b->d;
343 		/* Check if the previous number needs to be copied */
344 		if (B != NULL)
345 			{
346 #if 0
347 			/* This lot is an unrolled loop to copy b->top
348 			 * BN_ULONGs from B to A
349 			 */
350 /*
351  * I have nothing against unrolling but it's usually done for
352  * several reasons, namely:
353  * - minimize percentage of decision making code, i.e. branches;
354  * - avoid cache trashing;
355  * - make it possible to schedule loads earlier;
356  * Now let's examine the code below. The cornerstone of C is
357  * "programmer is always right" and that's what we love it for:-)
358  * For this very reason C compilers have to be paranoid when it
359  * comes to data aliasing and assume the worst. Yeah, but what
360  * does it mean in real life? This means that loop body below will
361  * be compiled to sequence of loads immediately followed by stores
362  * as compiler assumes the worst, something in A==B+1 style. As a
363  * result CPU pipeline is going to starve for incoming data. Secondly
364  * if A and B happen to share same cache line such code is going to
365  * cause severe cache trashing. Both factors have severe impact on
366  * performance of modern CPUs and this is the reason why this
367  * particular piece of code is #ifdefed away and replaced by more
368  * "friendly" version found in #else section below. This comment
369  * also applies to BN_copy function.
370  *
371  *					<appro@fy.chalmers.se>
372  */
373 			for (i=b->top&(~7); i>0; i-=8)
374 				{
375 				A[0]=B[0]; A[1]=B[1]; A[2]=B[2]; A[3]=B[3];
376 				A[4]=B[4]; A[5]=B[5]; A[6]=B[6]; A[7]=B[7];
377 				A+=8;
378 				B+=8;
379 				}
380 			switch (b->top&7)
381 				{
382 			case 7:
383 				A[6]=B[6];
384 			case 6:
385 				A[5]=B[5];
386 			case 5:
387 				A[4]=B[4];
388 			case 4:
389 				A[3]=B[3];
390 			case 3:
391 				A[2]=B[2];
392 			case 2:
393 				A[1]=B[1];
394 			case 1:
395 				A[0]=B[0];
396 			case 0:
397 				/* I need the 'case 0' entry for utrix cc.
398 				 * If the optimizer is turned on, it does the
399 				 * switch table by doing
400 				 * a=top&7
401 				 * a--;
402 				 * goto jump_table[a];
403 				 * If top is 0, this makes us jump to 0xffffffc
404 				 * which is rather bad :-(.
405 				 * eric 23-Apr-1998
406 				 */
407 				;
408 				}
409 #else
410 			for (i=b->top>>2; i>0; i--,A+=4,B+=4)
411 				{
412 				/*
413 				 * The fact that the loop is unrolled
414 				 * 4-wise is a tribute to Intel. It's
415 				 * the one that doesn't have enough
416 				 * registers to accomodate more data.
417 				 * I'd unroll it 8-wise otherwise:-)
418 				 *
419 				 *		<appro@fy.chalmers.se>
420 				 */
421 				BN_ULONG a0,a1,a2,a3;
422 				a0=B[0]; a1=B[1]; a2=B[2]; a3=B[3];
423 				A[0]=a0; A[1]=a1; A[2]=a2; A[3]=a3;
424 				}
425 			switch (b->top&3)
426 				{
427 				case 3:	A[2]=B[2];
428 				case 2:	A[1]=B[1];
429 				case 1:	A[0]=B[0];
430 				case 0:	; /* ultrix cc workaround, see above */
431 				}
432 #endif
433 			OPENSSL_free(b->d);
434 			}
435 
436 		b->d=a;
437 		b->dmax=words;
438 
439 		/* Now need to zero any data between b->top and b->max */
440 
441 		A= &(b->d[b->top]);
442 		for (i=(b->dmax - b->top)>>3; i>0; i--,A+=8)
443 			{
444 			A[0]=0; A[1]=0; A[2]=0; A[3]=0;
445 			A[4]=0; A[5]=0; A[6]=0; A[7]=0;
446 			}
447 		for (i=(b->dmax - b->top)&7; i>0; i--,A++)
448 			A[0]=0;
449 #else
450 			memset(A,0,sizeof(BN_ULONG)*(words+1));
451 			memcpy(A,b->d,sizeof(b->d[0])*b->top);
452 			b->d=a;
453 			b->max=words;
454 #endif
455 
456 /*		memset(&(p[b->max]),0,((words+1)-b->max)*sizeof(BN_ULONG)); */
457 /*	{ int i; for (i=b->max; i<words+1; i++) p[i]=i;} */
458 
459 		}
460 	return(b);
461 	}
462 
463 BIGNUM *BN_dup(const BIGNUM *a)
464 	{
465 	BIGNUM *r;
466 
467 	if (a == NULL) return NULL;
468 
469 	bn_check_top(a);
470 
471 	r=BN_new();
472 	if (r == NULL) return(NULL);
473 	return((BIGNUM *)BN_copy(r,a));
474 	}
475 
476 BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b)
477 	{
478 	int i;
479 	BN_ULONG *A;
480 	const BN_ULONG *B;
481 
482 	bn_check_top(b);
483 
484 	if (a == b) return(a);
485 	if (bn_wexpand(a,b->top) == NULL) return(NULL);
486 
487 #if 1
488 	A=a->d;
489 	B=b->d;
490 	for (i=b->top>>2; i>0; i--,A+=4,B+=4)
491 		{
492 		BN_ULONG a0,a1,a2,a3;
493 		a0=B[0]; a1=B[1]; a2=B[2]; a3=B[3];
494 		A[0]=a0; A[1]=a1; A[2]=a2; A[3]=a3;
495 		}
496 	switch (b->top&3)
497 		{
498 		case 3: A[2]=B[2];
499 		case 2: A[1]=B[1];
500 		case 1: A[0]=B[0];
501 		case 0: ; /* ultrix cc workaround, see comments in bn_expand2 */
502 		}
503 #else
504 	memcpy(a->d,b->d,sizeof(b->d[0])*b->top);
505 #endif
506 
507 /*	memset(&(a->d[b->top]),0,sizeof(a->d[0])*(a->max-b->top));*/
508 	a->top=b->top;
509 	if ((a->top == 0) && (a->d != NULL))
510 		a->d[0]=0;
511 	a->neg=b->neg;
512 	return(a);
513 	}
514 
515 void BN_clear(BIGNUM *a)
516 	{
517 	if (a->d != NULL)
518 		memset(a->d,0,a->dmax*sizeof(a->d[0]));
519 	a->top=0;
520 	a->neg=0;
521 	}
522 
523 BN_ULONG BN_get_word(BIGNUM *a)
524 	{
525 	int i,n;
526 	BN_ULONG ret=0;
527 
528 	n=BN_num_bytes(a);
529 	if (n > sizeof(BN_ULONG))
530 		return(BN_MASK2);
531 	for (i=a->top-1; i>=0; i--)
532 		{
533 #ifndef SIXTY_FOUR_BIT /* the data item > unsigned long */
534 		ret<<=BN_BITS4; /* stops the compiler complaining */
535 		ret<<=BN_BITS4;
536 #else
537 		ret=0;
538 #endif
539 		ret|=a->d[i];
540 		}
541 	return(ret);
542 	}
543 
544 int BN_set_word(BIGNUM *a, BN_ULONG w)
545 	{
546 	int i,n;
547 	if (bn_expand(a,sizeof(BN_ULONG)*8) == NULL) return(0);
548 
549 	n=sizeof(BN_ULONG)/BN_BYTES;
550 	a->neg=0;
551 	a->top=0;
552 	a->d[0]=(BN_ULONG)w&BN_MASK2;
553 	if (a->d[0] != 0) a->top=1;
554 	for (i=1; i<n; i++)
555 		{
556 		/* the following is done instead of
557 		 * w>>=BN_BITS2 so compilers don't complain
558 		 * on builds where sizeof(long) == BN_TYPES */
559 #ifndef SIXTY_FOUR_BIT /* the data item > unsigned long */
560 		w>>=BN_BITS4;
561 		w>>=BN_BITS4;
562 #else
563 		w=0;
564 #endif
565 		a->d[i]=(BN_ULONG)w&BN_MASK2;
566 		if (a->d[i] != 0) a->top=i+1;
567 		}
568 	return(1);
569 	}
570 
571 /* ignore negative */
572 BIGNUM *BN_bin2bn(const unsigned char *s, int len, BIGNUM *ret)
573 	{
574 	unsigned int i,m;
575 	unsigned int n;
576 	BN_ULONG l;
577 
578 	if (ret == NULL) ret=BN_new();
579 	if (ret == NULL) return(NULL);
580 	l=0;
581 	n=len;
582 	if (n == 0)
583 		{
584 		ret->top=0;
585 		return(ret);
586 		}
587 	if (bn_expand(ret,(int)(n+2)*8) == NULL)
588 		return(NULL);
589 	i=((n-1)/BN_BYTES)+1;
590 	m=((n-1)%(BN_BYTES));
591 	ret->top=i;
592 	while (n-- > 0)
593 		{
594 		l=(l<<8L)| *(s++);
595 		if (m-- == 0)
596 			{
597 			ret->d[--i]=l;
598 			l=0;
599 			m=BN_BYTES-1;
600 			}
601 		}
602 	/* need to call this due to clear byte at top if avoiding
603 	 * having the top bit set (-ve number) */
604 	bn_fix_top(ret);
605 	return(ret);
606 	}
607 
608 /* ignore negative */
609 int BN_bn2bin(const BIGNUM *a, unsigned char *to)
610 	{
611 	int n,i;
612 	BN_ULONG l;
613 
614 	n=i=BN_num_bytes(a);
615 	while (i-- > 0)
616 		{
617 		l=a->d[i/BN_BYTES];
618 		*(to++)=(unsigned char)(l>>(8*(i%BN_BYTES)))&0xff;
619 		}
620 	return(n);
621 	}
622 
623 int BN_ucmp(const BIGNUM *a, const BIGNUM *b)
624 	{
625 	int i;
626 	BN_ULONG t1,t2,*ap,*bp;
627 
628 	bn_check_top(a);
629 	bn_check_top(b);
630 
631 	i=a->top-b->top;
632 	if (i != 0) return(i);
633 	ap=a->d;
634 	bp=b->d;
635 	for (i=a->top-1; i>=0; i--)
636 		{
637 		t1= ap[i];
638 		t2= bp[i];
639 		if (t1 != t2)
640 			return(t1 > t2?1:-1);
641 		}
642 	return(0);
643 	}
644 
645 int BN_cmp(const BIGNUM *a, const BIGNUM *b)
646 	{
647 	int i;
648 	int gt,lt;
649 	BN_ULONG t1,t2;
650 
651 	if ((a == NULL) || (b == NULL))
652 		{
653 		if (a != NULL)
654 			return(-1);
655 		else if (b != NULL)
656 			return(1);
657 		else
658 			return(0);
659 		}
660 
661 	bn_check_top(a);
662 	bn_check_top(b);
663 
664 	if (a->neg != b->neg)
665 		{
666 		if (a->neg)
667 			return(-1);
668 		else	return(1);
669 		}
670 	if (a->neg == 0)
671 		{ gt=1; lt= -1; }
672 	else	{ gt= -1; lt=1; }
673 
674 	if (a->top > b->top) return(gt);
675 	if (a->top < b->top) return(lt);
676 	for (i=a->top-1; i>=0; i--)
677 		{
678 		t1=a->d[i];
679 		t2=b->d[i];
680 		if (t1 > t2) return(gt);
681 		if (t1 < t2) return(lt);
682 		}
683 	return(0);
684 	}
685 
686 int BN_set_bit(BIGNUM *a, int n)
687 	{
688 	int i,j,k;
689 
690 	i=n/BN_BITS2;
691 	j=n%BN_BITS2;
692 	if (a->top <= i)
693 		{
694 		if (bn_wexpand(a,i+1) == NULL) return(0);
695 		for(k=a->top; k<i+1; k++)
696 			a->d[k]=0;
697 		a->top=i+1;
698 		}
699 
700 	a->d[i]|=(((BN_ULONG)1)<<j);
701 	return(1);
702 	}
703 
704 int BN_clear_bit(BIGNUM *a, int n)
705 	{
706 	int i,j;
707 
708 	i=n/BN_BITS2;
709 	j=n%BN_BITS2;
710 	if (a->top <= i) return(0);
711 
712 	a->d[i]&=(~(((BN_ULONG)1)<<j));
713 	bn_fix_top(a);
714 	return(1);
715 	}
716 
717 int BN_is_bit_set(const BIGNUM *a, int n)
718 	{
719 	int i,j;
720 
721 	if (n < 0) return(0);
722 	i=n/BN_BITS2;
723 	j=n%BN_BITS2;
724 	if (a->top <= i) return(0);
725 	return((a->d[i]&(((BN_ULONG)1)<<j))?1:0);
726 	}
727 
728 int BN_mask_bits(BIGNUM *a, int n)
729 	{
730 	int b,w;
731 
732 	w=n/BN_BITS2;
733 	b=n%BN_BITS2;
734 	if (w >= a->top) return(0);
735 	if (b == 0)
736 		a->top=w;
737 	else
738 		{
739 		a->top=w+1;
740 		a->d[w]&= ~(BN_MASK2<<b);
741 		}
742 	bn_fix_top(a);
743 	return(1);
744 	}
745 
746 int bn_cmp_words(BN_ULONG *a, BN_ULONG *b, int n)
747 	{
748 	int i;
749 	BN_ULONG aa,bb;
750 
751 	aa=a[n-1];
752 	bb=b[n-1];
753 	if (aa != bb) return((aa > bb)?1:-1);
754 	for (i=n-2; i>=0; i--)
755 		{
756 		aa=a[i];
757 		bb=b[i];
758 		if (aa != bb) return((aa > bb)?1:-1);
759 		}
760 	return(0);
761 	}
762 
763