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1 /* crypto/bn/bn_lcl.h */
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) 1998-2000 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 #ifndef HEADER_BN_LCL_H
113 #define HEADER_BN_LCL_H
114 
115 #include <openssl/bn.h>
116 
117 #ifdef  __cplusplus
118 extern "C" {
119 #endif
120 
121 
122 /*
123  * BN_window_bits_for_exponent_size -- macro for sliding window mod_exp functions
124  *
125  *
126  * For window size 'w' (w >= 2) and a random 'b' bits exponent,
127  * the number of multiplications is a constant plus on average
128  *
129  *    2^(w-1) + (b-w)/(w+1);
130  *
131  * here  2^(w-1)  is for precomputing the table (we actually need
132  * entries only for windows that have the lowest bit set), and
133  * (b-w)/(w+1)  is an approximation for the expected number of
134  * w-bit windows, not counting the first one.
135  *
136  * Thus we should use
137  *
138  *    w >= 6  if        b > 671
139  *     w = 5  if  671 > b > 239
140  *     w = 4  if  239 > b >  79
141  *     w = 3  if   79 > b >  23
142  *    w <= 2  if   23 > b
143  *
144  * (with draws in between).  Very small exponents are often selected
145  * with low Hamming weight, so we use  w = 1  for b <= 23.
146  */
147 #if 1
148 #define BN_window_bits_for_exponent_size(b) \
149 		((b) > 671 ? 6 : \
150 		 (b) > 239 ? 5 : \
151 		 (b) >  79 ? 4 : \
152 		 (b) >  23 ? 3 : 1)
153 #else
154 /* Old SSLeay/OpenSSL table.
155  * Maximum window size was 5, so this table differs for b==1024;
156  * but it coincides for other interesting values (b==160, b==512).
157  */
158 #define BN_window_bits_for_exponent_size(b) \
159 		((b) > 255 ? 5 : \
160 		 (b) > 127 ? 4 : \
161 		 (b) >  17 ? 3 : 1)
162 #endif
163 
164 
165 
166 /* BN_mod_exp_mont_conttime is based on the assumption that the
167  * L1 data cache line width of the target processor is at least
168  * the following value.
169  */
170 #define MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH	( 64 )
171 #define MOD_EXP_CTIME_MIN_CACHE_LINE_MASK	(MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - 1)
172 
173 /* Window sizes optimized for fixed window size modular exponentiation
174  * algorithm (BN_mod_exp_mont_consttime).
175  *
176  * To achieve the security goals of BN_mode_exp_mont_consttime, the
177  * maximum size of the window must not exceed
178  * log_2(MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH).
179  *
180  * Window size thresholds are defined for cache line sizes of 32 and 64,
181  * cache line sizes where log_2(32)=5 and log_2(64)=6 respectively. A
182  * window size of 7 should only be used on processors that have a 128
183  * byte or greater cache line size.
184  */
185 #if MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 64
186 
187 #  define BN_window_bits_for_ctime_exponent_size(b) \
188 		((b) > 937 ? 6 : \
189 		 (b) > 306 ? 5 : \
190 		 (b) >  89 ? 4 : \
191 		 (b) >  22 ? 3 : 1)
192 #  define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE	(6)
193 
194 #elif MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 32
195 
196 #  define BN_window_bits_for_ctime_exponent_size(b) \
197 		((b) > 306 ? 5 : \
198 		 (b) >  89 ? 4 : \
199 		 (b) >  22 ? 3 : 1)
200 #  define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE	(5)
201 
202 #endif
203 
204 
205 /* Pentium pro 16,16,16,32,64 */
206 /* Alpha       16,16,16,16.64 */
207 #define BN_MULL_SIZE_NORMAL			(16) /* 32 */
208 #define BN_MUL_RECURSIVE_SIZE_NORMAL		(16) /* 32 less than */
209 #define BN_SQR_RECURSIVE_SIZE_NORMAL		(16) /* 32 */
210 #define BN_MUL_LOW_RECURSIVE_SIZE_NORMAL	(32) /* 32 */
211 #define BN_MONT_CTX_SET_SIZE_WORD		(64) /* 32 */
212 
213 #if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) && !defined(PEDANTIC)
214 /*
215  * BN_UMULT_HIGH section.
216  *
217  * No, I'm not trying to overwhelm you when stating that the
218  * product of N-bit numbers is 2*N bits wide:-) No, I don't expect
219  * you to be impressed when I say that if the compiler doesn't
220  * support 2*N integer type, then you have to replace every N*N
221  * multiplication with 4 (N/2)*(N/2) accompanied by some shifts
222  * and additions which unavoidably results in severe performance
223  * penalties. Of course provided that the hardware is capable of
224  * producing 2*N result... That's when you normally start
225  * considering assembler implementation. However! It should be
226  * pointed out that some CPUs (most notably Alpha, PowerPC and
227  * upcoming IA-64 family:-) provide *separate* instruction
228  * calculating the upper half of the product placing the result
229  * into a general purpose register. Now *if* the compiler supports
230  * inline assembler, then it's not impossible to implement the
231  * "bignum" routines (and have the compiler optimize 'em)
232  * exhibiting "native" performance in C. That's what BN_UMULT_HIGH
233  * macro is about:-)
234  *
235  *					<appro@fy.chalmers.se>
236  */
237 # if defined(__alpha) && (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT))
238 #  if defined(__DECC)
239 #   include <c_asm.h>
240 #   define BN_UMULT_HIGH(a,b)	(BN_ULONG)asm("umulh %a0,%a1,%v0",(a),(b))
241 #  elif defined(__GNUC__) && __GNUC__>=2
242 #   define BN_UMULT_HIGH(a,b)	({	\
243 	register BN_ULONG ret;		\
244 	asm ("umulh	%1,%2,%0"	\
245 	     : "=r"(ret)		\
246 	     : "r"(a), "r"(b));		\
247 	ret;			})
248 #  endif	/* compiler */
249 # elif defined(_ARCH_PPC) && defined(__64BIT__) && defined(SIXTY_FOUR_BIT_LONG)
250 #  if defined(__GNUC__) && __GNUC__>=2
251 #   define BN_UMULT_HIGH(a,b)	({	\
252 	register BN_ULONG ret;		\
253 	asm ("mulhdu	%0,%1,%2"	\
254 	     : "=r"(ret)		\
255 	     : "r"(a), "r"(b));		\
256 	ret;			})
257 #  endif	/* compiler */
258 # elif (defined(__x86_64) || defined(__x86_64__)) && \
259        (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT))
260 #  if defined(__GNUC__) && __GNUC__>=2
261 #   define BN_UMULT_HIGH(a,b)	({	\
262 	register BN_ULONG ret,discard;	\
263 	asm ("mulq	%3"		\
264 	     : "=a"(discard),"=d"(ret)	\
265 	     : "a"(a), "g"(b)		\
266 	     : "cc");			\
267 	ret;			})
268 #   define BN_UMULT_LOHI(low,high,a,b)	\
269 	asm ("mulq	%3"		\
270 		: "=a"(low),"=d"(high)	\
271 		: "a"(a),"g"(b)		\
272 		: "cc");
273 #  endif
274 # elif (defined(_M_AMD64) || defined(_M_X64)) && defined(SIXTY_FOUR_BIT)
275 #  if defined(_MSC_VER) && _MSC_VER>=1400
276     unsigned __int64 __umulh	(unsigned __int64 a,unsigned __int64 b);
277     unsigned __int64 _umul128	(unsigned __int64 a,unsigned __int64 b,
278 				 unsigned __int64 *h);
279 #   pragma intrinsic(__umulh,_umul128)
280 #   define BN_UMULT_HIGH(a,b)		__umulh((a),(b))
281 #   define BN_UMULT_LOHI(low,high,a,b)	((low)=_umul128((a),(b),&(high)))
282 #  endif
283 # elif defined(__mips) && (defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG))
284 #  if defined(__GNUC__) && __GNUC__>=2
285 #   if __GNUC__>=4 && __GNUC_MINOR__>=4 /* "h" constraint is no more since 4.4 */
286 #     define BN_UMULT_HIGH(a,b)		 (((__uint128_t)(a)*(b))>>64)
287 #     define BN_UMULT_LOHI(low,high,a,b) ({	\
288 	__uint128_t ret=(__uint128_t)(a)*(b);	\
289 	(high)=ret>>64; (low)=ret;	 })
290 #   else
291 #     define BN_UMULT_HIGH(a,b)	({	\
292 	register BN_ULONG ret;		\
293 	asm ("dmultu	%1,%2"		\
294 	     : "=h"(ret)		\
295 	     : "r"(a), "r"(b) : "l");	\
296 	ret;			})
297 #     define BN_UMULT_LOHI(low,high,a,b)\
298 	asm ("dmultu	%2,%3"		\
299 	     : "=l"(low),"=h"(high)	\
300 	     : "r"(a), "r"(b));
301 #    endif
302 #  endif
303 # endif		/* cpu */
304 #endif		/* OPENSSL_NO_ASM */
305 
306 /*************************************************************
307  * Using the long long type
308  */
309 #define Lw(t)    (((BN_ULONG)(t))&BN_MASK2)
310 #define Hw(t)    (((BN_ULONG)((t)>>BN_BITS2))&BN_MASK2)
311 
312 #ifdef BN_DEBUG_RAND
313 #define bn_clear_top2max(a) \
314 	{ \
315 	int      ind = (a)->dmax - (a)->top; \
316 	BN_ULONG *ftl = &(a)->d[(a)->top-1]; \
317 	for (; ind != 0; ind--) \
318 		*(++ftl) = 0x0; \
319 	}
320 #else
321 #define bn_clear_top2max(a)
322 #endif
323 
324 #ifdef BN_LLONG
325 #define mul_add(r,a,w,c) { \
326 	BN_ULLONG t; \
327 	t=(BN_ULLONG)w * (a) + (r) + (c); \
328 	(r)= Lw(t); \
329 	(c)= Hw(t); \
330 	}
331 
332 #define mul(r,a,w,c) { \
333 	BN_ULLONG t; \
334 	t=(BN_ULLONG)w * (a) + (c); \
335 	(r)= Lw(t); \
336 	(c)= Hw(t); \
337 	}
338 
339 #define sqr(r0,r1,a) { \
340 	BN_ULLONG t; \
341 	t=(BN_ULLONG)(a)*(a); \
342 	(r0)=Lw(t); \
343 	(r1)=Hw(t); \
344 	}
345 
346 #elif defined(BN_UMULT_LOHI)
347 #define mul_add(r,a,w,c) {		\
348 	BN_ULONG high,low,ret,tmp=(a);	\
349 	ret =  (r);			\
350 	BN_UMULT_LOHI(low,high,w,tmp);	\
351 	ret += (c);			\
352 	(c) =  (ret<(c))?1:0;		\
353 	(c) += high;			\
354 	ret += low;			\
355 	(c) += (ret<low)?1:0;		\
356 	(r) =  ret;			\
357 	}
358 
359 #define mul(r,a,w,c)	{		\
360 	BN_ULONG high,low,ret,ta=(a);	\
361 	BN_UMULT_LOHI(low,high,w,ta);	\
362 	ret =  low + (c);		\
363 	(c) =  high;			\
364 	(c) += (ret<low)?1:0;		\
365 	(r) =  ret;			\
366 	}
367 
368 #define sqr(r0,r1,a)	{		\
369 	BN_ULONG tmp=(a);		\
370 	BN_UMULT_LOHI(r0,r1,tmp,tmp);	\
371 	}
372 
373 #elif defined(BN_UMULT_HIGH)
374 #define mul_add(r,a,w,c) {		\
375 	BN_ULONG high,low,ret,tmp=(a);	\
376 	ret =  (r);			\
377 	high=  BN_UMULT_HIGH(w,tmp);	\
378 	ret += (c);			\
379 	low =  (w) * tmp;		\
380 	(c) =  (ret<(c))?1:0;		\
381 	(c) += high;			\
382 	ret += low;			\
383 	(c) += (ret<low)?1:0;		\
384 	(r) =  ret;			\
385 	}
386 
387 #define mul(r,a,w,c)	{		\
388 	BN_ULONG high,low,ret,ta=(a);	\
389 	low =  (w) * ta;		\
390 	high=  BN_UMULT_HIGH(w,ta);	\
391 	ret =  low + (c);		\
392 	(c) =  high;			\
393 	(c) += (ret<low)?1:0;		\
394 	(r) =  ret;			\
395 	}
396 
397 #define sqr(r0,r1,a)	{		\
398 	BN_ULONG tmp=(a);		\
399 	(r0) = tmp * tmp;		\
400 	(r1) = BN_UMULT_HIGH(tmp,tmp);	\
401 	}
402 
403 #else
404 /*************************************************************
405  * No long long type
406  */
407 
408 #define LBITS(a)	((a)&BN_MASK2l)
409 #define HBITS(a)	(((a)>>BN_BITS4)&BN_MASK2l)
410 #define	L2HBITS(a)	(((a)<<BN_BITS4)&BN_MASK2)
411 
412 #define LLBITS(a)	((a)&BN_MASKl)
413 #define LHBITS(a)	(((a)>>BN_BITS2)&BN_MASKl)
414 #define	LL2HBITS(a)	((BN_ULLONG)((a)&BN_MASKl)<<BN_BITS2)
415 
416 #define mul64(l,h,bl,bh) \
417 	{ \
418 	BN_ULONG m,m1,lt,ht; \
419  \
420 	lt=l; \
421 	ht=h; \
422 	m =(bh)*(lt); \
423 	lt=(bl)*(lt); \
424 	m1=(bl)*(ht); \
425 	ht =(bh)*(ht); \
426 	m=(m+m1)&BN_MASK2; if (m < m1) ht+=L2HBITS((BN_ULONG)1); \
427 	ht+=HBITS(m); \
428 	m1=L2HBITS(m); \
429 	lt=(lt+m1)&BN_MASK2; if (lt < m1) ht++; \
430 	(l)=lt; \
431 	(h)=ht; \
432 	}
433 
434 #define sqr64(lo,ho,in) \
435 	{ \
436 	BN_ULONG l,h,m; \
437  \
438 	h=(in); \
439 	l=LBITS(h); \
440 	h=HBITS(h); \
441 	m =(l)*(h); \
442 	l*=l; \
443 	h*=h; \
444 	h+=(m&BN_MASK2h1)>>(BN_BITS4-1); \
445 	m =(m&BN_MASK2l)<<(BN_BITS4+1); \
446 	l=(l+m)&BN_MASK2; if (l < m) h++; \
447 	(lo)=l; \
448 	(ho)=h; \
449 	}
450 
451 #define mul_add(r,a,bl,bh,c) { \
452 	BN_ULONG l,h; \
453  \
454 	h= (a); \
455 	l=LBITS(h); \
456 	h=HBITS(h); \
457 	mul64(l,h,(bl),(bh)); \
458  \
459 	/* non-multiply part */ \
460 	l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
461 	(c)=(r); \
462 	l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
463 	(c)=h&BN_MASK2; \
464 	(r)=l; \
465 	}
466 
467 #define mul(r,a,bl,bh,c) { \
468 	BN_ULONG l,h; \
469  \
470 	h= (a); \
471 	l=LBITS(h); \
472 	h=HBITS(h); \
473 	mul64(l,h,(bl),(bh)); \
474  \
475 	/* non-multiply part */ \
476 	l+=(c); if ((l&BN_MASK2) < (c)) h++; \
477 	(c)=h&BN_MASK2; \
478 	(r)=l&BN_MASK2; \
479 	}
480 #endif /* !BN_LLONG */
481 
482 #if defined(OPENSSL_DOING_MAKEDEPEND) && defined(OPENSSL_FIPS)
483 #undef bn_div_words
484 #endif
485 
486 void bn_mul_normal(BN_ULONG *r,BN_ULONG *a,int na,BN_ULONG *b,int nb);
487 void bn_mul_comba8(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b);
488 void bn_mul_comba4(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b);
489 void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp);
490 void bn_sqr_comba8(BN_ULONG *r,const BN_ULONG *a);
491 void bn_sqr_comba4(BN_ULONG *r,const BN_ULONG *a);
492 int bn_cmp_words(const BN_ULONG *a,const BN_ULONG *b,int n);
493 int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b,
494 	int cl, int dl);
495 void bn_mul_recursive(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,int n2,
496 	int dna,int dnb,BN_ULONG *t);
497 void bn_mul_part_recursive(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,
498 	int n,int tna,int tnb,BN_ULONG *t);
499 void bn_sqr_recursive(BN_ULONG *r,const BN_ULONG *a, int n2, BN_ULONG *t);
500 void bn_mul_low_normal(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b, int n);
501 void bn_mul_low_recursive(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,int n2,
502 	BN_ULONG *t);
503 void bn_mul_high(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,BN_ULONG *l,int n2,
504 	BN_ULONG *t);
505 BN_ULONG bn_add_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
506 	int cl, int dl);
507 BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
508 	int cl, int dl);
509 int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp, const BN_ULONG *np,const BN_ULONG *n0, int num);
510 
511 #ifdef  __cplusplus
512 }
513 #endif
514 
515 #endif
516