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      1 /* crypto/bn/bn_lcl.h */
      2 /* Copyright (C) 1995-1998 Eric Young (eay (at) cryptsoft.com)
      3  * All rights reserved.
      4  *
      5  * This package is an SSL implementation written
      6  * by Eric Young (eay (at) 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 (at) 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 (at) 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 (at) 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 (at) 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 (at) cryptsoft.com).  This product includes software written by Tim
    108  * Hudson (tjh (at) 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 (at) 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