release/src/router/openssl/crypto/bn/bn_lcl.h

   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