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 "internal/bn_int.h"
 116
 117 #ifdef  __cplusplus
 118 extern "C" {
 119 #endif
 120
 121 /*-
 122  * Bignum consistency macros
 123  * There is one "API" macro, bn_fix_top(), for stripping leading zeroes from
 124  * bignum data after direct manipulations on the data. There is also an
 125  * "internal" macro, bn_check_top(), for verifying that there are no leading
 126  * zeroes. Unfortunately, some auditing is required due to the fact that
 127  * bn_fix_top() has become an overabused duct-tape because bignum data is
 128  * occasionally passed around in an inconsistent state. So the following
 129  * changes have been made to sort this out;
 130  * - bn_fix_top()s implementation has been moved to bn_correct_top()
 131  * - if BN_DEBUG isn't defined, bn_fix_top() maps to bn_correct_top(), and
 132  *   bn_check_top() is as before.
 133  * - if BN_DEBUG *is* defined;
 134  *   - bn_check_top() tries to pollute unused words even if the bignum 'top' is
 135  *     consistent. (ed: only if BN_DEBUG_RAND is defined)
 136  *   - bn_fix_top() maps to bn_check_top() rather than "fixing" anything.
 137  * The idea is to have debug builds flag up inconsistent bignums when they
 138  * occur. If that occurs in a bn_fix_top(), we examine the code in question; if
 139  * the use of bn_fix_top() was appropriate (ie. it follows directly after code
 140  * that manipulates the bignum) it is converted to bn_correct_top(), and if it
 141  * was not appropriate, we convert it permanently to bn_check_top() and track
 142  * down the cause of the bug. Eventually, no internal code should be using the
 143  * bn_fix_top() macro. External applications and libraries should try this with
 144  * their own code too, both in terms of building against the openssl headers
 145  * with BN_DEBUG defined *and* linking with a version of OpenSSL built with it
 146  * defined. This not only improves external code, it provides more test
 147  * coverage for openssl's own code.
 148  */
 149
 150 # ifdef BN_DEBUG
 151
 152 /* We only need assert() when debugging */
 153 #  include <assert.h>
 154
 155 #  ifdef BN_DEBUG_RAND
 156 /* To avoid "make update" cvs wars due to BN_DEBUG, use some tricks */
 157 #   ifndef RAND_pseudo_bytes
 158 int RAND_pseudo_bytes(unsigned char *buf, int num);
 159 #    define BN_DEBUG_TRIX
 160 #   endif
 161 #   define bn_pollute(a) \
 162         do { \
 163                 const BIGNUM *_bnum1 = (a); \
 164                 if(_bnum1->top < _bnum1->dmax) { \
 165                         unsigned char _tmp_char; \
 166                         /* We cast away const without the compiler knowing, any \
 167                          * *genuinely* constant variables that aren't mutable \
 168                          * wouldn't be constructed with top!=dmax. */ \
 169                         BN_ULONG *_not_const; \
 170                         memcpy(&_not_const, &_bnum1->d, sizeof(BN_ULONG*)); \
 171                         RAND_pseudo_bytes(&_tmp_char, 1); \
 172                         memset((unsigned char *)(_not_const + _bnum1->top), _tmp_char, \
 173                                 (_bnum1->dmax - _bnum1->top) * sizeof(BN_ULONG)); \
 174                 } \
 175         } while(0)
 176 #   ifdef BN_DEBUG_TRIX
 177 #    undef RAND_pseudo_bytes
 178 #   endif
 179 #  else
 180 #   define bn_pollute(a)
 181 #  endif
 182 #  define bn_check_top(a) \
 183         do { \
 184                 const BIGNUM *_bnum2 = (a); \
 185                 if (_bnum2 != NULL) { \
 186                         assert((_bnum2->top == 0) || \
 187                                 (_bnum2->d[_bnum2->top - 1] != 0)); \
 188                         bn_pollute(_bnum2); \
 189                 } \
 190         } while(0)
 191
 192 #  define bn_fix_top(a)           bn_check_top(a)
 193
 194 #  define bn_check_size(bn, bits) bn_wcheck_size(bn, ((bits+BN_BITS2-1))/BN_BITS2)
 195 #  define bn_wcheck_size(bn, words) \
 196         do { \
 197                 const BIGNUM *_bnum2 = (bn); \
 198                 assert((words) <= (_bnum2)->dmax && (words) >= (_bnum2)->top); \
 199                 /* avoid unused variable warning with NDEBUG */ \
 200                 (void)(_bnum2); \
 201         } while(0)
 202
 203 # else                          /* !BN_DEBUG */
 204
 205 #  define bn_pollute(a)
 206 #  define bn_check_top(a)
 207 #  define bn_fix_top(a)           bn_correct_top(a)
 208 #  define bn_check_size(bn, bits)
 209 #  define bn_wcheck_size(bn, words)
 210
 211 # endif
 212
 213 BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num,
 214                           BN_ULONG w);
 215 BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
 216 void bn_sqr_words(BN_ULONG *rp, const BN_ULONG *ap, int num);
 217 BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d);
 218 BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
 219                       int num);
 220 BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
 221                       int num);
 222
 223 struct bignum_st {
 224     BN_ULONG *d;                /* Pointer to an array of 'BN_BITS2' bit
 225                                  * chunks. */
 226     int top;                    /* Index of last used d +1. */
 227     /* The next are internal book keeping for bn_expand. */
 228     int dmax;                   /* Size of the d array. */
 229     int neg;                    /* one if the number is negative */
 230     int flags;
 231 };
 232
 233 /* Used for montgomery multiplication */
 234 struct bn_mont_ctx_st {
 235     int ri;                     /* number of bits in R */
 236     BIGNUM RR;                  /* used to convert to montgomery form */
 237     BIGNUM N;                   /* The modulus */
 238     BIGNUM Ni;                  /* R*(1/R mod N) - N*Ni = 1 (Ni is only
 239                                  * stored for bignum algorithm) */
 240     BN_ULONG n0[2];             /* least significant word(s) of Ni; (type
 241                                  * changed with 0.9.9, was "BN_ULONG n0;"
 242                                  * before) */
 243     int flags;
 244 };
 245
 246 /*
 247  * Used for reciprocal division/mod functions It cannot be shared between
 248  * threads
 249  */
 250 struct bn_recp_ctx_st {
 251     BIGNUM N;                   /* the divisor */
 252     BIGNUM Nr;                  /* the reciprocal */
 253     int num_bits;
 254     int shift;
 255     int flags;
 256 };
 257
 258 /* Used for slow "generation" functions. */
 259 struct bn_gencb_st {
 260     unsigned int ver;           /* To handle binary (in)compatibility */
 261     void *arg;                  /* callback-specific data */
 262     union {
 263         /* if(ver==1) - handles old style callbacks */
 264         void (*cb_1) (int, int, void *);
 265         /* if(ver==2) - new callback style */
 266         int (*cb_2) (int, int, BN_GENCB *);
 267     } cb;
 268 };
 269
 270 /*-
 271  * BN_window_bits_for_exponent_size -- macro for sliding window mod_exp functions
 272  *
 273  *
 274  * For window size 'w' (w >= 2) and a random 'b' bits exponent,
 275  * the number of multiplications is a constant plus on average
 276  *
 277  *    2^(w-1) + (b-w)/(w+1);
 278  *
 279  * here  2^(w-1)  is for precomputing the table (we actually need
 280  * entries only for windows that have the lowest bit set), and
 281  * (b-w)/(w+1)  is an approximation for the expected number of
 282  * w-bit windows, not counting the first one.
 283  *
 284  * Thus we should use
 285  *
 286  *    w >= 6  if        b > 671
 287  *     w = 5  if  671 > b > 239
 288  *     w = 4  if  239 > b >  79
 289  *     w = 3  if   79 > b >  23
 290  *    w <= 2  if   23 > b
 291  *
 292  * (with draws in between).  Very small exponents are often selected
 293  * with low Hamming weight, so we use  w = 1  for b <= 23.
 294  */
 295 # if 1
 296 #  define BN_window_bits_for_exponent_size(b) \
 297                 ((b) > 671 ? 6 : \
 298                  (b) > 239 ? 5 : \
 299                  (b) >  79 ? 4 : \
 300                  (b) >  23 ? 3 : 1)
 301 # else
 302 /*
 303  * Old SSLeay/OpenSSL table. Maximum window size was 5, so this table differs
 304  * for b==1024; but it coincides for other interesting values (b==160,
 305  * b==512).
 306  */
 307 #  define BN_window_bits_for_exponent_size(b) \
 308                 ((b) > 255 ? 5 : \
 309                  (b) > 127 ? 4 : \
 310                  (b) >  17 ? 3 : 1)
 311 # endif
 312
 313 /*
 314  * BN_mod_exp_mont_conttime is based on the assumption that the L1 data cache
 315  * line width of the target processor is at least the following value.
 316  */
 317 # define MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH      ( 64 )
 318 # define MOD_EXP_CTIME_MIN_CACHE_LINE_MASK       (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - 1)
 319
 320 /*
 321  * Window sizes optimized for fixed window size modular exponentiation
 322  * algorithm (BN_mod_exp_mont_consttime). To achieve the security goals of
 323  * BN_mode_exp_mont_consttime, the maximum size of the window must not exceed
 324  * log_2(MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH). Window size thresholds are
 325  * defined for cache line sizes of 32 and 64, cache line sizes where
 326  * log_2(32)=5 and log_2(64)=6 respectively. A window size of 7 should only be
 327  * used on processors that have a 128 byte or greater cache line size.
 328  */
 329 # if MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 64
 330
 331 #  define BN_window_bits_for_ctime_exponent_size(b) \
 332                 ((b) > 937 ? 6 : \
 333                  (b) > 306 ? 5 : \
 334                  (b) >  89 ? 4 : \
 335                  (b) >  22 ? 3 : 1)
 336 #  define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE    (6)
 337
 338 # elif MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 32
 339
 340 #  define BN_window_bits_for_ctime_exponent_size(b) \
 341                 ((b) > 306 ? 5 : \
 342                  (b) >  89 ? 4 : \
 343                  (b) >  22 ? 3 : 1)
 344 #  define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE    (5)
 345
 346 # endif
 347
 348 /* Pentium pro 16,16,16,32,64 */
 349 /* Alpha       16,16,16,16.64 */
 350 # define BN_MULL_SIZE_NORMAL                     (16)/* 32 */
 351 # define BN_MUL_RECURSIVE_SIZE_NORMAL            (16)/* 32 less than */
 352 # define BN_SQR_RECURSIVE_SIZE_NORMAL            (16)/* 32 */
 353 # define BN_MUL_LOW_RECURSIVE_SIZE_NORMAL        (32)/* 32 */
 354 # define BN_MONT_CTX_SET_SIZE_WORD               (64)/* 32 */
 355
 356 /*
 357  * 2011-02-22 SMS. In various places, a size_t variable or a type cast to
 358  * size_t was used to perform integer-only operations on pointers.  This
 359  * failed on VMS with 64-bit pointers (CC /POINTER_SIZE = 64) because size_t
 360  * is still only 32 bits.  What's needed in these cases is an integer type
 361  * with the same size as a pointer, which size_t is not certain to be. The
 362  * only fix here is VMS-specific.
 363  */
 364 # if defined(OPENSSL_SYS_VMS)
 365 #  if __INITIAL_POINTER_SIZE == 64
 366 #   define PTR_SIZE_INT long long
 367 #  else                         /* __INITIAL_POINTER_SIZE == 64 */
 368 #   define PTR_SIZE_INT int
 369 #  endif                        /* __INITIAL_POINTER_SIZE == 64 [else] */
 370 # elif !defined(PTR_SIZE_INT)   /* defined(OPENSSL_SYS_VMS) */
 371 #  define PTR_SIZE_INT size_t
 372 # endif                         /* defined(OPENSSL_SYS_VMS) [else] */
 373
 374 # if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) && !defined(PEDANTIC)
 375 /*
 376  * BN_UMULT_HIGH section.
 377  *
 378  * No, I'm not trying to overwhelm you when stating that the
 379  * product of N-bit numbers is 2*N bits wide:-) No, I don't expect
 380  * you to be impressed when I say that if the compiler doesn't
 381  * support 2*N integer type, then you have to replace every N*N
 382  * multiplication with 4 (N/2)*(N/2) accompanied by some shifts
 383  * and additions which unavoidably results in severe performance
 384  * penalties. Of course provided that the hardware is capable of
 385  * producing 2*N result... That's when you normally start
 386  * considering assembler implementation. However! It should be
 387  * pointed out that some CPUs (most notably Alpha, PowerPC and
 388  * upcoming IA-64 family:-) provide *separate* instruction
 389  * calculating the upper half of the product placing the result
 390  * into a general purpose register. Now *if* the compiler supports
 391  * inline assembler, then it's not impossible to implement the
 392  * "bignum" routines (and have the compiler optimize 'em)
 393  * exhibiting "native" performance in C. That's what BN_UMULT_HIGH
 394  * macro is about:-)
 395  *
 396  *                                      <appro@fy.chalmers.se>
 397  */
 398 #  if defined(__alpha) && (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT))
 399 #   if defined(__DECC)
 400 #    include <c_asm.h>
 401 #    define BN_UMULT_HIGH(a,b)   (BN_ULONG)asm("umulh %a0,%a1,%v0",(a),(b))
 402 #   elif defined(__GNUC__) && __GNUC__>=2
 403 #    define BN_UMULT_HIGH(a,b)   ({      \
 404         register BN_ULONG ret;          \
 405         asm ("umulh     %1,%2,%0"       \
 406              : "=r"(ret)                \
 407              : "r"(a), "r"(b));         \
 408         ret;                    })
 409 #   endif                       /* compiler */
 410 #  elif defined(_ARCH_PPC) && defined(__64BIT__) && defined(SIXTY_FOUR_BIT_LONG)
 411 #   if defined(__GNUC__) && __GNUC__>=2
 412 #    define BN_UMULT_HIGH(a,b)   ({      \
 413         register BN_ULONG ret;          \
 414         asm ("mulhdu    %0,%1,%2"       \
 415              : "=r"(ret)                \
 416              : "r"(a), "r"(b));         \
 417         ret;                    })
 418 #   endif                       /* compiler */
 419 #  elif (defined(__x86_64) || defined(__x86_64__)) && \
 420        (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT))
 421 #   if defined(__GNUC__) && __GNUC__>=2
 422 #    define BN_UMULT_HIGH(a,b)   ({      \
 423         register BN_ULONG ret,discard;  \
 424         asm ("mulq      %3"             \
 425              : "=a"(discard),"=d"(ret)  \
 426              : "a"(a), "g"(b)           \
 427              : "cc");                   \
 428         ret;                    })
 429 #    define BN_UMULT_LOHI(low,high,a,b)  \
 430         asm ("mulq      %3"             \
 431                 : "=a"(low),"=d"(high)  \
 432                 : "a"(a),"g"(b)         \
 433                 : "cc");
 434 #   endif
 435 #  elif (defined(_M_AMD64) || defined(_M_X64)) && defined(SIXTY_FOUR_BIT)
 436 #   if defined(_MSC_VER) && _MSC_VER>=1400
 437 unsigned __int64 __umulh(unsigned __int64 a, unsigned __int64 b);
 438 unsigned __int64 _umul128(unsigned __int64 a, unsigned __int64 b,
 439                           unsigned __int64 *h);
 440 #    pragma intrinsic(__umulh,_umul128)
 441 #    define BN_UMULT_HIGH(a,b)           __umulh((a),(b))
 442 #    define BN_UMULT_LOHI(low,high,a,b)  ((low)=_umul128((a),(b),&(high)))
 443 #   endif
 444 #  elif defined(__mips) && (defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG))
 445 #   if defined(__GNUC__) && __GNUC__>=2
 446 #    if __GNUC__>=4 && __GNUC_MINOR__>=4
 447                                      /* "h" constraint is no more since 4.4 */
 448 #     define BN_UMULT_HIGH(a,b)          (((__uint128_t)(a)*(b))>>64)
 449 #     define BN_UMULT_LOHI(low,high,a,b) ({     \
 450         __uint128_t ret=(__uint128_t)(a)*(b);   \
 451         (high)=ret>>64; (low)=ret;       })
 452 #    else
 453 #     define BN_UMULT_HIGH(a,b) ({      \
 454         register BN_ULONG ret;          \
 455         asm ("dmultu    %1,%2"          \
 456              : "=h"(ret)                \
 457              : "r"(a), "r"(b) : "l");   \
 458         ret;                    })
 459 #     define BN_UMULT_LOHI(low,high,a,b)\
 460         asm ("dmultu    %2,%3"          \
 461              : "=l"(low),"=h"(high)     \
 462              : "r"(a), "r"(b));
 463 #    endif
 464 #   endif
 465 #  elif defined(__aarch64__) && defined(SIXTY_FOUR_BIT_LONG)
 466 #   if defined(__GNUC__) && __GNUC__>=2
 467 #    define BN_UMULT_HIGH(a,b)   ({      \
 468         register BN_ULONG ret;          \
 469         asm ("umulh     %0,%1,%2"       \
 470              : "=r"(ret)                \
 471              : "r"(a), "r"(b));         \
 472         ret;                    })
 473 #   endif
 474 #  endif                        /* cpu */
 475 # endif                         /* OPENSSL_NO_ASM */
 476
 477 /*************************************************************
 478  * Using the long long type
 479  */
 480 # define Lw(t)    (((BN_ULONG)(t))&BN_MASK2)
 481 # define Hw(t)    (((BN_ULONG)((t)>>BN_BITS2))&BN_MASK2)
 482
 483 # ifdef BN_DEBUG_RAND
 484 #  define bn_clear_top2max(a) \
 485         { \
 486         int      ind = (a)->dmax - (a)->top; \
 487         BN_ULONG *ftl = &(a)->d[(a)->top-1]; \
 488         for (; ind != 0; ind--) \
 489                 *(++ftl) = 0x0; \
 490         }
 491 # else
 492 #  define bn_clear_top2max(a)
 493 # endif
 494
 495 # ifdef BN_LLONG
 496 #  define mul_add(r,a,w,c) { \
 497         BN_ULLONG t; \
 498         t=(BN_ULLONG)w * (a) + (r) + (c); \
 499         (r)= Lw(t); \
 500         (c)= Hw(t); \
 501         }
 502
 503 #  define mul(r,a,w,c) { \
 504         BN_ULLONG t; \
 505         t=(BN_ULLONG)w * (a) + (c); \
 506         (r)= Lw(t); \
 507         (c)= Hw(t); \
 508         }
 509
 510 #  define sqr(r0,r1,a) { \
 511         BN_ULLONG t; \
 512         t=(BN_ULLONG)(a)*(a); \
 513         (r0)=Lw(t); \
 514         (r1)=Hw(t); \
 515         }
 516
 517 # elif defined(BN_UMULT_LOHI)
 518 #  define mul_add(r,a,w,c) {              \
 519         BN_ULONG high,low,ret,tmp=(a);  \
 520         ret =  (r);                     \
 521         BN_UMULT_LOHI(low,high,w,tmp);  \
 522         ret += (c);                     \
 523         (c) =  (ret<(c))?1:0;           \
 524         (c) += high;                    \
 525         ret += low;                     \
 526         (c) += (ret<low)?1:0;           \
 527         (r) =  ret;                     \
 528         }
 529
 530 #  define mul(r,a,w,c)    {               \
 531         BN_ULONG high,low,ret,ta=(a);   \
 532         BN_UMULT_LOHI(low,high,w,ta);   \
 533         ret =  low + (c);               \
 534         (c) =  high;                    \
 535         (c) += (ret<low)?1:0;           \
 536         (r) =  ret;                     \
 537         }
 538
 539 #  define sqr(r0,r1,a)    {               \
 540         BN_ULONG tmp=(a);               \
 541         BN_UMULT_LOHI(r0,r1,tmp,tmp);   \
 542         }
 543
 544 # elif defined(BN_UMULT_HIGH)
 545 #  define mul_add(r,a,w,c) {              \
 546         BN_ULONG high,low,ret,tmp=(a);  \
 547         ret =  (r);                     \
 548         high=  BN_UMULT_HIGH(w,tmp);    \
 549         ret += (c);                     \
 550         low =  (w) * tmp;               \
 551         (c) =  (ret<(c))?1:0;           \
 552         (c) += high;                    \
 553         ret += low;                     \
 554         (c) += (ret<low)?1:0;           \
 555         (r) =  ret;                     \
 556         }
 557
 558 #  define mul(r,a,w,c)    {               \
 559         BN_ULONG high,low,ret,ta=(a);   \
 560         low =  (w) * ta;                \
 561         high=  BN_UMULT_HIGH(w,ta);     \
 562         ret =  low + (c);               \
 563         (c) =  high;                    \
 564         (c) += (ret<low)?1:0;           \
 565         (r) =  ret;                     \
 566         }
 567
 568 #  define sqr(r0,r1,a)    {               \
 569         BN_ULONG tmp=(a);               \
 570         (r0) = tmp * tmp;               \
 571         (r1) = BN_UMULT_HIGH(tmp,tmp);  \
 572         }
 573
 574 # else
 575 /*************************************************************
 576  * No long long type
 577  */
 578
 579 #  define LBITS(a)        ((a)&BN_MASK2l)
 580 #  define HBITS(a)        (((a)>>BN_BITS4)&BN_MASK2l)
 581 #  define L2HBITS(a)      (((a)<<BN_BITS4)&BN_MASK2)
 582
 583 #  define LLBITS(a)       ((a)&BN_MASKl)
 584 #  define LHBITS(a)       (((a)>>BN_BITS2)&BN_MASKl)
 585 #  define LL2HBITS(a)     ((BN_ULLONG)((a)&BN_MASKl)<<BN_BITS2)
 586
 587 #  define mul64(l,h,bl,bh) \
 588         { \
 589         BN_ULONG m,m1,lt,ht; \
 590  \
 591         lt=l; \
 592         ht=h; \
 593         m =(bh)*(lt); \
 594         lt=(bl)*(lt); \
 595         m1=(bl)*(ht); \
 596         ht =(bh)*(ht); \
 597         m=(m+m1)&BN_MASK2; if (m < m1) ht+=L2HBITS((BN_ULONG)1); \
 598         ht+=HBITS(m); \
 599         m1=L2HBITS(m); \
 600         lt=(lt+m1)&BN_MASK2; if (lt < m1) ht++; \
 601         (l)=lt; \
 602         (h)=ht; \
 603         }
 604
 605 #  define sqr64(lo,ho,in) \
 606         { \
 607         BN_ULONG l,h,m; \
 608  \
 609         h=(in); \
 610         l=LBITS(h); \
 611         h=HBITS(h); \
 612         m =(l)*(h); \
 613         l*=l; \
 614         h*=h; \
 615         h+=(m&BN_MASK2h1)>>(BN_BITS4-1); \
 616         m =(m&BN_MASK2l)<<(BN_BITS4+1); \
 617         l=(l+m)&BN_MASK2; if (l < m) h++; \
 618         (lo)=l; \
 619         (ho)=h; \
 620         }
 621
 622 #  define mul_add(r,a,bl,bh,c) { \
 623         BN_ULONG l,h; \
 624  \
 625         h= (a); \
 626         l=LBITS(h); \
 627         h=HBITS(h); \
 628         mul64(l,h,(bl),(bh)); \
 629  \
 630         /* non-multiply part */ \
 631         l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
 632         (c)=(r); \
 633         l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
 634         (c)=h&BN_MASK2; \
 635         (r)=l; \
 636         }
 637
 638 #  define mul(r,a,bl,bh,c) { \
 639         BN_ULONG l,h; \
 640  \
 641         h= (a); \
 642         l=LBITS(h); \
 643         h=HBITS(h); \
 644         mul64(l,h,(bl),(bh)); \
 645  \
 646         /* non-multiply part */ \
 647         l+=(c); if ((l&BN_MASK2) < (c)) h++; \
 648         (c)=h&BN_MASK2; \
 649         (r)=l&BN_MASK2; \
 650         }
 651 # endif                         /* !BN_LLONG */
 652
 653 void BN_init(BIGNUM *a);
 654 void BN_RECP_CTX_init(BN_RECP_CTX *recp);
 655 void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
 656
 657 void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb);
 658 void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
 659 void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
 660 void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp);
 661 void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a);
 662 void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a);
 663 int bn_cmp_words(const BN_ULONG *a, const BN_ULONG *b, int n);
 664 int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b, int cl, int dl);
 665 void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
 666                       int dna, int dnb, BN_ULONG *t);
 667 void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b,
 668                            int n, int tna, int tnb, BN_ULONG *t);
 669 void bn_sqr_recursive(BN_ULONG *r, const BN_ULONG *a, int n2, BN_ULONG *t);
 670 void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n);
 671 void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
 672                           BN_ULONG *t);
 673 void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2,
 674                  BN_ULONG *t);
 675 BN_ULONG bn_add_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
 676                            int cl, int dl);
 677 BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
 678                            int cl, int dl);
 679 int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
 680                 const BN_ULONG *np, const BN_ULONG *n0, int num);
 681
 682 BIGNUM *int_bn_mod_inverse(BIGNUM *in,
 683                            const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx,
 684                            int *noinv);
 685
 686 int bn_probable_prime_dh(BIGNUM *rnd, int bits,
 687                          const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx);
 688 int bn_probable_prime_dh_retry(BIGNUM *rnd, int bits, BN_CTX *ctx);
 689 int bn_probable_prime_dh_coprime(BIGNUM *rnd, int bits, BN_CTX *ctx);
 690
 691 #ifdef  __cplusplus
 692 }
 693 #endif
 694
 695 #endif