crypto/bn/bn_local.h

   1 /*
   2  * Copyright 1995-2019 The OpenSSL Project Authors. All Rights Reserved.
   3  *
   4  * Licensed under the Apache License 2.0 (the "License").  You may not use
   5  * this file except in compliance with the License.  You can obtain a copy
   6  * in the file LICENSE in the source distribution or at
   7  * https://www.openssl.org/source/license.html
   8  */
   9
  10 #ifndef OSSL_CRYPTO_BN_LOCAL_H
  11 # define OSSL_CRYPTO_BN_LOCAL_H
  12
  13 /*
  14  * The EDK2 build doesn't use bn_conf.h; it sets THIRTY_TWO_BIT or
  15  * SIXTY_FOUR_BIT in its own environment since it doesn't re-run our
  16  * Configure script and needs to support both 32-bit and 64-bit.
  17  */
  18 # include <openssl/opensslconf.h>
  19
  20 # if !defined(OPENSSL_SYS_UEFI)
  21 #  include "crypto/bn_conf.h"
  22 # endif
  23
  24 # include "crypto/bn.h"
  25 # include "internal/cryptlib.h"
  26
  27 /*
  28  * These preprocessor symbols control various aspects of the bignum headers
  29  * and library code. They're not defined by any "normal" configuration, as
  30  * they are intended for development and testing purposes. NB: defining all
  31  * three can be useful for debugging application code as well as openssl
  32  * itself. BN_DEBUG - turn on various debugging alterations to the bignum
  33  * code BN_DEBUG_RAND - uses random poisoning of unused words to trip up
  34  * mismanagement of bignum internals. You must also define BN_DEBUG.
  35  */
  36 /* #define BN_DEBUG */
  37 /* #define BN_DEBUG_RAND */
  38
  39 # ifndef OPENSSL_SMALL_FOOTPRINT
  40 #  define BN_MUL_COMBA
  41 #  define BN_SQR_COMBA
  42 #  define BN_RECURSION
  43 # endif
  44
  45 /*
  46  * This next option uses the C libraries (2 word)/(1 word) function. If it is
  47  * not defined, I use my C version (which is slower). The reason for this
  48  * flag is that when the particular C compiler library routine is used, and
  49  * the library is linked with a different compiler, the library is missing.
  50  * This mostly happens when the library is built with gcc and then linked
  51  * using normal cc.  This would be a common occurrence because gcc normally
  52  * produces code that is 2 times faster than system compilers for the big
  53  * number stuff. For machines with only one compiler (or shared libraries),
  54  * this should be on.  Again this in only really a problem on machines using
  55  * "long long's", are 32bit, and are not using my assembler code.
  56  */
  57 # if defined(OPENSSL_SYS_MSDOS) || defined(OPENSSL_SYS_WINDOWS) || \
  58     defined(OPENSSL_SYS_WIN32) || defined(linux)
  59 #  define BN_DIV2W
  60 # endif
  61
  62 /*
  63  * 64-bit processor with LP64 ABI
  64  */
  65 # ifdef SIXTY_FOUR_BIT_LONG
  66 #  define BN_ULLONG       unsigned long long
  67 #  define BN_BITS4        32
  68 #  define BN_MASK2        (0xffffffffffffffffL)
  69 #  define BN_MASK2l       (0xffffffffL)
  70 #  define BN_MASK2h       (0xffffffff00000000L)
  71 #  define BN_MASK2h1      (0xffffffff80000000L)
  72 #  define BN_DEC_CONV     (10000000000000000000UL)
  73 #  define BN_DEC_NUM      19
  74 #  define BN_DEC_FMT1     "%lu"
  75 #  define BN_DEC_FMT2     "%019lu"
  76 # endif
  77
  78 /*
  79  * 64-bit processor other than LP64 ABI
  80  */
  81 # ifdef SIXTY_FOUR_BIT
  82 #  undef BN_LLONG
  83 #  undef BN_ULLONG
  84 #  define BN_BITS4        32
  85 #  define BN_MASK2        (0xffffffffffffffffLL)
  86 #  define BN_MASK2l       (0xffffffffL)
  87 #  define BN_MASK2h       (0xffffffff00000000LL)
  88 #  define BN_MASK2h1      (0xffffffff80000000LL)
  89 #  define BN_DEC_CONV     (10000000000000000000ULL)
  90 #  define BN_DEC_NUM      19
  91 #  define BN_DEC_FMT1     "%llu"
  92 #  define BN_DEC_FMT2     "%019llu"
  93 # endif
  94
  95 # ifdef THIRTY_TWO_BIT
  96 #  ifdef BN_LLONG
  97 #   if defined(_WIN32) && !defined(__GNUC__)
  98 #    define BN_ULLONG     unsigned __int64
  99 #   else
 100 #    define BN_ULLONG     unsigned long long
 101 #   endif
 102 #  endif
 103 #  define BN_BITS4        16
 104 #  define BN_MASK2        (0xffffffffL)
 105 #  define BN_MASK2l       (0xffff)
 106 #  define BN_MASK2h1      (0xffff8000L)
 107 #  define BN_MASK2h       (0xffff0000L)
 108 #  define BN_DEC_CONV     (1000000000L)
 109 #  define BN_DEC_NUM      9
 110 #  define BN_DEC_FMT1     "%u"
 111 #  define BN_DEC_FMT2     "%09u"
 112 # endif
 113
 114
 115 /*-
 116  * Bignum consistency macros
 117  * There is one "API" macro, bn_fix_top(), for stripping leading zeroes from
 118  * bignum data after direct manipulations on the data. There is also an
 119  * "internal" macro, bn_check_top(), for verifying that there are no leading
 120  * zeroes. Unfortunately, some auditing is required due to the fact that
 121  * bn_fix_top() has become an overabused duct-tape because bignum data is
 122  * occasionally passed around in an inconsistent state. So the following
 123  * changes have been made to sort this out;
 124  * - bn_fix_top()s implementation has been moved to bn_correct_top()
 125  * - if BN_DEBUG isn't defined, bn_fix_top() maps to bn_correct_top(), and
 126  *   bn_check_top() is as before.
 127  * - if BN_DEBUG *is* defined;
 128  *   - bn_check_top() tries to pollute unused words even if the bignum 'top' is
 129  *     consistent. (ed: only if BN_DEBUG_RAND is defined)
 130  *   - bn_fix_top() maps to bn_check_top() rather than "fixing" anything.
 131  * The idea is to have debug builds flag up inconsistent bignums when they
 132  * occur. If that occurs in a bn_fix_top(), we examine the code in question; if
 133  * the use of bn_fix_top() was appropriate (ie. it follows directly after code
 134  * that manipulates the bignum) it is converted to bn_correct_top(), and if it
 135  * was not appropriate, we convert it permanently to bn_check_top() and track
 136  * down the cause of the bug. Eventually, no internal code should be using the
 137  * bn_fix_top() macro. External applications and libraries should try this with
 138  * their own code too, both in terms of building against the openssl headers
 139  * with BN_DEBUG defined *and* linking with a version of OpenSSL built with it
 140  * defined. This not only improves external code, it provides more test
 141  * coverage for openssl's own code.
 142  */
 143
 144 # ifdef BN_DEBUG
 145 /*
 146  * The new BN_FLG_FIXED_TOP flag marks vectors that were not treated with
 147  * bn_correct_top, in other words such vectors are permitted to have zeros
 148  * in most significant limbs. Such vectors are used internally to achieve
 149  * execution time invariance for critical operations with private keys.
 150  * It's BN_DEBUG-only flag, because user application is not supposed to
 151  * observe it anyway. Moreover, optimizing compiler would actually remove
 152  * all operations manipulating the bit in question in non-BN_DEBUG build.
 153  */
 154 #  define BN_FLG_FIXED_TOP 0x10000
 155 #  ifdef BN_DEBUG_RAND
 156 #   define bn_pollute(a) \
 157         do { \
 158             const BIGNUM *_bnum1 = (a); \
 159             if (_bnum1->top < _bnum1->dmax) { \
 160                 unsigned char _tmp_char; \
 161                 /* We cast away const without the compiler knowing, any \
 162                  * *genuinely* constant variables that aren't mutable \
 163                  * wouldn't be constructed with top!=dmax. */ \
 164                 BN_ULONG *_not_const; \
 165                 memcpy(&_not_const, &_bnum1->d, sizeof(_not_const)); \
 166                 RAND_bytes(&_tmp_char, 1); /* Debug only - safe to ignore error return */\
 167                 memset(_not_const + _bnum1->top, _tmp_char, \
 168                        sizeof(*_not_const) * (_bnum1->dmax - _bnum1->top)); \
 169             } \
 170         } while(0)
 171 #  else
 172 #   define bn_pollute(a)
 173 #  endif
 174 #  define bn_check_top(a) \
 175         do { \
 176                 const BIGNUM *_bnum2 = (a); \
 177                 if (_bnum2 != NULL) { \
 178                         int _top = _bnum2->top; \
 179                         (void)ossl_assert((_top == 0 && !_bnum2->neg) || \
 180                                   (_top && ((_bnum2->flags & BN_FLG_FIXED_TOP) \
 181                                             || _bnum2->d[_top - 1] != 0))); \
 182                         bn_pollute(_bnum2); \
 183                 } \
 184         } while(0)
 185
 186 #  define bn_fix_top(a)           bn_check_top(a)
 187
 188 #  define bn_check_size(bn, bits) bn_wcheck_size(bn, ((bits+BN_BITS2-1))/BN_BITS2)
 189 #  define bn_wcheck_size(bn, words) \
 190         do { \
 191                 const BIGNUM *_bnum2 = (bn); \
 192                 assert((words) <= (_bnum2)->dmax && \
 193                        (words) >= (_bnum2)->top); \
 194                 /* avoid unused variable warning with NDEBUG */ \
 195                 (void)(_bnum2); \
 196         } while(0)
 197
 198 # else                          /* !BN_DEBUG */
 199
 200 #  define BN_FLG_FIXED_TOP 0
 201 #  define bn_pollute(a)
 202 #  define bn_check_top(a)
 203 #  define bn_fix_top(a)           bn_correct_top(a)
 204 #  define bn_check_size(bn, bits)
 205 #  define bn_wcheck_size(bn, words)
 206
 207 # endif
 208
 209 BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num,
 210                           BN_ULONG w);
 211 BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
 212 void bn_sqr_words(BN_ULONG *rp, const BN_ULONG *ap, int num);
 213 BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d);
 214 BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
 215                       int num);
 216 BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
 217                       int num);
 218
 219 struct bignum_st {
 220     BN_ULONG *d;                /* Pointer to an array of 'BN_BITS2' bit
 221                                  * chunks. */
 222     int top;                    /* Index of last used d +1. */
 223     /* The next are internal book keeping for bn_expand. */
 224     int dmax;                   /* Size of the d array. */
 225     int neg;                    /* one if the number is negative */
 226     int flags;
 227 };
 228
 229 /* Used for montgomery multiplication */
 230 struct bn_mont_ctx_st {
 231     int ri;                     /* number of bits in R */
 232     BIGNUM RR;                  /* used to convert to montgomery form,
 233                                    possibly zero-padded */
 234     BIGNUM N;                   /* The modulus */
 235     BIGNUM Ni;                  /* R*(1/R mod N) - N*Ni = 1 (Ni is only
 236                                  * stored for bignum algorithm) */
 237     BN_ULONG n0[2];             /* least significant word(s) of Ni; (type
 238                                  * changed with 0.9.9, was "BN_ULONG n0;"
 239                                  * before) */
 240     int flags;
 241 };
 242
 243 /*
 244  * Used for reciprocal division/mod functions It cannot be shared between
 245  * threads
 246  */
 247 struct bn_recp_ctx_st {
 248     BIGNUM N;                   /* the divisor */
 249     BIGNUM Nr;                  /* the reciprocal */
 250     int num_bits;
 251     int shift;
 252     int flags;
 253 };
 254
 255 /* Used for slow "generation" functions. */
 256 struct bn_gencb_st {
 257     unsigned int ver;           /* To handle binary (in)compatibility */
 258     void *arg;                  /* callback-specific data */
 259     union {
 260         /* if (ver==1) - handles old style callbacks */
 261         void (*cb_1) (int, int, void *);
 262         /* if (ver==2) - new callback style */
 263         int (*cb_2) (int, int, BN_GENCB *);
 264     } cb;
 265 };
 266
 267 /*-
 268  * BN_window_bits_for_exponent_size -- macro for sliding window mod_exp functions
 269  *
 270  *
 271  * For window size 'w' (w >= 2) and a random 'b' bits exponent,
 272  * the number of multiplications is a constant plus on average
 273  *
 274  *    2^(w-1) + (b-w)/(w+1);
 275  *
 276  * here  2^(w-1)  is for precomputing the table (we actually need
 277  * entries only for windows that have the lowest bit set), and
 278  * (b-w)/(w+1)  is an approximation for the expected number of
 279  * w-bit windows, not counting the first one.
 280  *
 281  * Thus we should use
 282  *
 283  *    w >= 6  if        b > 671
 284  *     w = 5  if  671 > b > 239
 285  *     w = 4  if  239 > b >  79
 286  *     w = 3  if   79 > b >  23
 287  *    w <= 2  if   23 > b
 288  *
 289  * (with draws in between).  Very small exponents are often selected
 290  * with low Hamming weight, so we use  w = 1  for b <= 23.
 291  */
 292 # define BN_window_bits_for_exponent_size(b) \
 293                 ((b) > 671 ? 6 : \
 294                  (b) > 239 ? 5 : \
 295                  (b) >  79 ? 4 : \
 296                  (b) >  23 ? 3 : 1)
 297
 298 /*
 299  * BN_mod_exp_mont_consttime is based on the assumption that the L1 data cache
 300  * line width of the target processor is at least the following value.
 301  */
 302 # define MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH      ( 64 )
 303 # define MOD_EXP_CTIME_MIN_CACHE_LINE_MASK       (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - 1)
 304
 305 /*
 306  * Window sizes optimized for fixed window size modular exponentiation
 307  * algorithm (BN_mod_exp_mont_consttime). To achieve the security goals of
 308  * BN_mode_exp_mont_consttime, the maximum size of the window must not exceed
 309  * log_2(MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH). Window size thresholds are
 310  * defined for cache line sizes of 32 and 64, cache line sizes where
 311  * log_2(32)=5 and log_2(64)=6 respectively. A window size of 7 should only be
 312  * used on processors that have a 128 byte or greater cache line size.
 313  */
 314 # if MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 64
 315
 316 #  define BN_window_bits_for_ctime_exponent_size(b) \
 317                 ((b) > 937 ? 6 : \
 318                  (b) > 306 ? 5 : \
 319                  (b) >  89 ? 4 : \
 320                  (b) >  22 ? 3 : 1)
 321 #  define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE    (6)
 322
 323 # elif MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 32
 324
 325 #  define BN_window_bits_for_ctime_exponent_size(b) \
 326                 ((b) > 306 ? 5 : \
 327                  (b) >  89 ? 4 : \
 328                  (b) >  22 ? 3 : 1)
 329 #  define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE    (5)
 330
 331 # endif
 332
 333 /* Pentium pro 16,16,16,32,64 */
 334 /* Alpha       16,16,16,16.64 */
 335 # define BN_MULL_SIZE_NORMAL                     (16)/* 32 */
 336 # define BN_MUL_RECURSIVE_SIZE_NORMAL            (16)/* 32 less than */
 337 # define BN_SQR_RECURSIVE_SIZE_NORMAL            (16)/* 32 */
 338 # define BN_MUL_LOW_RECURSIVE_SIZE_NORMAL        (32)/* 32 */
 339 # define BN_MONT_CTX_SET_SIZE_WORD               (64)/* 32 */
 340
 341 /*
 342  * 2011-02-22 SMS. In various places, a size_t variable or a type cast to
 343  * size_t was used to perform integer-only operations on pointers.  This
 344  * failed on VMS with 64-bit pointers (CC /POINTER_SIZE = 64) because size_t
 345  * is still only 32 bits.  What's needed in these cases is an integer type
 346  * with the same size as a pointer, which size_t is not certain to be. The
 347  * only fix here is VMS-specific.
 348  */
 349 # if defined(OPENSSL_SYS_VMS)
 350 #  if __INITIAL_POINTER_SIZE == 64
 351 #   define PTR_SIZE_INT long long
 352 #  else                         /* __INITIAL_POINTER_SIZE == 64 */
 353 #   define PTR_SIZE_INT int
 354 #  endif                        /* __INITIAL_POINTER_SIZE == 64 [else] */
 355 # elif !defined(PTR_SIZE_INT)   /* defined(OPENSSL_SYS_VMS) */
 356 #  define PTR_SIZE_INT size_t
 357 # endif                         /* defined(OPENSSL_SYS_VMS) [else] */
 358
 359 # if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) && !defined(PEDANTIC)
 360 /*
 361  * BN_UMULT_HIGH section.
 362  * If the compiler doesn't support 2*N integer type, then you have to
 363  * replace every N*N multiplication with 4 (N/2)*(N/2) accompanied by some
 364  * shifts and additions which unavoidably results in severe performance
 365  * penalties. Of course provided that the hardware is capable of producing
 366  * 2*N result... That's when you normally start considering assembler
 367  * implementation. However! It should be pointed out that some CPUs (e.g.,
 368  * PowerPC, Alpha, and IA-64) provide *separate* instruction calculating
 369  * the upper half of the product placing the result into a general
 370  * purpose register. Now *if* the compiler supports inline assembler,
 371  * then it's not impossible to implement the "bignum" routines (and have
 372  * the compiler optimize 'em) exhibiting "native" performance in C. That's
 373  * what BN_UMULT_HIGH macro is about:-) Note that more recent compilers do
 374  * support 2*64 integer type, which is also used here.
 375  */
 376 #  if defined(__SIZEOF_INT128__) && __SIZEOF_INT128__==16 && \
 377       (defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG))
 378 #   define BN_UMULT_HIGH(a,b)          (((__uint128_t)(a)*(b))>>64)
 379 #   define BN_UMULT_LOHI(low,high,a,b) ({       \
 380         __uint128_t ret=(__uint128_t)(a)*(b);   \
 381         (high)=ret>>64; (low)=ret;      })
 382 #  elif defined(__alpha) && (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT))
 383 #   if defined(__DECC)
 384 #    include <c_asm.h>
 385 #    define BN_UMULT_HIGH(a,b)   (BN_ULONG)asm("umulh %a0,%a1,%v0",(a),(b))
 386 #   elif defined(__GNUC__) && __GNUC__>=2
 387 #    define BN_UMULT_HIGH(a,b)   ({     \
 388         register BN_ULONG ret;          \
 389         asm ("umulh     %1,%2,%0"       \
 390              : "=r"(ret)                \
 391              : "r"(a), "r"(b));         \
 392         ret;                      })
 393 #   endif                       /* compiler */
 394 #  elif defined(_ARCH_PPC64) && defined(SIXTY_FOUR_BIT_LONG)
 395 #   if defined(__GNUC__) && __GNUC__>=2
 396 #    define BN_UMULT_HIGH(a,b)   ({     \
 397         register BN_ULONG ret;          \
 398         asm ("mulhdu    %0,%1,%2"       \
 399              : "=r"(ret)                \
 400              : "r"(a), "r"(b));         \
 401         ret;                      })
 402 #   endif                       /* compiler */
 403 #  elif (defined(__x86_64) || defined(__x86_64__)) && \
 404        (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT))
 405 #   if defined(__GNUC__) && __GNUC__>=2
 406 #    define BN_UMULT_HIGH(a,b)   ({     \
 407         register BN_ULONG ret,discard;  \
 408         asm ("mulq      %3"             \
 409              : "=a"(discard),"=d"(ret)  \
 410              : "a"(a), "g"(b)           \
 411              : "cc");                   \
 412         ret;                      })
 413 #    define BN_UMULT_LOHI(low,high,a,b) \
 414         asm ("mulq      %3"             \
 415                 : "=a"(low),"=d"(high)  \
 416                 : "a"(a),"g"(b)         \
 417                 : "cc");
 418 #   endif
 419 #  elif (defined(_M_AMD64) || defined(_M_X64)) && defined(SIXTY_FOUR_BIT)
 420 #   if defined(_MSC_VER) && _MSC_VER>=1400
 421 unsigned __int64 __umulh(unsigned __int64 a, unsigned __int64 b);
 422 unsigned __int64 _umul128(unsigned __int64 a, unsigned __int64 b,
 423                           unsigned __int64 *h);
 424 #    pragma intrinsic(__umulh,_umul128)
 425 #    define BN_UMULT_HIGH(a,b)           __umulh((a),(b))
 426 #    define BN_UMULT_LOHI(low,high,a,b)  ((low)=_umul128((a),(b),&(high)))
 427 #   endif
 428 #  elif defined(__mips) && (defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG))
 429 #   if defined(__GNUC__) && __GNUC__>=2
 430 #    define BN_UMULT_HIGH(a,b) ({       \
 431         register BN_ULONG ret;          \
 432         asm ("dmultu    %1,%2"          \
 433              : "=h"(ret)                \
 434              : "r"(a), "r"(b) : "l");   \
 435         ret;                    })
 436 #    define BN_UMULT_LOHI(low,high,a,b) \
 437         asm ("dmultu    %2,%3"          \
 438              : "=l"(low),"=h"(high)     \
 439              : "r"(a), "r"(b));
 440 #   endif
 441 #  elif defined(__aarch64__) && defined(SIXTY_FOUR_BIT_LONG)
 442 #   if defined(__GNUC__) && __GNUC__>=2
 443 #    define BN_UMULT_HIGH(a,b)   ({     \
 444         register BN_ULONG ret;          \
 445         asm ("umulh     %0,%1,%2"       \
 446              : "=r"(ret)                \
 447              : "r"(a), "r"(b));         \
 448         ret;                      })
 449 #   endif
 450 #  endif                        /* cpu */
 451 # endif                         /* OPENSSL_NO_ASM */
 452
 453 # ifdef BN_DEBUG_RAND
 454 #  define bn_clear_top2max(a) \
 455         { \
 456         int      ind = (a)->dmax - (a)->top; \
 457         BN_ULONG *ftl = &(a)->d[(a)->top-1]; \
 458         for (; ind != 0; ind--) \
 459                 *(++ftl) = 0x0; \
 460         }
 461 # else
 462 #  define bn_clear_top2max(a)
 463 # endif
 464
 465 # ifdef BN_LLONG
 466 /*******************************************************************
 467  * Using the long long type, has to be twice as wide as BN_ULONG...
 468  */
 469 #  define Lw(t)    (((BN_ULONG)(t))&BN_MASK2)
 470 #  define Hw(t)    (((BN_ULONG)((t)>>BN_BITS2))&BN_MASK2)
 471
 472 #  define mul_add(r,a,w,c) { \
 473         BN_ULLONG t; \
 474         t=(BN_ULLONG)w * (a) + (r) + (c); \
 475         (r)= Lw(t); \
 476         (c)= Hw(t); \
 477         }
 478
 479 #  define mul(r,a,w,c) { \
 480         BN_ULLONG t; \
 481         t=(BN_ULLONG)w * (a) + (c); \
 482         (r)= Lw(t); \
 483         (c)= Hw(t); \
 484         }
 485
 486 #  define sqr(r0,r1,a) { \
 487         BN_ULLONG t; \
 488         t=(BN_ULLONG)(a)*(a); \
 489         (r0)=Lw(t); \
 490         (r1)=Hw(t); \
 491         }
 492
 493 # elif defined(BN_UMULT_LOHI)
 494 #  define mul_add(r,a,w,c) {              \
 495         BN_ULONG high,low,ret,tmp=(a);  \
 496         ret =  (r);                     \
 497         BN_UMULT_LOHI(low,high,w,tmp);  \
 498         ret += (c);                     \
 499         (c) =  (ret<(c))?1:0;           \
 500         (c) += high;                    \
 501         ret += low;                     \
 502         (c) += (ret<low)?1:0;           \
 503         (r) =  ret;                     \
 504         }
 505
 506 #  define mul(r,a,w,c)    {               \
 507         BN_ULONG high,low,ret,ta=(a);   \
 508         BN_UMULT_LOHI(low,high,w,ta);   \
 509         ret =  low + (c);               \
 510         (c) =  high;                    \
 511         (c) += (ret<low)?1:0;           \
 512         (r) =  ret;                     \
 513         }
 514
 515 #  define sqr(r0,r1,a)    {               \
 516         BN_ULONG tmp=(a);               \
 517         BN_UMULT_LOHI(r0,r1,tmp,tmp);   \
 518         }
 519
 520 # elif defined(BN_UMULT_HIGH)
 521 #  define mul_add(r,a,w,c) {              \
 522         BN_ULONG high,low,ret,tmp=(a);  \
 523         ret =  (r);                     \
 524         high=  BN_UMULT_HIGH(w,tmp);    \
 525         ret += (c);                     \
 526         low =  (w) * tmp;               \
 527         (c) =  (ret<(c))?1:0;           \
 528         (c) += high;                    \
 529         ret += low;                     \
 530         (c) += (ret<low)?1:0;           \
 531         (r) =  ret;                     \
 532         }
 533
 534 #  define mul(r,a,w,c)    {               \
 535         BN_ULONG high,low,ret,ta=(a);   \
 536         low =  (w) * ta;                \
 537         high=  BN_UMULT_HIGH(w,ta);     \
 538         ret =  low + (c);               \
 539         (c) =  high;                    \
 540         (c) += (ret<low)?1:0;           \
 541         (r) =  ret;                     \
 542         }
 543
 544 #  define sqr(r0,r1,a)    {               \
 545         BN_ULONG tmp=(a);               \
 546         (r0) = tmp * tmp;               \
 547         (r1) = BN_UMULT_HIGH(tmp,tmp);  \
 548         }
 549
 550 # else
 551 /*************************************************************
 552  * No long long type
 553  */
 554
 555 #  define LBITS(a)        ((a)&BN_MASK2l)
 556 #  define HBITS(a)        (((a)>>BN_BITS4)&BN_MASK2l)
 557 #  define L2HBITS(a)      (((a)<<BN_BITS4)&BN_MASK2)
 558
 559 #  define LLBITS(a)       ((a)&BN_MASKl)
 560 #  define LHBITS(a)       (((a)>>BN_BITS2)&BN_MASKl)
 561 #  define LL2HBITS(a)     ((BN_ULLONG)((a)&BN_MASKl)<<BN_BITS2)
 562
 563 #  define mul64(l,h,bl,bh) \
 564         { \
 565         BN_ULONG m,m1,lt,ht; \
 566  \
 567         lt=l; \
 568         ht=h; \
 569         m =(bh)*(lt); \
 570         lt=(bl)*(lt); \
 571         m1=(bl)*(ht); \
 572         ht =(bh)*(ht); \
 573         m=(m+m1)&BN_MASK2; if (m < m1) ht+=L2HBITS((BN_ULONG)1); \
 574         ht+=HBITS(m); \
 575         m1=L2HBITS(m); \
 576         lt=(lt+m1)&BN_MASK2; if (lt < m1) ht++; \
 577         (l)=lt; \
 578         (h)=ht; \
 579         }
 580
 581 #  define sqr64(lo,ho,in) \
 582         { \
 583         BN_ULONG l,h,m; \
 584  \
 585         h=(in); \
 586         l=LBITS(h); \
 587         h=HBITS(h); \
 588         m =(l)*(h); \
 589         l*=l; \
 590         h*=h; \
 591         h+=(m&BN_MASK2h1)>>(BN_BITS4-1); \
 592         m =(m&BN_MASK2l)<<(BN_BITS4+1); \
 593         l=(l+m)&BN_MASK2; if (l < m) h++; \
 594         (lo)=l; \
 595         (ho)=h; \
 596         }
 597
 598 #  define mul_add(r,a,bl,bh,c) { \
 599         BN_ULONG l,h; \
 600  \
 601         h= (a); \
 602         l=LBITS(h); \
 603         h=HBITS(h); \
 604         mul64(l,h,(bl),(bh)); \
 605  \
 606         /* non-multiply part */ \
 607         l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
 608         (c)=(r); \
 609         l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
 610         (c)=h&BN_MASK2; \
 611         (r)=l; \
 612         }
 613
 614 #  define mul(r,a,bl,bh,c) { \
 615         BN_ULONG l,h; \
 616  \
 617         h= (a); \
 618         l=LBITS(h); \
 619         h=HBITS(h); \
 620         mul64(l,h,(bl),(bh)); \
 621  \
 622         /* non-multiply part */ \
 623         l+=(c); if ((l&BN_MASK2) < (c)) h++; \
 624         (c)=h&BN_MASK2; \
 625         (r)=l&BN_MASK2; \
 626         }
 627 # endif                         /* !BN_LLONG */
 628
 629 void BN_RECP_CTX_init(BN_RECP_CTX *recp);
 630 void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
 631
 632 void bn_init(BIGNUM *a);
 633 void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb);
 634 void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
 635 void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
 636 void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp);
 637 void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a);
 638 void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a);
 639 int bn_cmp_words(const BN_ULONG *a, const BN_ULONG *b, int n);
 640 int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b, int cl, int dl);
 641 void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
 642                       int dna, int dnb, BN_ULONG *t);
 643 void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b,
 644                            int n, int tna, int tnb, BN_ULONG *t);
 645 void bn_sqr_recursive(BN_ULONG *r, const BN_ULONG *a, int n2, BN_ULONG *t);
 646 void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n);
 647 void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
 648                           BN_ULONG *t);
 649 BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
 650                            int cl, int dl);
 651 int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
 652                 const BN_ULONG *np, const BN_ULONG *n0, int num);
 653
 654 BIGNUM *int_bn_mod_inverse(BIGNUM *in,
 655                            const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx,
 656                            int *noinv);
 657
 658 static ossl_inline BIGNUM *bn_expand(BIGNUM *a, int bits)
 659 {
 660     if (bits > (INT_MAX - BN_BITS2 + 1))
 661         return NULL;
 662
 663     if (((bits+BN_BITS2-1)/BN_BITS2) <= (a)->dmax)
 664         return a;
 665
 666     return bn_expand2((a),(bits+BN_BITS2-1)/BN_BITS2);
 667 }
 668
 669 int bn_check_prime_int(const BIGNUM *w, int checks, BN_CTX *ctx,
 670                       int do_trial_division, BN_GENCB *cb);
 671
 672 #endif