crypto/bn/bn_local.h

   1 /*
   2  * Copyright 1995-2021 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 # include "internal/numbers.h"
  27
  28 /*
  29  * These preprocessor symbols control various aspects of the bignum headers
  30  * and library code. They're not defined by any "normal" configuration, as
  31  * they are intended for development and testing purposes. NB: defining all
  32  * three can be useful for debugging application code as well as openssl
  33  * itself. BN_DEBUG - turn on various debugging alterations to the bignum
  34  * code BN_DEBUG_RAND - uses random poisoning of unused words to trip up
  35  * mismanagement of bignum internals. You must also define BN_DEBUG.
  36  */
  37 /* #define BN_DEBUG */
  38 /* #define BN_DEBUG_RAND */
  39
  40 # ifndef OPENSSL_SMALL_FOOTPRINT
  41 #  define BN_MUL_COMBA
  42 #  define BN_SQR_COMBA
  43 #  define BN_RECURSION
  44 # endif
  45
  46 /*
  47  * This next option uses the C libraries (2 word)/(1 word) function. If it is
  48  * not defined, I use my C version (which is slower). The reason for this
  49  * flag is that when the particular C compiler library routine is used, and
  50  * the library is linked with a different compiler, the library is missing.
  51  * This mostly happens when the library is built with gcc and then linked
  52  * using normal cc.  This would be a common occurrence because gcc normally
  53  * produces code that is 2 times faster than system compilers for the big
  54  * number stuff. For machines with only one compiler (or shared libraries),
  55  * this should be on.  Again this in only really a problem on machines using
  56  * "long long's", are 32bit, and are not using my assembler code.
  57  */
  58 # if defined(OPENSSL_SYS_MSDOS) || defined(OPENSSL_SYS_WINDOWS) || \
  59     defined(OPENSSL_SYS_WIN32) || defined(linux)
  60 #  define BN_DIV2W
  61 # endif
  62
  63 /*
  64  * 64-bit processor with LP64 ABI
  65  */
  66 # ifdef SIXTY_FOUR_BIT_LONG
  67 #  define BN_ULLONG       unsigned long long
  68 #  define BN_BITS4        32
  69 #  define BN_MASK2        (0xffffffffffffffffL)
  70 #  define BN_MASK2l       (0xffffffffL)
  71 #  define BN_MASK2h       (0xffffffff00000000L)
  72 #  define BN_MASK2h1      (0xffffffff80000000L)
  73 #  define BN_DEC_CONV     (10000000000000000000UL)
  74 #  define BN_DEC_NUM      19
  75 #  define BN_DEC_FMT1     "%lu"
  76 #  define BN_DEC_FMT2     "%019lu"
  77 # endif
  78
  79 /*
  80  * 64-bit processor other than LP64 ABI
  81  */
  82 # ifdef SIXTY_FOUR_BIT
  83 #  undef BN_LLONG
  84 #  undef BN_ULLONG
  85 #  define BN_BITS4        32
  86 #  define BN_MASK2        (0xffffffffffffffffLL)
  87 #  define BN_MASK2l       (0xffffffffL)
  88 #  define BN_MASK2h       (0xffffffff00000000LL)
  89 #  define BN_MASK2h1      (0xffffffff80000000LL)
  90 #  define BN_DEC_CONV     (10000000000000000000ULL)
  91 #  define BN_DEC_NUM      19
  92 #  define BN_DEC_FMT1     "%llu"
  93 #  define BN_DEC_FMT2     "%019llu"
  94 # endif
  95
  96 # ifdef THIRTY_TWO_BIT
  97 #  ifdef BN_LLONG
  98 #   if defined(_WIN32) && !defined(__GNUC__)
  99 #    define BN_ULLONG     unsigned __int64
 100 #   else
 101 #    define BN_ULLONG     unsigned long long
 102 #   endif
 103 #  endif
 104 #  define BN_BITS4        16
 105 #  define BN_MASK2        (0xffffffffL)
 106 #  define BN_MASK2l       (0xffff)
 107 #  define BN_MASK2h1      (0xffff8000L)
 108 #  define BN_MASK2h       (0xffff0000L)
 109 #  define BN_DEC_CONV     (1000000000L)
 110 #  define BN_DEC_NUM      9
 111 #  define BN_DEC_FMT1     "%u"
 112 #  define BN_DEC_FMT2     "%09u"
 113 # endif
 114
 115
 116 /*-
 117  * Bignum consistency macros
 118  * There is one "API" macro, bn_fix_top(), for stripping leading zeroes from
 119  * bignum data after direct manipulations on the data. There is also an
 120  * "internal" macro, bn_check_top(), for verifying that there are no leading
 121  * zeroes. Unfortunately, some auditing is required due to the fact that
 122  * bn_fix_top() has become an overabused duct-tape because bignum data is
 123  * occasionally passed around in an inconsistent state. So the following
 124  * changes have been made to sort this out;
 125  * - bn_fix_top()s implementation has been moved to bn_correct_top()
 126  * - if BN_DEBUG isn't defined, bn_fix_top() maps to bn_correct_top(), and
 127  *   bn_check_top() is as before.
 128  * - if BN_DEBUG *is* defined;
 129  *   - bn_check_top() tries to pollute unused words even if the bignum 'top' is
 130  *     consistent. (ed: only if BN_DEBUG_RAND is defined)
 131  *   - bn_fix_top() maps to bn_check_top() rather than "fixing" anything.
 132  * The idea is to have debug builds flag up inconsistent bignums when they
 133  * occur. If that occurs in a bn_fix_top(), we examine the code in question; if
 134  * the use of bn_fix_top() was appropriate (ie. it follows directly after code
 135  * that manipulates the bignum) it is converted to bn_correct_top(), and if it
 136  * was not appropriate, we convert it permanently to bn_check_top() and track
 137  * down the cause of the bug. Eventually, no internal code should be using the
 138  * bn_fix_top() macro. External applications and libraries should try this with
 139  * their own code too, both in terms of building against the openssl headers
 140  * with BN_DEBUG defined *and* linking with a version of OpenSSL built with it
 141  * defined. This not only improves external code, it provides more test
 142  * coverage for openssl's own code.
 143  */
 144
 145 # ifdef BN_DEBUG
 146 /*
 147  * The new BN_FLG_FIXED_TOP flag marks vectors that were not treated with
 148  * bn_correct_top, in other words such vectors are permitted to have zeros
 149  * in most significant limbs. Such vectors are used internally to achieve
 150  * execution time invariance for critical operations with private keys.
 151  * It's BN_DEBUG-only flag, because user application is not supposed to
 152  * observe it anyway. Moreover, optimizing compiler would actually remove
 153  * all operations manipulating the bit in question in non-BN_DEBUG build.
 154  */
 155 #  define BN_FLG_FIXED_TOP 0x10000
 156 #  ifdef BN_DEBUG_RAND
 157 #   define bn_pollute(a) \
 158         do { \
 159             const BIGNUM *_bnum1 = (a); \
 160             if (_bnum1->top < _bnum1->dmax) { \
 161                 unsigned char _tmp_char; \
 162                 /* We cast away const without the compiler knowing, any \
 163                  * *genuinely* constant variables that aren't mutable \
 164                  * wouldn't be constructed with top!=dmax. */ \
 165                 BN_ULONG *_not_const; \
 166                 memcpy(&_not_const, &_bnum1->d, sizeof(_not_const)); \
 167                 RAND_bytes(&_tmp_char, 1); /* Debug only - safe to ignore error return */\
 168                 memset(_not_const + _bnum1->top, _tmp_char, \
 169                        sizeof(*_not_const) * (_bnum1->dmax - _bnum1->top)); \
 170             } \
 171         } while(0)
 172 #  else
 173 #   define bn_pollute(a)
 174 #  endif
 175 #  define bn_check_top(a) \
 176         do { \
 177                 const BIGNUM *_bnum2 = (a); \
 178                 if (_bnum2 != NULL) { \
 179                         int _top = _bnum2->top; \
 180                         (void)ossl_assert((_top == 0 && !_bnum2->neg) || \
 181                                   (_top && ((_bnum2->flags & BN_FLG_FIXED_TOP) \
 182                                             || _bnum2->d[_top - 1] != 0))); \
 183                         bn_pollute(_bnum2); \
 184                 } \
 185         } while(0)
 186
 187 #  define bn_fix_top(a)           bn_check_top(a)
 188
 189 #  define bn_check_size(bn, bits) bn_wcheck_size(bn, ((bits+BN_BITS2-1))/BN_BITS2)
 190 #  define bn_wcheck_size(bn, words) \
 191         do { \
 192                 const BIGNUM *_bnum2 = (bn); \
 193                 assert((words) <= (_bnum2)->dmax && \
 194                        (words) >= (_bnum2)->top); \
 195                 /* avoid unused variable warning with NDEBUG */ \
 196                 (void)(_bnum2); \
 197         } while(0)
 198
 199 # else                          /* !BN_DEBUG */
 200
 201 #  define BN_FLG_FIXED_TOP 0
 202 #  define bn_pollute(a)
 203 #  define bn_check_top(a)
 204 #  define bn_fix_top(a)           bn_correct_top(a)
 205 #  define bn_check_size(bn, bits)
 206 #  define bn_wcheck_size(bn, words)
 207
 208 # endif
 209
 210 BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num,
 211                           BN_ULONG w);
 212 BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
 213 void bn_sqr_words(BN_ULONG *rp, const BN_ULONG *ap, int num);
 214 BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d);
 215 BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
 216                       int num);
 217 BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
 218                       int num);
 219
 220 struct bignum_st {
 221     BN_ULONG *d;                /* Pointer to an array of 'BN_BITS2' bit
 222                                  * chunks. */
 223     int top;                    /* Index of last used d +1. */
 224     /* The next are internal book keeping for bn_expand. */
 225     int dmax;                   /* Size of the d array. */
 226     int neg;                    /* one if the number is negative */
 227     int flags;
 228 };
 229
 230 /* Used for montgomery multiplication */
 231 struct bn_mont_ctx_st {
 232     int ri;                     /* number of bits in R */
 233     BIGNUM RR;                  /* used to convert to montgomery form,
 234                                    possibly zero-padded */
 235     BIGNUM N;                   /* The modulus */
 236     BIGNUM Ni;                  /* R*(1/R mod N) - N*Ni = 1 (Ni is only
 237                                  * stored for bignum algorithm) */
 238     BN_ULONG n0[2];             /* least significant word(s) of Ni; (type
 239                                  * changed with 0.9.9, was "BN_ULONG n0;"
 240                                  * before) */
 241     int flags;
 242 };
 243
 244 /*
 245  * Used for reciprocal division/mod functions It cannot be shared between
 246  * threads
 247  */
 248 struct bn_recp_ctx_st {
 249     BIGNUM N;                   /* the divisor */
 250     BIGNUM Nr;                  /* the reciprocal */
 251     int num_bits;
 252     int shift;
 253     int flags;
 254 };
 255
 256 /* Used for slow "generation" functions. */
 257 struct bn_gencb_st {
 258     unsigned int ver;           /* To handle binary (in)compatibility */
 259     void *arg;                  /* callback-specific data */
 260     union {
 261         /* if (ver==1) - handles old style callbacks */
 262         void (*cb_1) (int, int, void *);
 263         /* if (ver==2) - new callback style */
 264         int (*cb_2) (int, int, BN_GENCB *);
 265     } cb;
 266 };
 267
 268 /*-
 269  * BN_window_bits_for_exponent_size -- macro for sliding window mod_exp functions
 270  *
 271  *
 272  * For window size 'w' (w >= 2) and a random 'b' bits exponent,
 273  * the number of multiplications is a constant plus on average
 274  *
 275  *    2^(w-1) + (b-w)/(w+1);
 276  *
 277  * here  2^(w-1)  is for precomputing the table (we actually need
 278  * entries only for windows that have the lowest bit set), and
 279  * (b-w)/(w+1)  is an approximation for the expected number of
 280  * w-bit windows, not counting the first one.
 281  *
 282  * Thus we should use
 283  *
 284  *    w >= 6  if        b > 671
 285  *     w = 5  if  671 > b > 239
 286  *     w = 4  if  239 > b >  79
 287  *     w = 3  if   79 > b >  23
 288  *    w <= 2  if   23 > b
 289  *
 290  * (with draws in between).  Very small exponents are often selected
 291  * with low Hamming weight, so we use  w = 1  for b <= 23.
 292  */
 293 # define BN_window_bits_for_exponent_size(b) \
 294                 ((b) > 671 ? 6 : \
 295                  (b) > 239 ? 5 : \
 296                  (b) >  79 ? 4 : \
 297                  (b) >  23 ? 3 : 1)
 298
 299 /*
 300  * BN_mod_exp_mont_consttime is based on the assumption that the L1 data cache
 301  * line width of the target processor is at least the following value.
 302  */
 303 # define MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH      ( 64 )
 304 # define MOD_EXP_CTIME_MIN_CACHE_LINE_MASK       (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - 1)
 305
 306 /*
 307  * Window sizes optimized for fixed window size modular exponentiation
 308  * algorithm (BN_mod_exp_mont_consttime). To achieve the security goals of
 309  * BN_mode_exp_mont_consttime, the maximum size of the window must not exceed
 310  * log_2(MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH). Window size thresholds are
 311  * defined for cache line sizes of 32 and 64, cache line sizes where
 312  * log_2(32)=5 and log_2(64)=6 respectively. A window size of 7 should only be
 313  * used on processors that have a 128 byte or greater cache line size.
 314  */
 315 # if MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 64
 316
 317 #  define BN_window_bits_for_ctime_exponent_size(b) \
 318                 ((b) > 937 ? 6 : \
 319                  (b) > 306 ? 5 : \
 320                  (b) >  89 ? 4 : \
 321                  (b) >  22 ? 3 : 1)
 322 #  define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE    (6)
 323
 324 # elif MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 32
 325
 326 #  define BN_window_bits_for_ctime_exponent_size(b) \
 327                 ((b) > 306 ? 5 : \
 328                  (b) >  89 ? 4 : \
 329                  (b) >  22 ? 3 : 1)
 330 #  define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE    (5)
 331
 332 # endif
 333
 334 /* Pentium pro 16,16,16,32,64 */
 335 /* Alpha       16,16,16,16.64 */
 336 # define BN_MULL_SIZE_NORMAL                     (16)/* 32 */
 337 # define BN_MUL_RECURSIVE_SIZE_NORMAL            (16)/* 32 less than */
 338 # define BN_SQR_RECURSIVE_SIZE_NORMAL            (16)/* 32 */
 339 # define BN_MUL_LOW_RECURSIVE_SIZE_NORMAL        (32)/* 32 */
 340 # define BN_MONT_CTX_SET_SIZE_WORD               (64)/* 32 */
 341
 342 /*
 343  * 2011-02-22 SMS. In various places, a size_t variable or a type cast to
 344  * size_t was used to perform integer-only operations on pointers.  This
 345  * failed on VMS with 64-bit pointers (CC /POINTER_SIZE = 64) because size_t
 346  * is still only 32 bits.  What's needed in these cases is an integer type
 347  * with the same size as a pointer, which size_t is not certain to be. The
 348  * only fix here is VMS-specific.
 349  */
 350 # if defined(OPENSSL_SYS_VMS)
 351 #  if __INITIAL_POINTER_SIZE == 64
 352 #   define PTR_SIZE_INT long long
 353 #  else                         /* __INITIAL_POINTER_SIZE == 64 */
 354 #   define PTR_SIZE_INT int
 355 #  endif                        /* __INITIAL_POINTER_SIZE == 64 [else] */
 356 # elif !defined(PTR_SIZE_INT)   /* defined(OPENSSL_SYS_VMS) */
 357 #  define PTR_SIZE_INT size_t
 358 # endif                         /* defined(OPENSSL_SYS_VMS) [else] */
 359
 360 # if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) && !defined(PEDANTIC)
 361 /*
 362  * BN_UMULT_HIGH section.
 363  * If the compiler doesn't support 2*N integer type, then you have to
 364  * replace every N*N multiplication with 4 (N/2)*(N/2) accompanied by some
 365  * shifts and additions which unavoidably results in severe performance
 366  * penalties. Of course provided that the hardware is capable of producing
 367  * 2*N result... That's when you normally start considering assembler
 368  * implementation. However! It should be pointed out that some CPUs (e.g.,
 369  * PowerPC, Alpha, and IA-64) provide *separate* instruction calculating
 370  * the upper half of the product placing the result into a general
 371  * purpose register. Now *if* the compiler supports inline assembler,
 372  * then it's not impossible to implement the "bignum" routines (and have
 373  * the compiler optimize 'em) exhibiting "native" performance in C. That's
 374  * what BN_UMULT_HIGH macro is about:-) Note that more recent compilers do
 375  * support 2*64 integer type, which is also used here.
 376  */
 377 #  if defined(__SIZEOF_INT128__) && __SIZEOF_INT128__==16 && \
 378       (defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG))
 379 #   define BN_UMULT_HIGH(a,b)          (((uint128_t)(a)*(b))>>64)
 380 #   define BN_UMULT_LOHI(low,high,a,b) ({       \
 381         uint128_t ret=(uint128_t)(a)*(b);   \
 382         (high)=ret>>64; (low)=ret;      })
 383 #  elif defined(__alpha) && (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT))
 384 #   if defined(__DECC)
 385 #    include <c_asm.h>
 386 #    define BN_UMULT_HIGH(a,b)   (BN_ULONG)asm("umulh %a0,%a1,%v0",(a),(b))
 387 #   elif defined(__GNUC__) && __GNUC__>=2
 388 #    define BN_UMULT_HIGH(a,b)   ({     \
 389         register BN_ULONG ret;          \
 390         asm ("umulh     %1,%2,%0"       \
 391              : "=r"(ret)                \
 392              : "r"(a), "r"(b));         \
 393         ret;                      })
 394 #   endif                       /* compiler */
 395 #  elif defined(_ARCH_PPC64) && defined(SIXTY_FOUR_BIT_LONG)
 396 #   if defined(__GNUC__) && __GNUC__>=2
 397 #    define BN_UMULT_HIGH(a,b)   ({     \
 398         register BN_ULONG ret;          \
 399         asm ("mulhdu    %0,%1,%2"       \
 400              : "=r"(ret)                \
 401              : "r"(a), "r"(b));         \
 402         ret;                      })
 403 #   endif                       /* compiler */
 404 #  elif (defined(__x86_64) || defined(__x86_64__)) && \
 405        (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT))
 406 #   if defined(__GNUC__) && __GNUC__>=2
 407 #    define BN_UMULT_HIGH(a,b)   ({     \
 408         register BN_ULONG ret,discard;  \
 409         asm ("mulq      %3"             \
 410              : "=a"(discard),"=d"(ret)  \
 411              : "a"(a), "g"(b)           \
 412              : "cc");                   \
 413         ret;                      })
 414 #    define BN_UMULT_LOHI(low,high,a,b) \
 415         asm ("mulq      %3"             \
 416                 : "=a"(low),"=d"(high)  \
 417                 : "a"(a),"g"(b)         \
 418                 : "cc");
 419 #   endif
 420 #  elif (defined(_M_AMD64) || defined(_M_X64)) && defined(SIXTY_FOUR_BIT)
 421 #   if defined(_MSC_VER) && _MSC_VER>=1400
 422 unsigned __int64 __umulh(unsigned __int64 a, unsigned __int64 b);
 423 unsigned __int64 _umul128(unsigned __int64 a, unsigned __int64 b,
 424                           unsigned __int64 *h);
 425 #    pragma intrinsic(__umulh,_umul128)
 426 #    define BN_UMULT_HIGH(a,b)           __umulh((a),(b))
 427 #    define BN_UMULT_LOHI(low,high,a,b)  ((low)=_umul128((a),(b),&(high)))
 428 #   endif
 429 #  elif defined(__mips) && (defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG))
 430 #   if defined(__GNUC__) && __GNUC__>=2
 431 #    define BN_UMULT_HIGH(a,b) ({       \
 432         register BN_ULONG ret;          \
 433         asm ("dmultu    %1,%2"          \
 434              : "=h"(ret)                \
 435              : "r"(a), "r"(b) : "l");   \
 436         ret;                    })
 437 #    define BN_UMULT_LOHI(low,high,a,b) \
 438         asm ("dmultu    %2,%3"          \
 439              : "=l"(low),"=h"(high)     \
 440              : "r"(a), "r"(b));
 441 #   endif
 442 #  elif defined(__aarch64__) && defined(SIXTY_FOUR_BIT_LONG)
 443 #   if defined(__GNUC__) && __GNUC__>=2
 444 #    define BN_UMULT_HIGH(a,b)   ({     \
 445         register BN_ULONG ret;          \
 446         asm ("umulh     %0,%1,%2"       \
 447              : "=r"(ret)                \
 448              : "r"(a), "r"(b));         \
 449         ret;                      })
 450 #   endif
 451 #  endif                        /* cpu */
 452 # endif                         /* OPENSSL_NO_ASM */
 453
 454 # ifdef BN_DEBUG_RAND
 455 #  define bn_clear_top2max(a) \
 456         { \
 457         int      ind = (a)->dmax - (a)->top; \
 458         BN_ULONG *ftl = &(a)->d[(a)->top-1]; \
 459         for (; ind != 0; ind--) \
 460                 *(++ftl) = 0x0; \
 461         }
 462 # else
 463 #  define bn_clear_top2max(a)
 464 # endif
 465
 466 # ifdef BN_LLONG
 467 /*******************************************************************
 468  * Using the long long type, has to be twice as wide as BN_ULONG...
 469  */
 470 #  define Lw(t)    (((BN_ULONG)(t))&BN_MASK2)
 471 #  define Hw(t)    (((BN_ULONG)((t)>>BN_BITS2))&BN_MASK2)
 472
 473 #  define mul_add(r,a,w,c) { \
 474         BN_ULLONG t; \
 475         t=(BN_ULLONG)w * (a) + (r) + (c); \
 476         (r)= Lw(t); \
 477         (c)= Hw(t); \
 478         }
 479
 480 #  define mul(r,a,w,c) { \
 481         BN_ULLONG t; \
 482         t=(BN_ULLONG)w * (a) + (c); \
 483         (r)= Lw(t); \
 484         (c)= Hw(t); \
 485         }
 486
 487 #  define sqr(r0,r1,a) { \
 488         BN_ULLONG t; \
 489         t=(BN_ULLONG)(a)*(a); \
 490         (r0)=Lw(t); \
 491         (r1)=Hw(t); \
 492         }
 493
 494 # elif defined(BN_UMULT_LOHI)
 495 #  define mul_add(r,a,w,c) {              \
 496         BN_ULONG high,low,ret,tmp=(a);  \
 497         ret =  (r);                     \
 498         BN_UMULT_LOHI(low,high,w,tmp);  \
 499         ret += (c);                     \
 500         (c) =  (ret<(c))?1:0;           \
 501         (c) += high;                    \
 502         ret += low;                     \
 503         (c) += (ret<low)?1:0;           \
 504         (r) =  ret;                     \
 505         }
 506
 507 #  define mul(r,a,w,c)    {               \
 508         BN_ULONG high,low,ret,ta=(a);   \
 509         BN_UMULT_LOHI(low,high,w,ta);   \
 510         ret =  low + (c);               \
 511         (c) =  high;                    \
 512         (c) += (ret<low)?1:0;           \
 513         (r) =  ret;                     \
 514         }
 515
 516 #  define sqr(r0,r1,a)    {               \
 517         BN_ULONG tmp=(a);               \
 518         BN_UMULT_LOHI(r0,r1,tmp,tmp);   \
 519         }
 520
 521 # elif defined(BN_UMULT_HIGH)
 522 #  define mul_add(r,a,w,c) {              \
 523         BN_ULONG high,low,ret,tmp=(a);  \
 524         ret =  (r);                     \
 525         high=  BN_UMULT_HIGH(w,tmp);    \
 526         ret += (c);                     \
 527         low =  (w) * tmp;               \
 528         (c) =  (ret<(c))?1:0;           \
 529         (c) += high;                    \
 530         ret += low;                     \
 531         (c) += (ret<low)?1:0;           \
 532         (r) =  ret;                     \
 533         }
 534
 535 #  define mul(r,a,w,c)    {               \
 536         BN_ULONG high,low,ret,ta=(a);   \
 537         low =  (w) * ta;                \
 538         high=  BN_UMULT_HIGH(w,ta);     \
 539         ret =  low + (c);               \
 540         (c) =  high;                    \
 541         (c) += (ret<low)?1:0;           \
 542         (r) =  ret;                     \
 543         }
 544
 545 #  define sqr(r0,r1,a)    {               \
 546         BN_ULONG tmp=(a);               \
 547         (r0) = tmp * tmp;               \
 548         (r1) = BN_UMULT_HIGH(tmp,tmp);  \
 549         }
 550
 551 # else
 552 /*************************************************************
 553  * No long long type
 554  */
 555
 556 #  define LBITS(a)        ((a)&BN_MASK2l)
 557 #  define HBITS(a)        (((a)>>BN_BITS4)&BN_MASK2l)
 558 #  define L2HBITS(a)      (((a)<<BN_BITS4)&BN_MASK2)
 559
 560 #  define LLBITS(a)       ((a)&BN_MASKl)
 561 #  define LHBITS(a)       (((a)>>BN_BITS2)&BN_MASKl)
 562 #  define LL2HBITS(a)     ((BN_ULLONG)((a)&BN_MASKl)<<BN_BITS2)
 563
 564 #  define mul64(l,h,bl,bh) \
 565         { \
 566         BN_ULONG m,m1,lt,ht; \
 567  \
 568         lt=l; \
 569         ht=h; \
 570         m =(bh)*(lt); \
 571         lt=(bl)*(lt); \
 572         m1=(bl)*(ht); \
 573         ht =(bh)*(ht); \
 574         m=(m+m1)&BN_MASK2; if (m < m1) ht+=L2HBITS((BN_ULONG)1); \
 575         ht+=HBITS(m); \
 576         m1=L2HBITS(m); \
 577         lt=(lt+m1)&BN_MASK2; if (lt < m1) ht++; \
 578         (l)=lt; \
 579         (h)=ht; \
 580         }
 581
 582 #  define sqr64(lo,ho,in) \
 583         { \
 584         BN_ULONG l,h,m; \
 585  \
 586         h=(in); \
 587         l=LBITS(h); \
 588         h=HBITS(h); \
 589         m =(l)*(h); \
 590         l*=l; \
 591         h*=h; \
 592         h+=(m&BN_MASK2h1)>>(BN_BITS4-1); \
 593         m =(m&BN_MASK2l)<<(BN_BITS4+1); \
 594         l=(l+m)&BN_MASK2; if (l < m) h++; \
 595         (lo)=l; \
 596         (ho)=h; \
 597         }
 598
 599 #  define mul_add(r,a,bl,bh,c) { \
 600         BN_ULONG l,h; \
 601  \
 602         h= (a); \
 603         l=LBITS(h); \
 604         h=HBITS(h); \
 605         mul64(l,h,(bl),(bh)); \
 606  \
 607         /* non-multiply part */ \
 608         l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
 609         (c)=(r); \
 610         l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
 611         (c)=h&BN_MASK2; \
 612         (r)=l; \
 613         }
 614
 615 #  define mul(r,a,bl,bh,c) { \
 616         BN_ULONG l,h; \
 617  \
 618         h= (a); \
 619         l=LBITS(h); \
 620         h=HBITS(h); \
 621         mul64(l,h,(bl),(bh)); \
 622  \
 623         /* non-multiply part */ \
 624         l+=(c); if ((l&BN_MASK2) < (c)) h++; \
 625         (c)=h&BN_MASK2; \
 626         (r)=l&BN_MASK2; \
 627         }
 628 # endif                         /* !BN_LLONG */
 629
 630 void BN_RECP_CTX_init(BN_RECP_CTX *recp);
 631 void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
 632
 633 void bn_init(BIGNUM *a);
 634 void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb);
 635 void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
 636 void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
 637 void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp);
 638 void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a);
 639 void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a);
 640 int bn_cmp_words(const BN_ULONG *a, const BN_ULONG *b, int n);
 641 int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b, int cl, int dl);
 642 void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
 643                       int dna, int dnb, BN_ULONG *t);
 644 void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b,
 645                            int n, int tna, int tnb, BN_ULONG *t);
 646 void bn_sqr_recursive(BN_ULONG *r, const BN_ULONG *a, int n2, BN_ULONG *t);
 647 void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n);
 648 void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
 649                           BN_ULONG *t);
 650 BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
 651                            int cl, int dl);
 652 int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
 653                 const BN_ULONG *np, const BN_ULONG *n0, int num);
 654
 655 BIGNUM *int_bn_mod_inverse(BIGNUM *in,
 656                            const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx,
 657                            int *noinv);
 658
 659 static ossl_inline BIGNUM *bn_expand(BIGNUM *a, int bits)
 660 {
 661     if (bits > (INT_MAX - BN_BITS2 + 1))
 662         return NULL;
 663
 664     if (((bits+BN_BITS2-1)/BN_BITS2) <= (a)->dmax)
 665         return a;
 666
 667     return bn_expand2((a),(bits+BN_BITS2-1)/BN_BITS2);
 668 }
 669
 670 int bn_check_prime_int(const BIGNUM *w, int checks, BN_CTX *ctx,
 671                       int do_trial_division, BN_GENCB *cb);
 672
 673 #endif