crypto/bn/bn_local.h

   1 /*
   2  * Copyright 1995-2022 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
  32  * them 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_RAND_DEBUG - uses random poisoning of unused words to trip up
  35  * mismanagement of bignum internals. Enable BN_RAND_DEBUG is known to
  36  * break some of the OpenSSL tests.
  37  */
  38 # if defined(BN_RAND_DEBUG) && !defined(BN_DEBUG)
  39 #  define BN_DEBUG
  40 # endif
  41 # if defined(BN_RAND_DEBUG)
  42 #  include <openssl/rand.h>
  43 # endif
  44
  45 # ifndef OPENSSL_SMALL_FOOTPRINT
  46 #  define BN_MUL_COMBA
  47 #  define BN_SQR_COMBA
  48 #  define BN_RECURSION
  49 # endif
  50
  51 /*
  52  * This next option uses the C libraries (2 word)/(1 word) function. If it is
  53  * not defined, I use my C version (which is slower). The reason for this
  54  * flag is that when the particular C compiler library routine is used, and
  55  * the library is linked with a different compiler, the library is missing.
  56  * This mostly happens when the library is built with gcc and then linked
  57  * using normal cc.  This would be a common occurrence because gcc normally
  58  * produces code that is 2 times faster than system compilers for the big
  59  * number stuff. For machines with only one compiler (or shared libraries),
  60  * this should be on.  Again this in only really a problem on machines using
  61  * "long long's", are 32bit, and are not using my assembler code.
  62  */
  63 # if defined(OPENSSL_SYS_MSDOS) || defined(OPENSSL_SYS_WINDOWS) || \
  64     defined(OPENSSL_SYS_WIN32) || defined(linux)
  65 #  define BN_DIV2W
  66 # endif
  67
  68 /*
  69  * 64-bit processor with LP64 ABI
  70  */
  71 # ifdef SIXTY_FOUR_BIT_LONG
  72 #  define BN_ULLONG       unsigned long long
  73 #  define BN_BITS4        32
  74 #  define BN_MASK2        (0xffffffffffffffffL)
  75 #  define BN_MASK2l       (0xffffffffL)
  76 #  define BN_MASK2h       (0xffffffff00000000L)
  77 #  define BN_MASK2h1      (0xffffffff80000000L)
  78 #  define BN_DEC_CONV     (10000000000000000000UL)
  79 #  define BN_DEC_NUM      19
  80 #  define BN_DEC_FMT1     "%lu"
  81 #  define BN_DEC_FMT2     "%019lu"
  82 # endif
  83
  84 /*
  85  * 64-bit processor other than LP64 ABI
  86  */
  87 # ifdef SIXTY_FOUR_BIT
  88 #  undef BN_LLONG
  89 #  undef BN_ULLONG
  90 #  define BN_BITS4        32
  91 #  define BN_MASK2        (0xffffffffffffffffLL)
  92 #  define BN_MASK2l       (0xffffffffL)
  93 #  define BN_MASK2h       (0xffffffff00000000LL)
  94 #  define BN_MASK2h1      (0xffffffff80000000LL)
  95 #  define BN_DEC_CONV     (10000000000000000000ULL)
  96 #  define BN_DEC_NUM      19
  97 #  define BN_DEC_FMT1     "%llu"
  98 #  define BN_DEC_FMT2     "%019llu"
  99 # endif
 100
 101 # ifdef THIRTY_TWO_BIT
 102 #  ifdef BN_LLONG
 103 #   if defined(_WIN32) && !defined(__GNUC__)
 104 #    define BN_ULLONG     unsigned __int64
 105 #   else
 106 #    define BN_ULLONG     unsigned long long
 107 #   endif
 108 #  endif
 109 #  define BN_BITS4        16
 110 #  define BN_MASK2        (0xffffffffL)
 111 #  define BN_MASK2l       (0xffff)
 112 #  define BN_MASK2h1      (0xffff8000L)
 113 #  define BN_MASK2h       (0xffff0000L)
 114 #  define BN_DEC_CONV     (1000000000L)
 115 #  define BN_DEC_NUM      9
 116 #  define BN_DEC_FMT1     "%u"
 117 #  define BN_DEC_FMT2     "%09u"
 118 # endif
 119
 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_RAND_DEBUG 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  * The new BN_FLG_FIXED_TOP flag marks vectors that were not treated with
 153  * bn_correct_top, in other words such vectors are permitted to have zeros
 154  * in most significant limbs. Such vectors are used internally to achieve
 155  * execution time invariance for critical operations with private keys.
 156  * It's BN_DEBUG-only flag, because user application is not supposed to
 157  * observe it anyway. Moreover, optimizing compiler would actually remove
 158  * all operations manipulating the bit in question in non-BN_DEBUG build.
 159  */
 160 #  define BN_FLG_FIXED_TOP 0x10000
 161 #  ifdef BN_RAND_DEBUG
 162 #   define bn_pollute(a) \
 163         do { \
 164             const BIGNUM *_bnum1 = (a); \
 165             if (_bnum1->top < _bnum1->dmax) { \
 166                 unsigned char _tmp_char; \
 167                 /* We cast away const without the compiler knowing, any \
 168                  * *genuinely* constant variables that aren't mutable \
 169                  * wouldn't be constructed with top!=dmax. */ \
 170                 BN_ULONG *_not_const; \
 171                 memcpy(&_not_const, &_bnum1->d, sizeof(_not_const)); \
 172                 (void)RAND_bytes(&_tmp_char, 1); /* Debug only - safe to ignore error return */\
 173                 memset(_not_const + _bnum1->top, _tmp_char, \
 174                        sizeof(*_not_const) * (_bnum1->dmax - _bnum1->top)); \
 175             } \
 176         } while(0)
 177 #  else
 178 #   define bn_pollute(a)
 179 #  endif
 180 #  define bn_check_top(a) \
 181         do { \
 182                 const BIGNUM *_bnum2 = (a); \
 183                 if (_bnum2 != NULL) { \
 184                         int _top = _bnum2->top; \
 185                         (void)ossl_assert((_top == 0 && !_bnum2->neg) || \
 186                                   (_top && ((_bnum2->flags & BN_FLG_FIXED_TOP) \
 187                                             || _bnum2->d[_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 && \
 199                        (words) >= (_bnum2)->top); \
 200                 /* avoid unused variable warning with NDEBUG */ \
 201                 (void)(_bnum2); \
 202         } while(0)
 203
 204 # else                          /* !BN_DEBUG */
 205
 206 #  define BN_FLG_FIXED_TOP 0
 207 #  define bn_pollute(a)
 208 #  define bn_check_top(a)
 209 #  define bn_fix_top(a)           bn_correct_top(a)
 210 #  define bn_check_size(bn, bits)
 211 #  define bn_wcheck_size(bn, words)
 212
 213 # endif
 214
 215 BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num,
 216                           BN_ULONG w);
 217 BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
 218 void bn_sqr_words(BN_ULONG *rp, const BN_ULONG *ap, int num);
 219 BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d);
 220 BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
 221                       int num);
 222 BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
 223                       int num);
 224
 225 struct bignum_st {
 226     BN_ULONG *d;                /*
 227                                  * Pointer to an array of 'BN_BITS2' bit
 228                                  * chunks. These chunks are organised in
 229                                  * a least significant chunk first order.
 230                                  */
 231     int top;                    /* Index of last used d +1. */
 232     /* The next are internal book keeping for bn_expand. */
 233     int dmax;                   /* Size of the d array. */
 234     int neg;                    /* one if the number is negative */
 235     int flags;
 236 };
 237
 238 /* Used for montgomery multiplication */
 239 struct bn_mont_ctx_st {
 240     int ri;                     /* number of bits in R */
 241     BIGNUM RR;                  /* used to convert to montgomery form,
 242                                    possibly zero-padded */
 243     BIGNUM N;                   /* The modulus */
 244     BIGNUM Ni;                  /* R*(1/R mod N) - N*Ni = 1 (Ni is only
 245                                  * stored for bignum algorithm) */
 246     BN_ULONG n0[2];             /* least significant word(s) of Ni; (type
 247                                  * changed with 0.9.9, was "BN_ULONG n0;"
 248                                  * before) */
 249     int flags;
 250 };
 251
 252 /*
 253  * Used for reciprocal division/mod functions It cannot be shared between
 254  * threads
 255  */
 256 struct bn_recp_ctx_st {
 257     BIGNUM N;                   /* the divisor */
 258     BIGNUM Nr;                  /* the reciprocal */
 259     int num_bits;
 260     int shift;
 261     int flags;
 262 };
 263
 264 /* Used for slow "generation" functions. */
 265 struct bn_gencb_st {
 266     unsigned int ver;           /* To handle binary (in)compatibility */
 267     void *arg;                  /* callback-specific data */
 268     union {
 269         /* if (ver==1) - handles old style callbacks */
 270         void (*cb_1) (int, int, void *);
 271         /* if (ver==2) - new callback style */
 272         int (*cb_2) (int, int, BN_GENCB *);
 273     } cb;
 274 };
 275
 276 /*-
 277  * BN_window_bits_for_exponent_size -- macro for sliding window mod_exp functions
 278  *
 279  *
 280  * For window size 'w' (w >= 2) and a random 'b' bits exponent,
 281  * the number of multiplications is a constant plus on average
 282  *
 283  *    2^(w-1) + (b-w)/(w+1);
 284  *
 285  * here  2^(w-1)  is for precomputing the table (we actually need
 286  * entries only for windows that have the lowest bit set), and
 287  * (b-w)/(w+1)  is an approximation for the expected number of
 288  * w-bit windows, not counting the first one.
 289  *
 290  * Thus we should use
 291  *
 292  *    w >= 6  if        b > 671
 293  *     w = 5  if  671 > b > 239
 294  *     w = 4  if  239 > b >  79
 295  *     w = 3  if   79 > b >  23
 296  *    w <= 2  if   23 > b
 297  *
 298  * (with draws in between).  Very small exponents are often selected
 299  * with low Hamming weight, so we use  w = 1  for b <= 23.
 300  */
 301 # define BN_window_bits_for_exponent_size(b) \
 302                 ((b) > 671 ? 6 : \
 303                  (b) > 239 ? 5 : \
 304                  (b) >  79 ? 4 : \
 305                  (b) >  23 ? 3 : 1)
 306
 307 /*
 308  * BN_mod_exp_mont_consttime is based on the assumption that the L1 data cache
 309  * line width of the target processor is at least the following value.
 310  */
 311 # define MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH      ( 64 )
 312 # define MOD_EXP_CTIME_MIN_CACHE_LINE_MASK       (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - 1)
 313
 314 /*
 315  * Window sizes optimized for fixed window size modular exponentiation
 316  * algorithm (BN_mod_exp_mont_consttime). To achieve the security goals of
 317  * BN_mode_exp_mont_consttime, the maximum size of the window must not exceed
 318  * log_2(MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH). Window size thresholds are
 319  * defined for cache line sizes of 32 and 64, cache line sizes where
 320  * log_2(32)=5 and log_2(64)=6 respectively. A window size of 7 should only be
 321  * used on processors that have a 128 byte or greater cache line size.
 322  */
 323 # if MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 64
 324
 325 #  define BN_window_bits_for_ctime_exponent_size(b) \
 326                 ((b) > 937 ? 6 : \
 327                  (b) > 306 ? 5 : \
 328                  (b) >  89 ? 4 : \
 329                  (b) >  22 ? 3 : 1)
 330 #  define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE    (6)
 331
 332 # elif MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 32
 333
 334 #  define BN_window_bits_for_ctime_exponent_size(b) \
 335                 ((b) > 306 ? 5 : \
 336                  (b) >  89 ? 4 : \
 337                  (b) >  22 ? 3 : 1)
 338 #  define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE    (5)
 339
 340 # endif
 341
 342 /* Pentium pro 16,16,16,32,64 */
 343 /* Alpha       16,16,16,16.64 */
 344 # define BN_MULL_SIZE_NORMAL                     (16)/* 32 */
 345 # define BN_MUL_RECURSIVE_SIZE_NORMAL            (16)/* 32 less than */
 346 # define BN_SQR_RECURSIVE_SIZE_NORMAL            (16)/* 32 */
 347 # define BN_MUL_LOW_RECURSIVE_SIZE_NORMAL        (32)/* 32 */
 348 # define BN_MONT_CTX_SET_SIZE_WORD               (64)/* 32 */
 349
 350 /*
 351  * 2011-02-22 SMS. In various places, a size_t variable or a type cast to
 352  * size_t was used to perform integer-only operations on pointers.  This
 353  * failed on VMS with 64-bit pointers (CC /POINTER_SIZE = 64) because size_t
 354  * is still only 32 bits.  What's needed in these cases is an integer type
 355  * with the same size as a pointer, which size_t is not certain to be. The
 356  * only fix here is VMS-specific.
 357  */
 358 # if defined(OPENSSL_SYS_VMS)
 359 #  if __INITIAL_POINTER_SIZE == 64
 360 #   define PTR_SIZE_INT long long
 361 #  else                         /* __INITIAL_POINTER_SIZE == 64 */
 362 #   define PTR_SIZE_INT int
 363 #  endif                        /* __INITIAL_POINTER_SIZE == 64 [else] */
 364 # elif !defined(PTR_SIZE_INT)   /* defined(OPENSSL_SYS_VMS) */
 365 #  define PTR_SIZE_INT size_t
 366 # endif                         /* defined(OPENSSL_SYS_VMS) [else] */
 367
 368 # if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) && !defined(PEDANTIC)
 369 /*
 370  * BN_UMULT_HIGH section.
 371  * If the compiler doesn't support 2*N integer type, then you have to
 372  * replace every N*N multiplication with 4 (N/2)*(N/2) accompanied by some
 373  * shifts and additions which unavoidably results in severe performance
 374  * penalties. Of course provided that the hardware is capable of producing
 375  * 2*N result... That's when you normally start considering assembler
 376  * implementation. However! It should be pointed out that some CPUs (e.g.,
 377  * PowerPC, Alpha, and IA-64) provide *separate* instruction calculating
 378  * the upper half of the product placing the result into a general
 379  * purpose register. Now *if* the compiler supports inline assembler,
 380  * then it's not impossible to implement the "bignum" routines (and have
 381  * the compiler optimize 'em) exhibiting "native" performance in C. That's
 382  * what BN_UMULT_HIGH macro is about:-) Note that more recent compilers do
 383  * support 2*64 integer type, which is also used here.
 384  */
 385 #  if defined(__SIZEOF_INT128__) && __SIZEOF_INT128__==16 && \
 386       (defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG))
 387 #   define BN_UMULT_HIGH(a,b)          (((uint128_t)(a)*(b))>>64)
 388 #   define BN_UMULT_LOHI(low,high,a,b) ({       \
 389         uint128_t ret=(uint128_t)(a)*(b);   \
 390         (high)=ret>>64; (low)=ret;      })
 391 #  elif defined(__alpha) && (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT))
 392 #   if defined(__DECC)
 393 #    include <c_asm.h>
 394 #    define BN_UMULT_HIGH(a,b)   (BN_ULONG)asm("umulh %a0,%a1,%v0",(a),(b))
 395 #   elif defined(__GNUC__) && __GNUC__>=2
 396 #    define BN_UMULT_HIGH(a,b)   ({     \
 397         register BN_ULONG ret;          \
 398         asm ("umulh     %1,%2,%0"       \
 399              : "=r"(ret)                \
 400              : "r"(a), "r"(b));         \
 401         ret;                      })
 402 #   endif                       /* compiler */
 403 #  elif defined(_ARCH_PPC64) && defined(SIXTY_FOUR_BIT_LONG)
 404 #   if defined(__GNUC__) && __GNUC__>=2
 405 #    define BN_UMULT_HIGH(a,b)   ({     \
 406         register BN_ULONG ret;          \
 407         asm ("mulhdu    %0,%1,%2"       \
 408              : "=r"(ret)                \
 409              : "r"(a), "r"(b));         \
 410         ret;                      })
 411 #   endif                       /* compiler */
 412 #  elif (defined(__x86_64) || defined(__x86_64__)) && \
 413        (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT))
 414 #   if defined(__GNUC__) && __GNUC__>=2
 415 #    define BN_UMULT_HIGH(a,b)   ({     \
 416         register BN_ULONG ret,discard;  \
 417         asm ("mulq      %3"             \
 418              : "=a"(discard),"=d"(ret)  \
 419              : "a"(a), "g"(b)           \
 420              : "cc");                   \
 421         ret;                      })
 422 #    define BN_UMULT_LOHI(low,high,a,b) \
 423         asm ("mulq      %3"             \
 424                 : "=a"(low),"=d"(high)  \
 425                 : "a"(a),"g"(b)         \
 426                 : "cc");
 427 #   endif
 428 #  elif (defined(_M_AMD64) || defined(_M_X64)) && defined(SIXTY_FOUR_BIT)
 429 #   if defined(_MSC_VER) && _MSC_VER>=1400
 430 unsigned __int64 __umulh(unsigned __int64 a, unsigned __int64 b);
 431 unsigned __int64 _umul128(unsigned __int64 a, unsigned __int64 b,
 432                           unsigned __int64 *h);
 433 #    pragma intrinsic(__umulh,_umul128)
 434 #    define BN_UMULT_HIGH(a,b)           __umulh((a),(b))
 435 #    define BN_UMULT_LOHI(low,high,a,b)  ((low)=_umul128((a),(b),&(high)))
 436 #   endif
 437 #  elif defined(__mips) && (defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG))
 438 #   if defined(__GNUC__) && __GNUC__>=2
 439 #    define BN_UMULT_HIGH(a,b) ({       \
 440         register BN_ULONG ret;          \
 441         asm ("dmultu    %1,%2"          \
 442              : "=h"(ret)                \
 443              : "r"(a), "r"(b) : "l");   \
 444         ret;                    })
 445 #    define BN_UMULT_LOHI(low,high,a,b) \
 446         asm ("dmultu    %2,%3"          \
 447              : "=l"(low),"=h"(high)     \
 448              : "r"(a), "r"(b));
 449 #   endif
 450 #  elif defined(__aarch64__) && defined(SIXTY_FOUR_BIT_LONG)
 451 #   if defined(__GNUC__) && __GNUC__>=2
 452 #    define BN_UMULT_HIGH(a,b)   ({     \
 453         register BN_ULONG ret;          \
 454         asm ("umulh     %0,%1,%2"       \
 455              : "=r"(ret)                \
 456              : "r"(a), "r"(b));         \
 457         ret;                      })
 458 #   endif
 459 #  endif                        /* cpu */
 460 # endif                         /* OPENSSL_NO_ASM */
 461
 462 # ifdef BN_RAND_DEBUG
 463 #  define bn_clear_top2max(a) \
 464         { \
 465         int      ind = (a)->dmax - (a)->top; \
 466         BN_ULONG *ftl = &(a)->d[(a)->top-1]; \
 467         for (; ind != 0; ind--) \
 468                 *(++ftl) = 0x0; \
 469         }
 470 # else
 471 #  define bn_clear_top2max(a)
 472 # endif
 473
 474 # ifdef BN_LLONG
 475 /*******************************************************************
 476  * Using the long long type, has to be twice as wide as BN_ULONG...
 477  */
 478 #  define Lw(t)    (((BN_ULONG)(t))&BN_MASK2)
 479 #  define Hw(t)    (((BN_ULONG)((t)>>BN_BITS2))&BN_MASK2)
 480
 481 #  define mul_add(r,a,w,c) { \
 482         BN_ULLONG t; \
 483         t=(BN_ULLONG)w * (a) + (r) + (c); \
 484         (r)= Lw(t); \
 485         (c)= Hw(t); \
 486         }
 487
 488 #  define mul(r,a,w,c) { \
 489         BN_ULLONG t; \
 490         t=(BN_ULLONG)w * (a) + (c); \
 491         (r)= Lw(t); \
 492         (c)= Hw(t); \
 493         }
 494
 495 #  define sqr(r0,r1,a) { \
 496         BN_ULLONG t; \
 497         t=(BN_ULLONG)(a)*(a); \
 498         (r0)=Lw(t); \
 499         (r1)=Hw(t); \
 500         }
 501
 502 # elif defined(BN_UMULT_LOHI)
 503 #  define mul_add(r,a,w,c) {              \
 504         BN_ULONG high,low,ret,tmp=(a);  \
 505         ret =  (r);                     \
 506         BN_UMULT_LOHI(low,high,w,tmp);  \
 507         ret += (c);                     \
 508         (c) =  (ret<(c))?1:0;           \
 509         (c) += high;                    \
 510         ret += low;                     \
 511         (c) += (ret<low)?1:0;           \
 512         (r) =  ret;                     \
 513         }
 514
 515 #  define mul(r,a,w,c)    {               \
 516         BN_ULONG high,low,ret,ta=(a);   \
 517         BN_UMULT_LOHI(low,high,w,ta);   \
 518         ret =  low + (c);               \
 519         (c) =  high;                    \
 520         (c) += (ret<low)?1:0;           \
 521         (r) =  ret;                     \
 522         }
 523
 524 #  define sqr(r0,r1,a)    {               \
 525         BN_ULONG tmp=(a);               \
 526         BN_UMULT_LOHI(r0,r1,tmp,tmp);   \
 527         }
 528
 529 # elif defined(BN_UMULT_HIGH)
 530 #  define mul_add(r,a,w,c) {              \
 531         BN_ULONG high,low,ret,tmp=(a);  \
 532         ret =  (r);                     \
 533         high=  BN_UMULT_HIGH(w,tmp);    \
 534         ret += (c);                     \
 535         low =  (w) * tmp;               \
 536         (c) =  (ret<(c))?1:0;           \
 537         (c) += high;                    \
 538         ret += low;                     \
 539         (c) += (ret<low)?1:0;           \
 540         (r) =  ret;                     \
 541         }
 542
 543 #  define mul(r,a,w,c)    {               \
 544         BN_ULONG high,low,ret,ta=(a);   \
 545         low =  (w) * ta;                \
 546         high=  BN_UMULT_HIGH(w,ta);     \
 547         ret =  low + (c);               \
 548         (c) =  high;                    \
 549         (c) += (ret<low)?1:0;           \
 550         (r) =  ret;                     \
 551         }
 552
 553 #  define sqr(r0,r1,a)    {               \
 554         BN_ULONG tmp=(a);               \
 555         (r0) = tmp * tmp;               \
 556         (r1) = BN_UMULT_HIGH(tmp,tmp);  \
 557         }
 558
 559 # else
 560 /*************************************************************
 561  * No long long type
 562  */
 563
 564 #  define LBITS(a)        ((a)&BN_MASK2l)
 565 #  define HBITS(a)        (((a)>>BN_BITS4)&BN_MASK2l)
 566 #  define L2HBITS(a)      (((a)<<BN_BITS4)&BN_MASK2)
 567
 568 #  define LLBITS(a)       ((a)&BN_MASKl)
 569 #  define LHBITS(a)       (((a)>>BN_BITS2)&BN_MASKl)
 570 #  define LL2HBITS(a)     ((BN_ULLONG)((a)&BN_MASKl)<<BN_BITS2)
 571
 572 #  define mul64(l,h,bl,bh) \
 573         { \
 574         BN_ULONG m,m1,lt,ht; \
 575  \
 576         lt=l; \
 577         ht=h; \
 578         m =(bh)*(lt); \
 579         lt=(bl)*(lt); \
 580         m1=(bl)*(ht); \
 581         ht =(bh)*(ht); \
 582         m=(m+m1)&BN_MASK2; if (m < m1) ht+=L2HBITS((BN_ULONG)1); \
 583         ht+=HBITS(m); \
 584         m1=L2HBITS(m); \
 585         lt=(lt+m1)&BN_MASK2; if (lt < m1) ht++; \
 586         (l)=lt; \
 587         (h)=ht; \
 588         }
 589
 590 #  define sqr64(lo,ho,in) \
 591         { \
 592         BN_ULONG l,h,m; \
 593  \
 594         h=(in); \
 595         l=LBITS(h); \
 596         h=HBITS(h); \
 597         m =(l)*(h); \
 598         l*=l; \
 599         h*=h; \
 600         h+=(m&BN_MASK2h1)>>(BN_BITS4-1); \
 601         m =(m&BN_MASK2l)<<(BN_BITS4+1); \
 602         l=(l+m)&BN_MASK2; if (l < m) h++; \
 603         (lo)=l; \
 604         (ho)=h; \
 605         }
 606
 607 #  define mul_add(r,a,bl,bh,c) { \
 608         BN_ULONG l,h; \
 609  \
 610         h= (a); \
 611         l=LBITS(h); \
 612         h=HBITS(h); \
 613         mul64(l,h,(bl),(bh)); \
 614  \
 615         /* non-multiply part */ \
 616         l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
 617         (c)=(r); \
 618         l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
 619         (c)=h&BN_MASK2; \
 620         (r)=l; \
 621         }
 622
 623 #  define mul(r,a,bl,bh,c) { \
 624         BN_ULONG l,h; \
 625  \
 626         h= (a); \
 627         l=LBITS(h); \
 628         h=HBITS(h); \
 629         mul64(l,h,(bl),(bh)); \
 630  \
 631         /* non-multiply part */ \
 632         l+=(c); if ((l&BN_MASK2) < (c)) h++; \
 633         (c)=h&BN_MASK2; \
 634         (r)=l&BN_MASK2; \
 635         }
 636 # endif                         /* !BN_LLONG */
 637
 638 void BN_RECP_CTX_init(BN_RECP_CTX *recp);
 639 void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
 640
 641 void bn_init(BIGNUM *a);
 642 void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb);
 643 void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
 644 void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
 645 void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp);
 646 void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a);
 647 void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a);
 648 int bn_cmp_words(const BN_ULONG *a, const BN_ULONG *b, int n);
 649 int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b, int cl, int dl);
 650 void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
 651                       int dna, int dnb, BN_ULONG *t);
 652 void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b,
 653                            int n, int tna, int tnb, BN_ULONG *t);
 654 void bn_sqr_recursive(BN_ULONG *r, const BN_ULONG *a, int n2, BN_ULONG *t);
 655 void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n);
 656 void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
 657                           BN_ULONG *t);
 658 BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
 659                            int cl, int dl);
 660 int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
 661                 const BN_ULONG *np, const BN_ULONG *n0, int num);
 662
 663 BIGNUM *int_bn_mod_inverse(BIGNUM *in,
 664                            const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx,
 665                            int *noinv);
 666
 667 static ossl_inline BIGNUM *bn_expand(BIGNUM *a, int bits)
 668 {
 669     if (bits > (INT_MAX - BN_BITS2 + 1))
 670         return NULL;
 671
 672     if (((bits+BN_BITS2-1)/BN_BITS2) <= (a)->dmax)
 673         return a;
 674
 675     return bn_expand2((a),(bits+BN_BITS2-1)/BN_BITS2);
 676 }
 677
 678 int ossl_bn_check_prime(const BIGNUM *w, int checks, BN_CTX *ctx,
 679                         int do_trial_division, BN_GENCB *cb);
 680
 681 #endif