2 * Copyright 1995-2021 The OpenSSL Project Authors. All Rights Reserved.
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
10 #ifndef OSSL_CRYPTO_BN_LOCAL_H
11 # define OSSL_CRYPTO_BN_LOCAL_H
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.
18 # include <openssl/opensslconf.h>
20 # if !defined(OPENSSL_SYS_UEFI)
21 # include "crypto/bn_conf.h"
24 # include "crypto/bn.h"
25 # include "internal/cryptlib.h"
26 # include "internal/numbers.h"
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.
38 # if defined(BN_RAND_DEBUG) && !defined(BN_DEBUG)
41 # if defined(BN_RAND_DEBUG)
42 # include <openssl/rand.h>
45 # ifndef OPENSSL_SMALL_FOOTPRINT
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.
63 # if defined(OPENSSL_SYS_MSDOS) || defined(OPENSSL_SYS_WINDOWS) || \
64 defined(OPENSSL_SYS_WIN32) || defined(linux)
69 * 64-bit processor with LP64 ABI
71 # ifdef SIXTY_FOUR_BIT_LONG
72 # define BN_ULLONG unsigned long long
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"
85 * 64-bit processor other than LP64 ABI
87 # ifdef SIXTY_FOUR_BIT
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"
101 # ifdef THIRTY_TWO_BIT
103 # if defined(_WIN32) && !defined(__GNUC__)
104 # define BN_ULLONG unsigned __int64
106 # define BN_ULLONG unsigned long long
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"
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.
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.
160 # define BN_FLG_FIXED_TOP 0x10000
161 # ifdef BN_RAND_DEBUG
162 # define bn_pollute(a) \
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)); \
178 # define bn_pollute(a)
180 # define bn_check_top(a) \
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); \
192 # define bn_fix_top(a) bn_check_top(a)
194 # define bn_check_size(bn, bits) bn_wcheck_size(bn, ((bits+BN_BITS2-1))/BN_BITS2)
195 # define bn_wcheck_size(bn, words) \
197 const BIGNUM *_bnum2 = (bn); \
198 assert((words) <= (_bnum2)->dmax && \
199 (words) >= (_bnum2)->top); \
200 /* avoid unused variable warning with NDEBUG */ \
204 # else /* !BN_DEBUG */
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)
215 BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num,
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,
222 BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
226 BN_ULONG *d; /* Pointer to an array of 'BN_BITS2' bit
228 int top; /* Index of last used d +1. */
229 /* The next are internal book keeping for bn_expand. */
230 int dmax; /* Size of the d array. */
231 int neg; /* one if the number is negative */
235 /* Used for montgomery multiplication */
236 struct bn_mont_ctx_st {
237 int ri; /* number of bits in R */
238 BIGNUM RR; /* used to convert to montgomery form,
239 possibly zero-padded */
240 BIGNUM N; /* The modulus */
241 BIGNUM Ni; /* R*(1/R mod N) - N*Ni = 1 (Ni is only
242 * stored for bignum algorithm) */
243 BN_ULONG n0[2]; /* least significant word(s) of Ni; (type
244 * changed with 0.9.9, was "BN_ULONG n0;"
250 * Used for reciprocal division/mod functions It cannot be shared between
253 struct bn_recp_ctx_st {
254 BIGNUM N; /* the divisor */
255 BIGNUM Nr; /* the reciprocal */
261 /* Used for slow "generation" functions. */
263 unsigned int ver; /* To handle binary (in)compatibility */
264 void *arg; /* callback-specific data */
266 /* if (ver==1) - handles old style callbacks */
267 void (*cb_1) (int, int, void *);
268 /* if (ver==2) - new callback style */
269 int (*cb_2) (int, int, BN_GENCB *);
274 * BN_window_bits_for_exponent_size -- macro for sliding window mod_exp functions
277 * For window size 'w' (w >= 2) and a random 'b' bits exponent,
278 * the number of multiplications is a constant plus on average
280 * 2^(w-1) + (b-w)/(w+1);
282 * here 2^(w-1) is for precomputing the table (we actually need
283 * entries only for windows that have the lowest bit set), and
284 * (b-w)/(w+1) is an approximation for the expected number of
285 * w-bit windows, not counting the first one.
290 * w = 5 if 671 > b > 239
291 * w = 4 if 239 > b > 79
292 * w = 3 if 79 > b > 23
295 * (with draws in between). Very small exponents are often selected
296 * with low Hamming weight, so we use w = 1 for b <= 23.
298 # define BN_window_bits_for_exponent_size(b) \
305 * BN_mod_exp_mont_consttime is based on the assumption that the L1 data cache
306 * line width of the target processor is at least the following value.
308 # define MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH ( 64 )
309 # define MOD_EXP_CTIME_MIN_CACHE_LINE_MASK (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - 1)
312 * Window sizes optimized for fixed window size modular exponentiation
313 * algorithm (BN_mod_exp_mont_consttime). To achieve the security goals of
314 * BN_mode_exp_mont_consttime, the maximum size of the window must not exceed
315 * log_2(MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH). Window size thresholds are
316 * defined for cache line sizes of 32 and 64, cache line sizes where
317 * log_2(32)=5 and log_2(64)=6 respectively. A window size of 7 should only be
318 * used on processors that have a 128 byte or greater cache line size.
320 # if MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 64
322 # define BN_window_bits_for_ctime_exponent_size(b) \
327 # define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (6)
329 # elif MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 32
331 # define BN_window_bits_for_ctime_exponent_size(b) \
335 # define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (5)
339 /* Pentium pro 16,16,16,32,64 */
340 /* Alpha 16,16,16,16.64 */
341 # define BN_MULL_SIZE_NORMAL (16)/* 32 */
342 # define BN_MUL_RECURSIVE_SIZE_NORMAL (16)/* 32 less than */
343 # define BN_SQR_RECURSIVE_SIZE_NORMAL (16)/* 32 */
344 # define BN_MUL_LOW_RECURSIVE_SIZE_NORMAL (32)/* 32 */
345 # define BN_MONT_CTX_SET_SIZE_WORD (64)/* 32 */
348 * 2011-02-22 SMS. In various places, a size_t variable or a type cast to
349 * size_t was used to perform integer-only operations on pointers. This
350 * failed on VMS with 64-bit pointers (CC /POINTER_SIZE = 64) because size_t
351 * is still only 32 bits. What's needed in these cases is an integer type
352 * with the same size as a pointer, which size_t is not certain to be. The
353 * only fix here is VMS-specific.
355 # if defined(OPENSSL_SYS_VMS)
356 # if __INITIAL_POINTER_SIZE == 64
357 # define PTR_SIZE_INT long long
358 # else /* __INITIAL_POINTER_SIZE == 64 */
359 # define PTR_SIZE_INT int
360 # endif /* __INITIAL_POINTER_SIZE == 64 [else] */
361 # elif !defined(PTR_SIZE_INT) /* defined(OPENSSL_SYS_VMS) */
362 # define PTR_SIZE_INT size_t
363 # endif /* defined(OPENSSL_SYS_VMS) [else] */
365 # if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) && !defined(PEDANTIC)
367 * BN_UMULT_HIGH section.
368 * If the compiler doesn't support 2*N integer type, then you have to
369 * replace every N*N multiplication with 4 (N/2)*(N/2) accompanied by some
370 * shifts and additions which unavoidably results in severe performance
371 * penalties. Of course provided that the hardware is capable of producing
372 * 2*N result... That's when you normally start considering assembler
373 * implementation. However! It should be pointed out that some CPUs (e.g.,
374 * PowerPC, Alpha, and IA-64) provide *separate* instruction calculating
375 * the upper half of the product placing the result into a general
376 * purpose register. Now *if* the compiler supports inline assembler,
377 * then it's not impossible to implement the "bignum" routines (and have
378 * the compiler optimize 'em) exhibiting "native" performance in C. That's
379 * what BN_UMULT_HIGH macro is about:-) Note that more recent compilers do
380 * support 2*64 integer type, which is also used here.
382 # if defined(__SIZEOF_INT128__) && __SIZEOF_INT128__==16 && \
383 (defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG))
384 # define BN_UMULT_HIGH(a,b) (((uint128_t)(a)*(b))>>64)
385 # define BN_UMULT_LOHI(low,high,a,b) ({ \
386 uint128_t ret=(uint128_t)(a)*(b); \
387 (high)=ret>>64; (low)=ret; })
388 # elif defined(__alpha) && (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT))
391 # define BN_UMULT_HIGH(a,b) (BN_ULONG)asm("umulh %a0,%a1,%v0",(a),(b))
392 # elif defined(__GNUC__) && __GNUC__>=2
393 # define BN_UMULT_HIGH(a,b) ({ \
394 register BN_ULONG ret; \
395 asm ("umulh %1,%2,%0" \
399 # endif /* compiler */
400 # elif defined(_ARCH_PPC64) && defined(SIXTY_FOUR_BIT_LONG)
401 # if defined(__GNUC__) && __GNUC__>=2
402 # define BN_UMULT_HIGH(a,b) ({ \
403 register BN_ULONG ret; \
404 asm ("mulhdu %0,%1,%2" \
408 # endif /* compiler */
409 # elif (defined(__x86_64) || defined(__x86_64__)) && \
410 (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT))
411 # if defined(__GNUC__) && __GNUC__>=2
412 # define BN_UMULT_HIGH(a,b) ({ \
413 register BN_ULONG ret,discard; \
415 : "=a"(discard),"=d"(ret) \
419 # define BN_UMULT_LOHI(low,high,a,b) \
421 : "=a"(low),"=d"(high) \
425 # elif (defined(_M_AMD64) || defined(_M_X64)) && defined(SIXTY_FOUR_BIT)
426 # if defined(_MSC_VER) && _MSC_VER>=1400
427 unsigned __int64 __umulh(unsigned __int64 a, unsigned __int64 b);
428 unsigned __int64 _umul128(unsigned __int64 a, unsigned __int64 b,
429 unsigned __int64 *h);
430 # pragma intrinsic(__umulh,_umul128)
431 # define BN_UMULT_HIGH(a,b) __umulh((a),(b))
432 # define BN_UMULT_LOHI(low,high,a,b) ((low)=_umul128((a),(b),&(high)))
434 # elif defined(__mips) && (defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG))
435 # if defined(__GNUC__) && __GNUC__>=2
436 # define BN_UMULT_HIGH(a,b) ({ \
437 register BN_ULONG ret; \
438 asm ("dmultu %1,%2" \
440 : "r"(a), "r"(b) : "l"); \
442 # define BN_UMULT_LOHI(low,high,a,b) \
443 asm ("dmultu %2,%3" \
444 : "=l"(low),"=h"(high) \
447 # elif defined(__aarch64__) && defined(SIXTY_FOUR_BIT_LONG)
448 # if defined(__GNUC__) && __GNUC__>=2
449 # define BN_UMULT_HIGH(a,b) ({ \
450 register BN_ULONG ret; \
451 asm ("umulh %0,%1,%2" \
457 # endif /* OPENSSL_NO_ASM */
459 # ifdef BN_RAND_DEBUG
460 # define bn_clear_top2max(a) \
462 int ind = (a)->dmax - (a)->top; \
463 BN_ULONG *ftl = &(a)->d[(a)->top-1]; \
464 for (; ind != 0; ind--) \
468 # define bn_clear_top2max(a)
472 /*******************************************************************
473 * Using the long long type, has to be twice as wide as BN_ULONG...
475 # define Lw(t) (((BN_ULONG)(t))&BN_MASK2)
476 # define Hw(t) (((BN_ULONG)((t)>>BN_BITS2))&BN_MASK2)
478 # define mul_add(r,a,w,c) { \
480 t=(BN_ULLONG)w * (a) + (r) + (c); \
485 # define mul(r,a,w,c) { \
487 t=(BN_ULLONG)w * (a) + (c); \
492 # define sqr(r0,r1,a) { \
494 t=(BN_ULLONG)(a)*(a); \
499 # elif defined(BN_UMULT_LOHI)
500 # define mul_add(r,a,w,c) { \
501 BN_ULONG high,low,ret,tmp=(a); \
503 BN_UMULT_LOHI(low,high,w,tmp); \
505 (c) = (ret<(c))?1:0; \
508 (c) += (ret<low)?1:0; \
512 # define mul(r,a,w,c) { \
513 BN_ULONG high,low,ret,ta=(a); \
514 BN_UMULT_LOHI(low,high,w,ta); \
517 (c) += (ret<low)?1:0; \
521 # define sqr(r0,r1,a) { \
523 BN_UMULT_LOHI(r0,r1,tmp,tmp); \
526 # elif defined(BN_UMULT_HIGH)
527 # define mul_add(r,a,w,c) { \
528 BN_ULONG high,low,ret,tmp=(a); \
530 high= BN_UMULT_HIGH(w,tmp); \
533 (c) = (ret<(c))?1:0; \
536 (c) += (ret<low)?1:0; \
540 # define mul(r,a,w,c) { \
541 BN_ULONG high,low,ret,ta=(a); \
543 high= BN_UMULT_HIGH(w,ta); \
546 (c) += (ret<low)?1:0; \
550 # define sqr(r0,r1,a) { \
553 (r1) = BN_UMULT_HIGH(tmp,tmp); \
557 /*************************************************************
561 # define LBITS(a) ((a)&BN_MASK2l)
562 # define HBITS(a) (((a)>>BN_BITS4)&BN_MASK2l)
563 # define L2HBITS(a) (((a)<<BN_BITS4)&BN_MASK2)
565 # define LLBITS(a) ((a)&BN_MASKl)
566 # define LHBITS(a) (((a)>>BN_BITS2)&BN_MASKl)
567 # define LL2HBITS(a) ((BN_ULLONG)((a)&BN_MASKl)<<BN_BITS2)
569 # define mul64(l,h,bl,bh) \
571 BN_ULONG m,m1,lt,ht; \
579 m=(m+m1)&BN_MASK2; if (m < m1) ht+=L2HBITS((BN_ULONG)1); \
582 lt=(lt+m1)&BN_MASK2; if (lt < m1) ht++; \
587 # define sqr64(lo,ho,in) \
597 h+=(m&BN_MASK2h1)>>(BN_BITS4-1); \
598 m =(m&BN_MASK2l)<<(BN_BITS4+1); \
599 l=(l+m)&BN_MASK2; if (l < m) h++; \
604 # define mul_add(r,a,bl,bh,c) { \
610 mul64(l,h,(bl),(bh)); \
612 /* non-multiply part */ \
613 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
615 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
620 # define mul(r,a,bl,bh,c) { \
626 mul64(l,h,(bl),(bh)); \
628 /* non-multiply part */ \
629 l+=(c); if ((l&BN_MASK2) < (c)) h++; \
633 # endif /* !BN_LLONG */
635 void BN_RECP_CTX_init(BN_RECP_CTX *recp);
636 void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
638 void bn_init(BIGNUM *a);
639 void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb);
640 void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
641 void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
642 void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp);
643 void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a);
644 void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a);
645 int bn_cmp_words(const BN_ULONG *a, const BN_ULONG *b, int n);
646 int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b, int cl, int dl);
647 void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
648 int dna, int dnb, BN_ULONG *t);
649 void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b,
650 int n, int tna, int tnb, BN_ULONG *t);
651 void bn_sqr_recursive(BN_ULONG *r, const BN_ULONG *a, int n2, BN_ULONG *t);
652 void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n);
653 void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
655 BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
657 int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
658 const BN_ULONG *np, const BN_ULONG *n0, int num);
660 BIGNUM *int_bn_mod_inverse(BIGNUM *in,
661 const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx,
664 static ossl_inline BIGNUM *bn_expand(BIGNUM *a, int bits)
666 if (bits > (INT_MAX - BN_BITS2 + 1))
669 if (((bits+BN_BITS2-1)/BN_BITS2) <= (a)->dmax)
672 return bn_expand2((a),(bits+BN_BITS2-1)/BN_BITS2);
675 int ossl_bn_check_prime(const BIGNUM *w, int checks, BN_CTX *ctx,
676 int do_trial_division, BN_GENCB *cb);