2 * Copyright 1995-2018 The OpenSSL Project Authors. All Rights Reserved.
4 * Licensed under the OpenSSL license (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 HEADER_BN_LCL_H
11 # define HEADER_BN_LCL_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 "internal/bn_conf.h"
24 # include "internal/bn_int.h"
31 * These preprocessor symbols control various aspects of the bignum headers
32 * and library code. They're not defined by any "normal" configuration, as
33 * they are intended for development and testing purposes. NB: defining all
34 * three can be useful for debugging application code as well as openssl
35 * itself. BN_DEBUG - turn on various debugging alterations to the bignum
36 * code BN_DEBUG_RAND - uses random poisoning of unused words to trip up
37 * mismanagement of bignum internals. You must also define BN_DEBUG.
39 /* #define BN_DEBUG */
40 /* #define BN_DEBUG_RAND */
42 # ifndef OPENSSL_SMALL_FOOTPRINT
49 * This next option uses the C libraries (2 word)/(1 word) function. If it is
50 * not defined, I use my C version (which is slower). The reason for this
51 * flag is that when the particular C compiler library routine is used, and
52 * the library is linked with a different compiler, the library is missing.
53 * This mostly happens when the library is built with gcc and then linked
54 * using normal cc. This would be a common occurrence because gcc normally
55 * produces code that is 2 times faster than system compilers for the big
56 * number stuff. For machines with only one compiler (or shared libraries),
57 * this should be on. Again this in only really a problem on machines using
58 * "long long's", are 32bit, and are not using my assembler code.
60 # if defined(OPENSSL_SYS_MSDOS) || defined(OPENSSL_SYS_WINDOWS) || \
61 defined(OPENSSL_SYS_WIN32) || defined(linux)
66 * 64-bit processor with LP64 ABI
68 # ifdef SIXTY_FOUR_BIT_LONG
69 # define BN_ULLONG unsigned long long
71 # define BN_MASK2 (0xffffffffffffffffL)
72 # define BN_MASK2l (0xffffffffL)
73 # define BN_MASK2h (0xffffffff00000000L)
74 # define BN_MASK2h1 (0xffffffff80000000L)
75 # define BN_DEC_CONV (10000000000000000000UL)
76 # define BN_DEC_NUM 19
77 # define BN_DEC_FMT1 "%lu"
78 # define BN_DEC_FMT2 "%019lu"
82 * 64-bit processor other than LP64 ABI
84 # ifdef SIXTY_FOUR_BIT
88 # define BN_MASK2 (0xffffffffffffffffLL)
89 # define BN_MASK2l (0xffffffffL)
90 # define BN_MASK2h (0xffffffff00000000LL)
91 # define BN_MASK2h1 (0xffffffff80000000LL)
92 # define BN_DEC_CONV (10000000000000000000ULL)
93 # define BN_DEC_NUM 19
94 # define BN_DEC_FMT1 "%llu"
95 # define BN_DEC_FMT2 "%019llu"
98 # ifdef THIRTY_TWO_BIT
100 # if defined(_WIN32) && !defined(__GNUC__)
101 # define BN_ULLONG unsigned __int64
103 # define BN_ULLONG unsigned long long
107 # define BN_MASK2 (0xffffffffL)
108 # define BN_MASK2l (0xffff)
109 # define BN_MASK2h1 (0xffff8000L)
110 # define BN_MASK2h (0xffff0000L)
111 # define BN_DEC_CONV (1000000000L)
112 # define BN_DEC_NUM 9
113 # define BN_DEC_FMT1 "%u"
114 # define BN_DEC_FMT2 "%09u"
119 * Bignum consistency macros
120 * There is one "API" macro, bn_fix_top(), for stripping leading zeroes from
121 * bignum data after direct manipulations on the data. There is also an
122 * "internal" macro, bn_check_top(), for verifying that there are no leading
123 * zeroes. Unfortunately, some auditing is required due to the fact that
124 * bn_fix_top() has become an overabused duct-tape because bignum data is
125 * occasionally passed around in an inconsistent state. So the following
126 * changes have been made to sort this out;
127 * - bn_fix_top()s implementation has been moved to bn_correct_top()
128 * - if BN_DEBUG isn't defined, bn_fix_top() maps to bn_correct_top(), and
129 * bn_check_top() is as before.
130 * - if BN_DEBUG *is* defined;
131 * - bn_check_top() tries to pollute unused words even if the bignum 'top' is
132 * consistent. (ed: only if BN_DEBUG_RAND is defined)
133 * - bn_fix_top() maps to bn_check_top() rather than "fixing" anything.
134 * The idea is to have debug builds flag up inconsistent bignums when they
135 * occur. If that occurs in a bn_fix_top(), we examine the code in question; if
136 * the use of bn_fix_top() was appropriate (ie. it follows directly after code
137 * that manipulates the bignum) it is converted to bn_correct_top(), and if it
138 * was not appropriate, we convert it permanently to bn_check_top() and track
139 * down the cause of the bug. Eventually, no internal code should be using the
140 * bn_fix_top() macro. External applications and libraries should try this with
141 * their own code too, both in terms of building against the openssl headers
142 * with BN_DEBUG defined *and* linking with a version of OpenSSL built with it
143 * defined. This not only improves external code, it provides more test
144 * coverage for openssl's own code.
149 * The new BN_FLG_FIXED_TOP flag marks vectors that were not treated with
150 * bn_correct_top, in other words such vectors are permitted to have zeros
151 * in most significant limbs. Such vectors are used internally to achieve
152 * execution time invariance for critical operations with private keys.
153 * It's BN_DEBUG-only flag, because user application is not supposed to
154 * observe it anyway. Moreover, optimizing compiler would actually remove
155 * all operations manipulating the bit in question in non-BN_DEBUG build.
157 # define BN_FLG_FIXED_TOP 0x10000
158 # ifdef BN_DEBUG_RAND
159 /* To avoid "make update" cvs wars due to BN_DEBUG, use some tricks */
161 int RAND_bytes(unsigned char *buf, int num);
162 # define BN_DEBUG_TRIX
164 # define bn_pollute(a) \
166 const BIGNUM *_bnum1 = (a); \
167 if (_bnum1->top < _bnum1->dmax) { \
168 unsigned char _tmp_char; \
169 /* We cast away const without the compiler knowing, any \
170 * *genuinely* constant variables that aren't mutable \
171 * wouldn't be constructed with top!=dmax. */ \
172 BN_ULONG *_not_const; \
173 memcpy(&_not_const, &_bnum1->d, sizeof(_not_const)); \
174 RAND_bytes(&_tmp_char, 1); /* Debug only - safe to ignore error return */\
175 memset(_not_const + _bnum1->top, _tmp_char, \
176 sizeof(*_not_const) * (_bnum1->dmax - _bnum1->top)); \
179 # ifdef BN_DEBUG_TRIX
183 # define bn_pollute(a)
185 # define bn_check_top(a) \
187 const BIGNUM *_bnum2 = (a); \
188 if (_bnum2 != NULL) { \
189 int _top = _bnum2->top; \
190 OPENSSL_assert((_top == 0 && !_bnum2->neg) || \
191 (_top && ((_bnum2->flags & BN_FLG_FIXED_TOP) \
192 || _bnum2->d[_top - 1] != 0))); \
193 bn_pollute(_bnum2); \
197 # define bn_fix_top(a) bn_check_top(a)
199 # define bn_check_size(bn, bits) bn_wcheck_size(bn, ((bits+BN_BITS2-1))/BN_BITS2)
200 # define bn_wcheck_size(bn, words) \
202 const BIGNUM *_bnum2 = (bn); \
203 OPENSSL_assert((words) <= (_bnum2)->dmax && \
204 (words) >= (_bnum2)->top); \
205 /* avoid unused variable warning with NDEBUG */ \
209 # else /* !BN_DEBUG */
211 # define BN_FLG_FIXED_TOP 0
212 # define bn_pollute(a)
213 # define bn_check_top(a)
214 # define bn_fix_top(a) bn_correct_top(a)
215 # define bn_check_size(bn, bits)
216 # define bn_wcheck_size(bn, words)
220 BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num,
222 BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
223 void bn_sqr_words(BN_ULONG *rp, const BN_ULONG *ap, int num);
224 BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d);
225 BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
227 BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
231 BN_ULONG *d; /* Pointer to an array of 'BN_BITS2' bit
233 int top; /* Index of last used d +1. */
234 /* The next are internal book keeping for bn_expand. */
235 int dmax; /* Size of the d array. */
236 int neg; /* one if the number is negative */
240 /* Used for montgomery multiplication */
241 struct bn_mont_ctx_st {
242 int ri; /* number of bits in R */
243 BIGNUM RR; /* used to convert to montgomery form,
244 possibly zero-padded */
245 BIGNUM N; /* The modulus */
246 BIGNUM Ni; /* R*(1/R mod N) - N*Ni = 1 (Ni is only
247 * stored for bignum algorithm) */
248 BN_ULONG n0[2]; /* least significant word(s) of Ni; (type
249 * changed with 0.9.9, was "BN_ULONG n0;"
255 * Used for reciprocal division/mod functions It cannot be shared between
258 struct bn_recp_ctx_st {
259 BIGNUM N; /* the divisor */
260 BIGNUM Nr; /* the reciprocal */
266 /* Used for slow "generation" functions. */
268 unsigned int ver; /* To handle binary (in)compatibility */
269 void *arg; /* callback-specific data */
271 /* if (ver==1) - handles old style callbacks */
272 void (*cb_1) (int, int, void *);
273 /* if (ver==2) - new callback style */
274 int (*cb_2) (int, int, BN_GENCB *);
279 * BN_window_bits_for_exponent_size -- macro for sliding window mod_exp functions
282 * For window size 'w' (w >= 2) and a random 'b' bits exponent,
283 * the number of multiplications is a constant plus on average
285 * 2^(w-1) + (b-w)/(w+1);
287 * here 2^(w-1) is for precomputing the table (we actually need
288 * entries only for windows that have the lowest bit set), and
289 * (b-w)/(w+1) is an approximation for the expected number of
290 * w-bit windows, not counting the first one.
295 * w = 5 if 671 > b > 239
296 * w = 4 if 239 > b > 79
297 * w = 3 if 79 > b > 23
300 * (with draws in between). Very small exponents are often selected
301 * with low Hamming weight, so we use w = 1 for b <= 23.
303 # define BN_window_bits_for_exponent_size(b) \
310 * BN_mod_exp_mont_conttime is based on the assumption that the L1 data cache
311 * line width of the target processor is at least the following value.
313 # define MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH ( 64 )
314 # define MOD_EXP_CTIME_MIN_CACHE_LINE_MASK (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - 1)
317 * Window sizes optimized for fixed window size modular exponentiation
318 * algorithm (BN_mod_exp_mont_consttime). To achieve the security goals of
319 * BN_mode_exp_mont_consttime, the maximum size of the window must not exceed
320 * log_2(MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH). Window size thresholds are
321 * defined for cache line sizes of 32 and 64, cache line sizes where
322 * log_2(32)=5 and log_2(64)=6 respectively. A window size of 7 should only be
323 * used on processors that have a 128 byte or greater cache line size.
325 # if MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 64
327 # define BN_window_bits_for_ctime_exponent_size(b) \
332 # define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (6)
334 # elif MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 32
336 # define BN_window_bits_for_ctime_exponent_size(b) \
340 # define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (5)
344 /* Pentium pro 16,16,16,32,64 */
345 /* Alpha 16,16,16,16.64 */
346 # define BN_MULL_SIZE_NORMAL (16)/* 32 */
347 # define BN_MUL_RECURSIVE_SIZE_NORMAL (16)/* 32 less than */
348 # define BN_SQR_RECURSIVE_SIZE_NORMAL (16)/* 32 */
349 # define BN_MUL_LOW_RECURSIVE_SIZE_NORMAL (32)/* 32 */
350 # define BN_MONT_CTX_SET_SIZE_WORD (64)/* 32 */
353 * 2011-02-22 SMS. In various places, a size_t variable or a type cast to
354 * size_t was used to perform integer-only operations on pointers. This
355 * failed on VMS with 64-bit pointers (CC /POINTER_SIZE = 64) because size_t
356 * is still only 32 bits. What's needed in these cases is an integer type
357 * with the same size as a pointer, which size_t is not certain to be. The
358 * only fix here is VMS-specific.
360 # if defined(OPENSSL_SYS_VMS)
361 # if __INITIAL_POINTER_SIZE == 64
362 # define PTR_SIZE_INT long long
363 # else /* __INITIAL_POINTER_SIZE == 64 */
364 # define PTR_SIZE_INT int
365 # endif /* __INITIAL_POINTER_SIZE == 64 [else] */
366 # elif !defined(PTR_SIZE_INT) /* defined(OPENSSL_SYS_VMS) */
367 # define PTR_SIZE_INT size_t
368 # endif /* defined(OPENSSL_SYS_VMS) [else] */
370 # if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) && !defined(PEDANTIC)
372 * BN_UMULT_HIGH section.
374 * No, I'm not trying to overwhelm you when stating that the
375 * product of N-bit numbers is 2*N bits wide:-) No, I don't expect
376 * you to be impressed when I say that if the compiler doesn't
377 * support 2*N integer type, then you have to replace every N*N
378 * multiplication with 4 (N/2)*(N/2) accompanied by some shifts
379 * and additions which unavoidably results in severe performance
380 * penalties. Of course provided that the hardware is capable of
381 * producing 2*N result... That's when you normally start
382 * considering assembler implementation. However! It should be
383 * pointed out that some CPUs (most notably Alpha, PowerPC and
384 * upcoming IA-64 family:-) provide *separate* instruction
385 * calculating the upper half of the product placing the result
386 * into a general purpose register. Now *if* the compiler supports
387 * inline assembler, then it's not impossible to implement the
388 * "bignum" routines (and have the compiler optimize 'em)
389 * exhibiting "native" performance in C. That's what BN_UMULT_HIGH
392 * <appro@fy.chalmers.se>
394 # if defined(__alpha) && (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT))
397 # define BN_UMULT_HIGH(a,b) (BN_ULONG)asm("umulh %a0,%a1,%v0",(a),(b))
398 # elif defined(__GNUC__) && __GNUC__>=2
399 # define BN_UMULT_HIGH(a,b) ({ \
400 register BN_ULONG ret; \
401 asm ("umulh %1,%2,%0" \
405 # endif /* compiler */
406 # elif defined(_ARCH_PPC) && defined(__64BIT__) && defined(SIXTY_FOUR_BIT_LONG)
407 # if defined(__GNUC__) && __GNUC__>=2
408 # define BN_UMULT_HIGH(a,b) ({ \
409 register BN_ULONG ret; \
410 asm ("mulhdu %0,%1,%2" \
414 # endif /* compiler */
415 # elif (defined(__x86_64) || defined(__x86_64__)) && \
416 (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT))
417 # if defined(__GNUC__) && __GNUC__>=2
418 # define BN_UMULT_HIGH(a,b) ({ \
419 register BN_ULONG ret,discard; \
421 : "=a"(discard),"=d"(ret) \
425 # define BN_UMULT_LOHI(low,high,a,b) \
427 : "=a"(low),"=d"(high) \
431 # elif (defined(_M_AMD64) || defined(_M_X64)) && defined(SIXTY_FOUR_BIT)
432 # if defined(_MSC_VER) && _MSC_VER>=1400
433 unsigned __int64 __umulh(unsigned __int64 a, unsigned __int64 b);
434 unsigned __int64 _umul128(unsigned __int64 a, unsigned __int64 b,
435 unsigned __int64 *h);
436 # pragma intrinsic(__umulh,_umul128)
437 # define BN_UMULT_HIGH(a,b) __umulh((a),(b))
438 # define BN_UMULT_LOHI(low,high,a,b) ((low)=_umul128((a),(b),&(high)))
440 # elif defined(__mips) && (defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG))
441 # if defined(__GNUC__) && __GNUC__>=2
442 # if defined(__SIZEOF_INT128__) && __SIZEOF_INT128__==16
443 /* "h" constraint is not an option on R6 and was removed in 4.4 */
444 # define BN_UMULT_HIGH(a,b) (((__uint128_t)(a)*(b))>>64)
445 # define BN_UMULT_LOHI(low,high,a,b) ({ \
446 __uint128_t ret=(__uint128_t)(a)*(b); \
447 (high)=ret>>64; (low)=ret; })
449 # define BN_UMULT_HIGH(a,b) ({ \
450 register BN_ULONG ret; \
451 asm ("dmultu %1,%2" \
453 : "r"(a), "r"(b) : "l"); \
455 # define BN_UMULT_LOHI(low,high,a,b)\
456 asm ("dmultu %2,%3" \
457 : "=l"(low),"=h"(high) \
461 # elif defined(__aarch64__) && defined(SIXTY_FOUR_BIT_LONG)
462 # if defined(__GNUC__) && __GNUC__>=2
463 # define BN_UMULT_HIGH(a,b) ({ \
464 register BN_ULONG ret; \
465 asm ("umulh %0,%1,%2" \
471 # endif /* OPENSSL_NO_ASM */
473 /*************************************************************
474 * Using the long long type
476 # define Lw(t) (((BN_ULONG)(t))&BN_MASK2)
477 # define Hw(t) (((BN_ULONG)((t)>>BN_BITS2))&BN_MASK2)
479 # ifdef BN_DEBUG_RAND
480 # define bn_clear_top2max(a) \
482 int ind = (a)->dmax - (a)->top; \
483 BN_ULONG *ftl = &(a)->d[(a)->top-1]; \
484 for (; ind != 0; ind--) \
488 # define bn_clear_top2max(a)
492 # define mul_add(r,a,w,c) { \
494 t=(BN_ULLONG)w * (a) + (r) + (c); \
499 # define mul(r,a,w,c) { \
501 t=(BN_ULLONG)w * (a) + (c); \
506 # define sqr(r0,r1,a) { \
508 t=(BN_ULLONG)(a)*(a); \
513 # elif defined(BN_UMULT_LOHI)
514 # define mul_add(r,a,w,c) { \
515 BN_ULONG high,low,ret,tmp=(a); \
517 BN_UMULT_LOHI(low,high,w,tmp); \
519 (c) = (ret<(c))?1:0; \
522 (c) += (ret<low)?1:0; \
526 # define mul(r,a,w,c) { \
527 BN_ULONG high,low,ret,ta=(a); \
528 BN_UMULT_LOHI(low,high,w,ta); \
531 (c) += (ret<low)?1:0; \
535 # define sqr(r0,r1,a) { \
537 BN_UMULT_LOHI(r0,r1,tmp,tmp); \
540 # elif defined(BN_UMULT_HIGH)
541 # define mul_add(r,a,w,c) { \
542 BN_ULONG high,low,ret,tmp=(a); \
544 high= BN_UMULT_HIGH(w,tmp); \
547 (c) = (ret<(c))?1:0; \
550 (c) += (ret<low)?1:0; \
554 # define mul(r,a,w,c) { \
555 BN_ULONG high,low,ret,ta=(a); \
557 high= BN_UMULT_HIGH(w,ta); \
560 (c) += (ret<low)?1:0; \
564 # define sqr(r0,r1,a) { \
567 (r1) = BN_UMULT_HIGH(tmp,tmp); \
571 /*************************************************************
575 # define LBITS(a) ((a)&BN_MASK2l)
576 # define HBITS(a) (((a)>>BN_BITS4)&BN_MASK2l)
577 # define L2HBITS(a) (((a)<<BN_BITS4)&BN_MASK2)
579 # define LLBITS(a) ((a)&BN_MASKl)
580 # define LHBITS(a) (((a)>>BN_BITS2)&BN_MASKl)
581 # define LL2HBITS(a) ((BN_ULLONG)((a)&BN_MASKl)<<BN_BITS2)
583 # define mul64(l,h,bl,bh) \
585 BN_ULONG m,m1,lt,ht; \
593 m=(m+m1)&BN_MASK2; if (m < m1) ht+=L2HBITS((BN_ULONG)1); \
596 lt=(lt+m1)&BN_MASK2; if (lt < m1) ht++; \
601 # define sqr64(lo,ho,in) \
611 h+=(m&BN_MASK2h1)>>(BN_BITS4-1); \
612 m =(m&BN_MASK2l)<<(BN_BITS4+1); \
613 l=(l+m)&BN_MASK2; if (l < m) h++; \
618 # define mul_add(r,a,bl,bh,c) { \
624 mul64(l,h,(bl),(bh)); \
626 /* non-multiply part */ \
627 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
629 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
634 # define mul(r,a,bl,bh,c) { \
640 mul64(l,h,(bl),(bh)); \
642 /* non-multiply part */ \
643 l+=(c); if ((l&BN_MASK2) < (c)) h++; \
647 # endif /* !BN_LLONG */
649 void BN_RECP_CTX_init(BN_RECP_CTX *recp);
650 void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
652 void bn_init(BIGNUM *a);
653 void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb);
654 void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
655 void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
656 void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp);
657 void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a);
658 void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a);
659 int bn_cmp_words(const BN_ULONG *a, const BN_ULONG *b, int n);
660 int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b, int cl, int dl);
661 void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
662 int dna, int dnb, BN_ULONG *t);
663 void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b,
664 int n, int tna, int tnb, BN_ULONG *t);
665 void bn_sqr_recursive(BN_ULONG *r, const BN_ULONG *a, int n2, BN_ULONG *t);
666 void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n);
667 void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
669 void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2,
671 BN_ULONG bn_add_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
673 BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
675 int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
676 const BN_ULONG *np, const BN_ULONG *n0, int num);
678 BIGNUM *int_bn_mod_inverse(BIGNUM *in,
679 const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx,
682 int bn_probable_prime_dh(BIGNUM *rnd, int bits,
683 const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx);
684 int bn_probable_prime_dh_retry(BIGNUM *rnd, int bits, BN_CTX *ctx);
685 int bn_probable_prime_dh_coprime(BIGNUM *rnd, int bits, BN_CTX *ctx);
687 static ossl_inline BIGNUM *bn_expand(BIGNUM *a, int bits)
689 if (bits > (INT_MAX - BN_BITS2 + 1))
692 if (((bits+BN_BITS2-1)/BN_BITS2) <= (a)->dmax)
695 return bn_expand2((a),(bits+BN_BITS2-1)/BN_BITS2);