1 /* crypto/bn/bn_lcl.h */
2 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
5 * This package is an SSL implementation written
6 * by Eric Young (eay@cryptsoft.com).
7 * The implementation was written so as to conform with Netscapes SSL.
9 * This library is free for commercial and non-commercial use as long as
10 * the following conditions are aheared to. The following conditions
11 * apply to all code found in this distribution, be it the RC4, RSA,
12 * lhash, DES, etc., code; not just the SSL code. The SSL documentation
13 * included with this distribution is covered by the same copyright terms
14 * except that the holder is Tim Hudson (tjh@cryptsoft.com).
16 * Copyright remains Eric Young's, and as such any Copyright notices in
17 * the code are not to be removed.
18 * If this package is used in a product, Eric Young should be given attribution
19 * as the author of the parts of the library used.
20 * This can be in the form of a textual message at program startup or
21 * in documentation (online or textual) provided with the package.
23 * Redistribution and use in source and binary forms, with or without
24 * modification, are permitted provided that the following conditions
26 * 1. Redistributions of source code must retain the copyright
27 * notice, this list of conditions and the following disclaimer.
28 * 2. Redistributions in binary form must reproduce the above copyright
29 * notice, this list of conditions and the following disclaimer in the
30 * documentation and/or other materials provided with the distribution.
31 * 3. All advertising materials mentioning features or use of this software
32 * must display the following acknowledgement:
33 * "This product includes cryptographic software written by
34 * Eric Young (eay@cryptsoft.com)"
35 * The word 'cryptographic' can be left out if the rouines from the library
36 * being used are not cryptographic related :-).
37 * 4. If you include any Windows specific code (or a derivative thereof) from
38 * the apps directory (application code) you must include an acknowledgement:
39 * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
41 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
42 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
43 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
44 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
45 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
46 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
47 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
48 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
49 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
50 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
53 * The licence and distribution terms for any publically available version or
54 * derivative of this code cannot be changed. i.e. this code cannot simply be
55 * copied and put under another distribution licence
56 * [including the GNU Public Licence.]
58 /* ====================================================================
59 * Copyright (c) 1998-2000 The OpenSSL Project. All rights reserved.
61 * Redistribution and use in source and binary forms, with or without
62 * modification, are permitted provided that the following conditions
65 * 1. Redistributions of source code must retain the above copyright
66 * notice, this list of conditions and the following disclaimer.
68 * 2. Redistributions in binary form must reproduce the above copyright
69 * notice, this list of conditions and the following disclaimer in
70 * the documentation and/or other materials provided with the
73 * 3. All advertising materials mentioning features or use of this
74 * software must display the following acknowledgment:
75 * "This product includes software developed by the OpenSSL Project
76 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
78 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
79 * endorse or promote products derived from this software without
80 * prior written permission. For written permission, please contact
81 * openssl-core@openssl.org.
83 * 5. Products derived from this software may not be called "OpenSSL"
84 * nor may "OpenSSL" appear in their names without prior written
85 * permission of the OpenSSL Project.
87 * 6. Redistributions of any form whatsoever must retain the following
89 * "This product includes software developed by the OpenSSL Project
90 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
92 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
93 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
94 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
95 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
96 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
97 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
98 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
99 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
100 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
101 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
102 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
103 * OF THE POSSIBILITY OF SUCH DAMAGE.
104 * ====================================================================
106 * This product includes cryptographic software written by Eric Young
107 * (eay@cryptsoft.com). This product includes software written by Tim
108 * Hudson (tjh@cryptsoft.com).
112 #ifndef HEADER_BN_LCL_H
113 # define HEADER_BN_LCL_H
115 # include "internal/bn_conf.h"
116 # include "internal/bn_int.h"
123 * Bignum consistency macros
124 * There is one "API" macro, bn_fix_top(), for stripping leading zeroes from
125 * bignum data after direct manipulations on the data. There is also an
126 * "internal" macro, bn_check_top(), for verifying that there are no leading
127 * zeroes. Unfortunately, some auditing is required due to the fact that
128 * bn_fix_top() has become an overabused duct-tape because bignum data is
129 * occasionally passed around in an inconsistent state. So the following
130 * changes have been made to sort this out;
131 * - bn_fix_top()s implementation has been moved to bn_correct_top()
132 * - if BN_DEBUG isn't defined, bn_fix_top() maps to bn_correct_top(), and
133 * bn_check_top() is as before.
134 * - if BN_DEBUG *is* defined;
135 * - bn_check_top() tries to pollute unused words even if the bignum 'top' is
136 * consistent. (ed: only if BN_DEBUG_RAND is defined)
137 * - bn_fix_top() maps to bn_check_top() rather than "fixing" anything.
138 * The idea is to have debug builds flag up inconsistent bignums when they
139 * occur. If that occurs in a bn_fix_top(), we examine the code in question; if
140 * the use of bn_fix_top() was appropriate (ie. it follows directly after code
141 * that manipulates the bignum) it is converted to bn_correct_top(), and if it
142 * was not appropriate, we convert it permanently to bn_check_top() and track
143 * down the cause of the bug. Eventually, no internal code should be using the
144 * bn_fix_top() macro. External applications and libraries should try this with
145 * their own code too, both in terms of building against the openssl headers
146 * with BN_DEBUG defined *and* linking with a version of OpenSSL built with it
147 * defined. This not only improves external code, it provides more test
148 * coverage for openssl's own code.
153 /* We only need assert() when debugging */
156 # ifdef BN_DEBUG_RAND
157 /* To avoid "make update" cvs wars due to BN_DEBUG, use some tricks */
158 # ifndef RAND_pseudo_bytes
159 int RAND_pseudo_bytes(unsigned char *buf, int num);
160 # define BN_DEBUG_TRIX
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 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)); \
177 # ifdef BN_DEBUG_TRIX
178 # undef RAND_pseudo_bytes
181 # define bn_pollute(a)
183 # define bn_check_top(a) \
185 const BIGNUM *_bnum2 = (a); \
186 if (_bnum2 != NULL) { \
187 assert((_bnum2->top == 0) || \
188 (_bnum2->d[_bnum2->top - 1] != 0)); \
189 bn_pollute(_bnum2); \
193 # define bn_fix_top(a) bn_check_top(a)
195 # define bn_check_size(bn, bits) bn_wcheck_size(bn, ((bits+BN_BITS2-1))/BN_BITS2)
196 # define bn_wcheck_size(bn, words) \
198 const BIGNUM *_bnum2 = (bn); \
199 assert((words) <= (_bnum2)->dmax && (words) >= (_bnum2)->top); \
200 /* avoid unused variable warning with NDEBUG */ \
204 # else /* !BN_DEBUG */
206 # define bn_pollute(a)
207 # define bn_check_top(a)
208 # define bn_fix_top(a) bn_correct_top(a)
209 # define bn_check_size(bn, bits)
210 # define bn_wcheck_size(bn, words)
214 BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num,
216 BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
217 void bn_sqr_words(BN_ULONG *rp, const BN_ULONG *ap, int num);
218 BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d);
219 BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
221 BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
225 BN_ULONG *d; /* Pointer to an array of 'BN_BITS2' bit
227 int top; /* Index of last used d +1. */
228 /* The next are internal book keeping for bn_expand. */
229 int dmax; /* Size of the d array. */
230 int neg; /* one if the number is negative */
234 /* Used for montgomery multiplication */
235 struct bn_mont_ctx_st {
236 int ri; /* number of bits in R */
237 BIGNUM RR; /* used to convert to montgomery form */
238 BIGNUM N; /* The modulus */
239 BIGNUM Ni; /* R*(1/R mod N) - N*Ni = 1 (Ni is only
240 * stored for bignum algorithm) */
241 BN_ULONG n0[2]; /* least significant word(s) of Ni; (type
242 * changed with 0.9.9, was "BN_ULONG n0;"
248 * Used for reciprocal division/mod functions It cannot be shared between
251 struct bn_recp_ctx_st {
252 BIGNUM N; /* the divisor */
253 BIGNUM Nr; /* the reciprocal */
259 /* Used for slow "generation" functions. */
261 unsigned int ver; /* To handle binary (in)compatibility */
262 void *arg; /* callback-specific data */
264 /* if(ver==1) - handles old style callbacks */
265 void (*cb_1) (int, int, void *);
266 /* if(ver==2) - new callback style */
267 int (*cb_2) (int, int, BN_GENCB *);
272 * BN_window_bits_for_exponent_size -- macro for sliding window mod_exp functions
275 * For window size 'w' (w >= 2) and a random 'b' bits exponent,
276 * the number of multiplications is a constant plus on average
278 * 2^(w-1) + (b-w)/(w+1);
280 * here 2^(w-1) is for precomputing the table (we actually need
281 * entries only for windows that have the lowest bit set), and
282 * (b-w)/(w+1) is an approximation for the expected number of
283 * w-bit windows, not counting the first one.
288 * w = 5 if 671 > b > 239
289 * w = 4 if 239 > b > 79
290 * w = 3 if 79 > b > 23
293 * (with draws in between). Very small exponents are often selected
294 * with low Hamming weight, so we use w = 1 for b <= 23.
296 # define BN_window_bits_for_exponent_size(b) \
303 * BN_mod_exp_mont_conttime is based on the assumption that the L1 data cache
304 * line width of the target processor is at least the following value.
306 # define MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH ( 64 )
307 # define MOD_EXP_CTIME_MIN_CACHE_LINE_MASK (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - 1)
310 * Window sizes optimized for fixed window size modular exponentiation
311 * algorithm (BN_mod_exp_mont_consttime). To achieve the security goals of
312 * BN_mode_exp_mont_consttime, the maximum size of the window must not exceed
313 * log_2(MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH). Window size thresholds are
314 * defined for cache line sizes of 32 and 64, cache line sizes where
315 * log_2(32)=5 and log_2(64)=6 respectively. A window size of 7 should only be
316 * used on processors that have a 128 byte or greater cache line size.
318 # if MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 64
320 # define BN_window_bits_for_ctime_exponent_size(b) \
325 # define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (6)
327 # elif MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 32
329 # define BN_window_bits_for_ctime_exponent_size(b) \
333 # define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (5)
337 /* Pentium pro 16,16,16,32,64 */
338 /* Alpha 16,16,16,16.64 */
339 # define BN_MULL_SIZE_NORMAL (16)/* 32 */
340 # define BN_MUL_RECURSIVE_SIZE_NORMAL (16)/* 32 less than */
341 # define BN_SQR_RECURSIVE_SIZE_NORMAL (16)/* 32 */
342 # define BN_MUL_LOW_RECURSIVE_SIZE_NORMAL (32)/* 32 */
343 # define BN_MONT_CTX_SET_SIZE_WORD (64)/* 32 */
346 * 2011-02-22 SMS. In various places, a size_t variable or a type cast to
347 * size_t was used to perform integer-only operations on pointers. This
348 * failed on VMS with 64-bit pointers (CC /POINTER_SIZE = 64) because size_t
349 * is still only 32 bits. What's needed in these cases is an integer type
350 * with the same size as a pointer, which size_t is not certain to be. The
351 * only fix here is VMS-specific.
353 # if defined(OPENSSL_SYS_VMS)
354 # if __INITIAL_POINTER_SIZE == 64
355 # define PTR_SIZE_INT long long
356 # else /* __INITIAL_POINTER_SIZE == 64 */
357 # define PTR_SIZE_INT int
358 # endif /* __INITIAL_POINTER_SIZE == 64 [else] */
359 # elif !defined(PTR_SIZE_INT) /* defined(OPENSSL_SYS_VMS) */
360 # define PTR_SIZE_INT size_t
361 # endif /* defined(OPENSSL_SYS_VMS) [else] */
363 # if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) && !defined(PEDANTIC)
365 * BN_UMULT_HIGH section.
367 * No, I'm not trying to overwhelm you when stating that the
368 * product of N-bit numbers is 2*N bits wide:-) No, I don't expect
369 * you to be impressed when I say that if the compiler doesn't
370 * support 2*N integer type, then you have to replace every N*N
371 * multiplication with 4 (N/2)*(N/2) accompanied by some shifts
372 * and additions which unavoidably results in severe performance
373 * penalties. Of course provided that the hardware is capable of
374 * producing 2*N result... That's when you normally start
375 * considering assembler implementation. However! It should be
376 * pointed out that some CPUs (most notably Alpha, PowerPC and
377 * upcoming IA-64 family:-) provide *separate* instruction
378 * calculating the upper half of the product placing the result
379 * into a general purpose register. Now *if* the compiler supports
380 * inline assembler, then it's not impossible to implement the
381 * "bignum" routines (and have the compiler optimize 'em)
382 * exhibiting "native" performance in C. That's what BN_UMULT_HIGH
385 * <appro@fy.chalmers.se>
387 # if defined(__alpha) && (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT))
390 # define BN_UMULT_HIGH(a,b) (BN_ULONG)asm("umulh %a0,%a1,%v0",(a),(b))
391 # elif defined(__GNUC__) && __GNUC__>=2
392 # define BN_UMULT_HIGH(a,b) ({ \
393 register BN_ULONG ret; \
394 asm ("umulh %1,%2,%0" \
398 # endif /* compiler */
399 # elif defined(_ARCH_PPC) && defined(__64BIT__) && defined(SIXTY_FOUR_BIT_LONG)
400 # if defined(__GNUC__) && __GNUC__>=2
401 # define BN_UMULT_HIGH(a,b) ({ \
402 register BN_ULONG ret; \
403 asm ("mulhdu %0,%1,%2" \
407 # endif /* compiler */
408 # elif (defined(__x86_64) || defined(__x86_64__)) && \
409 (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT))
410 # if defined(__GNUC__) && __GNUC__>=2
411 # define BN_UMULT_HIGH(a,b) ({ \
412 register BN_ULONG ret,discard; \
414 : "=a"(discard),"=d"(ret) \
418 # define BN_UMULT_LOHI(low,high,a,b) \
420 : "=a"(low),"=d"(high) \
424 # elif (defined(_M_AMD64) || defined(_M_X64)) && defined(SIXTY_FOUR_BIT)
425 # if defined(_MSC_VER) && _MSC_VER>=1400
426 unsigned __int64 __umulh(unsigned __int64 a, unsigned __int64 b);
427 unsigned __int64 _umul128(unsigned __int64 a, unsigned __int64 b,
428 unsigned __int64 *h);
429 # pragma intrinsic(__umulh,_umul128)
430 # define BN_UMULT_HIGH(a,b) __umulh((a),(b))
431 # define BN_UMULT_LOHI(low,high,a,b) ((low)=_umul128((a),(b),&(high)))
433 # elif defined(__mips) && (defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG))
434 # if defined(__GNUC__) && __GNUC__>=2
435 # if __GNUC__>4 || (__GNUC__>=4 && __GNUC_MINOR__>=4)
436 /* "h" constraint is no more since 4.4 */
437 # define BN_UMULT_HIGH(a,b) (((__uint128_t)(a)*(b))>>64)
438 # define BN_UMULT_LOHI(low,high,a,b) ({ \
439 __uint128_t ret=(__uint128_t)(a)*(b); \
440 (high)=ret>>64; (low)=ret; })
442 # define BN_UMULT_HIGH(a,b) ({ \
443 register BN_ULONG ret; \
444 asm ("dmultu %1,%2" \
446 : "r"(a), "r"(b) : "l"); \
448 # define BN_UMULT_LOHI(low,high,a,b)\
449 asm ("dmultu %2,%3" \
450 : "=l"(low),"=h"(high) \
454 # elif defined(__aarch64__) && defined(SIXTY_FOUR_BIT_LONG)
455 # if defined(__GNUC__) && __GNUC__>=2
456 # define BN_UMULT_HIGH(a,b) ({ \
457 register BN_ULONG ret; \
458 asm ("umulh %0,%1,%2" \
464 # endif /* OPENSSL_NO_ASM */
466 /*************************************************************
467 * Using the long long type
469 # define Lw(t) (((BN_ULONG)(t))&BN_MASK2)
470 # define Hw(t) (((BN_ULONG)((t)>>BN_BITS2))&BN_MASK2)
472 # ifdef BN_DEBUG_RAND
473 # define bn_clear_top2max(a) \
475 int ind = (a)->dmax - (a)->top; \
476 BN_ULONG *ftl = &(a)->d[(a)->top-1]; \
477 for (; ind != 0; ind--) \
481 # define bn_clear_top2max(a)
485 # define mul_add(r,a,w,c) { \
487 t=(BN_ULLONG)w * (a) + (r) + (c); \
492 # define mul(r,a,w,c) { \
494 t=(BN_ULLONG)w * (a) + (c); \
499 # define sqr(r0,r1,a) { \
501 t=(BN_ULLONG)(a)*(a); \
506 # elif defined(BN_UMULT_LOHI)
507 # define mul_add(r,a,w,c) { \
508 BN_ULONG high,low,ret,tmp=(a); \
510 BN_UMULT_LOHI(low,high,w,tmp); \
512 (c) = (ret<(c))?1:0; \
515 (c) += (ret<low)?1:0; \
519 # define mul(r,a,w,c) { \
520 BN_ULONG high,low,ret,ta=(a); \
521 BN_UMULT_LOHI(low,high,w,ta); \
524 (c) += (ret<low)?1:0; \
528 # define sqr(r0,r1,a) { \
530 BN_UMULT_LOHI(r0,r1,tmp,tmp); \
533 # elif defined(BN_UMULT_HIGH)
534 # define mul_add(r,a,w,c) { \
535 BN_ULONG high,low,ret,tmp=(a); \
537 high= BN_UMULT_HIGH(w,tmp); \
540 (c) = (ret<(c))?1:0; \
543 (c) += (ret<low)?1:0; \
547 # define mul(r,a,w,c) { \
548 BN_ULONG high,low,ret,ta=(a); \
550 high= BN_UMULT_HIGH(w,ta); \
553 (c) += (ret<low)?1:0; \
557 # define sqr(r0,r1,a) { \
560 (r1) = BN_UMULT_HIGH(tmp,tmp); \
564 /*************************************************************
568 # define LBITS(a) ((a)&BN_MASK2l)
569 # define HBITS(a) (((a)>>BN_BITS4)&BN_MASK2l)
570 # define L2HBITS(a) (((a)<<BN_BITS4)&BN_MASK2)
572 # define LLBITS(a) ((a)&BN_MASKl)
573 # define LHBITS(a) (((a)>>BN_BITS2)&BN_MASKl)
574 # define LL2HBITS(a) ((BN_ULLONG)((a)&BN_MASKl)<<BN_BITS2)
576 # define mul64(l,h,bl,bh) \
578 BN_ULONG m,m1,lt,ht; \
586 m=(m+m1)&BN_MASK2; if (m < m1) ht+=L2HBITS((BN_ULONG)1); \
589 lt=(lt+m1)&BN_MASK2; if (lt < m1) ht++; \
594 # define sqr64(lo,ho,in) \
604 h+=(m&BN_MASK2h1)>>(BN_BITS4-1); \
605 m =(m&BN_MASK2l)<<(BN_BITS4+1); \
606 l=(l+m)&BN_MASK2; if (l < m) h++; \
611 # define mul_add(r,a,bl,bh,c) { \
617 mul64(l,h,(bl),(bh)); \
619 /* non-multiply part */ \
620 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
622 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
627 # define mul(r,a,bl,bh,c) { \
633 mul64(l,h,(bl),(bh)); \
635 /* non-multiply part */ \
636 l+=(c); if ((l&BN_MASK2) < (c)) h++; \
640 # endif /* !BN_LLONG */
642 void BN_RECP_CTX_init(BN_RECP_CTX *recp);
643 void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
645 void bn_init(BIGNUM *a);
646 void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb);
647 void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
648 void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
649 void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp);
650 void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a);
651 void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a);
652 int bn_cmp_words(const BN_ULONG *a, const BN_ULONG *b, int n);
653 int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b, int cl, int dl);
654 void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
655 int dna, int dnb, BN_ULONG *t);
656 void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b,
657 int n, int tna, int tnb, BN_ULONG *t);
658 void bn_sqr_recursive(BN_ULONG *r, const BN_ULONG *a, int n2, BN_ULONG *t);
659 void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n);
660 void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
662 void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2,
664 BN_ULONG bn_add_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
666 BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
668 int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
669 const BN_ULONG *np, const BN_ULONG *n0, int num);
671 BIGNUM *int_bn_mod_inverse(BIGNUM *in,
672 const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx,
675 int bn_probable_prime_dh(BIGNUM *rnd, int bits,
676 const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx);
677 int bn_probable_prime_dh_retry(BIGNUM *rnd, int bits, BN_CTX *ctx);
678 int bn_probable_prime_dh_coprime(BIGNUM *rnd, int bits, BN_CTX *ctx);