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_int.h"
121 /* Bignum consistency macros
122 * There is one "API" macro, bn_fix_top(), for stripping leading zeroes from
123 * bignum data after direct manipulations on the data. There is also an
124 * "internal" macro, bn_check_top(), for verifying that there are no leading
125 * zeroes. Unfortunately, some auditing is required due to the fact that
126 * bn_fix_top() has become an overabused duct-tape because bignum data is
127 * occasionally passed around in an inconsistent state. So the following
128 * changes have been made to sort this out;
129 * - bn_fix_top()s implementation has been moved to bn_correct_top()
130 * - if BN_DEBUG isn't defined, bn_fix_top() maps to bn_correct_top(), and
131 * bn_check_top() is as before.
132 * - if BN_DEBUG *is* defined;
133 * - bn_check_top() tries to pollute unused words even if the bignum 'top' is
134 * consistent. (ed: only if BN_DEBUG_RAND is defined)
135 * - bn_fix_top() maps to bn_check_top() rather than "fixing" anything.
136 * The idea is to have debug builds flag up inconsistent bignums when they
137 * occur. If that occurs in a bn_fix_top(), we examine the code in question; if
138 * the use of bn_fix_top() was appropriate (ie. it follows directly after code
139 * that manipulates the bignum) it is converted to bn_correct_top(), and if it
140 * was not appropriate, we convert it permanently to bn_check_top() and track
141 * down the cause of the bug. Eventually, no internal code should be using the
142 * bn_fix_top() macro. External applications and libraries should try this with
143 * their own code too, both in terms of building against the openssl headers
144 * with BN_DEBUG defined *and* linking with a version of OpenSSL built with it
145 * defined. This not only improves external code, it provides more test
146 * coverage for openssl's own code.
151 /* We only need assert() when debugging */
155 /* To avoid "make update" cvs wars due to BN_DEBUG, use some tricks */
156 #ifndef RAND_pseudo_bytes
157 int RAND_pseudo_bytes(unsigned char *buf,int num);
158 #define BN_DEBUG_TRIX
160 #define bn_pollute(a) \
162 const BIGNUM *_bnum1 = (a); \
163 if(_bnum1->top < _bnum1->dmax) { \
164 unsigned char _tmp_char; \
165 /* We cast away const without the compiler knowing, any \
166 * *genuinely* constant variables that aren't mutable \
167 * wouldn't be constructed with top!=dmax. */ \
168 BN_ULONG *_not_const; \
169 memcpy(&_not_const, &_bnum1->d, sizeof(BN_ULONG*)); \
170 RAND_pseudo_bytes(&_tmp_char, 1); \
171 memset((unsigned char *)(_not_const + _bnum1->top), _tmp_char, \
172 (_bnum1->dmax - _bnum1->top) * sizeof(BN_ULONG)); \
176 #undef RAND_pseudo_bytes
179 #define bn_pollute(a)
181 #define bn_check_top(a) \
183 const BIGNUM *_bnum2 = (a); \
184 if (_bnum2 != NULL) { \
185 assert((_bnum2->top == 0) || \
186 (_bnum2->d[_bnum2->top - 1] != 0)); \
187 bn_pollute(_bnum2); \
191 #define bn_fix_top(a) bn_check_top(a)
193 #define bn_check_size(bn, bits) bn_wcheck_size(bn, ((bits+BN_BITS2-1))/BN_BITS2)
194 #define bn_wcheck_size(bn, words) \
196 const BIGNUM *_bnum2 = (bn); \
197 assert((words) <= (_bnum2)->dmax && (words) >= (_bnum2)->top); \
198 /* avoid unused variable warning with NDEBUG */ \
202 #else /* !BN_DEBUG */
204 #define bn_pollute(a)
205 #define bn_check_top(a)
206 #define bn_fix_top(a) bn_correct_top(a)
207 #define bn_check_size(bn, bits)
208 #define bn_wcheck_size(bn, words)
213 BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
214 BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
215 void bn_sqr_words(BN_ULONG *rp, const BN_ULONG *ap, int num);
216 BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d);
217 BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,int num);
218 BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,int num);
223 BN_ULONG *d; /* Pointer to an array of 'BN_BITS2' bit chunks. */
224 int top; /* Index of last used d +1. */
225 /* The next are internal book keeping for bn_expand. */
226 int dmax; /* Size of the d array. */
227 int neg; /* one if the number is negative */
231 /* Used for montgomery multiplication */
232 struct bn_mont_ctx_st
234 int ri; /* number of bits in R */
235 BIGNUM RR; /* used to convert to montgomery form */
236 BIGNUM N; /* The modulus */
237 BIGNUM Ni; /* R*(1/R mod N) - N*Ni = 1
238 * (Ni is only stored for bignum algorithm) */
239 BN_ULONG n0[2];/* least significant word(s) of Ni;
240 (type changed with 0.9.9, was "BN_ULONG n0;" before) */
244 /* Used for reciprocal division/mod functions
245 * It cannot be shared between threads
247 struct bn_recp_ctx_st
249 BIGNUM N; /* the divisor */
250 BIGNUM Nr; /* the reciprocal */
256 /* Used for slow "generation" functions. */
259 unsigned int ver; /* To handle binary (in)compatibility */
260 void *arg; /* callback-specific data */
263 /* if(ver==1) - handles old style callbacks */
264 void (*cb_1)(int, int, void *);
265 /* if(ver==2) - new callback style */
266 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.
297 #define BN_window_bits_for_exponent_size(b) \
303 /* Old SSLeay/OpenSSL table.
304 * Maximum window size was 5, so this table differs for b==1024;
305 * but it coincides for other interesting values (b==160, b==512).
307 #define BN_window_bits_for_exponent_size(b) \
315 /* BN_mod_exp_mont_conttime is based on the assumption that the
316 * L1 data cache line width of the target processor is at least
317 * the following value.
319 #define MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH ( 64 )
320 #define MOD_EXP_CTIME_MIN_CACHE_LINE_MASK (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - 1)
322 /* Window sizes optimized for fixed window size modular exponentiation
323 * algorithm (BN_mod_exp_mont_consttime).
325 * To achieve the security goals of BN_mode_exp_mont_consttime, the
326 * maximum size of the window must not exceed
327 * log_2(MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH).
329 * Window size thresholds are defined for cache line sizes of 32 and 64,
330 * cache line sizes where log_2(32)=5 and log_2(64)=6 respectively. A
331 * window size of 7 should only be used on processors that have a 128
332 * byte or greater cache line size.
334 #if MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 64
336 # define BN_window_bits_for_ctime_exponent_size(b) \
341 # define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (6)
343 #elif MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 32
345 # define BN_window_bits_for_ctime_exponent_size(b) \
349 # define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (5)
354 /* Pentium pro 16,16,16,32,64 */
355 /* Alpha 16,16,16,16.64 */
356 #define BN_MULL_SIZE_NORMAL (16) /* 32 */
357 #define BN_MUL_RECURSIVE_SIZE_NORMAL (16) /* 32 less than */
358 #define BN_SQR_RECURSIVE_SIZE_NORMAL (16) /* 32 */
359 #define BN_MUL_LOW_RECURSIVE_SIZE_NORMAL (32) /* 32 */
360 #define BN_MONT_CTX_SET_SIZE_WORD (64) /* 32 */
363 * In various places, a size_t variable or a type cast to size_t was
364 * used to perform integer-only operations on pointers. This failed on
365 * VMS with 64-bit pointers (CC /POINTER_SIZE = 64) because size_t is
366 * still only 32 bits. What's needed in these cases is an integer type
367 * with the same size as a pointer, which size_t is not certain to be.
368 * The only fix here is VMS-specific.
370 #if defined(OPENSSL_SYS_VMS)
371 # if __INITIAL_POINTER_SIZE == 64
372 # define PTR_SIZE_INT long long
373 # else /* __INITIAL_POINTER_SIZE == 64 */
374 # define PTR_SIZE_INT int
375 # endif /* __INITIAL_POINTER_SIZE == 64 [else] */
376 #elif !defined(PTR_SIZE_INT) /* defined(OPENSSL_SYS_VMS) */
377 # define PTR_SIZE_INT size_t
378 #endif /* defined(OPENSSL_SYS_VMS) [else] */
380 #if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) && !defined(PEDANTIC)
382 * BN_UMULT_HIGH section.
384 * No, I'm not trying to overwhelm you when stating that the
385 * product of N-bit numbers is 2*N bits wide:-) No, I don't expect
386 * you to be impressed when I say that if the compiler doesn't
387 * support 2*N integer type, then you have to replace every N*N
388 * multiplication with 4 (N/2)*(N/2) accompanied by some shifts
389 * and additions which unavoidably results in severe performance
390 * penalties. Of course provided that the hardware is capable of
391 * producing 2*N result... That's when you normally start
392 * considering assembler implementation. However! It should be
393 * pointed out that some CPUs (most notably Alpha, PowerPC and
394 * upcoming IA-64 family:-) provide *separate* instruction
395 * calculating the upper half of the product placing the result
396 * into a general purpose register. Now *if* the compiler supports
397 * inline assembler, then it's not impossible to implement the
398 * "bignum" routines (and have the compiler optimize 'em)
399 * exhibiting "native" performance in C. That's what BN_UMULT_HIGH
402 * <appro@fy.chalmers.se>
404 # if defined(__alpha) && (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT))
407 # define BN_UMULT_HIGH(a,b) (BN_ULONG)asm("umulh %a0,%a1,%v0",(a),(b))
408 # elif defined(__GNUC__) && __GNUC__>=2
409 # define BN_UMULT_HIGH(a,b) ({ \
410 register BN_ULONG ret; \
411 asm ("umulh %1,%2,%0" \
415 # endif /* compiler */
416 # elif defined(_ARCH_PPC) && defined(__64BIT__) && defined(SIXTY_FOUR_BIT_LONG)
417 # if defined(__GNUC__) && __GNUC__>=2
418 # define BN_UMULT_HIGH(a,b) ({ \
419 register BN_ULONG ret; \
420 asm ("mulhdu %0,%1,%2" \
424 # endif /* compiler */
425 # elif (defined(__x86_64) || defined(__x86_64__)) && \
426 (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT))
427 # if defined(__GNUC__) && __GNUC__>=2
428 # define BN_UMULT_HIGH(a,b) ({ \
429 register BN_ULONG ret,discard; \
431 : "=a"(discard),"=d"(ret) \
435 # define BN_UMULT_LOHI(low,high,a,b) \
437 : "=a"(low),"=d"(high) \
441 # elif (defined(_M_AMD64) || defined(_M_X64)) && defined(SIXTY_FOUR_BIT)
442 # if defined(_MSC_VER) && _MSC_VER>=1400
443 unsigned __int64 __umulh (unsigned __int64 a,unsigned __int64 b);
444 unsigned __int64 _umul128 (unsigned __int64 a,unsigned __int64 b,
445 unsigned __int64 *h);
446 # pragma intrinsic(__umulh,_umul128)
447 # define BN_UMULT_HIGH(a,b) __umulh((a),(b))
448 # define BN_UMULT_LOHI(low,high,a,b) ((low)=_umul128((a),(b),&(high)))
450 # elif defined(__mips) && (defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG))
451 # if defined(__GNUC__) && __GNUC__>=2
452 # if __GNUC__>=4 && __GNUC_MINOR__>=4 /* "h" constraint is no more since 4.4 */
453 # define BN_UMULT_HIGH(a,b) (((__uint128_t)(a)*(b))>>64)
454 # define BN_UMULT_LOHI(low,high,a,b) ({ \
455 __uint128_t ret=(__uint128_t)(a)*(b); \
456 (high)=ret>>64; (low)=ret; })
458 # define BN_UMULT_HIGH(a,b) ({ \
459 register BN_ULONG ret; \
460 asm ("dmultu %1,%2" \
462 : "r"(a), "r"(b) : "l"); \
464 # define BN_UMULT_LOHI(low,high,a,b)\
465 asm ("dmultu %2,%3" \
466 : "=l"(low),"=h"(high) \
470 # elif defined(__aarch64__) && defined(SIXTY_FOUR_BIT_LONG)
471 # if defined(__GNUC__) && __GNUC__>=2
472 # define BN_UMULT_HIGH(a,b) ({ \
473 register BN_ULONG ret; \
474 asm ("umulh %0,%1,%2" \
480 #endif /* OPENSSL_NO_ASM */
482 /*************************************************************
483 * Using the long long type
485 #define Lw(t) (((BN_ULONG)(t))&BN_MASK2)
486 #define Hw(t) (((BN_ULONG)((t)>>BN_BITS2))&BN_MASK2)
489 #define bn_clear_top2max(a) \
491 int ind = (a)->dmax - (a)->top; \
492 BN_ULONG *ftl = &(a)->d[(a)->top-1]; \
493 for (; ind != 0; ind--) \
497 #define bn_clear_top2max(a)
501 #define mul_add(r,a,w,c) { \
503 t=(BN_ULLONG)w * (a) + (r) + (c); \
508 #define mul(r,a,w,c) { \
510 t=(BN_ULLONG)w * (a) + (c); \
515 #define sqr(r0,r1,a) { \
517 t=(BN_ULLONG)(a)*(a); \
522 #elif defined(BN_UMULT_LOHI)
523 #define mul_add(r,a,w,c) { \
524 BN_ULONG high,low,ret,tmp=(a); \
526 BN_UMULT_LOHI(low,high,w,tmp); \
528 (c) = (ret<(c))?1:0; \
531 (c) += (ret<low)?1:0; \
535 #define mul(r,a,w,c) { \
536 BN_ULONG high,low,ret,ta=(a); \
537 BN_UMULT_LOHI(low,high,w,ta); \
540 (c) += (ret<low)?1:0; \
544 #define sqr(r0,r1,a) { \
546 BN_UMULT_LOHI(r0,r1,tmp,tmp); \
549 #elif defined(BN_UMULT_HIGH)
550 #define mul_add(r,a,w,c) { \
551 BN_ULONG high,low,ret,tmp=(a); \
553 high= BN_UMULT_HIGH(w,tmp); \
556 (c) = (ret<(c))?1:0; \
559 (c) += (ret<low)?1:0; \
563 #define mul(r,a,w,c) { \
564 BN_ULONG high,low,ret,ta=(a); \
566 high= BN_UMULT_HIGH(w,ta); \
569 (c) += (ret<low)?1:0; \
573 #define sqr(r0,r1,a) { \
576 (r1) = BN_UMULT_HIGH(tmp,tmp); \
580 /*************************************************************
584 #define LBITS(a) ((a)&BN_MASK2l)
585 #define HBITS(a) (((a)>>BN_BITS4)&BN_MASK2l)
586 #define L2HBITS(a) (((a)<<BN_BITS4)&BN_MASK2)
588 #define LLBITS(a) ((a)&BN_MASKl)
589 #define LHBITS(a) (((a)>>BN_BITS2)&BN_MASKl)
590 #define LL2HBITS(a) ((BN_ULLONG)((a)&BN_MASKl)<<BN_BITS2)
592 #define mul64(l,h,bl,bh) \
594 BN_ULONG m,m1,lt,ht; \
602 m=(m+m1)&BN_MASK2; if (m < m1) ht+=L2HBITS((BN_ULONG)1); \
605 lt=(lt+m1)&BN_MASK2; if (lt < m1) ht++; \
610 #define sqr64(lo,ho,in) \
620 h+=(m&BN_MASK2h1)>>(BN_BITS4-1); \
621 m =(m&BN_MASK2l)<<(BN_BITS4+1); \
622 l=(l+m)&BN_MASK2; if (l < m) h++; \
627 #define mul_add(r,a,bl,bh,c) { \
633 mul64(l,h,(bl),(bh)); \
635 /* non-multiply part */ \
636 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
638 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
643 #define mul(r,a,bl,bh,c) { \
649 mul64(l,h,(bl),(bh)); \
651 /* non-multiply part */ \
652 l+=(c); if ((l&BN_MASK2) < (c)) h++; \
656 #endif /* !BN_LLONG */
658 void BN_init(BIGNUM *a);
659 void BN_RECP_CTX_init(BN_RECP_CTX *recp);
660 void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
662 void bn_mul_normal(BN_ULONG *r,BN_ULONG *a,int na,BN_ULONG *b,int nb);
663 void bn_mul_comba8(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b);
664 void bn_mul_comba4(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b);
665 void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp);
666 void bn_sqr_comba8(BN_ULONG *r,const BN_ULONG *a);
667 void bn_sqr_comba4(BN_ULONG *r,const BN_ULONG *a);
668 int bn_cmp_words(const BN_ULONG *a,const BN_ULONG *b,int n);
669 int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b,
671 void bn_mul_recursive(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,int n2,
672 int dna,int dnb,BN_ULONG *t);
673 void bn_mul_part_recursive(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,
674 int n,int tna,int tnb,BN_ULONG *t);
675 void bn_sqr_recursive(BN_ULONG *r,const BN_ULONG *a, int n2, BN_ULONG *t);
676 void bn_mul_low_normal(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b, int n);
677 void bn_mul_low_recursive(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,int n2,
679 void bn_mul_high(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,BN_ULONG *l,int n2,
681 BN_ULONG bn_add_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
683 BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
685 int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp, const BN_ULONG *np,const BN_ULONG *n0, int num);
687 BIGNUM *int_bn_mod_inverse(BIGNUM *in,
688 const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx, int *noinv);
690 int bn_probable_prime_dh(BIGNUM *rnd, int bits,
691 const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx);
692 int bn_probable_prime_dh_retry(BIGNUM *rnd, int bits, BN_CTX *ctx);
693 int bn_probable_prime_dh_coprime(BIGNUM *rnd, int bits, BN_CTX *ctx);