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"
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_DEBUG_RAND 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 /* We only need assert() when debugging */
156 /* To avoid "make update" cvs wars due to BN_DEBUG, use some tricks */
157 #ifndef RAND_pseudo_bytes
158 int RAND_pseudo_bytes(unsigned char *buf,int num);
159 #define BN_DEBUG_TRIX
161 #define bn_pollute(a) \
163 const BIGNUM *_bnum1 = (a); \
164 if(_bnum1->top < _bnum1->dmax) { \
165 unsigned char _tmp_char; \
166 /* We cast away const without the compiler knowing, any \
167 * *genuinely* constant variables that aren't mutable \
168 * wouldn't be constructed with top!=dmax. */ \
169 BN_ULONG *_not_const; \
170 memcpy(&_not_const, &_bnum1->d, sizeof(BN_ULONG*)); \
171 RAND_pseudo_bytes(&_tmp_char, 1); \
172 memset((unsigned char *)(_not_const + _bnum1->top), _tmp_char, \
173 (_bnum1->dmax - _bnum1->top) * sizeof(BN_ULONG)); \
177 #undef RAND_pseudo_bytes
180 #define bn_pollute(a)
182 #define bn_check_top(a) \
184 const BIGNUM *_bnum2 = (a); \
185 if (_bnum2 != NULL) { \
186 assert((_bnum2->top == 0) || \
187 (_bnum2->d[_bnum2->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 && (words) >= (_bnum2)->top); \
199 /* avoid unused variable warning with NDEBUG */ \
203 #else /* !BN_DEBUG */
205 #define bn_pollute(a)
206 #define bn_check_top(a)
207 #define bn_fix_top(a) bn_correct_top(a)
208 #define bn_check_size(bn, bits)
209 #define bn_wcheck_size(bn, words)
214 BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
215 BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
216 void bn_sqr_words(BN_ULONG *rp, const BN_ULONG *ap, int num);
217 BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d);
218 BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,int num);
219 BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,int num);
224 BN_ULONG *d; /* Pointer to an array of 'BN_BITS2' bit chunks. */
225 int top; /* Index of last used d +1. */
226 /* The next are internal book keeping for bn_expand. */
227 int dmax; /* Size of the d array. */
228 int neg; /* one if the number is negative */
232 /* Used for montgomery multiplication */
233 struct bn_mont_ctx_st
235 int ri; /* number of bits in R */
236 BIGNUM RR; /* used to convert to montgomery form */
237 BIGNUM N; /* The modulus */
238 BIGNUM Ni; /* R*(1/R mod N) - N*Ni = 1
239 * (Ni is only stored for bignum algorithm) */
240 BN_ULONG n0[2];/* least significant word(s) of Ni;
241 (type changed with 0.9.9, was "BN_ULONG n0;" before) */
245 /* Used for reciprocal division/mod functions
246 * It cannot be shared between threads
248 struct bn_recp_ctx_st
250 BIGNUM N; /* the divisor */
251 BIGNUM Nr; /* the reciprocal */
257 /* Used for slow "generation" functions. */
260 unsigned int ver; /* To handle binary (in)compatibility */
261 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 *);
273 * BN_window_bits_for_exponent_size -- macro for sliding window mod_exp functions
276 * For window size 'w' (w >= 2) and a random 'b' bits exponent,
277 * the number of multiplications is a constant plus on average
279 * 2^(w-1) + (b-w)/(w+1);
281 * here 2^(w-1) is for precomputing the table (we actually need
282 * entries only for windows that have the lowest bit set), and
283 * (b-w)/(w+1) is an approximation for the expected number of
284 * w-bit windows, not counting the first one.
289 * w = 5 if 671 > b > 239
290 * w = 4 if 239 > b > 79
291 * w = 3 if 79 > b > 23
294 * (with draws in between). Very small exponents are often selected
295 * with low Hamming weight, so we use w = 1 for b <= 23.
298 #define BN_window_bits_for_exponent_size(b) \
304 /* Old SSLeay/OpenSSL table.
305 * Maximum window size was 5, so this table differs for b==1024;
306 * but it coincides for other interesting values (b==160, b==512).
308 #define BN_window_bits_for_exponent_size(b) \
316 /* BN_mod_exp_mont_conttime is based on the assumption that the
317 * L1 data cache line width of the target processor is at least
318 * the following value.
320 #define MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH ( 64 )
321 #define MOD_EXP_CTIME_MIN_CACHE_LINE_MASK (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - 1)
323 /* Window sizes optimized for fixed window size modular exponentiation
324 * algorithm (BN_mod_exp_mont_consttime).
326 * To achieve the security goals of BN_mode_exp_mont_consttime, the
327 * maximum size of the window must not exceed
328 * log_2(MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH).
330 * Window size thresholds are defined for cache line sizes of 32 and 64,
331 * cache line sizes where log_2(32)=5 and log_2(64)=6 respectively. A
332 * window size of 7 should only be used on processors that have a 128
333 * byte or greater cache line size.
335 #if MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 64
337 # define BN_window_bits_for_ctime_exponent_size(b) \
342 # define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (6)
344 #elif MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 32
346 # define BN_window_bits_for_ctime_exponent_size(b) \
350 # define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (5)
355 /* Pentium pro 16,16,16,32,64 */
356 /* Alpha 16,16,16,16.64 */
357 #define BN_MULL_SIZE_NORMAL (16) /* 32 */
358 #define BN_MUL_RECURSIVE_SIZE_NORMAL (16) /* 32 less than */
359 #define BN_SQR_RECURSIVE_SIZE_NORMAL (16) /* 32 */
360 #define BN_MUL_LOW_RECURSIVE_SIZE_NORMAL (32) /* 32 */
361 #define BN_MONT_CTX_SET_SIZE_WORD (64) /* 32 */
364 * In various places, a size_t variable or a type cast to size_t was
365 * used to perform integer-only operations on pointers. This failed on
366 * VMS with 64-bit pointers (CC /POINTER_SIZE = 64) because size_t is
367 * still only 32 bits. What's needed in these cases is an integer type
368 * with the same size as a pointer, which size_t is not certain to be.
369 * The only fix here is VMS-specific.
371 #if defined(OPENSSL_SYS_VMS)
372 # if __INITIAL_POINTER_SIZE == 64
373 # define PTR_SIZE_INT long long
374 # else /* __INITIAL_POINTER_SIZE == 64 */
375 # define PTR_SIZE_INT int
376 # endif /* __INITIAL_POINTER_SIZE == 64 [else] */
377 #elif !defined(PTR_SIZE_INT) /* defined(OPENSSL_SYS_VMS) */
378 # define PTR_SIZE_INT size_t
379 #endif /* defined(OPENSSL_SYS_VMS) [else] */
381 #if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) && !defined(PEDANTIC)
383 * BN_UMULT_HIGH section.
385 * No, I'm not trying to overwhelm you when stating that the
386 * product of N-bit numbers is 2*N bits wide:-) No, I don't expect
387 * you to be impressed when I say that if the compiler doesn't
388 * support 2*N integer type, then you have to replace every N*N
389 * multiplication with 4 (N/2)*(N/2) accompanied by some shifts
390 * and additions which unavoidably results in severe performance
391 * penalties. Of course provided that the hardware is capable of
392 * producing 2*N result... That's when you normally start
393 * considering assembler implementation. However! It should be
394 * pointed out that some CPUs (most notably Alpha, PowerPC and
395 * upcoming IA-64 family:-) provide *separate* instruction
396 * calculating the upper half of the product placing the result
397 * into a general purpose register. Now *if* the compiler supports
398 * inline assembler, then it's not impossible to implement the
399 * "bignum" routines (and have the compiler optimize 'em)
400 * exhibiting "native" performance in C. That's what BN_UMULT_HIGH
403 * <appro@fy.chalmers.se>
405 # if defined(__alpha) && (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT))
408 # define BN_UMULT_HIGH(a,b) (BN_ULONG)asm("umulh %a0,%a1,%v0",(a),(b))
409 # elif defined(__GNUC__) && __GNUC__>=2
410 # define BN_UMULT_HIGH(a,b) ({ \
411 register BN_ULONG ret; \
412 asm ("umulh %1,%2,%0" \
416 # endif /* compiler */
417 # elif defined(_ARCH_PPC) && defined(__64BIT__) && defined(SIXTY_FOUR_BIT_LONG)
418 # if defined(__GNUC__) && __GNUC__>=2
419 # define BN_UMULT_HIGH(a,b) ({ \
420 register BN_ULONG ret; \
421 asm ("mulhdu %0,%1,%2" \
425 # endif /* compiler */
426 # elif (defined(__x86_64) || defined(__x86_64__)) && \
427 (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT))
428 # if defined(__GNUC__) && __GNUC__>=2
429 # define BN_UMULT_HIGH(a,b) ({ \
430 register BN_ULONG ret,discard; \
432 : "=a"(discard),"=d"(ret) \
436 # define BN_UMULT_LOHI(low,high,a,b) \
438 : "=a"(low),"=d"(high) \
442 # elif (defined(_M_AMD64) || defined(_M_X64)) && defined(SIXTY_FOUR_BIT)
443 # if defined(_MSC_VER) && _MSC_VER>=1400
444 unsigned __int64 __umulh (unsigned __int64 a,unsigned __int64 b);
445 unsigned __int64 _umul128 (unsigned __int64 a,unsigned __int64 b,
446 unsigned __int64 *h);
447 # pragma intrinsic(__umulh,_umul128)
448 # define BN_UMULT_HIGH(a,b) __umulh((a),(b))
449 # define BN_UMULT_LOHI(low,high,a,b) ((low)=_umul128((a),(b),&(high)))
451 # elif defined(__mips) && (defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG))
452 # if defined(__GNUC__) && __GNUC__>=2
453 # if __GNUC__>=4 && __GNUC_MINOR__>=4 /* "h" constraint is no more since 4.4 */
454 # define BN_UMULT_HIGH(a,b) (((__uint128_t)(a)*(b))>>64)
455 # define BN_UMULT_LOHI(low,high,a,b) ({ \
456 __uint128_t ret=(__uint128_t)(a)*(b); \
457 (high)=ret>>64; (low)=ret; })
459 # define BN_UMULT_HIGH(a,b) ({ \
460 register BN_ULONG ret; \
461 asm ("dmultu %1,%2" \
463 : "r"(a), "r"(b) : "l"); \
465 # define BN_UMULT_LOHI(low,high,a,b)\
466 asm ("dmultu %2,%3" \
467 : "=l"(low),"=h"(high) \
471 # elif defined(__aarch64__) && defined(SIXTY_FOUR_BIT_LONG)
472 # if defined(__GNUC__) && __GNUC__>=2
473 # define BN_UMULT_HIGH(a,b) ({ \
474 register BN_ULONG ret; \
475 asm ("umulh %0,%1,%2" \
481 #endif /* OPENSSL_NO_ASM */
483 /*************************************************************
484 * Using the long long type
486 #define Lw(t) (((BN_ULONG)(t))&BN_MASK2)
487 #define Hw(t) (((BN_ULONG)((t)>>BN_BITS2))&BN_MASK2)
490 #define bn_clear_top2max(a) \
492 int ind = (a)->dmax - (a)->top; \
493 BN_ULONG *ftl = &(a)->d[(a)->top-1]; \
494 for (; ind != 0; ind--) \
498 #define bn_clear_top2max(a)
502 #define mul_add(r,a,w,c) { \
504 t=(BN_ULLONG)w * (a) + (r) + (c); \
509 #define mul(r,a,w,c) { \
511 t=(BN_ULLONG)w * (a) + (c); \
516 #define sqr(r0,r1,a) { \
518 t=(BN_ULLONG)(a)*(a); \
523 #elif defined(BN_UMULT_LOHI)
524 #define mul_add(r,a,w,c) { \
525 BN_ULONG high,low,ret,tmp=(a); \
527 BN_UMULT_LOHI(low,high,w,tmp); \
529 (c) = (ret<(c))?1:0; \
532 (c) += (ret<low)?1:0; \
536 #define mul(r,a,w,c) { \
537 BN_ULONG high,low,ret,ta=(a); \
538 BN_UMULT_LOHI(low,high,w,ta); \
541 (c) += (ret<low)?1:0; \
545 #define sqr(r0,r1,a) { \
547 BN_UMULT_LOHI(r0,r1,tmp,tmp); \
550 #elif defined(BN_UMULT_HIGH)
551 #define mul_add(r,a,w,c) { \
552 BN_ULONG high,low,ret,tmp=(a); \
554 high= BN_UMULT_HIGH(w,tmp); \
557 (c) = (ret<(c))?1:0; \
560 (c) += (ret<low)?1:0; \
564 #define mul(r,a,w,c) { \
565 BN_ULONG high,low,ret,ta=(a); \
567 high= BN_UMULT_HIGH(w,ta); \
570 (c) += (ret<low)?1:0; \
574 #define sqr(r0,r1,a) { \
577 (r1) = BN_UMULT_HIGH(tmp,tmp); \
581 /*************************************************************
585 #define LBITS(a) ((a)&BN_MASK2l)
586 #define HBITS(a) (((a)>>BN_BITS4)&BN_MASK2l)
587 #define L2HBITS(a) (((a)<<BN_BITS4)&BN_MASK2)
589 #define LLBITS(a) ((a)&BN_MASKl)
590 #define LHBITS(a) (((a)>>BN_BITS2)&BN_MASKl)
591 #define LL2HBITS(a) ((BN_ULLONG)((a)&BN_MASKl)<<BN_BITS2)
593 #define mul64(l,h,bl,bh) \
595 BN_ULONG m,m1,lt,ht; \
603 m=(m+m1)&BN_MASK2; if (m < m1) ht+=L2HBITS((BN_ULONG)1); \
606 lt=(lt+m1)&BN_MASK2; if (lt < m1) ht++; \
611 #define sqr64(lo,ho,in) \
621 h+=(m&BN_MASK2h1)>>(BN_BITS4-1); \
622 m =(m&BN_MASK2l)<<(BN_BITS4+1); \
623 l=(l+m)&BN_MASK2; if (l < m) h++; \
628 #define mul_add(r,a,bl,bh,c) { \
634 mul64(l,h,(bl),(bh)); \
636 /* non-multiply part */ \
637 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
639 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
644 #define mul(r,a,bl,bh,c) { \
650 mul64(l,h,(bl),(bh)); \
652 /* non-multiply part */ \
653 l+=(c); if ((l&BN_MASK2) < (c)) h++; \
657 #endif /* !BN_LLONG */
659 void BN_init(BIGNUM *a);
660 void BN_RECP_CTX_init(BN_RECP_CTX *recp);
661 void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
663 void bn_mul_normal(BN_ULONG *r,BN_ULONG *a,int na,BN_ULONG *b,int nb);
664 void bn_mul_comba8(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b);
665 void bn_mul_comba4(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b);
666 void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp);
667 void bn_sqr_comba8(BN_ULONG *r,const BN_ULONG *a);
668 void bn_sqr_comba4(BN_ULONG *r,const BN_ULONG *a);
669 int bn_cmp_words(const BN_ULONG *a,const BN_ULONG *b,int n);
670 int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b,
672 void bn_mul_recursive(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,int n2,
673 int dna,int dnb,BN_ULONG *t);
674 void bn_mul_part_recursive(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,
675 int n,int tna,int tnb,BN_ULONG *t);
676 void bn_sqr_recursive(BN_ULONG *r,const BN_ULONG *a, int n2, BN_ULONG *t);
677 void bn_mul_low_normal(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b, int n);
678 void bn_mul_low_recursive(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,int n2,
680 void bn_mul_high(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,BN_ULONG *l,int n2,
682 BN_ULONG bn_add_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
684 BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
686 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);
688 BIGNUM *int_bn_mod_inverse(BIGNUM *in,
689 const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx, int *noinv);
691 int bn_probable_prime_dh(BIGNUM *rnd, int bits,
692 const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx);
693 int bn_probable_prime_dh_retry(BIGNUM *rnd, int bits, BN_CTX *ctx);
694 int bn_probable_prime_dh_coprime(BIGNUM *rnd, int bits, BN_CTX *ctx);