1/* crypto/bn/bn_lcl.h */
2/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
3 * All rights reserved.
4 *
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.
8 *
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).
15 *
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.
22 *
23 * Redistribution and use in source and binary forms, with or without
24 * modification, are permitted provided that the following conditions
25 * are met:
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)"
40 *
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
51 * SUCH DAMAGE.
52 *
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.]
57 */
58/* ====================================================================
59 * Copyright (c) 1998-2000 The OpenSSL Project. All rights reserved.
60 *
61 * Redistribution and use in source and binary forms, with or without
62 * modification, are permitted provided that the following conditions
63 * are met:
64 *
65 * 1. Redistributions of source code must retain the above copyright
66 * notice, this list of conditions and the following disclaimer.
67 *
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
71 * distribution.
72 *
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/)"
77 *
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.
82 *
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.
86 *
87 * 6. Redistributions of any form whatsoever must retain the following
88 * acknowledgment:
89 * "This product includes software developed by the OpenSSL Project
90 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
91 *
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 * ====================================================================
105 *
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).
109 *
110 */
111
112#ifndef HEADER_BN_LCL_H
113# define HEADER_BN_LCL_H
114
115# include "../bn/bn.h"
116
117/*-
118 * BN_window_bits_for_exponent_size -- macro for sliding window mod_exp functions
119 *
120 *
121 * For window size 'w' (w >= 2) and a random 'b' bits exponent,
122 * the number of multiplications is a constant plus on average
123 *
124 * 2^(w-1) + (b-w)/(w+1);
125 *
126 * here 2^(w-1) is for precomputing the table (we actually need
127 * entries only for windows that have the lowest bit set), and
128 * (b-w)/(w+1) is an approximation for the expected number of
129 * w-bit windows, not counting the first one.
130 *
131 * Thus we should use
132 *
133 * w >= 6 if b > 671
134 * w = 5 if 671 > b > 239
135 * w = 4 if 239 > b > 79
136 * w = 3 if 79 > b > 23
137 * w <= 2 if 23 > b
138 *
139 * (with draws in between). Very small exponents are often selected
140 * with low Hamming weight, so we use w = 1 for b <= 23.
141 */
142# if 1
143# define BN_window_bits_for_exponent_size(b) \
144 ((b) > 671 ? 6 : \
145 (b) > 239 ? 5 : \
146 (b) > 79 ? 4 : \
147 (b) > 23 ? 3 : 1)
148# else
149/*
150 * Old SSLeay/OpenSSL table. Maximum window size was 5, so this table differs
151 * for b==1024; but it coincides for other interesting values (b==160,
152 * b==512).
153 */
154# define BN_window_bits_for_exponent_size(b) \
155 ((b) > 255 ? 5 : \
156 (b) > 127 ? 4 : \
157 (b) > 17 ? 3 : 1)
158# endif
159
160/*
161 * BN_mod_exp_mont_conttime is based on the assumption that the L1 data cache
162 * line width of the target processor is at least the following value.
163 */
164# define MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH ( 64 )
165# define MOD_EXP_CTIME_MIN_CACHE_LINE_MASK (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - 1)
166
167/*
168 * Window sizes optimized for fixed window size modular exponentiation
169 * algorithm (BN_mod_exp_mont_consttime). To achieve the security goals of
170 * BN_mode_exp_mont_consttime, the maximum size of the window must not exceed
171 * log_2(MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH). Window size thresholds are
172 * defined for cache line sizes of 32 and 64, cache line sizes where
173 * log_2(32)=5 and log_2(64)=6 respectively. A window size of 7 should only be
174 * used on processors that have a 128 byte or greater cache line size.
175 */
176# if MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 64
177
178# define BN_window_bits_for_ctime_exponent_size(b) \
179 ((b) > 937 ? 6 : \
180 (b) > 306 ? 5 : \
181 (b) > 89 ? 4 : \
182 (b) > 22 ? 3 : 1)
183# define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (6)
184
185# elif MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 32
186
187# define BN_window_bits_for_ctime_exponent_size(b) \
188 ((b) > 306 ? 5 : \
189 (b) > 89 ? 4 : \
190 (b) > 22 ? 3 : 1)
191# define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (5)
192
193# endif
194
195/* Pentium pro 16,16,16,32,64 */
196/* Alpha 16,16,16,16.64 */
197# define BN_MULL_SIZE_NORMAL (16)/* 32 */
198# define BN_MUL_RECURSIVE_SIZE_NORMAL (16)/* 32 less than */
199# define BN_SQR_RECURSIVE_SIZE_NORMAL (16)/* 32 */
200# define BN_MUL_LOW_RECURSIVE_SIZE_NORMAL (32)/* 32 */
201# define BN_MONT_CTX_SET_SIZE_WORD (64)/* 32 */
202
203/*
204 * 2011-02-22 SMS. In various places, a size_t variable or a type cast to
205 * size_t was used to perform integer-only operations on pointers. This
206 * failed on VMS with 64-bit pointers (CC /POINTER_SIZE = 64) because size_t
207 * is still only 32 bits. What's needed in these cases is an integer type
208 * with the same size as a pointer, which size_t is not certain to be. The
209 * only fix here is VMS-specific.
210 */
211# if defined(OPENSSL_SYS_VMS)
212# if __INITIAL_POINTER_SIZE == 64
213# define PTR_SIZE_INT long long
214# else /* __INITIAL_POINTER_SIZE == 64 */
215# define PTR_SIZE_INT int
216# endif /* __INITIAL_POINTER_SIZE == 64 [else] */
217# elif !defined(PTR_SIZE_INT) /* defined(OPENSSL_SYS_VMS) */
218# define PTR_SIZE_INT size_t
219# endif /* defined(OPENSSL_SYS_VMS) [else] */
220
221# if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) && !defined(PEDANTIC)
222/*
223 * BN_UMULT_HIGH section.
224 *
225 * No, I'm not trying to overwhelm you when stating that the
226 * product of N-bit numbers is 2*N bits wide:-) No, I don't expect
227 * you to be impressed when I say that if the compiler doesn't
228 * support 2*N integer type, then you have to replace every N*N
229 * multiplication with 4 (N/2)*(N/2) accompanied by some shifts
230 * and additions which unavoidably results in severe performance
231 * penalties. Of course provided that the hardware is capable of
232 * producing 2*N result... That's when you normally start
233 * considering assembler implementation. However! It should be
234 * pointed out that some CPUs (most notably Alpha, PowerPC and
235 * upcoming IA-64 family:-) provide *separate* instruction
236 * calculating the upper half of the product placing the result
237 * into a general purpose register. Now *if* the compiler supports
238 * inline assembler, then it's not impossible to implement the
239 * "bignum" routines (and have the compiler optimize 'em)
240 * exhibiting "native" performance in C. That's what BN_UMULT_HIGH
241 * macro is about:-)
242 *
243 * <appro@fy.chalmers.se>
244 */
245# if defined(__alpha) && (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT))
246# if defined(__DECC)
247# include <c_asm.h>
248# define BN_UMULT_HIGH(a,b) (BN_ULONG)asm("umulh %a0,%a1,%v0",(a),(b))
249# elif defined(__GNUC__) && __GNUC__>=2
250# define BN_UMULT_HIGH(a,b) ({ \
251 register BN_ULONG ret; \
252 asm ("umulh %1,%2,%0" \
253 : "=r"(ret) \
254 : "r"(a), "r"(b)); \
255 ret; })
256# endif /* compiler */
257# elif defined(_ARCH_PPC) && defined(__64BIT__) && defined(SIXTY_FOUR_BIT_LONG)
258# if defined(__GNUC__) && __GNUC__>=2
259# define BN_UMULT_HIGH(a,b) ({ \
260 register BN_ULONG ret; \
261 asm ("mulhdu %0,%1,%2" \
262 : "=r"(ret) \
263 : "r"(a), "r"(b)); \
264 ret; })
265# endif /* compiler */
266# elif (defined(__x86_64) || defined(__x86_64__)) && \
267 (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT))
268# if defined(__GNUC__) && __GNUC__>=2
269# define BN_UMULT_HIGH(a,b) ({ \
270 register BN_ULONG ret,discard; \
271 asm ("mulq %3" \
272 : "=a"(discard),"=d"(ret) \
273 : "a"(a), "g"(b) \
274 : "cc"); \
275 ret; })
276# define BN_UMULT_LOHI(low,high,a,b) \
277 asm ("mulq %3" \
278 : "=a"(low),"=d"(high) \
279 : "a"(a),"g"(b) \
280 : "cc");
281# endif
282# elif (defined(_M_AMD64) || defined(_M_X64)) && defined(SIXTY_FOUR_BIT)
283# if defined(_MSC_VER) && _MSC_VER>=1400
284unsigned __int64 __umulh(unsigned __int64 a, unsigned __int64 b);
285unsigned __int64 _umul128(unsigned __int64 a, unsigned __int64 b,
286 unsigned __int64 *h);
287# pragma intrinsic(__umulh,_umul128)
288# define BN_UMULT_HIGH(a,b) __umulh((a),(b))
289# define BN_UMULT_LOHI(low,high,a,b) ((low)=_umul128((a),(b),&(high)))
290# endif
291# elif defined(__mips) && (defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG))
292# if defined(__GNUC__) && __GNUC__>=2
293# if __GNUC__>4 || (__GNUC__>=4 && __GNUC_MINOR__>=4)
294 /* "h" constraint is no more since 4.4 */
295# define BN_UMULT_HIGH(a,b) (((__uint128_t)(a)*(b))>>64)
296# define BN_UMULT_LOHI(low,high,a,b) ({ \
297 __uint128_t ret=(__uint128_t)(a)*(b); \
298 (high)=ret>>64; (low)=ret; })
299# else
300# define BN_UMULT_HIGH(a,b) ({ \
301 register BN_ULONG ret; \
302 asm ("dmultu %1,%2" \
303 : "=h"(ret) \
304 : "r"(a), "r"(b) : "l"); \
305 ret; })
306# define BN_UMULT_LOHI(low,high,a,b)\
307 asm ("dmultu %2,%3" \
308 : "=l"(low),"=h"(high) \
309 : "r"(a), "r"(b));
310# endif
311# endif
312# elif defined(__aarch64__) && defined(SIXTY_FOUR_BIT_LONG)
313# if defined(__GNUC__) && __GNUC__>=2
314# define BN_UMULT_HIGH(a,b) ({ \
315 register BN_ULONG ret; \
316 asm ("umulh %0,%1,%2" \
317 : "=r"(ret) \
318 : "r"(a), "r"(b)); \
319 ret; })
320# endif
321# endif /* cpu */
322# endif /* OPENSSL_NO_ASM */
323
324/*************************************************************
325 * Using the long long type
326 */
327# define Lw(t) (((BN_ULONG)(t))&BN_MASK2)
328# define Hw(t) (((BN_ULONG)((t)>>BN_BITS2))&BN_MASK2)
329
330# ifdef BN_DEBUG_RAND
331# define bn_clear_top2max(a) \
332 { \
333 int ind = (a)->dmax - (a)->top; \
334 BN_ULONG *ftl = &(a)->d[(a)->top-1]; \
335 for (; ind != 0; ind--) \
336 *(++ftl) = 0x0; \
337 }
338# else
339# define bn_clear_top2max(a)
340# endif
341
342# ifdef BN_LLONG
343# define mul_add(r,a,w,c) { \
344 BN_ULLONG t; \
345 t=(BN_ULLONG)w * (a) + (r) + (c); \
346 (r)= Lw(t); \
347 (c)= Hw(t); \
348 }
349
350# define mul(r,a,w,c) { \
351 BN_ULLONG t; \
352 t=(BN_ULLONG)w * (a) + (c); \
353 (r)= Lw(t); \
354 (c)= Hw(t); \
355 }
356
357# define sqr(r0,r1,a) { \
358 BN_ULLONG t; \
359 t=(BN_ULLONG)(a)*(a); \
360 (r0)=Lw(t); \
361 (r1)=Hw(t); \
362 }
363
364# elif defined(BN_UMULT_LOHI)
365# define mul_add(r,a,w,c) { \
366 BN_ULONG high,low,ret,tmp=(a); \
367 ret = (r); \
368 BN_UMULT_LOHI(low,high,w,tmp); \
369 ret += (c); \
370 (c) = (ret<(c))?1:0; \
371 (c) += high; \
372 ret += low; \
373 (c) += (ret<low)?1:0; \
374 (r) = ret; \
375 }
376
377# define mul(r,a,w,c) { \
378 BN_ULONG high,low,ret,ta=(a); \
379 BN_UMULT_LOHI(low,high,w,ta); \
380 ret = low + (c); \
381 (c) = high; \
382 (c) += (ret<low)?1:0; \
383 (r) = ret; \
384 }
385
386# define sqr(r0,r1,a) { \
387 BN_ULONG tmp=(a); \
388 BN_UMULT_LOHI(r0,r1,tmp,tmp); \
389 }
390
391# elif defined(BN_UMULT_HIGH)
392# define mul_add(r,a,w,c) { \
393 BN_ULONG high,low,ret,tmp=(a); \
394 ret = (r); \
395 high= BN_UMULT_HIGH(w,tmp); \
396 ret += (c); \
397 low = (w) * tmp; \
398 (c) = (ret<(c))?1:0; \
399 (c) += high; \
400 ret += low; \
401 (c) += (ret<low)?1:0; \
402 (r) = ret; \
403 }
404
405# define mul(r,a,w,c) { \
406 BN_ULONG high,low,ret,ta=(a); \
407 low = (w) * ta; \
408 high= BN_UMULT_HIGH(w,ta); \
409 ret = low + (c); \
410 (c) = high; \
411 (c) += (ret<low)?1:0; \
412 (r) = ret; \
413 }
414
415# define sqr(r0,r1,a) { \
416 BN_ULONG tmp=(a); \
417 (r0) = tmp * tmp; \
418 (r1) = BN_UMULT_HIGH(tmp,tmp); \
419 }
420
421# else
422/*************************************************************
423 * No long long type
424 */
425
426# define LBITS(a) ((a)&BN_MASK2l)
427# define HBITS(a) (((a)>>BN_BITS4)&BN_MASK2l)
428# define L2HBITS(a) (((a)<<BN_BITS4)&BN_MASK2)
429
430# define LLBITS(a) ((a)&BN_MASKl)
431# define LHBITS(a) (((a)>>BN_BITS2)&BN_MASKl)
432# define LL2HBITS(a) ((BN_ULLONG)((a)&BN_MASKl)<<BN_BITS2)
433
434# define mul64(l,h,bl,bh) \
435 { \
436 BN_ULONG m,m1,lt,ht; \
437 \
438 lt=l; \
439 ht=h; \
440 m =(bh)*(lt); \
441 lt=(bl)*(lt); \
442 m1=(bl)*(ht); \
443 ht =(bh)*(ht); \
444 m=(m+m1)&BN_MASK2; if (m < m1) ht+=L2HBITS((BN_ULONG)1); \
445 ht+=HBITS(m); \
446 m1=L2HBITS(m); \
447 lt=(lt+m1)&BN_MASK2; if (lt < m1) ht++; \
448 (l)=lt; \
449 (h)=ht; \
450 }
451
452# define sqr64(lo,ho,in) \
453 { \
454 BN_ULONG l,h,m; \
455 \
456 h=(in); \
457 l=LBITS(h); \
458 h=HBITS(h); \
459 m =(l)*(h); \
460 l*=l; \
461 h*=h; \
462 h+=(m&BN_MASK2h1)>>(BN_BITS4-1); \
463 m =(m&BN_MASK2l)<<(BN_BITS4+1); \
464 l=(l+m)&BN_MASK2; if (l < m) h++; \
465 (lo)=l; \
466 (ho)=h; \
467 }
468
469# define mul_add(r,a,bl,bh,c) { \
470 BN_ULONG l,h; \
471 \
472 h= (a); \
473 l=LBITS(h); \
474 h=HBITS(h); \
475 mul64(l,h,(bl),(bh)); \
476 \
477 /* non-multiply part */ \
478 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
479 (c)=(r); \
480 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
481 (c)=h&BN_MASK2; \
482 (r)=l; \
483 }
484
485# define mul(r,a,bl,bh,c) { \
486 BN_ULONG l,h; \
487 \
488 h= (a); \
489 l=LBITS(h); \
490 h=HBITS(h); \
491 mul64(l,h,(bl),(bh)); \
492 \
493 /* non-multiply part */ \
494 l+=(c); if ((l&BN_MASK2) < (c)) h++; \
495 (c)=h&BN_MASK2; \
496 (r)=l&BN_MASK2; \
497 }
498# endif /* !BN_LLONG */
499
500# if defined(OPENSSL_DOING_MAKEDEPEND) && defined(OPENSSL_FIPS)
501# undef bn_div_words
502# endif
503
504void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb);
505void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
506void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
507void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp);
508void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a);
509void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a);
510int bn_cmp_words(const BN_ULONG *a, const BN_ULONG *b, int n);
511int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b, int cl, int dl);
512void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
513 int dna, int dnb, BN_ULONG *t);
514void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b,
515 int n, int tna, int tnb, BN_ULONG *t);
516void bn_sqr_recursive(BN_ULONG *r, const BN_ULONG *a, int n2, BN_ULONG *t);
517void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n);
518void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
519 BN_ULONG *t);
520void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2,
521 BN_ULONG *t);
522BN_ULONG bn_add_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
523 int cl, int dl);
524BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
525 int cl, int dl);
526int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
527 const BN_ULONG *np, const BN_ULONG *n0, int num);
528
529#endif
530