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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 <openssl/bn.h>
116
117#ifdef __cplusplus
118extern "C" {
119#endif
120
121
122/* Used for temp variables */
123#define BN_CTX_NUM 32
124#define BN_CTX_NUM_POS 12
125struct bignum_ctx
126 {
127 int tos;
128 BIGNUM bn[BN_CTX_NUM];
129 int flags;
130 int depth;
131 int pos[BN_CTX_NUM_POS];
132 int too_many;
133 } /* BN_CTX */;
134
135
136/*
137 * BN_window_bits_for_exponent_size -- macro for sliding window mod_exp functions
138 *
139 *
140 * For window size 'w' (w >= 2) and a random 'b' bits exponent,
141 * the number of multiplications is a constant plus on average
142 *
143 * 2^(w-1) + (b-w)/(w+1);
144 *
145 * here 2^(w-1) is for precomputing the table (we actually need
146 * entries only for windows that have the lowest bit set), and
147 * (b-w)/(w+1) is an approximation for the expected number of
148 * w-bit windows, not counting the first one.
149 *
150 * Thus we should use
151 *
152 * w >= 6 if b > 671
153 * w = 5 if 671 > b > 239
154 * w = 4 if 239 > b > 79
155 * w = 3 if 79 > b > 23
156 * w <= 2 if 23 > b
157 *
158 * (with draws in between). Very small exponents are often selected
159 * with low Hamming weight, so we use w = 1 for b <= 23.
160 */
161#if 1
162#define BN_window_bits_for_exponent_size(b) \
163 ((b) > 671 ? 6 : \
164 (b) > 239 ? 5 : \
165 (b) > 79 ? 4 : \
166 (b) > 23 ? 3 : 1)
167#else
168/* Old SSLeay/OpenSSL table.
169 * Maximum window size was 5, so this table differs for b==1024;
170 * but it coincides for other interesting values (b==160, b==512).
171 */
172#define BN_window_bits_for_exponent_size(b) \
173 ((b) > 255 ? 5 : \
174 (b) > 127 ? 4 : \
175 (b) > 17 ? 3 : 1)
176#endif
177
178
179
180/* Pentium pro 16,16,16,32,64 */
181/* Alpha 16,16,16,16.64 */
182#define BN_MULL_SIZE_NORMAL (16) /* 32 */
183#define BN_MUL_RECURSIVE_SIZE_NORMAL (16) /* 32 less than */
184#define BN_SQR_RECURSIVE_SIZE_NORMAL (16) /* 32 */
185#define BN_MUL_LOW_RECURSIVE_SIZE_NORMAL (32) /* 32 */
186#define BN_MONT_CTX_SET_SIZE_WORD (64) /* 32 */
187
188#if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) && !defined(PEDANTIC)
189/*
190 * BN_UMULT_HIGH section.
191 *
192 * No, I'm not trying to overwhelm you when stating that the
193 * product of N-bit numbers is 2*N bits wide:-) No, I don't expect
194 * you to be impressed when I say that if the compiler doesn't
195 * support 2*N integer type, then you have to replace every N*N
196 * multiplication with 4 (N/2)*(N/2) accompanied by some shifts
197 * and additions which unavoidably results in severe performance
198 * penalties. Of course provided that the hardware is capable of
199 * producing 2*N result... That's when you normally start
200 * considering assembler implementation. However! It should be
201 * pointed out that some CPUs (most notably Alpha, PowerPC and
202 * upcoming IA-64 family:-) provide *separate* instruction
203 * calculating the upper half of the product placing the result
204 * into a general purpose register. Now *if* the compiler supports
205 * inline assembler, then it's not impossible to implement the
206 * "bignum" routines (and have the compiler optimize 'em)
207 * exhibiting "native" performance in C. That's what BN_UMULT_HIGH
208 * macro is about:-)
209 *
210 * <appro@fy.chalmers.se>
211 */
212# if defined(__alpha) && (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT))
213# if defined(__DECC)
214# include <c_asm.h>
215# define BN_UMULT_HIGH(a,b) (BN_ULONG)asm("umulh %a0,%a1,%v0",(a),(b))
216# elif defined(__GNUC__)
217# define BN_UMULT_HIGH(a,b) ({ \
218 register BN_ULONG ret; \
219 asm ("umulh %1,%2,%0" \
220 : "=r"(ret) \
221 : "r"(a), "r"(b)); \
222 ret; })
223# endif /* compiler */
224# elif defined(_ARCH_PPC) && defined(__64BIT__) && defined(SIXTY_FOUR_BIT_LONG)
225# if defined(__GNUC__)
226# define BN_UMULT_HIGH(a,b) ({ \
227 register BN_ULONG ret; \
228 asm ("mulhdu %0,%1,%2" \
229 : "=r"(ret) \
230 : "r"(a), "r"(b)); \
231 ret; })
232# endif /* compiler */
233# elif defined(__x86_64) && defined(SIXTY_FOUR_BIT_LONG)
234# if defined(__GNUC__)
235# define BN_UMULT_HIGH(a,b) ({ \
236 register BN_ULONG ret,discard; \
237 asm ("mulq %3" \
238 : "=a"(discard),"=d"(ret) \
239 : "a"(a), "g"(b) \
240 : "cc"); \
241 ret; })
242# define BN_UMULT_LOHI(low,high,a,b) \
243 asm ("mulq %3" \
244 : "=a"(low),"=d"(high) \
245 : "a"(a),"g"(b) \
246 : "cc");
247# endif
248# endif /* cpu */
249#endif /* OPENSSL_NO_ASM */
250
251/*************************************************************
252 * Using the long long type
253 */
254#define Lw(t) (((BN_ULONG)(t))&BN_MASK2)
255#define Hw(t) (((BN_ULONG)((t)>>BN_BITS2))&BN_MASK2)
256
257/* This is used for internal error checking and is not normally used */
258#ifdef BN_DEBUG
259# include <assert.h>
260# define bn_check_top(a) assert ((a)->top >= 0 && (a)->top <= (a)->dmax);
261#else
262# define bn_check_top(a)
263#endif
264
265/* This macro is to add extra stuff for development checking */
266#ifdef BN_DEBUG
267#define bn_set_max(r) ((r)->max=(r)->top,BN_set_flags((r),BN_FLG_STATIC_DATA))
268#else
269#define bn_set_max(r)
270#endif
271
272/* These macros are used to 'take' a section of a bignum for read only use */
273#define bn_set_low(r,a,n) \
274 { \
275 (r)->top=((a)->top > (n))?(n):(a)->top; \
276 (r)->d=(a)->d; \
277 (r)->neg=(a)->neg; \
278 (r)->flags|=BN_FLG_STATIC_DATA; \
279 bn_set_max(r); \
280 }
281
282#define bn_set_high(r,a,n) \
283 { \
284 if ((a)->top > (n)) \
285 { \
286 (r)->top=(a)->top-n; \
287 (r)->d= &((a)->d[n]); \
288 } \
289 else \
290 (r)->top=0; \
291 (r)->neg=(a)->neg; \
292 (r)->flags|=BN_FLG_STATIC_DATA; \
293 bn_set_max(r); \
294 }
295
296#ifdef BN_LLONG
297#define mul_add(r,a,w,c) { \
298 BN_ULLONG t; \
299 t=(BN_ULLONG)w * (a) + (r) + (c); \
300 (r)= Lw(t); \
301 (c)= Hw(t); \
302 }
303
304#define mul(r,a,w,c) { \
305 BN_ULLONG t; \
306 t=(BN_ULLONG)w * (a) + (c); \
307 (r)= Lw(t); \
308 (c)= Hw(t); \
309 }
310
311#define sqr(r0,r1,a) { \
312 BN_ULLONG t; \
313 t=(BN_ULLONG)(a)*(a); \
314 (r0)=Lw(t); \
315 (r1)=Hw(t); \
316 }
317
318#elif defined(BN_UMULT_HIGH)
319#define mul_add(r,a,w,c) { \
320 BN_ULONG high,low,ret,tmp=(a); \
321 ret = (r); \
322 high= BN_UMULT_HIGH(w,tmp); \
323 ret += (c); \
324 low = (w) * tmp; \
325 (c) = (ret<(c))?1:0; \
326 (c) += high; \
327 ret += low; \
328 (c) += (ret<low)?1:0; \
329 (r) = ret; \
330 }
331
332#define mul(r,a,w,c) { \
333 BN_ULONG high,low,ret,ta=(a); \
334 low = (w) * ta; \
335 high= BN_UMULT_HIGH(w,ta); \
336 ret = low + (c); \
337 (c) = high; \
338 (c) += (ret<low)?1:0; \
339 (r) = ret; \
340 }
341
342#define sqr(r0,r1,a) { \
343 BN_ULONG tmp=(a); \
344 (r0) = tmp * tmp; \
345 (r1) = BN_UMULT_HIGH(tmp,tmp); \
346 }
347
348#else
349/*************************************************************
350 * No long long type
351 */
352
353#define LBITS(a) ((a)&BN_MASK2l)
354#define HBITS(a) (((a)>>BN_BITS4)&BN_MASK2l)
355#define L2HBITS(a) (((a)<<BN_BITS4)&BN_MASK2)
356
357#define LLBITS(a) ((a)&BN_MASKl)
358#define LHBITS(a) (((a)>>BN_BITS2)&BN_MASKl)
359#define LL2HBITS(a) ((BN_ULLONG)((a)&BN_MASKl)<<BN_BITS2)
360
361#define mul64(l,h,bl,bh) \
362 { \
363 BN_ULONG m,m1,lt,ht; \
364 \
365 lt=l; \
366 ht=h; \
367 m =(bh)*(lt); \
368 lt=(bl)*(lt); \
369 m1=(bl)*(ht); \
370 ht =(bh)*(ht); \
371 m=(m+m1)&BN_MASK2; if (m < m1) ht+=L2HBITS((BN_ULONG)1); \
372 ht+=HBITS(m); \
373 m1=L2HBITS(m); \
374 lt=(lt+m1)&BN_MASK2; if (lt < m1) ht++; \
375 (l)=lt; \
376 (h)=ht; \
377 }
378
379#define sqr64(lo,ho,in) \
380 { \
381 BN_ULONG l,h,m; \
382 \
383 h=(in); \
384 l=LBITS(h); \
385 h=HBITS(h); \
386 m =(l)*(h); \
387 l*=l; \
388 h*=h; \
389 h+=(m&BN_MASK2h1)>>(BN_BITS4-1); \
390 m =(m&BN_MASK2l)<<(BN_BITS4+1); \
391 l=(l+m)&BN_MASK2; if (l < m) h++; \
392 (lo)=l; \
393 (ho)=h; \
394 }
395
396#define mul_add(r,a,bl,bh,c) { \
397 BN_ULONG l,h; \
398 \
399 h= (a); \
400 l=LBITS(h); \
401 h=HBITS(h); \
402 mul64(l,h,(bl),(bh)); \
403 \
404 /* non-multiply part */ \
405 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
406 (c)=(r); \
407 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
408 (c)=h&BN_MASK2; \
409 (r)=l; \
410 }
411
412#define mul(r,a,bl,bh,c) { \
413 BN_ULONG l,h; \
414 \
415 h= (a); \
416 l=LBITS(h); \
417 h=HBITS(h); \
418 mul64(l,h,(bl),(bh)); \
419 \
420 /* non-multiply part */ \
421 l+=(c); if ((l&BN_MASK2) < (c)) h++; \
422 (c)=h&BN_MASK2; \
423 (r)=l&BN_MASK2; \
424 }
425#endif /* !BN_LLONG */
426
427void bn_mul_normal(BN_ULONG *r,BN_ULONG *a,int na,BN_ULONG *b,int nb);
428void bn_mul_comba8(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b);
429void bn_mul_comba4(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b);
430void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp);
431void bn_sqr_comba8(BN_ULONG *r,const BN_ULONG *a);
432void bn_sqr_comba4(BN_ULONG *r,const BN_ULONG *a);
433int bn_cmp_words(const BN_ULONG *a,const BN_ULONG *b,int n);
434int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b,
435 int cl, int dl);
436#ifdef BN_RECURSION
437void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
438 BN_ULONG *t);
439void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int tn,
440 int n, BN_ULONG *t);
441void bn_mul_low_recursive(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,int n2,
442 BN_ULONG *t);
443void bn_mul_high(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,BN_ULONG *l,int n2,
444 BN_ULONG *t);
445void bn_sqr_recursive(BN_ULONG *r,const BN_ULONG *a, int n2, BN_ULONG *t);
446#endif
447void bn_mul_low_normal(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b, int n);
448
449#ifdef __cplusplus
450}
451#endif
452
453#endif
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