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
118 extern "C" {
119 #endif
120 
121 
122 /* Used for temp variables */
123 #define BN_CTX_NUM	32
124 #define BN_CTX_NUM_POS	12
125 struct 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 /* BN_mod_exp_mont_conttime is based on the assumption that the
181  * L1 data cache line width of the target processor is at least
182  * the following value.
183  */
184 #define MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH	( 64 )
185 #define MOD_EXP_CTIME_MIN_CACHE_LINE_MASK	(MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - 1)
186 
187 /* Window sizes optimized for fixed window size modular exponentiation
188  * algorithm (BN_mod_exp_mont_consttime).
189  *
190  * To achieve the security goals of BN_mode_exp_mont_consttime, the
191  * maximum size of the window must not exceed
192  * log_2(MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH).
193  *
194  * Window size thresholds are defined for cache line sizes of 32 and 64,
195  * cache line sizes where log_2(32)=5 and log_2(64)=6 respectively. A
196  * window size of 7 should only be used on processors that have a 128
197  * byte or greater cache line size.
198  */
199 #if MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 64
200 
201 #  define BN_window_bits_for_ctime_exponent_size(b) \
202 		((b) > 937 ? 6 : \
203 		 (b) > 306 ? 5 : \
204 		 (b) >  89 ? 4 : \
205 		 (b) >  22 ? 3 : 1)
206 #  define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE	(6)
207 
208 #elif MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 32
209 
210 #  define BN_window_bits_for_ctime_exponent_size(b) \
211 		((b) > 306 ? 5 : \
212 		 (b) >  89 ? 4 : \
213 		 (b) >  22 ? 3 : 1)
214 #  define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE	(5)
215 
216 #endif
217 
218 
219 /* Pentium pro 16,16,16,32,64 */
220 /* Alpha       16,16,16,16.64 */
221 #define BN_MULL_SIZE_NORMAL			(16) /* 32 */
222 #define BN_MUL_RECURSIVE_SIZE_NORMAL		(16) /* 32 less than */
223 #define BN_SQR_RECURSIVE_SIZE_NORMAL		(16) /* 32 */
224 #define BN_MUL_LOW_RECURSIVE_SIZE_NORMAL	(32) /* 32 */
225 #define BN_MONT_CTX_SET_SIZE_WORD		(64) /* 32 */
226 
227 #if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) && !defined(PEDANTIC)
228 /*
229  * BN_UMULT_HIGH section.
230  *
231  * No, I'm not trying to overwhelm you when stating that the
232  * product of N-bit numbers is 2*N bits wide:-) No, I don't expect
233  * you to be impressed when I say that if the compiler doesn't
234  * support 2*N integer type, then you have to replace every N*N
235  * multiplication with 4 (N/2)*(N/2) accompanied by some shifts
236  * and additions which unavoidably results in severe performance
237  * penalties. Of course provided that the hardware is capable of
238  * producing 2*N result... That's when you normally start
239  * considering assembler implementation. However! It should be
240  * pointed out that some CPUs (most notably Alpha, PowerPC and
241  * upcoming IA-64 family:-) provide *separate* instruction
242  * calculating the upper half of the product placing the result
243  * into a general purpose register. Now *if* the compiler supports
244  * inline assembler, then it's not impossible to implement the
245  * "bignum" routines (and have the compiler optimize 'em)
246  * exhibiting "native" performance in C. That's what BN_UMULT_HIGH
247  * macro is about:-)
248  *
249  *					<appro@fy.chalmers.se>
250  */
251 # if defined(__alpha) && (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT))
252 #  if defined(__DECC)
253 #   include <c_asm.h>
254 #   define BN_UMULT_HIGH(a,b)	(BN_ULONG)asm("umulh %a0,%a1,%v0",(a),(b))
255 #  elif defined(__GNUC__)
256 #   define BN_UMULT_HIGH(a,b)	({	\
257 	register BN_ULONG ret;		\
258 	asm ("umulh	%1,%2,%0"	\
259 	     : "=r"(ret)		\
260 	     : "r"(a), "r"(b));		\
261 	ret;			})
262 #  endif	/* compiler */
263 # elif defined(_ARCH_PPC) && defined(__64BIT__) && defined(SIXTY_FOUR_BIT_LONG)
264 #  if defined(__GNUC__)
265 #   define BN_UMULT_HIGH(a,b)	({	\
266 	register BN_ULONG ret;		\
267 	asm ("mulhdu	%0,%1,%2"	\
268 	     : "=r"(ret)		\
269 	     : "r"(a), "r"(b));		\
270 	ret;			})
271 #  endif	/* compiler */
272 # elif defined(__x86_64) && defined(SIXTY_FOUR_BIT_LONG)
273 #  if defined(__GNUC__)
274 #   define BN_UMULT_HIGH(a,b)	({	\
275 	register BN_ULONG ret,discard;	\
276 	asm ("mulq	%3"		\
277 	     : "=a"(discard),"=d"(ret)	\
278 	     : "a"(a), "g"(b)		\
279 	     : "cc");			\
280 	ret;			})
281 #   define BN_UMULT_LOHI(low,high,a,b)	\
282 	asm ("mulq	%3"		\
283 		: "=a"(low),"=d"(high)	\
284 		: "a"(a),"g"(b)		\
285 		: "cc");
286 #  endif
287 # endif		/* cpu */
288 #endif		/* OPENSSL_NO_ASM */
289 
290 /*************************************************************
291  * Using the long long type
292  */
293 #define Lw(t)    (((BN_ULONG)(t))&BN_MASK2)
294 #define Hw(t)    (((BN_ULONG)((t)>>BN_BITS2))&BN_MASK2)
295 
296 /* This is used for internal error checking and is not normally used */
297 #ifdef BN_DEBUG
298 # include <assert.h>
299 # define bn_check_top(a) assert ((a)->top >= 0 && (a)->top <= (a)->dmax);
300 #else
301 # define bn_check_top(a)
302 #endif
303 
304 /* This macro is to add extra stuff for development checking */
305 #ifdef BN_DEBUG
306 #define	bn_set_max(r) ((r)->max=(r)->top,BN_set_flags((r),BN_FLG_STATIC_DATA))
307 #else
308 #define	bn_set_max(r)
309 #endif
310 
311 /* These macros are used to 'take' a section of a bignum for read only use */
312 #define bn_set_low(r,a,n) \
313 	{ \
314 	(r)->top=((a)->top > (n))?(n):(a)->top; \
315 	(r)->d=(a)->d; \
316 	(r)->neg=(a)->neg; \
317 	(r)->flags|=BN_FLG_STATIC_DATA; \
318 	bn_set_max(r); \
319 	}
320 
321 #define bn_set_high(r,a,n) \
322 	{ \
323 	if ((a)->top > (n)) \
324 		{ \
325 		(r)->top=(a)->top-n; \
326 		(r)->d= &((a)->d[n]); \
327 		} \
328 	else \
329 		(r)->top=0; \
330 	(r)->neg=(a)->neg; \
331 	(r)->flags|=BN_FLG_STATIC_DATA; \
332 	bn_set_max(r); \
333 	}
334 
335 #ifdef BN_LLONG
336 #define mul_add(r,a,w,c) { \
337 	BN_ULLONG t; \
338 	t=(BN_ULLONG)w * (a) + (r) + (c); \
339 	(r)= Lw(t); \
340 	(c)= Hw(t); \
341 	}
342 
343 #define mul(r,a,w,c) { \
344 	BN_ULLONG t; \
345 	t=(BN_ULLONG)w * (a) + (c); \
346 	(r)= Lw(t); \
347 	(c)= Hw(t); \
348 	}
349 
350 #define sqr(r0,r1,a) { \
351 	BN_ULLONG t; \
352 	t=(BN_ULLONG)(a)*(a); \
353 	(r0)=Lw(t); \
354 	(r1)=Hw(t); \
355 	}
356 
357 #elif defined(BN_UMULT_HIGH)
358 #define mul_add(r,a,w,c) {		\
359 	BN_ULONG high,low,ret,tmp=(a);	\
360 	ret =  (r);			\
361 	high=  BN_UMULT_HIGH(w,tmp);	\
362 	ret += (c);			\
363 	low =  (w) * tmp;		\
364 	(c) =  (ret<(c))?1:0;		\
365 	(c) += high;			\
366 	ret += low;			\
367 	(c) += (ret<low)?1:0;		\
368 	(r) =  ret;			\
369 	}
370 
371 #define mul(r,a,w,c)	{		\
372 	BN_ULONG high,low,ret,ta=(a);	\
373 	low =  (w) * ta;		\
374 	high=  BN_UMULT_HIGH(w,ta);	\
375 	ret =  low + (c);		\
376 	(c) =  high;			\
377 	(c) += (ret<low)?1:0;		\
378 	(r) =  ret;			\
379 	}
380 
381 #define sqr(r0,r1,a)	{		\
382 	BN_ULONG tmp=(a);		\
383 	(r0) = tmp * tmp;		\
384 	(r1) = BN_UMULT_HIGH(tmp,tmp);	\
385 	}
386 
387 #else
388 /*************************************************************
389  * No long long type
390  */
391 
392 #define LBITS(a)	((a)&BN_MASK2l)
393 #define HBITS(a)	(((a)>>BN_BITS4)&BN_MASK2l)
394 #define	L2HBITS(a)	(((a)<<BN_BITS4)&BN_MASK2)
395 
396 #define LLBITS(a)	((a)&BN_MASKl)
397 #define LHBITS(a)	(((a)>>BN_BITS2)&BN_MASKl)
398 #define	LL2HBITS(a)	((BN_ULLONG)((a)&BN_MASKl)<<BN_BITS2)
399 
400 #define mul64(l,h,bl,bh) \
401 	{ \
402 	BN_ULONG m,m1,lt,ht; \
403  \
404 	lt=l; \
405 	ht=h; \
406 	m =(bh)*(lt); \
407 	lt=(bl)*(lt); \
408 	m1=(bl)*(ht); \
409 	ht =(bh)*(ht); \
410 	m=(m+m1)&BN_MASK2; if (m < m1) ht+=L2HBITS((BN_ULONG)1); \
411 	ht+=HBITS(m); \
412 	m1=L2HBITS(m); \
413 	lt=(lt+m1)&BN_MASK2; if (lt < m1) ht++; \
414 	(l)=lt; \
415 	(h)=ht; \
416 	}
417 
418 #define sqr64(lo,ho,in) \
419 	{ \
420 	BN_ULONG l,h,m; \
421  \
422 	h=(in); \
423 	l=LBITS(h); \
424 	h=HBITS(h); \
425 	m =(l)*(h); \
426 	l*=l; \
427 	h*=h; \
428 	h+=(m&BN_MASK2h1)>>(BN_BITS4-1); \
429 	m =(m&BN_MASK2l)<<(BN_BITS4+1); \
430 	l=(l+m)&BN_MASK2; if (l < m) h++; \
431 	(lo)=l; \
432 	(ho)=h; \
433 	}
434 
435 #define mul_add(r,a,bl,bh,c) { \
436 	BN_ULONG l,h; \
437  \
438 	h= (a); \
439 	l=LBITS(h); \
440 	h=HBITS(h); \
441 	mul64(l,h,(bl),(bh)); \
442  \
443 	/* non-multiply part */ \
444 	l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
445 	(c)=(r); \
446 	l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
447 	(c)=h&BN_MASK2; \
448 	(r)=l; \
449 	}
450 
451 #define mul(r,a,bl,bh,c) { \
452 	BN_ULONG l,h; \
453  \
454 	h= (a); \
455 	l=LBITS(h); \
456 	h=HBITS(h); \
457 	mul64(l,h,(bl),(bh)); \
458  \
459 	/* non-multiply part */ \
460 	l+=(c); if ((l&BN_MASK2) < (c)) h++; \
461 	(c)=h&BN_MASK2; \
462 	(r)=l&BN_MASK2; \
463 	}
464 #endif /* !BN_LLONG */
465 
466 void bn_mul_normal(BN_ULONG *r,BN_ULONG *a,int na,BN_ULONG *b,int nb);
467 void bn_mul_comba8(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b);
468 void bn_mul_comba4(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b);
469 void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp);
470 void bn_sqr_comba8(BN_ULONG *r,const BN_ULONG *a);
471 void bn_sqr_comba4(BN_ULONG *r,const BN_ULONG *a);
472 int bn_cmp_words(const BN_ULONG *a,const BN_ULONG *b,int n);
473 int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b,
474 	int cl, int dl);
475 #ifdef BN_RECURSION
476 void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
477 	BN_ULONG *t);
478 void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int tn,
479 	int n, BN_ULONG *t);
480 void bn_mul_low_recursive(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,int n2,
481 	BN_ULONG *t);
482 void bn_mul_high(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,BN_ULONG *l,int n2,
483 	BN_ULONG *t);
484 void bn_sqr_recursive(BN_ULONG *r,const BN_ULONG *a, int n2, BN_ULONG *t);
485 #endif
486 void bn_mul_low_normal(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b, int n);
487 
488 #ifdef  __cplusplus
489 }
490 #endif
491 
492 #endif
493