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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/* 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
466void bn_mul_normal(BN_ULONG *r,BN_ULONG *a,int na,BN_ULONG *b,int nb);
467void bn_mul_comba8(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b);
468void bn_mul_comba4(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b);
469void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp);
470void bn_sqr_comba8(BN_ULONG *r,const BN_ULONG *a);
471void bn_sqr_comba4(BN_ULONG *r,const BN_ULONG *a);
472int bn_cmp_words(const BN_ULONG *a,const BN_ULONG *b,int n);
473int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b,
474 int cl, int dl);
475#ifdef BN_RECURSION
476void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
477 BN_ULONG *t);
478void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int tn,
479 int n, BN_ULONG *t);
480void bn_mul_low_recursive(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,int n2,
481 BN_ULONG *t);
482void bn_mul_high(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,BN_ULONG *l,int n2,
483 BN_ULONG *t);
484void bn_sqr_recursive(BN_ULONG *r,const BN_ULONG *a, int n2, BN_ULONG *t);
485#endif
486void 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
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