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