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1/* $OpenBSD: bn_lcl.h,v 1.22 2015/11/06 21:42:32 miod Exp $ */
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/opensslconf.h>
116
117#include <openssl/bn.h>
118
119#ifdef __cplusplus
120extern "C" {
121#endif
122
123
124/*
125 * BN_window_bits_for_exponent_size -- macro for sliding window mod_exp functions
126 *
127 *
128 * For window size 'w' (w >= 2) and a random 'b' bits exponent,
129 * the number of multiplications is a constant plus on average
130 *
131 * 2^(w-1) + (b-w)/(w+1);
132 *
133 * here 2^(w-1) is for precomputing the table (we actually need
134 * entries only for windows that have the lowest bit set), and
135 * (b-w)/(w+1) is an approximation for the expected number of
136 * w-bit windows, not counting the first one.
137 *
138 * Thus we should use
139 *
140 * w >= 6 if b > 671
141 * w = 5 if 671 > b > 239
142 * w = 4 if 239 > b > 79
143 * w = 3 if 79 > b > 23
144 * w <= 2 if 23 > b
145 *
146 * (with draws in between). Very small exponents are often selected
147 * with low Hamming weight, so we use w = 1 for b <= 23.
148 */
149#define BN_window_bits_for_exponent_size(b) \
150 ((b) > 671 ? 6 : \
151 (b) > 239 ? 5 : \
152 (b) > 79 ? 4 : \
153 (b) > 23 ? 3 : 1)
154
155
156/* BN_mod_exp_mont_consttime is based on the assumption that the
157 * L1 data cache line width of the target processor is at least
158 * the following value.
159 */
160#define MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH ( 64 )
161#define MOD_EXP_CTIME_MIN_CACHE_LINE_MASK (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - 1)
162
163/* Window sizes optimized for fixed window size modular exponentiation
164 * algorithm (BN_mod_exp_mont_consttime).
165 *
166 * To achieve the security goals of BN_mode_exp_mont_consttime, the
167 * maximum size of the window must not exceed
168 * log_2(MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH).
169 *
170 * Window size thresholds are defined for cache line sizes of 32 and 64,
171 * cache line sizes where log_2(32)=5 and log_2(64)=6 respectively. A
172 * window size of 7 should only be used on processors that have a 128
173 * byte or greater cache line size.
174 */
175#if MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 64
176
177# define BN_window_bits_for_ctime_exponent_size(b) \
178 ((b) > 937 ? 6 : \
179 (b) > 306 ? 5 : \
180 (b) > 89 ? 4 : \
181 (b) > 22 ? 3 : 1)
182# define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (6)
183
184#elif MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 32
185
186# define BN_window_bits_for_ctime_exponent_size(b) \
187 ((b) > 306 ? 5 : \
188 (b) > 89 ? 4 : \
189 (b) > 22 ? 3 : 1)
190# define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (5)
191
192#endif
193
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#if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM)
204/*
205 * BN_UMULT_HIGH section.
206 *
207 * No, I'm not trying to overwhelm you when stating that the
208 * product of N-bit numbers is 2*N bits wide:-) No, I don't expect
209 * you to be impressed when I say that if the compiler doesn't
210 * support 2*N integer type, then you have to replace every N*N
211 * multiplication with 4 (N/2)*(N/2) accompanied by some shifts
212 * and additions which unavoidably results in severe performance
213 * penalties. Of course provided that the hardware is capable of
214 * producing 2*N result... That's when you normally start
215 * considering assembler implementation. However! It should be
216 * pointed out that some CPUs (most notably Alpha, PowerPC and
217 * upcoming IA-64 family:-) provide *separate* instruction
218 * calculating the upper half of the product placing the result
219 * into a general purpose register. Now *if* the compiler supports
220 * inline assembler, then it's not impossible to implement the
221 * "bignum" routines (and have the compiler optimize 'em)
222 * exhibiting "native" performance in C. That's what BN_UMULT_HIGH
223 * macro is about:-)
224 *
225 * <appro@fy.chalmers.se>
226 */
227# if defined(__alpha)
228# if defined(__GNUC__) && __GNUC__>=2
229# define BN_UMULT_HIGH(a,b) ({ \
230 BN_ULONG ret; \
231 asm ("umulh %1,%2,%0" \
232 : "=r"(ret) \
233 : "r"(a), "r"(b)); \
234 ret; })
235# endif /* compiler */
236# elif defined(_ARCH_PPC) && defined(_LP64)
237# if defined(__GNUC__) && __GNUC__>=2
238# define BN_UMULT_HIGH(a,b) ({ \
239 BN_ULONG ret; \
240 asm ("mulhdu %0,%1,%2" \
241 : "=r"(ret) \
242 : "r"(a), "r"(b)); \
243 ret; })
244# endif /* compiler */
245# elif defined(__x86_64) || defined(__x86_64__)
246# if defined(__GNUC__) && __GNUC__>=2
247# define BN_UMULT_HIGH(a,b) ({ \
248 BN_ULONG ret,discard; \
249 asm ("mulq %3" \
250 : "=a"(discard),"=d"(ret) \
251 : "a"(a), "g"(b) \
252 : "cc"); \
253 ret; })
254# define BN_UMULT_LOHI(low,high,a,b) \
255 asm ("mulq %3" \
256 : "=a"(low),"=d"(high) \
257 : "a"(a),"g"(b) \
258 : "cc");
259# endif
260# elif defined(__mips) && defined(_LP64)
261# if defined(__GNUC__) && __GNUC__>=2
262# if __GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 4) /* "h" constraint is no more since 4.4 */
263# define BN_UMULT_HIGH(a,b) (((__uint128_t)(a)*(b))>>64)
264# define BN_UMULT_LOHI(low,high,a,b) ({ \
265 __uint128_t ret=(__uint128_t)(a)*(b); \
266 (high)=ret>>64; (low)=ret; })
267# else
268# define BN_UMULT_HIGH(a,b) ({ \
269 BN_ULONG ret; \
270 asm ("dmultu %1,%2" \
271 : "=h"(ret) \
272 : "r"(a), "r"(b) : "l"); \
273 ret; })
274# define BN_UMULT_LOHI(low,high,a,b)\
275 asm ("dmultu %2,%3" \
276 : "=l"(low),"=h"(high) \
277 : "r"(a), "r"(b));
278# endif
279# endif
280# endif /* cpu */
281#endif /* OPENSSL_NO_ASM */
282
283/*************************************************************
284 * Using the long long type
285 */
286#define Lw(t) (((BN_ULONG)(t))&BN_MASK2)
287#define Hw(t) (((BN_ULONG)((t)>>BN_BITS2))&BN_MASK2)
288
289#ifdef BN_DEBUG_RAND
290#define bn_clear_top2max(a) \
291 { \
292 int ind = (a)->dmax - (a)->top; \
293 BN_ULONG *ftl = &(a)->d[(a)->top-1]; \
294 for (; ind != 0; ind--) \
295 *(++ftl) = 0x0; \
296 }
297#else
298#define bn_clear_top2max(a)
299#endif
300
301#ifdef BN_LLONG
302#define mul_add(r,a,w,c) { \
303 BN_ULLONG t; \
304 t=(BN_ULLONG)w * (a) + (r) + (c); \
305 (r)= Lw(t); \
306 (c)= Hw(t); \
307 }
308
309#define mul(r,a,w,c) { \
310 BN_ULLONG t; \
311 t=(BN_ULLONG)w * (a) + (c); \
312 (r)= Lw(t); \
313 (c)= Hw(t); \
314 }
315
316#define sqr(r0,r1,a) { \
317 BN_ULLONG t; \
318 t=(BN_ULLONG)(a)*(a); \
319 (r0)=Lw(t); \
320 (r1)=Hw(t); \
321 }
322
323#elif defined(BN_UMULT_LOHI)
324#define mul_add(r,a,w,c) { \
325 BN_ULONG high,low,ret,tmp=(a); \
326 ret = (r); \
327 BN_UMULT_LOHI(low,high,w,tmp); \
328 ret += (c); \
329 (c) = (ret<(c))?1:0; \
330 (c) += high; \
331 ret += low; \
332 (c) += (ret<low)?1:0; \
333 (r) = ret; \
334 }
335
336#define mul(r,a,w,c) { \
337 BN_ULONG high,low,ret,ta=(a); \
338 BN_UMULT_LOHI(low,high,w,ta); \
339 ret = low + (c); \
340 (c) = high; \
341 (c) += (ret<low)?1:0; \
342 (r) = ret; \
343 }
344
345#define sqr(r0,r1,a) { \
346 BN_ULONG tmp=(a); \
347 BN_UMULT_LOHI(r0,r1,tmp,tmp); \
348 }
349
350#elif defined(BN_UMULT_HIGH)
351#define mul_add(r,a,w,c) { \
352 BN_ULONG high,low,ret,tmp=(a); \
353 ret = (r); \
354 high= BN_UMULT_HIGH(w,tmp); \
355 ret += (c); \
356 low = (w) * tmp; \
357 (c) = (ret<(c))?1:0; \
358 (c) += high; \
359 ret += low; \
360 (c) += (ret<low)?1:0; \
361 (r) = ret; \
362 }
363
364#define mul(r,a,w,c) { \
365 BN_ULONG high,low,ret,ta=(a); \
366 low = (w) * ta; \
367 high= BN_UMULT_HIGH(w,ta); \
368 ret = low + (c); \
369 (c) = high; \
370 (c) += (ret<low)?1:0; \
371 (r) = ret; \
372 }
373
374#define sqr(r0,r1,a) { \
375 BN_ULONG tmp=(a); \
376 (r0) = tmp * tmp; \
377 (r1) = BN_UMULT_HIGH(tmp,tmp); \
378 }
379
380#else
381/*************************************************************
382 * No long long type
383 */
384
385#define LBITS(a) ((a)&BN_MASK2l)
386#define HBITS(a) (((a)>>BN_BITS4)&BN_MASK2l)
387#define L2HBITS(a) (((a)<<BN_BITS4)&BN_MASK2)
388
389#define mul64(l,h,bl,bh) \
390 { \
391 BN_ULONG m,m1,lt,ht; \
392 \
393 lt=l; \
394 ht=h; \
395 m =(bh)*(lt); \
396 lt=(bl)*(lt); \
397 m1=(bl)*(ht); \
398 ht =(bh)*(ht); \
399 m=(m+m1)&BN_MASK2; if (m < m1) ht+=L2HBITS((BN_ULONG)1); \
400 ht+=HBITS(m); \
401 m1=L2HBITS(m); \
402 lt=(lt+m1)&BN_MASK2; if (lt < m1) ht++; \
403 (l)=lt; \
404 (h)=ht; \
405 }
406
407#define sqr64(lo,ho,in) \
408 { \
409 BN_ULONG l,h,m; \
410 \
411 h=(in); \
412 l=LBITS(h); \
413 h=HBITS(h); \
414 m =(l)*(h); \
415 l*=l; \
416 h*=h; \
417 h+=(m&BN_MASK2h1)>>(BN_BITS4-1); \
418 m =(m&BN_MASK2l)<<(BN_BITS4+1); \
419 l=(l+m)&BN_MASK2; if (l < m) h++; \
420 (lo)=l; \
421 (ho)=h; \
422 }
423
424#define mul_add(r,a,bl,bh,c) { \
425 BN_ULONG l,h; \
426 \
427 h= (a); \
428 l=LBITS(h); \
429 h=HBITS(h); \
430 mul64(l,h,(bl),(bh)); \
431 \
432 /* non-multiply part */ \
433 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
434 (c)=(r); \
435 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
436 (c)=h&BN_MASK2; \
437 (r)=l; \
438 }
439
440#define mul(r,a,bl,bh,c) { \
441 BN_ULONG l,h; \
442 \
443 h= (a); \
444 l=LBITS(h); \
445 h=HBITS(h); \
446 mul64(l,h,(bl),(bh)); \
447 \
448 /* non-multiply part */ \
449 l+=(c); if ((l&BN_MASK2) < (c)) h++; \
450 (c)=h&BN_MASK2; \
451 (r)=l&BN_MASK2; \
452 }
453#endif /* !BN_LLONG */
454
455 void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb);
456void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
457void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
458void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp);
459void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a);
460void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a);
461int bn_cmp_words(const BN_ULONG *a, const BN_ULONG *b, int n);
462int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b,
463 int cl, int dl);
464void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
465 int dna, int dnb, BN_ULONG *t);
466void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b,
467 int n, int tna, int tnb, BN_ULONG *t);
468void bn_sqr_recursive(BN_ULONG *r, const BN_ULONG *a, int n2, BN_ULONG *t);
469void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n);
470void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
471 BN_ULONG *t);
472void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2,
473 BN_ULONG *t);
474BN_ULONG bn_add_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
475 int cl, int dl);
476BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
477 int cl, int dl);
478int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp, const BN_ULONG *np, const BN_ULONG *n0, int num);
479
480#ifdef __cplusplus
481}
482#endif
483
484#endif
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