1 /* crypto/bn/bn_lcl.h */
2 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
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.
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).
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.
23 * Redistribution and use in source and binary forms, with or without
24 * modification, are permitted provided that the following conditions
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)"
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
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.]
58 /* ====================================================================
59 * Copyright (c) 1998-2000 The OpenSSL Project. All rights reserved.
61 * Redistribution and use in source and binary forms, with or without
62 * modification, are permitted provided that the following conditions
65 * 1. Redistributions of source code must retain the above copyright
66 * notice, this list of conditions and the following disclaimer.
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
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/)"
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.
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.
87 * 6. Redistributions of any form whatsoever must retain the following
89 * "This product includes software developed by the OpenSSL Project
90 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
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 * ====================================================================
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).
112 #ifndef HEADER_BN_LCL_H
113 # define HEADER_BN_LCL_H
115 # include <openssl/bn.h>
123 * BN_window_bits_for_exponent_size -- macro for sliding window mod_exp functions
126 * For window size 'w' (w >= 2) and a random 'b' bits exponent,
127 * the number of multiplications is a constant plus on average
129 * 2^(w-1) + (b-w)/(w+1);
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.
139 * w = 5 if 671 > b > 239
140 * w = 4 if 239 > b > 79
141 * w = 3 if 79 > b > 23
144 * (with draws in between). Very small exponents are often selected
145 * with low Hamming weight, so we use w = 1 for b <= 23.
148 # define BN_window_bits_for_exponent_size(b) \
155 * Old SSLeay/OpenSSL table. Maximum window size was 5, so this table differs
156 * for b==1024; but it coincides for other interesting values (b==160,
159 # define BN_window_bits_for_exponent_size(b) \
166 * BN_mod_exp_mont_conttime is based on the assumption that the L1 data cache
167 * line width of the target processor is at least the following value.
169 # define MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH ( 64 )
170 # define MOD_EXP_CTIME_MIN_CACHE_LINE_MASK (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - 1)
173 * Window sizes optimized for fixed window size modular exponentiation
174 * algorithm (BN_mod_exp_mont_consttime). To achieve the security goals of
175 * BN_mode_exp_mont_consttime, the maximum size of the window must not exceed
176 * log_2(MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH). Window size thresholds are
177 * defined for cache line sizes of 32 and 64, cache line sizes where
178 * log_2(32)=5 and log_2(64)=6 respectively. A window size of 7 should only be
179 * used on processors that have a 128 byte or greater cache line size.
181 # if MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 64
183 # define BN_window_bits_for_ctime_exponent_size(b) \
188 # define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (6)
190 # elif MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 32
192 # define BN_window_bits_for_ctime_exponent_size(b) \
196 # define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (5)
200 /* Pentium pro 16,16,16,32,64 */
201 /* Alpha 16,16,16,16.64 */
202 # define BN_MULL_SIZE_NORMAL (16)/* 32 */
203 # define BN_MUL_RECURSIVE_SIZE_NORMAL (16)/* 32 less than */
204 # define BN_SQR_RECURSIVE_SIZE_NORMAL (16)/* 32 */
205 # define BN_MUL_LOW_RECURSIVE_SIZE_NORMAL (32)/* 32 */
206 # define BN_MONT_CTX_SET_SIZE_WORD (64)/* 32 */
209 * 2011-02-22 SMS. In various places, a size_t variable or a type cast to
210 * size_t was used to perform integer-only operations on pointers. This
211 * failed on VMS with 64-bit pointers (CC /POINTER_SIZE = 64) because size_t
212 * is still only 32 bits. What's needed in these cases is an integer type
213 * with the same size as a pointer, which size_t is not certain to be. The
214 * only fix here is VMS-specific.
216 # if defined(OPENSSL_SYS_VMS)
217 # if __INITIAL_POINTER_SIZE == 64
218 # define PTR_SIZE_INT long long
219 # else /* __INITIAL_POINTER_SIZE == 64 */
220 # define PTR_SIZE_INT int
221 # endif /* __INITIAL_POINTER_SIZE == 64 [else] */
222 # elif !defined(PTR_SIZE_INT) /* defined(OPENSSL_SYS_VMS) */
223 # define PTR_SIZE_INT size_t
224 # endif /* defined(OPENSSL_SYS_VMS) [else] */
226 # if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) && !defined(PEDANTIC)
228 * BN_UMULT_HIGH section.
230 * No, I'm not trying to overwhelm you when stating that the
231 * product of N-bit numbers is 2*N bits wide:-) No, I don't expect
232 * you to be impressed when I say that if the compiler doesn't
233 * support 2*N integer type, then you have to replace every N*N
234 * multiplication with 4 (N/2)*(N/2) accompanied by some shifts
235 * and additions which unavoidably results in severe performance
236 * penalties. Of course provided that the hardware is capable of
237 * producing 2*N result... That's when you normally start
238 * considering assembler implementation. However! It should be
239 * pointed out that some CPUs (most notably Alpha, PowerPC and
240 * upcoming IA-64 family:-) provide *separate* instruction
241 * calculating the upper half of the product placing the result
242 * into a general purpose register. Now *if* the compiler supports
243 * inline assembler, then it's not impossible to implement the
244 * "bignum" routines (and have the compiler optimize 'em)
245 * exhibiting "native" performance in C. That's what BN_UMULT_HIGH
248 * <appro@fy.chalmers.se>
250 # if defined(__alpha) && (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT))
253 # define BN_UMULT_HIGH(a,b) (BN_ULONG)asm("umulh %a0,%a1,%v0",(a),(b))
254 # elif defined(__GNUC__) && __GNUC__>=2
255 # define BN_UMULT_HIGH(a,b) ({ \
256 register BN_ULONG ret; \
257 asm ("umulh %1,%2,%0" \
261 # endif /* compiler */
262 # elif defined(_ARCH_PPC) && defined(__64BIT__) && defined(SIXTY_FOUR_BIT_LONG)
263 # if defined(__GNUC__) && __GNUC__>=2
264 # define BN_UMULT_HIGH(a,b) ({ \
265 register BN_ULONG ret; \
266 asm ("mulhdu %0,%1,%2" \
270 # endif /* compiler */
271 # elif (defined(__x86_64) || defined(__x86_64__)) && \
272 (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT))
273 # if defined(__GNUC__) && __GNUC__>=2
274 # define BN_UMULT_HIGH(a,b) ({ \
275 register BN_ULONG ret,discard; \
277 : "=a"(discard),"=d"(ret) \
281 # define BN_UMULT_LOHI(low,high,a,b) \
283 : "=a"(low),"=d"(high) \
287 # elif (defined(_M_AMD64) || defined(_M_X64)) && defined(SIXTY_FOUR_BIT)
288 # if defined(_MSC_VER) && _MSC_VER>=1400
289 unsigned __int64 __umulh(unsigned __int64 a, unsigned __int64 b);
290 unsigned __int64 _umul128(unsigned __int64 a, unsigned __int64 b,
291 unsigned __int64 *h);
292 # pragma intrinsic(__umulh,_umul128)
293 # define BN_UMULT_HIGH(a,b) __umulh((a),(b))
294 # define BN_UMULT_LOHI(low,high,a,b) ((low)=_umul128((a),(b),&(high)))
296 # elif defined(__mips) && (defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG))
297 # if defined(__GNUC__) && __GNUC__>=2
298 # if __GNUC__>4 || (__GNUC__>=4 && __GNUC_MINOR__>=4)
299 /* "h" constraint is no more since 4.4 */
300 # define BN_UMULT_HIGH(a,b) (((__uint128_t)(a)*(b))>>64)
301 # define BN_UMULT_LOHI(low,high,a,b) ({ \
302 __uint128_t ret=(__uint128_t)(a)*(b); \
303 (high)=ret>>64; (low)=ret; })
305 # define BN_UMULT_HIGH(a,b) ({ \
306 register BN_ULONG ret; \
307 asm ("dmultu %1,%2" \
309 : "r"(a), "r"(b) : "l"); \
311 # define BN_UMULT_LOHI(low,high,a,b)\
312 asm ("dmultu %2,%3" \
313 : "=l"(low),"=h"(high) \
317 # elif defined(__aarch64__) && defined(SIXTY_FOUR_BIT_LONG)
318 # if defined(__GNUC__) && __GNUC__>=2
319 # define BN_UMULT_HIGH(a,b) ({ \
320 register BN_ULONG ret; \
321 asm ("umulh %0,%1,%2" \
327 # endif /* OPENSSL_NO_ASM */
329 /*************************************************************
330 * Using the long long type
332 # define Lw(t) (((BN_ULONG)(t))&BN_MASK2)
333 # define Hw(t) (((BN_ULONG)((t)>>BN_BITS2))&BN_MASK2)
335 # ifdef BN_DEBUG_RAND
336 # define bn_clear_top2max(a) \
338 int ind = (a)->dmax - (a)->top; \
339 BN_ULONG *ftl = &(a)->d[(a)->top-1]; \
340 for (; ind != 0; ind--) \
344 # define bn_clear_top2max(a)
348 # define mul_add(r,a,w,c) { \
350 t=(BN_ULLONG)w * (a) + (r) + (c); \
355 # define mul(r,a,w,c) { \
357 t=(BN_ULLONG)w * (a) + (c); \
362 # define sqr(r0,r1,a) { \
364 t=(BN_ULLONG)(a)*(a); \
369 # elif defined(BN_UMULT_LOHI)
370 # define mul_add(r,a,w,c) { \
371 BN_ULONG high,low,ret,tmp=(a); \
373 BN_UMULT_LOHI(low,high,w,tmp); \
375 (c) = (ret<(c))?1:0; \
378 (c) += (ret<low)?1:0; \
382 # define mul(r,a,w,c) { \
383 BN_ULONG high,low,ret,ta=(a); \
384 BN_UMULT_LOHI(low,high,w,ta); \
387 (c) += (ret<low)?1:0; \
391 # define sqr(r0,r1,a) { \
393 BN_UMULT_LOHI(r0,r1,tmp,tmp); \
396 # elif defined(BN_UMULT_HIGH)
397 # define mul_add(r,a,w,c) { \
398 BN_ULONG high,low,ret,tmp=(a); \
400 high= BN_UMULT_HIGH(w,tmp); \
403 (c) = (ret<(c))?1:0; \
406 (c) += (ret<low)?1:0; \
410 # define mul(r,a,w,c) { \
411 BN_ULONG high,low,ret,ta=(a); \
413 high= BN_UMULT_HIGH(w,ta); \
416 (c) += (ret<low)?1:0; \
420 # define sqr(r0,r1,a) { \
423 (r1) = BN_UMULT_HIGH(tmp,tmp); \
427 /*************************************************************
431 # define LBITS(a) ((a)&BN_MASK2l)
432 # define HBITS(a) (((a)>>BN_BITS4)&BN_MASK2l)
433 # define L2HBITS(a) (((a)<<BN_BITS4)&BN_MASK2)
435 # define LLBITS(a) ((a)&BN_MASKl)
436 # define LHBITS(a) (((a)>>BN_BITS2)&BN_MASKl)
437 # define LL2HBITS(a) ((BN_ULLONG)((a)&BN_MASKl)<<BN_BITS2)
439 # define mul64(l,h,bl,bh) \
441 BN_ULONG m,m1,lt,ht; \
449 m=(m+m1)&BN_MASK2; if (m < m1) ht+=L2HBITS((BN_ULONG)1); \
452 lt=(lt+m1)&BN_MASK2; if (lt < m1) ht++; \
457 # define sqr64(lo,ho,in) \
467 h+=(m&BN_MASK2h1)>>(BN_BITS4-1); \
468 m =(m&BN_MASK2l)<<(BN_BITS4+1); \
469 l=(l+m)&BN_MASK2; if (l < m) h++; \
474 # define mul_add(r,a,bl,bh,c) { \
480 mul64(l,h,(bl),(bh)); \
482 /* non-multiply part */ \
483 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
485 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
490 # define mul(r,a,bl,bh,c) { \
496 mul64(l,h,(bl),(bh)); \
498 /* non-multiply part */ \
499 l+=(c); if ((l&BN_MASK2) < (c)) h++; \
503 # endif /* !BN_LLONG */
505 # if defined(OPENSSL_DOING_MAKEDEPEND) && defined(OPENSSL_FIPS)
509 void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb);
510 void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
511 void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
512 void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp);
513 void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a);
514 void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a);
515 int bn_cmp_words(const BN_ULONG *a, const BN_ULONG *b, int n);
516 int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b, int cl, int dl);
517 void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
518 int dna, int dnb, BN_ULONG *t);
519 void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b,
520 int n, int tna, int tnb, BN_ULONG *t);
521 void bn_sqr_recursive(BN_ULONG *r, const BN_ULONG *a, int n2, BN_ULONG *t);
522 void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n);
523 void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
525 void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2,
527 BN_ULONG bn_add_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
529 BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
531 int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
532 const BN_ULONG *np, const BN_ULONG *n0, int num);