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) \
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).
158 #define BN_window_bits_for_exponent_size(b) \
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.
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)
173 /* Window sizes optimized for fixed window size modular exponentiation
174 * algorithm (BN_mod_exp_mont_consttime).
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).
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.
185 #if MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 64
187 # define BN_window_bits_for_ctime_exponent_size(b) \
192 # define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (6)
194 #elif MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 32
196 # define BN_window_bits_for_ctime_exponent_size(b) \
200 # define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (5)
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 */
214 * In various places, a size_t variable or a type cast to size_t was
215 * used to perform integer-only operations on pointers. This failed on
216 * VMS with 64-bit pointers (CC /POINTER_SIZE = 64) because size_t is
217 * still only 32 bits. What's needed in these cases is an integer type
218 * with the same size as a pointer, which size_t is not certain to be.
219 * The only fix here is VMS-specific.
221 #if defined(OPENSSL_SYS_VMS)
222 # if __INITIAL_POINTER_SIZE == 64
223 # define PTR_SIZE_INT long long
224 # else /* __INITIAL_POINTER_SIZE == 64 */
225 # define PTR_SIZE_INT int
226 # endif /* __INITIAL_POINTER_SIZE == 64 [else] */
227 #elif !defined(PTR_SIZE_INT) /* defined(OPENSSL_SYS_VMS) */
228 # define PTR_SIZE_INT size_t
229 #endif /* defined(OPENSSL_SYS_VMS) [else] */
231 #if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) && !defined(PEDANTIC)
233 * BN_UMULT_HIGH section.
235 * No, I'm not trying to overwhelm you when stating that the
236 * product of N-bit numbers is 2*N bits wide:-) No, I don't expect
237 * you to be impressed when I say that if the compiler doesn't
238 * support 2*N integer type, then you have to replace every N*N
239 * multiplication with 4 (N/2)*(N/2) accompanied by some shifts
240 * and additions which unavoidably results in severe performance
241 * penalties. Of course provided that the hardware is capable of
242 * producing 2*N result... That's when you normally start
243 * considering assembler implementation. However! It should be
244 * pointed out that some CPUs (most notably Alpha, PowerPC and
245 * upcoming IA-64 family:-) provide *separate* instruction
246 * calculating the upper half of the product placing the result
247 * into a general purpose register. Now *if* the compiler supports
248 * inline assembler, then it's not impossible to implement the
249 * "bignum" routines (and have the compiler optimize 'em)
250 * exhibiting "native" performance in C. That's what BN_UMULT_HIGH
253 * <appro@fy.chalmers.se>
255 # if defined(__alpha) && (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT))
258 # define BN_UMULT_HIGH(a,b) (BN_ULONG)asm("umulh %a0,%a1,%v0",(a),(b))
259 # elif defined(__GNUC__) && __GNUC__>=2
260 # define BN_UMULT_HIGH(a,b) ({ \
261 register BN_ULONG ret; \
262 asm ("umulh %1,%2,%0" \
266 # endif /* compiler */
267 # elif defined(_ARCH_PPC) && defined(__64BIT__) && defined(SIXTY_FOUR_BIT_LONG)
268 # if defined(__GNUC__) && __GNUC__>=2
269 # define BN_UMULT_HIGH(a,b) ({ \
270 register BN_ULONG ret; \
271 asm ("mulhdu %0,%1,%2" \
275 # endif /* compiler */
276 # elif (defined(__x86_64) || defined(__x86_64__)) && \
277 (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT))
278 # if defined(__GNUC__) && __GNUC__>=2
279 # define BN_UMULT_HIGH(a,b) ({ \
280 register BN_ULONG ret,discard; \
282 : "=a"(discard),"=d"(ret) \
286 # define BN_UMULT_LOHI(low,high,a,b) \
288 : "=a"(low),"=d"(high) \
292 # elif (defined(_M_AMD64) || defined(_M_X64)) && defined(SIXTY_FOUR_BIT)
293 # if defined(_MSC_VER) && _MSC_VER>=1400
294 unsigned __int64 __umulh (unsigned __int64 a,unsigned __int64 b);
295 unsigned __int64 _umul128 (unsigned __int64 a,unsigned __int64 b,
296 unsigned __int64 *h);
297 # pragma intrinsic(__umulh,_umul128)
298 # define BN_UMULT_HIGH(a,b) __umulh((a),(b))
299 # define BN_UMULT_LOHI(low,high,a,b) ((low)=_umul128((a),(b),&(high)))
301 # elif defined(__mips) && (defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG))
302 # if defined(__GNUC__) && __GNUC__>=2
303 # if __GNUC__>=4 && __GNUC_MINOR__>=4 /* "h" constraint is no more since 4.4 */
304 # define BN_UMULT_HIGH(a,b) (((__uint128_t)(a)*(b))>>64)
305 # define BN_UMULT_LOHI(low,high,a,b) ({ \
306 __uint128_t ret=(__uint128_t)(a)*(b); \
307 (high)=ret>>64; (low)=ret; })
309 # define BN_UMULT_HIGH(a,b) ({ \
310 register BN_ULONG ret; \
311 asm ("dmultu %1,%2" \
313 : "r"(a), "r"(b) : "l"); \
315 # define BN_UMULT_LOHI(low,high,a,b)\
316 asm ("dmultu %2,%3" \
317 : "=l"(low),"=h"(high) \
322 #endif /* OPENSSL_NO_ASM */
324 /*************************************************************
325 * Using the long long type
327 #define Lw(t) (((BN_ULONG)(t))&BN_MASK2)
328 #define Hw(t) (((BN_ULONG)((t)>>BN_BITS2))&BN_MASK2)
331 #define bn_clear_top2max(a) \
333 int ind = (a)->dmax - (a)->top; \
334 BN_ULONG *ftl = &(a)->d[(a)->top-1]; \
335 for (; ind != 0; ind--) \
339 #define bn_clear_top2max(a)
343 #define mul_add(r,a,w,c) { \
345 t=(BN_ULLONG)w * (a) + (r) + (c); \
350 #define mul(r,a,w,c) { \
352 t=(BN_ULLONG)w * (a) + (c); \
357 #define sqr(r0,r1,a) { \
359 t=(BN_ULLONG)(a)*(a); \
364 #elif defined(BN_UMULT_LOHI)
365 #define mul_add(r,a,w,c) { \
366 BN_ULONG high,low,ret,tmp=(a); \
368 BN_UMULT_LOHI(low,high,w,tmp); \
370 (c) = (ret<(c))?1:0; \
373 (c) += (ret<low)?1:0; \
377 #define mul(r,a,w,c) { \
378 BN_ULONG high,low,ret,ta=(a); \
379 BN_UMULT_LOHI(low,high,w,ta); \
382 (c) += (ret<low)?1:0; \
386 #define sqr(r0,r1,a) { \
388 BN_UMULT_LOHI(r0,r1,tmp,tmp); \
391 #elif defined(BN_UMULT_HIGH)
392 #define mul_add(r,a,w,c) { \
393 BN_ULONG high,low,ret,tmp=(a); \
395 high= BN_UMULT_HIGH(w,tmp); \
398 (c) = (ret<(c))?1:0; \
401 (c) += (ret<low)?1:0; \
405 #define mul(r,a,w,c) { \
406 BN_ULONG high,low,ret,ta=(a); \
408 high= BN_UMULT_HIGH(w,ta); \
411 (c) += (ret<low)?1:0; \
415 #define sqr(r0,r1,a) { \
418 (r1) = BN_UMULT_HIGH(tmp,tmp); \
422 /*************************************************************
426 #define LBITS(a) ((a)&BN_MASK2l)
427 #define HBITS(a) (((a)>>BN_BITS4)&BN_MASK2l)
428 #define L2HBITS(a) (((a)<<BN_BITS4)&BN_MASK2)
430 #define LLBITS(a) ((a)&BN_MASKl)
431 #define LHBITS(a) (((a)>>BN_BITS2)&BN_MASKl)
432 #define LL2HBITS(a) ((BN_ULLONG)((a)&BN_MASKl)<<BN_BITS2)
434 #define mul64(l,h,bl,bh) \
436 BN_ULONG m,m1,lt,ht; \
444 m=(m+m1)&BN_MASK2; if (m < m1) ht+=L2HBITS((BN_ULONG)1); \
447 lt=(lt+m1)&BN_MASK2; if (lt < m1) ht++; \
452 #define sqr64(lo,ho,in) \
462 h+=(m&BN_MASK2h1)>>(BN_BITS4-1); \
463 m =(m&BN_MASK2l)<<(BN_BITS4+1); \
464 l=(l+m)&BN_MASK2; if (l < m) h++; \
469 #define mul_add(r,a,bl,bh,c) { \
475 mul64(l,h,(bl),(bh)); \
477 /* non-multiply part */ \
478 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
480 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
485 #define mul(r,a,bl,bh,c) { \
491 mul64(l,h,(bl),(bh)); \
493 /* non-multiply part */ \
494 l+=(c); if ((l&BN_MASK2) < (c)) h++; \
498 #endif /* !BN_LLONG */
500 void bn_mul_normal(BN_ULONG *r,BN_ULONG *a,int na,BN_ULONG *b,int nb);
501 void bn_mul_comba8(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b);
502 void bn_mul_comba4(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b);
503 void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp);
504 void bn_sqr_comba8(BN_ULONG *r,const BN_ULONG *a);
505 void bn_sqr_comba4(BN_ULONG *r,const BN_ULONG *a);
506 int bn_cmp_words(const BN_ULONG *a,const BN_ULONG *b,int n);
507 int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b,
509 void bn_mul_recursive(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,int n2,
510 int dna,int dnb,BN_ULONG *t);
511 void bn_mul_part_recursive(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,
512 int n,int tna,int tnb,BN_ULONG *t);
513 void bn_sqr_recursive(BN_ULONG *r,const BN_ULONG *a, int n2, BN_ULONG *t);
514 void bn_mul_low_normal(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b, int n);
515 void bn_mul_low_recursive(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,int n2,
517 void bn_mul_high(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,BN_ULONG *l,int n2,
519 BN_ULONG bn_add_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
521 BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
523 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);
525 BIGNUM *int_bn_mod_inverse(BIGNUM *in,
526 const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx, int *noinv);