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 "bn.h" 116 117#ifdef __cplusplus 118extern "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#define BN_window_bits_for_exponent_size(b) \ 148 ((b) > 671 ? 6 : \ 149 (b) > 239 ? 5 : \ 150 (b) > 79 ? 4 : \ 151 (b) > 23 ? 3 : 1) 152 153 154 155/* BN_mod_exp_mont2_conttime is based on the assumption that the 156 * L1 data cache line width of the target processor is at least 157 * the following value. 158 */ 159#define MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH ( 64 ) 160#define MOD_EXP_CTIME_MIN_CACHE_LINE_MASK (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - 1) 161 162/* Window sizes optimized for fixed window size modular exponentiation 163 * algorithm (BN_mod_exp_mont2_consttime). 164 * 165 * To achieve the security goals of BN_mode_exp_mont_consttime, the 166 * maximum size of the window must not exceed 167 * log_2(MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH). 168 * 169 * Window size thresholds are defined for cache line sizes of 32 and 64, 170 * cache line sizes where log_2(32)=5 and log_2(64)=6 respectively. A 171 * window size of 7 should only be used on processors that have a 128 172 * byte or greater cache line size. 173 */ 174#if MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 64 175 176# define BN_window_bits_for_ctime_exponent_size(b) \ 177 ((b) > 937 ? 6 : \ 178 (b) > 306 ? 5 : \ 179 (b) > 89 ? 4 : \ 180 (b) > 22 ? 3 : 1) 181# define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (6) 182 183#elif MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 32 184 185# define BN_window_bits_for_ctime_exponent_size(b) \ 186 ((b) > 306 ? 5 : \ 187 (b) > 89 ? 4 : \ 188 (b) > 22 ? 3 : 1) 189# define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (5) 190 191#endif 192 193 194/* Pentium pro 16,16,16,32,64 */ 195/* Alpha 16,16,16,16.64 */ 196#define BN_MULL_SIZE_NORMAL (16) /* 32 */ 197#define BN_MUL_RECURSIVE_SIZE_NORMAL (16) /* 32 less than */ 198#define BN_SQR_RECURSIVE_SIZE_NORMAL (16) /* 32 */ 199#define BN_MUL_LOW_RECURSIVE_SIZE_NORMAL (32) /* 32 */ 200#define BN_MONT_CTX_SET_SIZE_WORD (64) /* 32 */ 201 202#if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) && !defined(PEDANTIC) 203/* 204 * BN_UMULT_HIGH section. 205 * 206 * No, I'm not trying to overwhelm you when stating that the 207 * product of N-bit numbers is 2*N bits wide:-) No, I don't expect 208 * you to be impressed when I say that if the compiler doesn't 209 * support 2*N integer type, then you have to replace every N*N 210 * multiplication with 4 (N/2)*(N/2) accompanied by some shifts 211 * and additions which unavoidably results in severe performance 212 * penalties. Of course provided that the hardware is capable of 213 * producing 2*N result... That's when you normally start 214 * considering assembler implementation. However! It should be 215 * pointed out that some CPUs (most notably Alpha, PowerPC and 216 * upcoming IA-64 family:-) provide *separate* instruction 217 * calculating the upper half of the product placing the result 218 * into a general purpose register. Now *if* the compiler supports 219 * inline assembler, then it's not impossible to implement the 220 * "bignum" routines (and have the compiler optimize 'em) 221 * exhibiting "native" performance in C. That's what BN_UMULT_HIGH 222 * macro is about:-) 223 * 224 * <appro@fy.chalmers.se> 225 */ 226# if defined(__alpha) && (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT)) 227# if defined(__DECC) 228# include <c_asm.h> 229# define BN_UMULT_HIGH(a,b) (BN_ULONG)asm("umulh %a0,%a1,%v0",(a),(b)) 230# elif defined(__GNUC__) 231# define BN_UMULT_HIGH(a,b) ({ \ 232 register BN_ULONG ret; \ 233 asm ("umulh %1,%2,%0" \ 234 : "=r"(ret) \ 235 : "r"(a), "r"(b)); \ 236 ret; }) 237# endif /* compiler */ 238# elif defined(_ARCH_PPC) && defined(__64BIT__) && defined(SIXTY_FOUR_BIT_LONG) 239# if defined(__GNUC__) 240# define BN_UMULT_HIGH(a,b) ({ \ 241 register BN_ULONG ret; \ 242 asm ("mulhdu %0,%1,%2" \ 243 : "=r"(ret) \ 244 : "r"(a), "r"(b)); \ 245 ret; }) 246# endif /* compiler */ 247# elif defined(__x86_64) && defined(SIXTY_FOUR_BIT_LONG) 248# if defined(__GNUC__) 249# define BN_UMULT_HIGH(a,b) ({ \ 250 register BN_ULONG ret,discard; \ 251 asm ("mulq %3" \ 252 : "=a"(discard),"=d"(ret) \ 253 : "a"(a), "g"(b) \ 254 : "cc"); \ 255 ret; }) 256# define BN_UMULT_LOHI(low,high,a,b) \ 257 asm ("mulq %3" \ 258 : "=a"(low),"=d"(high) \ 259 : "a"(a),"g"(b) \ 260 : "cc"); 261# endif 262# elif (defined(_M_AMD64) || defined(_M_X64)) && defined(SIXTY_FOUR_BIT) 263# if defined(_MSC_VER) && _MSC_VER>=1400 264 unsigned __int64 __umulh (unsigned __int64 a,unsigned __int64 b); 265 unsigned __int64 _umul128 (unsigned __int64 a,unsigned __int64 b, 266 unsigned __int64 *h); 267# pragma intrinsic(__umulh,_umul128) 268# define BN_UMULT_HIGH(a,b) __umulh((a),(b)) 269# define BN_UMULT_LOHI(low,high,a,b) ((low)=_umul128((a),(b),&(high))) 270# endif 271# endif /* cpu */ 272#endif /* OPENSSL_NO_ASM */ 273 274/************************************************************* 275 * Using the long long type 276 */ 277#define Lw(t) (((BN_ULONG)(t))&BN_MASK2) 278#define Hw(t) (((BN_ULONG)((t)>>BN_BITS2))&BN_MASK2) 279 280#ifdef BN_DEBUG_RAND 281#define bn_clear_top2max(a) \ 282 { \ 283 int ind = (a)->dmax - (a)->top; \ 284 BN_ULONG *ftl = &(a)->d[(a)->top-1]; \ 285 for (; ind != 0; ind--) \ 286 *(++ftl) = 0x0; \ 287 } 288#else 289#define bn_clear_top2max(a) 290#endif 291 292#ifdef BN_LLONG 293#define mul_add(r,a,w,c) { \ 294 BN_ULLONG t; \ 295 t=(BN_ULLONG)w * (a) + (r) + (c); \ 296 (r)= Lw(t); \ 297 (c)= Hw(t); \ 298 } 299 300#define mul(r,a,w,c) { \ 301 BN_ULLONG t; \ 302 t=(BN_ULLONG)w * (a) + (c); \ 303 (r)= Lw(t); \ 304 (c)= Hw(t); \ 305 } 306 307#define sqr(r0,r1,a) { \ 308 BN_ULLONG t; \ 309 t=(BN_ULLONG)(a)*(a); \ 310 (r0)=Lw(t); \ 311 (r1)=Hw(t); \ 312 } 313 314#elif defined(BN_UMULT_LOHI) 315#define mul_add(r,a,w,c) { \ 316 BN_ULONG high,low,ret,tmp=(a); \ 317 ret = (r); \ 318 BN_UMULT_LOHI(low,high,w,tmp); \ 319 ret += (c); \ 320 (c) = (ret<(c))?1:0; \ 321 (c) += high; \ 322 ret += low; \ 323 (c) += (ret<low)?1:0; \ 324 (r) = ret; \ 325 } 326 327#define mul(r,a,w,c) { \ 328 BN_ULONG high,low,ret,ta=(a); \ 329 BN_UMULT_LOHI(low,high,w,ta); \ 330 ret = low + (c); \ 331 (c) = high; \ 332 (c) += (ret<low)?1:0; \ 333 (r) = ret; \ 334 } 335 336#define sqr(r0,r1,a) { \ 337 BN_ULONG tmp=(a); \ 338 BN_UMULT_LOHI(r0,r1,tmp,tmp); \ 339 } 340 341#elif defined(BN_UMULT_HIGH) 342#define mul_add(r,a,w,c) { \ 343 BN_ULONG high,low,ret,tmp=(a); \ 344 ret = (r); \ 345 high= BN_UMULT_HIGH(w,tmp); \ 346 ret += (c); \ 347 low = (w) * tmp; \ 348 (c) = (ret<(c))?1:0; \ 349 (c) += high; \ 350 ret += low; \ 351 (c) += (ret<low)?1:0; \ 352 (r) = ret; \ 353 } 354 355#define mul(r,a,w,c) { \ 356 BN_ULONG high,low,ret,ta=(a); \ 357 low = (w) * ta; \ 358 high= BN_UMULT_HIGH(w,ta); \ 359 ret = low + (c); \ 360 (c) = high; \ 361 (c) += (ret<low)?1:0; \ 362 (r) = ret; \ 363 } 364 365#define sqr(r0,r1,a) { \ 366 BN_ULONG tmp=(a); \ 367 (r0) = tmp * tmp; \ 368 (r1) = BN_UMULT_HIGH(tmp,tmp); \ 369 } 370 371#else 372/************************************************************* 373 * No long long type 374 */ 375 376#define LBITS(a) ((a)&BN_MASK2l) 377#define HBITS(a) (((a)>>BN_BITS4)&BN_MASK2l) 378#define L2HBITS(a) (((a)<<BN_BITS4)&BN_MASK2) 379 380#define LLBITS(a) ((a)&BN_MASKl) 381#define LHBITS(a) (((a)>>BN_BITS2)&BN_MASKl) 382#define LL2HBITS(a) ((BN_ULLONG)((a)&BN_MASKl)<<BN_BITS2) 383 384#define mul64(l,h,bl,bh) \ 385 { \ 386 BN_ULONG m,m1,lt,ht; \ 387 \ 388 lt=l; \ 389 ht=h; \ 390 m =(bh)*(lt); \ 391 lt=(bl)*(lt); \ 392 m1=(bl)*(ht); \ 393 ht =(bh)*(ht); \ 394 m=(m+m1)&BN_MASK2; if (m < m1) ht+=L2HBITS((BN_ULONG)1); \ 395 ht+=HBITS(m); \ 396 m1=L2HBITS(m); \ 397 lt=(lt+m1)&BN_MASK2; if (lt < m1) ht++; \ 398 (l)=lt; \ 399 (h)=ht; \ 400 } 401 402#define sqr64(lo,ho,in) \ 403 { \ 404 BN_ULONG l,h,m; \ 405 \ 406 h=(in); \ 407 l=LBITS(h); \ 408 h=HBITS(h); \ 409 m =(l)*(h); \ 410 l*=l; \ 411 h*=h; \ 412 h+=(m&BN_MASK2h1)>>(BN_BITS4-1); \ 413 m =(m&BN_MASK2l)<<(BN_BITS4+1); \ 414 l=(l+m)&BN_MASK2; if (l < m) h++; \ 415 (lo)=l; \ 416 (ho)=h; \ 417 } 418 419#define mul_add(r,a,bl,bh,c) { \ 420 BN_ULONG l,h; \ 421 \ 422 h= (a); \ 423 l=LBITS(h); \ 424 h=HBITS(h); \ 425 mul64(l,h,(bl),(bh)); \ 426 \ 427 /* non-multiply part */ \ 428 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \ 429 (c)=(r); \ 430 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \ 431 (c)=h&BN_MASK2; \ 432 (r)=l; \ 433 } 434 435#define mul(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+=(c); if ((l&BN_MASK2) < (c)) h++; \ 445 (c)=h&BN_MASK2; \ 446 (r)=l&BN_MASK2; \ 447 } 448#endif /* !BN_LLONG */ 449 450void bn_mul_normal2(BN_ULONG *r,BN_ULONG *a,int na,BN_ULONG *b,int nb); 451void bn_mul_comba8_b(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b); 452void bn_mul_comba4_b(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b); 453void bn_sqr_normal2(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp); 454void bn_sqr_comba8_b(BN_ULONG *r,const BN_ULONG *a); 455void bn_sqr_comba4_b(BN_ULONG *r,const BN_ULONG *a); 456int bn_cmp_words2(const BN_ULONG *a,const BN_ULONG *b,int n); 457int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b, 458 int cl, int dl); 459void bn_mul_recursive2(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,int n2, 460 int dna,int dnb,BN_ULONG *t); 461void bn_mul_part_recursive2(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b, 462 int n,int tna,int tnb,BN_ULONG *t); 463void bn_sqr_recursive2(BN_ULONG *r,const BN_ULONG *a, int n2, BN_ULONG *t); 464void bn_mul_low_normal(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b, int n); 465void bn_mul_low_recursive(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,int n2, 466 BN_ULONG *t); 467void bn_mul_high2(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,BN_ULONG *l,int n2, 468 BN_ULONG *t); 469BN_ULONG bn_add_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, 470 int cl, int dl); 471BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, 472 int cl, int dl); 473 474#ifdef __cplusplus 475} 476#endif 477 478#endif 479