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__) 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__) 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(SIXTY_FOUR_BIT_LONG) 259 # if defined(__GNUC__) 260 # define BN_UMULT_HIGH(a,b) ({ \ 261 register BN_ULONG ret,discard; \ 262 __asm__ ("mulq %3" \ 263 : "=a"(discard),"=d"(ret) \ 264 : "a"(a), "g"(b) \ 265 : "cc"); \ 266 ret; }) 267 # define BN_UMULT_LOHI(low,high,a,b) \ 268 __asm__ ("mulq %3" \ 269 : "=a"(low),"=d"(high) \ 270 : "a"(a),"g"(b) \ 271 : "cc"); 272 # endif 273 # elif (defined(_M_AMD64) || defined(_M_X64)) && defined(SIXTY_FOUR_BIT) 274 # if defined(_MSC_VER) && _MSC_VER>=1400 275 unsigned __int64 __umulh (unsigned __int64 a,unsigned __int64 b); 276 unsigned __int64 _umul128 (unsigned __int64 a,unsigned __int64 b, 277 unsigned __int64 *h); 278 # pragma intrinsic(__umulh,_umul128) 279 # define BN_UMULT_HIGH(a,b) __umulh((a),(b)) 280 # define BN_UMULT_LOHI(low,high,a,b) ((low)=_umul128((a),(b),&(high))) 281 # endif 282 # endif /* cpu */ 283 #endif /* OPENSSL_NO_ASM */ 284 285 /************************************************************* 286 * Using the long long type 287 */ 288 #define Lw(t) (((BN_ULONG)(t))&BN_MASK2) 289 #define Hw(t) (((BN_ULONG)((t)>>BN_BITS2))&BN_MASK2) 290 291 #ifdef BN_DEBUG_RAND 292 #define bn_clear_top2max(a) \ 293 { \ 294 int ind = (a)->dmax - (a)->top; \ 295 BN_ULONG *ftl = &(a)->d[(a)->top-1]; \ 296 for (; ind != 0; ind--) \ 297 *(++ftl) = 0x0; \ 298 } 299 #else 300 #define bn_clear_top2max(a) 301 #endif 302 303 #ifdef BN_LLONG 304 #define mul_add(r,a,w,c) { \ 305 BN_ULLONG t; \ 306 t=(BN_ULLONG)w * (a) + (r) + (c); \ 307 (r)= Lw(t); \ 308 (c)= Hw(t); \ 309 } 310 311 #define mul(r,a,w,c) { \ 312 BN_ULLONG t; \ 313 t=(BN_ULLONG)w * (a) + (c); \ 314 (r)= Lw(t); \ 315 (c)= Hw(t); \ 316 } 317 318 #define sqr(r0,r1,a) { \ 319 BN_ULLONG t; \ 320 t=(BN_ULLONG)(a)*(a); \ 321 (r0)=Lw(t); \ 322 (r1)=Hw(t); \ 323 } 324 325 #elif defined(BN_UMULT_LOHI) 326 #define mul_add(r,a,w,c) { \ 327 BN_ULONG high,low,ret,tmp=(a); \ 328 ret = (r); \ 329 BN_UMULT_LOHI(low,high,w,tmp); \ 330 ret += (c); \ 331 (c) = (ret<(c))?1:0; \ 332 (c) += high; \ 333 ret += low; \ 334 (c) += (ret<low)?1:0; \ 335 (r) = ret; \ 336 } 337 338 #define mul(r,a,w,c) { \ 339 BN_ULONG high,low,ret,ta=(a); \ 340 BN_UMULT_LOHI(low,high,w,ta); \ 341 ret = low + (c); \ 342 (c) = high; \ 343 (c) += (ret<low)?1:0; \ 344 (r) = ret; \ 345 } 346 347 #define sqr(r0,r1,a) { \ 348 BN_ULONG tmp=(a); \ 349 BN_UMULT_LOHI(r0,r1,tmp,tmp); \ 350 } 351 352 #elif defined(BN_UMULT_HIGH) 353 #define mul_add(r,a,w,c) { \ 354 BN_ULONG high,low,ret,tmp=(a); \ 355 ret = (r); \ 356 high= BN_UMULT_HIGH(w,tmp); \ 357 ret += (c); \ 358 low = (w) * tmp; \ 359 (c) = (ret<(c))?1:0; \ 360 (c) += high; \ 361 ret += low; \ 362 (c) += (ret<low)?1:0; \ 363 (r) = ret; \ 364 } 365 366 #define mul(r,a,w,c) { \ 367 BN_ULONG high,low,ret,ta=(a); \ 368 low = (w) * ta; \ 369 high= BN_UMULT_HIGH(w,ta); \ 370 ret = low + (c); \ 371 (c) = high; \ 372 (c) += (ret<low)?1:0; \ 373 (r) = ret; \ 374 } 375 376 #define sqr(r0,r1,a) { \ 377 BN_ULONG tmp=(a); \ 378 (r0) = tmp * tmp; \ 379 (r1) = BN_UMULT_HIGH(tmp,tmp); \ 380 } 381 382 #else 383 /************************************************************* 384 * No long long type 385 */ 386 387 #define LBITS(a) ((a)&BN_MASK2l) 388 #define HBITS(a) (((a)>>BN_BITS4)&BN_MASK2l) 389 #define L2HBITS(a) (((a)<<BN_BITS4)&BN_MASK2) 390 391 #define LLBITS(a) ((a)&BN_MASKl) 392 #define LHBITS(a) (((a)>>BN_BITS2)&BN_MASKl) 393 #define LL2HBITS(a) ((BN_ULLONG)((a)&BN_MASKl)<<BN_BITS2) 394 395 #define mul64(l,h,bl,bh) \ 396 { \ 397 BN_ULONG m,m1,lt,ht; \ 398 \ 399 lt=l; \ 400 ht=h; \ 401 m =(bh)*(lt); \ 402 lt=(bl)*(lt); \ 403 m1=(bl)*(ht); \ 404 ht =(bh)*(ht); \ 405 m=(m+m1)&BN_MASK2; if (m < m1) ht+=L2HBITS((BN_ULONG)1); \ 406 ht+=HBITS(m); \ 407 m1=L2HBITS(m); \ 408 lt=(lt+m1)&BN_MASK2; if (lt < m1) ht++; \ 409 (l)=lt; \ 410 (h)=ht; \ 411 } 412 413 #define sqr64(lo,ho,in) \ 414 { \ 415 BN_ULONG l,h,m; \ 416 \ 417 h=(in); \ 418 l=LBITS(h); \ 419 h=HBITS(h); \ 420 m =(l)*(h); \ 421 l*=l; \ 422 h*=h; \ 423 h+=(m&BN_MASK2h1)>>(BN_BITS4-1); \ 424 m =(m&BN_MASK2l)<<(BN_BITS4+1); \ 425 l=(l+m)&BN_MASK2; if (l < m) h++; \ 426 (lo)=l; \ 427 (ho)=h; \ 428 } 429 430 #define mul_add(r,a,bl,bh,c) { \ 431 BN_ULONG l,h; \ 432 \ 433 h= (a); \ 434 l=LBITS(h); \ 435 h=HBITS(h); \ 436 mul64(l,h,(bl),(bh)); \ 437 \ 438 /* non-multiply part */ \ 439 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \ 440 (c)=(r); \ 441 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \ 442 (c)=h&BN_MASK2; \ 443 (r)=l; \ 444 } 445 446 #define mul(r,a,bl,bh,c) { \ 447 BN_ULONG l,h; \ 448 \ 449 h= (a); \ 450 l=LBITS(h); \ 451 h=HBITS(h); \ 452 mul64(l,h,(bl),(bh)); \ 453 \ 454 /* non-multiply part */ \ 455 l+=(c); if ((l&BN_MASK2) < (c)) h++; \ 456 (c)=h&BN_MASK2; \ 457 (r)=l&BN_MASK2; \ 458 } 459 #endif /* !BN_LLONG */ 460 461 void bn_mul_normal(BN_ULONG *r,BN_ULONG *a,int na,BN_ULONG *b,int nb); 462 void bn_mul_comba8(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b); 463 void bn_mul_comba4(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b); 464 void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp); 465 void bn_sqr_comba8(BN_ULONG *r,const BN_ULONG *a); 466 void bn_sqr_comba4(BN_ULONG *r,const BN_ULONG *a); 467 int bn_cmp_words(const BN_ULONG *a,const BN_ULONG *b,int n); 468 int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b, 469 int cl, int dl); 470 void bn_mul_recursive(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,int n2, 471 int dna,int dnb,BN_ULONG *t); 472 void bn_mul_part_recursive(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b, 473 int n,int tna,int tnb,BN_ULONG *t); 474 void bn_sqr_recursive(BN_ULONG *r,const BN_ULONG *a, int n2, BN_ULONG *t); 475 void bn_mul_low_normal(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b, int n); 476 void bn_mul_low_recursive(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,int n2, 477 BN_ULONG *t); 478 void bn_mul_high(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,BN_ULONG *l,int n2, 479 BN_ULONG *t); 480 BN_ULONG bn_add_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, 481 int cl, int dl); 482 BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, 483 int cl, int dl); 484 485 #ifdef __cplusplus 486 } 487 #endif 488 489 #endif 490