1 /* crypto/bn/bn_lcl.h */ 2 /* Copyright (C) 1995-1998 Eric Young (eay (at) cryptsoft.com) 3 * All rights reserved. 4 * 5 * This package is an SSL implementation written 6 * by Eric Young (eay (at) 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 (at) 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 (at) 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 (at) 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 (at) 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 (at) cryptsoft.com). This product includes software written by Tim 108 * Hudson (tjh (at) 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 (at) 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(__x86_64__)) && \ 259 (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT)) 260 # if defined(__GNUC__) 261 # define BN_UMULT_HIGH(a,b) ({ \ 262 register BN_ULONG ret,discard; \ 263 asm ("mulq %3" \ 264 : "=a"(discard),"=d"(ret) \ 265 : "a"(a), "g"(b) \ 266 : "cc"); \ 267 ret; }) 268 # define BN_UMULT_LOHI(low,high,a,b) \ 269 asm ("mulq %3" \ 270 : "=a"(low),"=d"(high) \ 271 : "a"(a),"g"(b) \ 272 : "cc"); 273 # endif 274 # elif (defined(_M_AMD64) || defined(_M_X64)) && defined(SIXTY_FOUR_BIT) 275 # if defined(_MSC_VER) && _MSC_VER>=1400 276 unsigned __int64 __umulh (unsigned __int64 a,unsigned __int64 b); 277 unsigned __int64 _umul128 (unsigned __int64 a,unsigned __int64 b, 278 unsigned __int64 *h); 279 # pragma intrinsic(__umulh,_umul128) 280 # define BN_UMULT_HIGH(a,b) __umulh((a),(b)) 281 # define BN_UMULT_LOHI(low,high,a,b) ((low)=_umul128((a),(b),&(high))) 282 # endif 283 # endif /* cpu */ 284 #endif /* OPENSSL_NO_ASM */ 285 286 /************************************************************* 287 * Using the long long type 288 */ 289 #define Lw(t) (((BN_ULONG)(t))&BN_MASK2) 290 #define Hw(t) (((BN_ULONG)((t)>>BN_BITS2))&BN_MASK2) 291 292 #ifdef BN_DEBUG_RAND 293 #define bn_clear_top2max(a) \ 294 { \ 295 int ind = (a)->dmax - (a)->top; \ 296 BN_ULONG *ftl = &(a)->d[(a)->top-1]; \ 297 for (; ind != 0; ind--) \ 298 *(++ftl) = 0x0; \ 299 } 300 #else 301 #define bn_clear_top2max(a) 302 #endif 303 304 #ifdef BN_LLONG 305 #define mul_add(r,a,w,c) { \ 306 BN_ULLONG t; \ 307 t=(BN_ULLONG)w * (a) + (r) + (c); \ 308 (r)= Lw(t); \ 309 (c)= Hw(t); \ 310 } 311 312 #define mul(r,a,w,c) { \ 313 BN_ULLONG t; \ 314 t=(BN_ULLONG)w * (a) + (c); \ 315 (r)= Lw(t); \ 316 (c)= Hw(t); \ 317 } 318 319 #define sqr(r0,r1,a) { \ 320 BN_ULLONG t; \ 321 t=(BN_ULLONG)(a)*(a); \ 322 (r0)=Lw(t); \ 323 (r1)=Hw(t); \ 324 } 325 326 #elif defined(BN_UMULT_LOHI) 327 #define mul_add(r,a,w,c) { \ 328 BN_ULONG high,low,ret,tmp=(a); \ 329 ret = (r); \ 330 BN_UMULT_LOHI(low,high,w,tmp); \ 331 ret += (c); \ 332 (c) = (ret<(c))?1:0; \ 333 (c) += high; \ 334 ret += low; \ 335 (c) += (ret<low)?1:0; \ 336 (r) = ret; \ 337 } 338 339 #define mul(r,a,w,c) { \ 340 BN_ULONG high,low,ret,ta=(a); \ 341 BN_UMULT_LOHI(low,high,w,ta); \ 342 ret = low + (c); \ 343 (c) = high; \ 344 (c) += (ret<low)?1:0; \ 345 (r) = ret; \ 346 } 347 348 #define sqr(r0,r1,a) { \ 349 BN_ULONG tmp=(a); \ 350 BN_UMULT_LOHI(r0,r1,tmp,tmp); \ 351 } 352 353 #elif defined(BN_UMULT_HIGH) 354 #define mul_add(r,a,w,c) { \ 355 BN_ULONG high,low,ret,tmp=(a); \ 356 ret = (r); \ 357 high= BN_UMULT_HIGH(w,tmp); \ 358 ret += (c); \ 359 low = (w) * tmp; \ 360 (c) = (ret<(c))?1:0; \ 361 (c) += high; \ 362 ret += low; \ 363 (c) += (ret<low)?1:0; \ 364 (r) = ret; \ 365 } 366 367 #define mul(r,a,w,c) { \ 368 BN_ULONG high,low,ret,ta=(a); \ 369 low = (w) * ta; \ 370 high= BN_UMULT_HIGH(w,ta); \ 371 ret = low + (c); \ 372 (c) = high; \ 373 (c) += (ret<low)?1:0; \ 374 (r) = ret; \ 375 } 376 377 #define sqr(r0,r1,a) { \ 378 BN_ULONG tmp=(a); \ 379 (r0) = tmp * tmp; \ 380 (r1) = BN_UMULT_HIGH(tmp,tmp); \ 381 } 382 383 #else 384 /************************************************************* 385 * No long long type 386 */ 387 388 #define LBITS(a) ((a)&BN_MASK2l) 389 #define HBITS(a) (((a)>>BN_BITS4)&BN_MASK2l) 390 #define L2HBITS(a) (((a)<<BN_BITS4)&BN_MASK2) 391 392 #define LLBITS(a) ((a)&BN_MASKl) 393 #define LHBITS(a) (((a)>>BN_BITS2)&BN_MASKl) 394 #define LL2HBITS(a) ((BN_ULLONG)((a)&BN_MASKl)<<BN_BITS2) 395 396 #define mul64(l,h,bl,bh) \ 397 { \ 398 BN_ULONG m,m1,lt,ht; \ 399 \ 400 lt=l; \ 401 ht=h; \ 402 m =(bh)*(lt); \ 403 lt=(bl)*(lt); \ 404 m1=(bl)*(ht); \ 405 ht =(bh)*(ht); \ 406 m=(m+m1)&BN_MASK2; if (m < m1) ht+=L2HBITS((BN_ULONG)1); \ 407 ht+=HBITS(m); \ 408 m1=L2HBITS(m); \ 409 lt=(lt+m1)&BN_MASK2; if (lt < m1) ht++; \ 410 (l)=lt; \ 411 (h)=ht; \ 412 } 413 414 #define sqr64(lo,ho,in) \ 415 { \ 416 BN_ULONG l,h,m; \ 417 \ 418 h=(in); \ 419 l=LBITS(h); \ 420 h=HBITS(h); \ 421 m =(l)*(h); \ 422 l*=l; \ 423 h*=h; \ 424 h+=(m&BN_MASK2h1)>>(BN_BITS4-1); \ 425 m =(m&BN_MASK2l)<<(BN_BITS4+1); \ 426 l=(l+m)&BN_MASK2; if (l < m) h++; \ 427 (lo)=l; \ 428 (ho)=h; \ 429 } 430 431 #define mul_add(r,a,bl,bh,c) { \ 432 BN_ULONG l,h; \ 433 \ 434 h= (a); \ 435 l=LBITS(h); \ 436 h=HBITS(h); \ 437 mul64(l,h,(bl),(bh)); \ 438 \ 439 /* non-multiply part */ \ 440 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \ 441 (c)=(r); \ 442 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \ 443 (c)=h&BN_MASK2; \ 444 (r)=l; \ 445 } 446 447 #define mul(r,a,bl,bh,c) { \ 448 BN_ULONG l,h; \ 449 \ 450 h= (a); \ 451 l=LBITS(h); \ 452 h=HBITS(h); \ 453 mul64(l,h,(bl),(bh)); \ 454 \ 455 /* non-multiply part */ \ 456 l+=(c); if ((l&BN_MASK2) < (c)) h++; \ 457 (c)=h&BN_MASK2; \ 458 (r)=l&BN_MASK2; \ 459 } 460 #endif /* !BN_LLONG */ 461 462 void bn_mul_normal(BN_ULONG *r,BN_ULONG *a,int na,BN_ULONG *b,int nb); 463 void bn_mul_comba8(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b); 464 void bn_mul_comba4(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b); 465 void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp); 466 void bn_sqr_comba8(BN_ULONG *r,const BN_ULONG *a); 467 void bn_sqr_comba4(BN_ULONG *r,const BN_ULONG *a); 468 int bn_cmp_words(const BN_ULONG *a,const BN_ULONG *b,int n); 469 int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b, 470 int cl, int dl); 471 void bn_mul_recursive(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,int n2, 472 int dna,int dnb,BN_ULONG *t); 473 void bn_mul_part_recursive(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b, 474 int n,int tna,int tnb,BN_ULONG *t); 475 void bn_sqr_recursive(BN_ULONG *r,const BN_ULONG *a, int n2, BN_ULONG *t); 476 void bn_mul_low_normal(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b, int n); 477 void bn_mul_low_recursive(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,int n2, 478 BN_ULONG *t); 479 void bn_mul_high(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,BN_ULONG *l,int n2, 480 BN_ULONG *t); 481 BN_ULONG bn_add_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, 482 int cl, int dl); 483 BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, 484 int cl, int dl); 485 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); 486 487 #ifdef __cplusplus 488 } 489 #endif 490 491 #endif 492
