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 /* Used for temp variables */ 123 #define BN_CTX_NUM 32 124 #define BN_CTX_NUM_POS 12 125 struct bignum_ctx 126 { 127 int tos; 128 BIGNUM bn[BN_CTX_NUM]; 129 int flags; 130 int depth; 131 int pos[BN_CTX_NUM_POS]; 132 int too_many; 133 } /* BN_CTX */; 134 135 136 /* 137 * BN_window_bits_for_exponent_size -- macro for sliding window mod_exp functions 138 * 139 * 140 * For window size 'w' (w >= 2) and a random 'b' bits exponent, 141 * the number of multiplications is a constant plus on average 142 * 143 * 2^(w-1) + (b-w)/(w+1); 144 * 145 * here 2^(w-1) is for precomputing the table (we actually need 146 * entries only for windows that have the lowest bit set), and 147 * (b-w)/(w+1) is an approximation for the expected number of 148 * w-bit windows, not counting the first one. 149 * 150 * Thus we should use 151 * 152 * w >= 6 if b > 671 153 * w = 5 if 671 > b > 239 154 * w = 4 if 239 > b > 79 155 * w = 3 if 79 > b > 23 156 * w <= 2 if 23 > b 157 * 158 * (with draws in between). Very small exponents are often selected 159 * with low Hamming weight, so we use w = 1 for b <= 23. 160 */ 161 #if 1 162 #define BN_window_bits_for_exponent_size(b) \ 163 ((b) > 671 ? 6 : \ 164 (b) > 239 ? 5 : \ 165 (b) > 79 ? 4 : \ 166 (b) > 23 ? 3 : 1) 167 #else 168 /* Old SSLeay/OpenSSL table. 169 * Maximum window size was 5, so this table differs for b==1024; 170 * but it coincides for other interesting values (b==160, b==512). 171 */ 172 #define BN_window_bits_for_exponent_size(b) \ 173 ((b) > 255 ? 5 : \ 174 (b) > 127 ? 4 : \ 175 (b) > 17 ? 3 : 1) 176 #endif 177 178 179 180 /* BN_mod_exp_mont_conttime is based on the assumption that the 181 * L1 data cache line width of the target processor is at least 182 * the following value. 183 */ 184 #define MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH ( 64 ) 185 #define MOD_EXP_CTIME_MIN_CACHE_LINE_MASK (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - 1) 186 187 /* Window sizes optimized for fixed window size modular exponentiation 188 * algorithm (BN_mod_exp_mont_consttime). 189 * 190 * To achieve the security goals of BN_mode_exp_mont_consttime, the 191 * maximum size of the window must not exceed 192 * log_2(MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH). 193 * 194 * Window size thresholds are defined for cache line sizes of 32 and 64, 195 * cache line sizes where log_2(32)=5 and log_2(64)=6 respectively. A 196 * window size of 7 should only be used on processors that have a 128 197 * byte or greater cache line size. 198 */ 199 #if MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 64 200 201 # define BN_window_bits_for_ctime_exponent_size(b) \ 202 ((b) > 937 ? 6 : \ 203 (b) > 306 ? 5 : \ 204 (b) > 89 ? 4 : \ 205 (b) > 22 ? 3 : 1) 206 # define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (6) 207 208 #elif MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 32 209 210 # define BN_window_bits_for_ctime_exponent_size(b) \ 211 ((b) > 306 ? 5 : \ 212 (b) > 89 ? 4 : \ 213 (b) > 22 ? 3 : 1) 214 # define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (5) 215 216 #endif 217 218 219 /* Pentium pro 16,16,16,32,64 */ 220 /* Alpha 16,16,16,16.64 */ 221 #define BN_MULL_SIZE_NORMAL (16) /* 32 */ 222 #define BN_MUL_RECURSIVE_SIZE_NORMAL (16) /* 32 less than */ 223 #define BN_SQR_RECURSIVE_SIZE_NORMAL (16) /* 32 */ 224 #define BN_MUL_LOW_RECURSIVE_SIZE_NORMAL (32) /* 32 */ 225 #define BN_MONT_CTX_SET_SIZE_WORD (64) /* 32 */ 226 227 #if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) && !defined(PEDANTIC) 228 /* 229 * BN_UMULT_HIGH section. 230 * 231 * No, I'm not trying to overwhelm you when stating that the 232 * product of N-bit numbers is 2*N bits wide:-) No, I don't expect 233 * you to be impressed when I say that if the compiler doesn't 234 * support 2*N integer type, then you have to replace every N*N 235 * multiplication with 4 (N/2)*(N/2) accompanied by some shifts 236 * and additions which unavoidably results in severe performance 237 * penalties. Of course provided that the hardware is capable of 238 * producing 2*N result... That's when you normally start 239 * considering assembler implementation. However! It should be 240 * pointed out that some CPUs (most notably Alpha, PowerPC and 241 * upcoming IA-64 family:-) provide *separate* instruction 242 * calculating the upper half of the product placing the result 243 * into a general purpose register. Now *if* the compiler supports 244 * inline assembler, then it's not impossible to implement the 245 * "bignum" routines (and have the compiler optimize 'em) 246 * exhibiting "native" performance in C. That's what BN_UMULT_HIGH 247 * macro is about:-) 248 * 249 * <appro@fy.chalmers.se> 250 */ 251 # if defined(__alpha) && (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT)) 252 # if defined(__DECC) 253 # include <c_asm.h> 254 # define BN_UMULT_HIGH(a,b) (BN_ULONG)asm("umulh %a0,%a1,%v0",(a),(b)) 255 # elif defined(__GNUC__) 256 # define BN_UMULT_HIGH(a,b) ({ \ 257 register BN_ULONG ret; \ 258 asm ("umulh %1,%2,%0" \ 259 : "=r"(ret) \ 260 : "r"(a), "r"(b)); \ 261 ret; }) 262 # endif /* compiler */ 263 # elif defined(_ARCH_PPC) && defined(__64BIT__) && defined(SIXTY_FOUR_BIT_LONG) 264 # if defined(__GNUC__) 265 # define BN_UMULT_HIGH(a,b) ({ \ 266 register BN_ULONG ret; \ 267 asm ("mulhdu %0,%1,%2" \ 268 : "=r"(ret) \ 269 : "r"(a), "r"(b)); \ 270 ret; }) 271 # endif /* compiler */ 272 # elif defined(__x86_64) && defined(SIXTY_FOUR_BIT_LONG) 273 # if defined(__GNUC__) 274 # define BN_UMULT_HIGH(a,b) ({ \ 275 register BN_ULONG ret,discard; \ 276 asm ("mulq %3" \ 277 : "=a"(discard),"=d"(ret) \ 278 : "a"(a), "g"(b) \ 279 : "cc"); \ 280 ret; }) 281 # define BN_UMULT_LOHI(low,high,a,b) \ 282 asm ("mulq %3" \ 283 : "=a"(low),"=d"(high) \ 284 : "a"(a),"g"(b) \ 285 : "cc"); 286 # endif 287 # endif /* cpu */ 288 #endif /* OPENSSL_NO_ASM */ 289 290 /************************************************************* 291 * Using the long long type 292 */ 293 #define Lw(t) (((BN_ULONG)(t))&BN_MASK2) 294 #define Hw(t) (((BN_ULONG)((t)>>BN_BITS2))&BN_MASK2) 295 296 /* This is used for internal error checking and is not normally used */ 297 #ifdef BN_DEBUG 298 # include <assert.h> 299 # define bn_check_top(a) assert ((a)->top >= 0 && (a)->top <= (a)->dmax); 300 #else 301 # define bn_check_top(a) 302 #endif 303 304 /* This macro is to add extra stuff for development checking */ 305 #ifdef BN_DEBUG 306 #define bn_set_max(r) ((r)->max=(r)->top,BN_set_flags((r),BN_FLG_STATIC_DATA)) 307 #else 308 #define bn_set_max(r) 309 #endif 310 311 /* These macros are used to 'take' a section of a bignum for read only use */ 312 #define bn_set_low(r,a,n) \ 313 { \ 314 (r)->top=((a)->top > (n))?(n):(a)->top; \ 315 (r)->d=(a)->d; \ 316 (r)->neg=(a)->neg; \ 317 (r)->flags|=BN_FLG_STATIC_DATA; \ 318 bn_set_max(r); \ 319 } 320 321 #define bn_set_high(r,a,n) \ 322 { \ 323 if ((a)->top > (n)) \ 324 { \ 325 (r)->top=(a)->top-n; \ 326 (r)->d= &((a)->d[n]); \ 327 } \ 328 else \ 329 (r)->top=0; \ 330 (r)->neg=(a)->neg; \ 331 (r)->flags|=BN_FLG_STATIC_DATA; \ 332 bn_set_max(r); \ 333 } 334 335 #ifdef BN_LLONG 336 #define mul_add(r,a,w,c) { \ 337 BN_ULLONG t; \ 338 t=(BN_ULLONG)w * (a) + (r) + (c); \ 339 (r)= Lw(t); \ 340 (c)= Hw(t); \ 341 } 342 343 #define mul(r,a,w,c) { \ 344 BN_ULLONG t; \ 345 t=(BN_ULLONG)w * (a) + (c); \ 346 (r)= Lw(t); \ 347 (c)= Hw(t); \ 348 } 349 350 #define sqr(r0,r1,a) { \ 351 BN_ULLONG t; \ 352 t=(BN_ULLONG)(a)*(a); \ 353 (r0)=Lw(t); \ 354 (r1)=Hw(t); \ 355 } 356 357 #elif defined(BN_UMULT_HIGH) 358 #define mul_add(r,a,w,c) { \ 359 BN_ULONG high,low,ret,tmp=(a); \ 360 ret = (r); \ 361 high= BN_UMULT_HIGH(w,tmp); \ 362 ret += (c); \ 363 low = (w) * tmp; \ 364 (c) = (ret<(c))?1:0; \ 365 (c) += high; \ 366 ret += low; \ 367 (c) += (ret<low)?1:0; \ 368 (r) = ret; \ 369 } 370 371 #define mul(r,a,w,c) { \ 372 BN_ULONG high,low,ret,ta=(a); \ 373 low = (w) * ta; \ 374 high= BN_UMULT_HIGH(w,ta); \ 375 ret = low + (c); \ 376 (c) = high; \ 377 (c) += (ret<low)?1:0; \ 378 (r) = ret; \ 379 } 380 381 #define sqr(r0,r1,a) { \ 382 BN_ULONG tmp=(a); \ 383 (r0) = tmp * tmp; \ 384 (r1) = BN_UMULT_HIGH(tmp,tmp); \ 385 } 386 387 #else 388 /************************************************************* 389 * No long long type 390 */ 391 392 #define LBITS(a) ((a)&BN_MASK2l) 393 #define HBITS(a) (((a)>>BN_BITS4)&BN_MASK2l) 394 #define L2HBITS(a) (((a)<<BN_BITS4)&BN_MASK2) 395 396 #define LLBITS(a) ((a)&BN_MASKl) 397 #define LHBITS(a) (((a)>>BN_BITS2)&BN_MASKl) 398 #define LL2HBITS(a) ((BN_ULLONG)((a)&BN_MASKl)<<BN_BITS2) 399 400 #define mul64(l,h,bl,bh) \ 401 { \ 402 BN_ULONG m,m1,lt,ht; \ 403 \ 404 lt=l; \ 405 ht=h; \ 406 m =(bh)*(lt); \ 407 lt=(bl)*(lt); \ 408 m1=(bl)*(ht); \ 409 ht =(bh)*(ht); \ 410 m=(m+m1)&BN_MASK2; if (m < m1) ht+=L2HBITS((BN_ULONG)1); \ 411 ht+=HBITS(m); \ 412 m1=L2HBITS(m); \ 413 lt=(lt+m1)&BN_MASK2; if (lt < m1) ht++; \ 414 (l)=lt; \ 415 (h)=ht; \ 416 } 417 418 #define sqr64(lo,ho,in) \ 419 { \ 420 BN_ULONG l,h,m; \ 421 \ 422 h=(in); \ 423 l=LBITS(h); \ 424 h=HBITS(h); \ 425 m =(l)*(h); \ 426 l*=l; \ 427 h*=h; \ 428 h+=(m&BN_MASK2h1)>>(BN_BITS4-1); \ 429 m =(m&BN_MASK2l)<<(BN_BITS4+1); \ 430 l=(l+m)&BN_MASK2; if (l < m) h++; \ 431 (lo)=l; \ 432 (ho)=h; \ 433 } 434 435 #define mul_add(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=(l+(c))&BN_MASK2; if (l < (c)) h++; \ 445 (c)=(r); \ 446 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \ 447 (c)=h&BN_MASK2; \ 448 (r)=l; \ 449 } 450 451 #define mul(r,a,bl,bh,c) { \ 452 BN_ULONG l,h; \ 453 \ 454 h= (a); \ 455 l=LBITS(h); \ 456 h=HBITS(h); \ 457 mul64(l,h,(bl),(bh)); \ 458 \ 459 /* non-multiply part */ \ 460 l+=(c); if ((l&BN_MASK2) < (c)) h++; \ 461 (c)=h&BN_MASK2; \ 462 (r)=l&BN_MASK2; \ 463 } 464 #endif /* !BN_LLONG */ 465 466 void bn_mul_normal(BN_ULONG *r,BN_ULONG *a,int na,BN_ULONG *b,int nb); 467 void bn_mul_comba8(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b); 468 void bn_mul_comba4(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b); 469 void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp); 470 void bn_sqr_comba8(BN_ULONG *r,const BN_ULONG *a); 471 void bn_sqr_comba4(BN_ULONG *r,const BN_ULONG *a); 472 int bn_cmp_words(const BN_ULONG *a,const BN_ULONG *b,int n); 473 int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b, 474 int cl, int dl); 475 #ifdef BN_RECURSION 476 void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2, 477 BN_ULONG *t); 478 void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int tn, 479 int n, BN_ULONG *t); 480 void bn_mul_low_recursive(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,int n2, 481 BN_ULONG *t); 482 void bn_mul_high(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,BN_ULONG *l,int n2, 483 BN_ULONG *t); 484 void bn_sqr_recursive(BN_ULONG *r,const BN_ULONG *a, int n2, BN_ULONG *t); 485 #endif 486 void bn_mul_low_normal(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b, int n); 487 488 #ifdef __cplusplus 489 } 490 #endif 491 492 #endif 493