1 /* $OpenBSD: bn_lcl.h,v 1.21 2014/10/28 07:35:58 jsg Exp $ */ 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/opensslconf.h> 116 117 #include <openssl/bn.h> 118 119 #ifdef __cplusplus 120 extern "C" { 121 #endif 122 123 124 /* 125 * BN_window_bits_for_exponent_size -- macro for sliding window mod_exp functions 126 * 127 * 128 * For window size 'w' (w >= 2) and a random 'b' bits exponent, 129 * the number of multiplications is a constant plus on average 130 * 131 * 2^(w-1) + (b-w)/(w+1); 132 * 133 * here 2^(w-1) is for precomputing the table (we actually need 134 * entries only for windows that have the lowest bit set), and 135 * (b-w)/(w+1) is an approximation for the expected number of 136 * w-bit windows, not counting the first one. 137 * 138 * Thus we should use 139 * 140 * w >= 6 if b > 671 141 * w = 5 if 671 > b > 239 142 * w = 4 if 239 > b > 79 143 * w = 3 if 79 > b > 23 144 * w <= 2 if 23 > b 145 * 146 * (with draws in between). Very small exponents are often selected 147 * with low Hamming weight, so we use w = 1 for b <= 23. 148 */ 149 #define BN_window_bits_for_exponent_size(b) \ 150 ((b) > 671 ? 6 : \ 151 (b) > 239 ? 5 : \ 152 (b) > 79 ? 4 : \ 153 (b) > 23 ? 3 : 1) 154 155 156 /* BN_mod_exp_mont_consttime is based on the assumption that the 157 * L1 data cache line width of the target processor is at least 158 * the following value. 159 */ 160 #define MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH ( 64 ) 161 #define MOD_EXP_CTIME_MIN_CACHE_LINE_MASK (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - 1) 162 163 /* Window sizes optimized for fixed window size modular exponentiation 164 * algorithm (BN_mod_exp_mont_consttime). 165 * 166 * To achieve the security goals of BN_mode_exp_mont_consttime, the 167 * maximum size of the window must not exceed 168 * log_2(MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH). 169 * 170 * Window size thresholds are defined for cache line sizes of 32 and 64, 171 * cache line sizes where log_2(32)=5 and log_2(64)=6 respectively. A 172 * window size of 7 should only be used on processors that have a 128 173 * byte or greater cache line size. 174 */ 175 #if MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 64 176 177 # define BN_window_bits_for_ctime_exponent_size(b) \ 178 ((b) > 937 ? 6 : \ 179 (b) > 306 ? 5 : \ 180 (b) > 89 ? 4 : \ 181 (b) > 22 ? 3 : 1) 182 # define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (6) 183 184 #elif MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 32 185 186 # define BN_window_bits_for_ctime_exponent_size(b) \ 187 ((b) > 306 ? 5 : \ 188 (b) > 89 ? 4 : \ 189 (b) > 22 ? 3 : 1) 190 # define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (5) 191 192 #endif 193 194 195 /* Pentium pro 16,16,16,32,64 */ 196 /* Alpha 16,16,16,16.64 */ 197 #define BN_MULL_SIZE_NORMAL (16) /* 32 */ 198 #define BN_MUL_RECURSIVE_SIZE_NORMAL (16) /* 32 less than */ 199 #define BN_SQR_RECURSIVE_SIZE_NORMAL (16) /* 32 */ 200 #define BN_MUL_LOW_RECURSIVE_SIZE_NORMAL (32) /* 32 */ 201 #define BN_MONT_CTX_SET_SIZE_WORD (64) /* 32 */ 202 203 #if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) 204 /* 205 * BN_UMULT_HIGH section. 206 * 207 * No, I'm not trying to overwhelm you when stating that the 208 * product of N-bit numbers is 2*N bits wide:-) No, I don't expect 209 * you to be impressed when I say that if the compiler doesn't 210 * support 2*N integer type, then you have to replace every N*N 211 * multiplication with 4 (N/2)*(N/2) accompanied by some shifts 212 * and additions which unavoidably results in severe performance 213 * penalties. Of course provided that the hardware is capable of 214 * producing 2*N result... That's when you normally start 215 * considering assembler implementation. However! It should be 216 * pointed out that some CPUs (most notably Alpha, PowerPC and 217 * upcoming IA-64 family:-) provide *separate* instruction 218 * calculating the upper half of the product placing the result 219 * into a general purpose register. Now *if* the compiler supports 220 * inline assembler, then it's not impossible to implement the 221 * "bignum" routines (and have the compiler optimize 'em) 222 * exhibiting "native" performance in C. That's what BN_UMULT_HIGH 223 * macro is about:-) 224 * 225 * <appro@fy.chalmers.se> 226 */ 227 # if defined(__alpha) 228 # if defined(__GNUC__) && __GNUC__>=2 229 # define BN_UMULT_HIGH(a,b) ({ \ 230 BN_ULONG ret; \ 231 asm ("umulh %1,%2,%0" \ 232 : "=r"(ret) \ 233 : "r"(a), "r"(b)); \ 234 ret; }) 235 # endif /* compiler */ 236 # elif defined(_ARCH_PPC) && defined(_LP64) 237 # if defined(__GNUC__) && __GNUC__>=2 238 # define BN_UMULT_HIGH(a,b) ({ \ 239 BN_ULONG ret; \ 240 asm ("mulhdu %0,%1,%2" \ 241 : "=r"(ret) \ 242 : "r"(a), "r"(b)); \ 243 ret; }) 244 # endif /* compiler */ 245 # elif defined(__x86_64) || defined(__x86_64__) 246 # if defined(__GNUC__) && __GNUC__>=2 247 # define BN_UMULT_HIGH(a,b) ({ \ 248 BN_ULONG ret,discard; \ 249 asm ("mulq %3" \ 250 : "=a"(discard),"=d"(ret) \ 251 : "a"(a), "g"(b) \ 252 : "cc"); \ 253 ret; }) 254 # define BN_UMULT_LOHI(low,high,a,b) \ 255 asm ("mulq %3" \ 256 : "=a"(low),"=d"(high) \ 257 : "a"(a),"g"(b) \ 258 : "cc"); 259 # endif 260 # elif defined(__mips) && defined(_LP64) 261 # if defined(__GNUC__) && __GNUC__>=2 262 # if __GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 4) /* "h" constraint is no more since 4.4 */ 263 # define BN_UMULT_HIGH(a,b) (((__uint128_t)(a)*(b))>>64) 264 # define BN_UMULT_LOHI(low,high,a,b) ({ \ 265 __uint128_t ret=(__uint128_t)(a)*(b); \ 266 (high)=ret>>64; (low)=ret; }) 267 # else 268 # define BN_UMULT_HIGH(a,b) ({ \ 269 BN_ULONG ret; \ 270 asm ("dmultu %1,%2" \ 271 : "=h"(ret) \ 272 : "r"(a), "r"(b) : "l"); \ 273 ret; }) 274 # define BN_UMULT_LOHI(low,high,a,b)\ 275 asm ("dmultu %2,%3" \ 276 : "=l"(low),"=h"(high) \ 277 : "r"(a), "r"(b)); 278 # endif 279 # endif 280 # endif /* cpu */ 281 #endif /* OPENSSL_NO_ASM */ 282 283 /************************************************************* 284 * Using the long long type 285 */ 286 #define Lw(t) (((BN_ULONG)(t))&BN_MASK2) 287 #define Hw(t) (((BN_ULONG)((t)>>BN_BITS2))&BN_MASK2) 288 289 #ifdef BN_DEBUG_RAND 290 #define bn_clear_top2max(a) \ 291 { \ 292 int ind = (a)->dmax - (a)->top; \ 293 BN_ULONG *ftl = &(a)->d[(a)->top-1]; \ 294 for (; ind != 0; ind--) \ 295 *(++ftl) = 0x0; \ 296 } 297 #else 298 #define bn_clear_top2max(a) 299 #endif 300 301 #ifdef BN_LLONG 302 #define mul_add(r,a,w,c) { \ 303 BN_ULLONG t; \ 304 t=(BN_ULLONG)w * (a) + (r) + (c); \ 305 (r)= Lw(t); \ 306 (c)= Hw(t); \ 307 } 308 309 #define mul(r,a,w,c) { \ 310 BN_ULLONG t; \ 311 t=(BN_ULLONG)w * (a) + (c); \ 312 (r)= Lw(t); \ 313 (c)= Hw(t); \ 314 } 315 316 #define sqr(r0,r1,a) { \ 317 BN_ULLONG t; \ 318 t=(BN_ULLONG)(a)*(a); \ 319 (r0)=Lw(t); \ 320 (r1)=Hw(t); \ 321 } 322 323 #elif defined(BN_UMULT_LOHI) 324 #define mul_add(r,a,w,c) { \ 325 BN_ULONG high,low,ret,tmp=(a); \ 326 ret = (r); \ 327 BN_UMULT_LOHI(low,high,w,tmp); \ 328 ret += (c); \ 329 (c) = (ret<(c))?1:0; \ 330 (c) += high; \ 331 ret += low; \ 332 (c) += (ret<low)?1:0; \ 333 (r) = ret; \ 334 } 335 336 #define mul(r,a,w,c) { \ 337 BN_ULONG high,low,ret,ta=(a); \ 338 BN_UMULT_LOHI(low,high,w,ta); \ 339 ret = low + (c); \ 340 (c) = high; \ 341 (c) += (ret<low)?1:0; \ 342 (r) = ret; \ 343 } 344 345 #define sqr(r0,r1,a) { \ 346 BN_ULONG tmp=(a); \ 347 BN_UMULT_LOHI(r0,r1,tmp,tmp); \ 348 } 349 350 #elif defined(BN_UMULT_HIGH) 351 #define mul_add(r,a,w,c) { \ 352 BN_ULONG high,low,ret,tmp=(a); \ 353 ret = (r); \ 354 high= BN_UMULT_HIGH(w,tmp); \ 355 ret += (c); \ 356 low = (w) * tmp; \ 357 (c) = (ret<(c))?1:0; \ 358 (c) += high; \ 359 ret += low; \ 360 (c) += (ret<low)?1:0; \ 361 (r) = ret; \ 362 } 363 364 #define mul(r,a,w,c) { \ 365 BN_ULONG high,low,ret,ta=(a); \ 366 low = (w) * ta; \ 367 high= BN_UMULT_HIGH(w,ta); \ 368 ret = low + (c); \ 369 (c) = high; \ 370 (c) += (ret<low)?1:0; \ 371 (r) = ret; \ 372 } 373 374 #define sqr(r0,r1,a) { \ 375 BN_ULONG tmp=(a); \ 376 (r0) = tmp * tmp; \ 377 (r1) = BN_UMULT_HIGH(tmp,tmp); \ 378 } 379 380 #else 381 /************************************************************* 382 * No long long type 383 */ 384 385 #define LBITS(a) ((a)&BN_MASK2l) 386 #define HBITS(a) (((a)>>BN_BITS4)&BN_MASK2l) 387 #define L2HBITS(a) (((a)<<BN_BITS4)&BN_MASK2) 388 389 #define mul64(l,h,bl,bh) \ 390 { \ 391 BN_ULONG m,m1,lt,ht; \ 392 \ 393 lt=l; \ 394 ht=h; \ 395 m =(bh)*(lt); \ 396 lt=(bl)*(lt); \ 397 m1=(bl)*(ht); \ 398 ht =(bh)*(ht); \ 399 m=(m+m1)&BN_MASK2; if (m < m1) ht+=L2HBITS((BN_ULONG)1); \ 400 ht+=HBITS(m); \ 401 m1=L2HBITS(m); \ 402 lt=(lt+m1)&BN_MASK2; if (lt < m1) ht++; \ 403 (l)=lt; \ 404 (h)=ht; \ 405 } 406 407 #define sqr64(lo,ho,in) \ 408 { \ 409 BN_ULONG l,h,m; \ 410 \ 411 h=(in); \ 412 l=LBITS(h); \ 413 h=HBITS(h); \ 414 m =(l)*(h); \ 415 l*=l; \ 416 h*=h; \ 417 h+=(m&BN_MASK2h1)>>(BN_BITS4-1); \ 418 m =(m&BN_MASK2l)<<(BN_BITS4+1); \ 419 l=(l+m)&BN_MASK2; if (l < m) h++; \ 420 (lo)=l; \ 421 (ho)=h; \ 422 } 423 424 #define mul_add(r,a,bl,bh,c) { \ 425 BN_ULONG l,h; \ 426 \ 427 h= (a); \ 428 l=LBITS(h); \ 429 h=HBITS(h); \ 430 mul64(l,h,(bl),(bh)); \ 431 \ 432 /* non-multiply part */ \ 433 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \ 434 (c)=(r); \ 435 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \ 436 (c)=h&BN_MASK2; \ 437 (r)=l; \ 438 } 439 440 #define mul(r,a,bl,bh,c) { \ 441 BN_ULONG l,h; \ 442 \ 443 h= (a); \ 444 l=LBITS(h); \ 445 h=HBITS(h); \ 446 mul64(l,h,(bl),(bh)); \ 447 \ 448 /* non-multiply part */ \ 449 l+=(c); if ((l&BN_MASK2) < (c)) h++; \ 450 (c)=h&BN_MASK2; \ 451 (r)=l&BN_MASK2; \ 452 } 453 #endif /* !BN_LLONG */ 454 455 void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb); 456 void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b); 457 void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b); 458 void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp); 459 void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a); 460 void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a); 461 int bn_cmp_words(const BN_ULONG *a, const BN_ULONG *b, int n); 462 int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b, 463 int cl, int dl); 464 void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2, 465 int dna, int dnb, BN_ULONG *t); 466 void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, 467 int n, int tna, int tnb, BN_ULONG *t); 468 void bn_sqr_recursive(BN_ULONG *r, const BN_ULONG *a, int n2, BN_ULONG *t); 469 void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n); 470 void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2, 471 BN_ULONG *t); 472 void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2, 473 BN_ULONG *t); 474 BN_ULONG bn_add_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, 475 int cl, int dl); 476 BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, 477 int cl, int dl); 478 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); 479 480 #ifdef __cplusplus 481 } 482 #endif 483 484 #endif 485