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 118extern "C" { 119#endif 120 121 122/* Used for temp variables */ 123#define BN_CTX_NUM 32 124#define BN_CTX_NUM_POS 12 125struct 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/* Pentium pro 16,16,16,32,64 */ 181/* Alpha 16,16,16,16.64 */ 182#define BN_MULL_SIZE_NORMAL (16) /* 32 */ 183#define BN_MUL_RECURSIVE_SIZE_NORMAL (16) /* 32 less than */ 184#define BN_SQR_RECURSIVE_SIZE_NORMAL (16) /* 32 */ 185#define BN_MUL_LOW_RECURSIVE_SIZE_NORMAL (32) /* 32 */ 186#define BN_MONT_CTX_SET_SIZE_WORD (64) /* 32 */ 187 188#if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) && !defined(PEDANTIC) 189/* 190 * BN_UMULT_HIGH section. 191 * 192 * No, I'm not trying to overwhelm you when stating that the 193 * product of N-bit numbers is 2*N bits wide:-) No, I don't expect 194 * you to be impressed when I say that if the compiler doesn't 195 * support 2*N integer type, then you have to replace every N*N 196 * multiplication with 4 (N/2)*(N/2) accompanied by some shifts 197 * and additions which unavoidably results in severe performance 198 * penalties. Of course provided that the hardware is capable of 199 * producing 2*N result... That's when you normally start 200 * considering assembler implementation. However! It should be 201 * pointed out that some CPUs (most notably Alpha, PowerPC and 202 * upcoming IA-64 family:-) provide *separate* instruction 203 * calculating the upper half of the product placing the result 204 * into a general purpose register. Now *if* the compiler supports 205 * inline assembler, then it's not impossible to implement the 206 * "bignum" routines (and have the compiler optimize 'em) 207 * exhibiting "native" performance in C. That's what BN_UMULT_HIGH 208 * macro is about:-) 209 * 210 * <appro@fy.chalmers.se> 211 */ 212# if defined(__alpha) && (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT)) 213# if defined(__DECC) 214# include <c_asm.h> 215# define BN_UMULT_HIGH(a,b) (BN_ULONG)asm("umulh %a0,%a1,%v0",(a),(b)) 216# elif defined(__GNUC__) 217# define BN_UMULT_HIGH(a,b) ({ \ 218 register BN_ULONG ret; \ 219 asm ("umulh %1,%2,%0" \ 220 : "=r"(ret) \ 221 : "r"(a), "r"(b)); \ 222 ret; }) 223# endif /* compiler */ 224# elif defined(_ARCH_PPC) && defined(__64BIT__) && defined(SIXTY_FOUR_BIT_LONG) 225# if defined(__GNUC__) 226# define BN_UMULT_HIGH(a,b) ({ \ 227 register BN_ULONG ret; \ 228 asm ("mulhdu %0,%1,%2" \ 229 : "=r"(ret) \ 230 : "r"(a), "r"(b)); \ 231 ret; }) 232# endif /* compiler */ 233# elif defined(__x86_64) && defined(SIXTY_FOUR_BIT_LONG) 234# if defined(__GNUC__) 235# define BN_UMULT_HIGH(a,b) ({ \ 236 register BN_ULONG ret,discard; \ 237 asm ("mulq %3" \ 238 : "=a"(discard),"=d"(ret) \ 239 : "a"(a), "g"(b) \ 240 : "cc"); \ 241 ret; }) 242# define BN_UMULT_LOHI(low,high,a,b) \ 243 asm ("mulq %3" \ 244 : "=a"(low),"=d"(high) \ 245 : "a"(a),"g"(b) \ 246 : "cc"); 247# endif 248# endif /* cpu */ 249#endif /* OPENSSL_NO_ASM */ 250 251/************************************************************* 252 * Using the long long type 253 */ 254#define Lw(t) (((BN_ULONG)(t))&BN_MASK2) 255#define Hw(t) (((BN_ULONG)((t)>>BN_BITS2))&BN_MASK2) 256 257/* This is used for internal error checking and is not normally used */ 258#ifdef BN_DEBUG 259# include <assert.h> 260# define bn_check_top(a) assert ((a)->top >= 0 && (a)->top <= (a)->dmax); 261#else 262# define bn_check_top(a) 263#endif 264 265/* This macro is to add extra stuff for development checking */ 266#ifdef BN_DEBUG 267#define bn_set_max(r) ((r)->max=(r)->top,BN_set_flags((r),BN_FLG_STATIC_DATA)) 268#else 269#define bn_set_max(r) 270#endif 271 272/* These macros are used to 'take' a section of a bignum for read only use */ 273#define bn_set_low(r,a,n) \ 274 { \ 275 (r)->top=((a)->top > (n))?(n):(a)->top; \ 276 (r)->d=(a)->d; \ 277 (r)->neg=(a)->neg; \ 278 (r)->flags|=BN_FLG_STATIC_DATA; \ 279 bn_set_max(r); \ 280 } 281 282#define bn_set_high(r,a,n) \ 283 { \ 284 if ((a)->top > (n)) \ 285 { \ 286 (r)->top=(a)->top-n; \ 287 (r)->d= &((a)->d[n]); \ 288 } \ 289 else \ 290 (r)->top=0; \ 291 (r)->neg=(a)->neg; \ 292 (r)->flags|=BN_FLG_STATIC_DATA; \ 293 bn_set_max(r); \ 294 } 295 296#ifdef BN_LLONG 297#define mul_add(r,a,w,c) { \ 298 BN_ULLONG t; \ 299 t=(BN_ULLONG)w * (a) + (r) + (c); \ 300 (r)= Lw(t); \ 301 (c)= Hw(t); \ 302 } 303 304#define mul(r,a,w,c) { \ 305 BN_ULLONG t; \ 306 t=(BN_ULLONG)w * (a) + (c); \ 307 (r)= Lw(t); \ 308 (c)= Hw(t); \ 309 } 310 311#define sqr(r0,r1,a) { \ 312 BN_ULLONG t; \ 313 t=(BN_ULLONG)(a)*(a); \ 314 (r0)=Lw(t); \ 315 (r1)=Hw(t); \ 316 } 317 318#elif defined(BN_UMULT_HIGH) 319#define mul_add(r,a,w,c) { \ 320 BN_ULONG high,low,ret,tmp=(a); \ 321 ret = (r); \ 322 high= BN_UMULT_HIGH(w,tmp); \ 323 ret += (c); \ 324 low = (w) * tmp; \ 325 (c) = (ret<(c))?1:0; \ 326 (c) += high; \ 327 ret += low; \ 328 (c) += (ret<low)?1:0; \ 329 (r) = ret; \ 330 } 331 332#define mul(r,a,w,c) { \ 333 BN_ULONG high,low,ret,ta=(a); \ 334 low = (w) * ta; \ 335 high= BN_UMULT_HIGH(w,ta); \ 336 ret = low + (c); \ 337 (c) = high; \ 338 (c) += (ret<low)?1:0; \ 339 (r) = ret; \ 340 } 341 342#define sqr(r0,r1,a) { \ 343 BN_ULONG tmp=(a); \ 344 (r0) = tmp * tmp; \ 345 (r1) = BN_UMULT_HIGH(tmp,tmp); \ 346 } 347 348#else 349/************************************************************* 350 * No long long type 351 */ 352 353#define LBITS(a) ((a)&BN_MASK2l) 354#define HBITS(a) (((a)>>BN_BITS4)&BN_MASK2l) 355#define L2HBITS(a) (((a)<<BN_BITS4)&BN_MASK2) 356 357#define LLBITS(a) ((a)&BN_MASKl) 358#define LHBITS(a) (((a)>>BN_BITS2)&BN_MASKl) 359#define LL2HBITS(a) ((BN_ULLONG)((a)&BN_MASKl)<<BN_BITS2) 360 361#define mul64(l,h,bl,bh) \ 362 { \ 363 BN_ULONG m,m1,lt,ht; \ 364 \ 365 lt=l; \ 366 ht=h; \ 367 m =(bh)*(lt); \ 368 lt=(bl)*(lt); \ 369 m1=(bl)*(ht); \ 370 ht =(bh)*(ht); \ 371 m=(m+m1)&BN_MASK2; if (m < m1) ht+=L2HBITS((BN_ULONG)1); \ 372 ht+=HBITS(m); \ 373 m1=L2HBITS(m); \ 374 lt=(lt+m1)&BN_MASK2; if (lt < m1) ht++; \ 375 (l)=lt; \ 376 (h)=ht; \ 377 } 378 379#define sqr64(lo,ho,in) \ 380 { \ 381 BN_ULONG l,h,m; \ 382 \ 383 h=(in); \ 384 l=LBITS(h); \ 385 h=HBITS(h); \ 386 m =(l)*(h); \ 387 l*=l; \ 388 h*=h; \ 389 h+=(m&BN_MASK2h1)>>(BN_BITS4-1); \ 390 m =(m&BN_MASK2l)<<(BN_BITS4+1); \ 391 l=(l+m)&BN_MASK2; if (l < m) h++; \ 392 (lo)=l; \ 393 (ho)=h; \ 394 } 395 396#define mul_add(r,a,bl,bh,c) { \ 397 BN_ULONG l,h; \ 398 \ 399 h= (a); \ 400 l=LBITS(h); \ 401 h=HBITS(h); \ 402 mul64(l,h,(bl),(bh)); \ 403 \ 404 /* non-multiply part */ \ 405 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \ 406 (c)=(r); \ 407 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \ 408 (c)=h&BN_MASK2; \ 409 (r)=l; \ 410 } 411 412#define mul(r,a,bl,bh,c) { \ 413 BN_ULONG l,h; \ 414 \ 415 h= (a); \ 416 l=LBITS(h); \ 417 h=HBITS(h); \ 418 mul64(l,h,(bl),(bh)); \ 419 \ 420 /* non-multiply part */ \ 421 l+=(c); if ((l&BN_MASK2) < (c)) h++; \ 422 (c)=h&BN_MASK2; \ 423 (r)=l&BN_MASK2; \ 424 } 425#endif /* !BN_LLONG */ 426 427void bn_mul_normal(BN_ULONG *r,BN_ULONG *a,int na,BN_ULONG *b,int nb); 428void bn_mul_comba8(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b); 429void bn_mul_comba4(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b); 430void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp); 431void bn_sqr_comba8(BN_ULONG *r,const BN_ULONG *a); 432void bn_sqr_comba4(BN_ULONG *r,const BN_ULONG *a); 433int bn_cmp_words(const BN_ULONG *a,const BN_ULONG *b,int n); 434int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b, 435 int cl, int dl); 436#ifdef BN_RECURSION 437void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2, 438 BN_ULONG *t); 439void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int tn, 440 int n, BN_ULONG *t); 441void bn_mul_low_recursive(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,int n2, 442 BN_ULONG *t); 443void bn_mul_high(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,BN_ULONG *l,int n2, 444 BN_ULONG *t); 445void bn_sqr_recursive(BN_ULONG *r,const BN_ULONG *a, int n2, BN_ULONG *t); 446#endif 447void bn_mul_low_normal(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b, int n); 448 449#ifdef __cplusplus 450} 451#endif 452 453#endif 454