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/* 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/* Pentium pro 16,16,16,32,64 */ 167/* Alpha 16,16,16,16.64 */ 168#define BN_MULL_SIZE_NORMAL (16) /* 32 */ 169#define BN_MUL_RECURSIVE_SIZE_NORMAL (16) /* 32 less than */ 170#define BN_SQR_RECURSIVE_SIZE_NORMAL (16) /* 32 */ 171#define BN_MUL_LOW_RECURSIVE_SIZE_NORMAL (32) /* 32 */ 172#define BN_MONT_CTX_SET_SIZE_WORD (64) /* 32 */ 173 174#if !defined(NO_ASM) && !defined(NO_INLINE_ASM) && !defined(PEDANTIC) 175/* 176 * BN_UMULT_HIGH section. 177 * 178 * No, I'm not trying to overwhelm you when stating that the 179 * product of N-bit numbers is 2*N bits wide:-) No, I don't expect 180 * you to be impressed when I say that if the compiler doesn't 181 * support 2*N integer type, then you have to replace every N*N 182 * multiplication with 4 (N/2)*(N/2) accompanied by some shifts 183 * and additions which unavoidably results in severe performance 184 * penalties. Of course provided that the hardware is capable of 185 * producing 2*N result... That's when you normally start 186 * considering assembler implementation. However! It should be 187 * pointed out that some CPUs (most notably Alpha, PowerPC and 188 * upcoming IA-64 family:-) provide *separate* instruction 189 * calculating the upper half of the product placing the result 190 * into a general purpose register. Now *if* the compiler supports 191 * inline assembler, then it's not impossible to implement the 192 * "bignum" routines (and have the compiler optimize 'em) 193 * exhibiting "native" performance in C. That's what BN_UMULT_HIGH 194 * macro is about:-) 195 * 196 * <appro@fy.chalmers.se> 197 */ 198# if defined(__alpha) && (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT)) 199# if defined(__DECC) 200# include <c_asm.h> 201# define BN_UMULT_HIGH(a,b) (BN_ULONG)asm("umulh %a0,%a1,%v0",(a),(b)) 202# elif defined(__GNUC__) 203# define BN_UMULT_HIGH(a,b) ({ \ 204 register BN_ULONG ret; \ 205 asm ("umulh %1,%2,%0" \ 206 : "=r"(ret) \ 207 : "r"(a), "r"(b)); \ 208 ret; }) 209# endif /* compiler */ 210# elif defined(_ARCH_PPC) && defined(__64BIT__) && defined(SIXTY_FOUR_BIT_LONG) 211# if defined(__GNUC__) 212# define BN_UMULT_HIGH(a,b) ({ \ 213 register BN_ULONG ret; \ 214 asm ("mulhdu %0,%1,%2" \ 215 : "=r"(ret) \ 216 : "r"(a), "r"(b)); \ 217 ret; }) 218# endif /* compiler */ 219# endif /* cpu */ 220#endif /* NO_ASM */ 221 222/************************************************************* 223 * Using the long long type 224 */ 225#define Lw(t) (((BN_ULONG)(t))&BN_MASK2) 226#define Hw(t) (((BN_ULONG)((t)>>BN_BITS2))&BN_MASK2) 227 228/* This is used for internal error checking and is not normally used */ 229#ifdef BN_DEBUG 230# include <assert.h> 231# define bn_check_top(a) assert ((a)->top >= 0 && (a)->top <= (a)->dmax); 232#else 233# define bn_check_top(a) 234#endif 235 236/* This macro is to add extra stuff for development checking */ 237#ifdef BN_DEBUG 238#define bn_set_max(r) ((r)->max=(r)->top,BN_set_flags((r),BN_FLG_STATIC_DATA)) 239#else 240#define bn_set_max(r) 241#endif 242 243/* These macros are used to 'take' a section of a bignum for read only use */ 244#define bn_set_low(r,a,n) \ 245 { \ 246 (r)->top=((a)->top > (n))?(n):(a)->top; \ 247 (r)->d=(a)->d; \ 248 (r)->neg=(a)->neg; \ 249 (r)->flags|=BN_FLG_STATIC_DATA; \ 250 bn_set_max(r); \ 251 } 252 253#define bn_set_high(r,a,n) \ 254 { \ 255 if ((a)->top > (n)) \ 256 { \ 257 (r)->top=(a)->top-n; \ 258 (r)->d= &((a)->d[n]); \ 259 } \ 260 else \ 261 (r)->top=0; \ 262 (r)->neg=(a)->neg; \ 263 (r)->flags|=BN_FLG_STATIC_DATA; \ 264 bn_set_max(r); \ 265 } 266 267#ifdef BN_LLONG 268#define mul_add(r,a,w,c) { \ 269 BN_ULLONG t; \ 270 t=(BN_ULLONG)w * (a) + (r) + (c); \ 271 (r)= Lw(t); \ 272 (c)= Hw(t); \ 273 } 274 275#define mul(r,a,w,c) { \ 276 BN_ULLONG t; \ 277 t=(BN_ULLONG)w * (a) + (c); \ 278 (r)= Lw(t); \ 279 (c)= Hw(t); \ 280 } 281 282#define sqr(r0,r1,a) { \ 283 BN_ULLONG t; \ 284 t=(BN_ULLONG)(a)*(a); \ 285 (r0)=Lw(t); \ 286 (r1)=Hw(t); \ 287 } 288 289#elif defined(BN_UMULT_HIGH) 290#define mul_add(r,a,w,c) { \ 291 BN_ULONG high,low,ret,tmp=(a); \ 292 ret = (r); \ 293 high= BN_UMULT_HIGH(w,tmp); \ 294 ret += (c); \ 295 low = (w) * tmp; \ 296 (c) = (ret<(c))?1:0; \ 297 (c) += high; \ 298 ret += low; \ 299 (c) += (ret<low)?1:0; \ 300 (r) = ret; \ 301 } 302 303#define mul(r,a,w,c) { \ 304 BN_ULONG high,low,ret,ta=(a); \ 305 low = (w) * ta; \ 306 high= BN_UMULT_HIGH(w,ta); \ 307 ret = low + (c); \ 308 (c) = high; \ 309 (c) += (ret<low)?1:0; \ 310 (r) = ret; \ 311 } 312 313#define sqr(r0,r1,a) { \ 314 BN_ULONG tmp=(a); \ 315 (r0) = tmp * tmp; \ 316 (r1) = BN_UMULT_HIGH(tmp,tmp); \ 317 } 318 319#else 320/************************************************************* 321 * No long long type 322 */ 323 324#define LBITS(a) ((a)&BN_MASK2l) 325#define HBITS(a) (((a)>>BN_BITS4)&BN_MASK2l) 326#define L2HBITS(a) ((BN_ULONG)((a)&BN_MASK2l)<<BN_BITS4) 327 328#define LLBITS(a) ((a)&BN_MASKl) 329#define LHBITS(a) (((a)>>BN_BITS2)&BN_MASKl) 330#define LL2HBITS(a) ((BN_ULLONG)((a)&BN_MASKl)<<BN_BITS2) 331 332#define mul64(l,h,bl,bh) \ 333 { \ 334 BN_ULONG m,m1,lt,ht; \ 335 \ 336 lt=l; \ 337 ht=h; \ 338 m =(bh)*(lt); \ 339 lt=(bl)*(lt); \ 340 m1=(bl)*(ht); \ 341 ht =(bh)*(ht); \ 342 m=(m+m1)&BN_MASK2; if (m < m1) ht+=L2HBITS(1L); \ 343 ht+=HBITS(m); \ 344 m1=L2HBITS(m); \ 345 lt=(lt+m1)&BN_MASK2; if (lt < m1) ht++; \ 346 (l)=lt; \ 347 (h)=ht; \ 348 } 349 350#define sqr64(lo,ho,in) \ 351 { \ 352 BN_ULONG l,h,m; \ 353 \ 354 h=(in); \ 355 l=LBITS(h); \ 356 h=HBITS(h); \ 357 m =(l)*(h); \ 358 l*=l; \ 359 h*=h; \ 360 h+=(m&BN_MASK2h1)>>(BN_BITS4-1); \ 361 m =(m&BN_MASK2l)<<(BN_BITS4+1); \ 362 l=(l+m)&BN_MASK2; if (l < m) h++; \ 363 (lo)=l; \ 364 (ho)=h; \ 365 } 366 367#define mul_add(r,a,bl,bh,c) { \ 368 BN_ULONG l,h; \ 369 \ 370 h= (a); \ 371 l=LBITS(h); \ 372 h=HBITS(h); \ 373 mul64(l,h,(bl),(bh)); \ 374 \ 375 /* non-multiply part */ \ 376 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \ 377 (c)=(r); \ 378 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \ 379 (c)=h&BN_MASK2; \ 380 (r)=l; \ 381 } 382 383#define mul(r,a,bl,bh,c) { \ 384 BN_ULONG l,h; \ 385 \ 386 h= (a); \ 387 l=LBITS(h); \ 388 h=HBITS(h); \ 389 mul64(l,h,(bl),(bh)); \ 390 \ 391 /* non-multiply part */ \ 392 l+=(c); if ((l&BN_MASK2) < (c)) h++; \ 393 (c)=h&BN_MASK2; \ 394 (r)=l&BN_MASK2; \ 395 } 396#endif /* !BN_LLONG */ 397 398void bn_mul_normal(BN_ULONG *r,BN_ULONG *a,int na,BN_ULONG *b,int nb); 399void bn_mul_comba8(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b); 400void bn_mul_comba4(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b); 401void bn_sqr_normal(BN_ULONG *r, BN_ULONG *a, int n, BN_ULONG *tmp); 402void bn_sqr_comba8(BN_ULONG *r,BN_ULONG *a); 403void bn_sqr_comba4(BN_ULONG *r,BN_ULONG *a); 404int bn_cmp_words(BN_ULONG *a,BN_ULONG *b,int n); 405void bn_mul_recursive(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,int n2,BN_ULONG *t); 406void bn_mul_part_recursive(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b, 407 int tn, int n,BN_ULONG *t); 408void bn_sqr_recursive(BN_ULONG *r,BN_ULONG *a, int n2, BN_ULONG *t); 409void bn_mul_low_normal(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b, int n); 410void bn_mul_low_recursive(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,int n2, 411 BN_ULONG *t); 412void bn_mul_high(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,BN_ULONG *l,int n2, 413 BN_ULONG *t); 414 415#ifdef __cplusplus 416} 417#endif 418 419#endif 420