| 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 <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 | /* 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 | |
| 398 | void bn_mul_normal(BN_ULONG *r,BN_ULONG *a,int na,BN_ULONG *b,int nb); |
| 399 | void bn_mul_comba8(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b); |
| 400 | void bn_mul_comba4(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b); |
| 401 | void bn_sqr_normal(BN_ULONG *r, BN_ULONG *a, int n, BN_ULONG *tmp); |
| 402 | void bn_sqr_comba8(BN_ULONG *r,BN_ULONG *a); |
| 403 | void bn_sqr_comba4(BN_ULONG *r,BN_ULONG *a); |
| 404 | int bn_cmp_words(BN_ULONG *a,BN_ULONG *b,int n); |
| 405 | void bn_mul_recursive(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,int n2,BN_ULONG *t); |
| 406 | void bn_mul_part_recursive(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b, |
| 407 | int tn, int n,BN_ULONG *t); |
| 408 | void bn_sqr_recursive(BN_ULONG *r,BN_ULONG *a, int n2, BN_ULONG *t); |
| 409 | void bn_mul_low_normal(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b, int n); |
| 410 | void bn_mul_low_recursive(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,int n2, |
| 411 | BN_ULONG *t); |
| 412 | void 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 | |
