bn_lcl.h revision 337982
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) 1998-2018 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# include "bn_int.h" 117 118#ifdef __cplusplus 119extern "C" { 120#endif 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/* 155 * Old SSLeay/OpenSSL table. Maximum window size was 5, so this table differs 156 * for b==1024; but it coincides for other interesting values (b==160, 157 * b==512). 158 */ 159# define BN_window_bits_for_exponent_size(b) \ 160 ((b) > 255 ? 5 : \ 161 (b) > 127 ? 4 : \ 162 (b) > 17 ? 3 : 1) 163# endif 164 165/* 166 * BN_mod_exp_mont_conttime is based on the assumption that the L1 data cache 167 * line width of the target processor is at least the following value. 168 */ 169# define MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH ( 64 ) 170# define MOD_EXP_CTIME_MIN_CACHE_LINE_MASK (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - 1) 171 172/* 173 * Window sizes optimized for fixed window size modular exponentiation 174 * algorithm (BN_mod_exp_mont_consttime). To achieve the security goals of 175 * BN_mode_exp_mont_consttime, the maximum size of the window must not exceed 176 * log_2(MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH). Window size thresholds are 177 * defined for cache line sizes of 32 and 64, cache line sizes where 178 * log_2(32)=5 and log_2(64)=6 respectively. A window size of 7 should only be 179 * used on processors that have a 128 byte or greater cache line size. 180 */ 181# if MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 64 182 183# define BN_window_bits_for_ctime_exponent_size(b) \ 184 ((b) > 937 ? 6 : \ 185 (b) > 306 ? 5 : \ 186 (b) > 89 ? 4 : \ 187 (b) > 22 ? 3 : 1) 188# define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (6) 189 190# elif MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 32 191 192# define BN_window_bits_for_ctime_exponent_size(b) \ 193 ((b) > 306 ? 5 : \ 194 (b) > 89 ? 4 : \ 195 (b) > 22 ? 3 : 1) 196# define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (5) 197 198# endif 199 200/* Pentium pro 16,16,16,32,64 */ 201/* Alpha 16,16,16,16.64 */ 202# define BN_MULL_SIZE_NORMAL (16)/* 32 */ 203# define BN_MUL_RECURSIVE_SIZE_NORMAL (16)/* 32 less than */ 204# define BN_SQR_RECURSIVE_SIZE_NORMAL (16)/* 32 */ 205# define BN_MUL_LOW_RECURSIVE_SIZE_NORMAL (32)/* 32 */ 206# define BN_MONT_CTX_SET_SIZE_WORD (64)/* 32 */ 207 208/* 209 * 2011-02-22 SMS. In various places, a size_t variable or a type cast to 210 * size_t was used to perform integer-only operations on pointers. This 211 * failed on VMS with 64-bit pointers (CC /POINTER_SIZE = 64) because size_t 212 * is still only 32 bits. What's needed in these cases is an integer type 213 * with the same size as a pointer, which size_t is not certain to be. The 214 * only fix here is VMS-specific. 215 */ 216# if defined(OPENSSL_SYS_VMS) 217# if __INITIAL_POINTER_SIZE == 64 218# define PTR_SIZE_INT long long 219# else /* __INITIAL_POINTER_SIZE == 64 */ 220# define PTR_SIZE_INT int 221# endif /* __INITIAL_POINTER_SIZE == 64 [else] */ 222# elif !defined(PTR_SIZE_INT) /* defined(OPENSSL_SYS_VMS) */ 223# define PTR_SIZE_INT size_t 224# endif /* defined(OPENSSL_SYS_VMS) [else] */ 225 226# if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) && !defined(PEDANTIC) 227/* 228 * BN_UMULT_HIGH section. 229 * 230 * No, I'm not trying to overwhelm you when stating that the 231 * product of N-bit numbers is 2*N bits wide:-) No, I don't expect 232 * you to be impressed when I say that if the compiler doesn't 233 * support 2*N integer type, then you have to replace every N*N 234 * multiplication with 4 (N/2)*(N/2) accompanied by some shifts 235 * and additions which unavoidably results in severe performance 236 * penalties. Of course provided that the hardware is capable of 237 * producing 2*N result... That's when you normally start 238 * considering assembler implementation. However! It should be 239 * pointed out that some CPUs (most notably Alpha, PowerPC and 240 * upcoming IA-64 family:-) provide *separate* instruction 241 * calculating the upper half of the product placing the result 242 * into a general purpose register. Now *if* the compiler supports 243 * inline assembler, then it's not impossible to implement the 244 * "bignum" routines (and have the compiler optimize 'em) 245 * exhibiting "native" performance in C. That's what BN_UMULT_HIGH 246 * macro is about:-) 247 * 248 * <appro@fy.chalmers.se> 249 */ 250# if defined(__alpha) && (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT)) 251# if defined(__DECC) 252# include <c_asm.h> 253# define BN_UMULT_HIGH(a,b) (BN_ULONG)asm("umulh %a0,%a1,%v0",(a),(b)) 254# elif defined(__GNUC__) && __GNUC__>=2 255# define BN_UMULT_HIGH(a,b) ({ \ 256 register BN_ULONG ret; \ 257 asm ("umulh %1,%2,%0" \ 258 : "=r"(ret) \ 259 : "r"(a), "r"(b)); \ 260 ret; }) 261# endif /* compiler */ 262# elif defined(_ARCH_PPC) && defined(__64BIT__) && defined(SIXTY_FOUR_BIT_LONG) 263# if defined(__GNUC__) && __GNUC__>=2 264# define BN_UMULT_HIGH(a,b) ({ \ 265 register BN_ULONG ret; \ 266 asm ("mulhdu %0,%1,%2" \ 267 : "=r"(ret) \ 268 : "r"(a), "r"(b)); \ 269 ret; }) 270# endif /* compiler */ 271# elif (defined(__x86_64) || defined(__x86_64__)) && \ 272 (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT)) 273# if defined(__GNUC__) && __GNUC__>=2 274# 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# elif (defined(_M_AMD64) || defined(_M_X64)) && defined(SIXTY_FOUR_BIT) 288# if defined(_MSC_VER) && _MSC_VER>=1400 289unsigned __int64 __umulh(unsigned __int64 a, unsigned __int64 b); 290unsigned __int64 _umul128(unsigned __int64 a, unsigned __int64 b, 291 unsigned __int64 *h); 292# pragma intrinsic(__umulh,_umul128) 293# define BN_UMULT_HIGH(a,b) __umulh((a),(b)) 294# define BN_UMULT_LOHI(low,high,a,b) ((low)=_umul128((a),(b),&(high))) 295# endif 296# elif defined(__mips) && (defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG)) 297# if defined(__GNUC__) && __GNUC__>=2 298# if __GNUC__>4 || (__GNUC__>=4 && __GNUC_MINOR__>=4) 299 /* "h" constraint is no more since 4.4 */ 300# define BN_UMULT_HIGH(a,b) (((__uint128_t)(a)*(b))>>64) 301# define BN_UMULT_LOHI(low,high,a,b) ({ \ 302 __uint128_t ret=(__uint128_t)(a)*(b); \ 303 (high)=ret>>64; (low)=ret; }) 304# else 305# define BN_UMULT_HIGH(a,b) ({ \ 306 register BN_ULONG ret; \ 307 asm ("dmultu %1,%2" \ 308 : "=h"(ret) \ 309 : "r"(a), "r"(b) : "l"); \ 310 ret; }) 311# define BN_UMULT_LOHI(low,high,a,b)\ 312 asm ("dmultu %2,%3" \ 313 : "=l"(low),"=h"(high) \ 314 : "r"(a), "r"(b)); 315# endif 316# endif 317# elif defined(__aarch64__) && defined(SIXTY_FOUR_BIT_LONG) 318# if defined(__GNUC__) && __GNUC__>=2 319# define BN_UMULT_HIGH(a,b) ({ \ 320 register BN_ULONG ret; \ 321 asm ("umulh %0,%1,%2" \ 322 : "=r"(ret) \ 323 : "r"(a), "r"(b)); \ 324 ret; }) 325# endif 326# endif /* cpu */ 327# endif /* OPENSSL_NO_ASM */ 328 329/************************************************************* 330 * Using the long long type 331 */ 332# define Lw(t) (((BN_ULONG)(t))&BN_MASK2) 333# define Hw(t) (((BN_ULONG)((t)>>BN_BITS2))&BN_MASK2) 334 335# ifdef BN_DEBUG_RAND 336# define bn_clear_top2max(a) \ 337 { \ 338 int ind = (a)->dmax - (a)->top; \ 339 BN_ULONG *ftl = &(a)->d[(a)->top-1]; \ 340 for (; ind != 0; ind--) \ 341 *(++ftl) = 0x0; \ 342 } 343# else 344# define bn_clear_top2max(a) 345# endif 346 347# ifdef BN_LLONG 348# define mul_add(r,a,w,c) { \ 349 BN_ULLONG t; \ 350 t=(BN_ULLONG)w * (a) + (r) + (c); \ 351 (r)= Lw(t); \ 352 (c)= Hw(t); \ 353 } 354 355# define mul(r,a,w,c) { \ 356 BN_ULLONG t; \ 357 t=(BN_ULLONG)w * (a) + (c); \ 358 (r)= Lw(t); \ 359 (c)= Hw(t); \ 360 } 361 362# define sqr(r0,r1,a) { \ 363 BN_ULLONG t; \ 364 t=(BN_ULLONG)(a)*(a); \ 365 (r0)=Lw(t); \ 366 (r1)=Hw(t); \ 367 } 368 369# elif defined(BN_UMULT_LOHI) 370# define mul_add(r,a,w,c) { \ 371 BN_ULONG high,low,ret,tmp=(a); \ 372 ret = (r); \ 373 BN_UMULT_LOHI(low,high,w,tmp); \ 374 ret += (c); \ 375 (c) = (ret<(c))?1:0; \ 376 (c) += high; \ 377 ret += low; \ 378 (c) += (ret<low)?1:0; \ 379 (r) = ret; \ 380 } 381 382# define mul(r,a,w,c) { \ 383 BN_ULONG high,low,ret,ta=(a); \ 384 BN_UMULT_LOHI(low,high,w,ta); \ 385 ret = low + (c); \ 386 (c) = high; \ 387 (c) += (ret<low)?1:0; \ 388 (r) = ret; \ 389 } 390 391# define sqr(r0,r1,a) { \ 392 BN_ULONG tmp=(a); \ 393 BN_UMULT_LOHI(r0,r1,tmp,tmp); \ 394 } 395 396# elif defined(BN_UMULT_HIGH) 397# define mul_add(r,a,w,c) { \ 398 BN_ULONG high,low,ret,tmp=(a); \ 399 ret = (r); \ 400 high= BN_UMULT_HIGH(w,tmp); \ 401 ret += (c); \ 402 low = (w) * tmp; \ 403 (c) = (ret<(c))?1:0; \ 404 (c) += high; \ 405 ret += low; \ 406 (c) += (ret<low)?1:0; \ 407 (r) = ret; \ 408 } 409 410# define mul(r,a,w,c) { \ 411 BN_ULONG high,low,ret,ta=(a); \ 412 low = (w) * ta; \ 413 high= BN_UMULT_HIGH(w,ta); \ 414 ret = low + (c); \ 415 (c) = high; \ 416 (c) += (ret<low)?1:0; \ 417 (r) = ret; \ 418 } 419 420# define sqr(r0,r1,a) { \ 421 BN_ULONG tmp=(a); \ 422 (r0) = tmp * tmp; \ 423 (r1) = BN_UMULT_HIGH(tmp,tmp); \ 424 } 425 426# else 427/************************************************************* 428 * No long long type 429 */ 430 431# define LBITS(a) ((a)&BN_MASK2l) 432# define HBITS(a) (((a)>>BN_BITS4)&BN_MASK2l) 433# define L2HBITS(a) (((a)<<BN_BITS4)&BN_MASK2) 434 435# define LLBITS(a) ((a)&BN_MASKl) 436# define LHBITS(a) (((a)>>BN_BITS2)&BN_MASKl) 437# define LL2HBITS(a) ((BN_ULLONG)((a)&BN_MASKl)<<BN_BITS2) 438 439# define mul64(l,h,bl,bh) \ 440 { \ 441 BN_ULONG m,m1,lt,ht; \ 442 \ 443 lt=l; \ 444 ht=h; \ 445 m =(bh)*(lt); \ 446 lt=(bl)*(lt); \ 447 m1=(bl)*(ht); \ 448 ht =(bh)*(ht); \ 449 m=(m+m1)&BN_MASK2; if (m < m1) ht+=L2HBITS((BN_ULONG)1); \ 450 ht+=HBITS(m); \ 451 m1=L2HBITS(m); \ 452 lt=(lt+m1)&BN_MASK2; if (lt < m1) ht++; \ 453 (l)=lt; \ 454 (h)=ht; \ 455 } 456 457# define sqr64(lo,ho,in) \ 458 { \ 459 BN_ULONG l,h,m; \ 460 \ 461 h=(in); \ 462 l=LBITS(h); \ 463 h=HBITS(h); \ 464 m =(l)*(h); \ 465 l*=l; \ 466 h*=h; \ 467 h+=(m&BN_MASK2h1)>>(BN_BITS4-1); \ 468 m =(m&BN_MASK2l)<<(BN_BITS4+1); \ 469 l=(l+m)&BN_MASK2; if (l < m) h++; \ 470 (lo)=l; \ 471 (ho)=h; \ 472 } 473 474# define mul_add(r,a,bl,bh,c) { \ 475 BN_ULONG l,h; \ 476 \ 477 h= (a); \ 478 l=LBITS(h); \ 479 h=HBITS(h); \ 480 mul64(l,h,(bl),(bh)); \ 481 \ 482 /* non-multiply part */ \ 483 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \ 484 (c)=(r); \ 485 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \ 486 (c)=h&BN_MASK2; \ 487 (r)=l; \ 488 } 489 490# define mul(r,a,bl,bh,c) { \ 491 BN_ULONG l,h; \ 492 \ 493 h= (a); \ 494 l=LBITS(h); \ 495 h=HBITS(h); \ 496 mul64(l,h,(bl),(bh)); \ 497 \ 498 /* non-multiply part */ \ 499 l+=(c); if ((l&BN_MASK2) < (c)) h++; \ 500 (c)=h&BN_MASK2; \ 501 (r)=l&BN_MASK2; \ 502 } 503# endif /* !BN_LLONG */ 504 505# if defined(OPENSSL_DOING_MAKEDEPEND) && defined(OPENSSL_FIPS) 506# undef bn_div_words 507# endif 508 509void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb); 510void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b); 511void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b); 512void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp); 513void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a); 514void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a); 515int bn_cmp_words(const BN_ULONG *a, const BN_ULONG *b, int n); 516int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b, int cl, int dl); 517void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2, 518 int dna, int dnb, BN_ULONG *t); 519void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, 520 int n, int tna, int tnb, BN_ULONG *t); 521void bn_sqr_recursive(BN_ULONG *r, const BN_ULONG *a, int n2, BN_ULONG *t); 522void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n); 523void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2, 524 BN_ULONG *t); 525void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2, 526 BN_ULONG *t); 527BN_ULONG bn_add_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, 528 int cl, int dl); 529BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, 530 int cl, int dl); 531int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp, 532 const BN_ULONG *np, const BN_ULONG *n0, int num); 533 534#ifdef __cplusplus 535} 536#endif 537 538#endif 539