1/* crypto/bn/bn.h */ 2/* Copyright (C) 1995-1997 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#ifndef HEADER_BN_H 60#define HEADER_BN_H 61 62#include <stdio.h> /* FILE */ 63#include "config.h" 64 65#ifdef __cplusplus 66extern "C" { 67#endif 68 69#ifdef VMS 70#undef BN_LLONG /* experimental, so far... */ 71#endif 72 73#undef BN_MUL_COMBA 74#undef BN_SQR_COMBA 75#undef BN_RECURSION 76#undef RECP_MUL_MOD 77#undef MONT_MUL_MOD 78 79#if defined(SIZEOF_LONG_LONG) && SIZEOF_LONG_LONG == 8 80# if SIZEOF_LONG == 4 81# define THIRTY_TWO_BIT 82# else 83# define SIXTY_FOUR_BIT_LONG 84# endif 85#else 86# if SIZEOF_LONG == 4 87# define THIRTY_TWO_BIT 88# endif 89#endif 90 91#undef BN_LLONG 92 93/* assuming long is 64bit - this is the DEC Alpha 94 * unsigned long long is only 64 bits :-(, don't define 95 * BN_LLONG for the DEC Alpha */ 96#ifdef SIXTY_FOUR_BIT_LONG 97#define BN_ULLONG unsigned long long 98#define BN_ULONG unsigned long 99#define BN_LONG long 100#define BN_BITS 128 101#define BN_BYTES 8 102#define BN_BITS2 64 103#define BN_BITS4 32 104#define BN_MASK (0xffffffffffffffffffffffffffffffffLL) 105#define BN_MASK2 (0xffffffffffffffffL) 106#define BN_MASK2l (0xffffffffL) 107#define BN_MASK2h (0xffffffff00000000L) 108#define BN_MASK2h1 (0xffffffff80000000L) 109#define BN_TBIT (0x8000000000000000L) 110#define BN_DEC_CONV (10000000000000000000UL) 111#define BN_DEC_FMT1 "%lu" 112#define BN_DEC_FMT2 "%019lu" 113#define BN_DEC_NUM 19 114#endif 115 116/* This is where the long long data type is 64 bits, but long is 32. 117 * For machines where there are 64bit registers, this is the mode to use. 118 * IRIX, on R4000 and above should use this mode, along with the relevant 119 * assembler code :-). Do NOT define BN_LLONG. 120 */ 121#ifdef SIXTY_FOUR_BIT 122#undef BN_LLONG 123#undef BN_ULLONG 124#define BN_ULONG unsigned long long 125#define BN_LONG long long 126#define BN_BITS 128 127#define BN_BYTES 8 128#define BN_BITS2 64 129#define BN_BITS4 32 130#define BN_MASK2 (0xffffffffffffffffLL) 131#define BN_MASK2l (0xffffffffL) 132#define BN_MASK2h (0xffffffff00000000LL) 133#define BN_MASK2h1 (0xffffffff80000000LL) 134#define BN_TBIT (0x8000000000000000LL) 135#define BN_DEC_CONV (10000000000000000000LL) 136#define BN_DEC_FMT1 "%llu" 137#define BN_DEC_FMT2 "%019llu" 138#define BN_DEC_NUM 19 139#endif 140 141#ifdef THIRTY_TWO_BIT 142#if defined(WIN32) && !defined(__GNUC__) 143#define BN_ULLONG unsigned _int64 144#else 145#define BN_ULLONG unsigned long long 146#endif 147#define BN_ULONG unsigned long 148#define BN_LONG long 149#define BN_BITS 64 150#define BN_BYTES 4 151#define BN_BITS2 32 152#define BN_BITS4 16 153#ifdef WIN32 154/* VC++ doesn't like the LL suffix */ 155#define BN_MASK (0xffffffffffffffffL) 156#else 157#define BN_MASK (0xffffffffffffffffLL) 158#endif 159#define BN_MASK2 (0xffffffffL) 160#define BN_MASK2l (0xffff) 161#define BN_MASK2h1 (0xffff8000L) 162#define BN_MASK2h (0xffff0000L) 163#define BN_TBIT (0x80000000L) 164#define BN_DEC_CONV (1000000000L) 165#define BN_DEC_FMT1 "%lu" 166#define BN_DEC_FMT2 "%09lu" 167#define BN_DEC_NUM 9 168#endif 169 170#ifdef SIXTEEN_BIT 171#ifndef BN_DIV2W 172#define BN_DIV2W 173#endif 174#define BN_ULLONG unsigned long 175#define BN_ULONG unsigned short 176#define BN_LONG short 177#define BN_BITS 32 178#define BN_BYTES 2 179#define BN_BITS2 16 180#define BN_BITS4 8 181#define BN_MASK (0xffffffff) 182#define BN_MASK2 (0xffff) 183#define BN_MASK2l (0xff) 184#define BN_MASK2h1 (0xff80) 185#define BN_MASK2h (0xff00) 186#define BN_TBIT (0x8000) 187#define BN_DEC_CONV (100000) 188#define BN_DEC_FMT1 "%u" 189#define BN_DEC_FMT2 "%05u" 190#define BN_DEC_NUM 5 191#endif 192 193#ifdef EIGHT_BIT 194#ifndef BN_DIV2W 195#define BN_DIV2W 196#endif 197#define BN_ULLONG unsigned short 198#define BN_ULONG unsigned char 199#define BN_LONG char 200#define BN_BITS 16 201#define BN_BYTES 1 202#define BN_BITS2 8 203#define BN_BITS4 4 204#define BN_MASK (0xffff) 205#define BN_MASK2 (0xff) 206#define BN_MASK2l (0xf) 207#define BN_MASK2h1 (0xf8) 208#define BN_MASK2h (0xf0) 209#define BN_TBIT (0x80) 210#define BN_DEC_CONV (100) 211#define BN_DEC_FMT1 "%u" 212#define BN_DEC_FMT2 "%02u" 213#define BN_DEC_NUM 2 214#endif 215 216#define BN_DEFAULT_BITS 1280 217 218#ifdef BIGNUM 219#undef BIGNUM 220#endif 221 222#define BN_FLG_MALLOCED 0x01 223#define BN_FLG_STATIC_DATA 0x02 224#define BN_FLG_FREE 0x8000 /* used for debuging */ 225#define BN_set_flags(b,n) ((b)->flags|=(n)) 226#define BN_get_flags(b,n) ((b)->flags&(n)) 227 228typedef struct bignum_st 229 { 230 BN_ULONG *d; /* Pointer to an array of 'BN_BITS2' bit chunks. */ 231 int top; /* Index of last used d +1. */ 232 /* The next are internal book keeping for bn_expand. */ 233 int dmax; /* Size of the d array. */ 234 int neg; /* one if the number is negative */ 235 int flags; 236 } BIGNUM; 237 238/* Used for temp variables */ 239#define BN_CTX_NUM 12 240#define BN_CTX_NUM_POS 12 241typedef struct bignum_ctx 242 { 243 int tos; 244 BIGNUM bn[BN_CTX_NUM]; 245 int flags; 246 int depth; 247 int pos[BN_CTX_NUM_POS]; 248 int too_many; 249 } BN_CTX; 250 251/* Used for montgomery multiplication */ 252typedef struct bn_mont_ctx_st 253 { 254 int ri; /* number of bits in R */ 255 BIGNUM RR; /* used to convert to montgomery form */ 256 BIGNUM N; /* The modulus */ 257 BIGNUM Ni; /* R*(1/R mod N) - N*Ni = 1 258 * (Ni is only stored for bignum algorithm) */ 259 BN_ULONG n0; /* least significant word of Ni */ 260 int flags; 261 } BN_MONT_CTX; 262 263/* Used for reciprocal division/mod functions 264 * It cannot be shared between threads 265 */ 266typedef struct bn_recp_ctx_st 267 { 268 BIGNUM N; /* the divisor */ 269 BIGNUM Nr; /* the reciprocal */ 270 int num_bits; 271 int shift; 272 int flags; 273 } BN_RECP_CTX; 274 275#define BN_to_montgomery(r,a,mont,ctx) BN_mod_mul_montgomery(\ 276 r,a,&((mont)->RR),(mont),ctx) 277 278#define BN_prime_checks 0 /* default: select number of iterations 279 based on the size of the number */ 280 281/* number of Miller-Rabin iterations for an error rate of less than 2^-80 282 * for random 'b'-bit input, b >= 100 (taken from table 4.4 in the Handbook 283 * of Applied Cryptography [Menezes, van Oorschot, Vanstone; CRC Press 1996]; 284 * original paper: Damgaard, Landrock, Pomerance: Average case error estimates 285 * for the strong probable prime test. -- Math. Comp. 61 (1993) 177-194) */ 286#define BN_prime_checks_for_size(b) ((b) >= 1300 ? 2 : \ 287 (b) >= 850 ? 3 : \ 288 (b) >= 650 ? 4 : \ 289 (b) >= 550 ? 5 : \ 290 (b) >= 450 ? 6 : \ 291 (b) >= 400 ? 7 : \ 292 (b) >= 350 ? 8 : \ 293 (b) >= 300 ? 9 : \ 294 (b) >= 250 ? 12 : \ 295 (b) >= 200 ? 15 : \ 296 (b) >= 150 ? 18 : \ 297 /* b >= 100 */ 27) 298 299#define BN_num_bytes(a) ((BN_num_bits(a)+7)/8) 300#define BN_is_word(a,w) (((a)->top == 1) && ((a)->d[0] == (BN_ULONG)(w))) 301#define BN_is_zero(a) (((a)->top == 0) || BN_is_word(a,0)) 302#define BN_is_one(a) (BN_is_word((a),1)) 303#define BN_is_odd(a) (((a)->top > 0) && ((a)->d[0] & 1)) 304#define BN_one(a) (BN_set_word((a),1)) 305#define BN_zero(a) (BN_set_word((a),0)) 306 307BIGNUM *BN_value_one(void); 308char * BN_options(void); 309BN_CTX *BN_CTX_new(void); 310void BN_CTX_init(BN_CTX *c); 311void BN_CTX_free(BN_CTX *c); 312void BN_CTX_start(BN_CTX *ctx); 313BIGNUM *BN_CTX_get(BN_CTX *ctx); 314void BN_CTX_end(BN_CTX *ctx); 315int BN_rand(BIGNUM *rnd, int bits, int top,int bottom); 316int BN_pseudo_rand(BIGNUM *rnd, int bits, int top,int bottom); 317int BN_num_bits(const BIGNUM *a); 318int BN_num_bits_word(BN_ULONG); 319BIGNUM *BN_new(void); 320void BN_init(BIGNUM *); 321void BN_clear_free(BIGNUM *a); 322BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b); 323BIGNUM *BN_bin2bn(const unsigned char *s,int len,BIGNUM *ret); 324int BN_bn2bin(const BIGNUM *a, unsigned char *to); 325int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); 326int BN_usub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); 327int BN_uadd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); 328int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); 329int BN_mod(BIGNUM *rem, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx); 330int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d, 331 BN_CTX *ctx); 332int BN_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx); 333int BN_sqr(BIGNUM *r, BIGNUM *a,BN_CTX *ctx); 334BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w); 335BN_ULONG BN_div_word(BIGNUM *a, BN_ULONG w); 336int BN_mul_word(BIGNUM *a, BN_ULONG w); 337int BN_add_word(BIGNUM *a, BN_ULONG w); 338int BN_sub_word(BIGNUM *a, BN_ULONG w); 339int BN_set_word(BIGNUM *a, BN_ULONG w); 340BN_ULONG BN_get_word(BIGNUM *a); 341int BN_cmp(const BIGNUM *a, const BIGNUM *b); 342void BN_free(BIGNUM *a); 343int BN_is_bit_set(const BIGNUM *a, int n); 344int BN_lshift(BIGNUM *r, const BIGNUM *a, int n); 345int BN_lshift1(BIGNUM *r, BIGNUM *a); 346int BN_exp(BIGNUM *r, BIGNUM *a, BIGNUM *p,BN_CTX *ctx); 347int BN_mod_exp(BIGNUM *r, BIGNUM *a, const BIGNUM *p, 348 const BIGNUM *m,BN_CTX *ctx); 349int BN_mod_exp_mont(BIGNUM *r, BIGNUM *a, const BIGNUM *p, 350 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx); 351int BN_mod_exp_mont_word(BIGNUM *r, BN_ULONG a, const BIGNUM *p, 352 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx); 353int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, 354 const BIGNUM *m,BN_CTX *ctx); 355int BN_mask_bits(BIGNUM *a,int n); 356int BN_mod_mul(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m, BN_CTX *ctx); 357int BN_reciprocal(BIGNUM *r, BIGNUM *m, int len, BN_CTX *ctx); 358int BN_rshift(BIGNUM *r, BIGNUM *a, int n); 359int BN_rshift1(BIGNUM *r, BIGNUM *a); 360void BN_clear(BIGNUM *a); 361BIGNUM *BN_dup(const BIGNUM *a); 362int BN_ucmp(const BIGNUM *a, const BIGNUM *b); 363int BN_set_bit(BIGNUM *a, int n); 364int BN_clear_bit(BIGNUM *a, int n); 365int BN_gcd(BIGNUM *r,BIGNUM *in_a,BIGNUM *in_b,BN_CTX *ctx); 366BIGNUM *BN_mod_inverse(BIGNUM *ret,BIGNUM *a, const BIGNUM *n,BN_CTX *ctx); 367BIGNUM *BN_generate_prime(BIGNUM *ret,int bits,int safe,BIGNUM *add, 368 BIGNUM *rem,void (*callback)(int,int,void *),void *cb_arg); 369int BN_is_prime(const BIGNUM *p,int nchecks, 370 void (*callback)(int,int,void *), 371 BN_CTX *ctx,void *cb_arg); 372int BN_is_prime_fasttest(const BIGNUM *p,int nchecks, 373 void (*callback)(int,int,void *),BN_CTX *ctx,void *cb_arg, 374 int do_trial_division); 375 376BN_MONT_CTX *BN_MONT_CTX_new(void ); 377void BN_MONT_CTX_init(BN_MONT_CTX *ctx); 378int BN_mod_mul_montgomery(BIGNUM *r,BIGNUM *a,BIGNUM *b,BN_MONT_CTX *mont, 379 BN_CTX *ctx); 380int BN_from_montgomery(BIGNUM *r,BIGNUM *a,BN_MONT_CTX *mont,BN_CTX *ctx); 381void BN_MONT_CTX_free(BN_MONT_CTX *mont); 382int BN_MONT_CTX_set(BN_MONT_CTX *mont,const BIGNUM *modulus,BN_CTX *ctx); 383BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to,BN_MONT_CTX *from); 384 385void BN_set_params(int mul,int high,int low,int mont); 386int BN_get_params(int which); /* 0, mul, 1 high, 2 low, 3 mont */ 387 388void BN_RECP_CTX_init(BN_RECP_CTX *recp); 389BN_RECP_CTX *BN_RECP_CTX_new(void); 390void BN_RECP_CTX_free(BN_RECP_CTX *recp); 391int BN_RECP_CTX_set(BN_RECP_CTX *recp,const BIGNUM *rdiv,BN_CTX *ctx); 392int BN_mod_mul_reciprocal(BIGNUM *r, BIGNUM *x, BIGNUM *y, 393 BN_RECP_CTX *recp,BN_CTX *ctx); 394int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, 395 const BIGNUM *m, BN_CTX *ctx); 396int BN_div_recp(BIGNUM *dv, BIGNUM *rem, BIGNUM *m, 397 BN_RECP_CTX *recp, BN_CTX *ctx); 398 399/* library internal functions */ 400 401#define bn_expand(a,bits) ((((((bits+BN_BITS2-1))/BN_BITS2)) <= (a)->dmax)?\ 402 (a):bn_expand2((a),(bits)/BN_BITS2+1)) 403#define bn_wexpand(a,words) (((words) <= (a)->dmax)?(a):bn_expand2((a),(words))) 404BIGNUM *bn_expand2(BIGNUM *a, int words); 405 406#define bn_fix_top(a) \ 407 { \ 408 BN_ULONG *ftl; \ 409 if ((a)->top > 0) \ 410 { \ 411 for (ftl= &((a)->d[(a)->top-1]); (a)->top > 0; (a)->top--) \ 412 if (*(ftl--)) break; \ 413 } \ 414 } 415 416BN_ULONG bn_mul_add_words(BN_ULONG *rp, BN_ULONG *ap, int num, BN_ULONG w); 417BN_ULONG bn_mul_words(BN_ULONG *rp, BN_ULONG *ap, int num, BN_ULONG w); 418void bn_sqr_words(BN_ULONG *rp, BN_ULONG *ap, int num); 419BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d); 420BN_ULONG bn_add_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp,int num); 421BN_ULONG bn_sub_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp,int num); 422 423#ifdef BN_DEBUG 424 void bn_dump1(FILE *o, const char *a, BN_ULONG *b,int n); 425# define bn_print(a) {fprintf(stderr, #a "="); BN_print_fp(stderr,a); \ 426 fprintf(stderr,"\n");} 427# define bn_dump(a,n) bn_dump1(stderr,#a,a,n); 428#else 429# define bn_print(a) 430# define bn_dump(a,b) 431#endif 432 433/* BEGIN ERROR CODES */ 434/* The following lines are auto generated by the script mkerr.pl. Any changes 435 * made after this point may be overwritten when the script is next run. 436 */ 437 438/* Error codes for the BN functions. */ 439 440/* Function codes. */ 441#define BN_F_BN_CTX_GET 116 442#define BN_F_BN_CTX_NEW 106 443#define BN_F_BN_DIV 107 444#define BN_F_BN_EXPAND2 108 445#define BN_F_BN_MOD_EXP2_MONT 118 446#define BN_F_BN_MOD_EXP_MONT 109 447#define BN_F_BN_MOD_EXP_MONT_WORD 117 448#define BN_F_BN_MOD_INVERSE 110 449#define BN_F_BN_MOD_MUL_RECIPROCAL 111 450#define BN_F_BN_MPI2BN 112 451#define BN_F_BN_NEW 113 452#define BN_F_BN_RAND 114 453#define BN_F_BN_USUB 115 454 455/* Reason codes. */ 456#define BN_R_ARG2_LT_ARG3 100 457#define BN_R_BAD_RECIPROCAL 101 458#define BN_R_CALLED_WITH_EVEN_MODULUS 102 459#define BN_R_DIV_BY_ZERO 103 460#define BN_R_ENCODING_ERROR 104 461#define BN_R_EXPAND_ON_STATIC_BIGNUM_DATA 105 462#define BN_R_INVALID_LENGTH 106 463#define BN_R_NOT_INITIALIZED 107 464#define BN_R_NO_INVERSE 108 465#define BN_R_TOO_MANY_TEMPORARY_VARIABLES 109 466 467#ifdef __cplusplus 468} 469#endif 470#endif 471 472