1 /* Copyright (C) 1995-1997 Eric Young (eay (at) cryptsoft.com) 2 * All rights reserved. 3 * 4 * This package is an SSL implementation written 5 * by Eric Young (eay (at) cryptsoft.com). 6 * The implementation was written so as to conform with Netscapes SSL. 7 * 8 * This library is free for commercial and non-commercial use as long as 9 * the following conditions are aheared to. The following conditions 10 * apply to all code found in this distribution, be it the RC4, RSA, 11 * lhash, DES, etc., code; not just the SSL code. The SSL documentation 12 * included with this distribution is covered by the same copyright terms 13 * except that the holder is Tim Hudson (tjh (at) cryptsoft.com). 14 * 15 * Copyright remains Eric Young's, and as such any Copyright notices in 16 * the code are not to be removed. 17 * If this package is used in a product, Eric Young should be given attribution 18 * as the author of the parts of the library used. 19 * This can be in the form of a textual message at program startup or 20 * in documentation (online or textual) provided with the package. 21 * 22 * Redistribution and use in source and binary forms, with or without 23 * modification, are permitted provided that the following conditions 24 * are met: 25 * 1. Redistributions of source code must retain the copyright 26 * notice, this list of conditions and the following disclaimer. 27 * 2. Redistributions in binary form must reproduce the above copyright 28 * notice, this list of conditions and the following disclaimer in the 29 * documentation and/or other materials provided with the distribution. 30 * 3. All advertising materials mentioning features or use of this software 31 * must display the following acknowledgement: 32 * "This product includes cryptographic software written by 33 * Eric Young (eay (at) cryptsoft.com)" 34 * The word 'cryptographic' can be left out if the rouines from the library 35 * being used are not cryptographic related :-). 36 * 4. If you include any Windows specific code (or a derivative thereof) from 37 * the apps directory (application code) you must include an acknowledgement: 38 * "This product includes software written by Tim Hudson (tjh (at) cryptsoft.com)" 39 * 40 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND 41 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 42 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 43 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE 44 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 45 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 46 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 47 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 48 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 49 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 50 * SUCH DAMAGE. 51 * 52 * The licence and distribution terms for any publically available version or 53 * derivative of this code cannot be changed. i.e. this code cannot simply be 54 * copied and put under another distribution licence 55 * [including the GNU Public Licence.] 56 */ 57 /* ==================================================================== 58 * Copyright (c) 1998-2006 The OpenSSL Project. All rights reserved. 59 * 60 * Redistribution and use in source and binary forms, with or without 61 * modification, are permitted provided that the following conditions 62 * are met: 63 * 64 * 1. Redistributions of source code must retain the above copyright 65 * notice, this list of conditions and the following disclaimer. 66 * 67 * 2. Redistributions in binary form must reproduce the above copyright 68 * notice, this list of conditions and the following disclaimer in 69 * the documentation and/or other materials provided with the 70 * distribution. 71 * 72 * 3. All advertising materials mentioning features or use of this 73 * software must display the following acknowledgment: 74 * "This product includes software developed by the OpenSSL Project 75 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" 76 * 77 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to 78 * endorse or promote products derived from this software without 79 * prior written permission. For written permission, please contact 80 * openssl-core (at) openssl.org. 81 * 82 * 5. Products derived from this software may not be called "OpenSSL" 83 * nor may "OpenSSL" appear in their names without prior written 84 * permission of the OpenSSL Project. 85 * 86 * 6. Redistributions of any form whatsoever must retain the following 87 * acknowledgment: 88 * "This product includes software developed by the OpenSSL Project 89 * for use in the OpenSSL Toolkit (http://www.openssl.org/)" 90 * 91 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY 92 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 93 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 94 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR 95 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, 96 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT 97 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; 98 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 99 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, 100 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 101 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED 102 * OF THE POSSIBILITY OF SUCH DAMAGE. 103 * ==================================================================== 104 * 105 * This product includes cryptographic software written by Eric Young 106 * (eay (at) cryptsoft.com). This product includes software written by Tim 107 * Hudson (tjh (at) cryptsoft.com). 108 * 109 */ 110 /* ==================================================================== 111 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. 112 * 113 * Portions of the attached software ("Contribution") are developed by 114 * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project. 115 * 116 * The Contribution is licensed pursuant to the Eric Young open source 117 * license provided above. 118 * 119 * The binary polynomial arithmetic software is originally written by 120 * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems 121 * Laboratories. */ 122 123 #ifndef OPENSSL_HEADER_BN_H 124 #define OPENSSL_HEADER_BN_H 125 126 #include <openssl/base.h> 127 #include <openssl/thread.h> 128 129 #include <inttypes.h> /* for PRIu64 and friends */ 130 #include <stdio.h> /* for FILE* */ 131 132 #if defined(__cplusplus) 133 extern "C" { 134 #endif 135 136 137 /* BN provides support for working with arbitary sized integers. For example, 138 * although the largest integer supported by the compiler might be 64 bits, BN 139 * will allow you to work with numbers until you run out of memory. */ 140 141 142 /* BN_ULONG is the native word size when working with big integers. 143 * 144 * Note: on some platforms, inttypes.h does not define print format macros in 145 * C++ unless |__STDC_FORMAT_MACROS| defined. As this is a public header, bn.h 146 * does not define |__STDC_FORMAT_MACROS| itself. C++ source files which use the 147 * FMT macros must define it externally. */ 148 #if defined(OPENSSL_64_BIT) 149 #define BN_ULONG uint64_t 150 #define BN_BITS2 64 151 #define BN_DEC_FMT1 "%" PRIu64 152 #define BN_DEC_FMT2 "%019" PRIu64 153 #define BN_HEX_FMT1 "%" PRIx64 154 #elif defined(OPENSSL_32_BIT) 155 #define BN_ULONG uint32_t 156 #define BN_BITS2 32 157 #define BN_DEC_FMT1 "%" PRIu32 158 #define BN_DEC_FMT2 "%09" PRIu32 159 #define BN_HEX_FMT1 "%" PRIx32 160 #else 161 #error "Must define either OPENSSL_32_BIT or OPENSSL_64_BIT" 162 #endif 163 164 165 /* Allocation and freeing. */ 166 167 /* BN_new creates a new, allocated BIGNUM and initialises it. */ 168 OPENSSL_EXPORT BIGNUM *BN_new(void); 169 170 /* BN_init initialises a stack allocated |BIGNUM|. */ 171 OPENSSL_EXPORT void BN_init(BIGNUM *bn); 172 173 /* BN_free frees the data referenced by |bn| and, if |bn| was originally 174 * allocated on the heap, frees |bn| also. */ 175 OPENSSL_EXPORT void BN_free(BIGNUM *bn); 176 177 /* BN_clear_free erases and frees the data referenced by |bn| and, if |bn| was 178 * originally allocated on the heap, frees |bn| also. */ 179 OPENSSL_EXPORT void BN_clear_free(BIGNUM *bn); 180 181 /* BN_dup allocates a new BIGNUM and sets it equal to |src|. It returns the 182 * allocated BIGNUM on success or NULL otherwise. */ 183 OPENSSL_EXPORT BIGNUM *BN_dup(const BIGNUM *src); 184 185 /* BN_copy sets |dest| equal to |src| and returns |dest|. */ 186 OPENSSL_EXPORT BIGNUM *BN_copy(BIGNUM *dest, const BIGNUM *src); 187 188 /* BN_clear sets |bn| to zero and erases the old data. */ 189 OPENSSL_EXPORT void BN_clear(BIGNUM *bn); 190 191 /* BN_value_one returns a static BIGNUM with value 1. */ 192 OPENSSL_EXPORT const BIGNUM *BN_value_one(void); 193 194 /* BN_with_flags initialises a stack allocated |BIGNUM| with pointers to the 195 * contents of |in| but with |flags| ORed into the flags field. 196 * 197 * Note: the two BIGNUMs share state and so |out| should /not/ be passed to 198 * |BN_free|. */ 199 OPENSSL_EXPORT void BN_with_flags(BIGNUM *out, const BIGNUM *in, int flags); 200 201 202 /* Basic functions. */ 203 204 /* BN_num_bits returns the minimum number of bits needed to represent the 205 * absolute value of |bn|. */ 206 OPENSSL_EXPORT unsigned BN_num_bits(const BIGNUM *bn); 207 208 /* BN_num_bytes returns the minimum number of bytes needed to represent the 209 * absolute value of |bn|. */ 210 OPENSSL_EXPORT unsigned BN_num_bytes(const BIGNUM *bn); 211 212 /* BN_zero sets |bn| to zero. */ 213 OPENSSL_EXPORT void BN_zero(BIGNUM *bn); 214 215 /* BN_one sets |bn| to one. It returns one on success or zero on allocation 216 * failure. */ 217 OPENSSL_EXPORT int BN_one(BIGNUM *bn); 218 219 /* BN_set_word sets |bn| to |value|. It returns one on success or zero on 220 * allocation failure. */ 221 OPENSSL_EXPORT int BN_set_word(BIGNUM *bn, BN_ULONG value); 222 223 /* BN_set_negative sets the sign of |bn|. */ 224 OPENSSL_EXPORT void BN_set_negative(BIGNUM *bn, int sign); 225 226 /* BN_is_negative returns one if |bn| is negative and zero otherwise. */ 227 OPENSSL_EXPORT int BN_is_negative(const BIGNUM *bn); 228 229 /* BN_get_flags returns |bn->flags| & |flags|. */ 230 OPENSSL_EXPORT int BN_get_flags(const BIGNUM *bn, int flags); 231 232 /* BN_set_flags sets |flags| on |bn|. */ 233 OPENSSL_EXPORT void BN_set_flags(BIGNUM *bn, int flags); 234 235 236 /* Conversion functions. */ 237 238 /* BN_bin2bn sets |*ret| to the value of |len| bytes from |in|, interpreted as 239 * a big-endian number, and returns |ret|. If |ret| is NULL then a fresh 240 * |BIGNUM| is allocated and returned. It returns NULL on allocation 241 * failure. */ 242 OPENSSL_EXPORT BIGNUM *BN_bin2bn(const uint8_t *in, size_t len, BIGNUM *ret); 243 244 /* BN_bn2bin serialises the absolute value of |in| to |out| as a big-endian 245 * integer, which must have |BN_num_bytes| of space available. It returns the 246 * number of bytes written. */ 247 OPENSSL_EXPORT size_t BN_bn2bin(const BIGNUM *in, uint8_t *out); 248 249 /* BN_bn2bin_padded serialises the absolute value of |in| to |out| as a 250 * big-endian integer. The integer is padded with leading zeros up to size 251 * |len|. If |len| is smaller than |BN_num_bytes|, the function fails and 252 * returns 0. Otherwise, it returns 1. */ 253 OPENSSL_EXPORT int BN_bn2bin_padded(uint8_t *out, size_t len, const BIGNUM *in); 254 255 /* BN_bn2hex returns an allocated string that contains a NUL-terminated, hex 256 * representation of |bn|. If |bn| is negative, the first char in the resulting 257 * string will be '-'. Returns NULL on allocation failure. */ 258 OPENSSL_EXPORT char *BN_bn2hex(const BIGNUM *bn); 259 260 /* BN_hex2bn parses the leading hex number from |in|, which may be proceeded by 261 * a '-' to indicate a negative number and may contain trailing, non-hex data. 262 * If |outp| is not NULL, it constructs a BIGNUM equal to the hex number and 263 * stores it in |*outp|. If |*outp| is NULL then it allocates a new BIGNUM and 264 * updates |*outp|. It returns the number of bytes of |in| processed or zero on 265 * error. */ 266 OPENSSL_EXPORT int BN_hex2bn(BIGNUM **outp, const char *in); 267 268 /* BN_bn2dec returns an allocated string that contains a NUL-terminated, 269 * decimal representation of |bn|. If |bn| is negative, the first char in the 270 * resulting string will be '-'. Returns NULL on allocation failure. */ 271 OPENSSL_EXPORT char *BN_bn2dec(const BIGNUM *a); 272 273 /* BN_dec2bn parses the leading decimal number from |in|, which may be 274 * proceeded by a '-' to indicate a negative number and may contain trailing, 275 * non-decimal data. If |outp| is not NULL, it constructs a BIGNUM equal to the 276 * decimal number and stores it in |*outp|. If |*outp| is NULL then it 277 * allocates a new BIGNUM and updates |*outp|. It returns the number of bytes 278 * of |in| processed or zero on error. */ 279 OPENSSL_EXPORT int BN_dec2bn(BIGNUM **outp, const char *in); 280 281 /* BN_asc2bn acts like |BN_dec2bn| or |BN_hex2bn| depending on whether |in| 282 * begins with "0X" or "0x" (indicating hex) or not (indicating decimal). A 283 * leading '-' is still permitted and comes before the optional 0X/0x. It 284 * returns one on success or zero on error. */ 285 OPENSSL_EXPORT int BN_asc2bn(BIGNUM **outp, const char *in); 286 287 /* BN_print writes a hex encoding of |a| to |bio|. It returns one on success 288 * and zero on error. */ 289 OPENSSL_EXPORT int BN_print(BIO *bio, const BIGNUM *a); 290 291 /* BN_print_fp acts like |BIO_print|, but wraps |fp| in a |BIO| first. */ 292 OPENSSL_EXPORT int BN_print_fp(FILE *fp, const BIGNUM *a); 293 294 /* BN_get_word returns the absolute value of |bn| as a single word. If |bn| is 295 * too large to be represented as a single word, the maximum possible value 296 * will be returned. */ 297 OPENSSL_EXPORT BN_ULONG BN_get_word(const BIGNUM *bn); 298 299 300 /* Internal functions. 301 * 302 * These functions are useful for code that is doing low-level manipulations of 303 * BIGNUM values. However, be sure that no other function in this file does 304 * what you want before turning to these. */ 305 306 /* bn_correct_top decrements |bn->top| until |bn->d[top-1]| is non-zero or 307 * until |top| is zero. */ 308 OPENSSL_EXPORT void bn_correct_top(BIGNUM *bn); 309 310 /* bn_wexpand ensures that |bn| has at least |words| works of space without 311 * altering its value. It returns one on success or zero on allocation 312 * failure. */ 313 OPENSSL_EXPORT BIGNUM *bn_wexpand(BIGNUM *bn, unsigned words); 314 315 316 /* BIGNUM pools. 317 * 318 * Certain BIGNUM operations need to use many temporary variables and 319 * allocating and freeing them can be quite slow. Thus such opertions typically 320 * take a |BN_CTX| parameter, which contains a pool of |BIGNUMs|. The |ctx| 321 * argument to a public function may be NULL, in which case a local |BN_CTX| 322 * will be created just for the lifetime of that call. 323 * 324 * A function must call |BN_CTX_start| first. Then, |BN_CTX_get| may be called 325 * repeatedly to obtain temporary |BIGNUM|s. All |BN_CTX_get| calls must be made 326 * before calling any other functions that use the |ctx| as an argument. 327 * 328 * Finally, |BN_CTX_end| must be called before returning from the function. 329 * When |BN_CTX_end| is called, the |BIGNUM| pointers obtained from 330 * |BN_CTX_get| become invalid. */ 331 332 /* BN_CTX_new returns a new, empty BN_CTX or NULL on allocation failure. */ 333 OPENSSL_EXPORT BN_CTX *BN_CTX_new(void); 334 335 /* BN_CTX_free frees all BIGNUMs contained in |ctx| and then frees |ctx| 336 * itself. */ 337 OPENSSL_EXPORT void BN_CTX_free(BN_CTX *ctx); 338 339 /* BN_CTX_start "pushes" a new entry onto the |ctx| stack and allows future 340 * calls to |BN_CTX_get|. */ 341 OPENSSL_EXPORT void BN_CTX_start(BN_CTX *ctx); 342 343 /* BN_CTX_get returns a new |BIGNUM|, or NULL on allocation failure. Once 344 * |BN_CTX_get| has returned NULL, all future calls will also return NULL until 345 * |BN_CTX_end| is called. */ 346 OPENSSL_EXPORT BIGNUM *BN_CTX_get(BN_CTX *ctx); 347 348 /* BN_CTX_end invalidates all |BIGNUM|s returned from |BN_CTX_get| since the 349 * matching |BN_CTX_start| call. */ 350 OPENSSL_EXPORT void BN_CTX_end(BN_CTX *ctx); 351 352 353 /* Simple arithmetic */ 354 355 /* BN_add sets |r| = |a| + |b|, where |r| may be the same pointer as either |a| 356 * or |b|. It returns one on success and zero on allocation failure. */ 357 OPENSSL_EXPORT int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); 358 359 /* BN_uadd sets |r| = |a| + |b|, where |a| and |b| are non-negative and |r| may 360 * be the same pointer as either |a| or |b|. It returns one on success and zero 361 * on allocation failure. */ 362 OPENSSL_EXPORT int BN_uadd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); 363 364 /* BN_add_word adds |w| to |a|. It returns one on success and zero otherwise. */ 365 OPENSSL_EXPORT int BN_add_word(BIGNUM *a, BN_ULONG w); 366 367 /* BN_sub sets |r| = |a| - |b|, where |r| must be a distinct pointer from |a| 368 * and |b|. It returns one on success and zero on allocation failure. */ 369 OPENSSL_EXPORT int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); 370 371 /* BN_usub sets |r| = |a| - |b|, where |a| and |b| are non-negative integers, 372 * |b| < |a| and |r| must be a distinct pointer from |a| and |b|. It returns 373 * one on success and zero on allocation failure. */ 374 OPENSSL_EXPORT int BN_usub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); 375 376 /* BN_sub_word subtracts |w| from |a|. It returns one on success and zero on 377 * allocation failure. */ 378 OPENSSL_EXPORT int BN_sub_word(BIGNUM *a, BN_ULONG w); 379 380 /* BN_mul sets |r| = |a| * |b|, where |r| may be the same pointer as |a| or 381 * |b|. Returns one on success and zero otherwise. */ 382 OPENSSL_EXPORT int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, 383 BN_CTX *ctx); 384 385 /* BN_mul_word sets |bn| = |bn| * |w|. It returns one on success or zero on 386 * allocation failure. */ 387 OPENSSL_EXPORT int BN_mul_word(BIGNUM *bn, BN_ULONG w); 388 389 /* BN_sqr sets |r| = |a|^2 (i.e. squares), where |r| may be the same pointer as 390 * |a|. Returns one on success and zero otherwise. This is more efficient than 391 * BN_mul(r, a, a, ctx). */ 392 OPENSSL_EXPORT int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx); 393 394 /* BN_div divides |numerator| by |divisor| and places the result in |quotient| 395 * and the remainder in |rem|. Either of |quotient| or |rem| may be NULL, in 396 * which case the respective value is not returned. The result is rounded 397 * towards zero; thus if |numerator| is negative, the remainder will be zero or 398 * negative. It returns one on success or zero on error. */ 399 OPENSSL_EXPORT int BN_div(BIGNUM *quotient, BIGNUM *rem, 400 const BIGNUM *numerator, const BIGNUM *divisor, 401 BN_CTX *ctx); 402 403 /* BN_div_word sets |numerator| = |numerator|/|divisor| and returns the 404 * remainder or (BN_ULONG)-1 on error. */ 405 OPENSSL_EXPORT BN_ULONG BN_div_word(BIGNUM *numerator, BN_ULONG divisor); 406 407 /* BN_sqrt sets |*out_sqrt| (which may be the same |BIGNUM| as |in|) to the 408 * square root of |in|, using |ctx|. It returns one on success or zero on 409 * error. Negative numbers and non-square numbers will result in an error with 410 * appropriate errors on the error queue. */ 411 OPENSSL_EXPORT int BN_sqrt(BIGNUM *out_sqrt, const BIGNUM *in, BN_CTX *ctx); 412 413 414 /* Comparison functions */ 415 416 /* BN_cmp returns a value less than, equal to or greater than zero if |a| is 417 * less than, equal to or greater than |b|, respectively. */ 418 OPENSSL_EXPORT int BN_cmp(const BIGNUM *a, const BIGNUM *b); 419 420 /* BN_ucmp returns a value less than, equal to or greater than zero if the 421 * absolute value of |a| is less than, equal to or greater than the absolute 422 * value of |b|, respectively. */ 423 OPENSSL_EXPORT int BN_ucmp(const BIGNUM *a, const BIGNUM *b); 424 425 /* BN_abs_is_word returns one if the absolute value of |bn| equals |w| and zero 426 * otherwise. */ 427 OPENSSL_EXPORT int BN_abs_is_word(const BIGNUM *bn, BN_ULONG w); 428 429 /* BN_is_zero returns one if |bn| is zero and zero otherwise. */ 430 OPENSSL_EXPORT int BN_is_zero(const BIGNUM *bn); 431 432 /* BN_is_one returns one if |bn| equals one and zero otherwise. */ 433 OPENSSL_EXPORT int BN_is_one(const BIGNUM *bn); 434 435 /* BN_is_word returns one if |bn| is exactly |w| and zero otherwise. */ 436 OPENSSL_EXPORT int BN_is_word(const BIGNUM *bn, BN_ULONG w); 437 438 /* BN_is_odd returns one if |bn| is odd and zero otherwise. */ 439 OPENSSL_EXPORT int BN_is_odd(const BIGNUM *bn); 440 441 442 /* Bitwise operations. */ 443 444 /* BN_lshift sets |r| equal to |a| << n. The |a| and |r| arguments may be the 445 * same |BIGNUM|. It returns one on success and zero on allocation failure. */ 446 OPENSSL_EXPORT int BN_lshift(BIGNUM *r, const BIGNUM *a, int n); 447 448 /* BN_lshift1 sets |r| equal to |a| << 1, where |r| and |a| may be the same 449 * pointer. It returns one on success and zero on allocation failure. */ 450 OPENSSL_EXPORT int BN_lshift1(BIGNUM *r, const BIGNUM *a); 451 452 /* BN_rshift sets |r| equal to |a| >> n, where |r| and |a| may be the same 453 * pointer. It returns one on success and zero on allocation failure. */ 454 OPENSSL_EXPORT int BN_rshift(BIGNUM *r, const BIGNUM *a, int n); 455 456 /* BN_rshift1 sets |r| equal to |a| >> 1, where |r| and |a| may be the same 457 * pointer. It returns one on success and zero on allocation failure. */ 458 OPENSSL_EXPORT int BN_rshift1(BIGNUM *r, const BIGNUM *a); 459 460 /* BN_set_bit sets the |n|th, least-significant bit in |a|. For example, if |a| 461 * is 2 then setting bit zero will make it 3. It returns one on success or zero 462 * on allocation failure. */ 463 OPENSSL_EXPORT int BN_set_bit(BIGNUM *a, int n); 464 465 /* BN_clear_bit clears the |n|th, least-significant bit in |a|. For example, if 466 * |a| is 3, clearing bit zero will make it two. It returns one on success or 467 * zero on allocation failure. */ 468 OPENSSL_EXPORT int BN_clear_bit(BIGNUM *a, int n); 469 470 /* BN_is_bit_set returns the value of the |n|th, least-significant bit in |a|, 471 * or zero if the bit doesn't exist. */ 472 OPENSSL_EXPORT int BN_is_bit_set(const BIGNUM *a, int n); 473 474 /* BN_mask_bits truncates |a| so that it is only |n| bits long. It returns one 475 * on success or zero if |n| is greater than the length of |a| already. */ 476 OPENSSL_EXPORT int BN_mask_bits(BIGNUM *a, int n); 477 478 479 /* Modulo arithmetic. */ 480 481 /* BN_mod_word returns |a| mod |w|. */ 482 OPENSSL_EXPORT BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w); 483 484 /* BN_mod is a helper macro that calls |BN_div| and discards the quotient. */ 485 #define BN_mod(rem, numerator, divisor, ctx) \ 486 BN_div(NULL, (rem), (numerator), (divisor), (ctx)) 487 488 /* BN_nnmod is a non-negative modulo function. It acts like |BN_mod|, but 0 <= 489 * |rem| < |divisor| is always true. It returns one on success and zero on 490 * error. */ 491 OPENSSL_EXPORT int BN_nnmod(BIGNUM *rem, const BIGNUM *numerator, 492 const BIGNUM *divisor, BN_CTX *ctx); 493 494 /* BN_mod_add sets |r| = |a| + |b| mod |m|. It returns one on success and zero 495 * on error. */ 496 OPENSSL_EXPORT int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, 497 const BIGNUM *m, BN_CTX *ctx); 498 499 /* BN_mod_add_quick acts like |BN_mod_add| but requires that |a| and |b| be 500 * non-negative and less than |m|. */ 501 OPENSSL_EXPORT int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, 502 const BIGNUM *m); 503 504 /* BN_mod_sub sets |r| = |a| - |b| mod |m|. It returns one on success and zero 505 * on error. */ 506 OPENSSL_EXPORT int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, 507 const BIGNUM *m, BN_CTX *ctx); 508 509 /* BN_mod_sub_quick acts like |BN_mod_sub| but requires that |a| and |b| be 510 * non-negative and less than |m|. */ 511 OPENSSL_EXPORT int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, 512 const BIGNUM *m); 513 514 /* BN_mod_mul sets |r| = |a|*|b| mod |m|. It returns one on success and zero 515 * on error. */ 516 OPENSSL_EXPORT int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, 517 const BIGNUM *m, BN_CTX *ctx); 518 519 /* BN_mod_mul sets |r| = |a|^2 mod |m|. It returns one on success and zero 520 * on error. */ 521 OPENSSL_EXPORT int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, 522 BN_CTX *ctx); 523 524 /* BN_mod_lshift sets |r| = (|a| << n) mod |m|, where |r| and |a| may be the 525 * same pointer. It returns one on success and zero on error. */ 526 OPENSSL_EXPORT int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, 527 const BIGNUM *m, BN_CTX *ctx); 528 529 /* BN_mod_lshift_quick acts like |BN_mod_lshift| but requires that |a| be 530 * non-negative and less than |m|. */ 531 OPENSSL_EXPORT int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, 532 const BIGNUM *m); 533 534 /* BN_mod_lshift1 sets |r| = (|a| << 1) mod |m|, where |r| and |a| may be the 535 * same pointer. It returns one on success and zero on error. */ 536 OPENSSL_EXPORT int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, 537 BN_CTX *ctx); 538 539 /* BN_mod_lshift1_quick acts like |BN_mod_lshift1| but requires that |a| be 540 * non-negative and less than |m|. */ 541 OPENSSL_EXPORT int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, 542 const BIGNUM *m); 543 544 /* BN_mod_sqrt returns a |BIGNUM|, r, such that r^2 == a (mod p). */ 545 OPENSSL_EXPORT BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p, 546 BN_CTX *ctx); 547 548 549 /* Random and prime number generation. */ 550 551 /* BN_rand sets |rnd| to a random number of length |bits|. If |top| is zero, the 552 * most-significant bit, if any, will be set. If |top| is one, the two most 553 * significant bits, if any, will be set. 554 * 555 * If |top| is -1 then no extra action will be taken and |BN_num_bits(rnd)| may 556 * not equal |bits| if the most significant bits randomly ended up as zeros. 557 * 558 * If |bottom| is non-zero, the least-significant bit, if any, will be set. The 559 * function returns one on success or zero otherwise. */ 560 OPENSSL_EXPORT int BN_rand(BIGNUM *rnd, int bits, int top, int bottom); 561 562 /* BN_pseudo_rand is an alias for |BN_rand|. */ 563 OPENSSL_EXPORT int BN_pseudo_rand(BIGNUM *rnd, int bits, int top, int bottom); 564 565 /* BN_rand_range sets |rnd| to a random value [0..range). It returns one on 566 * success and zero otherwise. */ 567 OPENSSL_EXPORT int BN_rand_range(BIGNUM *rnd, const BIGNUM *range); 568 569 /* BN_pseudo_rand_range is an alias for BN_rand_range. */ 570 OPENSSL_EXPORT int BN_pseudo_rand_range(BIGNUM *rnd, const BIGNUM *range); 571 572 /* BN_generate_dsa_nonce generates a random number 0 <= out < range. Unlike 573 * BN_rand_range, it also includes the contents of |priv| and |message| in the 574 * generation so that an RNG failure isn't fatal as long as |priv| remains 575 * secret. This is intended for use in DSA and ECDSA where an RNG weakness 576 * leads directly to private key exposure unless this function is used. 577 * It returns one on success and zero on error. */ 578 OPENSSL_EXPORT int BN_generate_dsa_nonce(BIGNUM *out, const BIGNUM *range, 579 const BIGNUM *priv, 580 const uint8_t *message, 581 size_t message_len, BN_CTX *ctx); 582 583 /* BN_GENCB holds a callback function that is used by generation functions that 584 * can take a very long time to complete. Use |BN_GENCB_set| to initialise a 585 * |BN_GENCB| structure. 586 * 587 * The callback receives the address of that |BN_GENCB| structure as its last 588 * argument and the user is free to put an arbitary pointer in |arg|. The other 589 * arguments are set as follows: 590 * event=BN_GENCB_GENERATED, n=i: after generating the i'th possible prime 591 * number. 592 * event=BN_GENCB_PRIME_TEST, n=-1: when finished trial division primality 593 * checks. 594 * event=BN_GENCB_PRIME_TEST, n=i: when the i'th primality test has finished. 595 * 596 * The callback can return zero to abort the generation progress or one to 597 * allow it to continue. 598 * 599 * When other code needs to call a BN generation function it will often take a 600 * BN_GENCB argument and may call the function with other argument values. */ 601 #define BN_GENCB_GENERATED 0 602 #define BN_GENCB_PRIME_TEST 1 603 604 struct bn_gencb_st { 605 void *arg; /* callback-specific data */ 606 int (*callback)(int event, int n, struct bn_gencb_st *); 607 }; 608 609 /* BN_GENCB_set configures |callback| to call |f| and sets |callout->arg| to 610 * |arg|. */ 611 OPENSSL_EXPORT void BN_GENCB_set(BN_GENCB *callback, 612 int (*f)(int event, int n, 613 struct bn_gencb_st *), 614 void *arg); 615 616 /* BN_GENCB_call calls |callback|, if not NULL, and returns the return value of 617 * the callback, or 1 if |callback| is NULL. */ 618 OPENSSL_EXPORT int BN_GENCB_call(BN_GENCB *callback, int event, int n); 619 620 /* BN_generate_prime_ex sets |ret| to a prime number of |bits| length. If safe 621 * is non-zero then the prime will be such that (ret-1)/2 is also a prime. 622 * (This is needed for Diffie-Hellman groups to ensure that the only subgroups 623 * are of size 2 and (p-1)/2.). 624 * 625 * If |add| is not NULL, the prime will fulfill the condition |ret| % |add| == 626 * |rem| in order to suit a given generator. (If |rem| is NULL then |ret| % 627 * |add| == 1.) 628 * 629 * If |cb| is not NULL, it will be called during processing to give an 630 * indication of progress. See the comments for |BN_GENCB|. It returns one on 631 * success and zero otherwise. */ 632 OPENSSL_EXPORT int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, 633 const BIGNUM *add, const BIGNUM *rem, 634 BN_GENCB *cb); 635 636 /* BN_prime_checks is magic value that can be used as the |checks| argument to 637 * the primality testing functions in order to automatically select a number of 638 * Miller-Rabin checks that gives a false positive rate of ~2^{-80}. */ 639 #define BN_prime_checks 0 640 641 /* BN_primality_test sets |*is_probably_prime| to one if |candidate| is 642 * probably a prime number by the Miller-Rabin test or zero if it's certainly 643 * not. 644 * 645 * If |do_trial_division| is non-zero then |candidate| will be tested against a 646 * list of small primes before Miller-Rabin tests. The probability of this 647 * function returning a false positive is 2^{2*checks}. If |checks| is 648 * |BN_prime_checks| then a value that results in approximately 2^{-80} false 649 * positive probability is used. If |cb| is not NULL then it is called during 650 * the checking process. See the comment above |BN_GENCB|. 651 * 652 * The function returns one on success and zero on error. 653 * 654 * (If you are unsure whether you want |do_trial_division|, don't set it.) */ 655 OPENSSL_EXPORT int BN_primality_test(int *is_probably_prime, 656 const BIGNUM *candidate, int checks, 657 BN_CTX *ctx, int do_trial_division, 658 BN_GENCB *cb); 659 660 /* BN_is_prime_fasttest_ex returns one if |candidate| is probably a prime 661 * number by the Miller-Rabin test, zero if it's certainly not and -1 on error. 662 * 663 * If |do_trial_division| is non-zero then |candidate| will be tested against a 664 * list of small primes before Miller-Rabin tests. The probability of this 665 * function returning one when |candidate| is composite is 2^{2*checks}. If 666 * |checks| is |BN_prime_checks| then a value that results in approximately 667 * 2^{-80} false positive probability is used. If |cb| is not NULL then it is 668 * called during the checking process. See the comment above |BN_GENCB|. 669 * 670 * WARNING: deprecated. Use |BN_primality_test|. */ 671 OPENSSL_EXPORT int BN_is_prime_fasttest_ex(const BIGNUM *candidate, int checks, 672 BN_CTX *ctx, int do_trial_division, 673 BN_GENCB *cb); 674 675 /* BN_is_prime_ex acts the same as |BN_is_prime_fasttest_ex| with 676 * |do_trial_division| set to zero. 677 * 678 * WARNING: deprecated: Use |BN_primality_test|. */ 679 OPENSSL_EXPORT int BN_is_prime_ex(const BIGNUM *candidate, int checks, 680 BN_CTX *ctx, BN_GENCB *cb); 681 682 683 /* Number theory functions */ 684 685 /* BN_gcd sets |r| = gcd(|a|, |b|). It returns one on success and zero 686 * otherwise. */ 687 OPENSSL_EXPORT int BN_gcd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, 688 BN_CTX *ctx); 689 690 /* BN_mod_inverse sets |out| equal to |a|^-1, mod |n|. If either of |a| or |n| 691 * have |BN_FLG_CONSTTIME| set then the operation is performed in constant 692 * time. If |out| is NULL, a fresh BIGNUM is allocated. It returns the result 693 * or NULL on error. */ 694 OPENSSL_EXPORT BIGNUM *BN_mod_inverse(BIGNUM *out, const BIGNUM *a, 695 const BIGNUM *n, BN_CTX *ctx); 696 697 /* BN_kronecker returns the Kronecker symbol of |a| and |b| (which is -1, 0 or 698 * 1), or -2 on error. */ 699 OPENSSL_EXPORT int BN_kronecker(const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); 700 701 702 /* Montgomery arithmetic. */ 703 704 /* BN_MONT_CTX contains the precomputed values needed to work in a specific 705 * Montgomery domain. */ 706 707 /* BN_MONT_CTX_new returns a fresh BN_MONT_CTX or NULL on allocation failure. */ 708 OPENSSL_EXPORT BN_MONT_CTX *BN_MONT_CTX_new(void); 709 710 /* BN_MONT_CTX_init initialises a stack allocated |BN_MONT_CTX|. */ 711 OPENSSL_EXPORT void BN_MONT_CTX_init(BN_MONT_CTX *mont); 712 713 /* BN_MONT_CTX_free frees the contexts of |mont| and, if it was originally 714 * allocated with |BN_MONT_CTX_new|, |mont| itself. */ 715 OPENSSL_EXPORT void BN_MONT_CTX_free(BN_MONT_CTX *mont); 716 717 /* BN_MONT_CTX_copy sets |to| equal to |from|. It returns |to| on success or 718 * NULL on error. */ 719 OPENSSL_EXPORT BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, 720 BN_MONT_CTX *from); 721 722 /* BN_MONT_CTX_set sets up a Montgomery context given the modulus, |mod|. It 723 * returns one on success and zero on error. */ 724 OPENSSL_EXPORT int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, 725 BN_CTX *ctx); 726 727 /* BN_MONT_CTX_set_locked takes |lock| and checks whether |*pmont| is NULL. If 728 * so, it creates a new |BN_MONT_CTX| and sets the modulus for it to |mod|. It 729 * then stores it as |*pmont| and returns it, or NULL on error. 730 * 731 * If |*pmont| is already non-NULL then the existing value is returned. */ 732 BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, CRYPTO_MUTEX *lock, 733 const BIGNUM *mod, BN_CTX *bn_ctx); 734 735 /* BN_to_montgomery sets |ret| equal to |a| in the Montgomery domain. It 736 * returns one on success and zero on error. */ 737 OPENSSL_EXPORT int BN_to_montgomery(BIGNUM *ret, const BIGNUM *a, 738 const BN_MONT_CTX *mont, BN_CTX *ctx); 739 740 /* BN_from_montgomery sets |ret| equal to |a| * R^-1, i.e. translates values 741 * out of the Montgomery domain. It returns one on success or zero on error. */ 742 OPENSSL_EXPORT int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, 743 const BN_MONT_CTX *mont, BN_CTX *ctx); 744 745 /* BN_mod_mul_montgomery set |r| equal to |a| * |b|, in the Montgomery domain. 746 * Both |a| and |b| must already be in the Montgomery domain (by 747 * |BN_to_montgomery|). It returns one on success or zero on error. */ 748 OPENSSL_EXPORT int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, 749 const BIGNUM *b, 750 const BN_MONT_CTX *mont, BN_CTX *ctx); 751 752 753 /* Exponentiation. */ 754 755 /* BN_exp sets |r| equal to |a|^{|p|}. It does so with a square-and-multiply 756 * algorithm that leaks side-channel information. It returns one on success or 757 * zero otherwise. */ 758 OPENSSL_EXPORT int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, 759 BN_CTX *ctx); 760 761 /* BN_mod_exp sets |r| equal to |a|^{|p|} mod |m|. It does so with the best 762 * algorithm for the values provided and can run in constant time if 763 * |BN_FLG_CONSTTIME| is set for |p|. It returns one on success or zero 764 * otherwise. */ 765 OPENSSL_EXPORT int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, 766 const BIGNUM *m, BN_CTX *ctx); 767 768 OPENSSL_EXPORT int BN_mod_exp_mont(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, 769 const BIGNUM *m, BN_CTX *ctx, 770 BN_MONT_CTX *m_ctx); 771 772 OPENSSL_EXPORT int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, 773 const BIGNUM *p, const BIGNUM *m, 774 BN_CTX *ctx, BN_MONT_CTX *in_mont); 775 776 OPENSSL_EXPORT int BN_mod_exp_mont_word(BIGNUM *r, BN_ULONG a, const BIGNUM *p, 777 const BIGNUM *m, BN_CTX *ctx, 778 BN_MONT_CTX *m_ctx); 779 OPENSSL_EXPORT int BN_mod_exp2_mont(BIGNUM *r, const BIGNUM *a1, 780 const BIGNUM *p1, const BIGNUM *a2, 781 const BIGNUM *p2, const BIGNUM *m, 782 BN_CTX *ctx, BN_MONT_CTX *m_ctx); 783 784 785 /* Private functions */ 786 787 struct bignum_st { 788 BN_ULONG *d; /* Pointer to an array of 'BN_BITS2' bit chunks in little-endian 789 order. */ 790 int top; /* Index of last used element in |d|, plus one. */ 791 int dmax; /* Size of |d|, in words. */ 792 int neg; /* one if the number is negative */ 793 int flags; /* bitmask of BN_FLG_* values */ 794 }; 795 796 struct bn_mont_ctx_st { 797 BIGNUM RR; /* used to convert to montgomery form */ 798 BIGNUM N; /* The modulus */ 799 BIGNUM Ni; /* R*(1/R mod N) - N*Ni = 1 800 * (Ni is only stored for bignum algorithm) */ 801 BN_ULONG n0[2]; /* least significant word(s) of Ni; 802 (type changed with 0.9.9, was "BN_ULONG n0;" before) */ 803 int flags; 804 int ri; /* number of bits in R */ 805 }; 806 807 OPENSSL_EXPORT unsigned BN_num_bits_word(BN_ULONG l); 808 809 #define BN_FLG_MALLOCED 0x01 810 #define BN_FLG_STATIC_DATA 0x02 811 /* avoid leaking exponent information through timing, BN_mod_exp_mont() will 812 * call BN_mod_exp_mont_consttime, BN_div() will call BN_div_no_branch, 813 * BN_mod_inverse() will call BN_mod_inverse_no_branch. */ 814 #define BN_FLG_CONSTTIME 0x04 815 816 817 /* Android compatibility section. 818 * 819 * These functions are declared, temporarily, for Android because 820 * wpa_supplicant will take a little time to sync with upstream. Outside of 821 * Android they'll have no definition. */ 822 823 OPENSSL_EXPORT BIGNUM *get_rfc3526_prime_1536(BIGNUM *bn); 824 825 826 #if defined(__cplusplus) 827 } /* extern C */ 828 #endif 829 830 #define BN_F_BN_CTX_get 100 831 #define BN_F_BN_CTX_new 101 832 #define BN_F_BN_CTX_start 102 833 #define BN_F_BN_bn2dec 103 834 #define BN_F_BN_bn2hex 104 835 #define BN_F_BN_div 105 836 #define BN_F_BN_div_recp 106 837 #define BN_F_BN_exp 107 838 #define BN_F_BN_generate_dsa_nonce 108 839 #define BN_F_BN_generate_prime_ex 109 840 #define BN_F_BN_mod_exp2_mont 110 841 #define BN_F_BN_mod_exp_mont 111 842 #define BN_F_BN_mod_exp_mont_consttime 112 843 #define BN_F_BN_mod_exp_mont_word 113 844 #define BN_F_BN_mod_inverse 114 845 #define BN_F_BN_mod_inverse_no_branch 115 846 #define BN_F_BN_mod_lshift_quick 116 847 #define BN_F_BN_mod_sqrt 117 848 #define BN_F_BN_new 118 849 #define BN_F_BN_rand 119 850 #define BN_F_BN_rand_range 120 851 #define BN_F_BN_sqrt 121 852 #define BN_F_BN_usub 122 853 #define BN_F_bn_wexpand 123 854 #define BN_F_mod_exp_recp 124 855 #define BN_F_BN_lshift 125 856 #define BN_F_BN_rshift 126 857 #define BN_R_ARG2_LT_ARG3 100 858 #define BN_R_BAD_RECIPROCAL 101 859 #define BN_R_BIGNUM_TOO_LONG 102 860 #define BN_R_BITS_TOO_SMALL 103 861 #define BN_R_CALLED_WITH_EVEN_MODULUS 104 862 #define BN_R_DIV_BY_ZERO 105 863 #define BN_R_EXPAND_ON_STATIC_BIGNUM_DATA 106 864 #define BN_R_INPUT_NOT_REDUCED 107 865 #define BN_R_INVALID_RANGE 108 866 #define BN_R_NEGATIVE_NUMBER 109 867 #define BN_R_NOT_A_SQUARE 110 868 #define BN_R_NOT_INITIALIZED 111 869 #define BN_R_NO_INVERSE 112 870 #define BN_R_PRIVATE_KEY_TOO_LARGE 113 871 #define BN_R_P_IS_NOT_PRIME 114 872 #define BN_R_TOO_MANY_ITERATIONS 115 873 #define BN_R_TOO_MANY_TEMPORARY_VARIABLES 116 874 875 #endif /* OPENSSL_HEADER_BN_H */ 876
