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| or NULL on allocation 186 * failure. */ 187 OPENSSL_EXPORT BIGNUM *BN_copy(BIGNUM *dest, const BIGNUM *src); 188 189 /* BN_clear sets |bn| to zero and erases the old data. */ 190 OPENSSL_EXPORT void BN_clear(BIGNUM *bn); 191 192 /* BN_value_one returns a static BIGNUM with value 1. */ 193 OPENSSL_EXPORT const BIGNUM *BN_value_one(void); 194 195 /* BN_with_flags initialises a stack allocated |BIGNUM| with pointers to the 196 * contents of |in| but with |flags| ORed into the flags field. 197 * 198 * Note: the two BIGNUMs share state and so |out| should /not/ be passed to 199 * |BN_free|. */ 200 OPENSSL_EXPORT void BN_with_flags(BIGNUM *out, const BIGNUM *in, int flags); 201 202 203 /* Basic functions. */ 204 205 /* BN_num_bits returns the minimum number of bits needed to represent the 206 * absolute value of |bn|. */ 207 OPENSSL_EXPORT unsigned BN_num_bits(const BIGNUM *bn); 208 209 /* BN_num_bytes returns the minimum number of bytes needed to represent the 210 * absolute value of |bn|. */ 211 OPENSSL_EXPORT unsigned BN_num_bytes(const BIGNUM *bn); 212 213 /* BN_zero sets |bn| to zero. */ 214 OPENSSL_EXPORT void BN_zero(BIGNUM *bn); 215 216 /* BN_one sets |bn| to one. It returns one on success or zero on allocation 217 * failure. */ 218 OPENSSL_EXPORT int BN_one(BIGNUM *bn); 219 220 /* BN_set_word sets |bn| to |value|. It returns one on success or zero on 221 * allocation failure. */ 222 OPENSSL_EXPORT int BN_set_word(BIGNUM *bn, BN_ULONG value); 223 224 /* BN_set_negative sets the sign of |bn|. */ 225 OPENSSL_EXPORT void BN_set_negative(BIGNUM *bn, int sign); 226 227 /* BN_is_negative returns one if |bn| is negative and zero otherwise. */ 228 OPENSSL_EXPORT int BN_is_negative(const BIGNUM *bn); 229 230 /* BN_get_flags returns |bn->flags| & |flags|. */ 231 OPENSSL_EXPORT int BN_get_flags(const BIGNUM *bn, int flags); 232 233 /* BN_set_flags sets |flags| on |bn|. */ 234 OPENSSL_EXPORT void BN_set_flags(BIGNUM *bn, int flags); 235 236 237 /* Conversion functions. */ 238 239 /* BN_bin2bn sets |*ret| to the value of |len| bytes from |in|, interpreted as 240 * a big-endian number, and returns |ret|. If |ret| is NULL then a fresh 241 * |BIGNUM| is allocated and returned. It returns NULL on allocation 242 * failure. */ 243 OPENSSL_EXPORT BIGNUM *BN_bin2bn(const uint8_t *in, size_t len, BIGNUM *ret); 244 245 /* BN_bn2bin serialises the absolute value of |in| to |out| as a big-endian 246 * integer, which must have |BN_num_bytes| of space available. It returns the 247 * number of bytes written. */ 248 OPENSSL_EXPORT size_t BN_bn2bin(const BIGNUM *in, uint8_t *out); 249 250 /* BN_bn2bin_padded serialises the absolute value of |in| to |out| as a 251 * big-endian integer. The integer is padded with leading zeros up to size 252 * |len|. If |len| is smaller than |BN_num_bytes|, the function fails and 253 * returns 0. Otherwise, it returns 1. */ 254 OPENSSL_EXPORT int BN_bn2bin_padded(uint8_t *out, size_t len, const BIGNUM *in); 255 256 /* BN_bn2cbb_padded behaves like |BN_bn2bin_padded| but writes to a |CBB|. */ 257 OPENSSL_EXPORT int BN_bn2cbb_padded(CBB *out, size_t len, const BIGNUM *in); 258 259 /* BN_bn2hex returns an allocated string that contains a NUL-terminated, hex 260 * representation of |bn|. If |bn| is negative, the first char in the resulting 261 * string will be '-'. Returns NULL on allocation failure. */ 262 OPENSSL_EXPORT char *BN_bn2hex(const BIGNUM *bn); 263 264 /* BN_hex2bn parses the leading hex number from |in|, which may be proceeded by 265 * a '-' to indicate a negative number and may contain trailing, non-hex data. 266 * If |outp| is not NULL, it constructs a BIGNUM equal to the hex number and 267 * stores it in |*outp|. If |*outp| is NULL then it allocates a new BIGNUM and 268 * updates |*outp|. It returns the number of bytes of |in| processed or zero on 269 * error. */ 270 OPENSSL_EXPORT int BN_hex2bn(BIGNUM **outp, const char *in); 271 272 /* BN_bn2dec returns an allocated string that contains a NUL-terminated, 273 * decimal representation of |bn|. If |bn| is negative, the first char in the 274 * resulting string will be '-'. Returns NULL on allocation failure. */ 275 OPENSSL_EXPORT char *BN_bn2dec(const BIGNUM *a); 276 277 /* BN_dec2bn parses the leading decimal number from |in|, which may be 278 * proceeded by a '-' to indicate a negative number and may contain trailing, 279 * non-decimal data. If |outp| is not NULL, it constructs a BIGNUM equal to the 280 * decimal number and stores it in |*outp|. If |*outp| is NULL then it 281 * allocates a new BIGNUM and updates |*outp|. It returns the number of bytes 282 * of |in| processed or zero on error. */ 283 OPENSSL_EXPORT int BN_dec2bn(BIGNUM **outp, const char *in); 284 285 /* BN_asc2bn acts like |BN_dec2bn| or |BN_hex2bn| depending on whether |in| 286 * begins with "0X" or "0x" (indicating hex) or not (indicating decimal). A 287 * leading '-' is still permitted and comes before the optional 0X/0x. It 288 * returns one on success or zero on error. */ 289 OPENSSL_EXPORT int BN_asc2bn(BIGNUM **outp, const char *in); 290 291 /* BN_print writes a hex encoding of |a| to |bio|. It returns one on success 292 * and zero on error. */ 293 OPENSSL_EXPORT int BN_print(BIO *bio, const BIGNUM *a); 294 295 /* BN_print_fp acts like |BIO_print|, but wraps |fp| in a |BIO| first. */ 296 OPENSSL_EXPORT int BN_print_fp(FILE *fp, const BIGNUM *a); 297 298 /* BN_get_word returns the absolute value of |bn| as a single word. If |bn| is 299 * too large to be represented as a single word, the maximum possible value 300 * will be returned. */ 301 OPENSSL_EXPORT BN_ULONG BN_get_word(const BIGNUM *bn); 302 303 304 /* ASN.1 functions. */ 305 306 /* BN_cbs2unsigned parses a non-negative DER INTEGER from |cbs| writes the 307 * result to |ret|. It returns one on success and zero on failure. */ 308 OPENSSL_EXPORT int BN_cbs2unsigned(CBS *cbs, BIGNUM *ret); 309 310 /* BN_cbs2unsigned_buggy acts like |BN_cbs2unsigned| but tolerates some invalid 311 * encodings. Do not use this function. */ 312 OPENSSL_EXPORT int BN_cbs2unsigned_buggy(CBS *cbs, BIGNUM *ret); 313 314 /* BN_bn2cbb marshals |bn| as a non-negative DER INTEGER and appends the result 315 * to |cbb|. It returns one on success and zero on failure. */ 316 OPENSSL_EXPORT int BN_bn2cbb(CBB *cbb, const BIGNUM *bn); 317 318 319 /* Internal functions. 320 * 321 * These functions are useful for code that is doing low-level manipulations of 322 * BIGNUM values. However, be sure that no other function in this file does 323 * what you want before turning to these. */ 324 325 /* bn_correct_top decrements |bn->top| until |bn->d[top-1]| is non-zero or 326 * until |top| is zero. */ 327 OPENSSL_EXPORT void bn_correct_top(BIGNUM *bn); 328 329 /* bn_wexpand ensures that |bn| has at least |words| works of space without 330 * altering its value. It returns one on success or zero on allocation 331 * failure. */ 332 OPENSSL_EXPORT BIGNUM *bn_wexpand(BIGNUM *bn, size_t words); 333 334 335 /* BIGNUM pools. 336 * 337 * Certain BIGNUM operations need to use many temporary variables and 338 * allocating and freeing them can be quite slow. Thus such opertions typically 339 * take a |BN_CTX| parameter, which contains a pool of |BIGNUMs|. The |ctx| 340 * argument to a public function may be NULL, in which case a local |BN_CTX| 341 * will be created just for the lifetime of that call. 342 * 343 * A function must call |BN_CTX_start| first. Then, |BN_CTX_get| may be called 344 * repeatedly to obtain temporary |BIGNUM|s. All |BN_CTX_get| calls must be made 345 * before calling any other functions that use the |ctx| as an argument. 346 * 347 * Finally, |BN_CTX_end| must be called before returning from the function. 348 * When |BN_CTX_end| is called, the |BIGNUM| pointers obtained from 349 * |BN_CTX_get| become invalid. */ 350 351 /* BN_CTX_new returns a new, empty BN_CTX or NULL on allocation failure. */ 352 OPENSSL_EXPORT BN_CTX *BN_CTX_new(void); 353 354 /* BN_CTX_free frees all BIGNUMs contained in |ctx| and then frees |ctx| 355 * itself. */ 356 OPENSSL_EXPORT void BN_CTX_free(BN_CTX *ctx); 357 358 /* BN_CTX_start "pushes" a new entry onto the |ctx| stack and allows future 359 * calls to |BN_CTX_get|. */ 360 OPENSSL_EXPORT void BN_CTX_start(BN_CTX *ctx); 361 362 /* BN_CTX_get returns a new |BIGNUM|, or NULL on allocation failure. Once 363 * |BN_CTX_get| has returned NULL, all future calls will also return NULL until 364 * |BN_CTX_end| is called. */ 365 OPENSSL_EXPORT BIGNUM *BN_CTX_get(BN_CTX *ctx); 366 367 /* BN_CTX_end invalidates all |BIGNUM|s returned from |BN_CTX_get| since the 368 * matching |BN_CTX_start| call. */ 369 OPENSSL_EXPORT void BN_CTX_end(BN_CTX *ctx); 370 371 372 /* Simple arithmetic */ 373 374 /* BN_add sets |r| = |a| + |b|, where |r| may be the same pointer as either |a| 375 * or |b|. It returns one on success and zero on allocation failure. */ 376 OPENSSL_EXPORT int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); 377 378 /* BN_uadd sets |r| = |a| + |b|, where |a| and |b| are non-negative and |r| may 379 * be the same pointer as either |a| or |b|. It returns one on success and zero 380 * on allocation failure. */ 381 OPENSSL_EXPORT int BN_uadd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); 382 383 /* BN_add_word adds |w| to |a|. It returns one on success and zero otherwise. */ 384 OPENSSL_EXPORT int BN_add_word(BIGNUM *a, BN_ULONG w); 385 386 /* BN_sub sets |r| = |a| - |b|, where |r| must be a distinct pointer from |a| 387 * and |b|. It returns one on success and zero on allocation failure. */ 388 OPENSSL_EXPORT int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); 389 390 /* BN_usub sets |r| = |a| - |b|, where |a| and |b| are non-negative integers, 391 * |b| < |a| and |r| must be a distinct pointer from |a| and |b|. It returns 392 * one on success and zero on allocation failure. */ 393 OPENSSL_EXPORT int BN_usub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); 394 395 /* BN_sub_word subtracts |w| from |a|. It returns one on success and zero on 396 * allocation failure. */ 397 OPENSSL_EXPORT int BN_sub_word(BIGNUM *a, BN_ULONG w); 398 399 /* BN_mul sets |r| = |a| * |b|, where |r| may be the same pointer as |a| or 400 * |b|. Returns one on success and zero otherwise. */ 401 OPENSSL_EXPORT int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, 402 BN_CTX *ctx); 403 404 /* BN_mul_word sets |bn| = |bn| * |w|. It returns one on success or zero on 405 * allocation failure. */ 406 OPENSSL_EXPORT int BN_mul_word(BIGNUM *bn, BN_ULONG w); 407 408 /* BN_sqr sets |r| = |a|^2 (i.e. squares), where |r| may be the same pointer as 409 * |a|. Returns one on success and zero otherwise. This is more efficient than 410 * BN_mul(r, a, a, ctx). */ 411 OPENSSL_EXPORT int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx); 412 413 /* BN_div divides |numerator| by |divisor| and places the result in |quotient| 414 * and the remainder in |rem|. Either of |quotient| or |rem| may be NULL, in 415 * which case the respective value is not returned. The result is rounded 416 * towards zero; thus if |numerator| is negative, the remainder will be zero or 417 * negative. It returns one on success or zero on error. */ 418 OPENSSL_EXPORT int BN_div(BIGNUM *quotient, BIGNUM *rem, 419 const BIGNUM *numerator, const BIGNUM *divisor, 420 BN_CTX *ctx); 421 422 /* BN_div_word sets |numerator| = |numerator|/|divisor| and returns the 423 * remainder or (BN_ULONG)-1 on error. */ 424 OPENSSL_EXPORT BN_ULONG BN_div_word(BIGNUM *numerator, BN_ULONG divisor); 425 426 /* BN_sqrt sets |*out_sqrt| (which may be the same |BIGNUM| as |in|) to the 427 * square root of |in|, using |ctx|. It returns one on success or zero on 428 * error. Negative numbers and non-square numbers will result in an error with 429 * appropriate errors on the error queue. */ 430 OPENSSL_EXPORT int BN_sqrt(BIGNUM *out_sqrt, const BIGNUM *in, BN_CTX *ctx); 431 432 433 /* Comparison functions */ 434 435 /* BN_cmp returns a value less than, equal to or greater than zero if |a| is 436 * less than, equal to or greater than |b|, respectively. */ 437 OPENSSL_EXPORT int BN_cmp(const BIGNUM *a, const BIGNUM *b); 438 439 /* BN_ucmp returns a value less than, equal to or greater than zero if the 440 * absolute value of |a| is less than, equal to or greater than the absolute 441 * value of |b|, respectively. */ 442 OPENSSL_EXPORT int BN_ucmp(const BIGNUM *a, const BIGNUM *b); 443 444 /* BN_abs_is_word returns one if the absolute value of |bn| equals |w| and zero 445 * otherwise. */ 446 OPENSSL_EXPORT int BN_abs_is_word(const BIGNUM *bn, BN_ULONG w); 447 448 /* BN_is_zero returns one if |bn| is zero and zero otherwise. */ 449 OPENSSL_EXPORT int BN_is_zero(const BIGNUM *bn); 450 451 /* BN_is_one returns one if |bn| equals one and zero otherwise. */ 452 OPENSSL_EXPORT int BN_is_one(const BIGNUM *bn); 453 454 /* BN_is_word returns one if |bn| is exactly |w| and zero otherwise. */ 455 OPENSSL_EXPORT int BN_is_word(const BIGNUM *bn, BN_ULONG w); 456 457 /* BN_is_odd returns one if |bn| is odd and zero otherwise. */ 458 OPENSSL_EXPORT int BN_is_odd(const BIGNUM *bn); 459 460 461 /* Bitwise operations. */ 462 463 /* BN_lshift sets |r| equal to |a| << n. The |a| and |r| arguments may be the 464 * same |BIGNUM|. It returns one on success and zero on allocation failure. */ 465 OPENSSL_EXPORT int BN_lshift(BIGNUM *r, const BIGNUM *a, int n); 466 467 /* BN_lshift1 sets |r| equal to |a| << 1, where |r| and |a| may be the same 468 * pointer. It returns one on success and zero on allocation failure. */ 469 OPENSSL_EXPORT int BN_lshift1(BIGNUM *r, const BIGNUM *a); 470 471 /* BN_rshift sets |r| equal to |a| >> n, where |r| and |a| may be the same 472 * pointer. It returns one on success and zero on allocation failure. */ 473 OPENSSL_EXPORT int BN_rshift(BIGNUM *r, const BIGNUM *a, int n); 474 475 /* BN_rshift1 sets |r| equal to |a| >> 1, where |r| and |a| may be the same 476 * pointer. It returns one on success and zero on allocation failure. */ 477 OPENSSL_EXPORT int BN_rshift1(BIGNUM *r, const BIGNUM *a); 478 479 /* BN_set_bit sets the |n|th, least-significant bit in |a|. For example, if |a| 480 * is 2 then setting bit zero will make it 3. It returns one on success or zero 481 * on allocation failure. */ 482 OPENSSL_EXPORT int BN_set_bit(BIGNUM *a, int n); 483 484 /* BN_clear_bit clears the |n|th, least-significant bit in |a|. For example, if 485 * |a| is 3, clearing bit zero will make it two. It returns one on success or 486 * zero on allocation failure. */ 487 OPENSSL_EXPORT int BN_clear_bit(BIGNUM *a, int n); 488 489 /* BN_is_bit_set returns the value of the |n|th, least-significant bit in |a|, 490 * or zero if the bit doesn't exist. */ 491 OPENSSL_EXPORT int BN_is_bit_set(const BIGNUM *a, int n); 492 493 /* BN_mask_bits truncates |a| so that it is only |n| bits long. It returns one 494 * on success or zero if |n| is greater than the length of |a| already. */ 495 OPENSSL_EXPORT int BN_mask_bits(BIGNUM *a, int n); 496 497 498 /* Modulo arithmetic. */ 499 500 /* BN_mod_word returns |a| mod |w|. */ 501 OPENSSL_EXPORT BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w); 502 503 /* BN_mod is a helper macro that calls |BN_div| and discards the quotient. */ 504 #define BN_mod(rem, numerator, divisor, ctx) \ 505 BN_div(NULL, (rem), (numerator), (divisor), (ctx)) 506 507 /* BN_nnmod is a non-negative modulo function. It acts like |BN_mod|, but 0 <= 508 * |rem| < |divisor| is always true. It returns one on success and zero on 509 * error. */ 510 OPENSSL_EXPORT int BN_nnmod(BIGNUM *rem, const BIGNUM *numerator, 511 const BIGNUM *divisor, BN_CTX *ctx); 512 513 /* BN_mod_add sets |r| = |a| + |b| mod |m|. It returns one on success and zero 514 * on error. */ 515 OPENSSL_EXPORT int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, 516 const BIGNUM *m, BN_CTX *ctx); 517 518 /* BN_mod_add_quick acts like |BN_mod_add| but requires that |a| and |b| be 519 * non-negative and less than |m|. */ 520 OPENSSL_EXPORT int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, 521 const BIGNUM *m); 522 523 /* BN_mod_sub sets |r| = |a| - |b| mod |m|. It returns one on success and zero 524 * on error. */ 525 OPENSSL_EXPORT int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, 526 const BIGNUM *m, BN_CTX *ctx); 527 528 /* BN_mod_sub_quick acts like |BN_mod_sub| but requires that |a| and |b| be 529 * non-negative and less than |m|. */ 530 OPENSSL_EXPORT int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, 531 const BIGNUM *m); 532 533 /* BN_mod_mul sets |r| = |a|*|b| mod |m|. It returns one on success and zero 534 * on error. */ 535 OPENSSL_EXPORT int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, 536 const BIGNUM *m, BN_CTX *ctx); 537 538 /* BN_mod_sqr sets |r| = |a|^2 mod |m|. It returns one on success and zero 539 * on error. */ 540 OPENSSL_EXPORT int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, 541 BN_CTX *ctx); 542 543 /* BN_mod_lshift sets |r| = (|a| << n) mod |m|, where |r| and |a| may be the 544 * same pointer. It returns one on success and zero on error. */ 545 OPENSSL_EXPORT int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, 546 const BIGNUM *m, BN_CTX *ctx); 547 548 /* BN_mod_lshift_quick acts like |BN_mod_lshift| but requires that |a| be 549 * non-negative and less than |m|. */ 550 OPENSSL_EXPORT int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, 551 const BIGNUM *m); 552 553 /* BN_mod_lshift1 sets |r| = (|a| << 1) mod |m|, where |r| and |a| may be the 554 * same pointer. It returns one on success and zero on error. */ 555 OPENSSL_EXPORT int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, 556 BN_CTX *ctx); 557 558 /* BN_mod_lshift1_quick acts like |BN_mod_lshift1| but requires that |a| be 559 * non-negative and less than |m|. */ 560 OPENSSL_EXPORT int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, 561 const BIGNUM *m); 562 563 /* BN_mod_sqrt returns a |BIGNUM|, r, such that r^2 == a (mod p). */ 564 OPENSSL_EXPORT BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p, 565 BN_CTX *ctx); 566 567 568 /* Random and prime number generation. */ 569 570 /* BN_rand sets |rnd| to a random number of length |bits|. If |top| is zero, the 571 * most-significant bit, if any, will be set. If |top| is one, the two most 572 * significant bits, if any, will be set. 573 * 574 * If |top| is -1 then no extra action will be taken and |BN_num_bits(rnd)| may 575 * not equal |bits| if the most significant bits randomly ended up as zeros. 576 * 577 * If |bottom| is non-zero, the least-significant bit, if any, will be set. The 578 * function returns one on success or zero otherwise. */ 579 OPENSSL_EXPORT int BN_rand(BIGNUM *rnd, int bits, int top, int bottom); 580 581 /* BN_pseudo_rand is an alias for |BN_rand|. */ 582 OPENSSL_EXPORT int BN_pseudo_rand(BIGNUM *rnd, int bits, int top, int bottom); 583 584 /* BN_rand_range sets |rnd| to a random value [0..range). It returns one on 585 * success and zero otherwise. */ 586 OPENSSL_EXPORT int BN_rand_range(BIGNUM *rnd, const BIGNUM *range); 587 588 /* BN_pseudo_rand_range is an alias for BN_rand_range. */ 589 OPENSSL_EXPORT int BN_pseudo_rand_range(BIGNUM *rnd, const BIGNUM *range); 590 591 /* BN_generate_dsa_nonce generates a random number 0 <= out < range. Unlike 592 * BN_rand_range, it also includes the contents of |priv| and |message| in the 593 * generation so that an RNG failure isn't fatal as long as |priv| remains 594 * secret. This is intended for use in DSA and ECDSA where an RNG weakness 595 * leads directly to private key exposure unless this function is used. 596 * It returns one on success and zero on error. */ 597 OPENSSL_EXPORT int BN_generate_dsa_nonce(BIGNUM *out, const BIGNUM *range, 598 const BIGNUM *priv, 599 const uint8_t *message, 600 size_t message_len, BN_CTX *ctx); 601 602 /* BN_GENCB holds a callback function that is used by generation functions that 603 * can take a very long time to complete. Use |BN_GENCB_set| to initialise a 604 * |BN_GENCB| structure. 605 * 606 * The callback receives the address of that |BN_GENCB| structure as its last 607 * argument and the user is free to put an arbitary pointer in |arg|. The other 608 * arguments are set as follows: 609 * event=BN_GENCB_GENERATED, n=i: after generating the i'th possible prime 610 * number. 611 * event=BN_GENCB_PRIME_TEST, n=-1: when finished trial division primality 612 * checks. 613 * event=BN_GENCB_PRIME_TEST, n=i: when the i'th primality test has finished. 614 * 615 * The callback can return zero to abort the generation progress or one to 616 * allow it to continue. 617 * 618 * When other code needs to call a BN generation function it will often take a 619 * BN_GENCB argument and may call the function with other argument values. */ 620 #define BN_GENCB_GENERATED 0 621 #define BN_GENCB_PRIME_TEST 1 622 623 struct bn_gencb_st { 624 void *arg; /* callback-specific data */ 625 int (*callback)(int event, int n, struct bn_gencb_st *); 626 }; 627 628 /* BN_GENCB_set configures |callback| to call |f| and sets |callout->arg| to 629 * |arg|. */ 630 OPENSSL_EXPORT void BN_GENCB_set(BN_GENCB *callback, 631 int (*f)(int event, int n, 632 struct bn_gencb_st *), 633 void *arg); 634 635 /* BN_GENCB_call calls |callback|, if not NULL, and returns the return value of 636 * the callback, or 1 if |callback| is NULL. */ 637 OPENSSL_EXPORT int BN_GENCB_call(BN_GENCB *callback, int event, int n); 638 639 /* BN_generate_prime_ex sets |ret| to a prime number of |bits| length. If safe 640 * is non-zero then the prime will be such that (ret-1)/2 is also a prime. 641 * (This is needed for Diffie-Hellman groups to ensure that the only subgroups 642 * are of size 2 and (p-1)/2.). 643 * 644 * If |add| is not NULL, the prime will fulfill the condition |ret| % |add| == 645 * |rem| in order to suit a given generator. (If |rem| is NULL then |ret| % 646 * |add| == 1.) 647 * 648 * If |cb| is not NULL, it will be called during processing to give an 649 * indication of progress. See the comments for |BN_GENCB|. It returns one on 650 * success and zero otherwise. */ 651 OPENSSL_EXPORT int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, 652 const BIGNUM *add, const BIGNUM *rem, 653 BN_GENCB *cb); 654 655 /* BN_prime_checks is magic value that can be used as the |checks| argument to 656 * the primality testing functions in order to automatically select a number of 657 * Miller-Rabin checks that gives a false positive rate of ~2^{-80}. */ 658 #define BN_prime_checks 0 659 660 /* BN_primality_test sets |*is_probably_prime| to one if |candidate| is 661 * probably a prime number by the Miller-Rabin test or zero if it's certainly 662 * not. 663 * 664 * If |do_trial_division| is non-zero then |candidate| will be tested against a 665 * list of small primes before Miller-Rabin tests. The probability of this 666 * function returning a false positive is 2^{2*checks}. If |checks| is 667 * |BN_prime_checks| then a value that results in approximately 2^{-80} false 668 * positive probability is used. If |cb| is not NULL then it is called during 669 * the checking process. See the comment above |BN_GENCB|. 670 * 671 * The function returns one on success and zero on error. 672 * 673 * (If you are unsure whether you want |do_trial_division|, don't set it.) */ 674 OPENSSL_EXPORT int BN_primality_test(int *is_probably_prime, 675 const BIGNUM *candidate, int checks, 676 BN_CTX *ctx, int do_trial_division, 677 BN_GENCB *cb); 678 679 /* BN_is_prime_fasttest_ex returns one if |candidate| is probably a prime 680 * number by the Miller-Rabin test, zero if it's certainly not and -1 on error. 681 * 682 * If |do_trial_division| is non-zero then |candidate| will be tested against a 683 * list of small primes before Miller-Rabin tests. The probability of this 684 * function returning one when |candidate| is composite is 2^{2*checks}. If 685 * |checks| is |BN_prime_checks| then a value that results in approximately 686 * 2^{-80} false positive probability is used. If |cb| is not NULL then it is 687 * called during the checking process. See the comment above |BN_GENCB|. 688 * 689 * WARNING: deprecated. Use |BN_primality_test|. */ 690 OPENSSL_EXPORT int BN_is_prime_fasttest_ex(const BIGNUM *candidate, int checks, 691 BN_CTX *ctx, int do_trial_division, 692 BN_GENCB *cb); 693 694 /* BN_is_prime_ex acts the same as |BN_is_prime_fasttest_ex| with 695 * |do_trial_division| set to zero. 696 * 697 * WARNING: deprecated: Use |BN_primality_test|. */ 698 OPENSSL_EXPORT int BN_is_prime_ex(const BIGNUM *candidate, int checks, 699 BN_CTX *ctx, BN_GENCB *cb); 700 701 702 /* Number theory functions */ 703 704 /* BN_gcd sets |r| = gcd(|a|, |b|). It returns one on success and zero 705 * otherwise. */ 706 OPENSSL_EXPORT int BN_gcd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, 707 BN_CTX *ctx); 708 709 /* BN_mod_inverse sets |out| equal to |a|^-1, mod |n|. If either of |a| or |n| 710 * have |BN_FLG_CONSTTIME| set then the operation is performed in constant 711 * time. If |out| is NULL, a fresh BIGNUM is allocated. It returns the result 712 * or NULL on error. */ 713 OPENSSL_EXPORT BIGNUM *BN_mod_inverse(BIGNUM *out, const BIGNUM *a, 714 const BIGNUM *n, BN_CTX *ctx); 715 716 /* BN_mod_inverse_ex acts like |BN_mod_inverse| except that, when it returns 717 * zero, it will set |*out_no_inverse| to one if the failure was caused because 718 * |a| has no inverse mod |n|. Otherwise it will set |*out_no_inverse| to 719 * zero. */ 720 OPENSSL_EXPORT BIGNUM *BN_mod_inverse_ex(BIGNUM *out, int *out_no_inverse, 721 const BIGNUM *a, const BIGNUM *n, 722 BN_CTX *ctx); 723 724 /* BN_kronecker returns the Kronecker symbol of |a| and |b| (which is -1, 0 or 725 * 1), or -2 on error. */ 726 OPENSSL_EXPORT int BN_kronecker(const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); 727 728 729 /* Montgomery arithmetic. */ 730 731 /* BN_MONT_CTX contains the precomputed values needed to work in a specific 732 * Montgomery domain. */ 733 734 /* BN_MONT_CTX_new returns a fresh BN_MONT_CTX or NULL on allocation failure. */ 735 OPENSSL_EXPORT BN_MONT_CTX *BN_MONT_CTX_new(void); 736 737 /* BN_MONT_CTX_free frees memory associated with |mont|. */ 738 OPENSSL_EXPORT void BN_MONT_CTX_free(BN_MONT_CTX *mont); 739 740 /* BN_MONT_CTX_copy sets |to| equal to |from|. It returns |to| on success or 741 * NULL on error. */ 742 OPENSSL_EXPORT BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, 743 const BN_MONT_CTX *from); 744 745 /* BN_MONT_CTX_set sets up a Montgomery context given the modulus, |mod|. It 746 * returns one on success and zero on error. */ 747 OPENSSL_EXPORT int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, 748 BN_CTX *ctx); 749 750 /* BN_MONT_CTX_set_locked takes |lock| and checks whether |*pmont| is NULL. If 751 * so, it creates a new |BN_MONT_CTX| and sets the modulus for it to |mod|. It 752 * then stores it as |*pmont| and returns it, or NULL on error. 753 * 754 * If |*pmont| is already non-NULL then the existing value is returned. */ 755 BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, CRYPTO_MUTEX *lock, 756 const BIGNUM *mod, BN_CTX *bn_ctx); 757 758 /* BN_to_montgomery sets |ret| equal to |a| in the Montgomery domain. It 759 * returns one on success and zero on error. */ 760 OPENSSL_EXPORT int BN_to_montgomery(BIGNUM *ret, const BIGNUM *a, 761 const BN_MONT_CTX *mont, BN_CTX *ctx); 762 763 /* BN_from_montgomery sets |ret| equal to |a| * R^-1, i.e. translates values 764 * out of the Montgomery domain. It returns one on success or zero on error. */ 765 OPENSSL_EXPORT int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, 766 const BN_MONT_CTX *mont, BN_CTX *ctx); 767 768 /* BN_mod_mul_montgomery set |r| equal to |a| * |b|, in the Montgomery domain. 769 * Both |a| and |b| must already be in the Montgomery domain (by 770 * |BN_to_montgomery|). It returns one on success or zero on error. */ 771 OPENSSL_EXPORT int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, 772 const BIGNUM *b, 773 const BN_MONT_CTX *mont, BN_CTX *ctx); 774 775 776 /* Exponentiation. */ 777 778 /* BN_exp sets |r| equal to |a|^{|p|}. It does so with a square-and-multiply 779 * algorithm that leaks side-channel information. It returns one on success or 780 * zero otherwise. */ 781 OPENSSL_EXPORT int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, 782 BN_CTX *ctx); 783 784 /* BN_mod_exp sets |r| equal to |a|^{|p|} mod |m|. It does so with the best 785 * algorithm for the values provided and can run in constant time if 786 * |BN_FLG_CONSTTIME| is set for |p|. It returns one on success or zero 787 * otherwise. */ 788 OPENSSL_EXPORT int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, 789 const BIGNUM *m, BN_CTX *ctx); 790 791 OPENSSL_EXPORT int BN_mod_exp_mont(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, 792 const BIGNUM *m, BN_CTX *ctx, 793 const BN_MONT_CTX *mont); 794 795 OPENSSL_EXPORT int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, 796 const BIGNUM *p, const BIGNUM *m, 797 BN_CTX *ctx, 798 const BN_MONT_CTX *mont); 799 800 OPENSSL_EXPORT int BN_mod_exp_mont_word(BIGNUM *r, BN_ULONG a, const BIGNUM *p, 801 const BIGNUM *m, BN_CTX *ctx, 802 const BN_MONT_CTX *mont); 803 OPENSSL_EXPORT int BN_mod_exp2_mont(BIGNUM *r, const BIGNUM *a1, 804 const BIGNUM *p1, const BIGNUM *a2, 805 const BIGNUM *p2, const BIGNUM *m, 806 BN_CTX *ctx, const BN_MONT_CTX *mont); 807 808 809 /* Deprecated functions */ 810 811 /* BN_bn2mpi serialises the value of |in| to |out|, using a format that consists 812 * of the number's length in bytes represented as a 4-byte big-endian number, 813 * and the number itself in big-endian format, where the most significant bit 814 * signals a negative number. (The representation of numbers with the MSB set is 815 * prefixed with null byte). |out| must have sufficient space available; to 816 * find the needed amount of space, call the function with |out| set to NULL. */ 817 OPENSSL_EXPORT size_t BN_bn2mpi(const BIGNUM *in, uint8_t *out); 818 819 /* BN_mpi2bn parses |len| bytes from |in| and returns the resulting value. The 820 * bytes at |in| are expected to be in the format emitted by |BN_bn2mpi|. 821 * 822 * If |out| is NULL then a fresh |BIGNUM| is allocated and returned, otherwise 823 * |out| is reused and returned. On error, NULL is returned and the error queue 824 * is updated. */ 825 OPENSSL_EXPORT BIGNUM *BN_mpi2bn(const uint8_t *in, size_t len, BIGNUM *out); 826 827 828 /* Private functions */ 829 830 struct bignum_st { 831 BN_ULONG *d; /* Pointer to an array of 'BN_BITS2' bit chunks in little-endian 832 order. */ 833 int top; /* Index of last used element in |d|, plus one. */ 834 int dmax; /* Size of |d|, in words. */ 835 int neg; /* one if the number is negative */ 836 int flags; /* bitmask of BN_FLG_* values */ 837 }; 838 839 struct bn_mont_ctx_st { 840 BIGNUM RR; /* used to convert to montgomery form */ 841 BIGNUM N; /* The modulus */ 842 BN_ULONG n0[2]; /* least significant words of (R*Ri-1)/N */ 843 }; 844 845 OPENSSL_EXPORT unsigned BN_num_bits_word(BN_ULONG l); 846 847 #define BN_FLG_MALLOCED 0x01 848 #define BN_FLG_STATIC_DATA 0x02 849 /* avoid leaking exponent information through timing, BN_mod_exp_mont() will 850 * call BN_mod_exp_mont_consttime, BN_div() will call BN_div_no_branch, 851 * BN_mod_inverse() will call BN_mod_inverse_no_branch. */ 852 #define BN_FLG_CONSTTIME 0x04 853 854 855 /* Android compatibility section. 856 * 857 * These functions are declared, temporarily, for Android because 858 * wpa_supplicant will take a little time to sync with upstream. Outside of 859 * Android they'll have no definition. */ 860 861 OPENSSL_EXPORT BIGNUM *get_rfc3526_prime_1536(BIGNUM *bn); 862 863 864 #if defined(__cplusplus) 865 } /* extern C */ 866 #endif 867 868 #define BN_R_ARG2_LT_ARG3 100 869 #define BN_R_BAD_RECIPROCAL 101 870 #define BN_R_BIGNUM_TOO_LONG 102 871 #define BN_R_BITS_TOO_SMALL 103 872 #define BN_R_CALLED_WITH_EVEN_MODULUS 104 873 #define BN_R_DIV_BY_ZERO 105 874 #define BN_R_EXPAND_ON_STATIC_BIGNUM_DATA 106 875 #define BN_R_INPUT_NOT_REDUCED 107 876 #define BN_R_INVALID_RANGE 108 877 #define BN_R_NEGATIVE_NUMBER 109 878 #define BN_R_NOT_A_SQUARE 110 879 #define BN_R_NOT_INITIALIZED 111 880 #define BN_R_NO_INVERSE 112 881 #define BN_R_PRIVATE_KEY_TOO_LARGE 113 882 #define BN_R_P_IS_NOT_PRIME 114 883 #define BN_R_TOO_MANY_ITERATIONS 115 884 #define BN_R_TOO_MANY_TEMPORARY_VARIABLES 116 885 #define BN_R_BAD_ENCODING 117 886 #define BN_R_ENCODE_ERROR 118 887 888 #endif /* OPENSSL_HEADER_BN_H */ 889
