Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1 | /* Copyright (C) 1995-1997 Eric Young (eay@cryptsoft.com) |
| 2 | * All rights reserved. |
| 3 | * |
| 4 | * This package is an SSL implementation written |
| 5 | * by Eric Young (eay@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@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@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@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@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@cryptsoft.com). This product includes software written by Tim |
| 107 | * Hudson (tjh@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> |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 127 | #include <openssl/thread.h> |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 128 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 129 | #include <inttypes.h> // for PRIu64 and friends |
| 130 | #include <stdio.h> // for FILE* |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 131 | |
| 132 | #if defined(__cplusplus) |
| 133 | extern "C" { |
| 134 | #endif |
| 135 | |
| 136 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 137 | // BN provides support for working with arbitrary 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. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 140 | |
| 141 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 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. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 148 | #if defined(OPENSSL_64_BIT) |
| 149 | #define BN_ULONG uint64_t |
| 150 | #define BN_BITS2 64 |
Steven Valdez | 909b19f | 2016-11-21 15:35:44 -0500 | [diff] [blame] | 151 | #define BN_DEC_FMT1 "%" PRIu64 |
| 152 | #define BN_DEC_FMT2 "%019" PRIu64 |
| 153 | #define BN_HEX_FMT1 "%" PRIx64 |
| 154 | #define BN_HEX_FMT2 "%016" PRIx64 |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 155 | #elif defined(OPENSSL_32_BIT) |
| 156 | #define BN_ULONG uint32_t |
| 157 | #define BN_BITS2 32 |
Steven Valdez | 909b19f | 2016-11-21 15:35:44 -0500 | [diff] [blame] | 158 | #define BN_DEC_FMT1 "%" PRIu32 |
| 159 | #define BN_DEC_FMT2 "%09" PRIu32 |
| 160 | #define BN_HEX_FMT1 "%" PRIx32 |
| 161 | #define BN_HEX_FMT2 "%08" PRIx64 |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 162 | #else |
| 163 | #error "Must define either OPENSSL_32_BIT or OPENSSL_64_BIT" |
| 164 | #endif |
| 165 | |
| 166 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 167 | // Allocation and freeing. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 168 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 169 | // BN_new creates a new, allocated BIGNUM and initialises it. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 170 | OPENSSL_EXPORT BIGNUM *BN_new(void); |
| 171 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 172 | // BN_init initialises a stack allocated |BIGNUM|. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 173 | OPENSSL_EXPORT void BN_init(BIGNUM *bn); |
| 174 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 175 | // BN_free frees the data referenced by |bn| and, if |bn| was originally |
| 176 | // allocated on the heap, frees |bn| also. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 177 | OPENSSL_EXPORT void BN_free(BIGNUM *bn); |
| 178 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 179 | // BN_clear_free erases and frees the data referenced by |bn| and, if |bn| was |
| 180 | // originally allocated on the heap, frees |bn| also. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 181 | OPENSSL_EXPORT void BN_clear_free(BIGNUM *bn); |
| 182 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 183 | // BN_dup allocates a new BIGNUM and sets it equal to |src|. It returns the |
| 184 | // allocated BIGNUM on success or NULL otherwise. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 185 | OPENSSL_EXPORT BIGNUM *BN_dup(const BIGNUM *src); |
| 186 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 187 | // BN_copy sets |dest| equal to |src| and returns |dest| or NULL on allocation |
| 188 | // failure. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 189 | OPENSSL_EXPORT BIGNUM *BN_copy(BIGNUM *dest, const BIGNUM *src); |
| 190 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 191 | // BN_clear sets |bn| to zero and erases the old data. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 192 | OPENSSL_EXPORT void BN_clear(BIGNUM *bn); |
| 193 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 194 | // BN_value_one returns a static BIGNUM with value 1. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 195 | OPENSSL_EXPORT const BIGNUM *BN_value_one(void); |
| 196 | |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 197 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 198 | // Basic functions. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 199 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 200 | // BN_num_bits returns the minimum number of bits needed to represent the |
| 201 | // absolute value of |bn|. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 202 | OPENSSL_EXPORT unsigned BN_num_bits(const BIGNUM *bn); |
| 203 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 204 | // BN_num_bytes returns the minimum number of bytes needed to represent the |
| 205 | // absolute value of |bn|. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 206 | OPENSSL_EXPORT unsigned BN_num_bytes(const BIGNUM *bn); |
| 207 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 208 | // BN_zero sets |bn| to zero. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 209 | OPENSSL_EXPORT void BN_zero(BIGNUM *bn); |
| 210 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 211 | // BN_one sets |bn| to one. It returns one on success or zero on allocation |
| 212 | // failure. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 213 | OPENSSL_EXPORT int BN_one(BIGNUM *bn); |
| 214 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 215 | // BN_set_word sets |bn| to |value|. It returns one on success or zero on |
| 216 | // allocation failure. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 217 | OPENSSL_EXPORT int BN_set_word(BIGNUM *bn, BN_ULONG value); |
| 218 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 219 | // BN_set_u64 sets |bn| to |value|. It returns one on success or zero on |
| 220 | // allocation failure. |
David Benjamin | 7c0d06c | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 221 | OPENSSL_EXPORT int BN_set_u64(BIGNUM *bn, uint64_t value); |
| 222 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 223 | // BN_set_negative sets the sign of |bn|. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 224 | OPENSSL_EXPORT void BN_set_negative(BIGNUM *bn, int sign); |
| 225 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 226 | // BN_is_negative returns one if |bn| is negative and zero otherwise. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 227 | OPENSSL_EXPORT int BN_is_negative(const BIGNUM *bn); |
| 228 | |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 229 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 230 | // Conversion functions. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 231 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 232 | // BN_bin2bn sets |*ret| to the value of |len| bytes from |in|, interpreted as |
| 233 | // a big-endian number, and returns |ret|. If |ret| is NULL then a fresh |
| 234 | // |BIGNUM| is allocated and returned. It returns NULL on allocation |
| 235 | // failure. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 236 | OPENSSL_EXPORT BIGNUM *BN_bin2bn(const uint8_t *in, size_t len, BIGNUM *ret); |
| 237 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 238 | // BN_bn2bin serialises the absolute value of |in| to |out| as a big-endian |
| 239 | // integer, which must have |BN_num_bytes| of space available. It returns the |
Robert Sloan | ab8b888 | 2018-03-26 11:39:51 -0700 | [diff] [blame^] | 240 | // number of bytes written. Note this function leaks the magnitude of |in|. If |
| 241 | // |in| is secret, use |BN_bn2bin_padded| instead. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 242 | OPENSSL_EXPORT size_t BN_bn2bin(const BIGNUM *in, uint8_t *out); |
| 243 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 244 | // BN_le2bn sets |*ret| to the value of |len| bytes from |in|, interpreted as |
| 245 | // a little-endian number, and returns |ret|. If |ret| is NULL then a fresh |
| 246 | // |BIGNUM| is allocated and returned. It returns NULL on allocation |
| 247 | // failure. |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 248 | OPENSSL_EXPORT BIGNUM *BN_le2bn(const uint8_t *in, size_t len, BIGNUM *ret); |
| 249 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 250 | // BN_bn2le_padded serialises the absolute value of |in| to |out| as a |
| 251 | // little-endian integer, which must have |len| of space available, padding |
| 252 | // out the remainder of out with zeros. If |len| is smaller than |BN_num_bytes|, |
| 253 | // the function fails and returns 0. Otherwise, it returns 1. |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 254 | OPENSSL_EXPORT int BN_bn2le_padded(uint8_t *out, size_t len, const BIGNUM *in); |
| 255 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 256 | // BN_bn2bin_padded serialises the absolute value of |in| to |out| as a |
| 257 | // big-endian integer. The integer is padded with leading zeros up to size |
| 258 | // |len|. If |len| is smaller than |BN_num_bytes|, the function fails and |
| 259 | // returns 0. Otherwise, it returns 1. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 260 | OPENSSL_EXPORT int BN_bn2bin_padded(uint8_t *out, size_t len, const BIGNUM *in); |
| 261 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 262 | // BN_bn2cbb_padded behaves like |BN_bn2bin_padded| but writes to a |CBB|. |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 263 | OPENSSL_EXPORT int BN_bn2cbb_padded(CBB *out, size_t len, const BIGNUM *in); |
| 264 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 265 | // BN_bn2hex returns an allocated string that contains a NUL-terminated, hex |
| 266 | // representation of |bn|. If |bn| is negative, the first char in the resulting |
| 267 | // string will be '-'. Returns NULL on allocation failure. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 268 | OPENSSL_EXPORT char *BN_bn2hex(const BIGNUM *bn); |
| 269 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 270 | // BN_hex2bn parses the leading hex number from |in|, which may be proceeded by |
| 271 | // a '-' to indicate a negative number and may contain trailing, non-hex data. |
| 272 | // If |outp| is not NULL, it constructs a BIGNUM equal to the hex number and |
| 273 | // stores it in |*outp|. If |*outp| is NULL then it allocates a new BIGNUM and |
| 274 | // updates |*outp|. It returns the number of bytes of |in| processed or zero on |
| 275 | // error. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 276 | OPENSSL_EXPORT int BN_hex2bn(BIGNUM **outp, const char *in); |
| 277 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 278 | // BN_bn2dec returns an allocated string that contains a NUL-terminated, |
| 279 | // decimal representation of |bn|. If |bn| is negative, the first char in the |
| 280 | // resulting string will be '-'. Returns NULL on allocation failure. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 281 | OPENSSL_EXPORT char *BN_bn2dec(const BIGNUM *a); |
| 282 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 283 | // BN_dec2bn parses the leading decimal number from |in|, which may be |
| 284 | // proceeded by a '-' to indicate a negative number and may contain trailing, |
| 285 | // non-decimal data. If |outp| is not NULL, it constructs a BIGNUM equal to the |
| 286 | // decimal number and stores it in |*outp|. If |*outp| is NULL then it |
| 287 | // allocates a new BIGNUM and updates |*outp|. It returns the number of bytes |
| 288 | // of |in| processed or zero on error. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 289 | OPENSSL_EXPORT int BN_dec2bn(BIGNUM **outp, const char *in); |
| 290 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 291 | // BN_asc2bn acts like |BN_dec2bn| or |BN_hex2bn| depending on whether |in| |
| 292 | // begins with "0X" or "0x" (indicating hex) or not (indicating decimal). A |
| 293 | // leading '-' is still permitted and comes before the optional 0X/0x. It |
| 294 | // returns one on success or zero on error. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 295 | OPENSSL_EXPORT int BN_asc2bn(BIGNUM **outp, const char *in); |
| 296 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 297 | // BN_print writes a hex encoding of |a| to |bio|. It returns one on success |
| 298 | // and zero on error. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 299 | OPENSSL_EXPORT int BN_print(BIO *bio, const BIGNUM *a); |
| 300 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 301 | // BN_print_fp acts like |BIO_print|, but wraps |fp| in a |BIO| first. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 302 | OPENSSL_EXPORT int BN_print_fp(FILE *fp, const BIGNUM *a); |
| 303 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 304 | // BN_get_word returns the absolute value of |bn| as a single word. If |bn| is |
| 305 | // too large to be represented as a single word, the maximum possible value |
| 306 | // will be returned. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 307 | OPENSSL_EXPORT BN_ULONG BN_get_word(const BIGNUM *bn); |
| 308 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 309 | // BN_get_u64 sets |*out| to the absolute value of |bn| as a |uint64_t| and |
| 310 | // returns one. If |bn| is too large to be represented as a |uint64_t|, it |
| 311 | // returns zero. |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 312 | OPENSSL_EXPORT int BN_get_u64(const BIGNUM *bn, uint64_t *out); |
| 313 | |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 314 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 315 | // ASN.1 functions. |
Kenny Root | b849459 | 2015-09-25 02:29:14 +0000 | [diff] [blame] | 316 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 317 | // BN_parse_asn1_unsigned parses a non-negative DER INTEGER from |cbs| writes |
| 318 | // the result to |ret|. It returns one on success and zero on failure. |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 319 | OPENSSL_EXPORT int BN_parse_asn1_unsigned(CBS *cbs, BIGNUM *ret); |
Kenny Root | b849459 | 2015-09-25 02:29:14 +0000 | [diff] [blame] | 320 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 321 | // BN_marshal_asn1 marshals |bn| as a non-negative DER INTEGER and appends the |
| 322 | // result to |cbb|. It returns one on success and zero on failure. |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 323 | OPENSSL_EXPORT int BN_marshal_asn1(CBB *cbb, const BIGNUM *bn); |
Kenny Root | b849459 | 2015-09-25 02:29:14 +0000 | [diff] [blame] | 324 | |
| 325 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 326 | // BIGNUM pools. |
| 327 | // |
| 328 | // Certain BIGNUM operations need to use many temporary variables and |
| 329 | // allocating and freeing them can be quite slow. Thus such operations typically |
| 330 | // take a |BN_CTX| parameter, which contains a pool of |BIGNUMs|. The |ctx| |
| 331 | // argument to a public function may be NULL, in which case a local |BN_CTX| |
| 332 | // will be created just for the lifetime of that call. |
| 333 | // |
| 334 | // A function must call |BN_CTX_start| first. Then, |BN_CTX_get| may be called |
| 335 | // repeatedly to obtain temporary |BIGNUM|s. All |BN_CTX_get| calls must be made |
| 336 | // before calling any other functions that use the |ctx| as an argument. |
| 337 | // |
| 338 | // Finally, |BN_CTX_end| must be called before returning from the function. |
| 339 | // When |BN_CTX_end| is called, the |BIGNUM| pointers obtained from |
| 340 | // |BN_CTX_get| become invalid. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 341 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 342 | // BN_CTX_new returns a new, empty BN_CTX or NULL on allocation failure. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 343 | OPENSSL_EXPORT BN_CTX *BN_CTX_new(void); |
| 344 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 345 | // BN_CTX_free frees all BIGNUMs contained in |ctx| and then frees |ctx| |
| 346 | // itself. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 347 | OPENSSL_EXPORT void BN_CTX_free(BN_CTX *ctx); |
| 348 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 349 | // BN_CTX_start "pushes" a new entry onto the |ctx| stack and allows future |
| 350 | // calls to |BN_CTX_get|. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 351 | OPENSSL_EXPORT void BN_CTX_start(BN_CTX *ctx); |
| 352 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 353 | // BN_CTX_get returns a new |BIGNUM|, or NULL on allocation failure. Once |
| 354 | // |BN_CTX_get| has returned NULL, all future calls will also return NULL until |
| 355 | // |BN_CTX_end| is called. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 356 | OPENSSL_EXPORT BIGNUM *BN_CTX_get(BN_CTX *ctx); |
| 357 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 358 | // BN_CTX_end invalidates all |BIGNUM|s returned from |BN_CTX_get| since the |
| 359 | // matching |BN_CTX_start| call. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 360 | OPENSSL_EXPORT void BN_CTX_end(BN_CTX *ctx); |
| 361 | |
| 362 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 363 | // Simple arithmetic |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 364 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 365 | // BN_add sets |r| = |a| + |b|, where |r| may be the same pointer as either |a| |
| 366 | // or |b|. It returns one on success and zero on allocation failure. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 367 | OPENSSL_EXPORT int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); |
| 368 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 369 | // BN_uadd sets |r| = |a| + |b|, where |a| and |b| are non-negative and |r| may |
| 370 | // be the same pointer as either |a| or |b|. It returns one on success and zero |
| 371 | // on allocation failure. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 372 | OPENSSL_EXPORT int BN_uadd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); |
| 373 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 374 | // BN_add_word adds |w| to |a|. It returns one on success and zero otherwise. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 375 | OPENSSL_EXPORT int BN_add_word(BIGNUM *a, BN_ULONG w); |
| 376 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 377 | // BN_sub sets |r| = |a| - |b|, where |r| may be the same pointer as either |a| |
| 378 | // or |b|. It returns one on success and zero on allocation failure. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 379 | OPENSSL_EXPORT int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); |
| 380 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 381 | // BN_usub sets |r| = |a| - |b|, where |a| and |b| are non-negative integers, |
| 382 | // |b| < |a| and |r| may be the same pointer as either |a| or |b|. It returns |
| 383 | // one on success and zero on allocation failure. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 384 | OPENSSL_EXPORT int BN_usub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); |
| 385 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 386 | // BN_sub_word subtracts |w| from |a|. It returns one on success and zero on |
| 387 | // allocation failure. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 388 | OPENSSL_EXPORT int BN_sub_word(BIGNUM *a, BN_ULONG w); |
| 389 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 390 | // BN_mul sets |r| = |a| * |b|, where |r| may be the same pointer as |a| or |
| 391 | // |b|. Returns one on success and zero otherwise. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 392 | OPENSSL_EXPORT int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, |
| 393 | BN_CTX *ctx); |
| 394 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 395 | // BN_mul_word sets |bn| = |bn| * |w|. It returns one on success or zero on |
| 396 | // allocation failure. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 397 | OPENSSL_EXPORT int BN_mul_word(BIGNUM *bn, BN_ULONG w); |
| 398 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 399 | // BN_sqr sets |r| = |a|^2 (i.e. squares), where |r| may be the same pointer as |
| 400 | // |a|. Returns one on success and zero otherwise. This is more efficient than |
| 401 | // BN_mul(r, a, a, ctx). |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 402 | OPENSSL_EXPORT int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx); |
| 403 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 404 | // BN_div divides |numerator| by |divisor| and places the result in |quotient| |
| 405 | // and the remainder in |rem|. Either of |quotient| or |rem| may be NULL, in |
| 406 | // which case the respective value is not returned. The result is rounded |
| 407 | // towards zero; thus if |numerator| is negative, the remainder will be zero or |
| 408 | // negative. It returns one on success or zero on error. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 409 | OPENSSL_EXPORT int BN_div(BIGNUM *quotient, BIGNUM *rem, |
| 410 | const BIGNUM *numerator, const BIGNUM *divisor, |
| 411 | BN_CTX *ctx); |
| 412 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 413 | // BN_div_word sets |numerator| = |numerator|/|divisor| and returns the |
| 414 | // remainder or (BN_ULONG)-1 on error. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 415 | OPENSSL_EXPORT BN_ULONG BN_div_word(BIGNUM *numerator, BN_ULONG divisor); |
| 416 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 417 | // BN_sqrt sets |*out_sqrt| (which may be the same |BIGNUM| as |in|) to the |
| 418 | // square root of |in|, using |ctx|. It returns one on success or zero on |
| 419 | // error. Negative numbers and non-square numbers will result in an error with |
| 420 | // appropriate errors on the error queue. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 421 | OPENSSL_EXPORT int BN_sqrt(BIGNUM *out_sqrt, const BIGNUM *in, BN_CTX *ctx); |
| 422 | |
| 423 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 424 | // Comparison functions |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 425 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 426 | // BN_cmp returns a value less than, equal to or greater than zero if |a| is |
| 427 | // less than, equal to or greater than |b|, respectively. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 428 | OPENSSL_EXPORT int BN_cmp(const BIGNUM *a, const BIGNUM *b); |
| 429 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 430 | // BN_cmp_word is like |BN_cmp| except it takes its second argument as a |
| 431 | // |BN_ULONG| instead of a |BIGNUM|. |
David Benjamin | c895d6b | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 432 | OPENSSL_EXPORT int BN_cmp_word(const BIGNUM *a, BN_ULONG b); |
| 433 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 434 | // BN_ucmp returns a value less than, equal to or greater than zero if the |
| 435 | // absolute value of |a| is less than, equal to or greater than the absolute |
| 436 | // value of |b|, respectively. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 437 | OPENSSL_EXPORT int BN_ucmp(const BIGNUM *a, const BIGNUM *b); |
| 438 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 439 | // BN_equal_consttime returns one if |a| is equal to |b|, and zero otherwise. |
| 440 | // It takes an amount of time dependent on the sizes of |a| and |b|, but |
| 441 | // independent of the contents (including the signs) of |a| and |b|. |
David Benjamin | 9aaebef | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 442 | OPENSSL_EXPORT int BN_equal_consttime(const BIGNUM *a, const BIGNUM *b); |
| 443 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 444 | // BN_abs_is_word returns one if the absolute value of |bn| equals |w| and zero |
| 445 | // otherwise. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 446 | OPENSSL_EXPORT int BN_abs_is_word(const BIGNUM *bn, BN_ULONG w); |
| 447 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 448 | // BN_is_zero returns one if |bn| is zero and zero otherwise. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 449 | OPENSSL_EXPORT int BN_is_zero(const BIGNUM *bn); |
| 450 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 451 | // BN_is_one returns one if |bn| equals one and zero otherwise. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 452 | OPENSSL_EXPORT int BN_is_one(const BIGNUM *bn); |
| 453 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 454 | // BN_is_word returns one if |bn| is exactly |w| and zero otherwise. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 455 | OPENSSL_EXPORT int BN_is_word(const BIGNUM *bn, BN_ULONG w); |
| 456 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 457 | // BN_is_odd returns one if |bn| is odd and zero otherwise. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 458 | OPENSSL_EXPORT int BN_is_odd(const BIGNUM *bn); |
| 459 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 460 | // BN_is_pow2 returns 1 if |a| is a power of two, and 0 otherwise. |
Robert Sloan | 5d62578 | 2017-02-13 09:55:39 -0800 | [diff] [blame] | 461 | OPENSSL_EXPORT int BN_is_pow2(const BIGNUM *a); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 462 | |
Robert Sloan | ab8b888 | 2018-03-26 11:39:51 -0700 | [diff] [blame^] | 463 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 464 | // Bitwise operations. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 465 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 466 | // BN_lshift sets |r| equal to |a| << n. The |a| and |r| arguments may be the |
| 467 | // same |BIGNUM|. It returns one on success and zero on allocation failure. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 468 | OPENSSL_EXPORT int BN_lshift(BIGNUM *r, const BIGNUM *a, int n); |
| 469 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 470 | // BN_lshift1 sets |r| equal to |a| << 1, where |r| and |a| may be the same |
| 471 | // pointer. It returns one on success and zero on allocation failure. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 472 | OPENSSL_EXPORT int BN_lshift1(BIGNUM *r, const BIGNUM *a); |
| 473 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 474 | // BN_rshift sets |r| equal to |a| >> n, where |r| and |a| may be the same |
| 475 | // pointer. It returns one on success and zero on allocation failure. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 476 | OPENSSL_EXPORT int BN_rshift(BIGNUM *r, const BIGNUM *a, int n); |
| 477 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 478 | // BN_rshift1 sets |r| equal to |a| >> 1, where |r| and |a| may be the same |
| 479 | // pointer. It returns one on success and zero on allocation failure. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 480 | OPENSSL_EXPORT int BN_rshift1(BIGNUM *r, const BIGNUM *a); |
| 481 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 482 | // BN_set_bit sets the |n|th, least-significant bit in |a|. For example, if |a| |
| 483 | // is 2 then setting bit zero will make it 3. It returns one on success or zero |
| 484 | // on allocation failure. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 485 | OPENSSL_EXPORT int BN_set_bit(BIGNUM *a, int n); |
| 486 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 487 | // BN_clear_bit clears the |n|th, least-significant bit in |a|. For example, if |
| 488 | // |a| is 3, clearing bit zero will make it two. It returns one on success or |
| 489 | // zero on allocation failure. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 490 | OPENSSL_EXPORT int BN_clear_bit(BIGNUM *a, int n); |
| 491 | |
Robert Sloan | 99319a1 | 2017-11-27 10:32:46 -0800 | [diff] [blame] | 492 | // BN_is_bit_set returns one if the |n|th least-significant bit in |a| exists |
| 493 | // and is set. Otherwise, it returns zero. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 494 | OPENSSL_EXPORT int BN_is_bit_set(const BIGNUM *a, int n); |
| 495 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 496 | // BN_mask_bits truncates |a| so that it is only |n| bits long. It returns one |
Robert Sloan | ab8b888 | 2018-03-26 11:39:51 -0700 | [diff] [blame^] | 497 | // on success or zero if |n| is negative. |
| 498 | // |
| 499 | // This differs from OpenSSL which additionally returns zero if |a|'s word |
| 500 | // length is less than or equal to |n|, rounded down to a number of words. Note |
| 501 | // word size is platform-dependent, so this behavior is also difficult to rely |
| 502 | // on in OpenSSL and not very useful. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 503 | OPENSSL_EXPORT int BN_mask_bits(BIGNUM *a, int n); |
| 504 | |
Robert Sloan | ab8b888 | 2018-03-26 11:39:51 -0700 | [diff] [blame^] | 505 | // BN_count_low_zero_bits returns the number of low-order zero bits in |bn|, or |
| 506 | // the number of factors of two which divide it. It returns zero if |bn| is |
| 507 | // zero. |
| 508 | OPENSSL_EXPORT int BN_count_low_zero_bits(const BIGNUM *bn); |
| 509 | |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 510 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 511 | // Modulo arithmetic. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 512 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 513 | // BN_mod_word returns |a| mod |w| or (BN_ULONG)-1 on error. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 514 | OPENSSL_EXPORT BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w); |
| 515 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 516 | // BN_mod_pow2 sets |r| = |a| mod 2^|e|. It returns 1 on success and |
| 517 | // 0 on error. |
Robert Sloan | 5d62578 | 2017-02-13 09:55:39 -0800 | [diff] [blame] | 518 | OPENSSL_EXPORT int BN_mod_pow2(BIGNUM *r, const BIGNUM *a, size_t e); |
| 519 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 520 | // BN_nnmod_pow2 sets |r| = |a| mod 2^|e| where |r| is always positive. |
| 521 | // It returns 1 on success and 0 on error. |
Robert Sloan | 5d62578 | 2017-02-13 09:55:39 -0800 | [diff] [blame] | 522 | OPENSSL_EXPORT int BN_nnmod_pow2(BIGNUM *r, const BIGNUM *a, size_t e); |
| 523 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 524 | // BN_mod is a helper macro that calls |BN_div| and discards the quotient. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 525 | #define BN_mod(rem, numerator, divisor, ctx) \ |
| 526 | BN_div(NULL, (rem), (numerator), (divisor), (ctx)) |
| 527 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 528 | // BN_nnmod is a non-negative modulo function. It acts like |BN_mod|, but 0 <= |
| 529 | // |rem| < |divisor| is always true. It returns one on success and zero on |
| 530 | // error. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 531 | OPENSSL_EXPORT int BN_nnmod(BIGNUM *rem, const BIGNUM *numerator, |
| 532 | const BIGNUM *divisor, BN_CTX *ctx); |
| 533 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 534 | // BN_mod_add sets |r| = |a| + |b| mod |m|. It returns one on success and zero |
| 535 | // on error. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 536 | OPENSSL_EXPORT int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, |
| 537 | const BIGNUM *m, BN_CTX *ctx); |
| 538 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 539 | // BN_mod_add_quick acts like |BN_mod_add| but requires that |a| and |b| be |
| 540 | // non-negative and less than |m|. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 541 | OPENSSL_EXPORT int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, |
| 542 | const BIGNUM *m); |
| 543 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 544 | // BN_mod_sub sets |r| = |a| - |b| mod |m|. It returns one on success and zero |
| 545 | // on error. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 546 | OPENSSL_EXPORT int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, |
| 547 | const BIGNUM *m, BN_CTX *ctx); |
| 548 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 549 | // BN_mod_sub_quick acts like |BN_mod_sub| but requires that |a| and |b| be |
| 550 | // non-negative and less than |m|. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 551 | OPENSSL_EXPORT int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, |
| 552 | const BIGNUM *m); |
| 553 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 554 | // BN_mod_mul sets |r| = |a|*|b| mod |m|. It returns one on success and zero |
| 555 | // on error. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 556 | OPENSSL_EXPORT int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, |
| 557 | const BIGNUM *m, BN_CTX *ctx); |
| 558 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 559 | // BN_mod_sqr sets |r| = |a|^2 mod |m|. It returns one on success and zero |
| 560 | // on error. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 561 | OPENSSL_EXPORT int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, |
| 562 | BN_CTX *ctx); |
| 563 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 564 | // BN_mod_lshift sets |r| = (|a| << n) mod |m|, where |r| and |a| may be the |
| 565 | // same pointer. It returns one on success and zero on error. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 566 | OPENSSL_EXPORT int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, |
| 567 | const BIGNUM *m, BN_CTX *ctx); |
| 568 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 569 | // BN_mod_lshift_quick acts like |BN_mod_lshift| but requires that |a| be |
| 570 | // non-negative and less than |m|. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 571 | OPENSSL_EXPORT int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, |
| 572 | const BIGNUM *m); |
| 573 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 574 | // BN_mod_lshift1 sets |r| = (|a| << 1) mod |m|, where |r| and |a| may be the |
| 575 | // same pointer. It returns one on success and zero on error. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 576 | OPENSSL_EXPORT int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, |
| 577 | BN_CTX *ctx); |
| 578 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 579 | // BN_mod_lshift1_quick acts like |BN_mod_lshift1| but requires that |a| be |
| 580 | // non-negative and less than |m|. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 581 | OPENSSL_EXPORT int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, |
| 582 | const BIGNUM *m); |
| 583 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 584 | // BN_mod_sqrt returns a newly-allocated |BIGNUM|, r, such that |
| 585 | // r^2 == a (mod p). |p| must be a prime. It returns NULL on error or if |a| is |
| 586 | // not a square mod |p|. In the latter case, it will add |BN_R_NOT_A_SQUARE| to |
| 587 | // the error queue. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 588 | OPENSSL_EXPORT BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p, |
| 589 | BN_CTX *ctx); |
| 590 | |
| 591 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 592 | // Random and prime number generation. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 593 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 594 | // The following are values for the |top| parameter of |BN_rand|. |
Steven Valdez | 909b19f | 2016-11-21 15:35:44 -0500 | [diff] [blame] | 595 | #define BN_RAND_TOP_ANY (-1) |
David Benjamin | f0c4a6c | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 596 | #define BN_RAND_TOP_ONE 0 |
| 597 | #define BN_RAND_TOP_TWO 1 |
| 598 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 599 | // The following are values for the |bottom| parameter of |BN_rand|. |
David Benjamin | f0c4a6c | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 600 | #define BN_RAND_BOTTOM_ANY 0 |
| 601 | #define BN_RAND_BOTTOM_ODD 1 |
| 602 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 603 | // BN_rand sets |rnd| to a random number of length |bits|. It returns one on |
| 604 | // success and zero otherwise. |
| 605 | // |
| 606 | // |top| must be one of the |BN_RAND_TOP_*| values. If |BN_RAND_TOP_ONE|, the |
| 607 | // most-significant bit, if any, will be set. If |BN_RAND_TOP_TWO|, the two |
| 608 | // most significant bits, if any, will be set. If |BN_RAND_TOP_ANY|, no extra |
| 609 | // action will be taken and |BN_num_bits(rnd)| may not equal |bits| if the most |
| 610 | // significant bits randomly ended up as zeros. |
| 611 | // |
| 612 | // |bottom| must be one of the |BN_RAND_BOTTOM_*| values. If |
| 613 | // |BN_RAND_BOTTOM_ODD|, the least-significant bit, if any, will be set. If |
| 614 | // |BN_RAND_BOTTOM_ANY|, no extra action will be taken. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 615 | OPENSSL_EXPORT int BN_rand(BIGNUM *rnd, int bits, int top, int bottom); |
| 616 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 617 | // BN_pseudo_rand is an alias for |BN_rand|. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 618 | OPENSSL_EXPORT int BN_pseudo_rand(BIGNUM *rnd, int bits, int top, int bottom); |
| 619 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 620 | // BN_rand_range is equivalent to |BN_rand_range_ex| with |min_inclusive| set |
| 621 | // to zero and |max_exclusive| set to |range|. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 622 | OPENSSL_EXPORT int BN_rand_range(BIGNUM *rnd, const BIGNUM *range); |
| 623 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 624 | // BN_rand_range_ex sets |rnd| to a random value in |
| 625 | // [min_inclusive..max_exclusive). It returns one on success and zero |
| 626 | // otherwise. |
David Benjamin | c895d6b | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 627 | OPENSSL_EXPORT int BN_rand_range_ex(BIGNUM *r, BN_ULONG min_inclusive, |
| 628 | const BIGNUM *max_exclusive); |
| 629 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 630 | // BN_pseudo_rand_range is an alias for BN_rand_range. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 631 | OPENSSL_EXPORT int BN_pseudo_rand_range(BIGNUM *rnd, const BIGNUM *range); |
| 632 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 633 | // BN_GENCB holds a callback function that is used by generation functions that |
| 634 | // can take a very long time to complete. Use |BN_GENCB_set| to initialise a |
| 635 | // |BN_GENCB| structure. |
| 636 | // |
| 637 | // The callback receives the address of that |BN_GENCB| structure as its last |
| 638 | // argument and the user is free to put an arbitrary pointer in |arg|. The other |
| 639 | // arguments are set as follows: |
| 640 | // event=BN_GENCB_GENERATED, n=i: after generating the i'th possible prime |
| 641 | // number. |
| 642 | // event=BN_GENCB_PRIME_TEST, n=-1: when finished trial division primality |
| 643 | // checks. |
| 644 | // event=BN_GENCB_PRIME_TEST, n=i: when the i'th primality test has finished. |
| 645 | // |
| 646 | // The callback can return zero to abort the generation progress or one to |
| 647 | // allow it to continue. |
| 648 | // |
| 649 | // When other code needs to call a BN generation function it will often take a |
| 650 | // BN_GENCB argument and may call the function with other argument values. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 651 | #define BN_GENCB_GENERATED 0 |
| 652 | #define BN_GENCB_PRIME_TEST 1 |
| 653 | |
| 654 | struct bn_gencb_st { |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 655 | void *arg; // callback-specific data |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 656 | int (*callback)(int event, int n, struct bn_gencb_st *); |
| 657 | }; |
| 658 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 659 | // BN_GENCB_set configures |callback| to call |f| and sets |callout->arg| to |
| 660 | // |arg|. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 661 | OPENSSL_EXPORT void BN_GENCB_set(BN_GENCB *callback, |
| 662 | int (*f)(int event, int n, |
| 663 | struct bn_gencb_st *), |
| 664 | void *arg); |
| 665 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 666 | // BN_GENCB_call calls |callback|, if not NULL, and returns the return value of |
| 667 | // the callback, or 1 if |callback| is NULL. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 668 | OPENSSL_EXPORT int BN_GENCB_call(BN_GENCB *callback, int event, int n); |
| 669 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 670 | // BN_generate_prime_ex sets |ret| to a prime number of |bits| length. If safe |
| 671 | // is non-zero then the prime will be such that (ret-1)/2 is also a prime. |
| 672 | // (This is needed for Diffie-Hellman groups to ensure that the only subgroups |
| 673 | // are of size 2 and (p-1)/2.). |
| 674 | // |
| 675 | // If |add| is not NULL, the prime will fulfill the condition |ret| % |add| == |
| 676 | // |rem| in order to suit a given generator. (If |rem| is NULL then |ret| % |
| 677 | // |add| == 1.) |
| 678 | // |
| 679 | // If |cb| is not NULL, it will be called during processing to give an |
| 680 | // indication of progress. See the comments for |BN_GENCB|. It returns one on |
| 681 | // success and zero otherwise. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 682 | OPENSSL_EXPORT int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, |
| 683 | const BIGNUM *add, const BIGNUM *rem, |
| 684 | BN_GENCB *cb); |
| 685 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 686 | // BN_prime_checks is magic value that can be used as the |checks| argument to |
| 687 | // the primality testing functions in order to automatically select a number of |
| 688 | // Miller-Rabin checks that gives a false positive rate of ~2^{-80}. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 689 | #define BN_prime_checks 0 |
| 690 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 691 | // bn_primality_result_t enumerates the outcomes of primality-testing. |
Robert Sloan | 9254e68 | 2017-04-24 09:42:06 -0700 | [diff] [blame] | 692 | enum bn_primality_result_t { |
| 693 | bn_probably_prime, |
| 694 | bn_composite, |
| 695 | bn_non_prime_power_composite, |
| 696 | }; |
| 697 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 698 | // BN_enhanced_miller_rabin_primality_test tests whether |w| is probably a prime |
| 699 | // number using the Enhanced Miller-Rabin Test (FIPS 186-4 C.3.2) with |
| 700 | // |iterations| iterations and returns the result in |out_result|. Enhanced |
| 701 | // Miller-Rabin tests primality for odd integers greater than 3, returning |
| 702 | // |bn_probably_prime| if the number is probably prime, |
| 703 | // |bn_non_prime_power_composite| if the number is a composite that is not the |
| 704 | // power of a single prime, and |bn_composite| otherwise. If |iterations| is |
| 705 | // |BN_prime_checks|, then a value that results in a false positive rate lower |
| 706 | // than the number-field sieve security level of |w| is used. It returns one on |
| 707 | // success and zero on failure. If |cb| is not NULL, then it is called during |
| 708 | // each iteration of the primality test. |
Robert Sloan | 9254e68 | 2017-04-24 09:42:06 -0700 | [diff] [blame] | 709 | int BN_enhanced_miller_rabin_primality_test( |
| 710 | enum bn_primality_result_t *out_result, const BIGNUM *w, int iterations, |
| 711 | BN_CTX *ctx, BN_GENCB *cb); |
| 712 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 713 | // BN_primality_test sets |*is_probably_prime| to one if |candidate| is |
| 714 | // probably a prime number by the Miller-Rabin test or zero if it's certainly |
| 715 | // not. |
| 716 | // |
| 717 | // If |do_trial_division| is non-zero then |candidate| will be tested against a |
| 718 | // list of small primes before Miller-Rabin tests. The probability of this |
| 719 | // function returning a false positive is 2^{2*checks}. If |checks| is |
| 720 | // |BN_prime_checks| then a value that results in a false positive rate lower |
| 721 | // than the number-field sieve security level of |candidate| is used. If |cb| is |
| 722 | // not NULL then it is called during the checking process. See the comment above |
| 723 | // |BN_GENCB|. |
| 724 | // |
| 725 | // The function returns one on success and zero on error. |
| 726 | // |
| 727 | // (If you are unsure whether you want |do_trial_division|, don't set it.) |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 728 | OPENSSL_EXPORT int BN_primality_test(int *is_probably_prime, |
| 729 | const BIGNUM *candidate, int checks, |
| 730 | BN_CTX *ctx, int do_trial_division, |
| 731 | BN_GENCB *cb); |
| 732 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 733 | // BN_is_prime_fasttest_ex returns one if |candidate| is probably a prime |
| 734 | // number by the Miller-Rabin test, zero if it's certainly not and -1 on error. |
| 735 | // |
| 736 | // If |do_trial_division| is non-zero then |candidate| will be tested against a |
| 737 | // list of small primes before Miller-Rabin tests. The probability of this |
| 738 | // function returning one when |candidate| is composite is 2^{2*checks}. If |
| 739 | // |checks| is |BN_prime_checks| then a value that results in a false positive |
| 740 | // rate lower than the number-field sieve security level of |candidate| is used. |
| 741 | // If |cb| is not NULL then it is called during the checking process. See the |
| 742 | // comment above |BN_GENCB|. |
| 743 | // |
| 744 | // WARNING: deprecated. Use |BN_primality_test|. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 745 | OPENSSL_EXPORT int BN_is_prime_fasttest_ex(const BIGNUM *candidate, int checks, |
| 746 | BN_CTX *ctx, int do_trial_division, |
| 747 | BN_GENCB *cb); |
| 748 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 749 | // BN_is_prime_ex acts the same as |BN_is_prime_fasttest_ex| with |
| 750 | // |do_trial_division| set to zero. |
| 751 | // |
| 752 | // WARNING: deprecated: Use |BN_primality_test|. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 753 | OPENSSL_EXPORT int BN_is_prime_ex(const BIGNUM *candidate, int checks, |
| 754 | BN_CTX *ctx, BN_GENCB *cb); |
| 755 | |
| 756 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 757 | // Number theory functions |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 758 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 759 | // BN_gcd sets |r| = gcd(|a|, |b|). It returns one on success and zero |
| 760 | // otherwise. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 761 | OPENSSL_EXPORT int BN_gcd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, |
| 762 | BN_CTX *ctx); |
| 763 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 764 | // BN_mod_inverse sets |out| equal to |a|^-1, mod |n|. If |out| is NULL, a |
| 765 | // fresh BIGNUM is allocated. It returns the result or NULL on error. |
| 766 | // |
| 767 | // If |n| is even then the operation is performed using an algorithm that avoids |
| 768 | // some branches but which isn't constant-time. This function shouldn't be used |
| 769 | // for secret values; use |BN_mod_inverse_blinded| instead. Or, if |n| is |
| 770 | // guaranteed to be prime, use |
| 771 | // |BN_mod_exp_mont_consttime(out, a, m_minus_2, m, ctx, m_mont)|, taking |
| 772 | // advantage of Fermat's Little Theorem. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 773 | OPENSSL_EXPORT BIGNUM *BN_mod_inverse(BIGNUM *out, const BIGNUM *a, |
| 774 | const BIGNUM *n, BN_CTX *ctx); |
| 775 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 776 | // BN_mod_inverse_blinded sets |out| equal to |a|^-1, mod |n|, where |n| is the |
| 777 | // Montgomery modulus for |mont|. |a| must be non-negative and must be less |
| 778 | // than |n|. |n| must be greater than 1. |a| is blinded (masked by a random |
| 779 | // value) to protect it against side-channel attacks. On failure, if the failure |
| 780 | // was caused by |a| having no inverse mod |n| then |*out_no_inverse| will be |
| 781 | // set to one; otherwise it will be set to zero. |
Robert Sloan | ab8b888 | 2018-03-26 11:39:51 -0700 | [diff] [blame^] | 782 | // |
| 783 | // Note this function may incorrectly report |a| has no inverse if the random |
| 784 | // blinding value has no inverse. It should only be used when |n| has few |
| 785 | // non-invertible elements, such as an RSA modulus. |
David Benjamin | c895d6b | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 786 | int BN_mod_inverse_blinded(BIGNUM *out, int *out_no_inverse, const BIGNUM *a, |
| 787 | const BN_MONT_CTX *mont, BN_CTX *ctx); |
| 788 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 789 | // BN_mod_inverse_odd sets |out| equal to |a|^-1, mod |n|. |a| must be |
| 790 | // non-negative and must be less than |n|. |n| must be odd. This function |
| 791 | // shouldn't be used for secret values; use |BN_mod_inverse_blinded| instead. |
| 792 | // Or, if |n| is guaranteed to be prime, use |
| 793 | // |BN_mod_exp_mont_consttime(out, a, m_minus_2, m, ctx, m_mont)|, taking |
| 794 | // advantage of Fermat's Little Theorem. It returns one on success or zero on |
| 795 | // failure. On failure, if the failure was caused by |a| having no inverse mod |
| 796 | // |n| then |*out_no_inverse| will be set to one; otherwise it will be set to |
| 797 | // zero. |
David Benjamin | c895d6b | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 798 | int BN_mod_inverse_odd(BIGNUM *out, int *out_no_inverse, const BIGNUM *a, |
| 799 | const BIGNUM *n, BN_CTX *ctx); |
Kenny Root | b849459 | 2015-09-25 02:29:14 +0000 | [diff] [blame] | 800 | |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 801 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 802 | // Montgomery arithmetic. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 803 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 804 | // BN_MONT_CTX contains the precomputed values needed to work in a specific |
| 805 | // Montgomery domain. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 806 | |
Robert Sloan | 8542c08 | 2018-02-05 09:07:34 -0800 | [diff] [blame] | 807 | // BN_MONT_CTX_new_for_modulus returns a fresh |BN_MONT_CTX| given the modulus, |
| 808 | // |mod| or NULL on error. |
| 809 | OPENSSL_EXPORT BN_MONT_CTX *BN_MONT_CTX_new_for_modulus(const BIGNUM *mod, |
| 810 | BN_CTX *ctx); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 811 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 812 | // BN_MONT_CTX_free frees memory associated with |mont|. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 813 | OPENSSL_EXPORT void BN_MONT_CTX_free(BN_MONT_CTX *mont); |
| 814 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 815 | // BN_MONT_CTX_copy sets |to| equal to |from|. It returns |to| on success or |
| 816 | // NULL on error. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 817 | OPENSSL_EXPORT BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 818 | const BN_MONT_CTX *from); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 819 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 820 | // BN_MONT_CTX_set_locked takes |lock| and checks whether |*pmont| is NULL. If |
| 821 | // so, it creates a new |BN_MONT_CTX| and sets the modulus for it to |mod|. It |
| 822 | // then stores it as |*pmont|. It returns one on success and zero on error. |
| 823 | // |
| 824 | // If |*pmont| is already non-NULL then it does nothing and returns one. |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 825 | int BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, CRYPTO_MUTEX *lock, |
| 826 | const BIGNUM *mod, BN_CTX *bn_ctx); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 827 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 828 | // BN_to_montgomery sets |ret| equal to |a| in the Montgomery domain. |a| is |
| 829 | // assumed to be in the range [0, n), where |n| is the Montgomery modulus. It |
| 830 | // returns one on success or zero on error. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 831 | OPENSSL_EXPORT int BN_to_montgomery(BIGNUM *ret, const BIGNUM *a, |
| 832 | const BN_MONT_CTX *mont, BN_CTX *ctx); |
| 833 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 834 | // BN_from_montgomery sets |ret| equal to |a| * R^-1, i.e. translates values out |
| 835 | // of the Montgomery domain. |a| is assumed to be in the range [0, n), where |n| |
| 836 | // is the Montgomery modulus. It returns one on success or zero on error. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 837 | OPENSSL_EXPORT int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, |
| 838 | const BN_MONT_CTX *mont, BN_CTX *ctx); |
| 839 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 840 | // BN_mod_mul_montgomery set |r| equal to |a| * |b|, in the Montgomery domain. |
| 841 | // Both |a| and |b| must already be in the Montgomery domain (by |
| 842 | // |BN_to_montgomery|). In particular, |a| and |b| are assumed to be in the |
| 843 | // range [0, n), where |n| is the Montgomery modulus. It returns one on success |
| 844 | // or zero on error. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 845 | OPENSSL_EXPORT int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, |
| 846 | const BIGNUM *b, |
| 847 | const BN_MONT_CTX *mont, BN_CTX *ctx); |
| 848 | |
| 849 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 850 | // Exponentiation. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 851 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 852 | // BN_exp sets |r| equal to |a|^{|p|}. It does so with a square-and-multiply |
| 853 | // algorithm that leaks side-channel information. It returns one on success or |
| 854 | // zero otherwise. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 855 | OPENSSL_EXPORT int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, |
| 856 | BN_CTX *ctx); |
| 857 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 858 | // BN_mod_exp sets |r| equal to |a|^{|p|} mod |m|. It does so with the best |
| 859 | // algorithm for the values provided. It returns one on success or zero |
| 860 | // otherwise. The |BN_mod_exp_mont_consttime| variant must be used if the |
| 861 | // exponent is secret. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 862 | OPENSSL_EXPORT int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, |
| 863 | const BIGNUM *m, BN_CTX *ctx); |
| 864 | |
| 865 | OPENSSL_EXPORT int BN_mod_exp_mont(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, |
| 866 | const BIGNUM *m, BN_CTX *ctx, |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 867 | const BN_MONT_CTX *mont); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 868 | |
| 869 | OPENSSL_EXPORT int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, |
| 870 | const BIGNUM *p, const BIGNUM *m, |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 871 | BN_CTX *ctx, |
| 872 | const BN_MONT_CTX *mont); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 873 | |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 874 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 875 | // Deprecated functions |
Kenny Root | b849459 | 2015-09-25 02:29:14 +0000 | [diff] [blame] | 876 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 877 | // BN_bn2mpi serialises the value of |in| to |out|, using a format that consists |
| 878 | // of the number's length in bytes represented as a 4-byte big-endian number, |
| 879 | // and the number itself in big-endian format, where the most significant bit |
| 880 | // signals a negative number. (The representation of numbers with the MSB set is |
| 881 | // prefixed with null byte). |out| must have sufficient space available; to |
| 882 | // find the needed amount of space, call the function with |out| set to NULL. |
Kenny Root | b849459 | 2015-09-25 02:29:14 +0000 | [diff] [blame] | 883 | OPENSSL_EXPORT size_t BN_bn2mpi(const BIGNUM *in, uint8_t *out); |
| 884 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 885 | // BN_mpi2bn parses |len| bytes from |in| and returns the resulting value. The |
| 886 | // bytes at |in| are expected to be in the format emitted by |BN_bn2mpi|. |
| 887 | // |
| 888 | // If |out| is NULL then a fresh |BIGNUM| is allocated and returned, otherwise |
| 889 | // |out| is reused and returned. On error, NULL is returned and the error queue |
| 890 | // is updated. |
Kenny Root | b849459 | 2015-09-25 02:29:14 +0000 | [diff] [blame] | 891 | OPENSSL_EXPORT BIGNUM *BN_mpi2bn(const uint8_t *in, size_t len, BIGNUM *out); |
| 892 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 893 | // BN_mod_exp_mont_word is like |BN_mod_exp_mont| except that the base |a| is |
| 894 | // given as a |BN_ULONG| instead of a |BIGNUM *|. It returns one on success |
| 895 | // or zero otherwise. |
David Benjamin | d316cba | 2016-06-02 16:17:39 -0400 | [diff] [blame] | 896 | OPENSSL_EXPORT int BN_mod_exp_mont_word(BIGNUM *r, BN_ULONG a, const BIGNUM *p, |
| 897 | const BIGNUM *m, BN_CTX *ctx, |
| 898 | const BN_MONT_CTX *mont); |
| 899 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 900 | // BN_mod_exp2_mont calculates (a1^p1) * (a2^p2) mod m. It returns 1 on success |
| 901 | // or zero otherwise. |
David Benjamin | d316cba | 2016-06-02 16:17:39 -0400 | [diff] [blame] | 902 | OPENSSL_EXPORT int BN_mod_exp2_mont(BIGNUM *r, const BIGNUM *a1, |
| 903 | const BIGNUM *p1, const BIGNUM *a2, |
| 904 | const BIGNUM *p2, const BIGNUM *m, |
| 905 | BN_CTX *ctx, const BN_MONT_CTX *mont); |
| 906 | |
Robert Sloan | 8542c08 | 2018-02-05 09:07:34 -0800 | [diff] [blame] | 907 | // BN_MONT_CTX_new returns a fresh |BN_MONT_CTX| or NULL on allocation failure. |
| 908 | // Use |BN_MONT_CTX_new_for_modulus| instead. |
| 909 | OPENSSL_EXPORT BN_MONT_CTX *BN_MONT_CTX_new(void); |
| 910 | |
| 911 | // BN_MONT_CTX_set sets up a Montgomery context given the modulus, |mod|. It |
| 912 | // returns one on success and zero on error. Use |BN_MONT_CTX_new_for_modulus| |
| 913 | // instead. |
| 914 | OPENSSL_EXPORT int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, |
| 915 | BN_CTX *ctx); |
| 916 | |
Kenny Root | b849459 | 2015-09-25 02:29:14 +0000 | [diff] [blame] | 917 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 918 | // Private functions |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 919 | |
| 920 | struct bignum_st { |
Robert Sloan | ab8b888 | 2018-03-26 11:39:51 -0700 | [diff] [blame^] | 921 | // d is a pointer to an array of |width| |BN_BITS2|-bit chunks in |
| 922 | // little-endian order. This stores the absolute value of the number. |
| 923 | BN_ULONG *d; |
| 924 | // width is the number of elements of |d| which are valid. This value is not |
| 925 | // necessarily minimal; the most-significant words of |d| may be zero. |
| 926 | // |width| determines a potentially loose upper-bound on the absolute value |
| 927 | // of the |BIGNUM|. |
| 928 | // |
| 929 | // Functions taking |BIGNUM| inputs must compute the same answer for all |
| 930 | // possible widths. |bn_minimal_width|, |bn_set_minimal_width|, and other |
| 931 | // helpers may be used to recover the minimal width, provided it is not |
| 932 | // secret. If it is secret, use a different algorithm. Functions may output |
| 933 | // minimal or non-minimal |BIGNUM|s depending on secrecy requirements, but |
| 934 | // those which cause widths to unboundedly grow beyond the minimal value |
| 935 | // should be documented such. |
| 936 | // |
| 937 | // Note this is different from historical |BIGNUM| semantics. |
| 938 | int width; |
| 939 | // dmax is number of elements of |d| which are allocated. |
| 940 | int dmax; |
| 941 | // neg is one if the number if negative and zero otherwise. |
| 942 | int neg; |
| 943 | // flags is a bitmask of |BN_FLG_*| values |
| 944 | int flags; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 945 | }; |
| 946 | |
| 947 | struct bn_mont_ctx_st { |
Robert Sloan | 8542c08 | 2018-02-05 09:07:34 -0800 | [diff] [blame] | 948 | // RR is R^2, reduced modulo |N|. It is used to convert to Montgomery form. |
| 949 | BIGNUM RR; |
| 950 | // N is the modulus. It is always stored in minimal form, so |N.top| |
| 951 | // determines R. |
| 952 | BIGNUM N; |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 953 | BN_ULONG n0[2]; // least significant words of (R*Ri-1)/N |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 954 | }; |
| 955 | |
| 956 | OPENSSL_EXPORT unsigned BN_num_bits_word(BN_ULONG l); |
| 957 | |
| 958 | #define BN_FLG_MALLOCED 0x01 |
| 959 | #define BN_FLG_STATIC_DATA 0x02 |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 960 | // |BN_FLG_CONSTTIME| has been removed and intentionally omitted so code relying |
| 961 | // on it will not compile. Consumers outside BoringSSL should use the |
| 962 | // higher-level cryptographic algorithms exposed by other modules. Consumers |
| 963 | // within the library should call the appropriate timing-sensitive algorithm |
| 964 | // directly. |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 965 | |
| 966 | |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 967 | #if defined(__cplusplus) |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 968 | } // extern C |
David Benjamin | f0c4a6c | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 969 | |
Robert Sloan | b6d070c | 2017-07-24 08:40:01 -0700 | [diff] [blame] | 970 | #if !defined(BORINGSSL_NO_CXX) |
David Benjamin | f0c4a6c | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 971 | extern "C++" { |
| 972 | |
| 973 | namespace bssl { |
| 974 | |
| 975 | BORINGSSL_MAKE_DELETER(BIGNUM, BN_free) |
| 976 | BORINGSSL_MAKE_DELETER(BN_CTX, BN_CTX_free) |
| 977 | BORINGSSL_MAKE_DELETER(BN_MONT_CTX, BN_MONT_CTX_free) |
| 978 | |
Robert Sloan | a12bf46 | 2017-07-17 07:08:26 -0700 | [diff] [blame] | 979 | class BN_CTXScope { |
| 980 | public: |
| 981 | BN_CTXScope(BN_CTX *ctx) : ctx_(ctx) { BN_CTX_start(ctx_); } |
| 982 | ~BN_CTXScope() { BN_CTX_end(ctx_); } |
| 983 | |
| 984 | private: |
| 985 | BN_CTX *ctx_; |
| 986 | |
| 987 | BN_CTXScope(BN_CTXScope &) = delete; |
| 988 | BN_CTXScope &operator=(BN_CTXScope &) = delete; |
| 989 | }; |
| 990 | |
David Benjamin | f0c4a6c | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 991 | } // namespace bssl |
| 992 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 993 | } // extern C++ |
Robert Sloan | a12bf46 | 2017-07-17 07:08:26 -0700 | [diff] [blame] | 994 | #endif |
David Benjamin | f0c4a6c | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 995 | |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 996 | #endif |
| 997 | |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 998 | #define BN_R_ARG2_LT_ARG3 100 |
| 999 | #define BN_R_BAD_RECIPROCAL 101 |
| 1000 | #define BN_R_BIGNUM_TOO_LONG 102 |
| 1001 | #define BN_R_BITS_TOO_SMALL 103 |
| 1002 | #define BN_R_CALLED_WITH_EVEN_MODULUS 104 |
| 1003 | #define BN_R_DIV_BY_ZERO 105 |
| 1004 | #define BN_R_EXPAND_ON_STATIC_BIGNUM_DATA 106 |
| 1005 | #define BN_R_INPUT_NOT_REDUCED 107 |
| 1006 | #define BN_R_INVALID_RANGE 108 |
| 1007 | #define BN_R_NEGATIVE_NUMBER 109 |
| 1008 | #define BN_R_NOT_A_SQUARE 110 |
| 1009 | #define BN_R_NOT_INITIALIZED 111 |
| 1010 | #define BN_R_NO_INVERSE 112 |
| 1011 | #define BN_R_PRIVATE_KEY_TOO_LARGE 113 |
| 1012 | #define BN_R_P_IS_NOT_PRIME 114 |
| 1013 | #define BN_R_TOO_MANY_ITERATIONS 115 |
| 1014 | #define BN_R_TOO_MANY_TEMPORARY_VARIABLES 116 |
Kenny Root | b849459 | 2015-09-25 02:29:14 +0000 | [diff] [blame] | 1015 | #define BN_R_BAD_ENCODING 117 |
| 1016 | #define BN_R_ENCODE_ERROR 118 |
Robert Sloan | 9254e68 | 2017-04-24 09:42:06 -0700 | [diff] [blame] | 1017 | #define BN_R_INVALID_INPUT 119 |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1018 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 1019 | #endif // OPENSSL_HEADER_BN_H |