/* Copyright (C) 1995-1997 Eric Young (eay@cryptsoft.com) | |

* All rights reserved. | |

* | |

* This package is an SSL implementation written | |

* by Eric Young (eay@cryptsoft.com). | |

* The implementation was written so as to conform with Netscapes SSL. | |

* | |

* This library is free for commercial and non-commercial use as long as | |

* the following conditions are aheared to. The following conditions | |

* apply to all code found in this distribution, be it the RC4, RSA, | |

* lhash, DES, etc., code; not just the SSL code. The SSL documentation | |

* included with this distribution is covered by the same copyright terms | |

* except that the holder is Tim Hudson (tjh@cryptsoft.com). | |

* | |

* Copyright remains Eric Young's, and as such any Copyright notices in | |

* the code are not to be removed. | |

* If this package is used in a product, Eric Young should be given attribution | |

* as the author of the parts of the library used. | |

* This can be in the form of a textual message at program startup or | |

* in documentation (online or textual) provided with the package. | |

* | |

* Redistribution and use in source and binary forms, with or without | |

* modification, are permitted provided that the following conditions | |

* are met: | |

* 1. Redistributions of source code must retain the copyright | |

* notice, this list of conditions and the following disclaimer. | |

* 2. Redistributions in binary form must reproduce the above copyright | |

* notice, this list of conditions and the following disclaimer in the | |

* documentation and/or other materials provided with the distribution. | |

* 3. All advertising materials mentioning features or use of this software | |

* must display the following acknowledgement: | |

* "This product includes cryptographic software written by | |

* Eric Young (eay@cryptsoft.com)" | |

* The word 'cryptographic' can be left out if the rouines from the library | |

* being used are not cryptographic related :-). | |

* 4. If you include any Windows specific code (or a derivative thereof) from | |

* the apps directory (application code) you must include an acknowledgement: | |

* "This product includes software written by Tim Hudson (tjh@cryptsoft.com)" | |

* | |

* THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND | |

* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE | |

* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE | |

* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE | |

* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL | |

* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS | |

* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) | |

* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT | |

* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY | |

* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF | |

* SUCH DAMAGE. | |

* | |

* The licence and distribution terms for any publically available version or | |

* derivative of this code cannot be changed. i.e. this code cannot simply be | |

* copied and put under another distribution licence | |

* [including the GNU Public Licence.] | |

*/ | |

/* ==================================================================== | |

* Copyright (c) 1998-2006 The OpenSSL Project. All rights reserved. | |

* | |

* Redistribution and use in source and binary forms, with or without | |

* modification, are permitted provided that the following conditions | |

* are met: | |

* | |

* 1. Redistributions of source code must retain the above copyright | |

* notice, this list of conditions and the following disclaimer. | |

* | |

* 2. Redistributions in binary form must reproduce the above copyright | |

* notice, this list of conditions and the following disclaimer in | |

* the documentation and/or other materials provided with the | |

* distribution. | |

* | |

* 3. All advertising materials mentioning features or use of this | |

* software must display the following acknowledgment: | |

* "This product includes software developed by the OpenSSL Project | |

* for use in the OpenSSL Toolkit. (http://www.openssl.org/)" | |

* | |

* 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to | |

* endorse or promote products derived from this software without | |

* prior written permission. For written permission, please contact | |

* openssl-core@openssl.org. | |

* | |

* 5. Products derived from this software may not be called "OpenSSL" | |

* nor may "OpenSSL" appear in their names without prior written | |

* permission of the OpenSSL Project. | |

* | |

* 6. Redistributions of any form whatsoever must retain the following | |

* acknowledgment: | |

* "This product includes software developed by the OpenSSL Project | |

* for use in the OpenSSL Toolkit (http://www.openssl.org/)" | |

* | |

* THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY | |

* EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE | |

* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR | |

* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR | |

* ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, | |

* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT | |

* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; | |

* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) | |

* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, | |

* STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) | |

* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED | |

* OF THE POSSIBILITY OF SUCH DAMAGE. | |

* ==================================================================== | |

* | |

* This product includes cryptographic software written by Eric Young | |

* (eay@cryptsoft.com). This product includes software written by Tim | |

* Hudson (tjh@cryptsoft.com). | |

* | |

*/ | |

/* ==================================================================== | |

* Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. | |

* | |

* Portions of the attached software ("Contribution") are developed by | |

* SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project. | |

* | |

* The Contribution is licensed pursuant to the Eric Young open source | |

* license provided above. | |

* | |

* The binary polynomial arithmetic software is originally written by | |

* Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems | |

* Laboratories. */ | |

#ifndef OPENSSL_HEADER_BN_H | |

#define OPENSSL_HEADER_BN_H | |

#include <openssl/base.h> | |

#include <openssl/thread.h> | |

#include <inttypes.h> /* for PRIu64 and friends */ | |

#include <stdio.h> /* for FILE* */ | |

#if defined(__cplusplus) | |

extern "C" { | |

#endif | |

/* BN provides support for working with arbitary sized integers. For example, | |

* although the largest integer supported by the compiler might be 64 bits, BN | |

* will allow you to work with numbers until you run out of memory. */ | |

/* BN_ULONG is the native word size when working with big integers. | |

* | |

* Note: on some platforms, inttypes.h does not define print format macros in | |

* C++ unless |__STDC_FORMAT_MACROS| defined. As this is a public header, bn.h | |

* does not define |__STDC_FORMAT_MACROS| itself. C++ source files which use the | |

* FMT macros must define it externally. */ | |

#if defined(OPENSSL_64_BIT) | |

#define BN_ULONG uint64_t | |

#define BN_BITS2 64 | |

#define BN_DEC_FMT1 "%" PRIu64 | |

#define BN_DEC_FMT2 "%019" PRIu64 | |

#define BN_HEX_FMT1 "%" PRIx64 | |

#elif defined(OPENSSL_32_BIT) | |

#define BN_ULONG uint32_t | |

#define BN_BITS2 32 | |

#define BN_DEC_FMT1 "%" PRIu32 | |

#define BN_DEC_FMT2 "%09" PRIu32 | |

#define BN_HEX_FMT1 "%" PRIx32 | |

#else | |

#error "Must define either OPENSSL_32_BIT or OPENSSL_64_BIT" | |

#endif | |

/* Allocation and freeing. */ | |

/* BN_new creates a new, allocated BIGNUM and initialises it. */ | |

OPENSSL_EXPORT BIGNUM *BN_new(void); | |

/* BN_init initialises a stack allocated |BIGNUM|. */ | |

OPENSSL_EXPORT void BN_init(BIGNUM *bn); | |

/* BN_free frees the data referenced by |bn| and, if |bn| was originally | |

* allocated on the heap, frees |bn| also. */ | |

OPENSSL_EXPORT void BN_free(BIGNUM *bn); | |

/* BN_clear_free erases and frees the data referenced by |bn| and, if |bn| was | |

* originally allocated on the heap, frees |bn| also. */ | |

OPENSSL_EXPORT void BN_clear_free(BIGNUM *bn); | |

/* BN_dup allocates a new BIGNUM and sets it equal to |src|. It returns the | |

* allocated BIGNUM on success or NULL otherwise. */ | |

OPENSSL_EXPORT BIGNUM *BN_dup(const BIGNUM *src); | |

/* BN_copy sets |dest| equal to |src| and returns |dest| or NULL on allocation | |

* failure. */ | |

OPENSSL_EXPORT BIGNUM *BN_copy(BIGNUM *dest, const BIGNUM *src); | |

/* BN_clear sets |bn| to zero and erases the old data. */ | |

OPENSSL_EXPORT void BN_clear(BIGNUM *bn); | |

/* BN_value_one returns a static BIGNUM with value 1. */ | |

OPENSSL_EXPORT const BIGNUM *BN_value_one(void); | |

/* BN_with_flags initialises a stack allocated |BIGNUM| with pointers to the | |

* contents of |in| but with |flags| ORed into the flags field. | |

* | |

* Note: the two BIGNUMs share state and so |out| should /not/ be passed to | |

* |BN_free|. */ | |

OPENSSL_EXPORT void BN_with_flags(BIGNUM *out, const BIGNUM *in, int flags); | |

/* Basic functions. */ | |

/* BN_num_bits returns the minimum number of bits needed to represent the | |

* absolute value of |bn|. */ | |

OPENSSL_EXPORT unsigned BN_num_bits(const BIGNUM *bn); | |

/* BN_num_bytes returns the minimum number of bytes needed to represent the | |

* absolute value of |bn|. */ | |

OPENSSL_EXPORT unsigned BN_num_bytes(const BIGNUM *bn); | |

/* BN_zero sets |bn| to zero. */ | |

OPENSSL_EXPORT void BN_zero(BIGNUM *bn); | |

/* BN_one sets |bn| to one. It returns one on success or zero on allocation | |

* failure. */ | |

OPENSSL_EXPORT int BN_one(BIGNUM *bn); | |

/* BN_set_word sets |bn| to |value|. It returns one on success or zero on | |

* allocation failure. */ | |

OPENSSL_EXPORT int BN_set_word(BIGNUM *bn, BN_ULONG value); | |

/* BN_set_negative sets the sign of |bn|. */ | |

OPENSSL_EXPORT void BN_set_negative(BIGNUM *bn, int sign); | |

/* BN_is_negative returns one if |bn| is negative and zero otherwise. */ | |

OPENSSL_EXPORT int BN_is_negative(const BIGNUM *bn); | |

/* BN_get_flags returns |bn->flags| & |flags|. */ | |

OPENSSL_EXPORT int BN_get_flags(const BIGNUM *bn, int flags); | |

/* BN_set_flags sets |flags| on |bn|. */ | |

OPENSSL_EXPORT void BN_set_flags(BIGNUM *bn, int flags); | |

/* Conversion functions. */ | |

/* BN_bin2bn sets |*ret| to the value of |len| bytes from |in|, interpreted as | |

* a big-endian number, and returns |ret|. If |ret| is NULL then a fresh | |

* |BIGNUM| is allocated and returned. It returns NULL on allocation | |

* failure. */ | |

OPENSSL_EXPORT BIGNUM *BN_bin2bn(const uint8_t *in, size_t len, BIGNUM *ret); | |

/* BN_bn2bin serialises the absolute value of |in| to |out| as a big-endian | |

* integer, which must have |BN_num_bytes| of space available. It returns the | |

* number of bytes written. */ | |

OPENSSL_EXPORT size_t BN_bn2bin(const BIGNUM *in, uint8_t *out); | |

/* BN_bn2bin_padded serialises the absolute value of |in| to |out| as a | |

* big-endian integer. The integer is padded with leading zeros up to size | |

* |len|. If |len| is smaller than |BN_num_bytes|, the function fails and | |

* returns 0. Otherwise, it returns 1. */ | |

OPENSSL_EXPORT int BN_bn2bin_padded(uint8_t *out, size_t len, const BIGNUM *in); | |

/* BN_bn2hex returns an allocated string that contains a NUL-terminated, hex | |

* representation of |bn|. If |bn| is negative, the first char in the resulting | |

* string will be '-'. Returns NULL on allocation failure. */ | |

OPENSSL_EXPORT char *BN_bn2hex(const BIGNUM *bn); | |

/* BN_hex2bn parses the leading hex number from |in|, which may be proceeded by | |

* a '-' to indicate a negative number and may contain trailing, non-hex data. | |

* If |outp| is not NULL, it constructs a BIGNUM equal to the hex number and | |

* stores it in |*outp|. If |*outp| is NULL then it allocates a new BIGNUM and | |

* updates |*outp|. It returns the number of bytes of |in| processed or zero on | |

* error. */ | |

OPENSSL_EXPORT int BN_hex2bn(BIGNUM **outp, const char *in); | |

/* BN_bn2dec returns an allocated string that contains a NUL-terminated, | |

* decimal representation of |bn|. If |bn| is negative, the first char in the | |

* resulting string will be '-'. Returns NULL on allocation failure. */ | |

OPENSSL_EXPORT char *BN_bn2dec(const BIGNUM *a); | |

/* BN_dec2bn parses the leading decimal number from |in|, which may be | |

* proceeded by a '-' to indicate a negative number and may contain trailing, | |

* non-decimal data. If |outp| is not NULL, it constructs a BIGNUM equal to the | |

* decimal number and stores it in |*outp|. If |*outp| is NULL then it | |

* allocates a new BIGNUM and updates |*outp|. It returns the number of bytes | |

* of |in| processed or zero on error. */ | |

OPENSSL_EXPORT int BN_dec2bn(BIGNUM **outp, const char *in); | |

/* BN_asc2bn acts like |BN_dec2bn| or |BN_hex2bn| depending on whether |in| | |

* begins with "0X" or "0x" (indicating hex) or not (indicating decimal). A | |

* leading '-' is still permitted and comes before the optional 0X/0x. It | |

* returns one on success or zero on error. */ | |

OPENSSL_EXPORT int BN_asc2bn(BIGNUM **outp, const char *in); | |

/* BN_print writes a hex encoding of |a| to |bio|. It returns one on success | |

* and zero on error. */ | |

OPENSSL_EXPORT int BN_print(BIO *bio, const BIGNUM *a); | |

/* BN_print_fp acts like |BIO_print|, but wraps |fp| in a |BIO| first. */ | |

OPENSSL_EXPORT int BN_print_fp(FILE *fp, const BIGNUM *a); | |

/* BN_get_word returns the absolute value of |bn| as a single word. If |bn| is | |

* too large to be represented as a single word, the maximum possible value | |

* will be returned. */ | |

OPENSSL_EXPORT BN_ULONG BN_get_word(const BIGNUM *bn); | |

/* ASN.1 functions. */ | |

/* BN_cbs2unsigned parses a non-negative DER INTEGER from |cbs| writes the | |

* result to |ret|. It returns one on success and zero on failure. */ | |

OPENSSL_EXPORT int BN_cbs2unsigned(CBS *cbs, BIGNUM *ret); | |

/* BN_cbs2unsigned_buggy acts like |BN_cbs2unsigned| but tolerates some invalid | |

* encodings. Do not use this function. */ | |

OPENSSL_EXPORT int BN_cbs2unsigned_buggy(CBS *cbs, BIGNUM *ret); | |

/* BN_bn2cbb marshals |bn| as a non-negative DER INTEGER and appends the result | |

* to |cbb|. It returns one on success and zero on failure. */ | |

OPENSSL_EXPORT int BN_bn2cbb(CBB *cbb, const BIGNUM *bn); | |

/* Internal functions. | |

* | |

* These functions are useful for code that is doing low-level manipulations of | |

* BIGNUM values. However, be sure that no other function in this file does | |

* what you want before turning to these. */ | |

/* bn_correct_top decrements |bn->top| until |bn->d[top-1]| is non-zero or | |

* until |top| is zero. */ | |

OPENSSL_EXPORT void bn_correct_top(BIGNUM *bn); | |

/* bn_wexpand ensures that |bn| has at least |words| works of space without | |

* altering its value. It returns one on success or zero on allocation | |

* failure. */ | |

OPENSSL_EXPORT BIGNUM *bn_wexpand(BIGNUM *bn, size_t words); | |

/* BIGNUM pools. | |

* | |

* Certain BIGNUM operations need to use many temporary variables and | |

* allocating and freeing them can be quite slow. Thus such opertions typically | |

* take a |BN_CTX| parameter, which contains a pool of |BIGNUMs|. The |ctx| | |

* argument to a public function may be NULL, in which case a local |BN_CTX| | |

* will be created just for the lifetime of that call. | |

* | |

* A function must call |BN_CTX_start| first. Then, |BN_CTX_get| may be called | |

* repeatedly to obtain temporary |BIGNUM|s. All |BN_CTX_get| calls must be made | |

* before calling any other functions that use the |ctx| as an argument. | |

* | |

* Finally, |BN_CTX_end| must be called before returning from the function. | |

* When |BN_CTX_end| is called, the |BIGNUM| pointers obtained from | |

* |BN_CTX_get| become invalid. */ | |

/* BN_CTX_new returns a new, empty BN_CTX or NULL on allocation failure. */ | |

OPENSSL_EXPORT BN_CTX *BN_CTX_new(void); | |

/* BN_CTX_free frees all BIGNUMs contained in |ctx| and then frees |ctx| | |

* itself. */ | |

OPENSSL_EXPORT void BN_CTX_free(BN_CTX *ctx); | |

/* BN_CTX_start "pushes" a new entry onto the |ctx| stack and allows future | |

* calls to |BN_CTX_get|. */ | |

OPENSSL_EXPORT void BN_CTX_start(BN_CTX *ctx); | |

/* BN_CTX_get returns a new |BIGNUM|, or NULL on allocation failure. Once | |

* |BN_CTX_get| has returned NULL, all future calls will also return NULL until | |

* |BN_CTX_end| is called. */ | |

OPENSSL_EXPORT BIGNUM *BN_CTX_get(BN_CTX *ctx); | |

/* BN_CTX_end invalidates all |BIGNUM|s returned from |BN_CTX_get| since the | |

* matching |BN_CTX_start| call. */ | |

OPENSSL_EXPORT void BN_CTX_end(BN_CTX *ctx); | |

/* Simple arithmetic */ | |

/* BN_add sets |r| = |a| + |b|, where |r| may be the same pointer as either |a| | |

* or |b|. It returns one on success and zero on allocation failure. */ | |

OPENSSL_EXPORT int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); | |

/* BN_uadd sets |r| = |a| + |b|, where |a| and |b| are non-negative and |r| may | |

* be the same pointer as either |a| or |b|. It returns one on success and zero | |

* on allocation failure. */ | |

OPENSSL_EXPORT int BN_uadd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); | |

/* BN_add_word adds |w| to |a|. It returns one on success and zero otherwise. */ | |

OPENSSL_EXPORT int BN_add_word(BIGNUM *a, BN_ULONG w); | |

/* BN_sub sets |r| = |a| - |b|, where |r| must be a distinct pointer from |a| | |

* and |b|. It returns one on success and zero on allocation failure. */ | |

OPENSSL_EXPORT int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); | |

/* BN_usub sets |r| = |a| - |b|, where |a| and |b| are non-negative integers, | |

* |b| < |a| and |r| must be a distinct pointer from |a| and |b|. It returns | |

* one on success and zero on allocation failure. */ | |

OPENSSL_EXPORT int BN_usub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); | |

/* BN_sub_word subtracts |w| from |a|. It returns one on success and zero on | |

* allocation failure. */ | |

OPENSSL_EXPORT int BN_sub_word(BIGNUM *a, BN_ULONG w); | |

/* BN_mul sets |r| = |a| * |b|, where |r| may be the same pointer as |a| or | |

* |b|. Returns one on success and zero otherwise. */ | |

OPENSSL_EXPORT int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, | |

BN_CTX *ctx); | |

/* BN_mul_word sets |bn| = |bn| * |w|. It returns one on success or zero on | |

* allocation failure. */ | |

OPENSSL_EXPORT int BN_mul_word(BIGNUM *bn, BN_ULONG w); | |

/* BN_sqr sets |r| = |a|^2 (i.e. squares), where |r| may be the same pointer as | |

* |a|. Returns one on success and zero otherwise. This is more efficient than | |

* BN_mul(r, a, a, ctx). */ | |

OPENSSL_EXPORT int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx); | |

/* BN_div divides |numerator| by |divisor| and places the result in |quotient| | |

* and the remainder in |rem|. Either of |quotient| or |rem| may be NULL, in | |

* which case the respective value is not returned. The result is rounded | |

* towards zero; thus if |numerator| is negative, the remainder will be zero or | |

* negative. It returns one on success or zero on error. */ | |

OPENSSL_EXPORT int BN_div(BIGNUM *quotient, BIGNUM *rem, | |

const BIGNUM *numerator, const BIGNUM *divisor, | |

BN_CTX *ctx); | |

/* BN_div_word sets |numerator| = |numerator|/|divisor| and returns the | |

* remainder or (BN_ULONG)-1 on error. */ | |

OPENSSL_EXPORT BN_ULONG BN_div_word(BIGNUM *numerator, BN_ULONG divisor); | |

/* BN_sqrt sets |*out_sqrt| (which may be the same |BIGNUM| as |in|) to the | |

* square root of |in|, using |ctx|. It returns one on success or zero on | |

* error. Negative numbers and non-square numbers will result in an error with | |

* appropriate errors on the error queue. */ | |

OPENSSL_EXPORT int BN_sqrt(BIGNUM *out_sqrt, const BIGNUM *in, BN_CTX *ctx); | |

/* Comparison functions */ | |

/* BN_cmp returns a value less than, equal to or greater than zero if |a| is | |

* less than, equal to or greater than |b|, respectively. */ | |

OPENSSL_EXPORT int BN_cmp(const BIGNUM *a, const BIGNUM *b); | |

/* BN_ucmp returns a value less than, equal to or greater than zero if the | |

* absolute value of |a| is less than, equal to or greater than the absolute | |

* value of |b|, respectively. */ | |

OPENSSL_EXPORT int BN_ucmp(const BIGNUM *a, const BIGNUM *b); | |

/* BN_abs_is_word returns one if the absolute value of |bn| equals |w| and zero | |

* otherwise. */ | |

OPENSSL_EXPORT int BN_abs_is_word(const BIGNUM *bn, BN_ULONG w); | |

/* BN_is_zero returns one if |bn| is zero and zero otherwise. */ | |

OPENSSL_EXPORT int BN_is_zero(const BIGNUM *bn); | |

/* BN_is_one returns one if |bn| equals one and zero otherwise. */ | |

OPENSSL_EXPORT int BN_is_one(const BIGNUM *bn); | |

/* BN_is_word returns one if |bn| is exactly |w| and zero otherwise. */ | |

OPENSSL_EXPORT int BN_is_word(const BIGNUM *bn, BN_ULONG w); | |

/* BN_is_odd returns one if |bn| is odd and zero otherwise. */ | |

OPENSSL_EXPORT int BN_is_odd(const BIGNUM *bn); | |

/* Bitwise operations. */ | |

/* BN_lshift sets |r| equal to |a| << n. The |a| and |r| arguments may be the | |

* same |BIGNUM|. It returns one on success and zero on allocation failure. */ | |

OPENSSL_EXPORT int BN_lshift(BIGNUM *r, const BIGNUM *a, int n); | |

/* BN_lshift1 sets |r| equal to |a| << 1, where |r| and |a| may be the same | |

* pointer. It returns one on success and zero on allocation failure. */ | |

OPENSSL_EXPORT int BN_lshift1(BIGNUM *r, const BIGNUM *a); | |

/* BN_rshift sets |r| equal to |a| >> n, where |r| and |a| may be the same | |

* pointer. It returns one on success and zero on allocation failure. */ | |

OPENSSL_EXPORT int BN_rshift(BIGNUM *r, const BIGNUM *a, int n); | |

/* BN_rshift1 sets |r| equal to |a| >> 1, where |r| and |a| may be the same | |

* pointer. It returns one on success and zero on allocation failure. */ | |

OPENSSL_EXPORT int BN_rshift1(BIGNUM *r, const BIGNUM *a); | |

/* BN_set_bit sets the |n|th, least-significant bit in |a|. For example, if |a| | |

* is 2 then setting bit zero will make it 3. It returns one on success or zero | |

* on allocation failure. */ | |

OPENSSL_EXPORT int BN_set_bit(BIGNUM *a, int n); | |

/* BN_clear_bit clears the |n|th, least-significant bit in |a|. For example, if | |

* |a| is 3, clearing bit zero will make it two. It returns one on success or | |

* zero on allocation failure. */ | |

OPENSSL_EXPORT int BN_clear_bit(BIGNUM *a, int n); | |

/* BN_is_bit_set returns the value of the |n|th, least-significant bit in |a|, | |

* or zero if the bit doesn't exist. */ | |

OPENSSL_EXPORT int BN_is_bit_set(const BIGNUM *a, int n); | |

/* BN_mask_bits truncates |a| so that it is only |n| bits long. It returns one | |

* on success or zero if |n| is greater than the length of |a| already. */ | |

OPENSSL_EXPORT int BN_mask_bits(BIGNUM *a, int n); | |

/* Modulo arithmetic. */ | |

/* BN_mod_word returns |a| mod |w|. */ | |

OPENSSL_EXPORT BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w); | |

/* BN_mod is a helper macro that calls |BN_div| and discards the quotient. */ | |

#define BN_mod(rem, numerator, divisor, ctx) \ | |

BN_div(NULL, (rem), (numerator), (divisor), (ctx)) | |

/* BN_nnmod is a non-negative modulo function. It acts like |BN_mod|, but 0 <= | |

* |rem| < |divisor| is always true. It returns one on success and zero on | |

* error. */ | |

OPENSSL_EXPORT int BN_nnmod(BIGNUM *rem, const BIGNUM *numerator, | |

const BIGNUM *divisor, BN_CTX *ctx); | |

/* BN_mod_add sets |r| = |a| + |b| mod |m|. It returns one on success and zero | |

* on error. */ | |

OPENSSL_EXPORT int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, | |

const BIGNUM *m, BN_CTX *ctx); | |

/* BN_mod_add_quick acts like |BN_mod_add| but requires that |a| and |b| be | |

* non-negative and less than |m|. */ | |

OPENSSL_EXPORT int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, | |

const BIGNUM *m); | |

/* BN_mod_sub sets |r| = |a| - |b| mod |m|. It returns one on success and zero | |

* on error. */ | |

OPENSSL_EXPORT int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, | |

const BIGNUM *m, BN_CTX *ctx); | |

/* BN_mod_sub_quick acts like |BN_mod_sub| but requires that |a| and |b| be | |

* non-negative and less than |m|. */ | |

OPENSSL_EXPORT int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, | |

const BIGNUM *m); | |

/* BN_mod_mul sets |r| = |a|*|b| mod |m|. It returns one on success and zero | |

* on error. */ | |

OPENSSL_EXPORT int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, | |

const BIGNUM *m, BN_CTX *ctx); | |

/* BN_mod_sqr sets |r| = |a|^2 mod |m|. It returns one on success and zero | |

* on error. */ | |

OPENSSL_EXPORT int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, | |

BN_CTX *ctx); | |

/* BN_mod_lshift sets |r| = (|a| << n) mod |m|, where |r| and |a| may be the | |

* same pointer. It returns one on success and zero on error. */ | |

OPENSSL_EXPORT int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, | |

const BIGNUM *m, BN_CTX *ctx); | |

/* BN_mod_lshift_quick acts like |BN_mod_lshift| but requires that |a| be | |

* non-negative and less than |m|. */ | |

OPENSSL_EXPORT int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, | |

const BIGNUM *m); | |

/* BN_mod_lshift1 sets |r| = (|a| << 1) mod |m|, where |r| and |a| may be the | |

* same pointer. It returns one on success and zero on error. */ | |

OPENSSL_EXPORT int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, | |

BN_CTX *ctx); | |

/* BN_mod_lshift1_quick acts like |BN_mod_lshift1| but requires that |a| be | |

* non-negative and less than |m|. */ | |

OPENSSL_EXPORT int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, | |

const BIGNUM *m); | |

/* BN_mod_sqrt returns a |BIGNUM|, r, such that r^2 == a (mod p). */ | |

OPENSSL_EXPORT BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p, | |

BN_CTX *ctx); | |

/* Random and prime number generation. */ | |

/* BN_rand sets |rnd| to a random number of length |bits|. If |top| is zero, the | |

* most-significant bit, if any, will be set. If |top| is one, the two most | |

* significant bits, if any, will be set. | |

* | |

* If |top| is -1 then no extra action will be taken and |BN_num_bits(rnd)| may | |

* not equal |bits| if the most significant bits randomly ended up as zeros. | |

* | |

* If |bottom| is non-zero, the least-significant bit, if any, will be set. The | |

* function returns one on success or zero otherwise. */ | |

OPENSSL_EXPORT int BN_rand(BIGNUM *rnd, int bits, int top, int bottom); | |

/* BN_pseudo_rand is an alias for |BN_rand|. */ | |

OPENSSL_EXPORT int BN_pseudo_rand(BIGNUM *rnd, int bits, int top, int bottom); | |

/* BN_rand_range sets |rnd| to a random value [0..range). It returns one on | |

* success and zero otherwise. */ | |

OPENSSL_EXPORT int BN_rand_range(BIGNUM *rnd, const BIGNUM *range); | |

/* BN_pseudo_rand_range is an alias for BN_rand_range. */ | |

OPENSSL_EXPORT int BN_pseudo_rand_range(BIGNUM *rnd, const BIGNUM *range); | |

/* BN_generate_dsa_nonce generates a random number 0 <= out < range. Unlike | |

* BN_rand_range, it also includes the contents of |priv| and |message| in the | |

* generation so that an RNG failure isn't fatal as long as |priv| remains | |

* secret. This is intended for use in DSA and ECDSA where an RNG weakness | |

* leads directly to private key exposure unless this function is used. | |

* It returns one on success and zero on error. */ | |

OPENSSL_EXPORT int BN_generate_dsa_nonce(BIGNUM *out, const BIGNUM *range, | |

const BIGNUM *priv, | |

const uint8_t *message, | |

size_t message_len, BN_CTX *ctx); | |

/* BN_GENCB holds a callback function that is used by generation functions that | |

* can take a very long time to complete. Use |BN_GENCB_set| to initialise a | |

* |BN_GENCB| structure. | |

* | |

* The callback receives the address of that |BN_GENCB| structure as its last | |

* argument and the user is free to put an arbitary pointer in |arg|. The other | |

* arguments are set as follows: | |

* event=BN_GENCB_GENERATED, n=i: after generating the i'th possible prime | |

* number. | |

* event=BN_GENCB_PRIME_TEST, n=-1: when finished trial division primality | |

* checks. | |

* event=BN_GENCB_PRIME_TEST, n=i: when the i'th primality test has finished. | |

* | |

* The callback can return zero to abort the generation progress or one to | |

* allow it to continue. | |

* | |

* When other code needs to call a BN generation function it will often take a | |

* BN_GENCB argument and may call the function with other argument values. */ | |

#define BN_GENCB_GENERATED 0 | |

#define BN_GENCB_PRIME_TEST 1 | |

struct bn_gencb_st { | |

void *arg; /* callback-specific data */ | |

int (*callback)(int event, int n, struct bn_gencb_st *); | |

}; | |

/* BN_GENCB_set configures |callback| to call |f| and sets |callout->arg| to | |

* |arg|. */ | |

OPENSSL_EXPORT void BN_GENCB_set(BN_GENCB *callback, | |

int (*f)(int event, int n, | |

struct bn_gencb_st *), | |

void *arg); | |

/* BN_GENCB_call calls |callback|, if not NULL, and returns the return value of | |

* the callback, or 1 if |callback| is NULL. */ | |

OPENSSL_EXPORT int BN_GENCB_call(BN_GENCB *callback, int event, int n); | |

/* BN_generate_prime_ex sets |ret| to a prime number of |bits| length. If safe | |

* is non-zero then the prime will be such that (ret-1)/2 is also a prime. | |

* (This is needed for Diffie-Hellman groups to ensure that the only subgroups | |

* are of size 2 and (p-1)/2.). | |

* | |

* If |add| is not NULL, the prime will fulfill the condition |ret| % |add| == | |

* |rem| in order to suit a given generator. (If |rem| is NULL then |ret| % | |

* |add| == 1.) | |

* | |

* If |cb| is not NULL, it will be called during processing to give an | |

* indication of progress. See the comments for |BN_GENCB|. It returns one on | |

* success and zero otherwise. */ | |

OPENSSL_EXPORT int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, | |

const BIGNUM *add, const BIGNUM *rem, | |

BN_GENCB *cb); | |

/* BN_prime_checks is magic value that can be used as the |checks| argument to | |

* the primality testing functions in order to automatically select a number of | |

* Miller-Rabin checks that gives a false positive rate of ~2^{-80}. */ | |

#define BN_prime_checks 0 | |

/* BN_primality_test sets |*is_probably_prime| to one if |candidate| is | |

* probably a prime number by the Miller-Rabin test or zero if it's certainly | |

* not. | |

* | |

* If |do_trial_division| is non-zero then |candidate| will be tested against a | |

* list of small primes before Miller-Rabin tests. The probability of this | |

* function returning a false positive is 2^{2*checks}. If |checks| is | |

* |BN_prime_checks| then a value that results in approximately 2^{-80} false | |

* positive probability is used. If |cb| is not NULL then it is called during | |

* the checking process. See the comment above |BN_GENCB|. | |

* | |

* The function returns one on success and zero on error. | |

* | |

* (If you are unsure whether you want |do_trial_division|, don't set it.) */ | |

OPENSSL_EXPORT int BN_primality_test(int *is_probably_prime, | |

const BIGNUM *candidate, int checks, | |

BN_CTX *ctx, int do_trial_division, | |

BN_GENCB *cb); | |

/* BN_is_prime_fasttest_ex returns one if |candidate| is probably a prime | |

* number by the Miller-Rabin test, zero if it's certainly not and -1 on error. | |

* | |

* If |do_trial_division| is non-zero then |candidate| will be tested against a | |

* list of small primes before Miller-Rabin tests. The probability of this | |

* function returning one when |candidate| is composite is 2^{2*checks}. If | |

* |checks| is |BN_prime_checks| then a value that results in approximately | |

* 2^{-80} false positive probability is used. If |cb| is not NULL then it is | |

* called during the checking process. See the comment above |BN_GENCB|. | |

* | |

* WARNING: deprecated. Use |BN_primality_test|. */ | |

OPENSSL_EXPORT int BN_is_prime_fasttest_ex(const BIGNUM *candidate, int checks, | |

BN_CTX *ctx, int do_trial_division, | |

BN_GENCB *cb); | |

/* BN_is_prime_ex acts the same as |BN_is_prime_fasttest_ex| with | |

* |do_trial_division| set to zero. | |

* | |

* WARNING: deprecated: Use |BN_primality_test|. */ | |

OPENSSL_EXPORT int BN_is_prime_ex(const BIGNUM *candidate, int checks, | |

BN_CTX *ctx, BN_GENCB *cb); | |

/* Number theory functions */ | |

/* BN_gcd sets |r| = gcd(|a|, |b|). It returns one on success and zero | |

* otherwise. */ | |

OPENSSL_EXPORT int BN_gcd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, | |

BN_CTX *ctx); | |

/* BN_mod_inverse sets |out| equal to |a|^-1, mod |n|. If either of |a| or |n| | |

* have |BN_FLG_CONSTTIME| set then the operation is performed in constant | |

* time. If |out| is NULL, a fresh BIGNUM is allocated. It returns the result | |

* or NULL on error. */ | |

OPENSSL_EXPORT BIGNUM *BN_mod_inverse(BIGNUM *out, const BIGNUM *a, | |

const BIGNUM *n, BN_CTX *ctx); | |

/* BN_mod_inverse_ex acts like |BN_mod_inverse| except that, when it returns | |

* zero, it will set |*out_no_inverse| to one if the failure was caused because | |

* |a| has no inverse mod |n|. Otherwise it will set |*out_no_inverse| to | |

* zero. */ | |

OPENSSL_EXPORT BIGNUM *BN_mod_inverse_ex(BIGNUM *out, int *out_no_inverse, | |

const BIGNUM *a, const BIGNUM *n, | |

BN_CTX *ctx); | |

/* BN_kronecker returns the Kronecker symbol of |a| and |b| (which is -1, 0 or | |

* 1), or -2 on error. */ | |

OPENSSL_EXPORT int BN_kronecker(const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); | |

/* Montgomery arithmetic. */ | |

/* BN_MONT_CTX contains the precomputed values needed to work in a specific | |

* Montgomery domain. */ | |

/* BN_MONT_CTX_new returns a fresh BN_MONT_CTX or NULL on allocation failure. */ | |

OPENSSL_EXPORT BN_MONT_CTX *BN_MONT_CTX_new(void); | |

/* BN_MONT_CTX_free frees memory associated with |mont|. */ | |

OPENSSL_EXPORT void BN_MONT_CTX_free(BN_MONT_CTX *mont); | |

/* BN_MONT_CTX_copy sets |to| equal to |from|. It returns |to| on success or | |

* NULL on error. */ | |

OPENSSL_EXPORT BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, | |

BN_MONT_CTX *from); | |

/* BN_MONT_CTX_set sets up a Montgomery context given the modulus, |mod|. It | |

* returns one on success and zero on error. */ | |

OPENSSL_EXPORT int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, | |

BN_CTX *ctx); | |

/* BN_MONT_CTX_set_locked takes |lock| and checks whether |*pmont| is NULL. If | |

* so, it creates a new |BN_MONT_CTX| and sets the modulus for it to |mod|. It | |

* then stores it as |*pmont| and returns it, or NULL on error. | |

* | |

* If |*pmont| is already non-NULL then the existing value is returned. */ | |

BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, CRYPTO_MUTEX *lock, | |

const BIGNUM *mod, BN_CTX *bn_ctx); | |

/* BN_to_montgomery sets |ret| equal to |a| in the Montgomery domain. It | |

* returns one on success and zero on error. */ | |

OPENSSL_EXPORT int BN_to_montgomery(BIGNUM *ret, const BIGNUM *a, | |

const BN_MONT_CTX *mont, BN_CTX *ctx); | |

/* BN_from_montgomery sets |ret| equal to |a| * R^-1, i.e. translates values | |

* out of the Montgomery domain. It returns one on success or zero on error. */ | |

OPENSSL_EXPORT int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, | |

const BN_MONT_CTX *mont, BN_CTX *ctx); | |

/* BN_mod_mul_montgomery set |r| equal to |a| * |b|, in the Montgomery domain. | |

* Both |a| and |b| must already be in the Montgomery domain (by | |

* |BN_to_montgomery|). It returns one on success or zero on error. */ | |

OPENSSL_EXPORT int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, | |

const BIGNUM *b, | |

const BN_MONT_CTX *mont, BN_CTX *ctx); | |

/* Exponentiation. */ | |

/* BN_exp sets |r| equal to |a|^{|p|}. It does so with a square-and-multiply | |

* algorithm that leaks side-channel information. It returns one on success or | |

* zero otherwise. */ | |

OPENSSL_EXPORT int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, | |

BN_CTX *ctx); | |

/* BN_mod_exp sets |r| equal to |a|^{|p|} mod |m|. It does so with the best | |

* algorithm for the values provided and can run in constant time if | |

* |BN_FLG_CONSTTIME| is set for |p|. It returns one on success or zero | |

* otherwise. */ | |

OPENSSL_EXPORT int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, | |

const BIGNUM *m, BN_CTX *ctx); | |

OPENSSL_EXPORT int BN_mod_exp_mont(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, | |

const BIGNUM *m, BN_CTX *ctx, | |

BN_MONT_CTX *m_ctx); | |

OPENSSL_EXPORT int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, | |

const BIGNUM *p, const BIGNUM *m, | |

BN_CTX *ctx, | |

const BN_MONT_CTX *mont); | |

OPENSSL_EXPORT int BN_mod_exp_mont_word(BIGNUM *r, BN_ULONG a, const BIGNUM *p, | |

const BIGNUM *m, BN_CTX *ctx, | |

BN_MONT_CTX *m_ctx); | |

OPENSSL_EXPORT int BN_mod_exp2_mont(BIGNUM *r, const BIGNUM *a1, | |

const BIGNUM *p1, const BIGNUM *a2, | |

const BIGNUM *p2, const BIGNUM *m, | |

BN_CTX *ctx, BN_MONT_CTX *m_ctx); | |

/* Deprecated functions */ | |

/* BN_bn2mpi serialises the value of |in| to |out|, using a format that consists | |

* of the number's length in bytes represented as a 4-byte big-endian number, | |

* and the number itself in big-endian format, where the most significant bit | |

* signals a negative number. (The representation of numbers with the MSB set is | |

* prefixed with null byte). |out| must have sufficient space available; to | |

* find the needed amount of space, call the function with |out| set to NULL. */ | |

OPENSSL_EXPORT size_t BN_bn2mpi(const BIGNUM *in, uint8_t *out); | |

/* BN_mpi2bn parses |len| bytes from |in| and returns the resulting value. The | |

* bytes at |in| are expected to be in the format emitted by |BN_bn2mpi|. | |

* | |

* If |out| is NULL then a fresh |BIGNUM| is allocated and returned, otherwise | |

* |out| is reused and returned. On error, NULL is returned and the error queue | |

* is updated. */ | |

OPENSSL_EXPORT BIGNUM *BN_mpi2bn(const uint8_t *in, size_t len, BIGNUM *out); | |

/* Private functions */ | |

struct bignum_st { | |

BN_ULONG *d; /* Pointer to an array of 'BN_BITS2' bit chunks in little-endian | |

order. */ | |

int top; /* Index of last used element in |d|, plus one. */ | |

int dmax; /* Size of |d|, in words. */ | |

int neg; /* one if the number is negative */ | |

int flags; /* bitmask of BN_FLG_* values */ | |

}; | |

struct bn_mont_ctx_st { | |

BIGNUM RR; /* used to convert to montgomery form */ | |

BIGNUM N; /* The modulus */ | |

BIGNUM Ni; /* R*(1/R mod N) - N*Ni = 1 | |

* (Ni is only stored for bignum algorithm) */ | |

BN_ULONG n0[2]; /* least significant word(s) of Ni; | |

(type changed with 0.9.9, was "BN_ULONG n0;" before) */ | |

int ri; /* number of bits in R */ | |

}; | |

OPENSSL_EXPORT unsigned BN_num_bits_word(BN_ULONG l); | |

#define BN_FLG_MALLOCED 0x01 | |

#define BN_FLG_STATIC_DATA 0x02 | |

/* avoid leaking exponent information through timing, BN_mod_exp_mont() will | |

* call BN_mod_exp_mont_consttime, BN_div() will call BN_div_no_branch, | |

* BN_mod_inverse() will call BN_mod_inverse_no_branch. */ | |

#define BN_FLG_CONSTTIME 0x04 | |

/* Android compatibility section. | |

* | |

* These functions are declared, temporarily, for Android because | |

* wpa_supplicant will take a little time to sync with upstream. Outside of | |

* Android they'll have no definition. */ | |

OPENSSL_EXPORT BIGNUM *get_rfc3526_prime_1536(BIGNUM *bn); | |

#if defined(__cplusplus) | |

} /* extern C */ | |

#endif | |

#define BN_R_ARG2_LT_ARG3 100 | |

#define BN_R_BAD_RECIPROCAL 101 | |

#define BN_R_BIGNUM_TOO_LONG 102 | |

#define BN_R_BITS_TOO_SMALL 103 | |

#define BN_R_CALLED_WITH_EVEN_MODULUS 104 | |

#define BN_R_DIV_BY_ZERO 105 | |

#define BN_R_EXPAND_ON_STATIC_BIGNUM_DATA 106 | |

#define BN_R_INPUT_NOT_REDUCED 107 | |

#define BN_R_INVALID_RANGE 108 | |

#define BN_R_NEGATIVE_NUMBER 109 | |

#define BN_R_NOT_A_SQUARE 110 | |

#define BN_R_NOT_INITIALIZED 111 | |

#define BN_R_NO_INVERSE 112 | |

#define BN_R_PRIVATE_KEY_TOO_LARGE 113 | |

#define BN_R_P_IS_NOT_PRIME 114 | |

#define BN_R_TOO_MANY_ITERATIONS 115 | |

#define BN_R_TOO_MANY_TEMPORARY_VARIABLES 116 | |

#define BN_R_BAD_ENCODING 117 | |

#define BN_R_ENCODE_ERROR 118 | |

#endif /* OPENSSL_HEADER_BN_H */ |