| /* 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 <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. */ |
| #if defined(OPENSSL_64_BIT) |
| #define BN_ULONG uint64_t |
| #define BN_BITS2 64 |
| #elif defined(OPENSSL_32_BIT) |
| #define BN_ULONG uint32_t |
| #define BN_BITS2 32 |
| #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|. */ |
| 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); |
| |
| |
| /* 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, unsigned 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. */ |
| 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_mul 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 will be set. If |top| is one, the two most |
| * significant bits 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 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_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_init initialises a stack allocated |BN_MONT_CTX|. */ |
| OPENSSL_EXPORT void BN_MONT_CTX_init(BN_MONT_CTX *mont); |
| |
| /* BN_MONT_CTX_free frees the contexts of |mont| and, if it was originally |
| * allocated with |BN_MONT_CTX_new|, |mont| itself. */ |
| 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 the lock indicated by |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. */ |
| OPENSSL_EXPORT BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, |
| int lock, const BIGNUM *mod, |
| BN_CTX *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, BN_MONT_CTX *in_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); |
| |
| |
| /* 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 flags; |
| 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 |
| |
| |
| #if defined(__cplusplus) |
| } /* extern C */ |
| #endif |
| |
| #define BN_F_BN_bn2hex 100 |
| #define BN_F_BN_new 101 |
| #define BN_F_BN_exp 102 |
| #define BN_F_mod_exp_recp 103 |
| #define BN_F_BN_mod_sqrt 104 |
| #define BN_F_BN_rand 105 |
| #define BN_F_BN_rand_range 106 |
| #define BN_F_bn_wexpand 107 |
| #define BN_F_BN_mod_exp_mont 108 |
| #define BN_F_BN_mod_exp2_mont 109 |
| #define BN_F_BN_CTX_get 110 |
| #define BN_F_BN_mod_inverse 111 |
| #define BN_F_BN_bn2dec 112 |
| #define BN_F_BN_div 113 |
| #define BN_F_BN_div_recp 114 |
| #define BN_F_BN_mod_exp_mont_consttime 115 |
| #define BN_F_BN_mod_exp_mont_word 116 |
| #define BN_F_BN_CTX_start 117 |
| #define BN_F_BN_usub 118 |
| #define BN_F_BN_mod_lshift_quick 119 |
| #define BN_F_BN_CTX_new 120 |
| #define BN_F_BN_mod_inverse_no_branch 121 |
| #define BN_F_BN_generate_dsa_nonce 122 |
| #define BN_F_BN_generate_prime_ex 123 |
| #define BN_F_BN_sqrt 124 |
| #define BN_R_NOT_A_SQUARE 100 |
| #define BN_R_TOO_MANY_ITERATIONS 101 |
| #define BN_R_INPUT_NOT_REDUCED 102 |
| #define BN_R_TOO_MANY_TEMPORARY_VARIABLES 103 |
| #define BN_R_NO_INVERSE 104 |
| #define BN_R_NOT_INITIALIZED 105 |
| #define BN_R_DIV_BY_ZERO 106 |
| #define BN_R_CALLED_WITH_EVEN_MODULUS 107 |
| #define BN_R_EXPAND_ON_STATIC_BIGNUM_DATA 108 |
| #define BN_R_BAD_RECIPROCAL 109 |
| #define BN_R_P_IS_NOT_PRIME 110 |
| #define BN_R_INVALID_RANGE 111 |
| #define BN_R_ARG2_LT_ARG3 112 |
| #define BN_R_BIGNUM_TOO_LONG 113 |
| #define BN_R_PRIVATE_KEY_TOO_LARGE 114 |
| #define BN_R_BITS_TOO_SMALL 115 |
| #define BN_R_NEGATIVE_NUMBER 116 |
| |
| #endif /* OPENSSL_HEADER_BN_H */ |