/* 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 #include #include // for PRIu64 and friends #include // for FILE* #if defined(__cplusplus) extern "C" { #endif // BN provides support for working with arbitrary 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 #define BN_HEX_FMT2 "%016" 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 #define BN_HEX_FMT2 "%08" PRIx64 #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); // 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_u64 sets |bn| to |value|. It returns one on success or zero on // allocation failure. OPENSSL_EXPORT int BN_set_u64(BIGNUM *bn, uint64_t 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); // 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. Note this function leaks the magnitude of |in|. If // |in| is secret, use |BN_bn2bin_padded| instead. OPENSSL_EXPORT size_t BN_bn2bin(const BIGNUM *in, uint8_t *out); // BN_le2bn sets |*ret| to the value of |len| bytes from |in|, interpreted as // a little-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_le2bn(const uint8_t *in, size_t len, BIGNUM *ret); // BN_bn2le_padded serialises the absolute value of |in| to |out| as a // little-endian integer, which must have |len| of space available, padding // out the remainder of out with zeros. If |len| is smaller than |BN_num_bytes|, // the function fails and returns 0. Otherwise, it returns 1. OPENSSL_EXPORT int BN_bn2le_padded(uint8_t *out, size_t len, const BIGNUM *in); // 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_bn2cbb_padded behaves like |BN_bn2bin_padded| but writes to a |CBB|. OPENSSL_EXPORT int BN_bn2cbb_padded(CBB *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); // BN_get_u64 sets |*out| to the absolute value of |bn| as a |uint64_t| and // returns one. If |bn| is too large to be represented as a |uint64_t|, it // returns zero. OPENSSL_EXPORT int BN_get_u64(const BIGNUM *bn, uint64_t *out); // ASN.1 functions. // BN_parse_asn1_unsigned 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_parse_asn1_unsigned(CBS *cbs, BIGNUM *ret); // BN_marshal_asn1 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_marshal_asn1(CBB *cbb, const BIGNUM *bn); // BIGNUM pools. // // Certain BIGNUM operations need to use many temporary variables and // allocating and freeing them can be quite slow. Thus such operations 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| may be the same pointer as either |a| // or |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| may be the same pointer as either |a| or |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_cmp_word is like |BN_cmp| except it takes its second argument as a // |BN_ULONG| instead of a |BIGNUM|. OPENSSL_EXPORT int BN_cmp_word(const BIGNUM *a, BN_ULONG 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_equal_consttime returns one if |a| is equal to |b|, and zero otherwise. // It takes an amount of time dependent on the sizes of |a| and |b|, but // independent of the contents (including the signs) of |a| and |b|. OPENSSL_EXPORT int BN_equal_consttime(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); // BN_is_pow2 returns 1 if |a| is a power of two, and 0 otherwise. OPENSSL_EXPORT int BN_is_pow2(const BIGNUM *a); // 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 one if the |n|th least-significant bit in |a| exists // and is set. Otherwise, it returns zero. 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 negative. // // This differs from OpenSSL which additionally returns zero if |a|'s word // length is less than or equal to |n|, rounded down to a number of words. Note // word size is platform-dependent, so this behavior is also difficult to rely // on in OpenSSL and not very useful. OPENSSL_EXPORT int BN_mask_bits(BIGNUM *a, int n); // BN_count_low_zero_bits returns the number of low-order zero bits in |bn|, or // the number of factors of two which divide it. It returns zero if |bn| is // zero. OPENSSL_EXPORT int BN_count_low_zero_bits(const BIGNUM *bn); // Modulo arithmetic. // BN_mod_word returns |a| mod |w| or (BN_ULONG)-1 on error. OPENSSL_EXPORT BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w); // BN_mod_pow2 sets |r| = |a| mod 2^|e|. It returns 1 on success and // 0 on error. OPENSSL_EXPORT int BN_mod_pow2(BIGNUM *r, const BIGNUM *a, size_t e); // BN_nnmod_pow2 sets |r| = |a| mod 2^|e| where |r| is always positive. // It returns 1 on success and 0 on error. OPENSSL_EXPORT int BN_nnmod_pow2(BIGNUM *r, const BIGNUM *a, size_t e); // 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 newly-allocated |BIGNUM|, r, such that // r^2 == a (mod p). |p| must be a prime. It returns NULL on error or if |a| is // not a square mod |p|. In the latter case, it will add |BN_R_NOT_A_SQUARE| to // the error queue. OPENSSL_EXPORT BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx); // Random and prime number generation. // The following are values for the |top| parameter of |BN_rand|. #define BN_RAND_TOP_ANY (-1) #define BN_RAND_TOP_ONE 0 #define BN_RAND_TOP_TWO 1 // The following are values for the |bottom| parameter of |BN_rand|. #define BN_RAND_BOTTOM_ANY 0 #define BN_RAND_BOTTOM_ODD 1 // BN_rand sets |rnd| to a random number of length |bits|. It returns one on // success and zero otherwise. // // |top| must be one of the |BN_RAND_TOP_*| values. If |BN_RAND_TOP_ONE|, the // most-significant bit, if any, will be set. If |BN_RAND_TOP_TWO|, the two // most significant bits, if any, will be set. If |BN_RAND_TOP_ANY|, 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. // // |bottom| must be one of the |BN_RAND_BOTTOM_*| values. If // |BN_RAND_BOTTOM_ODD|, the least-significant bit, if any, will be set. If // |BN_RAND_BOTTOM_ANY|, no extra action will be taken. 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 is equivalent to |BN_rand_range_ex| with |min_inclusive| set // to zero and |max_exclusive| set to |range|. OPENSSL_EXPORT int BN_rand_range(BIGNUM *rnd, const BIGNUM *range); // BN_rand_range_ex sets |rnd| to a random value in // [min_inclusive..max_exclusive). It returns one on success and zero // otherwise. OPENSSL_EXPORT int BN_rand_range_ex(BIGNUM *r, BN_ULONG min_inclusive, const BIGNUM *max_exclusive); // BN_pseudo_rand_range is an alias for BN_rand_range. OPENSSL_EXPORT int BN_pseudo_rand_range(BIGNUM *rnd, const BIGNUM *range); // 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 arbitrary 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_result_t enumerates the outcomes of primality-testing. enum bn_primality_result_t { bn_probably_prime, bn_composite, bn_non_prime_power_composite, }; // BN_enhanced_miller_rabin_primality_test tests whether |w| is probably a prime // number using the Enhanced Miller-Rabin Test (FIPS 186-4 C.3.2) with // |iterations| iterations and returns the result in |out_result|. Enhanced // Miller-Rabin tests primality for odd integers greater than 3, returning // |bn_probably_prime| if the number is probably prime, // |bn_non_prime_power_composite| if the number is a composite that is not the // power of a single prime, and |bn_composite| otherwise. It returns one on // success and zero on failure. If |cb| is not NULL, then it is called during // each iteration of the primality test. // // If |iterations| is |BN_prime_checks|, then a value that results in a false // positive rate lower than the number-field sieve security level of |w| is // used, provided |w| was generated randomly. |BN_prime_checks| is not suitable // for inputs potentially crafted by an adversary. OPENSSL_EXPORT int BN_enhanced_miller_rabin_primality_test( enum bn_primality_result_t *out_result, const BIGNUM *w, int iterations, BN_CTX *ctx, BN_GENCB *cb); // 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 a false positive rate lower // than the number-field sieve security level of |candidate| is used, provided // |candidate| was generated randomly. |BN_prime_checks| is not suitable for // inputs potentially crafted by an adversary. // // 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. 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 a false positive // rate lower than the number-field sieve security level of |candidate| is used, // provided |candidate| was generated randomly. |BN_prime_checks| is not // suitable for inputs potentially crafted by an adversary. // // 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 |out| is NULL, a // fresh BIGNUM is allocated. It returns the result or NULL on error. // // If |n| is even then the operation is performed using an algorithm that avoids // some branches but which isn't constant-time. This function shouldn't be used // for secret values; use |BN_mod_inverse_blinded| instead. Or, if |n| is // guaranteed to be prime, use // |BN_mod_exp_mont_consttime(out, a, m_minus_2, m, ctx, m_mont)|, taking // advantage of Fermat's Little Theorem. OPENSSL_EXPORT BIGNUM *BN_mod_inverse(BIGNUM *out, const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx); // BN_mod_inverse_blinded sets |out| equal to |a|^-1, mod |n|, where |n| is the // Montgomery modulus for |mont|. |a| must be non-negative and must be less // than |n|. |n| must be greater than 1. |a| is blinded (masked by a random // value) to protect it against side-channel attacks. On failure, if the failure // was caused by |a| having no inverse mod |n| then |*out_no_inverse| will be // set to one; otherwise it will be set to zero. // // Note this function may incorrectly report |a| has no inverse if the random // blinding value has no inverse. It should only be used when |n| has few // non-invertible elements, such as an RSA modulus. int BN_mod_inverse_blinded(BIGNUM *out, int *out_no_inverse, const BIGNUM *a, const BN_MONT_CTX *mont, BN_CTX *ctx); // BN_mod_inverse_odd sets |out| equal to |a|^-1, mod |n|. |a| must be // non-negative and must be less than |n|. |n| must be odd. This function // shouldn't be used for secret values; use |BN_mod_inverse_blinded| instead. // Or, if |n| is guaranteed to be prime, use // |BN_mod_exp_mont_consttime(out, a, m_minus_2, m, ctx, m_mont)|, taking // advantage of Fermat's Little Theorem. It returns one on success or zero on // failure. On failure, if the failure was caused by |a| having no inverse mod // |n| then |*out_no_inverse| will be set to one; otherwise it will be set to // zero. int BN_mod_inverse_odd(BIGNUM *out, int *out_no_inverse, const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx); // Montgomery arithmetic. // BN_MONT_CTX contains the precomputed values needed to work in a specific // Montgomery domain. // BN_MONT_CTX_new_for_modulus returns a fresh |BN_MONT_CTX| given the modulus, // |mod| or NULL on error. OPENSSL_EXPORT BN_MONT_CTX *BN_MONT_CTX_new_for_modulus(const BIGNUM *mod, BN_CTX *ctx); // 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, const BN_MONT_CTX *from); // 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|. It returns one on success and zero on error. // // If |*pmont| is already non-NULL then it does nothing and returns one. int 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. |a| is // assumed to be in the range [0, n), where |n| is the Montgomery modulus. It // returns one on success or 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. |a| is assumed to be in the range [0, n), where |n| // is the Montgomery modulus. 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|). In particular, |a| and |b| are assumed to be in the // range [0, n), where |n| is the Montgomery modulus. 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. It returns one on success or zero // otherwise. The |BN_mod_exp_mont_consttime| variant must be used if the // exponent is secret. 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, const BN_MONT_CTX *mont); 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); // 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); // BN_mod_exp_mont_word is like |BN_mod_exp_mont| except that the base |a| is // given as a |BN_ULONG| instead of a |BIGNUM *|. It returns one on success // or zero otherwise. OPENSSL_EXPORT int BN_mod_exp_mont_word(BIGNUM *r, BN_ULONG a, const BIGNUM *p, const BIGNUM *m, BN_CTX *ctx, const BN_MONT_CTX *mont); // BN_mod_exp2_mont calculates (a1^p1) * (a2^p2) mod m. It returns 1 on success // or zero otherwise. 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, const BN_MONT_CTX *mont); // BN_MONT_CTX_new returns a fresh |BN_MONT_CTX| or NULL on allocation failure. // Use |BN_MONT_CTX_new_for_modulus| instead. OPENSSL_EXPORT BN_MONT_CTX *BN_MONT_CTX_new(void); // BN_MONT_CTX_set sets up a Montgomery context given the modulus, |mod|. It // returns one on success and zero on error. Use |BN_MONT_CTX_new_for_modulus| // instead. OPENSSL_EXPORT int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx); // Private functions struct bignum_st { // d is a pointer to an array of |width| |BN_BITS2|-bit chunks in // little-endian order. This stores the absolute value of the number. BN_ULONG *d; // width is the number of elements of |d| which are valid. This value is not // necessarily minimal; the most-significant words of |d| may be zero. // |width| determines a potentially loose upper-bound on the absolute value // of the |BIGNUM|. // // Functions taking |BIGNUM| inputs must compute the same answer for all // possible widths. |bn_minimal_width|, |bn_set_minimal_width|, and other // helpers may be used to recover the minimal width, provided it is not // secret. If it is secret, use a different algorithm. Functions may output // minimal or non-minimal |BIGNUM|s depending on secrecy requirements, but // those which cause widths to unboundedly grow beyond the minimal value // should be documented such. // // Note this is different from historical |BIGNUM| semantics. int width; // dmax is number of elements of |d| which are allocated. int dmax; // neg is one if the number if negative and zero otherwise. int neg; // flags is a bitmask of |BN_FLG_*| values int flags; }; struct bn_mont_ctx_st { // RR is R^2, reduced modulo |N|. It is used to convert to Montgomery form. BIGNUM RR; // N is the modulus. It is always stored in minimal form, so |N.top| // determines R. BIGNUM N; BN_ULONG n0[2]; // least significant words of (R*Ri-1)/N }; OPENSSL_EXPORT unsigned BN_num_bits_word(BN_ULONG l); #define BN_FLG_MALLOCED 0x01 #define BN_FLG_STATIC_DATA 0x02 // |BN_FLG_CONSTTIME| has been removed and intentionally omitted so code relying // on it will not compile. Consumers outside BoringSSL should use the // higher-level cryptographic algorithms exposed by other modules. Consumers // within the library should call the appropriate timing-sensitive algorithm // directly. #if defined(__cplusplus) } // extern C #if !defined(BORINGSSL_NO_CXX) extern "C++" { namespace bssl { BORINGSSL_MAKE_DELETER(BIGNUM, BN_free) BORINGSSL_MAKE_DELETER(BN_CTX, BN_CTX_free) BORINGSSL_MAKE_DELETER(BN_MONT_CTX, BN_MONT_CTX_free) class BN_CTXScope { public: BN_CTXScope(BN_CTX *ctx) : ctx_(ctx) { BN_CTX_start(ctx_); } ~BN_CTXScope() { BN_CTX_end(ctx_); } private: BN_CTX *ctx_; BN_CTXScope(BN_CTXScope &) = delete; BN_CTXScope &operator=(BN_CTXScope &) = delete; }; } // namespace bssl } // extern C++ #endif #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 #define BN_R_INVALID_INPUT 119 #endif // OPENSSL_HEADER_BN_H