// Copyright 1995-2016 The OpenSSL Project Authors. All Rights Reserved.

// Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved.

//

// Licensed under the Apache License, Version 2.0 (the "License");

// you may not use this file except in compliance with the License.

// You may obtain a copy of the License at

//

//     https://www.apache.org/licenses/LICENSE-2.0

//

// Unless required by applicable law or agreed to in writing, software

// distributed under the License is distributed on an "AS IS" BASIS,

// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.

// See the License for the specific language governing permissions and

// limitations under the License.

#ifndef OPENSSL_HEADER_BN_H

#define OPENSSL_HEADER_BN_H

#include <openssl/base.h>   // IWYU pragma: export

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

#include <stdio.h>  // 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 much larger numbers.

//

// This library is developed for use inside BoringSSL, and uses implementation

// strategies that may not be ideal for other applications. Non-cryptographic

// uses should use a more general-purpose integer library, especially if

// performance-sensitive.

//

// Many functions in BN scale quadratically or higher in the bit length of their

// input. Callers at this layer are assumed to have capped input sizes within

// their performance tolerances.

// 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. This is due to text in C99 which

// was never adopted in any C++ standard and explicitly overruled in C++11. As

// this is a public header, bn.h does not define |__STDC_FORMAT_MACROS| itself.

// Projects which use |BN_*_FMT*| with outdated C headers may need to define it

// externally.

#if defined(OPENSSL_64_BIT)

typedef uint64_t BN_ULONG;

#define BN_BITS2 64

#define BN_DEC_FMT1 "%" PRIu64

#define BN_HEX_FMT1 "%" PRIx64

#define BN_HEX_FMT2 "%016" PRIx64

#elif defined(OPENSSL_32_BIT)

typedef uint32_t BN_ULONG;

#define BN_BITS2 32

#define BN_DEC_FMT1 "%" PRIu32

#define BN_HEX_FMT1 "%" PRIx32

#define BN_HEX_FMT2 "%08" 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);

// 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|.

//

// While |size_t| is the preferred type for byte counts, callers can assume that

// |BIGNUM|s are bounded such that this value, and its corresponding bit count,

// will always fit in |int|.

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_lebin2bn 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_lebin2bn(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.

//

// Converting an arbitrarily large integer to decimal is quadratic in the bit

// length of |a|. This function assumes the caller has capped the input within

// performance tolerances.

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.

//

// Converting an arbitrarily large integer to decimal is quadratic in the bit

// length of |a|. This function assumes the caller has capped the input within

// performance tolerances.

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|, considering only the absolute values of |a| and

// |b|. |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|, considering only the absolute values of |a| and

// |b|. The result must be non-negative, i.e. |b| <= |a|. |r| may be the same

// pointer as either |a| or |b|. It returns one on success and zero on error.

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. It returns one on success or

// zero on error. It is an error condition if |divisor| is zero.

//

// The outputs will be such that |quotient| * |divisor| + |rem| = |numerator|,

// with the quotient rounded towards zero. Thus, if |numerator| is negative,

// |rem| will be zero or negative. If |divisor| is negative, the sign of

// |quotient| will be flipped to compensate but otherwise rounding will be as if

// |divisor| were its absolute value.

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). 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.

// If |a| is a square and |p| > 2, there are two possible square roots. This

// function may return either and may even select one non-deterministically.

//

// If |in| is non-NULL, the function, instead of allocating the result, stores

// the result in |in| and returns |in| on success or NULL on failure.

//

// This function only works if |p| is a prime. If |p| is composite, it may fail

// or return an arbitrary value. Callers should not pass attacker-controlled

// values of |p|.

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);

#define BN_GENCB_GENERATED 0

#define BN_GENCB_PRIME_TEST 1

// bn_gencb_st, or |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.

struct bn_gencb_st {

  void *arg;        // callback-specific data

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

};

// BN_GENCB_new returns a newly-allocated |BN_GENCB| object, or NULL on

// allocation failure. The result must be released with |BN_GENCB_free| when

// done.

OPENSSL_EXPORT BN_GENCB *BN_GENCB_new(void);

// BN_GENCB_free releases memory associated with |callback|.

OPENSSL_EXPORT void BN_GENCB_free(BN_GENCB *callback);

// 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, BN_GENCB *),

                                 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_GENCB_get_arg returns |callback->arg|.

OPENSSL_EXPORT void *BN_GENCB_get_arg(const BN_GENCB *callback);

// 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_for_validation can be used as the |checks| argument to the

// primarily testing functions when validating an externally-supplied candidate

// prime. It gives a false positive rate of at most 2^{-128}. (The worst case

// false positive rate for a single iteration is 1/4 per

// https://eprint.iacr.org/2018/749. (1/4)^64 = 2^{-128}.)

#define BN_prime_checks_for_validation 64

// BN_prime_checks_for_generation can be used as the |checks| argument to the

// primality testing functions when generating random primes. It gives a false

// positive rate at most the security level of the corresponding RSA key size.

//

// Note this value only performs enough checks if the candidate prime was

// selected randomly. If validating an externally-supplied candidate, especially

// one that may be selected adversarially, use |BN_prime_checks_for_validation|

// instead.

#define BN_prime_checks_for_generation 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 186-5 B.3.2) with

// |checks| 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.

//

// See |BN_prime_checks_for_validation| and |BN_prime_checks_for_generation| for

// recommended values of |checks|.

OPENSSL_EXPORT int BN_enhanced_miller_rabin_primality_test(

    enum bn_primality_result_t *out_result, const BIGNUM *w, int checks,

    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 at most 2^{2*checks}. See

// |BN_prime_checks_for_validation| and |BN_prime_checks_for_generation| for

// recommended values of |checks|.

//

// 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 at most 2^{2*checks}.

// See |BN_prime_checks_for_validation| and |BN_prime_checks_for_generation| for

// recommended values of |checks|.

//

// 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.

OPENSSL_EXPORT 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. Note this function assumes |mod| is public.

OPENSSL_EXPORT BN_MONT_CTX *BN_MONT_CTX_new_for_modulus(const BIGNUM *mod,

                                                        BN_CTX *ctx);

// BN_MONT_CTX_new_consttime behaves like |BN_MONT_CTX_new_for_modulus| but

// treats |mod| as secret.

OPENSSL_EXPORT BN_MONT_CTX *BN_MONT_CTX_new_consttime(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_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*R), where

// |n| is the Montgomery modulus. Note n < R, so inputs in the range [0, n*n)

// are valid. This function 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);

// BN_mod_exp_mont behaves like |BN_mod_exp| but treats |a| as secret and

// requires 0 <= |a| < |m|.

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);

// BN_mod_exp_mont_consttime behaves like |BN_mod_exp| but treats |a|, |p|, and

// |m| as secret and requires 0 <= |a| < |m|.

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);

// BN_bn2binpad behaves like |BN_bn2bin_padded|, but it returns |len| on success

// and -1 on error.

//

// Use |BN_bn2bin_padded| instead. It is |size_t|-clean.

OPENSSL_EXPORT int BN_bn2binpad(const BIGNUM *in, uint8_t *out, int len);

// BN_bn2lebinpad behaves like |BN_bn2le_padded|, but it returns |len| on

// success and -1 on error.

//

// Use |BN_bn2le_padded| instead. It is |size_t|-clean.

OPENSSL_EXPORT int BN_bn2lebinpad(const BIGNUM *in, uint8_t *out, int len);

// BN_prime_checks is a deprecated alias for |BN_prime_checks_for_validation|.

// Use |BN_prime_checks_for_generation| or |BN_prime_checks_for_validation|

// instead. (This defaults to the |_for_validation| value in order to be

// conservative.)

#define BN_prime_checks BN_prime_checks_for_validation

// BN_secure_new calls |BN_new|.

OPENSSL_EXPORT BIGNUM *BN_secure_new(void);

// BN_le2bn calls |BN_lebin2bn|.

OPENSSL_EXPORT BIGNUM *BN_le2bn(const uint8_t *in, size_t len, BIGNUM *ret);

// 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;

};

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++" {

BSSL_NAMESPACE_BEGIN

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;

};

BSSL_NAMESPACE_END

}  // 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