boringssl/include/openssl/bn.h

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// Projects which use `BN_*_FMT*` with outdated C headers may need to define it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