/* MIT License
 *
 * Copyright (c) 2016-2022 INRIA, CMU and Microsoft Corporation
 * Copyright (c) 2022-2023 HACL* Contributors
 *
 * Permission is hereby granted, free of charge, to any person obtaining a copy
 * of this software and associated documentation files (the "Software"), to deal
 * in the Software without restriction, including without limitation the rights
 * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 * copies of the Software, and to permit persons to whom the Software is
 * furnished to do so, subject to the following conditions:
 *
 * The above copyright notice and this permission notice shall be included in all
 * copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
 * SOFTWARE.
 */


#ifndef __Hacl_Bignum4096_H
#define __Hacl_Bignum4096_H

#if defined(__cplusplus)
extern "C" {
#endif

#include <string.h>
#include "krml/internal/types.h"
#include "krml/lowstar_endianness.h"
#include "krml/internal/target.h"

#include "Hacl_Bignum.h"

/*******************************************************************************

A verified 4096-bit bignum library.

This is a 64-bit optimized version, where bignums are represented as an array
of sixty four unsigned 64-bit integers, i.e. uint64_t[64]. Furthermore, the
limbs are stored in little-endian format, i.e. the least significant limb is at
index 0. Each limb is stored in native format in memory. Example:

  uint64_t sixteen[64] = { 0x10 }

  (relying on the fact that when an initializer-list is provided, the remainder
  of the object gets initialized as if it had static storage duration, i.e. with
  zeroes)

We strongly encourage users to go through the conversion functions, e.g.
bn_from_bytes_be, to i) not depend on internal representation choices and ii)
have the ability to switch easily to a 32-bit optimized version in the future.

*******************************************************************************/

/************************/
/* Arithmetic functions */
/************************/


/**
Write `a + b mod 2^4096` in `res`.

  This functions returns the carry.

  The arguments a, b and res are meant to be 4096-bit bignums, i.e. uint64_t[64]
*/
uint64_t Hacl_Bignum4096_add(uint64_t *a, uint64_t *b, uint64_t *res);

/**
Write `a - b mod 2^4096` in `res`.

  This functions returns the carry.

  The arguments a, b and res are meant to be 4096-bit bignums, i.e. uint64_t[64]
*/
uint64_t Hacl_Bignum4096_sub(uint64_t *a, uint64_t *b, uint64_t *res);

/**
Write `(a + b) mod n` in `res`.

  The arguments a, b, n and the outparam res are meant to be 4096-bit bignums, i.e. uint64_t[64].

  Before calling this function, the caller will need to ensure that the following
  preconditions are observed.
  • a < n
  • b < n
*/
void Hacl_Bignum4096_add_mod(uint64_t *n, uint64_t *a, uint64_t *b, uint64_t *res);

/**
Write `(a - b) mod n` in `res`.

  The arguments a, b, n and the outparam res are meant to be 4096-bit bignums, i.e. uint64_t[64].

  Before calling this function, the caller will need to ensure that the following
  preconditions are observed.
  • a < n
  • b < n
*/
void Hacl_Bignum4096_sub_mod(uint64_t *n, uint64_t *a, uint64_t *b, uint64_t *res);

/**
Write `a * b` in `res`.

  The arguments a and b are meant to be 4096-bit bignums, i.e. uint64_t[64].
  The outparam res is meant to be a 8192-bit bignum, i.e. uint64_t[128].
*/
void Hacl_Bignum4096_mul(uint64_t *a, uint64_t *b, uint64_t *res);

/**
Write `a * a` in `res`.

  The argument a is meant to be a 4096-bit bignum, i.e. uint64_t[64].
  The outparam res is meant to be a 8192-bit bignum, i.e. uint64_t[128].
*/
void Hacl_Bignum4096_sqr(uint64_t *a, uint64_t *res);

/**
Write `a mod n` in `res`.

  The argument a is meant to be a 8192-bit bignum, i.e. uint64_t[128].
  The argument n and the outparam res are meant to be 4096-bit bignums, i.e. uint64_t[64].

  The function returns false if any of the following preconditions are violated,
  true otherwise.
   • 1 < n
   • n % 2 = 1 
*/
bool Hacl_Bignum4096_mod(uint64_t *n, uint64_t *a, uint64_t *res);

/**
Write `a ^ b mod n` in `res`.

  The arguments a, n and the outparam res are meant to be 4096-bit bignums, i.e. uint64_t[64].

  The argument b is a bignum of any size, and bBits is an upper bound on the
  number of significant bits of b. A tighter bound results in faster execution
  time. When in doubt, the number of bits for the bignum size is always a safe
  default, e.g. if b is a 4096-bit bignum, bBits should be 4096.

  The function is *NOT* constant-time on the argument b. See the
  mod_exp_consttime_* functions for constant-time variants.

  The function returns false if any of the following preconditions are violated,
  true otherwise.
   • n % 2 = 1
   • 1 < n
   • b < pow2 bBits
   • a < n
*/
bool
Hacl_Bignum4096_mod_exp_vartime(
  uint64_t *n,
  uint64_t *a,
  uint32_t bBits,
  uint64_t *b,
  uint64_t *res
);

/**
Write `a ^ b mod n` in `res`.

  The arguments a, n and the outparam res are meant to be 4096-bit bignums, i.e. uint64_t[64].

  The argument b is a bignum of any size, and bBits is an upper bound on the
  number of significant bits of b. A tighter bound results in faster execution
  time. When in doubt, the number of bits for the bignum size is always a safe
  default, e.g. if b is a 4096-bit bignum, bBits should be 4096.

  This function is constant-time over its argument b, at the cost of a slower
  execution time than mod_exp_vartime.

  The function returns false if any of the following preconditions are violated,
  true otherwise.
   • n % 2 = 1
   • 1 < n
   • b < pow2 bBits
   • a < n
*/
bool
Hacl_Bignum4096_mod_exp_consttime(
  uint64_t *n,
  uint64_t *a,
  uint32_t bBits,
  uint64_t *b,
  uint64_t *res
);

/**
Write `a ^ (-1) mod n` in `res`.

  The arguments a, n and the outparam res are meant to be 4096-bit bignums, i.e. uint64_t[64].

  Before calling this function, the caller will need to ensure that the following
  preconditions are observed.
  • n is a prime

  The function returns false if any of the following preconditions are violated, true otherwise.
  • n % 2 = 1
  • 1 < n
  • 0 < a
  • a < n
*/
bool Hacl_Bignum4096_mod_inv_prime_vartime(uint64_t *n, uint64_t *a, uint64_t *res);


/**********************************************/
/* Arithmetic functions with precomputations. */
/**********************************************/


/**
Heap-allocate and initialize a montgomery context.

  The argument n is meant to be a 4096-bit bignum, i.e. uint64_t[64].

  Before calling this function, the caller will need to ensure that the following
  preconditions are observed.
  • n % 2 = 1
  • 1 < n

  The caller will need to call Hacl_Bignum4096_mont_ctx_free on the return value
  to avoid memory leaks.
*/
Hacl_Bignum_MontArithmetic_bn_mont_ctx_u64 *Hacl_Bignum4096_mont_ctx_init(uint64_t *n);

/**
Deallocate the memory previously allocated by Hacl_Bignum4096_mont_ctx_init.

  The argument k is a montgomery context obtained through Hacl_Bignum4096_mont_ctx_init.
*/
void Hacl_Bignum4096_mont_ctx_free(Hacl_Bignum_MontArithmetic_bn_mont_ctx_u64 *k);

/**
Write `a mod n` in `res`.

  The argument a is meant to be a 8192-bit bignum, i.e. uint64_t[128].
  The outparam res is meant to be a 4096-bit bignum, i.e. uint64_t[64].
  The argument k is a montgomery context obtained through Hacl_Bignum4096_mont_ctx_init.
*/
void
Hacl_Bignum4096_mod_precomp(
  Hacl_Bignum_MontArithmetic_bn_mont_ctx_u64 *k,
  uint64_t *a,
  uint64_t *res
);

/**
Write `a ^ b mod n` in `res`.

  The arguments a and the outparam res are meant to be 4096-bit bignums, i.e. uint64_t[64].
  The argument k is a montgomery context obtained through Hacl_Bignum4096_mont_ctx_init.

  The argument b is a bignum of any size, and bBits is an upper bound on the
  number of significant bits of b. A tighter bound results in faster execution
  time. When in doubt, the number of bits for the bignum size is always a safe
  default, e.g. if b is a 4096-bit bignum, bBits should be 4096.

  The function is *NOT* constant-time on the argument b. See the
  mod_exp_consttime_* functions for constant-time variants.

  Before calling this function, the caller will need to ensure that the following
  preconditions are observed.
  • b < pow2 bBits
  • a < n
*/
void
Hacl_Bignum4096_mod_exp_vartime_precomp(
  Hacl_Bignum_MontArithmetic_bn_mont_ctx_u64 *k,
  uint64_t *a,
  uint32_t bBits,
  uint64_t *b,
  uint64_t *res
);

/**
Write `a ^ b mod n` in `res`.

  The arguments a and the outparam res are meant to be 4096-bit bignums, i.e. uint64_t[64].
  The argument k is a montgomery context obtained through Hacl_Bignum4096_mont_ctx_init.

  The argument b is a bignum of any size, and bBits is an upper bound on the
  number of significant bits of b. A tighter bound results in faster execution
  time. When in doubt, the number of bits for the bignum size is always a safe
  default, e.g. if b is a 4096-bit bignum, bBits should be 4096.

  This function is constant-time over its argument b, at the cost of a slower
  execution time than mod_exp_vartime_*.

  Before calling this function, the caller will need to ensure that the following
  preconditions are observed.
  • b < pow2 bBits
  • a < n
*/
void
Hacl_Bignum4096_mod_exp_consttime_precomp(
  Hacl_Bignum_MontArithmetic_bn_mont_ctx_u64 *k,
  uint64_t *a,
  uint32_t bBits,
  uint64_t *b,
  uint64_t *res
);

/**
Write `a ^ (-1) mod n` in `res`.

  The argument a and the outparam res are meant to be 4096-bit bignums, i.e. uint64_t[64].
  The argument k is a montgomery context obtained through Hacl_Bignum4096_mont_ctx_init.

  Before calling this function, the caller will need to ensure that the following
  preconditions are observed.
  • n is a prime
  • 0 < a
  • a < n
*/
void
Hacl_Bignum4096_mod_inv_prime_vartime_precomp(
  Hacl_Bignum_MontArithmetic_bn_mont_ctx_u64 *k,
  uint64_t *a,
  uint64_t *res
);


/********************/
/* Loads and stores */
/********************/


/**
Load a bid-endian bignum from memory.

  The argument b points to len bytes of valid memory.
  The function returns a heap-allocated bignum of size sufficient to hold the
   result of loading b, or NULL if either the allocation failed, or the amount of
    required memory would exceed 4GB.

  If the return value is non-null, clients must eventually call free(3) on it to
  avoid memory leaks.
*/
uint64_t *Hacl_Bignum4096_new_bn_from_bytes_be(uint32_t len, uint8_t *b);

/**
Load a little-endian bignum from memory.

  The argument b points to len bytes of valid memory.
  The function returns a heap-allocated bignum of size sufficient to hold the
   result of loading b, or NULL if either the allocation failed, or the amount of
    required memory would exceed 4GB.

  If the return value is non-null, clients must eventually call free(3) on it to
  avoid memory leaks.
*/
uint64_t *Hacl_Bignum4096_new_bn_from_bytes_le(uint32_t len, uint8_t *b);

/**
Serialize a bignum into big-endian memory.

  The argument b points to a 4096-bit bignum.
  The outparam res points to 512 bytes of valid memory.
*/
void Hacl_Bignum4096_bn_to_bytes_be(uint64_t *b, uint8_t *res);

/**
Serialize a bignum into little-endian memory.

  The argument b points to a 4096-bit bignum.
  The outparam res points to 512 bytes of valid memory.
*/
void Hacl_Bignum4096_bn_to_bytes_le(uint64_t *b, uint8_t *res);


/***************/
/* Comparisons */
/***************/


/**
Returns 2^64 - 1 if a < b, otherwise returns 0.

 The arguments a and b are meant to be 4096-bit bignums, i.e. uint64_t[64].
*/
uint64_t Hacl_Bignum4096_lt_mask(uint64_t *a, uint64_t *b);

/**
Returns 2^64 - 1 if a = b, otherwise returns 0.

 The arguments a and b are meant to be 4096-bit bignums, i.e. uint64_t[64].
*/
uint64_t Hacl_Bignum4096_eq_mask(uint64_t *a, uint64_t *b);

#if defined(__cplusplus)
}
#endif

#define __Hacl_Bignum4096_H_DEFINED
#endif
