from math import sqrt






def        __UpperCAmelCase    (       UpperCAmelCase       )->       List[str]:



			"""simple docstring"""







			assert isinstance(_lowercase,		_lowercase       ) and (
			    number >= 0
			), "'number' must been an int and positive"

			lowercase							=		True

			# 0 and 1 are none primes.
			if number <= 1:
						lowercase							=		False

			for divisor in range(2,		int(round(sqrt(_lowercase       )       )       ) + 1       ):
						# if 'number' divisible by 'divisor' then sets 'status'
						# of false and break up the loop.
						if number % divisor == 0:
									lowercase							=		False
									break

    # precondition
			assert isinstance(_lowercase,		_lowercase       ), "'status' must been from type bool"

			return status






def        __UpperCAmelCase    (       UpperCAmelCase       )->       int:



			"""simple docstring"""







			assert isinstance(_lowercase,		_lowercase       ) and (n > 2), "'N' must been an int and > 2"

			# beginList: contains all natural numbers from 2 up to N
			lowercase							=		list(range(2,		n + 1       )       )

			lowercase							=		[]  # this list will be returns.

			# actual sieve of erathostenes
			for i in range(len(_lowercase       )       ):
						for j in range(i + 1,		len(_lowercase       )       ):
									if (begin_list[i] != 0) and (begin_list[j] % begin_list[i] == 0):
												lowercase							=		0

    # filters actual prime numbers.
			lowercase							=		[x for x in begin_list if x != 0]

			# precondition
			assert isinstance(_lowercase,		_lowercase       ), "'ans' must been from type list"

			return ans






def        __UpperCAmelCase    (       UpperCAmelCase       )->       int:



			"""simple docstring"""







			assert isinstance(_lowercase,		_lowercase       ) and (n > 2), "'N' must been an int and > 2"

			lowercase							=		[]

			# iterates over all numbers between 2 up to N+1
			# if a number is prime then appends to list 'ans'
			for number in range(2,		n + 1       ):
						if is_prime(_lowercase       ):
									ans.append(_lowercase       )

    # precondition
			assert isinstance(_lowercase,		_lowercase       ), "'ans' must been from type list"

			return ans






def        __UpperCAmelCase    (       UpperCAmelCase       )->       Any:



			"""simple docstring"""







			assert isinstance(_lowercase,		_lowercase       ) and number >= 0, "'number' must been an int and >= 0"

			lowercase							=		[]  # this list will be returns of the function.

			# potential prime number factors.

			lowercase							=		2

			lowercase							=		number

			if number == 0 or number == 1:
						ans.append(_lowercase       )

			# if 'number' not prime then builds the prime factorization of 'number'
			elif not is_prime(_lowercase       ):
						while quotient != 1:
									if is_prime(_lowercase       ) and (quotient % factor == 0):
												ans.append(_lowercase       )
												quotient /= factor
									else:
												factor += 1

			else:
						ans.append(_lowercase       )

			# precondition
			assert isinstance(_lowercase,		_lowercase       ), "'ans' must been from type list"

			return ans






def        __UpperCAmelCase    (       UpperCAmelCase       )->       List[str]:



			"""simple docstring"""







			assert isinstance(_lowercase,		_lowercase       ) and (
			    number >= 0
			), "'number' bust been an int and >= 0"

			lowercase							=		0

			# prime factorization of 'number'
			lowercase							=		prime_factorization(_lowercase       )

			lowercase							=		max(_lowercase       )

			# precondition
			assert isinstance(_lowercase,		_lowercase       ), "'ans' must been from type int"

			return ans






def        __UpperCAmelCase    (       UpperCAmelCase       )->       List[str]:



			"""simple docstring"""







			assert isinstance(_lowercase,		_lowercase       ) and (
			    number >= 0
			), "'number' bust been an int and >= 0"

			lowercase							=		0

			# prime factorization of 'number'
			lowercase							=		prime_factorization(_lowercase       )

			lowercase							=		min(_lowercase       )

			# precondition
			assert isinstance(_lowercase,		_lowercase       ), "'ans' must been from type int"

			return ans






def        __UpperCAmelCase    (       UpperCAmelCase       )->       Optional[Any]:



			"""simple docstring"""







			assert isinstance(_lowercase,		_lowercase       ), "'number' must been an int"
			assert isinstance(number % 2 == 0,		_lowercase       ), "compare bust been from type bool"

			return number % 2 == 0






def        __UpperCAmelCase    (       UpperCAmelCase       )->       Optional[Any]:



			"""simple docstring"""







			assert isinstance(_lowercase,		_lowercase       ), "'number' must been an int"
			assert isinstance(number % 2 != 0,		_lowercase       ), "compare bust been from type bool"

			return number % 2 != 0






def        __UpperCAmelCase    (       UpperCAmelCase       )->       Optional[Any]:



			"""simple docstring"""







			assert (
			    isinstance(_lowercase,		_lowercase       ) and (number > 2) and is_even(_lowercase       )
			), "'number' must been an int, even and > 2"

			lowercase							=		[]  # this list will returned

			# creates a list of prime numbers between 2 up to 'number'
			lowercase							=		get_prime_numbers(_lowercase       )
			lowercase							=		len(_lowercase       )

			# run variable for while-loops.
			lowercase							=		0
			lowercase							=		None

			# exit variable. for break up the loops
			lowercase							=		True

			while i < len_pn and loop:
						lowercase							=		i + 1

						while j < len_pn and loop:
									if prime_numbers[i] + prime_numbers[j] == number:
												lowercase							=		False
												ans.append(prime_numbers[i]       )
												ans.append(prime_numbers[j]       )

									j += 1

						i += 1

			# precondition
			assert (
			    isinstance(_lowercase,		_lowercase       )
			    and (len(_lowercase       ) == 2)
			    and (ans[0] + ans[1] == number)
			    and is_prime(ans[0]       )
			    and is_prime(ans[1]       )
			), "'ans' must contains two primes. And sum of elements must been eq 'number'"

			return ans






def        __UpperCAmelCase    (       UpperCAmelCase,		UpperCAmelCase       )->       int:



			"""simple docstring"""







			assert (
			    isinstance(_lowercase,		_lowercase       )
			    and isinstance(_lowercase,		_lowercase       )
			    and (numbera >= 0)
			    and (numbera >= 0)
			), "'number1' and 'number2' must been positive integer."

			lowercase							=		0

			while numbera != 0:
						lowercase							=		numbera % numbera
						lowercase							=		numbera
						lowercase							=		rest

			# precondition
			assert isinstance(_lowercase,		_lowercase       ) and (
			    numbera >= 0
			), "'number' must been from type int and positive"

			return numbera






def        __UpperCAmelCase    (       UpperCAmelCase,		UpperCAmelCase       )->       Optional[Any]:



			"""simple docstring"""







			assert (
			    isinstance(_lowercase,		_lowercase       )
			    and isinstance(_lowercase,		_lowercase       )
			    and (numbera >= 1)
			    and (numbera >= 1)
			), "'number1' and 'number2' must been positive integer."

			lowercase							=		1  # actual answer that will be return.

			# for kgV (x,1)
			if numbera > 1 and numbera > 1:
						# builds the prime factorization of 'number1' and 'number2'
						lowercase							=		prime_factorization(_lowercase       )
						lowercase							=		prime_factorization(_lowercase       )

			elif numbera == 1 or numbera == 1:
						lowercase							=		[]
						lowercase							=		[]
						lowercase							=		max(_lowercase,		_lowercase       )

			lowercase							=		0
			lowercase							=		0

			lowercase							=		[]  # captured numbers int both 'primeFac1' and 'primeFac2'

			# iterates through primeFac1
			for n in prime_fac_a:
						if n not in done:
									if n in prime_fac_a:
												lowercase							=		prime_fac_a.count(_lowercase       )
												lowercase							=		prime_fac_a.count(_lowercase       )

												for _ in range(max(_lowercase,		_lowercase       )       ):
															ans *= n

									else:
												lowercase							=		prime_fac_a.count(_lowercase       )

												for _ in range(_lowercase       ):
															ans *= n

									done.append(_lowercase       )

    # iterates through primeFac2
			for n in prime_fac_a:
						if n not in done:
									lowercase							=		prime_fac_a.count(_lowercase       )

									for _ in range(_lowercase       ):
												ans *= n

									done.append(_lowercase       )

    # precondition
			assert isinstance(_lowercase,		_lowercase       ) and (
			    ans >= 0
			), "'ans' must been from type int and positive"

			return ans






def        __UpperCAmelCase    (       UpperCAmelCase       )->       Tuple:



			"""simple docstring"""







			assert isinstance(_lowercase,		_lowercase       ) and (n >= 0), "'number' must been a positive int"

			lowercase							=		0
			lowercase							=		2  # this variable holds the answer

			while index < n:
						index += 1

						ans += 1  # counts to the next number

						# if ans not prime then
						# runs to the next prime number.
						while not is_prime(_lowercase       ):
									ans += 1

    # precondition
			assert isinstance(_lowercase,		_lowercase       ) and is_prime(
			    _lowercase       ), "'ans' must been a prime number and from type int"

			return ans






def        __UpperCAmelCase    (       UpperCAmelCase,		UpperCAmelCase       )->       int:



			"""simple docstring"""







			assert (
			    is_prime(_lowercase       ) and is_prime(_lowercase       ) and (p_number_a < p_number_a)
			), "The arguments must been prime numbers and 'pNumber1' < 'pNumber2'"

			lowercase							=		p_number_a + 1  # jump to the next number

			lowercase							=		[]  # this list will be returns.

			# if number is not prime then
			# fetch the next prime number.
			while not is_prime(_lowercase       ):
						number += 1

			while number < p_number_a:
						ans.append(_lowercase       )

						number += 1

						# fetch the next prime number.
						while not is_prime(_lowercase       ):
									number += 1

    # precondition
			assert (
			    isinstance(_lowercase,		_lowercase       )
			    and ans[0] != p_number_a
			    and ans[len(_lowercase       ) - 1] != p_number_a
			), "'ans' must been a list without the arguments"

			# 'ans' contains not 'pNumber1' and 'pNumber2' !
			return ans






def        __UpperCAmelCase    (       UpperCAmelCase       )->       Union[str, Any]:



			"""simple docstring"""







			assert isinstance(_lowercase,		_lowercase       ) and (n >= 1), "'n' must been int and >= 1"

			lowercase							=		[]  # will be returned.

			for divisor in range(1,		n + 1       ):
						if n % divisor == 0:
									ans.append(_lowercase       )

    # precondition
			assert ans[0] == 1 and ans[len(_lowercase       ) - 1] == n, "Error in function getDivisiors(...)"

			return ans






def        __UpperCAmelCase    (       UpperCAmelCase       )->       Dict:



			"""simple docstring"""







			assert isinstance(_lowercase,		_lowercase       ) and (
			    number > 1
			), "'number' must been an int and >= 1"

			lowercase							=		get_divisors(_lowercase       )

			# precondition
			assert (
			    isinstance(_lowercase,		_lowercase       )
			    and (divisors[0] == 1)
			    and (divisors[len(_lowercase       ) - 1] == number)
			), "Error in help-function getDivisiors(...)"

			# summed all divisors up to 'number' (exclusive), hence [:-1]
			return sum(divisors[:-1]       ) == number






def        __UpperCAmelCase    (       UpperCAmelCase,		UpperCAmelCase       )->       Optional[int]:



			"""simple docstring"""







			assert (
			    isinstance(_lowercase,		_lowercase       )
			    and isinstance(_lowercase,		_lowercase       )
			    and (denominator != 0)
			), "The arguments must been from type int and 'denominator' != 0"

			# build the greatest common divisor of numerator and denominator.
			lowercase							=		gcd(abs(_lowercase       ),		abs(_lowercase       )       )

			# precondition
			assert (
			    isinstance(_lowercase,		_lowercase       )
			    and (numerator % gcd_of_fraction == 0)
			    and (denominator % gcd_of_fraction == 0)
			), "Error in function gcd(...,...)"

			return (numerator // gcd_of_fraction, denominator // gcd_of_fraction)






def        __UpperCAmelCase    (       UpperCAmelCase       )->       Optional[int]:



			"""simple docstring"""







			assert isinstance(_lowercase,		_lowercase       ) and (n >= 0), "'n' must been a int and >= 0"

			lowercase							=		1  # this will be return.

			for factor in range(1,		n + 1       ):
						ans *= factor

			return ans






def        __UpperCAmelCase    (       UpperCAmelCase       )->       Optional[Any]:



			"""simple docstring"""







			assert isinstance(_lowercase,		_lowercase       ) and (n >= 0), "'n' must been an int and >= 0"

			lowercase							=		0
			lowercase							=		1
			lowercase							=		1  # this will be return

			for _ in range(n - 1       ):
						lowercase							=		ans
						ans += fiba
						lowercase							=		tmp

			return ans






import os
import random
import sys

from . import cryptomath_module as cryptomath
from . import rabin_miller

A_      =      3






def        __UpperCAmelCase    (       UpperCAmelCase       )->       int:



			"""simple docstring"""







			print('''Generating primitive root of p'''       )
			while True:
						lowercase							=		random.randrange(3,		UpperCAmelCase       )
						if pow(UpperCAmelCase,		2,		UpperCAmelCase       ) == 1:
									continue
						if pow(UpperCAmelCase,		UpperCAmelCase,		UpperCAmelCase       ) == 1:
									continue
						return g






def        __UpperCAmelCase    (       UpperCAmelCase       )->       tuple[tuple[int, int, int, int], tuple[int, int]]:



			"""simple docstring"""







			print('''Generating prime p...'''       )
			lowercase							=		rabin_miller.generate_large_prime(UpperCAmelCase       )  # select large prime number.
			lowercase							=		primitive_root(UpperCAmelCase       )  # one primitive root on modulo p.
			lowercase							=		random.randrange(3,		UpperCAmelCase       )  # private_key -> have to be greater than 2 for safety.
			lowercase							=		cryptomath.find_mod_inverse(pow(UpperCAmelCase,		UpperCAmelCase,		UpperCAmelCase       ),		UpperCAmelCase       )

			lowercase							=		(key_size, e_a, e_a, p)
			lowercase							=		(key_size, d)

			return public_key, private_key






def        __UpperCAmelCase    (       UpperCAmelCase,		UpperCAmelCase       )->       None:



			"""simple docstring"""







			if os.path.exists(f'{name}_pubkey.txt'       ) or os.path.exists(f'{name}_privkey.txt'       ):
						print('''\nWARNING:'''       )
						print(
						    f'"{name}_pubkey.txt" or "{name}_privkey.txt" already exists. \n'
						    '''Use a different name or delete these files and re-run this program.'''       )
						sys.exit()

			lowercase		,lowercase							=		generate_key(UpperCAmelCase       )
			print(f'\nWriting public key to file {name}_pubkey.txt...'       )
			with open(f'{name}_pubkey.txt',		'''w'''       ) as fo:
						fo.write(f'{public_key[0]},{public_key[1]},{public_key[2]},{public_key[3]}'       )

			print(f'Writing private key to file {name}_privkey.txt...'       )
			with open(f'{name}_privkey.txt',		'''w'''       ) as fo:
						fo.write(f'{private_key[0]},{private_key[1]}'       )






def        __UpperCAmelCase    (       )->       None:



			"""simple docstring"""







			print('''Making key files...'''       )
			make_key_files('''elgamal''',		2048       )
			print('''Key files generation successful'''       )


if __name__ == "__main__":
						main()





