
from __future__ import annotations



def 		UpperCamelCase     (       _UpperCAmelCase  :   int  )   ->			list[int]:






						'''simple docstring'''

						_lowercase       :	Optional[Any]           =   [True] * limit
						_lowercase       :	List[str]           =   False
						_lowercase       :	Tuple           =   False
						_lowercase       :	str           =   True

						for i in range(3 ,			int(limit**0.5 + 1  ) ,			2  ):
												_lowercase       :	List[str]           =   i * 2
												while index < limit:
																		_lowercase       :	Tuple           =   False
																		_lowercase       :	Tuple           =   index + i

						_lowercase       :	int           =   [2]

						for i in range(3 ,			_UpperCAmelCase ,			2  ):
												if is_prime[i]:
																		primes.append(_UpperCAmelCase  )

						return primes



def 		UpperCamelCase     (       _UpperCAmelCase  :   int = 100_0000  )   ->			int:






						'''simple docstring'''

						_lowercase       :	List[Any]           =   prime_sieve(_UpperCAmelCase  )
						_lowercase       :	Dict           =   0
						_lowercase       :	Dict           =   0

						for i in range(len(_UpperCAmelCase  )  ):
												for j in range(i + length ,			len(_UpperCAmelCase  )  ):
																		_lowercase       :	Optional[Any]           =   sum(primes[i:j]  )
																		if sol >= ceiling:
																								break

																		if sol in primes:
																								_lowercase       :	Tuple           =   j - i
																								_lowercase       :	List[Any]           =   sol

						return largest


if __name__ == "__main__":
							print(f'''{solution() = }''')






import os
import random
import sys

from . import cryptomath_module as cryptomath
from . import rabin_miller

UpperCamelCase_						:     List[Any]	       =							3



def 		UpperCamelCase     (       _UpperCAmelCase  :   int  )   ->			int:






						'''simple docstring'''

						print("Generating primitive root of p"  )
						while True:
												_lowercase       :	Any           =   random.randrange(3 ,			_UpperCAmelCase  )
												if pow(_UpperCAmelCase ,			2 ,			_UpperCAmelCase  ) == 1:
																		continue
												if pow(_UpperCAmelCase ,			_UpperCAmelCase ,			_UpperCAmelCase  ) == 1:
																		continue
												return g



def 		UpperCamelCase     (       _UpperCAmelCase  :   int  )   ->			tuple[tuple[int, int, int, int], tuple[int, int]]:






						'''simple docstring'''

						print("Generating prime p..."  )
						_lowercase       :	Optional[int]           =   rabin_miller.generate_large_prime(_UpperCAmelCase  )  # select large prime number.
						_lowercase       :	Dict           =   primitive_root(_UpperCAmelCase  )  # one primitive root on modulo p.
						_lowercase       :	Any           =   random.randrange(3 ,			_UpperCAmelCase  )  # private_key -> have to be greater than 2 for safety.
						_lowercase       :	Tuple           =   cryptomath.find_mod_inverse(pow(_UpperCAmelCase ,			_UpperCAmelCase ,			_UpperCAmelCase  ) ,			_UpperCAmelCase  )

						_lowercase       :	List[Any]           =   (key_size, e_a, e_a, p)
						_lowercase       :	Union[str, Any]           =   (key_size, d)

						return public_key, private_key



def 		UpperCamelCase     (       _UpperCAmelCase  :   str ,			_UpperCAmelCase  :   int  )   ->			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       :	Optional[Any]           =   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()




