





from binascii import hexlify
from hashlib import shaaaa
from os import urandom

# RFC 3526 - More Modular Exponential (MODP) Diffie-Hellman groups for
# Internet Key Exchange (IKE) https://tools.ietf.org/html/rfc3526

__A									=				{
    # 1536-bit
    5: {
        "prime": int(
            "FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1"
            + "29024E088A67CC74020BBEA63B139B22514A08798E3404DD"
            + "EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245"
            + "E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED"
            + "EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D"
            + "C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F"
            + "83655D23DCA3AD961C62F356208552BB9ED529077096966D"
            + "670C354E4ABC9804F1746C08CA237327FFFFFFFFFFFFFFFF",
            base=16,
        ),
        "generator": 2,
    },
    # 2048-bit
    14: {
        "prime": int(
            "FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1"
            + "29024E088A67CC74020BBEA63B139B22514A08798E3404DD"
            + "EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245"
            + "E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED"
            + "EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D"
            + "C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F"
            + "83655D23DCA3AD961C62F356208552BB9ED529077096966D"
            + "670C354E4ABC9804F1746C08CA18217C32905E462E36CE3B"
            + "E39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9"
            + "DE2BCBF6955817183995497CEA956AE515D2261898FA0510"
            + "15728E5A8AACAA68FFFFFFFFFFFFFFFF",
            base=16,
        ),
        "generator": 2,
    },
    # 3072-bit
    15: {
        "prime": int(
            "FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1"
            + "29024E088A67CC74020BBEA63B139B22514A08798E3404DD"
            + "EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245"
            + "E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED"
            + "EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D"
            + "C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F"
            + "83655D23DCA3AD961C62F356208552BB9ED529077096966D"
            + "670C354E4ABC9804F1746C08CA18217C32905E462E36CE3B"
            + "E39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9"
            + "DE2BCBF6955817183995497CEA956AE515D2261898FA0510"
            + "15728E5A8AAAC42DAD33170D04507A33A85521ABDF1CBA64"
            + "ECFB850458DBEF0A8AEA71575D060C7DB3970F85A6E1E4C7"
            + "ABF5AE8CDB0933D71E8C94E04A25619DCEE3D2261AD2EE6B"
            + "F12FFA06D98A0864D87602733EC86A64521F2B18177B200C"
            + "BBE117577A615D6C770988C0BAD946E208E24FA074E5AB31"
            + "43DB5BFCE0FD108E4B82D120A93AD2CAFFFFFFFFFFFFFFFF",
            base=16,
        ),
        "generator": 2,
    },
    # 4096-bit
    16: {
        "prime": int(
            "FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1"
            + "29024E088A67CC74020BBEA63B139B22514A08798E3404DD"
            + "EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245"
            + "E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED"
            + "EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D"
            + "C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F"
            + "83655D23DCA3AD961C62F356208552BB9ED529077096966D"
            + "670C354E4ABC9804F1746C08CA18217C32905E462E36CE3B"
            + "E39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9"
            + "DE2BCBF6955817183995497CEA956AE515D2261898FA0510"
            + "15728E5A8AAAC42DAD33170D04507A33A85521ABDF1CBA64"
            + "ECFB850458DBEF0A8AEA71575D060C7DB3970F85A6E1E4C7"
            + "ABF5AE8CDB0933D71E8C94E04A25619DCEE3D2261AD2EE6B"
            + "F12FFA06D98A0864D87602733EC86A64521F2B18177B200C"
            + "BBE117577A615D6C770988C0BAD946E208E24FA074E5AB31"
            + "43DB5BFCE0FD108E4B82D120A92108011A723C12A787E6D7"
            + "88719A10BDBA5B2699C327186AF4E23C1A946834B6150BDA"
            + "2583E9CA2AD44CE8DBBBC2DB04DE8EF92E8EFC141FBECAA6"
            + "287C59474E6BC05D99B2964FA090C3A2233BA186515BE7ED"
            + "1F612970CEE2D7AFB81BDD762170481CD0069127D5B05AA9"
            + "93B4EA988D8FDDC186FFB7DC90A6C08F4DF435C934063199"
            + "FFFFFFFFFFFFFFFF",
            base=16,
        ),
        "generator": 2,
    },
    # 6144-bit
    17: {
        "prime": int(
            "FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD129024E08"
            + "8A67CC74020BBEA63B139B22514A08798E3404DDEF9519B3CD3A431B"
            + "302B0A6DF25F14374FE1356D6D51C245E485B576625E7EC6F44C42E9"
            + "A637ED6B0BFF5CB6F406B7EDEE386BFB5A899FA5AE9F24117C4B1FE6"
            + "49286651ECE45B3DC2007CB8A163BF0598DA48361C55D39A69163FA8"
            + "FD24CF5F83655D23DCA3AD961C62F356208552BB9ED529077096966D"
            + "670C354E4ABC9804F1746C08CA18217C32905E462E36CE3BE39E772C"
            + "180E86039B2783A2EC07A28FB5C55DF06F4C52C9DE2BCBF695581718"
            + "3995497CEA956AE515D2261898FA051015728E5A8AAAC42DAD33170D"
            + "04507A33A85521ABDF1CBA64ECFB850458DBEF0A8AEA71575D060C7D"
            + "B3970F85A6E1E4C7ABF5AE8CDB0933D71E8C94E04A25619DCEE3D226"
            + "1AD2EE6BF12FFA06D98A0864D87602733EC86A64521F2B18177B200C"
            + "BBE117577A615D6C770988C0BAD946E208E24FA074E5AB3143DB5BFC"
            + "E0FD108E4B82D120A92108011A723C12A787E6D788719A10BDBA5B26"
            + "99C327186AF4E23C1A946834B6150BDA2583E9CA2AD44CE8DBBBC2DB"
            + "04DE8EF92E8EFC141FBECAA6287C59474E6BC05D99B2964FA090C3A2"
            + "233BA186515BE7ED1F612970CEE2D7AFB81BDD762170481CD0069127"
            + "D5B05AA993B4EA988D8FDDC186FFB7DC90A6C08F4DF435C934028492"
            + "36C3FAB4D27C7026C1D4DCB2602646DEC9751E763DBA37BDF8FF9406"
            + "AD9E530EE5DB382F413001AEB06A53ED9027D831179727B0865A8918"
            + "DA3EDBEBCF9B14ED44CE6CBACED4BB1BDB7F1447E6CC254B33205151"
            + "2BD7AF426FB8F401378CD2BF5983CA01C64B92ECF032EA15D1721D03"
            + "F482D7CE6E74FEF6D55E702F46980C82B5A84031900B1C9E59E7C97F"
            + "BEC7E8F323A97A7E36CC88BE0F1D45B7FF585AC54BD407B22B4154AA"
            + "CC8F6D7EBF48E1D814CC5ED20F8037E0A79715EEF29BE32806A1D58B"
            + "B7C5DA76F550AA3D8A1FBFF0EB19CCB1A313D55CDA56C9EC2EF29632"
            + "387FE8D76E3C0468043E8F663F4860EE12BF2D5B0B7474D6E694F91E"
            + "6DCC4024FFFFFFFFFFFFFFFF",
            base=16,
        ),
        "generator": 2,
    },
    # 8192-bit
    18: {
        "prime": int(
            "FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1"
            + "29024E088A67CC74020BBEA63B139B22514A08798E3404DD"
            + "EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245"
            + "E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED"
            + "EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D"
            + "C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F"
            + "83655D23DCA3AD961C62F356208552BB9ED529077096966D"
            + "670C354E4ABC9804F1746C08CA18217C32905E462E36CE3B"
            + "E39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9"
            + "DE2BCBF6955817183995497CEA956AE515D2261898FA0510"
            + "15728E5A8AAAC42DAD33170D04507A33A85521ABDF1CBA64"
            + "ECFB850458DBEF0A8AEA71575D060C7DB3970F85A6E1E4C7"
            + "ABF5AE8CDB0933D71E8C94E04A25619DCEE3D2261AD2EE6B"
            + "F12FFA06D98A0864D87602733EC86A64521F2B18177B200C"
            + "BBE117577A615D6C770988C0BAD946E208E24FA074E5AB31"
            + "43DB5BFCE0FD108E4B82D120A92108011A723C12A787E6D7"
            + "88719A10BDBA5B2699C327186AF4E23C1A946834B6150BDA"
            + "2583E9CA2AD44CE8DBBBC2DB04DE8EF92E8EFC141FBECAA6"
            + "287C59474E6BC05D99B2964FA090C3A2233BA186515BE7ED"
            + "1F612970CEE2D7AFB81BDD762170481CD0069127D5B05AA9"
            + "93B4EA988D8FDDC186FFB7DC90A6C08F4DF435C934028492"
            + "36C3FAB4D27C7026C1D4DCB2602646DEC9751E763DBA37BD"
            + "F8FF9406AD9E530EE5DB382F413001AEB06A53ED9027D831"
            + "179727B0865A8918DA3EDBEBCF9B14ED44CE6CBACED4BB1B"
            + "DB7F1447E6CC254B332051512BD7AF426FB8F401378CD2BF"
            + "5983CA01C64B92ECF032EA15D1721D03F482D7CE6E74FEF6"
            + "D55E702F46980C82B5A84031900B1C9E59E7C97FBEC7E8F3"
            + "23A97A7E36CC88BE0F1D45B7FF585AC54BD407B22B4154AA"
            + "CC8F6D7EBF48E1D814CC5ED20F8037E0A79715EEF29BE328"
            + "06A1D58BB7C5DA76F550AA3D8A1FBFF0EB19CCB1A313D55C"
            + "DA56C9EC2EF29632387FE8D76E3C0468043E8F663F4860EE"
            + "12BF2D5B0B7474D6E694F91E6DBE115974A3926F12FEE5E4"
            + "38777CB6A932DF8CD8BEC4D073B931BA3BC832B68D9DD300"
            + "741FA7BF8AFC47ED2576F6936BA424663AAB639C5AE4F568"
            + "3423B4742BF1C978238F16CBE39D652DE3FDB8BEFC848AD9"
            + "22222E04A4037C0713EB57A81A23F0C73473FC646CEA306B"
            + "4BCBC8862F8385DDFA9D4B7FA2C087E879683303ED5BDD3A"
            + "062B3CF5B3A278A66D2A13F83F44F82DDF310EE074AB6A36"
            + "4597E899A0255DC164F31CC50846851DF9AB48195DED7EA1"
            + "B1D510BD7EE74D73FAF36BC31ECFA268359046F4EB879F92"
            + "4009438B481C6CD7889A002ED5EE382BC9190DA6FC026E47"
            + "9558E4475677E9AA9E3050E2765694DFC81F56E880B96E71"
            + "60C980DD98EDD3DFFFFFFFFFFFFFFFFF",
            base=16,
        ),
        "generator": 2,
    },
}



class    _SCREAMING_SNAKE_CASE						:







 '''simple docstring'''

 def __init__(self				:   int       , UpperCAmelCase_				:   int = 14)       ->None:



   '''simple docstring'''



   if group not in primes:
     raise ValueError("Unsupported Group")
   lowerCamelCase__:      Union[str, Any]			  =primes[group]["prime"]
   lowerCamelCase__:      Optional[int]			  =primes[group]["generator"]

   lowerCamelCase__:      Dict			  =int(hexlify(urandom(32))       , base=16)

 def 							SCREAMING_SNAKE_CASE_					(self				:   str)       ->str:



   '''simple docstring'''



   return hex(self.__private_key)[2:]

 def 							SCREAMING_SNAKE_CASE_					(self				:   List[Any])       ->str:



   '''simple docstring'''



   lowerCamelCase__:      str			  =pow(self.generator       , self.__private_key       , self.prime)
   return hex(UpperCAmelCase_)[2:]

 def 							SCREAMING_SNAKE_CASE_					(self				:   int       , UpperCAmelCase_				:   int)       ->bool:



   '''simple docstring'''



   return (
       2 <= key <= self.prime - 2
       and pow(UpperCAmelCase_       , (self.prime - 1) // 2       , self.prime) == 1
   )

 def 							SCREAMING_SNAKE_CASE_					(self				:   Optional[int]       , UpperCAmelCase_				:   str)       ->str:



   '''simple docstring'''



   lowerCamelCase__:      int			  =int(UpperCAmelCase_       , base=16)
   if not self.is_valid_public_key(UpperCAmelCase_):
     raise ValueError("Invalid public key")
   lowerCamelCase__:      Dict			  =pow(UpperCAmelCase_       , self.__private_key       , self.prime)
   return shaaaa(str(UpperCAmelCase_).encode()).hexdigest()

 @staticmethod
 def 							SCREAMING_SNAKE_CASE_					(UpperCAmelCase_				:   int       , UpperCAmelCase_				:   int)       ->bool:



   '''simple docstring'''



   return (
       2 <= remote_public_key_str <= prime - 2
       and pow(UpperCAmelCase_       , (prime - 1) // 2       , UpperCAmelCase_) == 1
   )







 @staticmethod
 def 							SCREAMING_SNAKE_CASE_					(UpperCAmelCase_				:   str       , UpperCAmelCase_				:   str       , UpperCAmelCase_				:   int = 14)       ->str:



   '''simple docstring'''



   lowerCamelCase__:      Dict			  =int(UpperCAmelCase_       , base=16)
   lowerCamelCase__:      str			  =int(UpperCAmelCase_       , base=16)
   lowerCamelCase__:      Union[str, Any]			  =primes[group]["prime"]
   if not DiffieHellman.is_valid_public_key_static(UpperCAmelCase_       , UpperCAmelCase_):
     raise ValueError("Invalid public key")
   lowerCamelCase__:      List[Any]			  =pow(UpperCAmelCase_       , UpperCAmelCase_       , UpperCAmelCase_)
   return shaaaa(str(UpperCAmelCase_).encode()).hexdigest()


if __name__ == "__main__":
     import doctest

     doctest.testmod()




'''simple docstring'''
import copy
import re







class 							A__    :
  A__		 =				'hp'
  A__		 =				{}
  A__		 =				None





  @classmethod
  def 						A  (		cls      :	Optional[Any]							,					_a      :	Optional[Any]							,					_a      :	Any )	->    Union[str, Any]:





       '''simple docstring'''






       _SCREAMING_SNAKE_CASE							    =prefix
       _SCREAMING_SNAKE_CASE							    =defaults
       cls.build_naming_info()





  @staticmethod
  def 						A  (		_a      :	Optional[Any]							,					_a      :	List[Any] )	->    Any:





       '''simple docstring'''






       if len(_a ) == 0:
            return ""
       _SCREAMING_SNAKE_CASE							    =None
       if any(char.isdigit() for char in word ):
            raise Exception(f"Parameters should not contain numbers: '{word}' contains a number" )
       if word in info["short_word"]:
            return info["short_word"][word]
       for prefix_len in range(1							,					len(_a ) + 1 ):
            _SCREAMING_SNAKE_CASE							    =word[:prefix_len]
            if prefix in info["reverse_short_word"]:
                 continue
            else:
                 _SCREAMING_SNAKE_CASE							    =prefix
                 break

       if short_word is None:
            # Paranoid fallback
            def int_to_alphabetic(_a      :	str ):
                 _SCREAMING_SNAKE_CASE							    =''
                 while integer != 0:
                      _SCREAMING_SNAKE_CASE							    =chr(ord('A' ) + integer % 10 ) + s
                      integer //= 10
                 return s

            _SCREAMING_SNAKE_CASE							    =0
            while True:
                 _SCREAMING_SNAKE_CASE							    =word + '#' + int_to_alphabetic(_a )
                 if sword in info["reverse_short_word"]:
                      continue
                 else:
                      _SCREAMING_SNAKE_CASE							    =sword
                      break

       _SCREAMING_SNAKE_CASE							    =short_word
       _SCREAMING_SNAKE_CASE							    =word
       return short_word





  @staticmethod
  def 						A  (		_a      :	Optional[Any]							,					_a      :	int )	->    Optional[int]:





       '''simple docstring'''






       _SCREAMING_SNAKE_CASE							    =param_name.split('_' )

       _SCREAMING_SNAKE_CASE							    =[TrialShortNamer.shortname_for_word(_a							,					_a ) for word in words]

       # We try to create a separatorless short name, but if there is a collision we have to fallback
       # to a separated short name
       _SCREAMING_SNAKE_CASE							    =['', '_']

       for separator in separators:
            _SCREAMING_SNAKE_CASE							    =separator.join(_a )
            if shortname not in info["reverse_short_param"]:
                 _SCREAMING_SNAKE_CASE							    =shortname
                 _SCREAMING_SNAKE_CASE							    =param_name
                 return shortname

       return param_name





  @staticmethod
  def 						A  (		_a      :	Dict							,					_a      :	int )	->    Optional[Any]:





       '''simple docstring'''






       _SCREAMING_SNAKE_CASE							    =TrialShortNamer.shortname_for_key(_a							,					_a )
       _SCREAMING_SNAKE_CASE							    =short_name
       _SCREAMING_SNAKE_CASE							    =param_name





  @classmethod
  def 						A  (		cls      :	Optional[int] )	->    Tuple:





       '''simple docstring'''






       if cls.NAMING_INFO is not None:
            return

       _SCREAMING_SNAKE_CASE							    ={
           'short_word': {},
           'reverse_short_word': {},
           'short_param': {},
           'reverse_short_param': {},
       }

       _SCREAMING_SNAKE_CASE							    =list(cls.DEFAULTS.keys() )

       for k in field_keys:
            cls.add_new_param_name(_a							,					_a )

       _SCREAMING_SNAKE_CASE							    =info





  @classmethod
  def 						A  (		cls      :	List[Any]							,					_a      :	int )	->    int:





       '''simple docstring'''






       cls.build_naming_info()
       assert cls.PREFIX is not None
       _SCREAMING_SNAKE_CASE							    =[copy.copy(cls.PREFIX )]

       for k, v in params.items():
            if k not in cls.DEFAULTS:
                 raise Exception(f"You should provide a default value for the param name {k} with value {v}" )
            if v == cls.DEFAULTS[k]:
                 # The default value is not added to the name
                 continue

            _SCREAMING_SNAKE_CASE							    =cls.NAMING_INFO['short_param'][k]

            if isinstance(_a							,					_a ):
                 _SCREAMING_SNAKE_CASE							    =1 if v else 0

            _SCREAMING_SNAKE_CASE							    ='' if isinstance(_a							,					(int, float) ) else '-'
            _SCREAMING_SNAKE_CASE							    =f"{key}{sep}{v}"
            name.append(_a )

       return "_".join(_a )





  @classmethod
  def 						A  (		cls      :	Optional[Any]							,					_a      :	List[Any] )	->    Dict:





       '''simple docstring'''






       _SCREAMING_SNAKE_CASE							    =repr[len(cls.PREFIX ) + 1 :]
       if repr == "":
            _SCREAMING_SNAKE_CASE							    =[]
       else:
            _SCREAMING_SNAKE_CASE							    =repr.split('_' )

       _SCREAMING_SNAKE_CASE							    ={}

       for value in values:
            if "-" in value:
                 _SCREAMING_SNAKE_CASE    ,						_SCREAMING_SNAKE_CASE							    =value.split('-' )
            else:
                 _SCREAMING_SNAKE_CASE							    =re.sub('[0-9.]'							,					''							,					_a )
                 _SCREAMING_SNAKE_CASE							    =float(re.sub('[^0-9.]'							,					''							,					_a ) )

            _SCREAMING_SNAKE_CASE							    =cls.NAMING_INFO['reverse_short_param'][p_k]

            _SCREAMING_SNAKE_CASE							    =p_v

       for k in cls.DEFAULTS:
            if k not in parameters:
                 _SCREAMING_SNAKE_CASE							    =cls.DEFAULTS[k]

       return parameters
