diff --git a/DIRECTORY.md b/DIRECTORY.md index 4f17cf9c0..d487b3949 100644 --- a/DIRECTORY.md +++ b/DIRECTORY.md @@ -59,6 +59,7 @@ * [Decrypt Caesar With Chi Squared](https://github.com/TheAlgorithms/Python/blob/master/ciphers/decrypt_caesar_with_chi_squared.py) * [Deterministic Miller Rabin](https://github.com/TheAlgorithms/Python/blob/master/ciphers/deterministic_miller_rabin.py) * [Diffie](https://github.com/TheAlgorithms/Python/blob/master/ciphers/diffie.py) + * [Diffie Hellman](https://github.com/TheAlgorithms/Python/blob/master/ciphers/diffie_hellman.py) * [Elgamal Key Generator](https://github.com/TheAlgorithms/Python/blob/master/ciphers/elgamal_key_generator.py) * [Enigma Machine2](https://github.com/TheAlgorithms/Python/blob/master/ciphers/enigma_machine2.py) * [Hill Cipher](https://github.com/TheAlgorithms/Python/blob/master/ciphers/hill_cipher.py) @@ -224,7 +225,6 @@ * [Abbreviation](https://github.com/TheAlgorithms/Python/blob/master/dynamic_programming/abbreviation.py) * [Bitmask](https://github.com/TheAlgorithms/Python/blob/master/dynamic_programming/bitmask.py) * [Climbing Stairs](https://github.com/TheAlgorithms/Python/blob/master/dynamic_programming/climbing_stairs.py) - * [Coin Change](https://github.com/TheAlgorithms/Python/blob/master/dynamic_programming/coin_change.py) * [Edit Distance](https://github.com/TheAlgorithms/Python/blob/master/dynamic_programming/edit_distance.py) * [Factorial](https://github.com/TheAlgorithms/Python/blob/master/dynamic_programming/factorial.py) * [Fast Fibonacci](https://github.com/TheAlgorithms/Python/blob/master/dynamic_programming/fast_fibonacci.py) @@ -243,6 +243,7 @@ * [Max Non Adjacent Sum](https://github.com/TheAlgorithms/Python/blob/master/dynamic_programming/max_non_adjacent_sum.py) * [Max Sub Array](https://github.com/TheAlgorithms/Python/blob/master/dynamic_programming/max_sub_array.py) * [Max Sum Contiguous Subsequence](https://github.com/TheAlgorithms/Python/blob/master/dynamic_programming/max_sum_contiguous_subsequence.py) + * [Minimum Coin Change](https://github.com/TheAlgorithms/Python/blob/master/dynamic_programming/minimum_coin_change.py) * [Minimum Cost Path](https://github.com/TheAlgorithms/Python/blob/master/dynamic_programming/minimum_cost_path.py) * [Minimum Partition](https://github.com/TheAlgorithms/Python/blob/master/dynamic_programming/minimum_partition.py) * [Minimum Steps To One](https://github.com/TheAlgorithms/Python/blob/master/dynamic_programming/minimum_steps_to_one.py) diff --git a/ciphers/diffie_hellman.py b/ciphers/diffie_hellman.py new file mode 100644 index 000000000..ea35b67b4 --- /dev/null +++ b/ciphers/diffie_hellman.py @@ -0,0 +1,271 @@ +from binascii import hexlify +from hashlib import sha256 +from os import urandom + +# RFC 3526 - More Modular Exponential (MODP) Diffie-Hellman groups for +# Internet Key Exchange (IKE) https://tools.ietf.org/html/rfc3526 + +primes = { + # 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 DiffieHellman: + """ + Class to represent the Diffie-Hellman key exchange protocol + + + >>> alice = DiffieHellman() + >>> bob = DiffieHellman() + + >>> alice_private = alice.get_private_key() + >>> alice_public = alice.generate_public_key() + + >>> bob_private = bob.get_private_key() + >>> bob_public = bob.generate_public_key() + + >>> # generating shared key using the DH object + >>> alice_shared = alice.generate_shared_key(bob_public) + >>> bob_shared = bob.generate_shared_key(alice_public) + + >>> assert alice_shared == bob_shared + + >>> # generating shared key using static methods + >>> alice_shared = DiffieHellman.generate_shared_key_static( + ... alice_private, bob_public + ... ) + >>> bob_shared = DiffieHellman.generate_shared_key_static( + ... bob_private, alice_public + ... ) + + >>> assert alice_shared == bob_shared + """ + + # Current minimum recommendation is 2048 bit (group 14) + def __init__(self, group: int = 14) -> None: + if group not in primes: + raise ValueError("Unsupported Group") + self.prime = primes[group]["prime"] + self.generator = primes[group]["generator"] + + self.__private_key = int(hexlify(urandom(32)), base=16) + + def get_private_key(self) -> str: + return hex(self.__private_key)[2:] + + def generate_public_key(self) -> str: + public_key = pow(self.generator, self.__private_key, self.prime) + return hex(public_key)[2:] + + def is_valid_public_key(self, key: int) -> bool: + # check if the other public key is valid based on NIST SP800-56 + if 2 <= key and key <= self.prime - 2: + if pow(key, (self.prime - 1) // 2, self.prime) == 1: + return True + return False + + def generate_shared_key(self, other_key_str: str) -> str: + other_key = int(other_key_str, base=16) + if not self.is_valid_public_key(other_key): + raise ValueError("Invalid public key") + shared_key = pow(other_key, self.__private_key, self.prime) + return sha256(str(shared_key).encode()).hexdigest() + + @staticmethod + def is_valid_public_key_static( + local_private_key_str: str, remote_public_key_str: str, prime: int + ) -> bool: + # check if the other public key is valid based on NIST SP800-56 + if 2 <= remote_public_key_str and remote_public_key_str <= prime - 2: + if pow(remote_public_key_str, (prime - 1) // 2, prime) == 1: + return True + return False + + @staticmethod + def generate_shared_key_static( + local_private_key_str: str, remote_public_key_str: str, group: int = 14 + ) -> str: + local_private_key = int(local_private_key_str, base=16) + remote_public_key = int(remote_public_key_str, base=16) + prime = primes[group]["prime"] + if not DiffieHellman.is_valid_public_key_static( + local_private_key, remote_public_key, prime + ): + raise ValueError("Invalid public key") + shared_key = pow(remote_public_key, local_private_key, prime) + return sha256(str(shared_key).encode()).hexdigest() + + +if __name__ == "__main__": + import doctest + + doctest.testmod()