TheAlgorithms · ruppysuppy · Jan 21, 2021 · Oct 4, 2020 · Oct 9, 2020 · Nov 2, 2020
diff --git 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
@@ -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()