python:实现Diffie-Hellman算法
from binascii import hexlify from hashlib import sha256 from os import urandom 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,/span> }, # 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(remote_public_key_str: int, 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(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()