forked from TheAlgorithms/Python
-
Notifications
You must be signed in to change notification settings - Fork 0
/
diffie_hellman.py
271 lines (248 loc) · 12.3 KB
/
diffie_hellman.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
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()