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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
(
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
()
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