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"""
This module contains several functions that authenticate the client machine
with Telegram's servers, effectively creating an authorization key.
"""
import os
import time
from hashlib import sha1
from ..tl.types import (
ResPQ, PQInnerData, ServerDHParamsFail, ServerDHParamsOk,
ServerDHInnerData, ClientDHInnerData, DhGenOk, DhGenRetry, DhGenFail
)
from .. import helpers
from ..crypto import AES, AuthKey, Factorization, rsa
from ..errors import SecurityError
from ..extensions import BinaryReader
from ..tl.functions import (
ReqPqMultiRequest, ReqDHParamsRequest, SetClientDHParamsRequest
)
async def do_authentication(sender):
"""
Executes the authentication process with the Telegram servers.
:param sender: a connected `MTProtoPlainSender`.
:return: returns a (authorization key, time offset) tuple.
"""
# Step 1 sending: PQ Request, endianness doesn't matter since it's random
nonce = int.from_bytes(os.urandom(16), 'big', signed=True)
res_pq = await sender.send(ReqPqMultiRequest(nonce))
assert isinstance(res_pq, ResPQ), 'Step 1 answer was %s' % res_pq
if res_pq.nonce != nonce:
raise SecurityError('Step 1 invalid nonce from server')
pq = get_int(res_pq.pq)
# Step 2 sending: DH Exchange
p, q = Factorization.factorize(pq)
p, q = rsa.get_byte_array(p), rsa.get_byte_array(q)
new_nonce = int.from_bytes(os.urandom(32), 'little', signed=True)
pq_inner_data = bytes(PQInnerData(
pq=rsa.get_byte_array(pq), p=p, q=q,
nonce=res_pq.nonce,
server_nonce=res_pq.server_nonce,
new_nonce=new_nonce
))
# sha_digest + data + random_bytes
cipher_text, target_fingerprint = None, None
for fingerprint in res_pq.server_public_key_fingerprints:
cipher_text = rsa.encrypt(fingerprint, pq_inner_data)
if cipher_text is not None:
target_fingerprint = fingerprint
break
if cipher_text is None:
# Second attempt, but now we're allowed to use old keys
for fingerprint in res_pq.server_public_key_fingerprints:
cipher_text = rsa.encrypt(fingerprint, pq_inner_data, use_old=True)
if cipher_text is not None:
target_fingerprint = fingerprint
break
if cipher_text is None:
raise SecurityError(
'Step 2 could not find a valid key for fingerprints: {}'
.format(', '.join(
[str(f) for f in res_pq.server_public_key_fingerprints])
)
)
server_dh_params = await sender.send(ReqDHParamsRequest(
nonce=res_pq.nonce,
server_nonce=res_pq.server_nonce,
p=p, q=q,
public_key_fingerprint=target_fingerprint,
encrypted_data=cipher_text
))
assert isinstance(
server_dh_params, (ServerDHParamsOk, ServerDHParamsFail)),\
'Step 2.1 answer was %s' % server_dh_params
if server_dh_params.nonce != res_pq.nonce:
raise SecurityError('Step 2 invalid nonce from server')
if server_dh_params.server_nonce != res_pq.server_nonce:
raise SecurityError('Step 2 invalid server nonce from server')
if isinstance(server_dh_params, ServerDHParamsFail):
nnh = int.from_bytes(
sha1(new_nonce.to_bytes(32, 'little', signed=True)).digest()[4:20],
'little', signed=True
)
if server_dh_params.new_nonce_hash != nnh:
raise SecurityError('Step 2 invalid DH fail nonce from server')
assert isinstance(server_dh_params, ServerDHParamsOk),\
'Step 2.2 answer was %s' % server_dh_params
# Step 3 sending: Complete DH Exchange
key, iv = helpers.generate_key_data_from_nonce(
res_pq.server_nonce, new_nonce
)
if len(server_dh_params.encrypted_answer) % 16 != 0:
# See PR#453
raise SecurityError('Step 3 AES block size mismatch')
plain_text_answer = AES.decrypt_ige(
server_dh_params.encrypted_answer, key, iv
)
with BinaryReader(plain_text_answer) as reader:
reader.read(20) # hash sum
server_dh_inner = reader.tgread_object()
assert isinstance(server_dh_inner, ServerDHInnerData),\
'Step 3 answer was %s' % server_dh_inner
if server_dh_inner.nonce != res_pq.nonce:
raise SecurityError('Step 3 Invalid nonce in encrypted answer')
if server_dh_inner.server_nonce != res_pq.server_nonce:
raise SecurityError('Step 3 Invalid server nonce in encrypted answer')
dh_prime = get_int(server_dh_inner.dh_prime, signed=False)
g = server_dh_inner.g
g_a = get_int(server_dh_inner.g_a, signed=False)
time_offset = server_dh_inner.server_time - int(time.time())
b = get_int(os.urandom(256), signed=False)
g_b = pow(g, b, dh_prime)
gab = pow(g_a, b, dh_prime)
# IMPORTANT: Apart from the conditions on the Diffie-Hellman prime
# dh_prime and generator g, both sides are to check that g, g_a and
# g_b are greater than 1 and less than dh_prime - 1. We recommend
# checking that g_a and g_b are between 2^{2048-64} and
# dh_prime - 2^{2048-64} as well.
# (https://core.telegram.org/mtproto/auth_key#dh-key-exchange-complete)
if not (1 < g < (dh_prime - 1)):
raise SecurityError('g_a is not within (1, dh_prime - 1)')
if not (1 < g_a < (dh_prime - 1)):
raise SecurityError('g_a is not within (1, dh_prime - 1)')
if not (1 < g_b < (dh_prime - 1)):
raise SecurityError('g_b is not within (1, dh_prime - 1)')
safety_range = 2 ** (2048 - 64)
if not (safety_range <= g_a <= (dh_prime - safety_range)):
raise SecurityError('g_a is not within (2^{2048-64}, dh_prime - 2^{2048-64})')
if not (safety_range <= g_b <= (dh_prime - safety_range)):
raise SecurityError('g_b is not within (2^{2048-64}, dh_prime - 2^{2048-64})')
# Prepare client DH Inner Data
client_dh_inner = bytes(ClientDHInnerData(
nonce=res_pq.nonce,
server_nonce=res_pq.server_nonce,
retry_id=0, # TODO Actual retry ID
g_b=rsa.get_byte_array(g_b)
))
client_dh_inner_hashed = sha1(client_dh_inner).digest() + client_dh_inner
# Encryption
client_dh_encrypted = AES.encrypt_ige(client_dh_inner_hashed, key, iv)
# Prepare Set client DH params
dh_gen = await sender.send(SetClientDHParamsRequest(
nonce=res_pq.nonce,
server_nonce=res_pq.server_nonce,
encrypted_data=client_dh_encrypted,
))
nonce_types = (DhGenOk, DhGenRetry, DhGenFail)
assert isinstance(dh_gen, nonce_types), 'Step 3.1 answer was %s' % dh_gen
name = dh_gen.__class__.__name__
if dh_gen.nonce != res_pq.nonce:
raise SecurityError('Step 3 invalid {} nonce from server'.format(name))
if dh_gen.server_nonce != res_pq.server_nonce:
raise SecurityError(
'Step 3 invalid {} server nonce from server'.format(name))
auth_key = AuthKey(rsa.get_byte_array(gab))
nonce_number = 1 + nonce_types.index(type(dh_gen))
new_nonce_hash = auth_key.calc_new_nonce_hash(new_nonce, nonce_number)
dh_hash = getattr(dh_gen, 'new_nonce_hash{}'.format(nonce_number))
if dh_hash != new_nonce_hash:
raise SecurityError('Step 3 invalid new nonce hash')
if not isinstance(dh_gen, DhGenOk):
raise AssertionError('Step 3.2 answer was %s' % dh_gen)
return auth_key, time_offset
def get_int(byte_array, signed=True):
"""
Gets the specified integer from its byte array.
This should be used by this module alone, as it works with big endian.
:param byte_array: the byte array representing th integer.
:param signed: whether the number is signed or not.
:return: the integer representing the given byte array.
"""
return int.from_bytes(byte_array, byteorder='big', signed=signed)
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