""" This module contains several functions that authenticate the client machine with Telegram's servers, effectively creating an authorization key. """ import asyncio import functools import os import time from hashlib import sha1 from .. import _tl from .._misc import helpers from .._crypto import AES, AuthKey, Factorization, rsa from ..errors._custom import SecurityError from .._misc.binaryreader import BinaryReader 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(_tl.fn.ReqPqMulti(nonce)) assert isinstance(res_pq, _tl.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 = await asyncio.get_running_loop().run_in_executor( None, functools.partial(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(_tl.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(_tl.fn.ReqDHParams( 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, (_tl.ServerDHParamsOk, _tl.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, _tl.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, _tl.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, _tl.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(_tl.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(_tl.fn.SetClientDHParams( nonce=res_pq.nonce, server_nonce=res_pq.server_nonce, encrypted_data=client_dh_encrypted, )) nonce_types = (_tl.DhGenOk, _tl.DhGenRetry, _tl.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, _tl.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)