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+from enum import Enum
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+
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+class MessageType(Enum):
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+ """
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+ Defines possible botnet message types
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+ """
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+
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+ TIMEOUT = 3
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+ SALITY_NL_REQUEST = 101
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+ SALITY_NL_REPLY = 102
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+ SALITY_HELLO = 103
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+ SALITY_HELLO_REPLY = 104
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+
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+class Message():
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+ """
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+ Defines a compact message type that contains all necessary information.
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+ """
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+ def __init__(self, msg_id: int, src, dst, type_: MessageType, time: float, refer_msg_id: int=-1):
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+ """
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+ Constructs a message with the given parameters.
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+
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+ :param msg_id: the ID of the message
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+ :param src: something identifiying the source, e.g. ID or configuration
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+ :param dst: something identifiying the destination, e.g. ID or configuration
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+ :param type_: the type of the message
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+ :param time: the timestamp of the message
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+ :param refer_msg_id: the ID this message is a request for or reply to. -1 if there is no related message.
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+ """
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+ self.msg_id = msg_id
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+ self.src = src
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+ self.dst = dst
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+ self.type = type_
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+ self.time = time
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+ self.refer_msg_id = refer_msg_id
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+
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+ def __str__(self):
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+ str_ = "{0}. at {1}: {2}-->{3}, {4}, refer:{5}".format(self.msg_id, self.time, self.src, self.dst, self.type, self.refer_msg_id)
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+ return str_
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+
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+from random import randint, randrange, choice, uniform
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+from collections import deque
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+from scipy.stats import gamma
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+from lea import Lea
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+from datetime import datetime
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+
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+from Attack import BaseAttack
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+from Attack.AttackParameters import Parameter as Param
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+from Attack.AttackParameters import ParameterTypes
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+
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+from ID2TLib import FileUtils, PaddingGenerator
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+from ID2TLib.PacketGenerator import PacketGenerator
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+from ID2TLib.IPGenerator import IPGenerator
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+from ID2TLib.PcapAddressOperations import PcapAddressOperations
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+from ID2TLib.CommunicationProcessor import CommunicationProcessor
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+from ID2TLib.MacAddressGenerator import MacAddressGenerator
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+from ID2TLib.PortGenerator import gen_random_server_port
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+
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+
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+class MembersMgmtCommAttack(BaseAttack.BaseAttack):
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+ def __init__(self):
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+ """
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+ Creates a new instance of the Membership Management Communication.
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+
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+ """
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+ # Initialize communication
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+ super(MembersMgmtCommAttack, self).__init__("Membership Management Communication Attack (MembersMgmtCommAttack)",
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+ "Injects Membership Management Communication", "Botnet communication")
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+
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+ # Define allowed parameters and their type
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+ self.supported_params = {
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+ # parameters regarding attack
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+ Param.INJECT_AT_TIMESTAMP: ParameterTypes.TYPE_FLOAT,
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+ Param.INJECT_AFTER_PACKET: ParameterTypes.TYPE_PACKET_POSITION,
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+ Param.PACKETS_PER_SECOND: ParameterTypes.TYPE_FLOAT,
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+ Param.PACKETS_LIMIT: ParameterTypes.TYPE_INTEGER_POSITIVE,
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+ Param.ATTACK_DURATION: ParameterTypes.TYPE_INTEGER_POSITIVE,
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+
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+ # use num_attackers to specify number of communicating devices?
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+ Param.NUMBER_INITIATOR_BOTS: ParameterTypes.TYPE_INTEGER_POSITIVE,
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+
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+ # input file containing botnet communication
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+ Param.FILE_CSV: ParameterTypes.TYPE_FILEPATH,
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+ Param.FILE_XML: ParameterTypes.TYPE_FILEPATH,
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+
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+ # the percentage of IP reuse (if total and other is specified, percentages are multiplied)
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+ Param.IP_REUSE_TOTAL: ParameterTypes.TYPE_PERCENTAGE,
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+ Param.IP_REUSE_LOCAL: ParameterTypes.TYPE_PERCENTAGE,
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+ Param.IP_REUSE_EXTERNAL: ParameterTypes.TYPE_PERCENTAGE,
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+
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+ # the user-selected padding to add to every packet
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+ Param.PACKET_PADDING: ParameterTypes.TYPE_PADDING,
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+
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+ # presence of NAT at the gateway of the network
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+ Param.NAT_PRESENT: ParameterTypes.TYPE_BOOLEAN
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+ }
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+
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+ # create dict with MessageType values for fast name lookup
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+ self.msg_types = {}
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+ for msg_type in MessageType:
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+ self.msg_types[msg_type.value] = msg_type
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+
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+ def init_params(self):
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+ """
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+ Initialize some parameters of this communication-attack using the user supplied command line parameters.
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+ The remaining parameters are implicitly set in the provided data file. Note: the timestamps in the file
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+ have to be sorted in ascending order
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+
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+ :param statistics: Reference to a statistics object.
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+ """
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+ # set class constants
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+ self.DEFAULT_XML_PATH = "resources/MembersMgmtComm_example.xml"
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+ # probability for responder ID to be local if comm_type is mixed
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+ self.PROB_RESPND_IS_LOCAL = 0
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+
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+ # PARAMETERS: initialize with default values
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+ # (values are overwritten if user specifies them)
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+ self.add_param_value(Param.INJECT_AFTER_PACKET, randint(1, int(self.statistics.get_packet_count()/5)))
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+ #self.add_param_value(Param.INJECT_AFTER_PACKET, 1)
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+
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+ self.add_param_value(Param.PACKETS_PER_SECOND, 0)
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+ self.add_param_value(Param.FILE_XML, self.DEFAULT_XML_PATH)
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+
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+ # Alternatively new attack parameter?
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+ duration = int(float(self._get_capture_duration()))
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+ # if duration == 0:
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+ # duration = 1
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+ self.add_param_value(Param.ATTACK_DURATION, duration)
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+ self.add_param_value(Param.NUMBER_INITIATOR_BOTS, 1)
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+ # NAT on by default
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+ self.add_param_value(Param.NAT_PRESENT, True)
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+
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+ # default locality behavior
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+ # self.add_param_value(Param.COMM_TYPE, "mixed")
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+ # TODO: change 1 to something better
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+ self.add_param_value(Param.IP_REUSE_TOTAL, 1)
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+ self.add_param_value(Param.IP_REUSE_LOCAL, 0.5)
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+ self.add_param_value(Param.IP_REUSE_EXTERNAL, 0.5)
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+
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+ # add default additional padding
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+ self.add_param_value(Param.PACKET_PADDING, 20)
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+
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+
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+
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+ def generate_attack_pcap(self):
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+ # create the final messages that have to be sent, including all bot configurations
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+ messages = self._create_messages()
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+
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+ if messages == []:
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+ return 0, []
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+
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+ # Setup (initial) parameters for packet creation loop
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+ BUFFER_SIZE = 1000
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+ pkt_gen = PacketGenerator()
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+ file_timestamp_prv = messages[0].time
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+ pcap_timestamp = self.get_param_value(Param.INJECT_AT_TIMESTAMP)
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+ padding = self.get_param_value(Param.PACKET_PADDING)
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+ packets = deque(maxlen=BUFFER_SIZE)
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+ total_pkts = 0
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+ limit_packetcount = self.get_param_value(Param.PACKETS_LIMIT)
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+ limit_duration = self.get_param_value(Param.ATTACK_DURATION)
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+ duration = 0
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+ path_attack_pcap = None
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+ # create packets to write to PCAP file
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+ for msg in messages:
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+ # retrieve the source and destination configurations
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+ id_src, id_dst = msg.src["ID"], msg.dst["ID"]
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+ ip_src, ip_dst = msg.src["IP"], msg.dst["IP"]
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+ mac_src, mac_dst = msg.src["MAC"], msg.dst["MAC"]
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+ port_src, port_dst = msg.src["Port"], msg.dst["Port"]
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+ ttl = msg.src["TTL"]
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+
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+ # update timestamps and duration
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+ file_timestamp = msg.time
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+ file_time_delta = file_timestamp - file_timestamp_prv
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+ pcap_timestamp += file_time_delta
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+ duration += file_time_delta
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+ file_timestamp_prv = file_timestamp
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+
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+ # if total number of packets has been sent or the attack duration has been exceeded, stop
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+ if ((limit_packetcount is not None and total_pkts >= limit_packetcount) or
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+ (limit_duration is not None and duration >= limit_duration)):
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+ break
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+
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+ # if the type of the message is a NL reply, determine the number of entries
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+ nl_size = 0
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+ if msg.type == MessageType.SALITY_NL_REPLY:
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+ nl_size = randint(1, 25) # what is max NL entries?
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+
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+ # create suitable IP/UDP packet and add to packets list
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+ packet = pkt_gen.generate_mmcom_packet(ip_src=ip_src, ip_dst=ip_dst, ttl=ttl, mac_src=mac_src, mac_dst=mac_dst,
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+ port_src=port_src, port_dst=port_dst, message_type=msg.type, neighborlist_entries=nl_size)
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+ PaddingGenerator.add_padding(packet, padding,True, True)
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+
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+ packet.time = pcap_timestamp
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+ packets.append(packet)
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+ total_pkts += 1
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+
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+ # Store timestamp of first packet (for attack label)
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+ if total_pkts <= 1:
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+ self.attack_start_utime = packets[0].time
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+ elif total_pkts % BUFFER_SIZE == 0: # every 1000 packets write them to the PCAP file (append)
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+ packets = list(packets)
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+ PaddingGenerator.equal_length(packets, padding = padding)
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+ last_packet = packets[-1]
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+ path_attack_pcap = self.write_attack_pcap(packets, True, path_attack_pcap)
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+ packets = deque(maxlen=BUFFER_SIZE)
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+
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+ # if there are unwritten packets remaining, write them to the PCAP file
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+ if len(packets) > 0:
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+ packets = list(packets)
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+ PaddingGenerator.equal_length(packets, padding = padding)
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+ path_attack_pcap = self.write_attack_pcap(packets, True, path_attack_pcap)
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+ last_packet = packets[-1]
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+
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+ # Store timestamp of last packet
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+ self.attack_end_utime = last_packet.time
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+
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+ # Return packets sorted by packet by timestamp and total number of packets (sent)
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+ return total_pkts , path_attack_pcap
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+
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+
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+ def _create_messages(self):
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+ def add_ids_to_config(ids_to_add: list, existing_ips: list, new_ips: list, bot_configs: dict, idtype:str="local", router_mac:str=""):
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+ """
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+ Creates IP and MAC configurations for the given IDs and adds them to the existing configurations object.
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+
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+ :param ids_to_add: all sorted IDs that have to be configured and added
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+ :param existing_ips: the existing IPs in the PCAP file that should be assigned to some, or all, IDs
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+ :param new_ips: the newly generated IPs that should be assigned to some, or all, IDs
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+ :param bot_configs: the existing configurations for the bots
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+ :param idtype: the locality type of the IDs
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+ :param router_mac: the MAC address of the router in the PCAP
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+ """
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+
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+ ids = ids_to_add.copy()
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+ # macgen only needed, when IPs are new local IPs (therefore creating the object here suffices for the current callers
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+ # to not end up with the same MAC paired with different IPs)
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+ macgen = MacAddressGenerator()
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+
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+ # assign existing IPs and the corresponding MAC addresses in the PCAP to the IDs
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+ for ip in existing_ips:
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+ random_id = choice(ids)
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+ mac = self.statistics.process_db_query("macAddress(IPAddress=%s)" % ip)
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+ bot_configs[random_id] = {"Type": idtype, "IP": ip, "MAC": mac}
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+ ids.remove(random_id)
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+
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+ # assign new IPs and for local IPs new MACs or for external IPs the router MAC to the IDs
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+ for ip in new_ips:
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+ random_id = choice(ids)
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+ if idtype == "local":
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+ mac = macgen.random_mac()
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+ elif idtype == "external":
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+ mac = router_mac
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+ bot_configs[random_id] = {"Type": idtype, "IP": ip, "MAC": mac}
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+ ids.remove(random_id)
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+
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+ def index_increment(number: int, max: int):
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+ """
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+ Number increment with rollover.
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+ """
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+ if number + 1 < max:
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+ return number + 1
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+ else:
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+ return 0
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+
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+ def assign_realistic_ttls2(bot_configs):
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+ # Gamma distribution parameters derived from MAWI 13.8G dataset
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+ ids = sorted(bot_configs.keys())
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+ alpha, loc, beta = (2.3261710235, -0.188306914406, 44.4853123884)
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+ gd = gamma.rvs(alpha, loc=loc, scale=beta, size=len(ids))
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+
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+ for pos, bot in enumerate(ids):
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+ # print(bot)
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+ is_invalid = True
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+ pos_max = len(gd)
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+ while is_invalid:
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+ ttl = int(round(gd[pos]))
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+ if 0 < ttl < 256: # validity check
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+ is_invalid = False
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+ else:
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+ pos = index_increment(pos, pos_max)
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+ bot_configs[bot]["TTL"] = ttl
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+
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+
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+ def assign_realistic_ttls(bot_configs):
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+ '''
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+ Assigns a realisitic ttl to each bot from @param: bot_configs. Uses statistics and distribution to be able
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+ to calculate a realisitc ttl.
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+ :param bot_configs:
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+ :return:
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+ '''
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+ ids = sorted(bot_configs.keys())
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+ for pos,bot in enumerate(ids):
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+ bot_type = bot_configs[bot]["Type"]
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+ # print(bot_type)
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+ if(bot_type == "local"): # Set fix TTL for local Bots
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+ bot_configs[bot]["TTL"] = 128
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+ # Set TTL based on TTL distribution of IP address
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+ else: # Set varying TTl for external Bots
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+ bot_ttl_dist = self.statistics.get_ttl_distribution(bot_configs[bot]["IP"])
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+ if len(bot_ttl_dist) > 0:
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+ source_ttl_prob_dict = Lea.fromValFreqsDict(bot_ttl_dist)
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+ bot_configs[bot]["TTL"] = source_ttl_prob_dict.random()
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+ else:
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+ bot_configs[bot]["TTL"] = self.statistics.process_db_query("most_used(ttlValue)")
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+
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+
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+ def add_delay(timestamp: float, minDelay: float, delay: float):
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+ '''
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+ Adds delay to a timestamp, with a minimum value of minDelay. But usually a value close to delay
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+ :param timestamp: the timestamp that is to be increased
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+ :param minDelay: the minimum value that is to be added to the timestamp
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+ :param delay: The general size of the delay. Statistically speaking: the expected value
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+ :return: the updated timestamp
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+ '''
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+
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+ randomdelay = Lea.fromValFreqsDict({0.15*delay: 7, 0.3*delay: 10, 0.7*delay:20,
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+ delay:33, 1.2*delay:20, 1.6*delay: 10, 1.9*delay: 7, 2.5*delay: 3, 4*delay: 1})
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+ if 0.1*delay < minDelay:
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+ print("Warning: minDelay probably too big when computing time_stamps")
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+
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+ # updated timestamps consist of the sum of the minimum delay, the magnitude of the delay
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+ # and a deviation by up to 10% in order to guarantee uniqueness
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+ general_offset = randomdelay.random()
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+ unique_offset = uniform(-0.1*general_offset, 0.1*general_offset)
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+ return timestamp + minDelay + general_offset + unique_offset
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+
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+ # parse input CSV or XML
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+ filepath_xml = self.get_param_value(Param.FILE_XML)
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+ filepath_csv = self.get_param_value(Param.FILE_CSV)
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+
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+ # prefer XML input over CSV input (in case both are given)
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+ if filepath_csv and filepath_xml == self.DEFAULT_XML_PATH:
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+ filepath_xml = FileUtils.parse_csv_to_xml(filepath_csv)
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+
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+ abstract_packets = FileUtils.parse_xml(filepath_xml)
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+
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+ # find a good communication mapping in the input file that matches the users parameters
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+ duration = self.get_param_value(Param.ATTACK_DURATION)
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+ number_init_bots = self.get_param_value(Param.NUMBER_INITIATOR_BOTS)
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+ nat = self.get_param_value(Param.NAT_PRESENT)
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+ comm_proc = CommunicationProcessor(abstract_packets, self.msg_types, nat)
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+
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+ comm_intervals = comm_proc.find_interval_most_comm(number_init_bots, duration)
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+ if comm_intervals == []:
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+ print("Error: There is no interval in the given CSV/XML that has enough communication initiating bots.")
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+ return []
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+ comm_interval = comm_intervals[randrange(0, len(comm_intervals))]
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+
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+ # retrieve the mapping information
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+ mapped_ids, packet_start_idx, packet_end_idx = comm_interval["IDs"], comm_interval["Start"], comm_interval["End"]
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+ while len(mapped_ids) > number_init_bots:
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+ rm_idx = randrange(0, len(mapped_ids))
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+ del(mapped_ids[sorted(mapped_ids)[rm_idx]])
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+
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+ # assign the communication processor this mapping for further processing
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+ comm_proc.set_mapping(abstract_packets[packet_start_idx:packet_end_idx+1], mapped_ids)
|
|
|
+ # print start and end time of mapped interval
|
|
|
+ #print(abstract_packets[packet_start_idx]["Time"])
|
|
|
+ #print(abstract_packets[packet_end_idx]["Time"])
|
|
|
+ #print(mapped_ids.keys())
|
|
|
+
|
|
|
+ # determine number of reused local and external IPs
|
|
|
+ reuse_percent_total = self.get_param_value(Param.IP_REUSE_TOTAL)
|
|
|
+ reuse_percent_external = self.get_param_value(Param.IP_REUSE_EXTERNAL)
|
|
|
+ reuse_percent_local = self.get_param_value(Param.IP_REUSE_LOCAL)
|
|
|
+ reuse_count_external = int(reuse_percent_total * reuse_percent_external * len(mapped_ids))
|
|
|
+ reuse_count_local = int(reuse_percent_total * reuse_percent_local * len(mapped_ids))
|
|
|
+
|
|
|
+ # create locality, IP and MAC configurations for the IDs/Bots
|
|
|
+ ipgen = IPGenerator()
|
|
|
+ pcapops = PcapAddressOperations(self.statistics)
|
|
|
+ router_mac = pcapops.get_probable_router_mac()
|
|
|
+ bot_configs = {}
|
|
|
+ # determine the roles of the IDs in the mapping communication-{initiator, responder}
|
|
|
+ local_init_ids, external_init_ids, respnd_ids, messages = comm_proc.det_id_roles_and_msgs()
|
|
|
+ # use these roles to determine which IDs are to be local and which external
|
|
|
+ local_ids, external_ids = comm_proc.det_ext_and_local_ids(self.PROB_RESPND_IS_LOCAL)
|
|
|
+
|
|
|
+ # retrieve and assign the IPs and MACs for the bots with respect to the given parameters
|
|
|
+ # (IDs are always added to bot_configs in the same order under a given seed)
|
|
|
+ number_local_ids, number_external_ids = len(local_ids), len(external_ids)
|
|
|
+ # assign addresses for local IDs
|
|
|
+ if number_local_ids > 0:
|
|
|
+ reuse_count_local = int(reuse_percent_total * reuse_percent_local * number_local_ids)
|
|
|
+ existing_local_ips = sorted(pcapops.get_existing_local_ips(reuse_count_local))
|
|
|
+ new_local_ips = sorted(pcapops.get_new_local_ips(number_local_ids - len(existing_local_ips)))
|
|
|
+ add_ids_to_config(sorted(local_ids), existing_local_ips, new_local_ips, bot_configs)
|
|
|
+
|
|
|
+ # assign addresses for external IDs
|
|
|
+ if number_external_ids > 0:
|
|
|
+ reuse_count_external = int(reuse_percent_total * reuse_percent_external * number_external_ids)
|
|
|
+ existing_external_ips = sorted(pcapops.get_existing_external_ips(reuse_count_external))
|
|
|
+ remaining = len(external_ids) - len(existing_external_ips)
|
|
|
+ new_external_ips = sorted([ipgen.random_ip() for _ in range(remaining)])
|
|
|
+ add_ids_to_config(sorted(external_ids), existing_external_ips, new_external_ips, bot_configs, idtype="external", router_mac=router_mac)
|
|
|
+
|
|
|
+ #### Set realistic timestamps for messages ####
|
|
|
+
|
|
|
+ most_used_ip_address = self.statistics.get_most_used_ip_address()
|
|
|
+ minDelay = self.get_reply_delay(most_used_ip_address)[0]
|
|
|
+ next_timestamp = self.get_param_value(Param.INJECT_AT_TIMESTAMP)
|
|
|
+ pcap_duration = float(self._get_capture_duration())
|
|
|
+ equi_timeslice = pcap_duration/len(messages)
|
|
|
+
|
|
|
+ # Dict, takes a tuple of 2 Bot_IDs as a key (ID with lower number first), returns the time when the Hello_reply came in
|
|
|
+ hello_times = {}
|
|
|
+ # msg_IDs with already updated timestamps
|
|
|
+ updated_msgs = []
|
|
|
+
|
|
|
+ for req_msg in messages:
|
|
|
+ updated = 0
|
|
|
+ if(req_msg.msg_id in updated_msgs):
|
|
|
+ # message already updated
|
|
|
+ continue
|
|
|
+
|
|
|
+ if(req_msg.msg_id == -1):
|
|
|
+ # message has no corresponding request/response
|
|
|
+ req_msg.time = next_timestamp
|
|
|
+ next_timestamp = add_delay(next_timestamp, minDelay, equi_timeslice)
|
|
|
+ updated_msgs.append(req_msg.msg_id)
|
|
|
+ continue
|
|
|
+
|
|
|
+
|
|
|
+ elif req_msg.type != MessageType.SALITY_HELLO:
|
|
|
+ # Hello messages must have preceded, so make sure the timestamp of this msg is after the HELLO_REPLY
|
|
|
+ if int(req_msg.src) < int(req_msg.dst):
|
|
|
+ hello_time = hello_times[(req_msg.src, req_msg.dst)]
|
|
|
+ else:
|
|
|
+ hello_time = hello_times[(req_msg.dst, req_msg.src)]
|
|
|
+
|
|
|
+ if next_timestamp < hello_time:
|
|
|
+ # use the time of the hello_reply instead of next_timestamp to update this pair of messages
|
|
|
+ post_hello = add_delay(hello_time, minDelay, equi_timeslice)
|
|
|
+ respns_msg = messages[req_msg.refer_msg_id]
|
|
|
+ respns_msg.time = add_delay(post_hello, minDelay, equi_timeslice)
|
|
|
+ req_msg.time = post_hello
|
|
|
+ updated = 1
|
|
|
+
|
|
|
+ if not updated:
|
|
|
+ # update normally
|
|
|
+ respns_msg = messages[req_msg.refer_msg_id]
|
|
|
+ respns_msg.time = add_delay(next_timestamp, minDelay, equi_timeslice)
|
|
|
+ req_msg.time = next_timestamp
|
|
|
+ next_timestamp = add_delay(next_timestamp, minDelay, equi_timeslice)
|
|
|
+
|
|
|
+ updated_msgs.append(req_msg.msg_id)
|
|
|
+ updated_msgs.append(req_msg.refer_msg_id)
|
|
|
+
|
|
|
+ if req_msg.type == MessageType.SALITY_HELLO:
|
|
|
+ # if hello messages have been exchanged, save timestamp of the HELLO_REPLY
|
|
|
+ if int(req_msg.src) < int(req_msg.dst):
|
|
|
+ hello_times[(req_msg.src, req_msg.dst)] = respns_msg.time
|
|
|
+ else:
|
|
|
+ hello_times[(req_msg.dst, req_msg.src)] = respns_msg.time
|
|
|
+
|
|
|
+ # create port configurations for the bots
|
|
|
+ for bot in bot_configs:
|
|
|
+ bot_configs[bot]["Port"] = gen_random_server_port()
|
|
|
+
|
|
|
+ # print(local_init_ids)
|
|
|
+ # print(bot_configs)
|
|
|
+
|
|
|
+ # assign realistic TTL for every bot
|
|
|
+ assign_realistic_ttls(bot_configs)
|
|
|
+ # put together the final messages including the full sender and receiver
|
|
|
+ # configurations (i.e. IP, MAC, port, ...) for easier later use
|
|
|
+ final_messages = []
|
|
|
+ messages = sorted(messages, key=lambda msg: msg.time)
|
|
|
+ new_id = 0
|
|
|
+
|
|
|
+ for msg in messages:
|
|
|
+ type_src, type_dst = bot_configs[msg.src]["Type"], bot_configs[msg.dst]["Type"]
|
|
|
+ id_src, id_dst = msg.src, msg.dst
|
|
|
+
|
|
|
+ # sort out messages that do not have a suitable locality setting
|
|
|
+ if type_src == "external" and type_dst == "external":
|
|
|
+ continue
|
|
|
+
|
|
|
+ msg.src, msg.dst = bot_configs[id_src], bot_configs[id_dst]
|
|
|
+ msg.src["ID"], msg.dst["ID"] = id_src, id_dst
|
|
|
+ msg.msg_id = new_id
|
|
|
+ new_id += 1
|
|
|
+ ### Important here to update refers, if needed later?
|
|
|
+ final_messages.append(msg)
|
|
|
+
|
|
|
+ return final_messages
|
|
|
+
|
|
|
+
|
|
|
+ def _get_capture_duration(self):
|
|
|
+ """
|
|
|
+ Returns the duration of the input PCAP (since statistics duration seems to be incorrect)
|
|
|
+ """
|
|
|
+ ts_date_format = "%Y-%m-%d %H:%M:%S.%f"
|
|
|
+ ts_first_date = datetime.strptime(self.statistics.get_pcap_timestamp_start(), ts_date_format)
|
|
|
+ ts_last_date = datetime.strptime(self.statistics.get_pcap_timestamp_end(), ts_date_format)
|
|
|
+ diff_date = ts_last_date - ts_first_date
|
|
|
+ duration = "%d.%d" % (diff_date.total_seconds(), diff_date.microseconds)
|
|
|
+ return duration
|