Using Game Theoretic Approach to Analyze Security Issues In Ad Hoc Networks Term Presentation Name: Li Xiaoqi, Gigi Supervisor: Michael R. Lyu Department: CSE, CUHK Date: 02/05/2006 Time: 2:00-2:45pm Location: HSB 121

2 Outline Overview and relevant work Motivation Game theory Our Game and solution Conclusion and future work

3 Attacks On Wireless Networks Passive:  Not disturb the routing protocol  Hard to detect  E.g.: Eavesdropping Selfish behavior  Refuse to forward packets of other nodes in order to Save own energy Economize own bandwidth ……

4 Attacks On Wireless Networks Active:  Disrupt the routing protocol  Modification, e.g.: Black hole Grey hole Wormhole  Fabrication E.g.: rushing attack  Impersonation E.g.: alter MAC/IP address

5 Relevant Work On selfish behaviors  Currency-based mechanism Forwarding packets is paid  Reputation-based mechanism Use reputation to incent nodes  Game theoretic based mechanism Model forwarding as a strategic game Result in a Nash equilibrium with a metric, e.g. best forwarding rate Utility function includes bandwidth, energy, etc.

6 Relevant Work On malicious attacks  For intrusion detection system (IDS) of MANET: use game theory to attempt to decrease false alarm rate  Less work on this issue  Almost none of them can effectively solve malicious node collusion

7 Motivation Game theory is mostly employed as a tool to analyze, formulate or solve selfishness issue. It seldom applied to detect/prevent/deter malicious behavior.

8 Game Theory It is a branch of economics that deals with strategic and rational behavior. It has applications in economics, international relations, evolutionary biology, political science, military strategy, and so on. It provides us with tools to study situations of conflict and cooperation.

9 Game Theory Game theory can be divided from three dimensions  Noncooperative and Cooperative Games A player may be an individual (noncooperative) or a group of individuals (cooperative)  Strategic and Extensive Games also called static and dynamic games  Games with Complete and Incomplete Information Players’ moves or types are fully informed or imperfectly informed

10 Game theory Our idea:  Security issues in ad hoc network also involve interactions among nodes.  So it is possible to use game theory for designing, formulating, and analyzing those interactions.  Then we may find some solutions to help detecting, preventing or detering malicious behaviors.

11 Possible Formulations Basic signaling game:  Multi-stage, dynamic, and non-cooperative game with incomplete information  It has perfect Bayesian equilibrium (PBE) Cooperative game:  Analyze payoffs from individual point of view and social point of view respectively Repeated game:  Capture the idea of a player’s current behavior and the other players’ future behavior.

12 Basic Signaling Game Two players:  Player 1, the sender  Player 2, the receiver Player 1 has a type θ, and player 2 believes that the probability of 1 is θ is p(θ). Player 1 observes information about his type θ, and chooses an action a 1 Player 2 observes a 1, chooses an action a 2 from her action space.

13 Basic Signaling Game Player i’s payoff is denoted by u i (a 1, a 2,θ). Player 1’s strategy is a probability distribution σ 1 (·|θ) over actions a 1 for each type θ Player 2’s strategy is a probability distribution σ 2 (·| a 1 ) over actions a 2 for each action a 1

14 Basic Signaling Game Player 1’s payoff is: Player 2’s payoff is Player 2 updates her beliefs about θ, and bases her choice of action a 2 on the posterior distribution μ(·|a 1 ).

15 Basic Signaling Game A perfect Bayesian equilibrium (PBE) of a signaling game is a strategy profile σ * and posterior beliefs μ(·|a 1 ) such that

16 Some Considerations What are the possible types of nodes?  {Malicious, Normal}  {Armed, Unarmed}  {Sensitive, Regular} What are the possible actions a node may take?  {Doubt, Trust}  {Defend, Miss}  {Cooperate, Not Cooperate}

17 Our Direction 1. Establish an expressive, realistic, non- trivial model of interactions between attacker(s) and target(s). 2. Try to solve the model and give a possible and reasonable Nash equilibrium. 3. Obtain some references about value choosing of a design factor. 4. Design a correspond application consistent with the strategies and beliefs in the above equilibrium.

18 Our Direction When establishing interaction model, possible players are: 1. One attacker and one target: 1 vs. 1  simple attack 2. Two attackers and one target: 2 vs. 1  collusion attack 3. One attacker and n targets: 1 vs. n  DIDS 4. N attackers and one target: n vs. 1  DoS 5. N attackers and n targets: n vs. n  DDoS

19 Our Direction When establishing interaction model, possible players are: 1. One attacker and one target: 1 vs. 1  normal attack 2. Two attackers and one target: 2 vs. 1  collusion attack 3. One attacker and n targets: 1 vs. n  DIDS 4. N attackers and one target: n vs. 1  DoS 5. N attackers and n targets: n vs. n  DDoS

20 Our Game Mixed strategies of the stranger:  The stranger may have two types: {Malicious, Regular}. The probability of a stranger is malicious is ε.  If the stranger is malicious, his action space is {Attack, Normal}. The probability of he performs attacks is s.  If the stranger is regular, he will always behave normally.

21 Our Game Mixed strategies of the target:  For the target node, she may perform two actions to the stranger: {Doubt, Trust}. The probability of she doubts is t.  When she doubts, she may ask for her neighbors’ help to get the trustworthiness of the stranger, or request the stranger to identify himself, or else.

22 Our Game Payoff formulation:  If the stranger is regular, and the target will get a amount of payoff if she trusts, where a>1.  If the stranger is malicious and he attacks successfully, he will cause a amount of harm to the target.  If the target doubts the stranger, she will cost 1.  If the doubt is deserved, the target will get b amount of feedback, where 0<b<1.  If the trust is not worthy, the target will lose b amount of payoff.

23 Our Game Payoff formulation:  If the stranger is malicious but he pretends to be normal, in the current round, the target will cost more to doubt him than to trust him, but the doubt will induce the stranger to get payoff of -1. in the long run game, the target may threat the stranger by doubting more frequently. We regard the stranger as Player 1, masculine and the target as Player 2, feminine.

24 Our Game The stranger knows his type assigned by a virtual player “Nature”. The target doesn’t know the stranger’s type, and is not sure what behavior the stranger has taken. This is a two-player, extensive, non- cooperative game with incomplete information.

25 The Game Tree

26 Our Solution This model has no Nash equilibrium on pure strategy.  Consider strategy: (Attack, Doubt) If player 1 is malicious and attacks, the best response of player 2 is to doubt. But if player 2 doubts, the best response of player 1 is to behave normal  Consider strategy: (Normal, Trust) If player 1 behaves normal, the best response of player 2 is to trust (doubt is costly). But if player 2 trusts, the best response of player 1 is to attack.  Both of these two reasonable strategy are not Nash equilibrium strategy.

27 Our Solution The model has Sequential Nash Equilibrium on mixed strategy, that is the actions that the players take is a probability distribution on the action spaces. The strategy profile is When σ is given, P σ (x) denotes the probability that node x is reached. h is information set containing more than one node. E.g. h={x 3, x 4, x 5 } Belief μ(x) specifies the probability the player assigns to x conditional on reaching h.

28 Our Solution The probability distribution on information set h is The expected payoff of player 2 is:

29 Our Solution Differential coefficient on s is So we have the following conclusion:  When, (1)>0. That is, if s is increased, the payoff of player 2 will increase.  When, (1)<0. That is, if s is decreased, the payoff of player 2 will increase.

30 Our Solution From the above solution, we get a threshold value that can be applied to the design of our corresponding secure routing protocol. In our previous secure routing protocol, if node’s opinion about another node exceeds a threshold, it will exchange opinions with its neighbors to get a more object trustworthiness value.

31 Conclusion and Future Work We give a game theoretic model of stranger-target interactions. We find out a solution of the model and get a helpful threshold value which can be applied to the design of secure routing protocol. We will extend our model from several aspects: long-run game, and 2 vs. 1 collusion attacks. Try to find out other conclusions which will be helpful to secure protocol design.

32 Q & A Thank You!