Using Game Theoretic Approach to Analyze Security Issues In Ad Hoc Networks

1. 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 a1 • Player 2 observes a1, chooses an action a2 from her action space.

13. Basic Signaling Game • Player i’s payoff is denoted by ui(a1, a2,θ). • Player 1’s strategy is a probability distribution σ1(·|θ) over actions a1 for each type θ • Player 2’s strategy is a probability distribution σ2(·| a1) over actions a2 for each action a1

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 a2 on the posterior distribution μ(·|a1).

15. Basic Signaling Game • A perfect Bayesian equilibrium (PBE) of a signaling game is a strategy profile σ*and posterior beliefs μ(·|a1) 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 • Establish an expressive, realistic, non-trivial model of interactions between attacker(s) and target(s). • Try to solve the model and give a possible and reasonable Nash equilibrium. • Obtain some references about value choosing of a design factor. • Design a correspond application consistent with the strategies and beliefs in the above equilibrium.

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

19. Our Direction • When establishing interaction model, possible players are: • One attacker and one target: 1 vs. 1  normal attack • Two attackers and one target: 2 vs. 1  collusion attack • One attacker and n targets: 1 vs. n  DIDS • N attackers and one target: n vs. 1  DoS • 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, Pσ(x) denotes the probability that node x is reached. • h is information set containing more than one node. E.g. h={x3, x4, x5} • 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!