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

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

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### 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

Outline

- Overview and relevant work
- Motivation
- Game theory
- Our Game and solution
- Conclusion and future work

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
- ……

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

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.

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

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.

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.

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

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.

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.

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.

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

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).

Basic Signaling Game

- A perfect Bayesian equilibrium (PBE) of a signaling game is a strategy profile σ*and posterior beliefs μ(·|a1) such that

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}

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.

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

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

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.

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.

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.

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.

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.

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.

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.

Our Solution

- The probability distribution on information set h is
- The expected payoff of player 2 is:

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.

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.

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.

Q & A

Thank You!

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