1. Preventing Collusion Between SDN Defenders and Attackers Using a Game Theoretical Approach

2. Contents of the Talk Preliminary Materials Motivation and Contribution
Trust Management
Game Theory
Motivation and Contribution
Model Description and Problem Statement
Our Solution in Nutshell
Utiliy Assumption
Utility Computation
Our Results

3. 4 (p) = 1/(4-1)  4j (p) = 1/3 (0.4 + 0.5 + 0.6) = 0.5
Trust and Reputation
Trust versus Reputation:
Trust is a personal quantity, created between “2” players, whereas
Reputation is a social quantity in a network of “n” players.
Trust Function: Let ij (p) be the trust value assigned by player Pj to Pi in period “p”. Let i be the trust function representing the reputation of Pi.
Example:
If all players have an equal view, trust = reputation. A1 A2 A3 A4
0.4
0.5
0.6
j=1 n
4 (p) = 1/(4-1)  4j (p) = 1/3 ( ) = 0.5

4. Trust Measurement
Our Function is not just a function of a single round, but of the history:
Reward more (or same) the better a participant is,
Penalize more (or same) the worse a participant is.
Discourage
Reward
TGood Pi  (,+1]
Opportunities
Give/Take
T New Pi: [,]
Penalize
Encourage
TBad Pi  [-1,)
Defection
Cooperation
Trust Value
Bad Pi (C)
Newcomer Pi (C)
Good Pi (C)
Bad Pi (D)
Newcomer Pi (D)
Good Pi (D)  

5. Games A game consists of: A set of finite players.
A set of actions and strategies (i.e., the way of choosing actions).
A pay-off function for each player; to compute the utility of a player.
Cooperative games
Participants join and split the gains out of cooperation.
Players can enforce cooperation by agreements.
Non-cooperative games
Participants can not form agreements to coordinate their behaviors.
Players can cooperate, but any cooperation must be self-enforcing.

6. Non-cooperative Games
Prisoner’s Dilemma: is a well-known non-cooperative game.
Players: P1 and P2
Actions: Confess or Keep Quiet
Payoffs:
Nash Equilibrium: no matter Pi selects “C” or “D”, Pj chooses “D”.
the ideal
outcome
-1 , -1
+1 , -2
D: Confess
-2 , +1
0 , 0
C: Quiet P2 P1
+1 : Free
0 : Jail for 1 year
-1 : Jail for 2 years
-2 : Jail for 3 years P2
-1 , -1
+1 , -2
-2 , +1
0 , 0 P1
P1: “what if I defect”
-1 , -1
+1 , -2
-2 , +1
0 , 0 P2
-1 , -1
+1 , -2
-2 , +1
0 , 0 P2
-1 , -1
+1 , -2
-2 , +1
0 , 0 P1
P1: “what if I cooperate” P1 P1 P2

7. Our Motivation and Contribution
A game-theoretical solution concept is utilized to tackle the collusion attack in a SDN-based framework.
We consider a repeated game where players (SDN controller, switches and the attacker) enter into a long-term interaction.
Contribution:
The defenders (i.e., switches) are incentivized not to collude with the attackers in a repeated-game setting that utilizes a reputation system.
A public trust network is constructed to incentivize the players to be cooperative, that is, they can then gain extra utilities.
In other words, the players avoid selfish behaviors due to the social reinforcement of the trust network.

8. Model Description Model: Goal:
The SDN controller that assigns a flow rule to every switch based on the selected route mutation strategy,
A group of “n” switches that act as defenders, and
The attacker who tries to collude with switches.
In the proposed model, we consider a 2-player game between two defenders (switches) that may/may not collude with an attacker.
Goal:
Colluders do not perform the route mutation; therefore, the attackers can find persistent links.
Colluders send their traffic to certain links in order to help the attacker to launch the DDoS attack.

9. Problem Statement Payoff function:
If both switches collude with the attacker, they each gain, for instance, $1 utility. That is, the attacker’s $2 budget will be shared between both switches.
However, if one switch colludes but the other one doesn’t collude, the colluder will receive $2 from the attacker.
As a result, collusion is Nash Equilibrium meaning that switches always collude because it’s in their best interest to do so.

10. Our Solution in Nutshell
Socio-Rational Model: we tackle the stated problem by considering a repeated game (which is played periodically) among rational players who have public trust values where these values affect players’ utilities:
In each round, the SDN controller selects a subset of switches based on their trust values using a non-uniform probability distribution.
The attacker utilizes his budget in order to collude with switches, and consequently, compromise the system.
Collusion in SR Model:
Colluder may gain a utility in the current round, however, that switch has less chance (lower probability) to be selected by the SDN controller in the future rounds due to the reduction of his trust value.
The SDN controller doesn’t know for sure if a switch has colluded with the attacker at each round, however, if a switch deviates from the SDN controller’s instructions, it might be an indication of collusion.

11. Utility Assumption
Socio-Rational Model: let denote if Si has colluded with the attacker in the current game, and define , i.e., the number of switches who have colluded with the attacker.
Let denote the reputation of Si after outcome in period p. Note that
and are two different outcomes of the game.
Each switch Si prefers to sustain a high trust value overtime despite of colluding/not colluding with the attacker as he can gain a higher long-term utility.
If a switch Si colludes with the attacker, he gains a short-term utility.
If Si colludes with the attacker and the total # of colluding parties in is less than the total # of colluding parties in , he gains a higher short-term utility in .

12. Utility Computation Socio-Rational Model:
Let be the reward coefficient that is defined by the SDN controller based on the reputation value of each switch.
be the difference of two consecutive trust values.
Note that is positive if the selected action in period p is cooperation and it is negative, if it is defection.
Long-term utility:
1st term: Si gains or loses units of utility (omega) in the future rounds due to his behavior as reflected in his trust value.
2nd term: Si gains one unit of utility (omega) if he colludes with the attacker in the current round and he loses this opportunity, otherwise.
3rd term: one unit of utility (omega) will be divided among all the colluders in the current round.
Short-term utility

13. Our Results
Socio-Rational Model: cooperation is always Nash Equilibrium in both (2,2) or (n,n)-socio-rational collusion game.
The reward factor is at least 1.5:
Defenders (switches) were incentivized not to collude with the attackers in a repeated-game setting that utilizes a reputation system.
In our model, cooperation with the SDN controller is always Nash Equilibrium due to the existence of a long-term utility function.

14. Thank You Very Much
Questions?

15. Realization of Our Approach
To realize our model, we can consider:
The defenders to be internal adversaries who manage the switches.
The attacker to be an outsider/external adversary.