SYNERGY: A Game-Theoretical Approach for Cooperative Key Generation in Wireless Networks Jingchao Sun, Xu Chen, Jinxue Zhang, Yanchao Zhang, and Junshan Zhang School of Electrical, Computer and Energy Engineering (ECEE) Arizona State University, Tempe, Arizona, USA

Overview Problem: – Secret Key Establishment between two adjacent device-to-device (D2D) communication. Method: – Cooperative Key Generation using Coalition Game. Issue: – Self interested and Reluctant to act as relays without acceptable reward in return. Proposal: – SYNERGY, a game-theoretical approach for stimulating cooperative key generation. Formulation: – Centralized and Distributed protocols for obtaining the core solution to the game.

PHY-based Cooperative Key Generation: CHANEEL ESTIMATION : KEY AGREEMENT:

Key Generation Rate Charlie act as Relay: Charlie and Dave act as Relays: T = Coherence time (Users estimation of common channel gain ) = Alice and Bob Channel Estimation (Correlated Information) = Alice and Charlie Channel Estimation (Correlated Information) Similarly for Charlie and Bob, Alice and Dave & Bob and Dave

Model Multi-hop D2D Scenario Same transmission Power & Range Selfish Node – (Every node will not act as relay to help for key establishment without incentive) Rational Node – (Every node in a coalition faithfully follows the protocol and collaborates) Peer pair Relay Contributor Assumption – Passive adversary (eavesdropper) – Relay node will not cooperate with adversaries.

Coalitional Game Formulation Key Rate function ( to any potential contributor) Preferred virtual node / contributor is define as:

Basic function of Coalition Game Formulation Players – N/2 virtual nodes Strategies – Contributor Selection Characteristic Function – In Coalition: select one virtual node as a contributor – Out Coalition: Cannot get any contributor Preference order – Performance based (Performance refers to the Key generation rate)

Core discovery algorithm Identify all the contributor cycles to form a core solution. 1.Construct a directed graph G. 2.Directed edge from any vertex to another vertex exists iff is the most preferred contributor of. 3.Every virtual node can choose at most one contributor that correspond to at most two relays. 4.The problem of discovering all the contributor cycles or the core solution can then be translated into simple cycle search in G.

Core Discovery Algorithm Use directed graph

Implementation C-SYNERGY: A Centralized Implementation – Every peer pair reports its own preference to a single server – Server computes all the contributor cycle – Returns contributor to the corresponding node – Mobile node will determine which node they use as relay and whom they should act as a relay. – Server can be BS or mobile node elected from the mobile nodes themselves – Server does the computation and does not participate in the cooperative key generation

D-SYNERGY Mobile nodes are enabled to discover the core solution (or contributor cycle) in distributed fashion. Every iteration is initiated by a mobile node New contributor cycle is identified in every iteration. Terminates when every node is included in a contributor cycle.

Simulation SNR vs. Average Key Rate SNR increases, Optimal key rates of all three cases increase – Key generation rate increases with the transmission power Key generation rate is better with two relays – More relay, more common channel randomness available for secret key generation.

No. of Nodes vs. Average Key Rate Impact of average number of nodes on optimal key rate Impact of average number of neighbors on optimal key rate

Computational & Communication Overhead Impact of no. of nodes on the average number of operation for discovering all contributor cycles Computational overhead dominated by contributor cycle discovery in both C/D- SYNERGY. For fixed no. of nodes, larger the region having fewer common neighbors

Communication Overhead (C-SYNERGY) Communication overhead lies in the messages for : 1.Neighbor discovery 2.Channel estimation 3.Communicating with server. No. of messages increases with the number of nodes. Larger the region, fewer neighbors each node has and thus fewer messages needed for neighbor discovery and channel estimation C-SYNERGY decreases as the region side length (D) increases.

Communication Overhead (D-SYNERGY) Impact of No. of nodes on the communication overhead. Larger region, decrease the chances of peer nodes to find a relay node in their common communication range. Leading to possible fewer edges between virtual nodes in the directed graph. D-SYNERGY has higher communication overhead due to distributed contributor cycle discovery but does not need BS or specific node as a server.

Conclusion In one sentence Improve key generation rate Details Game theoretical approach for stimulating PHY-based cooperative key generation. Incentive-aware (social Reciprocity) cooperative key generation is formulated C/D SYNERGY protocols for finding a core solution to the coalition game Mobile nodes are strongly motivated to collaborate with others in same coalition to improve their respective key generation rate.