Physical Layer Security Game: Interaction between Source, Eavesdropper, and Friendly Jammer

Abstract

Physical layer security is an emerging security area that achieves perfect secrecy data transmission between intended network nodes, while malicious nodes that eavesdrop the communication obtain zero information. The so-called secrecy capacity can be improved using friendly jammers that introduce extra interference to the eavesdroppers. We investigate the interaction between the source that transmits the useful data and friendly jammers who assist the source by "masking" the eavesdropper. To obtain distributed solution, we introduce a game theoretic approach. The game is defined such that the source pays the jammers to interfere the eavesdropper, therefore, increasing the secrecy capacity. The friendly jammers charge the source with a certain price for the jamming, and there is a tradeoff for the price. If too low, the profit of the jammers is low; and if too high, the source would not buy the "service" (jamming power) or would buy it from other jammers. To analyze the game outcome, we investigate a Stackelburg type of game and construct a distributed algorithm. Our analysis and simulation results show the effectiveness of friendly jamming and the tradeoff for setting the price. The distributed game solution is shown to have similar performances to those of the centralized one.

Improving Secrecy Rate via Spectrum Leasing for Friendly Jamming

“…Proof: It suffices to show that (19) is the solution of the winning jammer's J w(α,β) utility maximization problem over P J w(α,β) under the constraint R S α, β; P J w(α,β) ≥ R S,2 (α, β). This maximization problem is also illustrated in Figure 5.…”

“…To conclude this section, the outcome of the auction, as given by (19), constitutes the follower's response in the Stackelberg framework and the Stackelberg equilibrium thus reads…”

“…We will elaborate on the comparison between [18] and our scheme later in the manuscript, in particular in Section VI. Another gametheoretic model for jamming motivation was considered in [19] [20], where the friendly jammers are compensated with a credit-based incentive, rather than with a communication opportunity. Unlike [19] [20], our approach is entirely framed in the communication domain and does not require any policy alteration.…”

Optimization Schemes for Protective Jamming

“…In information-theoretic security, there exists a substantial number of works following the seminal work of [28], focusing on analysis of channel secrecy even when eavesdroppers have unlimited resources [12,15,23,25]. Other works include game-theoretic approaches for power allocation to jammers [6] and also identifying "forbidden" regions where eavesdroppers must not be present. However, the geometry has not been fully explored and optimization schemes providing guarantees are not presented.…”

Distributed Network Secrecy

“…where p (l) t = P {x ∈ T l−1 } is the probability that a node in level l has a GN in level l − 1, which results in (18). By substituting (22) into (21), we obtain (16).…”