Jamming Games in the MIMO Wiretap Channel With an Active Eavesdropper

This paper investigates reliable and covert transmission strategies in a multiple-input multiple-output (MIMO) wiretap channel with a transmitter, receiver and an adversarial wiretapper, each equipped with multiple antennas. In a departure from existing work, the wiretapper possesses a novel capability to act either as a passive eavesdropper or as an active jammer, under a half-duplex constraint. The transmitter therefore faces a choice between allocating all of its power for data, or broadcasting artificial interference along with the information signal in an attempt to jam the eavesdropper (assuming its instantaneous channel state is unknown). To examine the resulting trade-offs for the legitimate transmitter and the adversary, we model their interactions as a two-person zero-sum game with the ergodic MIMO secrecy rate as the payoff function. We first examine conditions for the existence of pure-strategy Nash equilibria (NE) and the structure of mixed-strategy NE for the strategic form of the game.We then derive equilibrium strategies for the extensive form of the game where players move sequentially under scenarios of perfect and imperfect information. Finally, numerical simulations are presented to examine the equilibrium outcomes of the various scenarios considered.Comment: 27 pages, 8 figures. To appear, IEEE Transactions on Signal Processin

Principles of Physical Layer Security in Multiuser Wireless Networks: A Survey

This paper provides a comprehensive review of the domain of physical layer security in multiuser wireless networks. The essential premise of physical-layer security is to enable the exchange of confidential messages over a wireless medium in the presence of unauthorized eavesdroppers without relying on higher-layer encryption. This can be achieved primarily in two ways: without the need for a secret key by intelligently designing transmit coding strategies, or by exploiting the wireless communication medium to develop secret keys over public channels. The survey begins with an overview of the foundations dating back to the pioneering work of Shannon and Wyner on information-theoretic security. We then describe the evolution of secure transmission strategies from point-to-point channels to multiple-antenna systems, followed by generalizations to multiuser broadcast, multiple-access, interference, and relay networks. Secret-key generation and establishment protocols based on physical layer mechanisms are subsequently covered. Approaches for secrecy based on channel coding design are then examined, along with a description of inter-disciplinary approaches based on game theory and stochastic geometry. The associated problem of physical-layer message authentication is also introduced briefly. The survey concludes with observations on potential research directions in this area.Comment: 23 pages, 10 figures, 303 refs. arXiv admin note: text overlap with arXiv:1303.1609 by other authors. IEEE Communications Surveys and Tutorials, 201

Physical Layer Security Game: How to Date a Girl with Her Boyfriend on the Same Table

International audiencePhysical layer security is an emerging security technology that achieves perfect secrecy data transmission between the intended network nodes, while the eavesdrop- ping malicious nodes obtain zero information. The so-called secrecy capacity can be improved using friendly jammers that introduce extra interference to the eavesdropping ma- licious nodes while the interference to the intended desti- nation is limited. In this paper, we investigate the interac- tion between the source that transmits the desired data and friendly jammers who assist the source by \disguising" the eavesdropper. In order to obtain a distributed solution, we introduce a game theoretic approach. The game is de¯ned in such a way that the source pays the friendly jammers to interfere the eavesdropper, therefore increasing its secrecy capacit; and the friendly jammers charge the source with a certain price for the jamming. There is a tradeo® for the price: If the price is too low, the pro¯t of the jammers is low; and if the price is too high, the source would not buy the \service" (jamming power) or would buy it from other jammers. To analyze the game outcome, we de¯ne and in- vestigate a Stackelburg game and construct a distributed algorithm. Our analysis and simulation results show the ef- fectiveness of friendly jamming and the tradeo® for setting the price. The fancy title comes from the fact that it is similar to a scenario where the main character, namely the \source" tries to send a dating message to a lady (the in- tended destination), whose poor boyfriend plays the role of the eavesdropper that may hear the message. Friends of the source, the so called \friendly jammers," try to distract the boyfriend, so that the dating message can be secretly trans- mitted. The game is de¯ned in order to derive what is the optimal price that the friends can charge for this \friendly" action

Cores of Cooperative Games in Information Theory

Cores of cooperative games are ubiquitous in information theory, and arise most frequently in the characterization of fundamental limits in various scenarios involving multiple users. Examples include classical settings in network information theory such as Slepian-Wolf source coding and multiple access channels, classical settings in statistics such as robust hypothesis testing, and new settings at the intersection of networking and statistics such as distributed estimation problems for sensor networks. Cooperative game theory allows one to understand aspects of all of these problems from a fresh and unifying perspective that treats users as players in a game, sometimes leading to new insights. At the heart of these analyses are fundamental dualities that have been long studied in the context of cooperative games; for information theoretic purposes, these are dualities between information inequalities on the one hand and properties of rate, capacity or other resource allocation regions on the other.Comment: 12 pages, published at http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/318704 in EURASIP Journal on Wireless Communications and Networking, Special Issue on "Theory and Applications in Multiuser/Multiterminal Communications", April 200

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

Special issue on physical layer securityInternational audiencePhysical layer security is an emerging security area that explores possibilities of achieving perfect secrecy data transmission between the intended network nodes, while possible 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. Here, we investigate the interaction between the source that transmits the useful data and friendly jammers who assist the source by \masking" the eavesdropper. In order to obtain a distributed solution, one possibility is to introduce a game theoretic approach. The game is de¯ned 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 tradeo® for the price. If the price is too low, the pro¯t of the jammers is low and if the price is too high, the source would not buy the \service" (jamming power) or would buy it from other jammers. To analyze the game outcome, we de¯ne and investigate a Stackelburg type of game and construct a distributed algorithm. Our analysis and simulation results show the e®ectiveness of friendly jamming and the tradeo® for setting the price. The distributed game solution is shown to have similar performances to those of the centralized one. This work was supported by NSF CNS-0831371, and was supported by the Research Council of Norway through the project entitled "Mobile-to-Mobile Communication Systems (M2M)"