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arXiv:1103.1306 · IEEE Transactions on Information Forensics and Security

A Secure Communication Game With a Relay Helping the Eavesdropper

M. Yuksel, Xi Liu, E. Erkip

Published Mar 15, 2011• 56 citations
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Abstract

In this work, a four-terminal complex Gaussian network composed of a source, a destination, an eavesdropper, and a jammer relay is studied under two different set of assumptions: 1) The jammer relay does not hear the source transmission, and 2) The jammer relay is causally given the source message. In both cases, the jammer relay assists the eavesdropper and aims to decrease the achievable secrecy rates. The source, on the other hand, aims to increase it. To help the eavesdropper, the jammer relay can use pure relaying and/or send interference. Each of the problems is formulated as a two-player, noncooperative, zero-sum continuous game. Assuming Gaussian strategies at the source and the jammer relay in the first problem, the Nash equilibrium is found and shown to be achieved with mixed strategies in general. The optimal cumulative distribution functions (cdfs) for the source and the jammer relay that achieve the value of the game, which is the Nash equilibrium secrecy rate, are found. For the second problem, the Nash equilibrium solution is found and the results are compared to the case when the jammer relay is not informed about the source message.

DOI
10.1109/tifs.2011.2125956

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In this work, a four-terminal complex Gaussian network composed of a source, a destination, an eavesdropper, and a jammer relay is studied under two different set of assumptions: 1) The jammer relay does not hear the source transmission, and 2) The jammer relay is causally given the source message. In both cases, the jammer relay assists the eavesdropper and aims to decrease the achievable secrecy rates. The source, on the other hand, aims to increase it. To help the eavesdropper, the jammer relay can use pure relaying and/or send interference. Each of the problems is formulated as a two-player, noncooperative, zero-sum continuous game. Assuming Gaussian strategies at the source and the jammer relay in the first problem, the Nash equilibrium is found and shown to be achieved with mixed strategies in general. The optimal cumulative distribution functions (cdfs) for the source and the jammer relay that achieve the value of the game, which is the Nash equilibrium secrecy rate, are found. For the second problem, the Nash equilibrium solution is found and the results are compared to the case when the jammer relay is not informed about the source message.
In this work a four terminal Gaussian network composed of a source, a destination, an eavesdropper and a jammer relay is studied. The jammer relay does not hear the source transmission. It assists the eavesdropper and aims to decrease the achievable secrecy rates. The source, on the other hand, aims to increase the achievable secrecy rates. Assuming Gaussian strategies at the source and the jammer relay, this problem is formulated as a two-player zero-sum continuous game, where the payoff is the achieved secrecy rate. For this game the Nash equilibrium is generally achieved with mixed strategies. The optimal cumulative distribution functions for the source and the jammer relay that achieve the value of the game, which is the equilibrium secrecy rate, are found.
In this work a four terminal Gaussian network composed of a source, a destination, an eavesdropper and a jammer relay is studied. The jammer relay does not hear the source transmission. It assists the eavesdropper and aims to decrease the achievable secrecy rates. The source, on the other hand, aims to increase the achievable secrecy rates. Assuming Gaussian strategies at the source and the jammer relay, this problem is formulated as a two-player zero-sum continuous game, where the payoff is the achieved secrecy rate. For this game the Nash Equilibrium is generally achieved with mixed strategies. The optimal cumulative distribution functions for the source and the jammer relay that achieve the value of the game, which is the equilibrium secrecy rate, are found.
A four terminal Gaussian network composed of a source, a destination, an eavesdropper and a jammer relay is investigated when the jammer relay is causally given the source message. The source aims to increase the achievable secrecy rates, whereas the jammer relay aims to decrease it. To help the eavesdropper and to decrease achievable perfect secrecy rates, the jammer relay can use pure relaying and/or send interference to assist eavesdropping. The problem is formulated as a zero-sum game and the saddle point solutions are found. The results are compared to the case when the jammer relay is not informed about the source message.
A four terminal Gaussian network, composed of a single source-destination pair, a relay and a wire-tapper is considered. Unlike the relay channel with a wire-tapper, it is assumed that the relay assists the wire-tapper, not the destination. The relay's objective is to decrease the achievable secrecy rates. However, since the destination is also allowed to listen to the relay's transmission, it also benefits from the relay in terms of achievable rates. Direct transmission, amplify-and-forward (AF), decode-and-forward (DF) and compress-and-forward (CF) relaying schemes are compared in terms of secrecy rates. It is shown that the best relaying strategy depends on relay's location. Comparison of relaying protocols and best power allocation schemes, when the relay assists the source-destination communication, do not readily extend to the case when the relay assists the wire-tapper.
We consider a Gaussian network consisting of a source that aims to communicate to its legitimate destination via an untrusted relay node in the presence of an external eavesdropper. The source wishes to send two independent messages to the destination: one message must be kept secret from the external eavesdropper only, while the other message must be kept secret from the external eavesdropper and the untrusted relay both. We identify achievable secure rates under these layered secrecy constraints. Considering a two-hop half-duplex setup, we employ the destination as a cooperative jammer in the first phase in order to help provide secrecy from the relay and the external eavesdropper, and the source as a cooperative jammer in the second phase in order to detriment the external eavesdropper. The source encodes its messages using stochastic encoding and security embedding coding. We provide the secrecy analysis and present numerical results to demonstrate the performance of the proposed achievability technique. Our study points to the value of the source serving as a cooperative jammer as well as the need for power control policies at the legitimate nodes in order to ensure secrecy in this system.