A Secure Communication Game with a Relay Helping the Eavesdropper

TL;DR

This paper models a four-terminal Gaussian network as a game where a relay helps an eavesdropper, analyzing strategies and equilibrium secrecy rates under different assumptions about the relay's knowledge.

Contribution

It formulates and solves a non-cooperative game for secure communication with a relay aiding the eavesdropper, deriving Nash equilibria and optimal strategies.

Findings

Nash equilibrium strategies are identified for both scenarios.

Optimal distributions for source and relay are derived.

Comparison shows the relay's knowledge impacts secrecy rates.

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: (i) The jammer relay does not hear the source transmission, and (ii) 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, non-cooperative, 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 (cdf) 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.