A Secure Communication Game with a Relay Helping the Eavesdropper

TL;DR

This paper models a four-terminal Gaussian network as a zero-sum game where a relay helps an eavesdropper, and finds the equilibrium strategies to maximize secrecy rates.

Contribution

It formulates the secure communication problem as a two-player game and derives the optimal strategies and equilibrium secrecy rate.

Findings

Optimal mixed strategies for source and relay are identified.

The equilibrium secrecy rate is characterized.

The game-theoretic approach provides insights into secure communication with adversarial relays.

Abstract

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.