Two-Hop Secure Communication Using an Untrusted Relay: A Case for Cooperative Jamming

Abstract

We consider a source-destination pair that can communicate only through an unauthenticated intermediate relay node. In this two-hop communication scenario, where the cooperation from the relay node is essential, we investigate whether achieving non-zero secrecy rate is possible. Specifically, we treat the relay node as an eavesdropper from whom the source information needs to be kept secret, despite the fact that its cooperation in relaying this information is needed. We find that a positive secrecy rate is indeed achievable, with the aid of the destination node or an external node that jams the relay, i.e., by cooperative jamming. We derive an upper bound on the secrecy rate by means of an eavesdropper-relay separation argument. We remark that this upper bound is the first of its kind in Gaussian channels with cooperative jamming. The upper bound is strictly smaller than the channel capacity without secrecy constraints. The achievable secrecy rates are found using stochastic encoding and compress-and-forward at the relay. Numerical results show that the gap between the bound and the achievable rate is small when the relay's power is larger than the power of the jammer and the source. In essence, this paper shows that a cooperative jammer enables secure communication to take place using an untrusted relay which would be otherwise impossible.