Weak Secrecy in the Multiway Untrusted Relay Channel With Compute-and-Forward

Abstract

We investigate the problem of secure communications in a Gaussian multiway relay channel applying the compute-and-forward scheme under usage of nested lattice codes. All nodes employ half-duplex operation and can exchange confidential messages only via an untrusted relay. The relay is assumed to be honest but curious, i.e., an eavesdropper that conforms to the system rules and applies the intended relaying scheme. We start with the general case of the single-input multiple-output L-user multiway relay channel and provide an achievable secrecy rate region under a weak secrecy criterion. We show that the securely achievable sum rate is equivalent to the difference between the computation rate and the multiple access channel (MAC) capacity. In particular, we show that all nodes must encode their messages such that the common computation rate tuple falls outside the MAC capacity region of the relay. We provide results for the single-input single-output and the multiple-input single-input L-user multiway relay channel as well as the two-way relay channel. We discuss these results and show the dependence between channel realization and achievable secrecy rate. We further compare our result to available results in the literature for different schemes and show that the proposed scheme operates close to the compute-and-forward rate without secrecy.