Weak Secrecy in the Multi-Way Untrusted Relay Channel with Compute-and-Forward

TL;DR

This paper explores secure communication in a multi-way relay channel using compute-and-forward with nested lattice codes, establishing achievable secrecy rates and analyzing the impact of channel conditions on security performance.

Contribution

It introduces a novel scheme for secure multi-way relay communication that achieves secrecy rates close to compute-and-forward rates, considering weak secrecy and various channel configurations.

Findings

Achievable secrecy rate equals computation rate minus MAC capacity.

Secure encoding requires the computation rate to be outside the MAC region.

Results show the scheme's performance depends on channel realization.

Abstract

We investigate the problem of secure communications in a Gaussian multi-way relay channel applying the compute-and-forward scheme using 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 (SIMO) L-user multi-way 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. Particularly, 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 (SISO) and the multiple-input single-input (MISO) L-user multi-way relay channel as well as the two-way relay channel. We discuss these results and show the dependency 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.