Secrecy in the two-way untrusted relay channel with compute-and-forward

We consider the problem of secure communications in a Gaussian two-way relay channel applying the compute-and-forward scheme using nested lattice codes. Two 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 provide an achievable secrecy rate region under a weak secrecy criterion and provide the proof. We show that the achievable sum secrecy rate is equivalent to the difference between the computation rate and the multiple access channel (MAC) capacity. Particularly, we show that both the nodes must encode their messages such that the common computation rate pair falls outside the MAC capacity region of the relay.