Lattice coding for strongly secure compute-and-forward in a bidirectional relay

We study the problem of secure bidirectional relaying in the presence of an “honest but curious” relay. We consider the setting where all links between nodes are additive white Gaussian noise (AWGN) channels, and show that using nested lattice codes, it is possible to obtain strong secrecy. A randomized encoder based on probability mass functions obtained by sampling the Gaussian function is used, and we show that the mutual information between the secret messages and the vector received by the relay is arbitrarily small for large block lengths. We determine sufficient conditions for secure and reliable communication, and find achievable rates. We then extend the results to the case of secure relaying in a multi-hop network with K +1 hops.