End-to-end secure multi-hop communication with untrusted relays

A multi-hop line network is considered, where each node can receive signals transmitted by its two neighbors. As such, the model embodies both the interference and broadcast aspects of wireless networks. The leftmost node wishes to send messages to the rightmost node, while keeping these messages confidential from all the intermediate relay nodes. In this setting where any or all of the relay nodes can be eavesdroppers, it is shown that end-to-end secure and reliable communication is possible. Notably, it is shown that an end-to-end secrecy rate that is independent of the number of hops, i.e., intermediate eavesdroppers, is achievable by means of a carefully designed transmission schedule, compute-and-forward relaying and coding strategy utilizing nested lattice codes. The achievable rate obtained indicates that imposing secrecy constraints penalizes the capacity by at most 1 bit per channel use. Therefore, it is concluded that information theoretic secrecy can be guaranteed for this model irrespective of eavesdropping relays and a fixed modest cost for the end-to-end rate.