End-to-end Secure Multi-hop Communication with Untrusted Relays is Possible

We consider a source-destination pair that can communicate only through a chain of unauthenticated intermediate relay nodes over AWGN links. In this scenario, it is desirable to use these relays-as otherwise communicating with the destination is impossible-without the relays being able to decode the information flowing through them. This in turn is tantamount to treating the relays as eavesdroppers from whom the information needs to be kept secret. An important question then becomes that of identifying the limits of reliable and secure communication in this network in the information theoretic sense. In particular, we ask whether it is possible to achieve a non-vanishing perfect secrecy rate regardless of the number of hops. In this work, we find that the answer is yes and show that a constant secrecy rate for an arbitrary number of hops is achievable by employing the combination of a lattice code and a random code.