Covert communications on renewal packet channels

In recent years, the information theory of covert communications, where the very presence of the communication is undetectable to a watchful adversary Willie, has been of great interest. Our recent work introduced the information-theoretic limits for communication by covert users Alice and Bob, over packet channels where the packet timings of legitimate users Jack and Steve are governed by a Poisson point process. Here we consider the extension to timing channels characterized by more general renewal processes of rate λ. We consider two scenarios. In the first scenario, the source of the packets on the channel cannot be authenticated by Willie, and therefore Alice can insert packets into the channel. We show that if the total number of transmitted packets by Jack is N, Alice can covertly insert O(√N)packets and, if she transmits more, she will be detected by Willie. In the second scenario, packets are authenticated by Willie but we assume that Alice and Bob share a secret key; hence, Alice alters the timings of the packets according to a pre-shared codebook with Bob to send information to him over a G/M/1 queue with service rate µ > λ. We show that Alice can covertly and reliably transmit O(N) bits to Bob when the total number of packets sent from Jack to Steve is N.