Covert Communications on Renewal Packet Channels

摘要

Security and privacy are major concerns in modern communication networks. Inrecent years, the information theory of covert communications, where the verypresence of the communication is undetectable to a watchful and determinedadversary, has been of great interest. This emerging body of work has focusedon additive white Gaussian noise (AWGN), discrete memoryless channels (DMCs),and optical channels. In contrast, our recent work introduced theinformation-theoretic limits for covert communications over packet channelswhose packet timings are governed by a Poisson point process. However, actualnetwork packet arrival times do not generally conform to the Poisson processassumption, and thus here we consider the extension of our work to timingchannels characterized by more general renewal processes of rate $\lambda$. Weconsider two scenarios. In the first scenario, the source of the packets on thechannel cannot be authenticated by Willie, and therefore Alice can insertpackets into the channel. We show that if the total number of transmittedpackets by Jack is $N$, Alice can covertly insert$\mathcal{O}\left(\sqrt{N}\right)$ packets and, if she transmits more, she willbe detected by Willie. In the second scenario, packets are authenticated byWillie but we assume that Alice and Bob share a secret key; hence, Alice altersthe timings of the packets according to a pre-shared codebook with Bob to sendinformation to him over a $G/M/1$ queue with service rate $\mu>\lambda$. Weshow that Alice can covertly and reliably transmit $\mathcal{O}(N)$ bits to Bobwhen the total number of packets sent from Jack to Steve is $N$.