Covert Communications on Poisson Packet Channels

TL;DR

This paper investigates covert communication over Poisson packet channels, establishing limits on the number of covert bits transmitted without detection and proposing methods for reliable covert messaging using packet timing and buffering strategies.

Contribution

It introduces the fundamental limits of covert communication in Poisson channels and develops a novel coding scheme leveraging packet timing and buffering for reliable covert transmission.

Findings

In the timing observation scenario, Alice can covertly transmit on the order of the square root of the number of packets.

In the content observation scenario, Alice can reliably transmit on the order of λT covert bits.

The proposed buffering strategy enables covert communication over M/M/1 queues with reliable decoding.

Abstract

Consider a channel where authorized transmitter Jack sends packets to authorized receiver Steve according to a Poisson process with rate $\lambda$ packets per second for a time period $T$. Suppose that covert transmitter Alice wishes to communicate information to covert receiver Bob on the same channel without being detected by a watchful adversary Willie. We consider two scenarios. In the first scenario, we assume that warden Willie cannot look at packet contents but rather can only observe packet timings, and Alice must send information by inserting her own packets into the channel. We show that the number of packets that Alice can covertly transmit to Bob is on the order of the square root of the number of packets that Jack transmits to Steve; conversely, if Alice transmits more than that, she will be detected by Willie with high probability. In the second scenario, we assume that Willie can look at packet contents but that Alice can communicate across an $M/M/1$ queue to Bob by altering the timings of the packets going from Jack to Steve. First, Alice builds a codebook, with each codeword consisting of a sequence of packet timings to be employed for conveying the information associated with that codeword. However, to successfully employ this codebook, Alice must always have a packet to send at the appropriate time. Hence, leveraging our result from the first scenario, we propose a construction where Alice covertly slows down the packet stream so as to buffer packets to use during a succeeding codeword transmission phase. Using this approach, Alice can covertly and reliably transmit $\mathcal{O}(\lambda T)$ covert bits to Bob in time period $T$ over an $M/M/1$ queue with service rate $\mu > \lambda$.