Perfectly Covert Communication with a Reflective Panel

Covert communication, a sub-field of information security, is focused on hiding the mere existence of communication from unwanted listeners via the physical layer, i.e., via signal and noise characteristics, rather than assuming coding or secure protocols at the higher layers. In this work, we consider the problem of perfect covert communication in wireless networks. Specifically, harnessing an Intelligent Reflecting Surface (IRS), we turn our attention to schemes which allow the transmitter to completely hide the communication, with zero energy at the unwanted listener (Willie) and hence zero probability of detection. Applications of such schemes go beyond simple covertness, as we prevent detectability or decoding even when the codebook, timings and channel characteristics are known to Willie. That is, perfect covertness also ensures Willie is unable to decode, even assuming communication took place and knowing the codebook. We define perfect covertness, give a necessary and sufficient condition for it in IRS-assisted communication and define the optimization problem. For $N=2$ IRS elements we compute the probability of finding a solution and give the solution analytically. For $N>2$, we also analytically compute the probability of such a zero-detection solution, and show that it tends to $1$ as the number of IRS elements increases. We provide a perfectly covert scheme achieving it and prove its convergence. The results are also supported by simulation results, showing that a small amount of IRS elements allows for a positive rate at the legitimate user yet with zero probability of detection at an unwanted listener.