Covert Communication Gains From Adversary’s Ignorance of Transmission Time

Abstract

The recent square root law (SRL) for covert communication demonstrates that Alice can reliably transmit $\mathcal {O}(\sqrt {n})$ bits to Bob in $n$ uses of an additive white Gaussian noise (AWGN) channel while keeping ineffective any detector employed by the adversary; conversely, exceeding this limit either results in detection by the adversary with high probability or non-zero decoding error probability at Bob. This SRL is under the assumption that the adversary knows when Alice transmits (if she transmits); however, in many operational scenarios, he does not know this. Hence, here, we study the impact of the adversary’s ignorance of the time of the communication attempt. We employ a slotted AWGN channel model with $T(n)$ slots each containing $n$ symbol periods, where Alice may use a single slot out of $T(n)$ . Provided that Alice’s slot selection is secret, the adversary needs to monitor all $T(n)$ slots for possible transmission. We show that this allows Alice to reliably transmit $\mathcal {O}(\min \{({n\log T(n)})^{1/2},n\})$ bits to Bob (but no more) while keeping the adversary’s detector ineffective. To achieve this gain over SRL, Bob does not have to know the time of transmission provided $T(n) , $c_{\mathrm{ T}}=\mathcal {O}(1)$ .