Covert Communication Gains from Adversary's Ignorance of Transmission Time

The recent square root law (SRL) for covert communication demonstrates that Alice can reliably transmit O(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 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)<2^c_Tⁿ, c_T =O(1).