Covert Communication over Adversarially Jammed Channels

TL;DR

This paper investigates covert and reliable communication over adversarially jammed channels, establishing bounds on throughput and developing efficient coding schemes that require shared keys, even when the adversary is active and has partial observation.

Contribution

It introduces the first bounds and coding schemes for covert communication over active adversarial channels, highlighting the necessity of shared keys and providing practical code constructions.

Findings

Shared keys are essential for covert communication against active adversaries.

Bounds on throughput depend on channel parameters and key size, with matching bounds in many cases.

Efficient coding schemes are feasible with sublinear shared key sizes, especially when the adversary is computationally bounded.

Abstract

Suppose that a transmitter Alice potentially wishes to communicate with a receiver Bob over an adversarially jammed binary channel. An active adversary James eavesdrops on their communication over a binary symmetric channel (BSC(q)), and may maliciously flip (up to) a certain fraction p of their transmitted bits based on his observations. We consider a setting where the communication must be simultaneously covert as well as reliable, i.e., James should be unable to accurately distinguish whether or not Alice is communicating, while Bob should be able to correctly recover Alice's message with high probability regardless of the adversarial jamming strategy. We show that, unlike the setting with passive adversaries, covert communication against active adversaries requires Alice and Bob to have a shared key (of length at least Omega(log n)) even when Bob has a better channel than James. We present lower and upper bounds on the information-theoretically optimal throughput as a function of the channel parameters, the desired level of covertness, and the amount of shared key available. These bounds match for a wide range of parameters of interest. We also develop a computationally efficient coding scheme (based on concatenated codes) when the amount of shared key available is $\Omega(\sqrt{n} \log n)$, and further show that this scheme can be implemented with much less amount of shared key when the adversary is assumed to be computationally bounded.