Covert Communication Over Noisy Channels: A Resolvability Perspective

Abstract

We consider the situation in which a transmitter attempts to communicate reliably over a discrete memoryless channel while simultaneously ensuring covertness (low probability of detection) with respect to a warden, who observes the signals through another discrete memoryless channel. We develop a coding scheme based on the principle of channel resolvability, which generalizes and extends prior work in several directions. First, it shows that, irrespective of the quality of the channels, it is possible to communicate on the order of √ n reliable and covert bits over n channel uses if the transmitter and the receiver share on the order of √ n key bits; this improves upon earlier results requiring on the order of √ n log n key bits. Second, it proves that, if the receiver's channel is "better" than the warden's channel in a sense that we make precise, it is possible to communicate on the order of √ n reliable and covert bits over n channel uses without a secret key; this generalizes earlier results established for binary symmetric channels. We also identify the fundamental limits of covert and secret communications in terms of the optimal asymptotic scaling of the message size and key size, and we extend the analysis to Gaussian channels. The main technical problem that we address is how to develop concentration inequalities for "low-weight" sequences; the crux of our approach is to define suitably modified typical sets that are amenable to concentration inequalities.M. R. Bloch is with the

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“…However, it is more effective that rather than scramble of the crucial information, the transmission of information stay imperceptible . Numerous ideas and methods of covert channels and communication are proposed in literature; however, most of work prominently use multimedia files like images, videos, and audios . This is due to the fact that multimedia files offer larger insertion spaces and induce the least suspicion due to their wide distributions.…”

Polar codes for covert communications over asynchronous Discrete Memoryless Channels

“…We assume that both P 1 and Q 1 are absolutely continuous with respect to (w.r.t.) P 0 and Q 0 , respectively, to avoid the special situations discussed in Appendix V of [3]. Formally, a message W ∈ 1, M n with uniform distribution is encoded into a codeword of length n, possibly with the help of secret key S ∈ 1, K n only known to Alice and Bob but using a public codebook known to all parties; the codeword is hidden within a larger transmission window of size N > n, with N a function of n, by choosing the starting index T of the codeword uniformly at random between 1 and N N − n + 1.…”

“…Note that Q N can be computed using knowledge of the codebook and the distribution of T. The covertness of the transmission is measured by the total variation V (n) V Q N , Q ⊗N 0 . A small value of V (n) ensures that the best binary hypothesis test is not significantly better than a "blind" test that would ignore the observation Z 1:N [3].…”

“…Our code construction follows the idea put forward in [3,6], which suggests to have the code induce a "covert process" at the output of the adversary's channel by leveraging the notion of channel resolvability [8], and to show that the covert process is itself indistinguishable from the product distribution Q 0 .…”

Secure Communication Under Channel Uncertainty and Adversarial Attacks

“…A related problem is the so-called covert communication in which the legitimate users wish to communicate in such a way that the whole communication itself is not detectable by non-legitimate eavesdroppers. This is another potential strategy for the legitimate users to ensure secrecy and even avoid adversarial attacks [43]- [45].…”