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 observation. 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, reliable covert communication against active adversaries requires Alice and Bob to have a shared key (of length at least Ω(log n)) even when Bob has a better channel than James. We present inner and outer bounds on the information-theoretically optimal throughputs as a function of the channel parameters, the desired level of covertness, and the amount of shared key available. Further, these bounds match for a wide range of parameters of interest.
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 observation. 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, reliable covert communication against active adversaries requires Alice and Bob to have a shared key (of length at least Ω(log n)) even when Bob has a better channel than James. We present inner and outer bounds on the information-theoretically optimal throughputs as a function of the channel parameters, the desired level of covertness, and the amount of shared key available. Further, these bounds match for a wide range of parameters of interest.
In this work, we consider a covert communication scenario, where a transmitter Alice communicates to a receiver Bob with the aid of a probabilistic and uninformed jammer against an adversary warden’s detection. The transmission status and power of the jammer are random and follow some priori probabilities. We first analyze the warden’s detection performance as a function of the jammer’s transmission probability, transmit power distribution, and Alice’s transmit power. We then maximize the covert throughput from Alice to Bob subject to a covertness constraint, by designing the covert communication strategies from three different perspectives: Alice’s perspective, the jammer’s perspective, and the global perspective. Our analysis reveals that the minimum jamming power should not always be zero in the probabilistic jamming strategy, which is different from that in the continuous jamming strategy presented in the literature. In addition, we prove that the minimum jamming power should be the same as Alice’s covert transmit power, depending on the covertness and average jamming power constraints. Furthermore, our results show that the probabilistic jamming can outperform the continuous jamming in terms of achieving a higher covert throughput under the same covertness and average jamming power constraints.
We consider a scenario in which K transmitters attempt to communicate covert messages reliably to a legitimate receiver over a discrete memoryless multiple-access channel (MAC) while simultaneously escaping detection from an adversary who observes their communication through another discrete memoryless MAC. We assume that each transmitter may use a secret key that is shared only between itself and the legitimate receiver. We show that each of the K transmitters can transmit on the order of √n reliable and covert bits per n channel uses, exceeding which, the warden will be able to detect the communication. We identify the optimal pre-constants of the scaling, which leads to a complete characterization of the covert capacity region of the K-user binary-input MAC. We show that, asymptotically, all sum-rate constraints are inactive unlike the traditional MAC capacity region. We also characterize the channel conditions that have to be satisfied for the transmitters to operate without a secret key.
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.
We consider the problem of covert communication over a state-dependent channel when the Channel State Information (CSI) is available either non-causally, causally, or strictly causally, either at the transmitter alone, or at both transmitter and receiver. Covert communication with respect to an adversary, called “warden,” is one in which, despite communication over the channel, the warden’s observation remains indistinguishable from an output induced by innocent channel-input symbols. Covert communication involves fooling an adversary in part by a proliferation of codebooks; for reliable decoding at the legitimate receiver, the codebook uncertainty is typically removed via a shared secret key that is unavailable to the warden. In contrast to previous work, we do not assume the availability of a large shared key at the transmitter and legitimate receiver. Instead, we only require a secret key with negligible rate to bootstrap the communication and our scheme extracts shared randomness from the CSI in a manner that keeps it secret from the warden, despite the influence of the CSI on the warden’s output. When CSI is available at the transmitter and receiver, we derive the covert capacity region. When CSI is only available at the transmitter, we derive inner and outer bounds on the covert capacity. We also provide examples for which the covert capacity is positive with knowledge of CSI but is zero without it.
We study a problem of covert communication over binary symmetric channels (BSC) in an asynchronous setup. Here, Alice seeks to communicate to Bob over a BSC while trying to be covert with respect to Willie, who observes any communication through possibly a different BSC. When Alice communicates, she transmits a message (using a codeword of length n) at a random time uniformly distributed in a window of size Awslots. We assume that Bob has side information about the time of transmission leading to a reduced uncertainty of Abslots for Bob, where Ab<Aw. In this setup, we seek to characterize the limits of covert communication as a function of the timing advantage. When Awis increasing exponentially in n, we characterize the covert capacity as a function of Awand Ab. When Awis increasing sub-exponentially in n, we characterize lower and upper bounds on achievable covert bits and show that positive covert rates are not feasible irrespective of timing advantage. Using numerical work, we illustrate our results for different network scenarios, and also highlight a tradeoff between timing advantage and channel advantage (between Bob and Willie).
In this paper, we consider fundamental communication limits over a compound channel. Covert communication in the information-theoretic context has been primarily concerned with fundamental limits when the transmitter wishes to communicate to legitimate receiver(s) while ensuring that the communication is not detected by an adversary. This paper, however, considers an alternative, and no less important, setting in which the object to be masked is the state of the compound channel. Such a communication model has applications in the prevention of malicious parties seeking to jam the communication signal when, for example, the signal-to-noise ratio of a wireless channel is found to be low. Our main contribution is the establishment of bounds on the throughput-key region when the covertness constraint is defined in terms of the total variation distance. In addition, for the scenario in which the key length is infinite, we provide a sufficient condition for when the bounds coincide for the scaling of the throughput, which follows the square-root law. Numerical examples, including that of a Gaussian channel, are provided to illustrate our results.