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IEEE Information Theory Workshop (ITW)

Keyless asynchronous covert communication

Keerthi Suria Kumar Arumugam, Matthieu R. Bloch

Published Sep 1, 2016• 21 citations
Publisher

Abstract

We consider a scenario in which Alice asynchronously communicates with Bob over a Discrete Memoryless Channel (DMC) while escaping detection from an adversary who observes their communication through another DMC. Specifically, Alice transmits codewords of length n and chooses the transmission epoch T uniformly at random among N available time epochs, where N ≫ n. This deliberate symbol level-asynchronism forces the adversary to monitor a window of size N' much larger than the codeword length n, and results in an increased covert throughput compared to the scenario without asynchronism. Our result generalizes a previous work in which asynchronism was introduced at the codeword level, i.e., having Alice choose a transmission window among non-overlapping windows of length n.

DOI
10.1109/itw.2016.7606822

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IEEE Information Theory Workshop (ITW)•Nov 1, 2018•17 citations
We consider a scenario in which Alice asynchronously communicates with Bob over a Discrete Memoryless Channel (DMC) while escaping detection from an adversary who observes their communication through another DMC. Specifically, Alice transmits codewords of length n and chooses the transmission epoch T uniformly at random among N available time epochs, where N ≫ n. This deliberate symbol level-asynchronism forces the adversary to monitor a window of size N' much larger than the codeword length n, and results in an increased covert throughput compared to the scenario without asynchronism. Our result generalizes a previous work in which asynchronism was introduced at the codeword level, i.e., having Alice choose a transmission window among non-overlapping windows of length n.
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<AwA_{b}\lt A_{w}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).
Consider a channel where authorized transmitter Jack sends packets to authorized receiver Steve according to a Poisson process with rate λ packets per second for a time period T. Suppose that covert transmitter Alice wishes to communicate information to covert receiver Bob on the same channel without being detected by a watchful adversary Willie. We consider two scenarios. In the first scenario, we assume that warden Willie cannot look at packet contents but rather can only observe packet timings, and Alice must send information by inserting her own packets into the channel. We show that the number of packets that Alice can covertly transmit to Bob is on the order of the square root of the number of packets that Jack transmits to Steve; conversely, if Alice transmits more than that, she will be detected by Willie with high probability. In the second scenario, we assume that Willie can look at packet contents but that Alice can communicate across an M/M/1 queue to Bob by altering the timings of the packets going from Jack to Steve. First, Alice builds a codebook, with each codeword consisting of a sequence of packet timings to be employed for conveying the information associated with that codeword. However, to successfully employ this codebook, Alice must always have a packet to send at the appropriate time. Hence, leveraging our result from the first scenario, we propose a construction where Alice covertly slows down the packet stream so as to buffer packets to use during a succeeding codeword transmission phase. Using this approach, Alice can covertly and reliably transmit O(λT) covert bits to Bob in time period T over an M/M/1 queue with service rate μ > e · λ.
Much of security research focuses on preventing an adversary from deciphering a message's content, but there are a number of applications that motivate the more challenging goal of “covert” communications: transmitter Alice conveying information to legitimate receiver Bob while preventing a capable and attentive adversary Willie from detecting the presence of the message. Willie detects Alice's transmission by looking for deviations from the background environment; hence, covert throughput can be increased if Willie has uncertainty about that background environment, as might be caused by user mobility or time-varying jamming. Here, we consider how the dynamics of the background environment impact the throughput of covert communications. Our previous work has shown that a background environment varying a constant number of times per codeword duration can greatly increase the covert throughput. In this paper, we consider the covert throughput for all potential rates of variation of the background. Neither extreme of variation is favorable to Alice: (1) when the background environment varies too quickly relative to the codeword length, Willie can average out the variation and hence limit Alice's covert throughput; (2) when the background environment varies too slowly, Willie can estimate the current environment and again limit Alice's covert throughput. We analyze a detector at Willie that provides an upper bound (converse) to the covert throughput of Alice for all potential rates of variation. Next, we provide an explicit construction for a scheme for Alice that provides a lower bound (achievability) on the covert throughput at each rate of variation.
We consider a scenario in which two legitimate transmitters attempt to communicate with a legitimate receiver over a discrete memoryless Multiple-Access Channel (MAC), while escaping detection from an adversary who observes their communication through another discrete memoryless MAC. If the MAC to the legitimate receiver is “better” than the one to the adversary, in a sense that we make precise, then the legitimate users can reliably communicate on the order of √n bits per n channel uses with arbitrarily Low Probability of Detection (LPD) without using a secret key. We also identify the pre-constants of the scaling, which leads to a characterization of the covert capacity region.
In this paper, we study covert communication over a compound discrete memoryless channel (DMC). There are two channel states in which one of them is arbitrarily chosen and remains fixed during the transmission. The objective is to reliably send a message from the transmitter to the receiver. An adversary who is observing the channel output should not be able to infer the channel state. Two covertness metrics are considered. In the first metric, covertness is measured using the KL-divergence of the channel output marginal of each state with a fixed distribution. Different cases where such a distribution can be specified, are studied. The optimal transmission rate of each case is established. In the second metric, the covertness is measured by using the total variation distance of the channel output marginals of the two states. Upper and lower bounds on the optimal transmission covert rate are derived. The bounds match for a special case and characterize the optimal throughput.
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.