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IEEE Transactions on Mobile Computing

Covert Communications in Multi-Channel Slotted ALOHA Systems

Azadeh Sheikholeslami, Majid Ghaderi, Dennis Goeckel

Published Nov 6, 2020• 7 citations
Publisher

Abstract

The fundamental limits of covert communication, where a message is sent from transmitter Alice to intended recipient Bob without detection by an attentive adversary warden Willie, has been considered extensively in recent years at the physical layer. The covert throughput depends critically on the warden's understanding of the characteristics of the radio environment and the type of receiver that he employs, and, as expected, the throughput increases when the warden has some uncertainty about the environment or some non-idealities in his receiver. In this paper, we consider the covert throughput when the adversary is only able to observe the medium access control (MAC) layer in a wireless communication system. In particular, given that the system has a rate of$\lambda$packets per slot transmitted over$n$channels by allowable system users, we study the allowable rate$\lambda _a$by covert users while maintaining covertness from an attentive warden observing the channel status in a slotted ALOHA system. We characterize performance for wardens with different abilities to discern the number of packets on a given channel, ranging from simple receivers that detect only whether there was a packet present to complicated receivers that can determine the number of packets involved in any collision, and also consider intended recipients Bob with varying abilities to perform multi-packet reception. In contrast to prior work in covert communications, the application considered motivates the consideration of results for finite (often small) observation vector lengths$n$at the adversary. Numerical results are provided both to illustrate the tightness of our achievability regions for the packet transmission rate of the covert transmitters and to demonstrate the covert throughput of the system as a function of$\lambda$and$n$.

DOI
10.1109/tmc.2020.3036022

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The fundamental limits of covert communication, where a message is sent from transmitter Alice to intended recipient Bob without detection by an attentive adversary warden Willie, has been considered extensively in recent years at the physical layer. The covert throughput depends critically on the warden's understanding of the characteristics of the radio environment and the type of receiver that he employs, and, as expected, the throughput increases when the warden has some uncertainty about the environment or some non-idealities in his receiver. In this paper, we consider the covert throughput when the adversary is only able to observe the medium access control (MAC) layer in a wireless communication system. In particular, given that the system has a rate ofλ\lambdaλpackets per slot transmitted overnnnchannels by allowable system users, we study the allowable rateλa\lambda _aλa​by covert users while maintaining covertness from an attentive warden observing the channel status in a slotted ALOHA system. We characterize performance for wardens with different abilities to discern the number of packets on a given channel, ranging from simple receivers that detect only whether there was a packet present to complicated receivers that can determine the number of packets involved in any collision, and also consider intended recipients Bob with varying abilities to perform multi-packet reception. In contrast to prior work in covert communications, the application considered motivates the consideration of results for finite (often small) observation vector lengthsnnnat the adversary. Numerical results are provided both to illustrate the tightness of our achievability regions for the packet transmission rate of the covert transmitters and to demonstrate the covert throughput of the system as a function ofλ\lambdaλandnnn.
Covert communications, where a transmitter Alice wishes to hide the presence of her transmitted signal from a watchful adversary Willie, has been considered extensively in recent years. Those investigations have generally considered physical-layer models, where the adversary has access to a sophisticated (often optimal) receiver to determine whether a transmission has taken place, and have addressed the question of what rate can information be communicated covertly. More recent investigations have begun to consider the change in covert rate when Willie has uncertainty about the physical layer environment. Here, we move up the protocol stack to consider the covert rate when Willie is watching the medium-access control (MAC) layer in a network employing a random access MAC such as slotted ALOHA. Based on the rate of collisions and potentially the number of users involved in those collisions, Willie attempts to determine whether unauthorized (covert) users are accessing the channel. In particular, we assume different levels of sophistication in Willie's receiver, ranging from a receiver that only can detect whether there was a collision or not, to one that can always tell exactly how many packets were on the channel in the random access system. In each case, we derive closed-form expressions for the achievable covert rates in the system. The achievable rates exhibit significantly different behavior than that observed in the study of covert systems at the physical layer.
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.
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.
Covert communication aims to hide the existence of the transmissions to guarantee the security in wireless communications. In this letter, channel uncertainty is exploited to achieve covert communication in relay networks. The transmitter Alice sends messages to the legitimate receiver Bob with the help of a relay, while the warden Willie wants to detect the existence of the transmission. The channel uncertainty introduces confusions to degrade the performance of Willie's detection. We show that Alice can transmit O{O}O (n{n}n ) bits in n{n}n channel uses covertly with the help of relay and channel uncertainty. Numerical results are shown to illustrate the achievability and the performance of the considered scenario.
Covert communication is achieved if the transmitter (Alice) sends messages to a legitimate receiver (Bob) without detection by an attentive warden (Willie). Recently, there has been significant work on establishing the limits of such covert communication, including our work demonstrating that a cooperative jammer can greatly improve the throughput of covert communication systems. However, this previous work has considered a discrete-time model, with the implicit implication that the results will be similar on the true continuous-time model of the physical channel. In this paper, we consider covert communication over the continuous-time channel model to understand the throughput scaling for large blocklengths. For the Alice-Bob-Willie scenario, the results from the discrete-time channel generally follow. However, when a jammer is added to the environment, we demonstrate that timing offsets between Alice's signal and that of the jammer allow for the application of co-channel interference mitigation techniques at Willie's detector, which call into question whether our previous results suggesting an improvement in the covert throughput with the help of the jammer will be obtained in practice. Finally, we consider initial approaches to thwart such a detector and achieve improved throughput scaling in the presence of the jammer.
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.