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arXiv:1610.00381 · Allerton Conference on Communication, Control, and Computing

Covert communications on Poisson packet channels

Ramin Soltani, Dennis Goeckel, Don Towsley, Amir Houmansadr

Published Sep 1, 2015• 19 citations
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Abstract

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.

DOI
10.1109/allerton.2015.7447124

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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.
In recent years, the information theory of covert communications, where the very presence of the communication is undetectable to a watchful adversary Willie, has been of great interest. Our recent work introduced the information-theoretic limits for communication by covert users Alice and Bob, over packet channels where the packet timings of legitimate users Jack and Steve are governed by a Poisson point process. Here we consider the extension to timing channels characterized by more general renewal processes of rate λ. We consider two scenarios. In the first scenario, the source of the packets on the channel cannot be authenticated by Willie, and therefore Alice can insert packets into the channel. We show that if the total number of transmitted packets by Jack is N, Alice can covertly insert O(√N)packets and, if she transmits more, she will be detected by Willie. In the second scenario, packets are authenticated by Willie but we assume that Alice and Bob share a secret key; hence, Alice alters the timings of the packets according to a pre-shared codebook with Bob to send information to him over a G/M/1 queue with service rate μ > λ. We show that Alice can covertly and reliably transmit O(N) bits to Bob when the total number of packets sent from Jack to Steve is N.
This dissertation focuses on covert communication in channels where the communication takes place by the transmission of packets. Consider a channel where authorized transmitter Jack sends packets to authorized receiver Steve according to a Poisson process with rate λ\lambdaλ packets per second for a time period TTT. Jack's transmitted packet visit Alice, Willie, Bob and Steve, respectively. Suppose that covert transmitter Alice wishes to communicate information to covert receiver Bob without being detected by a watchful adversary Willie. We consider three sets of assumptions for this channel. For each set of assumptions, we present a technique for establishing covert communication and analyze its fundamental limits: (1) if Willie cannot verify the sources of the packets but he is aware of the channel's packet rate λ\lambdaλ, Alice can insert packets of her own in the channel covertly and Bob can successfully extract them (packet insertion); (2) if Willie can verify the sources of the packets but Alice and Bob can share a codebook and Bob receives the packets after they pass through an M/M/1M/M/1M/M/1 queue, Alice can establish covert communication with Bob by embedding information in packet arrival timings (timing channel); and (3) if packets have available space and Willie knows the probability density function (pdf) of the packet sizes, Alice can insert her own bits in the packets covertly and Bob can extract them successfully (bit insertion). We discuss the extensions of the first and second techniques to packet channels whose packet timings are governed by a renewal process. Finally, we consider the use of timing channels for network fingerprinting which is a traffic analysis method applicable to breaking the anonymity of networks. Assume Alice and Bob have access to the input and the output links of a network, respectively, where the timings of the flows are governed by independent Poisson point processes. The connections between the input and output links are hidden. We show the degree to which Alice can use flow identifiers (fingerprints) and transmit them via a timing channel to Bob to reveal the input-output connections without being detected by Willie who protects the network. We model the network as parallel M/M/1M/M/1M/M/1 queues where each queue is shared by a flow from Alice to Bob and other flows independent of the flow from Alice to Bob.
The goal of covert communication is to establish a communication link between two parties (Alice and Bob) while assuring that a warden (Willie) will not be able to detect the very presence of communication. In this work, we address the covert communication problem over a packet insertion channel. Assuming a Poisson channel model, we first consider an all-aware warden, who wishes to minimize the sum of his miss detection and false alarm probabilities. We show that the covertness extent versus Alice's transmission rate can be computed exactly. We also derive simplified bounds which are tighter than previously known results. Such a warden, however, has to be aware of Alice's transmission rate. A more practical scenario, is when the warden does not have this information, hence wishes to operate at a certain false alarm rate. For this case, we discuss Alice's strategy to ensure the warden's miss detection probability is lower bounded. Finally, we study covertness in the case where Willie has uncertainty regarding the nominal channel rate as well, and show that in this case, Alice's covert transmission rate can be even higher.
Recent works have considered the ability of transmitter Alice to communicate reliably to receiver Bob without being detected by warden Willie. These works generally assume a standard discrete-time model. But the assumption of a discrete-time model in standard communication scenarios is often predicated on its equivalence to a continuous-time model, which has not been established for the covert communications problem. Here, we consider the continuous-time channel directly and study if efficient covert communication can still be achieved. We assume that an uninformed jammer is present to assist Alice, and we consider additive white Gaussian noise (AWGN) channels between all parties. For a channel with approximate bandwidth W, we establish constructions such that O(WT) information bits can be transmitted covertly and reliably from Alice to Bob in T seconds for two separate scenarios: 1) when the path-loss between Alice and Willie is known; and 2) when the path-loss between Alice and Willie is unknown.
Covert communication conceals the transmission of the message from an attentive adversary. Recent work on the limits of covert communication in additive white Gaussian noise channels has demonstrated that a covert transmitter (Alice) can reliably transmit a maximum of O(√n) bits to a covert receiver (Bob) without being detected by an adversary (Warden Willie) in n channel uses. This paper focuses on the scenario where other “friendly” nodes distributed according to a two-dimensional Poisson point process with density m are present. We propose a strategy where the friendly node closest to the adversary, without close coordination with Alice, produces artificial noise. We show that this method allows Alice to reliably and covertly send O(min{n, mγ/2√n}) bits to Bob in n channel uses, where γ is the path-loss exponent. We also consider a setting where there are Nw collaborating adversaries uniformly and randomly located in the environment and show that in n channel uses, Alice can reliably and covertly send O(min{n, (mγ/2√n/Nwγ)}) bits to Bob when γ>2, and O(min{n, (m√n/Nw2log2Nw)}) when γ=2. Conversely, we demonstrate that no higher covert throughput is possible for γ>2.
If the warden Willie attempting to detect the transmission knows the statistics of his receiver noise, Alice can transmit no more than O(√n) covert bits reliably to Bob in n channel uses of an AWGN channel. However, if Willie does not know his noise statistics exactly, Alice can covertly transmit O(n) bits. In this letter, Willie lacks knowledge of his channel statistics but observes T(n) length-n codeword slots, where some number may be used by Alice to attempt covert transmission. We show that Willie can often limit Alice to the same performance scaling as when he knows his channel statistics.