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IEEE International Symposium on Information Theory (ISIT)

LPD communication when the warden does not know when

Boulat A. Bash, Dennis Goeckel, Don Towsley

Published Jun 1, 2014• 88 citations
Publisher

Abstract

Unlike standard security methods (e.g. encryption), low probability of detection (LPD) communication does not merely protect the information contained in a transmission from unauthorized access, but prevents the detection of a transmission in the first place. In this work we study the impact of secretly pre-arranging the time of communication. We prove that if Alice has AWGN channels to Bob and the warden, and if she and Bob can choose a single n symbol period slot out of T(n) such slots, keeping the selection secret from the warden (and, thus, forcing him to monitor all T(n) slots), then Alice can reliably transmit O(min{√n log T(n),n}) bits to Bob while keeping the warden's detector ineffective. The result indicates that only an additional log T(n) secret bits need to be exchanged between Alice and Bpob prior to communication to produce a multiplicative gain of √log T(n) in the amount of transmitted covert information.

DOI
10.1109/isit.2014.6874904

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Unlike standard security methods (e.g. encryption), low probability of detection (LPD) communication does not merely protect the information contained in a transmission from unauthorized access, but prevents the detection of a transmission in the first place. In this work we study the impact of secretly pre-arranging the time of communication. We prove that if Alice has AWGN channels to Bob and the warden, and if she and Bob can choose a single n symbol period slot out of T(n) such slots, keeping the selection secret from the warden (and, thus, forcing him to monitor all T(n) slots), then Alice can reliably transmit O(min{√n log T(n),n}) bits to Bob while keeping the warden's detector ineffective. The result indicates that only an additional log T(n) secret bits need to be exchanged between Alice and Bpob prior to communication to produce a multiplicative gain of √log T(n) in the amount of transmitted covert information.
The recent square root law (SRL) for covert communication demonstrates that Alice can reliably transmit O(√n) bits to Bob in n uses of an additive white Gaussian noise (AWGN) channel while keeping ineffective any detector employed by the adversary; conversely, exceeding this limit either results in detection by the adversary with high probability or nonzero decoding error probability at Bob. This SRL is under the assumption that the adversary knows when Alice transmits (if she transmits); however, in many operational scenarios, he does not know this. Hence, here, we study the impact of the adversary's ignorance of the time of the communication attempt. We employ a slotted AWGN channel model with T(n) slots each containing n symbol periods, where Alice may use a single slot out of T(n). Provided that Alice's slot selection is secret, the adversary needs to monitor all T(n) slots for possible transmission. We show that this allows Alice to reliably transmit O(min{(n log T(n))1/2, n}) bits to Bob (but no more) while keeping the adversary's detector ineffective. To achieve this gain over SRL, Bob does not have to know the time of transmission provided T(n)cTn, cT= O(1).
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.
Covert communication, also known as low probability of detection (LPD) communication, prevents the adversary from knowing that a communication is taking place. Recent work has demonstrated that, in a three-party scenario with a transmitter (Alice), intended recipient (Bob), and adversary (Warden Willie), the maximum number of bits that can be transmitted reliably from Alice to Bob without detection by Willie, when additive white Gaussian noise (AWGN) channels exist between all parties, is on the order of the square root of the number of channel uses. In this paper, we begin consideration of network scenarios by studying the case where there are additional “friendly” nodes present in the environment that can produce artificial noise to aid in hiding the communication. We establish achievability results by considering constructions where the system node closest to the warden produces artificial noise and demonstrate a significant improvement in the throughput achieved covertly, without requiring close coordination between Alice and the noise-generating node. Conversely, under mild restrictions on the communication strategy, we demonstrate no higher covert throughput is possible. Extensions to the consideration of the achievable covert throughput when multiple wardens randomly located in the environment collaborate to attempt detection of the transmitter are also considered.
Covert communication has recently been recognized as a highly promising security technology that enables a transmitter Alice to reliably and covertly communicate with a receiver Bob without being detected by a malicious warden. Available works on covert communication mainly focus on scenarios with only one warden, while the fundamental limits of covert communication in more practical multi-warden scenarios remain largely unknown. This paper therefore investigates the fundamental limits of covert communication over an additive white Gaussian noise (AWGN) channel in the presence of multiple wardens. We first consider a scenario with two wardens and derive the maximum number of bits Alice can transmit to Bob over n channel uses while ensuring a negligible detection probability at wardens. We then generalize this result to the multi-warden case and find that the minimal power of wardens has impacts on the scaling law of the performance limits of covert communication over AWGN channels.
We present a square root limit on the amount of information transmitted reliably and with low probability of detection (LPD) over additive white Gaussian noise (AWGN) channels. Specifically, if the transmitter has AWGN channels to an intended receiver and a warden, both with non-zero noise power, we prove that o(√n) bits can be sent from the transmitter to the receiver in n channel uses while lower-bounding α + β ≥ 1-ε for any ε > 0, where α and β respectively denote the warden's probabilities of a false alarm when the sender is not transmitting and a missed detection when the sender is transmitting. Moreover, in most practical scenarios, a lower bound on the noise power on the channel between the transmitter and the warden is known and O(√n) bits can be sent in n LPD channel uses. Conversely, attempting to transmit more than O(√n) bits either results in detection by the warden with probability one or a non-zero probability of decoding error at the receiver as n→∞.
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.