Boulat A. Bash

Limits of Reliable Communication with Low Probability of Detection on AWGN Channels

We present a square root limit on low probability of detection (LPD) communication over additive white Gaussian noise (AWGN) channels. Specifically, if a warden has an AWGN channel to the transmitter with non-zero noise power, we prove that o(√n) bits can be sent from the transmitter to the receiver in n AWGN channel uses with probability of detection by the warden less than e for any ϵ >; 0, and, if a lower bound on the noise power on the wardens channel is known, then O(√n) bits can be covertly sent in n channel uses. Conversely, trying 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 as n → ∞. Further, we show that LPD communication on the AWGN channel allows one to send a nonzero symbol on every channel use, in contrast to what might be expected from the square root law found recently in image-based steganography.

Exact distributed Voronoi cell computation in sensor networks

Distributed computation of Voronoi cells in sensor networks, i.e. computing the locus of points in a sensor field closest to a given sensor, is a key building block that supports a number of applications in both the data and control planes. For example, knowledge of Voronoi cells facilitates efficient methods for computing the piece-wise approximation of a field, whereby each sensor acts as a representative for the set of points in its Voronoi cell; awareness of Voronoi boundaries and Voronoi neighbors is also useful in load balancing and energy conservation. The methods currently advocated for distributed Voronoi computation in sensor networks are heuristic approximations that can introduce significant inaccuracies that are difficult to rigorously quantify; we demonstrate that these methods may err by a factor of 5 or more in some circumstances. We present and prove an exact method which eliminates these inaccuracies, at the cost of increased messaging overhead, but without necessitating contact with the entire network. To our knowledge, this is the first distributed algorithm that computes accurate Voronoi cells without requiring all-to-all communication. We implement it as a TinyOS module and quantitatively analyze its performance.

Approximately uniform random sampling in sensor networks

Recent work in sensor databases has focused extensively on distributed query problems, notably distributed computation of aggregates. Existing methods for computing aggregates broadcast queries to all sensors and use in-network aggregation of responses to minimize messaging costs. In this work, we focus on uniform random sampling across nodes, which can serve both as an alternative building block for aggregation and as an integral component of many other useful randomized algorithms. Prior to our work, the best existing proposals for uniform random sampling of sensors involve contacting all nodes in the network. We propose a practical method which is only approximately uniform, but contacts a number of sensors proportional to the diameter of the network instead of its size. The approximation achieved is tunably close to exact uniform sampling, and only relies on well-known existing primitives, namely geographic routing, distributed computation of Voronoi regions and von Neumanns rejection method. Ultimately our sampling algorithm has the same worst-case asymptotic cost as routing a point-to-point message, and thus it is asymptotically optimal among request/reply-based sampling methods. We provide experimental results demonstrating the effectiveness of our algorithm on both synthetic and real sensor topologies.

Hiding information in noise: fundamental limits of covert wireless communication

Widely deployed encryption-based security prevents unauthorized decoding, but does not ensure undetectability of communication. However, covert, or low probability of detection/intercept communication is crucial in many scenarios ranging from covert military operations and the organization of social unrest, to privacy protection for users of wireless networks. In addition, encrypted data or even just the transmission of a signal can arouse suspicion, and even the most theoretically robust encryption can often be defeated by a determined adversary using non-computational methods such as side-channel analysis. Various covert communication techniques have been developed to address these concerns, including steganography for finite-alphabet noiseless applications and spread-spectrum systems for wireless communications. After reviewing these covert communication systems, this article discusses new results on the fundamental limits of their capabilities, and provides a vision for the future of such systems as well.

Square root law for communication with low probability of detection on AWGN channels

We present a square root limit on low probability of detection (LPD) communication over additive white Gaussian noise (AWGN) channels. Specifically, if a warden has an AWGN channel to the transmitter with non-zero noise power, we prove that o(√n) bits can be sent from the transmitter to the receiver in n AWGN channel uses with probability of detection by the warden less than e for any ∊ > 0, and, if a lower bound on the noise power on the wardens channel is known, then O(√n) bits can be covertly sent in n channel uses. Conversely, trying 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 as n → ∞. Further, we show that LPD communication on the AWGN channel allows one to send a nonzero symbol on every channel use, in contrast to what might be expected from the square root law found recently in image-based steganography.

LPD communication when the warden does not know when

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 wardens 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.

Covert Communications When the Warden Does Not Know the Background Noise Power

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.

Quantum-secure covert communication on bosonic channels

Computational encryption, information-theoretic secrecy and quantum cryptography offer progressively stronger security against unauthorized decoding of messages contained in communication transmissions. However, these approaches do not ensure stealth—that the mere presence of message-bearing transmissions be undetectable. We characterize the ultimate limit of how much data can be reliably and covertly communicated over the lossy thermal-noise bosonic channel (which models various practical communication channels). We show that whenever there is some channel noise that cannot in principle be controlled by an otherwise arbitrarily powerful adversary—for example, thermal noise from blackbody radiation—the number of reliably transmissible covert bits is at most proportional to the square root of the number of orthogonal modes (the time-bandwidth product) available in the transmission interval. We demonstrate this in a proof-of-principle experiment. Our result paves the way to realizing communications that are kept covert from an all-powerful quantum adversary.Boulat A. Bash, Andrei H. Gheorghe, Monika Patel, Jonathan L. Habif, Dennis Goeckel, Don Towsley, and Saikat Guha School of Computer Science, University of Massachusetts, Amherst, Massachusetts, USA 01003, Quantum Information Processing Group, Raytheon BBN Technologies, Cambridge, Massachusetts, USA 02138, Amherst College, Amherst, Massachusetts, USA 01002, Electrical and Computer Engineering Department, University of Massachusetts, Amherst, Massachusetts, USA 01003 ∗

Quantum noise limited optical communication with low probability of detection

We demonstrate the achievability of a square root limit on the amount of information transmitted reliably and with low probability of detection (LPD) over the single-mode lossy bosonic channel if either the eavesdroppers measurements or the channel itself is subject to the slightest amount of excess noise. Specifically, Alice can transmit O(√n) bits to Bob over n channel uses such that Bobs average codeword error probability is upper-bounded by an arbitrarily small δ > 0 while a passive eavesdropper, Warden Willie, who is assumed to be able to collect all the transmitted photons that do not reach Bob, has an average probability of detection error that is lower-bounded by 1/2 - ε for an arbitrarily small ε > 0. We analyze the thermal noise and pure loss channels. The square root law holds for the thermal noise channel even if Willie employs a quantum-optimal measurement, while Bob is equipped with a standard coherent detection receiver. We also show that LPD communication is not possible with coherent state transmission on the pure loss channel. However, this result assumes Willie to possess an ideal receiver that is not subject to excess noise. If Willie is restricted to a practical receiver with a non-zero dark current, the square root law is achievable on the pure loss channel.

Covert communication over classical-quantum channels

Recently, the fundamental limits of covert, i.e., reliable-yet-undetectable, communication have been established for general memoryless channels and for lossy-noisy bosonic (quantum) channels with a quantum-limited adversary. The key import of these results was the square-root law (SRL) for covert communication, which states that O(√n) covert bits, but no more, can be reliably transmitted over n channel uses with O(√n) bits of secret pre-shared between communicating parties. Here we prove the achievability of the SRL for a general memoryless classical-quantum channel, showing that SRL covert communication is achievable over any quantum communication channel with a product-state transmission strategy. We leave open the converse, which, if proven, would show that even using entangled transmissions and entangling measurements, the SRL for covert communication cannot be surpassed over an arbitrary quantum channel.