Secrecy Constrained Distributed Inference in Wireless Sensor Networks

Comprised of a large number of low-cost, low-power, mobile and miniature sensors, wireless sensor networks are widely employed in many applications, such as environmental monitoring, health-care, and diagnostics of complex systems. In wireless sensor networks, the sensor outputs are transmitted across a wireless communication network to legitimate users such as fusion centers for final decision-making. Because of the wireless links across the network, the data are vulnerable to security breaches. For many applications, the data collected by local sensors are extremely sensitive, and care must be taken to prevent that information from being leaked to any malicious third parties, e.g., eavesdroppers. Eavesdropping is one of the most significant threats to wireless sensor networks, where local sensors are tapped by an eavesdropper in order to intercept information. I considered distributed inference in the presence of a global, greedy and informed eavesdropper who has access to all local node outputs rather than access. My goal is to develop secured distributed systems against eavesdropping attacks using a physical-layer security approach instead of cryptography techniques because of the stringent constraints on sensor networks energy and computational capability. The physical-layer security approach utilizes the characteristics of the physical layer, including transmission channels noises, and the information of the source. Additionally, physical-layer security for distributed inference is scalable due to the low computational complexity. I first investigate secrecy constrained distributed detection under both Neyman-Pearson and Bayesian frameworks. I analyze the asymptotic detection performance and proposed a novel way of analyzing the maximum performance trade-off using Kullback-Leibler divergence ratio between the fusion center and eavesdropper. Under the Neyman-Pearson framework, I show that the eavesdropper\u27s detection performance can be limited such that her decision-making is no better than random guessing; meanwhile, the detection performance at the fusion center is guaranteed at the prespecified level. Similar analyses and proofs are provided under the Bayesian framework, where it was shown that an eavesdropper can be constrained to an error probability level equal to her prior information. Additionally, I derive the asymptotic error exponent and show that asymptotic perfect secrecy and asymptotic perfect detection are possible by increasing the number of sensors under both frameworks if the fusion center has noiseless channels to the sensors. For secrecy constrained distributed estimation, I conducted similar analysis under both a classical setting and Bayesian setting. I derived the maximum achievable secrecy performance and show that under the condition that the eavesdropper has noisy channels and the fusion center has noiseless channels, both asymptotic perfect secrecy and asymptotic perfect estimation can be achieved under a classical setting. Similarly, under a Bayesian setting, I derived the performance trade-off using Fisher information ratio and show that the fusion center outperforms the eavesdropper significantly in the simulation section. Secrecy constrained in distributed inference with Rayleigh fading binary symmetric channel is considered as well. Similarly, I derive the maximum achievable secrecy performance ratio for both detection and estimation. The maximum achievable trade-off turns out to be almost the same in distributed estimation as in distributed detection. This suggests that a universal framework for generally structured inference problems are feasible. Further investigations are needed to justify this conjecture for more general applications

A Survey of Physical Layer Security Techniques for 5G Wireless Networks and Challenges Ahead

Physical layer security which safeguards data confidentiality based on the information-theoretic approaches has received significant research interest recently. The key idea behind physical layer security is to utilize the intrinsic randomness of the transmission channel to guarantee the security in physical layer. The evolution towards 5G wireless communications poses new challenges for physical layer security research. This paper provides a latest survey of the physical layer security research on various promising 5G technologies, including physical layer security coding, massive multiple-input multiple-output, millimeter wave communications, heterogeneous networks, non-orthogonal multiple access, full duplex technology, etc. Technical challenges which remain unresolved at the time of writing are summarized and the future trends of physical layer security in 5G and beyond are discussed.Comment: To appear in IEEE Journal on Selected Areas in Communication

Lists that are smaller than their parts: A coding approach to tunable secrecy

We present a new information-theoretic definition and associated results, based on list decoding in a source coding setting. We begin by presenting list-source codes, which naturally map a key length (entropy) to list size. We then show that such codes can be analyzed in the context of a novel information-theoretic metric, \epsilon-symbol secrecy, that encompasses both the one-time pad and traditional rate-based asymptotic metrics, but, like most cryptographic constructs, can be applied in non-asymptotic settings. We derive fundamental bounds for \epsilon-symbol secrecy and demonstrate how these bounds can be achieved with MDS codes when the source is uniformly distributed. We discuss applications and implementation issues of our codes.Comment: Allerton 2012, 8 page

Principles of Physical Layer Security in Multiuser Wireless Networks: A Survey

This paper provides a comprehensive review of the domain of physical layer security in multiuser wireless networks. The essential premise of physical-layer security is to enable the exchange of confidential messages over a wireless medium in the presence of unauthorized eavesdroppers without relying on higher-layer encryption. This can be achieved primarily in two ways: without the need for a secret key by intelligently designing transmit coding strategies, or by exploiting the wireless communication medium to develop secret keys over public channels. The survey begins with an overview of the foundations dating back to the pioneering work of Shannon and Wyner on information-theoretic security. We then describe the evolution of secure transmission strategies from point-to-point channels to multiple-antenna systems, followed by generalizations to multiuser broadcast, multiple-access, interference, and relay networks. Secret-key generation and establishment protocols based on physical layer mechanisms are subsequently covered. Approaches for secrecy based on channel coding design are then examined, along with a description of inter-disciplinary approaches based on game theory and stochastic geometry. The associated problem of physical-layer message authentication is also introduced briefly. The survey concludes with observations on potential research directions in this area.Comment: 23 pages, 10 figures, 303 refs. arXiv admin note: text overlap with arXiv:1303.1609 by other authors. IEEE Communications Surveys and Tutorials, 201

Distributed Inference and Learning with Byzantine Data

We are living in an increasingly networked world with sensing networks of varying shapes and sizes: the network often comprises of several tiny devices (or nodes) communicating with each other via different topologies. To make the problem even more complicated, the nodes in the network can be unreliable due to a variety of reasons: noise, faults and attacks, thus, providing corrupted data. Although the area of statistical inference has been an active area of research in the past, distributed learning and inference in a networked setup with potentially unreliable components has only gained attention recently. The emergence of big and dirty data era demands new distributed learning and inference solutions to tackle the problem of inference with corrupted data. Distributed inference networks (DINs) consist of a group of networked entities which acquire observations regarding a phenomenon of interest (POI), collaborate with other entities in the network by sharing their inference via different topologies to make a global inference. The central goal of this thesis is to analyze the effect of corrupted (or falsified) data on the inference performance of DINs and design robust strategies to ensure reliable overall performance for several practical network architectures. Specifically, the inference (or learning) process can be that of detection or estimation or classification, and the topology of the system can be parallel, hierarchical or fully decentralized (peer to peer). Note that, the corrupted data model may seem similar to the scenario where local decisions are transmitted over a Binary Symmetric Channel (BSC) with a certain cross over probability, however, there are fundamental differences. Over the last three decades, research community has extensively studied the impact of transmission channels or faults on the distributed detection system and related problems due to its importance in several applications. However, corrupted (Byzantine) data models considered in this thesis, are philosophically different from the BSC or the faulty sensor cases. Byzantines are intentional and intelligent, therefore, they can optimize over the data corruption parameters. Thus, in contrast to channel aware detection, both the FC and the Byzantines can optimize their utility by choosing their actions based on the knowledge of their opponent’s behavior. Study of these practically motivated scenarios in the presence of Byzantines is of utmost importance, and is missing from the channel aware detection and fault tolerant detection literature. This thesis advances the distributed inference literature by providing fundamental limits of distributed inference with Byzantine data and provides optimal counter-measures (using the insights provided by these fundamental limits) from a network designer’s perspective. Note that, the analysis of problems related to strategical interaction between Byzantines and network designed is very challenging (NP-hard is many cases). However, we show that by utilizing the properties of the network architecture, efficient solutions can be obtained. Specifically, we found that several problems related to the design of optimal counter-measures in the inference context are, in fact, special cases of these NP-hard problems which can be solved in polynomial time. First, we consider the problem of distributed Bayesian detection in the presence of data falsification (or Byzantine) attacks in the parallel topology. Byzantines considered in this thesis are those nodes that are compromised and reprogrammed by an adversary to transmit false information to a centralized fusion center (FC) to degrade detection performance. We show that above a certain fraction of Byzantine attackers in the network, the detection scheme becomes completely incapable (or blind) of utilizing the sensor data for detection. When the fraction of Byzantines is not sufficient to blind the FC, we also provide closed form expressions for the optimal attacking strategies for the Byzantines that most degrade the detection performance. Optimal attacking strategies in certain cases have the minimax property and, therefore, the knowledge of these strategies has practical significance and can be used to implement a robust detector at the FC. In several practical situations, parallel topology cannot be implemented due to limiting factors, such as, the FC being outside the communication range of the nodes and limited energy budget of the nodes. In such scenarios, a multi-hop network is employed, where nodes are organized hierarchically into multiple levels (tree networks). Next, we study the problem of distributed inference in tree topologies in the presence of Byzantines under several practical scenarios. We analytically characterize the effect of Byzantines on the inference performance of the system. We also look at the possible counter-measures from the FC’s perspective to protect the network from these Byzantines. These counter-measures are of two kinds: Byzantine identification schemes and Byzantine tolerant schemes. Using learning based techniques, Byzantine identification schemes are designed that learn the identity of Byzantines in the network and use this information to improve system performance. For scenarios where this is not possible, Byzantine tolerant schemes, which use game theory and error-correcting codes, are developed that tolerate the effect of Byzantines while maintaining a reasonably good inference performance in the network. Going a step further, we also consider scenarios where a centralized FC is not available. In such scenarios, a solution is to employ detection approaches which are based on fully distributed consensus algorithms, where all of the nodes exchange information only with their neighbors. For such networks, we analytically characterize the negative effect of Byzantines on the steady-state and transient detection performance of conventional consensus-based detection schemes. To avoid performance deterioration, we propose a distributed weighted average consensus algorithm that is robust to Byzantine attacks. Next, we exploit the statistical distribution of the nodes’ data to devise techniques for mitigating the influence of data falsifying Byzantines on the distributed detection system. Since some parameters of the statistical distribution of the nodes’ data might not be known a priori, we propose learning based techniques to enable an adaptive design of the local fusion or update rules. The above considerations highlight the negative effect of the corrupted data on the inference performance. However, it is possible for a system designer to utilize the corrupted data for network’s benefit. Finally, we consider the problem of detecting a high dimensional signal based on compressed measurements with secrecy guarantees. We consider a scenario where the network operates in the presence of an eavesdropper who wants to discover the state of the nature being monitored by the system. To keep the data secret from the eavesdropper, we propose to use cooperating trustworthy nodes that assist the FC by injecting corrupted data in the system to deceive the eavesdropper. We also design the system by determining the optimal values of parameters which maximize the detection performance at the FC while ensuring perfect secrecy at the eavesdropper

Hiding Symbols and Functions: New Metrics and Constructions for Information-Theoretic Security

We present information-theoretic definitions and results for analyzing symmetric-key encryption schemes beyond the perfect secrecy regime, i.e. when perfect secrecy is not attained. We adopt two lines of analysis, one based on lossless source coding, and another akin to rate-distortion theory. We start by presenting a new information-theoretic metric for security, called symbol secrecy, and derive associated fundamental bounds. We then introduce list-source codes (LSCs), which are a general framework for mapping a key length (entropy) to a list size that an eavesdropper has to resolve in order to recover a secret message. We provide explicit constructions of LSCs, and demonstrate that, when the source is uniformly distributed, the highest level of symbol secrecy for a fixed key length can be achieved through a construction based on minimum-distance separable (MDS) codes. Using an analysis related to rate-distortion theory, we then show how symbol secrecy can be used to determine the probability that an eavesdropper correctly reconstructs functions of the original plaintext. We illustrate how these bounds can be applied to characterize security properties of symmetric-key encryption schemes, and, in particular, extend security claims based on symbol secrecy to a functional setting.Comment: Submitted to IEEE Transactions on Information Theor

Secure Wireless Communications Based on Compressive Sensing: A Survey

IEEE Compressive sensing (CS) has become a popular signal processing technique and has extensive applications in numerous fields such as wireless communications, image processing, magnetic resonance imaging, remote sensing imaging, and anology to information conversion, since it can realize simultaneous sampling and compression. In the information security field, secure CS has received much attention due to the fact that CS can be regarded as a cryptosystem to attain simultaneous sampling, compression and encryption when maintaining the secret measurement matrix. Considering that there are increasing works focusing on secure wireless communications based on CS in recent years, we produce a detailed review for the state-of-the-art in this paper. To be specific, the survey proceeds with two phases. The first phase reviews the security aspects of CS according to different types of random measurement matrices such as Gaussian matrix, circulant matrix, and other special random matrices, which establishes theoretical foundations for applications in secure wireless communications. The second phase reviews the applications of secure CS depending on communication scenarios such as wireless wiretap channel, wireless sensor network, internet of things, crowdsensing, smart grid, and wireless body area networks. Finally, some concluding remarks are given