Distributed compression involves compressing multiple data sources by exploiting the underlying correlation structure of the sources at separate non-cooperating encoders, while decoding is done jointly at a single decoder. Recent years have witnessed an increasing amount of research on the theoretical and practical aspects of distributed source codes, which find applications in distributed video compression, peer-to-peer data distribution systems, and sensor networks [1-3]. In many practical scenarios, limited network resources such as power and bandwidth, or physical limitations of the devices as in the case of sensor networks, pose challenges in terms of network performance and security. Oftentimes, the data aggregated in distributed compression systems may have commercial value as in the case of warehouse inventory monitoring systems, may contain sensitive information as in the case of distributed video surveillance systems, or might infringe personal privacy concerns as in the case of human body sensors measuring various health indicators. In all these scenarios, it is essential to develop distributed compression and communication protocols which exploit the limited power and bandwidth resources efficiently as well as satisfying the security requirements. Our goal in this chapter is to review fundamental limitations and tradeoffs for the overall performance optimization taking into account the quality and the security considerations jointly. There are two fundamental approaches to guarantee security in wireless networks. In the approach based on computational complexity , on which most practical cryptographic applications are based, the security of the system depends on the intractability assumption for a problem such as prime factorization. On the other hand, in the approach based on information theoretic secrecy introduced by Shannon in , the emphasis is on unconditional secrecy, which requires that, an eavesdropper with unbounded time and computational resources, and the knowledge of the encryption algorithm, does not gain any additional information about the underlying secret message upon intercepting the encrypted cryptogram. For a general review of recent progress in information theoretic security, see . Although the complexity based approach has been successful in satisfying the security concerns of many practical networking applications such as the Internet, wireless networks pose additional limitations and threats that cannot be solved solely through encryption. The broadcast nature of the wireless medium makes it particularly vulnerable to eavesdropping and authentication attacks, and the energy and bandwidth limitations of wireless devices restrict their computational power, hence rendering high complexity encryption techniques undesirable. Furthermore, especially in the sensor network scenario, where the sensor nodes are generally deployed in remote locations highly vulnerable to tampering, secure key management becomes impractical. Issues such as mobility and lack of infrastructure (e.g., in mobile ad hoc networks) also pose significant challenges to traditional approaches based on maintaining secret keys. In such applications information theoretic security can support and enhance the computational complexity based approach. In this chapter, we survey information theoretic security in distributed source compression, and in particular how compression and communication can be achieved in an information theoretically secure way. Consider, for example, a sensor network in which correlated sensor observations are to be reconstructed at an access point either in a lossless fashion or within a prescribed distortion requirement. While some sensors might have secure (possibly wired) connections to the access point, others might be transmitting over the wireless medium, which can be accessed by an adversary trying to obtain information about the underlying phenomenon. Furthermore, this adversary might have her own observation of the main source. Our goal is to explore the fundamental information theoretic limitations for secure distributed compression and communication in this kind of situation. In practical applications, encryption is considered to be a separate block in the protocol stack applied in concatenation with source compression and channel transmission. The information theoretic unconditional secrecy obtained through secure source and/or channel coding or joint source-channel coding hence can be used in parallel with the existing computational encryption schemes enhancing the overall level of security. In order to fully exploit this concept of information theoretic security practical secure source and channel codes need to be developed. While there are many recent developments in this direction for channel coding [7-9] little is known for secure compression. However, design of such secure source codes is beyond the scope of this chapter, and constitutes a potential research direction. The chapter is organized as follows. After reviewing Shannon's model and the preliminaries of information theoretic secrecy in Sect. 8.2, in Sect. 8.3 we analyze distributed lossless compression under security constraints and present related fundamental results. In Sect. 8.4, we focus on lossy reconstruction at the legitimate receiver, and analyze the achievable distortion for given secrecy and communication rate constraints. Section 8.5 focuses on secure joint source-channel coding followed by the Conclusions and the Appendix.
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