Lossless Compression with Security Constraints

📝 Abstract

Secure distributed data compression in the presence of an eavesdropper is explored. Two correlated sources that need to be reliably transmitted to a legitimate receiver are available at separate encoders. Noise-free, limited rate links from the encoders to the legitimate receiver, one of which can also be perfectly observed by the eavesdropper, are considered. The eavesdropper also has its own correlated observation. Inner and outer bounds on the achievable compression-equivocation rate region are given. Several different scenarios involving the side information at the transmitters as well as multiple receivers/eavesdroppers are also considered.

💡 Analysis

Secure distributed data compression in the presence of an eavesdropper is explored. Two correlated sources that need to be reliably transmitted to a legitimate receiver are available at separate encoders. Noise-free, limited rate links from the encoders to the legitimate receiver, one of which can also be perfectly observed by the eavesdropper, are considered. The eavesdropper also has its own correlated observation. Inner and outer bounds on the achievable compression-equivocation rate region are given. Several different scenarios involving the side information at the transmitters as well as multiple receivers/eavesdroppers are also considered.

📄 Content

arXiv:0805.2995v1 [cs.IT] 20 May 2008 Lossless Compression with Security Constraints Deniz G¨und¨uz∗†, Elza Erkip‡∗, H. Vincent Poor∗ ∗Dept. of Electrical Engineering, Princeton University, Princeton, NJ, 08544 †Dept. of Electrical Engineering, Stanford University,Stanford, CA, 94305 ‡Dept. of Electrical and Computer Engineering, Polytechnic University, Brooklyn, NY, 11201 Email: {dgunduz, poor}@princeton.edu, elza@poly.edu Abstract— Secure distributed data compression in the presence of an eavesdropper is explored. Two correlated sources that need to be reliably transmitted to a legitimate receiver are available at separate encoders. Noise-free, limited rate links from the encoders to the legitimate receiver, one of which can also be perfectly observed by the eavesdropper, are considered. The eavesdropper also has its own correlated observation. Inner and outer bounds on the achievable compression-equivocation rate region are given. Several different scenarios involving the side information at the transmitters as well as multiple receivers/eavesdroppers are also considered. I. INTRODUCTION With the emergence of wireless sensor networks and dis- tributed video applications, distributed source compression has become an important research area. A significant amount of effort has been devoted to understanding the information theoretic limits of distributed lossless and lossy compression and developing codes to achieve these limits. However, in many real-life applications involving distributed compression, such as distributed video surveillance or monitoring of some private information, secure compression and communication while meeting the end-to-end quality of service requirements becomes important. In this paper we consider the information theoretic limits of secure lossless source compression in the presence of an adversary who has access to some of the links in the network as well as its own correlated observation of the data to be compressed. We consider information theoretic secrecy, that is, we want to limit the information leakage to a computationally unbounded eavesdropper who has the full knowledge of the compression algorithms used. We first consider a simplified model of the general secure distributed compression problem, composed of two transmit- ters Alice and Charlie with correlated observations, a receiver Bob, and an eavesdropper Eve who is interested in the data of Alice. Eve eavesdrops Alice’s channel to Bob, i.e., it knows Alice’s message to Bob exactly. Eve also has her own correlated side information. We consider the scenario in which both Alice’s and Charlie’s data need to be reconstructed at Bob reliably while Eve is interested in only Alice’s infor- mation source. Later, we consider various cases involving the availability of the side information at different terminals. This research was supported in part by the US National Science Foundation under Grants ANI-03-38807, CCF-04-30885, CCF-06-35177, CCF-07-28208, and CNS-06-25637. CN AN RC RA EN ∆ ( ˆAN, ˆCN) Alice Bob Eve Charlie Fig. 1. Two terminal secure distributed compression. The eavesdropper (Eve) can only access one of the links. Finally, we analyze cases with multiple receivers or multiple eavesdroppers. In Wyner’s classical wiretap channel model [1], nonzero secrecy rate can be achieved without using a secure key, if the intended receiver has a better quality communication channel than the eavesdropper. It was observed in [3] and [4] that, secrecy can also be generated through correlated observations at the legitimate users. In our model, since the channels are not noisy, the techniques of [1] do not apply; however, based on the ideas of [3], [4], it is still possible to achieve secrecy by exploiting the correlated information transmitted over secure links. Unlike [3], [4] which focus on generating secret key using correlated information sources, we impose the requirement of lossless decoding of the source sequence at the legitimate receiver while keeping Alice’s information secret from Eve. In [8], Yamamoto considers lossy compression with security constraints over a noisy broadcast channel, while the users share a secure key as well. He showed that first applying lossy source compression, then encrypting the compressed bits using the secure key and finally transmitting over the channel using a good wiretap channel code is optimal. In [5], Merhav extends this result to the case in which the legitimate receiver and the eavesdropper have correlated side information under the assumption that both the channel output and the side information at the eavesdropper are physically degraded. He shows that replacing lossy compression with Wyner-Ziv compression in the coding scheme of [8] is optimal. In [6], the minimum leakage rate in secure lossless compression with arbitrary side information is explored. It is shown in [6] that, in the case of arbitrarily correlated receiver side information, the usual Slepian-Wolf compression is not alway

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