Secure Lossless Compression with Side Information

Secure data compression in the presence of side information at both a legitimate receiver and an eavesdropper is explored. A noise-free, limited rate link between the source and the receiver, whose output can be perfectly observed by the eavesdropper, is assumed. As opposed to the wiretap channel model, in which secure communication can be established by exploiting the noise in the channel, here the existence of side information at the receiver is used. Both coded and uncoded side information are considered. In the coded side information scenario, inner and outer bounds on the compression-equivocation rate region are given. In the uncoded side information scenario, the availability of the legitimate receiver's and the eavesdropper's side information at the encoder is considered, and the compression-equivocation rate region is characterized for these cases. It is shown that the side information at the encoder can increase the equivocation rate at the eavesdropper. Hence, the side information at the encoder is shown to be useful in terms of security; this is in contrast with the pure lossless data compression case where side information at the encoder would not help.Comment: To appear in the Proceedings of the 2008 IEEE Information Theory Workshop, Porto, Portugal, May 5-9, 200

Gaussian Secure Source Coding and Wyner's Common Information

We study secure source-coding with causal disclosure, under the Gaussian distribution. The optimality of Gaussian auxiliary random variables is shown in various scenarios. We explicitly characterize the tradeoff between the rates of communication and secret key. This tradeoff is the result of a mutual information optimization under Markov constraints. As a corollary, we deduce a general formula for Wyner's Common Information in the Gaussian setting.Comment: ISIT 2015, 5 pages, uses IEEEtran.cl

A Rate-Distortion Based Secrecy System with Side Information at the Decoders

A secrecy system with side information at the decoders is studied in the context of lossy source compression over a noiseless broadcast channel. The decoders have access to different side information sequences that are correlated with the source. The fidelity of the communication to the legitimate receiver is measured by a distortion metric, as is traditionally done in the Wyner-Ziv problem. The secrecy performance of the system is also evaluated under a distortion metric. An achievable rate-distortion region is derived for the general case of arbitrarily correlated side information. Exact bounds are obtained for several special cases in which the side information satisfies certain constraints. An example is considered in which the side information sequences come from a binary erasure channel and a binary symmetric channel.Comment: 8 pages. Allerton 201

Secure Lossy Source Coding with Side Information at the Decoders

This paper investigates the problem of secure lossy source coding in the presence of an eavesdropper with arbitrary correlated side informations at the legitimate decoder (referred to as Bob) and the eavesdropper (referred to as Eve). This scenario consists of an encoder that wishes to compress a source to satisfy the desired requirements on: (i) the distortion level at Bob and (ii) the equivocation rate at Eve. It is assumed that the decoders have access to correlated sources as side information. For instance, this problem can be seen as a generalization of the well-known Wyner-Ziv problem taking into account the security requirements. A complete characterization of the rate-distortion-equivocation region for the case of arbitrary correlated side informations at the decoders is derived. Several special cases of interest and an application example to secure lossy source coding of binary sources in the presence of binary and ternary side informations are also considered. It is shown that the statistical differences between the side information at the decoders and the presence of non-zero distortion at the legitimate decoder can be useful in terms of secrecy. Applications of these results arise in a variety of distributed sensor network scenarios.Comment: 7 pages, 5 figures, 1 table, to be presented at Allerton 201

Secret Communication with Feedback

Secure communication with feedback is studied. An achievability scheme in which the backward channel is used to generate a shared secret key is proposed. The scenario of binary symmetric forward and backward channels is considered, and a combination of the proposed scheme and Maurer's coding scheme is shown to achieve improved secrecy rates. The scenario of a Gaussian channel with perfect output feedback is also analyzed and the Schalkwijk-Kailath coding scheme is shown to achieve the secrecy capacity for this channel.Comment: Presented at the IEEE Int'l Symposium on Information Theory and its Applications (ISITA), Auckland, New Zealand, December 200

The CEO Problem with Secrecy Constraints

We study a lossy source coding problem with secrecy constraints in which a remote information source should be transmitted to a single destination via multiple agents in the presence of a passive eavesdropper. The agents observe noisy versions of the source and independently encode and transmit their observations to the destination via noiseless rate-limited links. The destination should estimate the remote source based on the information received from the agents within a certain mean distortion threshold. The eavesdropper, with access to side information correlated to the source, is able to listen in on one of the links from the agents to the destination in order to obtain as much information as possible about the source. This problem can be viewed as the so-called CEO problem with additional secrecy constraints. We establish inner and outer bounds on the rate-distortion-equivocation region of this problem. We also obtain the region in special cases where the bounds are tight. Furthermore, we study the quadratic Gaussian case and provide the optimal rate-distortion-equivocation region when the eavesdropper has no side information and an achievable region for a more general setup with side information at the eavesdropper.Comment: Accepted for publication in IEEE Transactions on Information Forensics and Security, 17 pages, 4 figure

Secure Multiterminal Source Coding with Side Information at the Eavesdropper

The problem of secure multiterminal source coding with side information at the eavesdropper is investigated. This scenario consists of a main encoder (referred to as Alice) that wishes to compress a single source but simultaneously satisfying the desired requirements on the distortion level at a legitimate receiver (referred to as Bob) and the equivocation rate --average uncertainty-- at an eavesdropper (referred to as Eve). It is further assumed the presence of a (public) rate-limited link between Alice and Bob. In this setting, Eve perfectly observes the information bits sent by Alice to Bob and has also access to a correlated source which can be used as side information. A second encoder (referred to as Charlie) helps Bob in estimating Alice's source by sending a compressed version of its own correlated observation via a (private) rate-limited link, which is only observed by Bob. For instance, the problem at hands can be seen as the unification between the Berger-Tung and the secure source coding setups. Inner and outer bounds on the so called rates-distortion-equivocation region are derived. The inner region turns to be tight for two cases: (i) uncoded side information at Bob and (ii) lossless reconstruction of both sources at Bob --secure distributed lossless compression. Application examples to secure lossy source coding of Gaussian and binary sources in the presence of Gaussian and binary/ternary (resp.) side informations are also considered. Optimal coding schemes are characterized for some cases of interest where the statistical differences between the side information at the decoders and the presence of a non-zero distortion at Bob can be fully exploited to guarantee secrecy.Comment: 26 pages, 16 figures, 2 table