Secure Multiterminal Source Coding with Side Information at the Eavesdropper

TL;DR

This paper investigates secure multiterminal source coding with side information at the eavesdropper, deriving bounds and optimal schemes to ensure data secrecy while satisfying distortion constraints in complex network settings.

Contribution

It introduces new bounds on the rate-distortion-equivocation region for secure source coding with multiple encoders and side information, unifying existing models and providing optimal coding schemes.

Findings

Inner and outer bounds on the rates-distortion-equivocation region are derived.

The bounds are tight for certain cases like lossless reconstruction and uncoded side information.

Application to Gaussian and binary sources demonstrates the practical relevance.

Abstract

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.