Secure Lossy Source Coding with Side Information at the Decoders

TL;DR

This paper characterizes the optimal trade-offs between compression rate, distortion, and secrecy in secure lossy source coding with correlated side information at both the legitimate receiver and eavesdropper, extending Wyner-Ziv to security scenarios.

Contribution

It provides a complete characterization of the rate-distortion-equivocation region for secure lossy source coding with arbitrary correlated side information at the decoders.

Findings

The statistical differences in side information can enhance secrecy.

Non-zero distortion at the legitimate decoder can improve security.

Results apply to distributed sensor network scenarios.

Abstract

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.