A Bit of Secrecy for Gaussian Source Compression

TL;DR

This paper investigates Gaussian source compression in an unsecure network using game theory, showing that one secret bit per symbol suffices for perfect secrecy regardless of the eavesdropper's side information.

Contribution

It introduces a new analysis of Gaussian source compression with limited secret keys in a game-theoretic framework, revealing that minimal secret key rates can ensure perfect secrecy.

Findings

One secret bit per source symbol achieves perfect secrecy.

Joint Gaussian variables do not optimize the information-theoretic region.

Secrecy performance holds across varying eavesdropper capabilities.

Abstract

In this paper, the compression of an independent and identically distributed Gaussian source sequence is studied in an unsecure network. Within a game theoretic setting for a three-party noiseless communication network (sender Alice, legitimate receiver Bob, and eavesdropper Eve), the problem of how to efficiently compress a Gaussian source with limited secret key in order to guarantee that Bob can reconstruct with high fidelity while preventing Eve from estimating an accurate reconstruction is investigated. It is assumed that Alice and Bob share a secret key with limited rate. Three scenarios are studied, in which the eavesdropper ranges from weak to strong in terms of the causal side information she has. It is shown that one bit of secret key per source symbol is enough to achieve perfect secrecy performance in the Gaussian squared error setting, and the information theoretic region is not optimized by joint Gaussian random variables.