A Bit of Secrecy for Gaussian Source Compression
This addresses secure communication for networks with eavesdroppers, but it appears incremental as it builds on existing game-theoretic and information-theoretic frameworks.
The paper tackles the problem of compressing a Gaussian source in an unsecure network with a limited secret key, showing that one bit of secret key per source symbol achieves perfect secrecy performance in the Gaussian squared error setting.
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.