Secure Source Coding Resilient Against Compromised Users via an Access Structure

TL;DR

This paper characterizes the fundamental trade-off between source coding rate and information leakage in a secure source coding system with an access structure, focusing on Gaussian sources and threshold access schemes.

Contribution

It provides a closed-form solution for the rate-leakage trade-off in secure source coding with access restrictions, including threshold structures.

Findings

Closed-form characterization of rate-leakage trade-off

Analysis of threshold access structures

Minimized leakage for non-authorized user sets

Abstract

Consider a source and multiple users who observe the independent and identically distributed (i.i.d.) copies of correlated Gaussian random variables. The source wishes to compress its observations and store the result in a public database such that (i) authorized sets of users are able to reconstruct the source with a certain distortion level, and (ii) information leakage to non-authorized sets of colluding users is minimized. In other words, the recovery of the source is restricted to a predefined access structure. The main result of this paper is a closed-form characterization of the fundamental trade-off between the source coding rate and the information leakage rate. As an example, threshold access structures are studied, i.e., the case where any set of at least $t$ users is able to reconstruct the source with some predefined distortion level and the information leakage at any set of users with a size smaller than $t$ is minimized.