Information Leakage in Index Coding With Sensitive and Non-Sensitive Messages

TL;DR

This paper investigates information leakage in index coding with sensitive and non-sensitive messages, proposing a linear coding scheme that minimizes leakage and establishing bounds that hold for all coding schemes.

Contribution

It introduces a deterministic linear coding scheme based on rank minimization to reduce leakage and provides tight bounds and a graph-theoretic converse applicable to all codes.

Findings

Proposed a rank minimization-based linear coding scheme.

Derived a tight upper bound on leakage rate.

Established a general converse bound for all coding schemes.

Abstract

Information leakage to a guessing adversary in index coding is studied, where some messages in the system are sensitive and others are not. The non-sensitive messages can be used by the server like secret keys to mitigate leakage of the sensitive messages to the adversary. We construct a deterministic linear coding scheme, developed from the rank minimization method based on fitting matrices (Bar-Yossef et al. 2011). The linear scheme leads to a novel upper bound on the optimal information leakage rate, which is proved to be tight over all deterministic scalar linear codes. We also derive a converse result from a graph-theoretic perspective, which holds in general over all deterministic and stochastic coding schemes.