On Converse Results for Secure Index Coding

TL;DR

This paper investigates the secure index coding problem with security constraints, providing new bounds on the symmetric secure capacity, including an extension of existing bounds and a novel lower bound, advancing understanding of secure communication limits.

Contribution

It introduces a new lower bound on the symmetric secure capacity for index coding, complementing existing upper bounds and enhancing theoretical understanding.

Findings

Extended acyclic chain bound considering security constraints

Novel information-theoretic lower bound on capacity

Improved bounds on secure index coding capacity

Abstract

In this work, we study the secure index coding problem where there are security constraints on both legitimate receivers and eavesdroppers. We develop two performance bounds (i.e., converse results) on the symmetric secure capacity. The first one is an extended version of the basic acyclic chain bound (Liu and Sadeghi, 2019) that takes security constraints into account. The second converse result is a novel information-theoretic lower bound on the symmetric secure capacity, which is interesting as all the existing converse results in the literature for secure index coding give upper bounds on the capacity.