Secretive Coded Caching with Shared Caches

TL;DR

This paper introduces a secretive coded caching scheme for shared cache systems that ensures perfect secrecy, requiring dedicated user caches and achieving results comparable to existing private caching schemes.

Contribution

It proposes a novel secretive coded caching scheme for shared caches with centralized placement, extending prior models to include secrecy constraints and dedicated user caches.

Findings

Achieves perfect secrecy in shared cache systems.

Matches performance of existing private caching schemes when applied to dedicated cache settings.

Provides a new framework for secretive coded caching with shared caches.

Abstract

We consider the problem of \emph{secretive coded caching} in a shared cache setup where the number of users accessing a particular \emph{helper cache} is more than one, and every user can access exactly one helper cache. In secretive coded caching, the constraint of \emph{perfect secrecy} must be satisfied. It requires that the users should not gain, either from their caches or from the transmissions, any information about the content of the files that they did not request from the server. In order to accommodate the secrecy constraint, our problem setup requires, in addition to a helper cache, a dedicated \emph{user cache} of minimum capacity of 1 unit to every user. This is where our formulation differs from the original work on shared caches (``Fundamental Limits of Coded Caching With Multiple Antennas, Shared Caches and Uncoded Prefetching'' by E.~Parrinello, A.~{\"{U}}nsal and P.~Elia in Trans. Inf. Theory, 2020). In this work, we propose a secretively achievable coded caching scheme with shared caches under centralized placement. When our scheme is applied to the dedicated cache setting, it matches the scheme by Ravindrakumar \emph{et al.} (``Private Coded Caching'', in Trans. Inf. Forensics and Security, 2018).