Secretive Coded Caching With Shared Caches

Abstract

We consider the problem of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">secretive coded caching</i> in a shared cache setup where the number of users accessing a particular <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">helper cache</i> is more than one, and every user can access exactly one helper cache. In secretive coded caching, the constraint of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">perfect secrecy</i> 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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">user cache</i> 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. Ünsal 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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> (“Private Coded Caching”, in Trans. Inf. Forensics and Security, 2018).