Robust and Secure Cache-aided Private Linear Function Retrieval from Coded Servers

TL;DR

This paper develops a robust, secure, and private cache-aided linear function retrieval scheme from coded servers, extending existing coded caching frameworks to include privacy, security, and robustness constraints with near-optimal performance.

Contribution

It introduces a novel scheme that modifies Placement Delivery Arrays to achieve privacy, security, and robustness in coded caching systems, with near-optimal load-memory tradeoffs.

Findings

Achieves robustness against server subset failures.

Ensures security from wiretappers and user privacy.

Near-optimal load-memory tradeoff, except in small memory regimes.

Abstract

This work investigates a system where each user aims to retrieve a scalar linear function of the files of a library, which are Maximum Distance Separable coded and stored at multiple distributed servers. The system needs to guarantee robust decoding in the sense that each user must decode its demanded function with signals received from any subset of servers whose cardinality exceeds a threshold. In addition, (a) the content of the library must be kept secure from a wiretapper who obtains all the signals from the servers;(b) any subset of users together can not obtain any information about the demands of the remaining users; and (c) the users' demands must be kept private against all the servers even if they collude. Achievable schemes are derived by modifying existing Placement Delivery Array (PDA) constructions, originally proposed for single-server single-file retrieval coded caching systems without any privacy or security or robustness constraints. It is shown that the PDAs describing the original Maddah-Ali and Niesen's coded caching scheme result in a load-memory tradeoff that is optimal to within a constant multiplicative gap, except for the small memory regime when the number of file is smaller than the number of users. As by-products, improved order optimality results are derived for three less restrictive systems in all parameter regimes.