Robust, Secure and Private Cache-aided Scalar Linear Function Retrieval from Distributed System with Blind and Adversarial Servers

TL;DR

This paper develops a secure, private, and robust cache-aided scalar linear function retrieval scheme for distributed systems, integrating secret sharing and PDA techniques to optimize storage and communication under adversarial and collusion constraints.

Contribution

It introduces a novel coding scheme combining Shamir's secret sharing and PDA for secure, private, and robust function retrieval in distributed systems.

Findings

Achieves near-optimal storage and communication efficiency.

Ensures security against wiretappers and privacy among users.

Handles adversarial and colluding server scenarios effectively.

Abstract

In this work, a distributed server system composed of multiple servers that holds some coded files and multiple users that are interested in retrieving the linear functions of the files is investigated, where the servers are robust, blind and adversarial in the sense that any $J$ servers can together recover all files, while any $I$ colluding servers cannot obtain any information about the files, and at most $A$ servers maliciously provides erroneous information. In addition, the file library must be secure from a wiretapper who obtains all the signals, and the demands of any subset of users must kept private from the other users and servers, even if they collude. A coding scheme is proposed by incorporating the ideas of Shamir's secret sharing and key superposition into the framework of Placement Delivery Array (PDA), originally proposed to characterize the single-server coded caching system without any security or privacy constraints. It is shown that PDAs associated to Maddah-Ali and Niesen's coded caching scheme results in an achievable memory-storage-communication region, such that the storage size and communication load were optimal to within a multiplicative gap, except for the small memory regime when the number of files was smaller than the number of users.