Secure Codes with Accessibility for Distributed Storage

A distributed storage system must support efficient access to stored data while ensuring recovery of temporally unavailable nodes. Another important aspect of a distributed storage system is security. In this paper, we bring these features together and investigate the problem of efficient access to stored data in presence of a passive eavesdropper with access to limited number of nodes. The access efficiency is measured in two different terms, namely, the number of accessed nodes and the volume of generated network traffic. These quantities possess a natural connection to locality and repair bandwidth in distributed storage system. For each of them we derive bounds on parameters and provide explicit constructions based on maximum distance separable codes. Motivated by practical perspectives we propose the techniques to ensure the same workload on each node as well as constructions over small fields based on subfield subcodes, Euclidean geometry codes and Reed-Muller codes. Finally, we derive an asymptotic random coding bound on parameters of a secure distributed storage system and propose further research directions.