Weakly secure regenerating codes for distributed storage

We consider the problem of securing distributed storage systems (DSS) against an eavesdropper Eve that can observe any subset of nodes of bounded size. The goal is to construct a weakly secure DSS that leaks no meaningful information to Eve. More specifically, Eve should not be able to get any information about any individual data file or a small group of files. The key benefit of the weak security paradigm is that it incurs no loss in the storage capacity, which makes it practically appealing. In this paper, we present an explicit construction of a coset coding based outer code to weakly secure a Product-Matrix framework based Minimum Bandwidth Regenerating code (proposed by Rashmi et al.). The proposed scheme is weakly secure against an eavesdropper that can observe any single storage node, even when it has side-information about any g files. We show that the proposed construction has good security properties in terms of the amount of side-information g that Eve can possess, and it requires a small finite field size.