Generalised regenerating codes for securing distributed storage systems against eavesdropping

Regenerating codes (RCs) are efficient at both storage cost and repair bandwidth, and thus are regarded as preferable candidates for distributed storage systems (DSSs). For DSSs with RCs, a file stored across n distributed nodes can be reconstructed from k (< n) nodes. The collection of the k nodes is called the reconstruction set. A failed node can be regenerated (i.e., repaired) from d (< n) remaining nodes. The collection of the d nodes is called the regeneration set. In traditional RCs, the numbers of reconstruction sets and regeneration sets are fixed to some specific values. In this paper, we introduce the concept of generalised RCs, in which the value ranges of the numbers of both reconstruction sets and regeneration sets are extended. Compared to traditional RCs, the generalised RCs possess more coding schemes and better system security level in terms of the probability of revealing original data file. An explicit construction of generalised RCs is provided, in which the numbers of both reconstruction sets and regeneration sets can be designed flexibly. Furthermore, based on the generalised RCs, an intruder model where an eavesdropper can access to some nodes is considered and a general upper bound on secrecy capacity is derived. The relationship between the obtained upper bound and existing ones achieved by traditional RCs is discussed in detail. The provided explicit construction is the first optimal construction of generalised RCs, which achieves the upper bound on secrecy capacity and has the flexibility in designing the numbers of reconstruction sets and regeneration sets.