On the secure conditions for distributed storage systems

The problem of secure distributed storage systems (DSS) with regenerating codes is concerned in this paper. We consider an eavesdropper model where an eavesdropper wiretaps a subset of storage nodes, and either their repairing data or stored data can be wiretapped. We focus on two typical and special cases, the Minimum Bandwidth Repair (MBR) and the Minimum Storage Repair (MSR). Our main contribution is to draw a connection between this problem and secure network coding theory introduced by Cai and Yeung, and the secrecy capacity can be determined in this method. We prove that for both MBR and MSR cases, if the maximal wiretapped information rate can be determined, the secrecy capacity can be achieved by linear secure network coding. Particularly, a static exact regenerating code can be transformed into a secure regenerating code for the MBR and MSR cases.