Information-Theoretic Security Problem in Cluster Distributed Storage Systems: Regenerating Code Against Two General Types of Eavesdroppers

In recent years, there has been growing interest in heterogeneous distributed storage systems (DSSs), such as clustered DSSs, which are widely used in practice. However, research regarding information-theoretic security in heterogeneous DSSs remains limited. Furthermore, unlike traditional DSSs, the heterogeneous DSSs face eavesdropper with diverse operating patterns, complicating the secrecy models. In this paper, we aim to investigate the secrecy capacity and code constructions for clustered DSSs (CDSSs), a type of heterogeneous DSSs in which the system is divided into clusters with an equal number of nodes and different repair bandwidths for intra-cluster and cross-cluster against two types of eavesdroppers: the occupying-type eavesdropper and the osmotic-type eavesdropper. We construct two CDSS secrecy models tailored to these aforementioned eavesdroppers, derive the upper bounds on adjustable secrecy capacities, and explore the relationships between the upper bounds of perfect secrecy capacities and the number of compromised nodes. Notably, the upper bounds obtained in this paper generalize those of the traditional DSS model. Additionally, we propose three repair-by-transfer code constructions that achieve the secrecy capacity under both eavesdropper scenarios. These codes are based on nested MDS code and represent a generalized form of the minimum bandwidth regenerating (MBR) codes in traditional DSSs.