Secure Determinant Codes for Distributed Storage Systems

The information-theoretic secure exact-repair regenerating codes for distributed storage systems (DSSs) with parameters (n,k=d,d,\ell) are studied in this paper. We consider distributed storage systems with n nodes, in which the original data can be recovered from any subset of k=d nodes, and the content of any node can be retrieved from those of any d helper nodes. Moreover, we consider two secrecy constraints, namely, Type-I, where the message remains secure against an eavesdropper with access to the content of any subset of up to \ell nodes, and Type-II, in which the message remains secure against an eavesdropper who can observe the incoming repair data from all possible nodes to a fixed but unknown subset of up to \ell compromised nodes. Two classes of secure determinant codes are proposed for Type-I and Type-II secrecy constraints. Each proposed code can be designed for a range of per-node storage capacity and repair bandwidth for any system parameters. They lead to two achievable secrecy trade-offs, for Type-I and Type-II security.