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.

The secure exact-repair regenerating codes are studied, for distributed storage systems with parameters (n,k=d,d,ℓ). The secrecy constraint guarantees that 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) ℓ compromised nodes (type II secrecy). A class of secure determinant codes are introduced for all system parameters, and an achievable secrecy trade-off between the per-node storage capacity and repair bandwidth is characterized.

1We present a construction for exact-repair regenerating codes with an information-theoretic secrecy guarantee against an eavesdropper with access to the content of (up to) ℓ nodes. The proposed construction works for the entire range of per-node storage and repair bandwidth for any distributed storage system with parameters (n, k = d, d, ℓ), aiming to maximize the size of the file that can be securely stored in the system. We provide an upper bound for the optimum trade-off for secure exact-repair regenerating codes.