Toward Optimal Secure Distributed Storage Systems With Exact Repair.

Distributed storage systems (DSSs) in the presence of an external wiretapper are considered. A DSS is parameterized by $(n, k, d)$ , in which the data are stored across $n$ nodes (each with storage capacity $\alpha $ ), and must be recoverable by accessing the contents stored on any $k$ out of $n$ nodes. If a node fails, any $d \geq k$ out of $(n-1)$ nodes help in the repair (regeneration) of the failed node (by sending $d\beta $ units of repair data, where $\beta \leq \alpha $ ), so that the data can still be recovered from the DSS. For such a $(n, k, d)$ -DSS, security from the two types of wiretappers is investigated: 1) Type-I (node data) wiretapper, which can read the data stored on any $\ell <k$ nodes and 2) Type-II (repair data) wiretapper, which can read the data that is used to repair a set of $\ell $ failed nodes. The focus of this paper is on the optimal tradeoff between the storage $(\alpha )$ and the repair bandwidth $(d\beta )$ in presence of a Type-I/Type-II wiretapper and the practically relevant constraint of exact repair in which a failed node must be replaced by its exact replica. In this paper, several new results and outer bounds for the storage-versus-exact-repair-bandwidth tradeoff(s) are obtained for the Type-I and Type-II security problems. Furthermore, new outer bounds are presented for the Type-II problem, which hold for general $(n, k, d,\ell )$ parameters. It is shown that these outer bounds strictly improve upon the existing cutset-based outer bounds. The key technical contribution of this paper is in developing novel information theoretic converse proofs for these problems. From our optimal characterization results, we show that in a Type-II setting, the only efficient point in the storage-versus-exact-repair-bandwidth tradeoff is the minimum bandwidth regenerating (MBR) point corresponding to $\alpha =d\beta $ . This is in sharp contrast to the Type-I setting in which the optimal tradeoff allows a spectrum of operating points beyond the MBR point. [ABSTRACT FROM PUBLISHER]