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 α), and must be recoverable by accessing the contents stored on any k out of n nodes. If a node fails, any d ≥ k out of (n-1) nodes help in the repair (regeneration) of the failed node (by sending dβ units of repair data, where β≤ α), 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 ℓ <k nodes and 2) Type-II (repair data) wiretapper, which can read the data that is used to repair a set of ℓ failed nodes. The focus of this paper is on the optimal tradeoff between the storage (α) and the repair bandwidth (dβ) 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,ℓ) 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 α =dβ . 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.