On Secure Exact-Repair Regenerating Codes With a Single Pareto Optimal Point

The problem of exact-repair regenerating codes against eavesdropping attack is studied. The eavesdropping model we consider is that the eavesdropper has the capability to observe the data involved in the repair of a subset of l nodes. An (n, k, d, l) secure exact-repair regenerating code is an (n, k, d) exact-repair regenerating code that is secure under this eavesdropping model. It has been shown that for some parameters (n, k, d, l), the associated optimal storage-bandwidth tradeoff curve, which has one corner point, can be determined. The focus of this paper is on characterizing such parameters. We establish a lower bound l on the number of wiretap nodes, and show that this bound is tight for the case k = d = n - 1.