On Secure Exact-repair Regenerating Codes with a Single Pareto Optimal Point

TL;DR

This paper investigates the security of exact-repair regenerating codes against eavesdroppers, establishing bounds on secure parameters and characterizing cases with a single Pareto optimal point in the tradeoff.

Contribution

It introduces a lower bound on the number of wiretap nodes and proves its tightness for specific parameters, advancing understanding of secure regenerating codes.

Findings

Established a lower bound $ ilde{ ext{ell}}$ on wiretap nodes.

Proved the bound is tight for $k=d=n-1$.

Characterized parameters with a single Pareto optimal point.

Abstract

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 $\ell$ nodes. An $(n,k,d,\ell)$ 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 $(n,k,d,\ell)$, 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 $\hat{\ell}$ on the number of wiretap nodes, and show that this bound is tight for the case $k = d = n-1$.