Data Secrecy in Distributed Storage Systems under Exact Repair

TL;DR

This paper investigates the maximum securely storable data in distributed storage systems with exact repair, providing new bounds and revealing exponential decrease in secure data capacity as compromised nodes increase.

Contribution

It introduces new bounds on secure file size for systems with various repair degrees, extending previous results limited to at most two compromised nodes.

Findings

Maximum secure file size decreases exponentially with compromised nodes.

New bounds for systems with less than full repair degree.

Results based on novel subspace intersection analysis.

Abstract

The problem of securing data against eavesdropping in distributed storage systems is studied. The focus is on systems that use linear codes and implement exact repair to recover from node failures.The maximum file size that can be stored securely is determined for systems in which all the available nodes help in repair (i.e., repair degree $d=n-1$, where $n$ is the total number of nodes) and for any number of compromised nodes. Similar results in the literature are restricted to the case of at most two compromised nodes. Moreover, new explicit upper bounds are given on the maximum secure file size for systems with $d<n-1$. The key ingredients for the contribution of this paper are new results on subspace intersection for the data downloaded during repair. The new bounds imply the interesting fact that the maximum data that can be stored securely decreases exponentially with the number of compromised nodes.