1Weakly Secure Regenerating Codes for Distributed Storage

We consider the problem of secure distributed data storage under the paradigm of weak security, in which no meaningful information is leaked to the eavesdropper. More specifically, the eavesdropper cannot get any information about any individual data packet or a small group of packets. The key benefit of the weak security paradigm is that it incurs no loss in the storage capacity, which makes it practically appealing. In this work, we present a coding scheme, using a coset coding based outer code and a Product-Matrix Minimum Bandwidth Regenerating code (proposed by Rashmi et al.), that achieves weak security when the eavesdropper can observe any single storage node. We show that the proposed construction has good security properties and requires small finite field size. I