On a weakly secure regenerating code construction for minimum storage regime

Weakly secure storage codes aim to hide information about individual files as well as small groups of files from an eavesdropper that has access to a limited number of storage nodes. Such codes are a practical alternative to traditional information-theoretic schemes that hide information about the entire set of files from the eavesdropper. The weakly secure codes do not use random keys, and as a result, provide a higher storage capacity compared to the traditional approach. In this paper, we focus on the design of weakly secure regenerating codes. In particular, we present an explicit construction of a coset coding based outer code to augment a Product-Matrix (PM) regenerating code (proposed by Rashmi et al.) operating at the minimum storage regime. The proposed outer code weakly secures the PM regenerating code against an eavesdropper that can observe any single storage node. More specifically, the outer code hides information about the groups of files whose size is roughly two times more than what can be achieved using only the PM code. Moreover, the proposed scheme requires a small finite field size and can be easily implemented in practical settings.