Security for Minimum Storage Regenerating Codes and Locally Repairable Codes

We consider the problem of designing repair efficient distributed storage systems, which are information-theoretically secure against a passive eavesdropper that can gain access to a limited number of storage nodes. We present a framework that enables design of a broad range of secure storage codes through a joint construction of inner and outer codes. As case studies, we focus on two specific families of storage codes: (i) minimum storage regenerating (MSR) codes, and (ii) maximally recoverable (MR) codes, which are a class of locally repairable codes (LRCs). The main idea of this framework is to utilize the existing constructions of storage codes to jointly design an outer coset code and inner storage code. Finally, we present a construction of an outer coset code over small field size to secure locally repairable codes presented by Tamo and Barg for the special case of an eavesdropper that can observe any subset of nodes of maximum possible size.