I. Introduction
We consider the problem of securing data in distributed storage systems (DSS) under failure and repair (rebuilding) dynamics against a malicious adversary that can control a certain number of nodes in the system. DSS experience frequent node failures due to the use of inexpensive commodity hardware [1], [2]. Data redundancy is used to prevent from data loss. Typically, replication codes are used and multiple copies of the data, typically 3, are stored in the DSS. Recently, major cloud storage companies [3], [4] have started using erasure codes, such as regenerating codes [5] and locally repairable codes [3], to achieve data reliability with a lower storage cost and better tradeoffs with other system resources, such as repair bandwidth and data locality.