We consider the problem of designing repair-efficient distributed storage systems that are secure against a passive eavesdropper that can observe the contents of any subset of nodes of limited size. First, we present a universal framework for the design of coset-coding based outer codes that enables information-theoretic security properties for a broad class of storage codes.  As case studies, we consider minimum storage regenerating codes with small repair degree, and maximally recoverable codes. The proposed framework allows us to construct secure coding schemes over small field size (in particular, linear in number of storage nodes). We also present an outer code over small field size to secure a locally repairable code against an eavesdropper that can observe any subset of nodes of maximum possible size.