Distributed storage codes have recently received a lot of attention in the community. Independently, another body of work has proposed integrity checking schemes for cloud storage, none of which, however, is customized for coding-based storage or can efficiently support repair. In this work, we bridge the gap between these two currently disconnected bodies of work. We propose NC-Audit, a novel cryptography-based remote data integrity checking scheme, designed specifically for network coding-based distributed storage systems. NC-Audit combines, for the first time, the following desired properties: (i) efficient checking of data integrity, (ii) efficient support for repairing failed nodes, and (iii) protection against information leakage when checking is performed by a third party. The key ingredient of the design of NC-Audit is a novel combination of SpaceMac, a homomorphic message authentication code (MAC) scheme for network coding, and NCrypt, a novel chosen-plaintext attack (CPA) secure encryption scheme that is compatible with SpaceMac. Our evaluation of a Java implementation of NC-Audit shows that an audit costs the storage node and the auditor a modest amount computation time and lower bandwidth than prior work.