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Advances in networking technologies have triggered the “storage as a service” (SAS) model. The SAS model allows content providers to leverage hardware and software solutions provided by the storage service providers (SSPs), without having to develop them on their own, thereby freeing them to concentrate on their core business. The SAS model is faced with at least two important security issues: (i) How to maintain the confidentiality and integrity of files stored at the SSPs? (ii) How to efficiently support flexible access control policies on the file system? The former problem is handled using a cryptographic file system, while the later problem is largely unexplored. In this paper, we propose secure, efficient and scalable key management algorithms to support monotone access structures on large file systems. We use key derivation algorithms to ensure that a user who is authorized to access a file, can efficiently derive the file's encryption key. However, it is computationally infeasible for a user to guess the encryption keys for those files that she is not authorized to access. We present concrete algorithms to efficiently and scaleably support a discretionary access control model (DAC) and handle dynamic access control updates & revocations. We also present a prototype implementation of our proposal on a distributed file system. A trace driven evaluation of our prototype shows that our algorithms meet the security requirements while incurring a low performance overhead on the file system.