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Petascale, high-performance file systems often hold sensitive data and thus require security, but authentication and authorization can dramatically reduce performance. Existing security solutions perform poorly in these environments because they cannot scale with the number of nodes, highly distributed data, and demanding workloads. To address these issues, we developed Maat, a security protocol designed to provide strong, scalable security to these systems. Maat introduces three new techniques. Extended capabilities limit the number of capabilities needed by allowing a capability to authorize I/O for any number of client-file pairs. Automatic Revocation uses short capability lifetimes to allow capability expiration to act as global revocation, while supporting non-revoked capability renewal. Secure Delegation allows clients to securely act on behalf of a group to open files and distribute access, facilitating secure joint computations. Experiments on the Maat prototype in the Ceph petascale file system show an overhead as little as 6--7%.