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This paper describes an asynchronous state-machine replication system that tolerates Byzantine faults, which can be caused by malicious attacks or software errors. Our system is the first to recover Byzantine-faulty replicas proactively and it performs well because it uses symmetric rather than public-key cryptography for authentication. The recovery mechanism allows us to tolerate any number of faults over the lifetime of the system provided fewer than 1/3 of the replicas become faulty within a window of vulnerability that is small under normal conditions. The window may increase under a denial-of-service attack but we can detect and respond to such attacks. The paper presents results of experiments showing that overall performance is good and that even a small window of vulnerability has little impact on service latency.