Self-stabilizing Byzantine digital clock synchronization

We present a scheme that achieves self-stabilizing Byzantine digital clock synchronization assuming a "synchronous" system. This synchronicity is established by the assumption of a common "beat" delivered with a regularity in the order of the network message delay, thus enabling the nodes to execute in lock-step. The system can be subjected to severe transient failures with a permanent presence of Byzantine nodes. Our algorithm guarantees eventually synchronized digital clock counters, i.e. common increasing integer counters associated with each beat. We then show how to achieve regular clock synchronization, progressing at real-time rate and with high granularity, from the synchronized digital clock counters. There is one previous self-stabilizing Byzantine clock synchronization algorithm, which also converges in linear time (relying on an underlying pulse mechanism), but it requires to execute and terminate Byzantine agreement in between consecutive pulses. Such a scheme, although it does not assume a synchronous system, cannot be easily transformed to a synchronous system in which the pulses (beats) are in the order of the message delay time apart. The only other digital clock synchronization algorithm operating in a similar synchronous model converges in expected exponential time. Our algorithm converges (deterministically) in linear time.