Self-stabilizing Byzantine Digital Clock Synchronization

We present a scheme that achieves self-stabilizing Byzantine digital clock synchronization assuming a “synchronous” system. This synchronous system is established by the assumption of a common external “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 that also converges in linear time (relying on an underlying distributed pulse mechanism), but it requires to execute and terminate Byzantine agreement in between consecutive pulses. That algorithm, although it does not assume a synchronous system, cannot be easily transformed to benefit from the stronger synchronous system model in which the pulses (beats) are in the order of the message delay time apart. The only other previous self-stabilizing Byzantine digital clock synchronization algorithm operating in a similar synchronous model converges in expected exponential time. Our algorithm converges (deterministically) in linear time and utilizes the synchronous model to achieve optimal precision and a simpler algorithm. Furthermore, it does not require the use of local physical timers in order to synchronize the clock counters.