Self-stabilizing clock synchronization in the presence of Byzantine faults

We initiate a study of bounded clock synchronization under a more severe fault model than that proposed by Lamport and Melliar-Smith [1985]. Realistic aspects of the problem of synchronizing clocks in the presence of faults are considered. One aspect is that clock synchronization is an on-going task, thus the assumption that some of the processors never fail is too optimistic. To cope with this reality, we suggest self-stabilizing protocols that stabilize in any (long enough) period in which less than a third of the processors are faulty. Another aspect is that the clock value of each processor is bounded. A single transient fault may cause the clock to reach the upper bound. Therefore, we suggest a bounded clock that wraps around when appropriate.We present two randomized self-stabilizing protocols for synchronizing bounded clocks in the presence of Byzantine processor failures. The first protocol assumes that processors have a common pulse, while the second protocol does not. A new type of distributed counter based on the Chinese remainder theorem is used as part of the first protocol.