Synchronizing clocks in the presence of faults

Algorithms are described for maintaining clock synchrony in a distributed multiprocess system where each process has its own clock. These algorithms work in the presence of arbitrary clock or process failures, including “two-faced clocks” that present different values to different processes. Two of the algorithms require that fewer than one-third of the processes be faulty. A third algorithm works if fewer than half the processes are faulty, but requires digital signatures.