Clock Synchronization in the Byzantine-Recovery Failure Model

Abstract

Abstract. We consider the problem of synchronizing clocks in synchronous systems prone to transient and dynamic process failures, i.e., we consider systems where all processes may alternate correct and Byzantine behaviors. We propose a clock synchronization algorithm based on periodical resynchronizations which is based on the assumption that no more than f < n/3 processes (with n the number of processors in the system) are simultaneously faulty. Both, accuracy (clocks being within a linear envelope of real-time) and precision (maximum deviation between clocks) perpetually hold for processes which sufficiently long follow their algorithm. We provide expressions for both the recovery time and the failure turn-over rates. Both expressions are independent of f , and are less than the time needed to execute 3 resynchronizations.

Consensus when all processes may be Byzantine for some time

“…Recovery from arbitrary faults was previously considered in the context of clock synchronization [20][21][22]. A stronger model, where the system is synchronous and Byzantine processes eventually crash (but do not recover) is considered in [3] to solve consensus.…”

Consensus in the presence of mortal Byzantine faulty processes

“…Assume by contradiction that there is a phase after φ where a correct process locks 1 − w and let φ > φ be the smallest of these phases. By line 32 we must have |M p (v, φ )| ≥ n − t which is required to lock a value at any correct process p. By our choice of φ , at the beginning of phase φ the t + 1 processes still have a lock on w such that v ∈ acceptable or have already halted. Thus their messages do not show up in M p (v, φ ), i.e., a distinct set of processes of cardinality n −t must have sent messages for v. Summing up the sizes of these sets we get (n − t) + (t + 1).…”

“…Proof By lines [31][32][33][34][35][36][37] it follows obviously that a value must be in the set acceptable p of a correct process p in order to be decided upon. Initially, only the initial value of p is in acceptable p and only values broadcast by at least t + 1 processes, i.e., by at least one correct process, are added.…”

“…Another approach was to augment the asynchronous system with failure detectors [10,26,27]. Other approaches aim at optimizing normal case behavior [28][29][30] or consider more elaborate fault models in an effort to improve fault resilience as, for instance, Byzantine faults with recovery [31,32] or hybrid failure models [33][34][35].…”