Self-Stabilising Byzantine Clock Synchronisation Is Almost as Easy as Consensus

Abstract

We give fault-tolerant algorithms for establishing synchrony in distributed systems in which each of the n nodes has its own clock. Our algorithms operate in a very strong fault model: we require self-stabilisation, i.e., the initial state of the system may be arbitrary, and there can be up to f < n/3 ongoing Byzantine faults, i.e., nodes that deviate from the protocol in an arbitrary manner. Furthermore, we assume that the local clocks of the nodes may progress at di erent speeds (clock dri ) and communication has bounded delay. In this model, we study the pulse synchronisation problem, where the task is to guarantee that eventually all correct nodes generate well-separated local pulse events (i.e., unlabelled logical clock ticks) in a synchronised manner.Compared to prior work, we achieve exponential improvements in stabilisation time and the number of communicated bits, and give the rst sublinear-time algorithm for the problem:• In the deterministic se ing, the state-of-the-art solutions stabilise in time Θ(f ) and have each node broadcast Θ(f log f ) bits per time unit. We exponentially reduce the number of bits broadcasted per time unit to Θ(log f ) while retaining the same stabilisation time.• In the randomised se ing, the state-of-the-art solutions stabilise in time Θ(f ) and have each node broadcast O(1) bits per time unit. We exponentially reduce the stabilisation time to polylog f while each node broadcasts polylog f bits per time unit. ese results are obtained by means of a recursive approach reducing the above task of self-stabilising pulse synchronisation in the bounded-delay model to non-self-stabilising binary consensus in the synchronous model. In general, our approach introduces at most logarithmic overheads in terms of stabilisation time and broadcasted bits over the underlying consensus routine.

Self-stabilizing Byzantine-tolerant Broadcast

“…In the broader context of self-stabilizing Byzantine-tolerant solutions for message-passing systems, we find solutions for topology discovery [18], storage [11,10,9,8,7], clock synchronization [20,27,25], approximate agreement [12], asynchronous unison [23] to name a few. Also, Byzantine-tolerant state-machine replication by Binun et al [4,5] for synchronous systems and Dolev et al [16] for practically-self-stabilizing partially-synchronous systems.…”

Self-Stabilizing Periodic Mutual-exclusive Propagation in Sparse Networks

“…Upon this, some high-layer Byzantine fault-tolerant protocols can be efficiently builtin some easy-understood ways [21,22]. In the same vein, high-layer self-stabilizing protocols can be built upon a selfstabilizing Byzantine agreement which in turn be built upon some low-layer self-stabilizing propagation primitives [9,23]. However, most of these propagation primitives require high network connectivity of the distributed systems.…”

Self-stabilizing Byzantine- and Intrusion-tolerant Consensus

“…Georgiou et al's solution can be used as the selfstabilizing Byzantine-tolerant Binary consensus object needed for our solution. In the broader context of self-stabilizing Byzantine-tolerant solutions for message-passing systems, we find solutions for topology discovery [22], storage [11,10,9,8,7], clock synchronization [24,31,29], approximate agreement [12], asynchronous unison [25] to name a few. Also, Byzantine-tolerant state-machine replication by Binun et al [4,5] for synchronous systems and Dolev et al [20] for practically-self-stabilizing partially-synchronous systems.…”