A Fault-Resistant Asynchronous Clock Function

TL;DR

This paper introduces a new fault-resistant asynchronous clock function and presents a randomized self-stabilizing Byzantine tolerant clock synchronization algorithm, addressing challenges in asynchronous networks with Byzantine and transient failures.

Contribution

It defines a generalized clock-function problem and provides a novel randomized self-stabilizing Byzantine tolerant algorithm with a key building block for asynchronous systems.

Findings

The algorithm is self-stabilizing and Byzantine tolerant.

Convergence time is exponential, matching known bounds in asynchronous Byzantine agreement.

A new building block ensures nodes advance at similar rates.

Abstract

Consider an asynchronous network in a shared-memory environment consisting of n nodes. Assume that up to f of the nodes might be Byzantine (n > 12f), where the adversary is full-information and dynamic (sometimes called adaptive). In addition, the non-Byzantine nodes may undergo transient failures. Nodes advance in atomic steps, which consist of reading all registers, performing some calculation and writing to all registers. This paper contains three main contributions. First, the clock-function problem is defined, which is a generalization of the clock synchronization problem. This generalization encapsulates previous clock synchronization problem definitions while extending them to the current paper's model. Second, a randomized asynchronous self-stabilizing Byzantine tolerant clock synchronization algorithm is presented. In the construction of the clock synchronization algorithm, a building block that ensures different nodes advance at similar rates is developed. This feature is the third contribution of the paper. It is self-stabilizing and Byzantine tolerant and can be used as a building block for different algorithms that operate in an asynchronous self-stabilizing Byzantine model. The convergence time of the presented algorithm is exponential. Observe that in the asynchronous setting the best known full-information dynamic Byzantine agreement also has expected exponential convergence time, even though currently there is no known reduction between the two.