An Improved Approximate Consensus Algorithm in the Presence of Mobile Faults

TL;DR

This paper introduces an improved approximate consensus algorithm for synchronous networks with mobile Byzantine faults, reducing the number of nodes needed for fault tolerance and demonstrating optimality within a class of algorithms.

Contribution

It presents a novel technique using 'confession' and reliable broadcast to lower the node requirement from 4f+1 to approximately 3.5f+1, enhancing fault tolerance.

Findings

Requires fewer nodes than previous algorithms.

Achieves optimality within round-based algorithms.

Improves fault-tolerance in mobile Byzantine fault models.

Abstract

This paper explores the problem of reaching approximate consensus in synchronous point-to-point networks, where each pair of nodes is able to communicate with each other directly and reliably. We consider the mobile Byzantine fault model proposed by Garay '94 -- in the model, an omniscient adversary can corrupt up to $f$ nodes in each round, and at the beginning of each round, faults may "move" in the system (i.e., different sets of nodes may become faulty in different rounds). Recent work by Bonomi et al. '16 proposed a simple iterative approximate consensus algorithm which requires at least $4f+1$ nodes. This paper proposes a novel technique of using "confession" (a mechanism to allow others to ignore past behavior) and a variant of reliable broadcast to improve the fault-tolerance level. In particular, we present an approximate consensus algorithm that requires only $\lceil 7f/2\rceil + 1$ nodes, an $\lfloor f/2 \rfloor$ improvement over the state-of-the-art algorithms. Moreover, we also show that the proposed algorithm is optimal within a family of round-based algorithms.