Communication Efficient Byzantine Agreement with Predictions

TL;DR

This paper presents communication-efficient Byzantine agreement algorithms leveraging predictions, achieving near-optimal complexity and tolerating many prediction errors without excessive message exchange.

Contribution

It introduces algorithms that significantly reduce communication complexity in Byzantine agreement with predictions, surpassing previous limitations and achieving optimal round complexity.

Findings

Unauthenticated algorithm with $ ilde{O}(n^{2.5})$ communication complexity.

Authenticated algorithm with optimal $O(n^2 ext{kappa})$ communication complexity.

All algorithms have optimal round complexity regardless of prediction errors.

Abstract

In Byzantine agreement with predictions each process begins with an input value and some (unreliable) prediction bits. Recently, it has been shown that with \emph{classification predictions} -- where the predictions predict each process to be honest or faulty -- Byzantine agreement can be completed more quickly than without predictions, circumventing the traditional $\Omega(f)$ round lower bound. However, existing algorithms either handle limited prediction errors or send too many messages. Moreover, they all exchange $\Omega(n^3)$ bits -- enough to allow the processes to approximately agree on the classifications. In fact, it almost seemed necessary to share a significant number of prediction bits if one wanted to tolerate a high number of incorrect predictions. In this paper, we show that this high level of communication (and sharing of predictions) is not inherent by developing an unauthenticated algorithm with $\tilde{O}(n^{2.5})$ communication complexity. Furthermore, with authentication, we give an algorithm with optimal $O(n^2\kappa)$ communication complexity (where $\kappa$ is a security parameter). All of our results have optimal round complexity for any number of errors in the predictions.