Revisiting Asynchronous Fault Tolerant Computation with Optimal Resilience

TL;DR

This paper revisits a fundamental lower bound for asynchronous fault-tolerant computation, providing a more rigorous proof and introducing a protocol that overcomes this bound using a strong common coin, achieving almost sure termination and fair validity.

Contribution

It offers a rigorous proof of a known lower bound and introduces a new protocol that achieves almost sure termination and fair validity in asynchronous Byzantine agreement.

Findings

Revised and more general proof of the lower bound.

Protocol with almost sure termination using a strong common coin.

First asynchronous Byzantine agreement with fair validity in the information-theoretic setting.

Abstract

The celebrated result of Fischer, Lynch and Paterson is the fundamental lower bound for asynchronous fault tolerant computation: any 1-crash resilient asynchronous agreement protocol must have some (possibly measure zero) probability of not terminating. In 1994, Ben-Or, Kelmer and Rabin published a proof-sketch of a lesser known lower bound for asynchronous fault tolerant computation with optimal resilience against a Byzantine adversary: if $n\le 4t$ then any t-resilient asynchronous verifiable secret sharing protocol must have some non-zero probability of not terminating. Our main contribution is to revisit this lower bound and provide a rigorous and more general proof. Our second contribution is to show how to avoid this lower bound. We provide a protocol with optimal resilience that is almost surely terminating for a strong common coin functionality. Using this new primitive we provide an almost surely terminating protocol with optimal resilience for asynchronous Byzantine agreement that has a new fair validity property. To the best of our knowledge this is the first asynchronous Byzantine agreement with fair validity in the information theoretic setting.