# A Generic Efficient Biased Optimizer for Consensus Protocols

## TL;DR

This paper introduces a generic optimizer that enhances any consensus protocol to achieve single-round termination under certain conditions, with minimal cryptographic requirements and varying fault tolerance levels.

## Contribution

It presents a universal optimizer that converts existing consensus protocols into single-round solutions under specific fault and validity assumptions.

## Key findings

- Achieves single-round consensus when all nodes start with the same value and no Byzantine failures.
- Works with benign failures for $f<n/2$ and Byzantine failures for $f<n/4$ or $f<n/3$ depending on validity.
- Relies only on oral messages, requiring minimal cryptographic assumptions.

## Abstract

Consensus is one of the most fundamental distributed computing problems. In particular, it serves as a building block in many replication based fault-tolerant systems and in particular in multiple recent blockchain solutions. Depending on its exact variant and other environmental assumptions, solving consensus requires multiple communication rounds. Yet, there are known optimistic protocols that guarantee termination in a single communication round under favorable conditions. In this paper we present a generic optimizer than can turn any consensus protocol into an optimized protocol that terminates in a single communication round whenever all nodes start with the same predetermined value and no Byzantine failures occur (although node crashes are allowed). This is regardless of the network timing assumptions and additional oracle capabilities assumed by the base consensus protocol being optimized. In the case of benign failures, our optimizer works whenever the number of faulty nodes $f<n/2$. For Byzantine behavior, our optimizer's resiliency depends on the validity variant sought. In the case of classical validity, it can accommodate $f<n/4$ Byzantine failures. With the more recent external validity function assumption, it works whenever $f<n/3$. Either way, our optimizer only relies on oral messages, thereby imposing very light-weight crypto requirements.