Frugal Byzantine Computing

TL;DR

This paper introduces a frugal approach to Byzantine computing, reducing the number of replicas and signatures needed for reliable communication and consensus, thus making Byzantine fault tolerance more economical.

Contribution

It establishes a separation between Consistent and Reliable Broadcast in signature requirements and presents a practical consensus algorithm using Consistent Broadcast with minimal signatures.

Findings

Consistent Broadcast can require fewer signatures than Reliable Broadcast.

A new consensus algorithm achieves agreement with minimal signatures and 2f+1 replicas.

The work demonstrates practical, signature-efficient Byzantine fault-tolerant consensus.

Abstract

Traditional techniques for handling Byzantine failures are expensive: digital signatures are too costly, while using $3f{+}1$ replicas is uneconomical ($f$ denotes the maximum number of Byzantine processes). We seek algorithms that reduce the number of replicas to $2f{+}1$ and minimize the number of signatures. While the first goal can be achieved in the message-and-memory model, accomplishing the second goal simultaneously is challenging. We first address this challenge for the problem of broadcasting messages reliably. We consider two variants of this problem, Consistent Broadcast and Reliable Broadcast, typically considered very close. Perhaps surprisingly, we establish a separation between them in terms of signatures required. In particular, we show that Consistent Broadcast requires at least 1 signature in some execution, while Reliable Broadcast requires $O(n)$ signatures in some execution. We present matching upper bounds for both primitives within constant factors. We then turn to the problem of consensus and argue that this separation matters for solving consensus with Byzantine failures: we present a practical consensus algorithm that uses Consistent Broadcast as its main communication primitive. This algorithm works for $n=2f{+}1$ and avoids signatures in the common-case -- properties that have not been simultaneously achieved previously. Overall, our work approaches Byzantine computing in a frugal manner and motivates the use of Consistent Broadcast -- rather than Reliable Broadcast -- as a key primitive for reaching agreement.