Consensus Beyond Thresholds: Generalized Byzantine Quorums Made Live

TL;DR

This paper introduces the first implementation of Byzantine fault-tolerant consensus with generalized quorums, enabling more flexible trust assumptions beyond simple thresholds, and evaluates their performance in practical blockchain settings.

Contribution

It formalizes trust assumptions using monotone Boolean formulas and span programs, and integrates these into HotStuff BFT consensus, demonstrating practical viability and performance trade-offs.

Findings

MBF specifications do not slow down HotStuff significantly

MSP expressions impact latency and throughput

Generalized quorums enable more flexible trust models

Abstract

Existing Byzantine fault-tolerant (BFT) consensus protocols address only threshold failures, where the participating nodes fail independently of each other, each one fails equally likely, and the protocol's guarantees follow from a simple bound on the number of faulty nodes. With the widespread deployment of Byzantine consensus in blockchains and distributed ledgers today, however, more sophisticated trust assumptions are needed. This paper presents the first implementation of BFT consensus with generalized quorums. It starts from a number of generalized trust structures motivated by practice and explores methods to specify and implement them efficiently. In particular, it expresses the trust assumption by a monotone Boolean formula (MBF) with threshold operators and by a monotone span program (MSP), a linear-algebraic model for computation. An implementation of HotStuff BFT consensus using these quorum systems is described as well and compared to the existing threshold model. Benchmarks with HotStuff running on up to 40 replicas demonstrate that the MBF specification incurs no significant slowdown, whereas the MSP expression affects latency and throughput noticeably due to the involved computations.