Quorum Subsumption for Heterogeneous Quorum Systems

TL;DR

This paper investigates heterogeneous Byzantine quorum systems, introduces quorum subsumption, and demonstrates that combining intersection, availability, and subsumption ensures reliable broadcast and consensus.

Contribution

It defines quorum subsumption and proves that combining it with intersection and availability guarantees correctness of broadcast and consensus protocols.

Findings

Quorum intersection and availability are necessary but not sufficient.

Quorum subsumption is introduced as a new property.

Protocols are developed and proven correct under the combined properties.

Abstract

Byzantine quorum systems provide higher throughput than proof-of-work and incur modest energy consumption. Further, their modern incarnations incorporate personalized and heterogeneous trust. Thus, they are emerging as an appealing candidate for global financial infrastructure. However, since their quorums are not uniform across processes anymore, the properties that they should maintain to support abstractions such as reliable broadcast and consensus are not well-understood. It has been shown that the two properties quorum intersection and availability are necessary. In this paper, we prove that they are not sufficient. We then define the notion of quorum subsumption, and show that the three conditions together are sufficient: we present reliable broadcast and consensus protocols, and prove their correctness for quorum systems that provide the three properties.