Byzantine set-union consensus using efficient set reconciliation

Florian Dold,Christian Grothoff

doi:10.1186/s13635-017-0066-3

Abstract

Applications of secure multiparty computation such as certain electronic voting or auction protocols require Byzantine agreement on large sets of elements. Implementations proposed in the literature so far have relied on state machine replication and reach agreement on each individual set element in sequence.We introduce set-union consensus, a specialization of Byzantine consensus that reaches agreement over whole sets. This primitive admits an efficient and simple implementation by the composition of Eppstein’s set reconciliation protocol with Ben-Or’s ByzConsensus protocol.A free software implementation of this construction is available in GNUnet. Experimental results indicate that our approach results in an efficient protocol for very large sets, especially in the absence of Byzantine faults. We show the versatility of set-union consensus by using it to implement distributed key generation, ballot collection, and cooperative decryption for an electronic voting protocol implemented in GNUnet.This is a revised and extended version of a paper published under the same title at ARES 2016.

Highlights

Byzantine consensus is a fundamental building block for fault-tolerant distributed systems
More recent approaches for practical applications are mainly based on state machine replication (SMR), wherein peers agree on a sequence of state machine transitions
We introduce Byzantine set-union consensus (BSC) as an alternative communication primitive that allows this aggregation to be implemented more efficiently

Summary

Introduction

Byzantine consensus is a fundamental building block for fault-tolerant distributed systems. More recent approaches for practical applications are mainly based on state machine replication (SMR), wherein peers agree on a sequence of state machine transitions. State machine replication makes it relatively easy to lift existing, non-fault-tolerant services to a Byzantine fault-tolerant implementation [15]. Each request from a client triggers a state transition in the replicated state machine that provides the service. Some definitions of the consensus problem include strong validity, which requires the value that is agreed upon to be the initial value of some correct peer [45]. The consensus protocol presented in this paper does not offer strong validity; for a set-union operation, this is not exactly desirable as the goal is to have all peers agree a union of all of the original sets, not on some peer’s initial subset

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Results

Conclusion