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.

中文翻译：

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使用有效集合对帐的拜占庭集合联盟共识

安全多方计算的应用（例如某些电子投票或拍卖协议）要求在大量元素上达成拜占庭协议。迄今为止，文献中提出的实现方式都依赖于状态机复制，并且在顺序上对每个单独的集合元素都达成了共识。我们介绍了集合联盟共识，这是拜占庭共识的一种特质，可以在整个集合中达成共识。通过使用Eppstein的集合和解协议与Ben-Or的ByzConsensus协议的组合，此原语承认有效而简单的实现。GNUnet中提供了此构造的免费软件实现。实验结果表明，我们的方法可为非常大的集合提供有效的协议，尤其是在没有拜占庭断层的情况下。我们通过使用集联盟共识来实现分布式密钥生成，投票收集和GNUnet中实现的电子投票协议的协作解密来展示其多功能性。这是在ARES 2016上以相同标题发表的论文的修订和扩展版本。