Interactive consistency is the problem in which $n$ distinct nodes, each having its own private value, where up to $t$ may be Byzantine, run an algorithm that allows all non-faulty nodes to infer the values of each other node. This problem is relevant to critical applications that rely on the combination of the opinions of multiple peers to provide a service. Examples include monitoring a content source to prevent equivocation or to track variability in the content provided, and resolving divergent state amongst the nodes of a distributed system. Previous works assume a fully synchronous system, where one can make strong assumptions such as negligible message delivery delays and/or detection of absent messages. However, practical, real-world systems are mostly asynchronous, i.e., they exhibit only some periods of synchrony during which message delivery is timely, thus requiring a different approach. In this paper, we present a thorough study of practical interactive consistency. We leverage the vast prior work on broadcast and Byzantine consensus algorithms to design, implement and evaluate a set of randomized algorithms, with only a single synchronization barrier and varying message complexities, that can be used to achieve interactive consistency in real-world distributed systems. We present formal proofs of correctness and message complexity of our proposed algorithms. We provide a complete, open-source implementation of each proposed interactive consistency algorithm by building a multi-layered software stack of algorithms that includes several broadcast algorithms, as well as a binary and a multi-valued consensus algorithm. Most of these algorithms have never been implemented and evaluated in a real system before. Finally, we analyze the performance of our suite of algorithms experimentally by testing both single instance and multiple parallel instances of each alternative and present a case study of achieving interactive consistency in a real-world distributed e-voting system.

交互式一致性是其中的问题 $ñ$ 不同的节点，每个节点都有自己的私有值，最多 $Ť$可能是拜占庭，请运行一种算法，该算法允许所有非故障节点推断每个其他节点的值。此问题与依赖多个对等方的意见的组合来提供服务的关键应用程序有关。示例包括监视内容源以防止模棱两可或跟踪所提供内容的可变性，以及解决分布式系统节点之间的分歧状态。先前的工作假设一个完全同步的系统，其中可以做出强有力的假设，例如可以忽略的消息传递延迟和/或检测到缺少的消息。但是，实际的实际系统大多数情况下是异步的，即，它们仅表现出某些同步时间段，在此期间消息传递是及时的，因此需要使用不同的方法。在本文中，我们将对实际的互动一致性。我们利用广播和拜占庭共识算法方面的大量先验工作来设计，实现和评估一组随机算法，这些算法只有一个同步屏障和变化的消息复杂性，可用于在现实世界的分布式系统中实现交互式一致性。我们提出了所提出算法的正确性和消息复杂性的形式证明。通过构建算法的多层软件堆栈，其中包括几个广播算法以及二进制和多值共识算法，我们为每个提出的交互式一致性算法提供了完整的开源实现。这些算法中的大多数以前从未在实际系统中实现和评估过。最后，