Blockchains facilitate decentralization, security, identity, and data management in cyber-physical systems. However, consensus protocols used in blockchains are prone to high message and computational complexity costs and are not suitable to be used in IoT. One way to reduce message complexity is to randomly assign network nodes into committees or shards. Keeping committee sizes small is then desirable in order to achieve lower message complexity, but this comes with a penalty of reduced reliability as there is a higher probability that a large number of faulty nodes will end up in a committee. In this work, we study the problem of estimating a probability of a failure in randomly sharded networks. We provide new results and improve existing bounds on the failure probability. Thus, our framework also paves the way to reduce committee sizes without reducing reliability.

翻译：区块链技术为信息物理系统提供了去中心化、安全性、身份认证及数据管理等功能。然而，区块链中使用的共识协议存在消息复杂度与计算复杂度成本较高的问题，难以适用于物联网场景。降低消息复杂度的一种途径是将网络节点随机分配至委员会或分片中。为实现更低的消息复杂度，需要保持较小的委员会规模，但这将带来可靠性降低的代价——因为更多故障节点可能聚集在同一委员会的概率随之增加。本研究针对随机分片网络中的故障概率估计问题展开探讨，提出了新的研究成果，并对现有故障概率边界进行了优化改进。因此，本框架也为不降低可靠性前提下减小委员会规模提供了可行路径。