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With its explosive development, the Internet has come to offer an increasing multitude of online service applications. In order to better facilitate such services, a cloud computing environment, composed of a large number of processors and memories, high-speed networks, and various applications, has been developed, and continues to grow, providing convenient and quick network services. In this cloud computing environment, each server processor in the environment must cooperate with other processors to satisfy various user demands. As a result, the issue of fault-tolerance needs to be revised in order to ensure the reliability of cloud computing environments. One of the most important issue of fault-tolerance is the Byzantine agreement (BA), which requires that, even if some components are damaged, a set of fault-free service processors are able to agree on a common value. Furthermore, the faulty service …