The Byzantine Agreement (BA) problem is a fundamental problem to consider in designing a fault-tolerance distributed system. Most BA protocols require all the fault-free processors to reach a common agreement at the same round, called an Immediate Byzantine Agreement (IBA), whereas another type of BA protocol allows the fault-free processors to reach a common agreement, called an Eventual Byzantine Agreement (EBA), at different rounds when they receive enough information. Up to now, all the existing EBA protocols are designed to solve the EBA problem based on the single failure type assumption (dormant fault only or malicious fault only) as to fallible processors over a reliable fully connected network. However, in practice, most network topologies would not be fully connected, and the underlying network would not be reliable, which means both dormant and malicious faults may occur within the same network simultaneously. In this study, we shall propose a new protocol to solve the EBA problem with dual failure mode on both processors and communication media (both dormant and malicious faults can happen simultaneously to either the processors or the communication media or both) over an unreliable un-fully connected network. The proposed protocol is the optimal when the above assumptions are considered.
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