Illia Melnyk¹,², Oleksandr Kurbatov², Oleg Fomenko², Volodymyr Dubinin² and Yaroslav Panasenko², ¹Igor Sikorsky Kyiv Polytechnic Institute, Ukraine,² Distributed Lab, Ukraine

Byzantine fault tolerant consensus plays a critical role in maintaining the reliability of distributed systems. This paper surveys and evaluates five Paxos-based algorithms " Byzantine classic Paxos consensus, Castro-Liskov algorithm, Byzantine generalized Paxos consensus, Byzantine vertical Paxos, and Optimistic Byzantine Agreement " comparing their efficiency in terms of process requirements, communication rounds, and message complexity, as well as their resilience against Byzantine behaviors. Through detailed examination of protocol structures and performance trade-offs, we identify the strengths and limitations of each approach under typical and adversarial conditions. Our analysis reveals that the two-phase Byzantine classic Paxos consensus protocol achieves an optimal balance of simplicity, low process overhead, and robust security guarantees, making it a compelling choice for practical Byzantine fault tolerant deployments. We conclude with recommendations for selecting an appropriate consensus algorithm based on system constraints.

Byzantine fault tolerance, Paxos-based consensus, Communication complexity, Process requirements, Distributed system security