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Abstract

The integrity of many Proof-of-Stake (PoS) payment systems relies on quorum-based State Machine Replication (SMR) protocols mitigating diverse adversarial attacks. While traditional analyses assume a purely Byzantine threat model, practical security depends on resilience against both arbitrary faults and strategic, profit-driven actors. In this work, we study this challenge by analyzing SMR protocols under a hybrid threat model comprising honest, Byzantine, and rational validators. We first establish the fundamental limitations of traditional consensus mechanisms, proving two impossibility results: (1) in partially synchronous networks, no quorumbased protocol can achieve SMR when rational and Byzantine validators collectively exceed 1 / 3 of the participants; and (2) even under synchronous network assumptions, SMR remains unattainable if this coalition comprises more than 2 / 3 of the validator set. Motivated by these boundaries, we develop a protocol that achieves SMR in the presence of up to 1 / 3 Byzantine and 1 / 3 rational validators. Our approach relies on two complementary mechanisms to circumvent our impossibility results. First, we introduce a protocol constraint that enforces an upper bound on the transaction volume finalized within any time window, and we prove that such a bound is a necessary condition for security. Second, we define the strongest chain rule, a finality gadget that enables instant transaction confirmation when a supermajority of participants provably supports the execution. We validate the feasibility of this design through an empirical analysis of the Ethereum and Cosmos networks, demonstrating that validator participation exceeds the required 5 / 6 threshold in over 99% of observed blocks. Finally, we explore adversarial settings beyond the classical Byzantine threshold. CoBRA supports recovery from consistency violations even when Byzantine validators control less than 2 / 3 of the stake, while providing an additional client-level economic security guarantee: every transaction accepted by clients, including those on conflicting branches, is accounted for during recovery, enabling full reimbursement of provable losses without requiring client participation and without minting new coins.