The mempool plays a crucial role in blockchain systems as a buffer zone for pending transactions before they are executed and included in a block. However, existing works primarily focus on mitigating defenses against already identified real-world attacks. This paper introduces secure blockchain-mempool designs capable of defending against any form of asymmetric eviction DoS attacks. We establish formal security definitions for mempools under the eviction-based attack vector. Our proposed secure transaction admission algorithm, named \textsc{saferAd-PR}, ensures eviction-security by providing a provable lower bound on the cost of executing eviction DoS attacks. Through evaluation with real transaction trace replays, \textsc{saferAd-PR} demonstrates negligible latency and significantly high lower bounds against any eviction attack, highlighting its effectiveness and robustness in securing blockchain mempools.
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