Fairness Matters: A Tit-For-Tat Strategy Against Selfish Mining

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Abstract

The proof-of-work (PoW) based blockchains are more secure nowadays since profit-oriented miners contribute more computing powers in exchange for fair revenues. This virtuous circle only works under an incentive-compatible consensus, which is found to be fragile under selfish mining attacks. Specifically, selfish miners can conceal and reveal blocks strategically to earn unfairly higher revenue compared to honest behaviors. Previous countermeasures either require incompatible modifications or fail to consider the asynchronous network and multiple honest nodes setting in reality. In this paper, we introduce the unfairness measurement based on the KL-divergence from the computing power distribution to the revenue distribution of miners. To improve fairness with the existence of selfish miners, we propose a novel block promotion strategy namely Tit-for-Tat (TFT), for honest miners. In particular, based on a miner’s local observation of forks, we design the suspicious probability measurement of other nodes. Rather than promoting a fresh block instantly, miners withhold it for difierent time periods according to others’ suspicious probability before delivery. Meanwhile, to minimize the attacker’s unfair revenue, we formulate the delay vector (DV) problem for honest miners to determine the optimal withholding time. We prove that DV problem is nonconvex, and thus propose two approximation algorithms that yield n-suboptimal solutions. In addition, we extend TFT strategy to support dynamic networks. Extensive experiments validate the eficiency and efiectiveness of our strategy and algorithms to reduce unfairness by 54.62% within bounded withholding time.