Optimal mixed block withholding attacks based on reinforcement learning

The vulnerabilities in cryptographic currencies facilitate the adversarial attacks. Therefore, the attackers have incentives to increase their rewards by strategic behaviors. Block withholding attacks (BWH) are such behaviors that attackers withhold blocks in the target pools to subvert the blockchain ecosystem. Furthermore, BWH attacks may dwarf the countermeasures by combining with selfish mining attacks or other strategic behaviors, for example, fork after withholding (FAW) attacks and power adaptive withholding (PAW) attacks. That is, the attackers may be intelligent enough such that they can dynamically gear their behaviors to optimal attacking strategies. In this paper, we propose mixed-BWH attacks with respect to intelligent attackers, who leverage reinforcement learning to pin down optimal strategic behaviors to maximize their rewards. More specifically, the intelligent attackers strategically toggle among BWH, FAW, and PAW attacks. Their main target is to fine-tune the optimal behaviors, which incur maximal rewards. The attackers pinpoint the optimal attacking actions with reinforcement learning, which is formalized into a Markov decision process. The simulation results show that the rewards of the mixed strategy are much higher than that of honest strategy for the attackers. Therefore, the attackers have enough incentives to adopt the mixed strategy.