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Due to the monetary value of Bitcoin, the most influential digital cryptocurrency in the world, Bitcoin has naturally become a valuable target of attacks, resulting in the emergence of many attack strategies on it. Among those attack strategies, selfish mining and block withholding attacks are two typical ones and attackers can obtain higher revenues under certain conditions than with an honest mining strategy. However, the combination of them will be a new type and more serious attack, which has not been analyzed in depth. In this paper, we propose GenSelfHolding, a general combined attack model with one selfish mining pool and random multiple honest pools on Bitcoin. Based on Markov chain, a general state transition graph and a general state distribution probability are presented to describe the internal features of our model. A general principle is then provided to calculate the attacker’s revenue. In addition, we give a detailed proof of the unique stable distribution of state transition probabilities. Such proof is an essential prerequisite for us to further present stable attacker revenue expressions under two specific scenarios, the GenSelfHolding model with two/three honest mining pools. Simulation results validate that the revenues of the attacker in these two specific models can reach up to 40% higher than those of classic selfish attackers in some cases.

GenSelfHolding: Fusing Selfish Mining and Block Withholding Attacks on Bitcoin Revisited