Abstract
A trend in clustering mining power into mining pools in proof-of-work (PoW) blockchain systems raises severe concerns on the stability and security of these systems. Such pools can misbehave by strategically withhold found solutions (i.e., blocks). It has been shown that the reward of a large malicious mining pool can be significantly increased by deviating from the honest mining strategy. Moreover, a malicious pool can launch the block withholding (BWH) attack making the target's pool reward system unfair by letting malicious participants receive unearned shares while pretending to contribute work. Although these attacks are well-known, they are usually investigated in a simplified static reward model. This paper gives a detailed analysis of the dynamic reward of the BWH attacker while considering a more realistic model with the computing power changing incessantly. We propose a novel attack called the intermittent block withholding (IBWH) attack and we prove that this attack is optimal in our model. IBWH is a strategy where an attacker influences the reward period time, consequently enlarging the reward rate. Furthermore, in our model, we include the dynamics of the Bitcoin network's computing power, and even with the changing attacker's reward rates, we show that the IBWH's reward rate remains optimal. We consider both the selfish mining attack and the fork after withholding (FAW) attack, and we show that these attacks do not outperform IBWH.