The Intermittent Withholding Attack:the Block Withholding Attack For The Optimal Dynamic Reward Rate

In the proof of work blockchain system,miners form a relatively large pool of computing power in order to obtain more stable benefits.The impact of this phenomenon on the stability and safety of these systems has aroused widespread concern among researchers.Many studies have shown that by deviating from honest mining strategies,the return of malicious miners or mining pools can be increased.The miners in the mining pool withhold the blocks they had found,and the target mine pool reward system was out of balance,allowing the malicious miners to obtain the benefits that did not belong to them,thus the mine pool suffers losses.Although these attacks are widely known,these attack models are usually studied in a simplified static model.This paper analyzes the comparison of the reward of the attacker,the victim's pool and the third-party's miners in the block withholding attack,and gives a comparison of different attack scenarios,such as employ block withholding attack and fork after withholding attack,etc.In order to get closer to the real situation,this paper analyzes the dynamic reward rate of the attacker in the block withholding attack in detail,we consider a more realistic model with the changing computing power.In the analysis process,we divided the average return into four stages,which represent the dynamic reward rate under different miner's strategies.We propose a new attack strategy called the intermittent block withholding attack and prove that this attack is optimal for the reward rate in the dynamic model.The main idea of the intermittent block withholding attacks is to reduce the duration of a certain phase,thereby increasing the average reward of the attacker.In addition,we analyzed different attacks related to the changing of computing power,such as selfish mining attack and fork after withholding attack.The results suggest that the intermittent strategies are still optimal for those attacks' dynamic average returns.Because the specific conditions of the Bitcoin are easily changeable,our analysis is only qualitatively,the more detailed analysis is the direction of our future work.Finally,we simulated the reward and average reward rate of each strategy,the results also confirmed our results:the intermittent strategies can bring the greatest average reward rate to the attacker.