The Evolutionary Equilibrium of Block Withholding Attack

Bitcoin is the most famous and the most used cryptocurrency in the world,such that it has received extreme popularity in recent years.However the Bitcoin system is accompanied by different attacks,including the block withholding(BWH)attack.When a miner plays the BWH attack,it will withhold all the blocks newly discovered in the attack pool,damaging the honest miners’right to obtain the fair reward.In this paper,we consider a setting in which two miners may honestly mine or perform the BWH attack in a mining pool.Different strategy profiles will bring different payoffs,in addition influence the selection of the strategies.Therefore,we establish an evolutionary game model to study the behavior tendency of the miners and the evolutionary stable strategies under different conditions,by formulating the replicator dynamic equations.Through numerical simulations,we further verify the theoretical results on evolutionary stable solutions and discuss the impact of the factors on miners’strategic choice.Based on these simulation results,we also make some recommendations for the manager and the miners to mitigate the BWH attack and to promote the cooperation between miners in a mining pool.

Analysis of reputation-based mining paradigm under dishonest mining attacks

Since the introduction of Bitcoin,numerous studies on Bitcoin mining attacks have been conducted,and as a result,many countermeasures to these attacks have been proposed.The reputation-based mining paradigm is a comprehensive countermeasure solution to this problem with the goal of regulating the mining process and preventing mining attacks.This is accomplished by incentivizing miners to avoid dishonest mining strategies using reward and punishment mechanisms.This model was validated solely based on game theoretical analyses,and the real-world implications of this model are not known due to the lack of empirical data.To shed light on this issue,we designed a simulated mining platform to examine the effectiveness of the reputation-based mining paradigm through data analysis.We implemented block withholding attacks in our simulation and ran the following three scenarios:Reputation mode,non-reputation mode,and no attack mode.By comparing the results from these three scenarios,interestingly,we found that the reputation-based mining paradigm decreases the number of block withholding attacks,and as a result,the actual revenue of individual miners becomes closer to their theoretical expected revenue.In addition,we observed that the confidence interval test can effectively detect block withholding attacks;however,the test also results in a small number of false positive cases.Since the effectiveness of the reputation-based model relies on attack detection,further research is needed to investigate the effect of this model on other dishonest mining strategies.