An Evolutionary Game Theory-Based Method to Mitigate Block Withholding Attack in Blockchain System

Abstract

Consensus algorithms are the essential components of blockchain systems. They guarantee the blockchain’s fault tolerance and security. The Proof of Work (PoW) consensus algorithm is one of the most widely used consensus algorithms in blockchain systems, using computational puzzles to enable mining pools to compete for block rewards. However, this excessive competition for computational power will bring security threats to blockchain systems. A block withholding (BWH) attack is one of the most critical security threats blockchain systems face. A BWH attack obtains the reward of illegal block extraction by replacing full proof with partial mining proof. However, the current research on the BWH game could be more extensive, considering the problem from the perspective of a static game, and it needs an optimal strategy that dynamically reflects the mining pool for multiple games. Therefore, to solve the above problems, this paper uses the method of the evolutionary game to design a time-varying dynamic game model through the degree of system supervision and punishment. Based on establishing the game model, we use the method of replicating dynamic equations to analyze and find the optimal strategy for mining pool profits under different BWH attacks. The experimental results demonstrate that the mining pools will choose honest mining for the best profit over time under severe punishment and high supervision. On the contrary, if the blockchain system is supervised with a low penalty, the mining pools will eventually choose to launch BWH attacks against each other to obtain the optimal mining reward. These experimental results also prove the validity and correctness of our model and solution.