Equilibrium Analysis of Block Withholding Attack: An Evolutionary Game Perspective

Abstract

With the advancement of blockchain technology, blockchain-based digital cryptocurrencies, like Bitcoin, have received broad interest. Due to the permissionless environment, the blockchain is vulnerable to different kinds of attacks, such as the block withholding (BWH) attack. BWH attack is one common selfish mining attack, by which the attacking pool infiltrates the attacked pool, and the infiltrating miners withhold all the blocks newly discovered in the attacked pool. Therefore, the attacking pool benefit by withholding blocks, damaging the benefits of victim pools. In this paper, we introduce the reward reallocation mechanism by paying additional rewards to the miners who successfully mine blocks, and propose an evolutionary game model for BWH attack among pools to study the strategy selection of pools. By constructing the replicator dynamic equations, the evolutionary stable strategies of pools are explored based on different levels of additional rewards. Our results provide enlightening significance to mitigate the negative influence from BWH attacks in practice.