Mining Pool Selection under Block WithHolding Attack

Abstract

In current Proof-of-Work (PoW) blockchain systems, miners usually form mining pools to compete with other pools/miners in the mining competition. Forming pools can give miners steady revenues but will introduce two critical issues. One is mining pool selection, where miners select the pools to join in order to maximize their revenues. The other is a Block WithHolding (BWH) attack, where pools can inject part of their hash/mining power into other pools to obtain additional revenues without contributing to the mining process of the attacked pools. Reasoning that the BWH attack will have significant impacts on the pool selection, we therefore investigate the mining pool selection issue in the presence of a BWH attack in this paper. In particular, we model the pool selection process of miners as an evolutionary game and find the Evolutionarily Stable States (ESSs) of the game (i.e., stable pool population states) as the solutions. Previous studies investigated this problem from the perspective of pool managers and neglected the revenues from attacked pools (attacking revenues), leading to less accurate and insightful findings. This paper, however, focuses on the payoffs of miners and carefully takes the attacking revenues into consideration. To demonstrate how the problem is solved, we consider the scenario with two mining pools and further investigate the case where one pool attacks the other and the case where the two pools attack each other. The results in this paper show that pools can attract more miners to join by launching a BWH attack and the attack power significantly affects the stable pool populations.

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

“…Answer: Most current research on the game theory of mining pools facing BWH attacks uses static game methods to model two mining pools [36][37][38][39]. There are expected to be very few studies on the dynamic game of the two mining pools because when the two mining pools are modeled, there are only four situations in which the mining pool launches BWH attacks that are easy to model.…”

“…Numerous kinds of research focus on analyzing and addressing how miners choose mining pools to obtain optimal profits when facing BWH attacks. Fujita et al [37] applied reinforcement learning (RL) techniques to analyze the optimal pool selection of miners. This work effectively addressed the issue of the mining pool's strategy to attract more miners to obtain the optimal block reward when the two mining pools face a BWH attack.…”

The Miner’s Dilemma With Migration: The Control Effect of Solo-Mining

“…Reference [30] established a game model between mining pools based on the PoW consensus algorithm, and found that the mining pool can increase its infiltration rate and average income by increasing the mining pool power and the betrayal rate of miners. Reference [31] built a game model of mutual attacks between mining pools and study the impact of different block withholding (BWH) attack intensity on miners' income. It is found that only when the BWH attack intensity is lower than a certain threshold, it can lead to an improvement of miners' income in the mining pool, so as to attract more miners to join the mining pool.…”