Selfish Mining in Proof-of-Work Blockchain with Multiple Miners: An Empirical Evaluation

Abstract

Proof-of-Work blockchain, despite its numerous benefits, is still not an entirely secure technology due to the existence of Selfish Mining (SM) strategies that can disrupt the system and its mining economy. While the effect of SM has been studied mostly in a two-miners scenario, it has not been investigated in a more practical context where there are multiple malicious miners individually performing SM. To fill this gap, we carry out an empirical study that separately accounts for different numbers of SM miners (who always perform SM) and strategic miners (who choose either SM or Nakamoto's mining protocol depending on which maximises their individual mining reward). Our result shows that SM is generally more effective as the number of SM miners increases, however its effectiveness does not vary in the presence of a large number of strategic miners. Under specific mining power distributions, we also demonstrate that multiple miners can perform SM and simultaneously gain higher mining rewards than they should. Surprisingly, we also show that the more strategic miners there are, the more robust the systems become. Since blockchain miners should naturally be seen as self-interested strategic miners, our findings encourage blockchain system developers and engineers to attract as many miners as possible to prevent SM and similar behaviour.

A New Theoretical Framework of Pyramid Markov Processes for Blockchain Selfish Mining

“…Based on this, they A class of simple Markov chains following Eyal and Sirer [23]. Following the simple Markov chain given by Eyal and Sirer [23], some researchers have further extended and generalized to discuss other attack strategies of blockchain either from multiple mining pools or from Ethereum (and smart contract), among which important examples include stubborn mining by Nayak et al [74], Wang et al [91] and Liu et al [62]; Ethereum (and smart contract) by Niu and Feng [77]; multiple mining pools (or miners) by Leelavimolsilp et al [54,53], Liu et al [60] and Jain [39]; multi-stage blockchain by Chang et al [13]; no block reward by Carlsten et al [12]; Power adjusting by Gao et al [25]; extending Eyal and Sirer's Markov chain by Gervais et al [30], Mwale [70], Moustapha [68], Mulser [69], Bai et al [4], Marmolejo-Cossío et al [65], Dong et al [20], Lee and Kim [51] and Liu et al [61].…”

“…Generalizing selfish mining. To generalize the blockchain selfish mining, Courtois and Bahack [17] proposed a subversive miner strategy, Nayak et al [74] presented a stubborn mining strategy, and Lee and Kim [53] developed a detective mining by means of the information of miners.…”

Tree Representation, Growth Rate of Blockchain and Reward Allocation in Ethereum with Multiple Mining Pools

“…Leelavimolsilp et al [17] used simulation to provide a preliminary investigation on the selfish mining strategy adopted by multiple miners, and analyzed the relative reward, the power threshold of selfish miners, and the safety level of the Bitcoin system. Under the assumptions of [17], Leelavimolsilp et al [18] further studied the effectiveness of the selfish mining strategy. For (b) extending the Markov chain method of Eyal and Sirer [12], readers are referred to, for example, Liu et al [22],…”