Optimal Revenue Analysis of the Stubborn Mining Based on Markov Decision Process

Abstract

AbstractAs one of the most popular cryptocurrencies, Bitcoin is essentially a decentralized ledger. Each node maintains the security of the blockchain through the workload proof mechanism, and the block that obtains the accounting right will receive a block reward in the form of Bitcoin. Because the Bitcoin system follows the “longest legal chain” principle, when a fork occurs, orphan blocks will inevitably be generated, and some miners’ computing power will be a waste. In recent years, researchers have discovered that miners can obtain profits disproportionate to their own computing power by deviating from Bitcoin’s honest mining. Selfish Mining (SM1) is a case in dishonest mining strategy, and dishonest miners (attackers) can obtain higher returns by retaining the blocks they create and selectively delaying their release. The stubborn mining strategy is a generalized form of selfish mining. It increases the revenue of the stubborn miner by adopting a wider range of parameters. Its three mining strategies are: Lead-Stubborn, Equal Fork stubborn and Trail stubborn. The mining problem can be formulated as a Markov Decision Process (MDP), which can be resolved to give the optimal mining strategy. This work describes the three mining strategies of stubborn mining as a Markov decision process, solves it and gives the lower bound of the highest return under the optimal stubborn mining strategy. Our experimental results demonstrate that the revenue of the optimal stubborn mining strategy is higher than SM1 under certain circumstances, and this strategy allows dishonest miners (stubborn miners) to obtain revenue that does not match the actual computing power paid.KeywordsBlockchainSelfish miningStubborn miningMDP