Achieving optimal rewards in cryptocurrency stubborn mining with state transition analysis

Abstract

Bitcoin uses a decentralized network of miners and a distributed consensus algorithm to agree on blockchains to process transactions, and designs certain incentive strategy to ensure the system run persistently. However, recent research finds that it is vulnerable to specific game-theoretic attacks, in which a rational attack can gain a disproportionate share of reward by deviating from the honest behaviors. Among these attacks, stubborn mining is generally regarded as the most effective one. This paper propose the optimal stubborn mining strategy, trying to obtain the maximum revenue in stubborn mining. Through careful analysis, we find that the mining strategies in stubborn mining, under different conditions, can be represented as a Markovian Decision Process (MDP), and solving the MDP can result in the optimal strategy. In solving the MDP, we first transform it into a transition-reward Matrices, and then evaluate it to get the largest reward. With the method mentioned above, the attackers can get 46.9% additional than honest miners, and this attack outweighs traditional selfish mining (a compelling and well-studied mining attack) by up to 7.53%.