Analyzing Miners’ Dynamic Equilibrium in Blockchain Networks under DDoS Attacks

Abstract

Proof of work (PoW) is one of the most widely used consensus algorithms in blockchain networks. It mainly uses the competition between mining nodes to obtain block rewards. However, this competition for computational power will allow malicious nodes to obtain illegal profits, bringing potential security threats to blockchain systems. A distributed denial of service (DDoS) attack is a major threat to the PoW algorithm. It utilizes multiple nodes in the blockchain network to attack honest miners to obtain illegal rewards. To solve this problem, academia has proposed a DDoS attack detection mechanism based on reinforcement learning methods and static game modeling methods based on mining pools. However, these methods cannot effectively make miners choose the strategy with the best profit over time when facing DDoS attacks. Therefore, this paper proposes a dynamic evolutionary game model for miners facing DDoS attacks under blockchain networks to solve the above problems for the first time. We address the model by replicating the dynamic equation to obtain a stable solution. According to the theorem of the Lyapunov method, we also obtain the only stable strategy for miners facing DDoS attacks. The experimental results show that compared with the static method, the dynamic method can affect game playing and game evolution over time. Moreover, miners’ strategy to face DDoS attacks gradually shifts from honest mining to launching DDoS attacks against each other as the blockchain network improves.