Analysis of blockchain protocol against static adversarial miners corrupted by long delay attackers

Bitcoin, which was initially introduced by Nakamoto, is the most disruptive and impactive cryptocurrency. The core Bitcoin technology is the so-called blockchain protocol. In recent years, several studies have focused on rigorous analyses of the security of Nakamoto’s blockchain protocol in an asynchronous network where network delay must be considered. Wei, Yuan, and Zheng investigated the effect of a long delay attack against Nakamoto’s blockchain protocol. However, their proof only holds in the honest miner setting. In this study, we improve Wei, Yuan and Zheng’s result using a stronger model where the adversary can perform long delay attacks and corrupt a certain fraction of the miners. We propose a method to analyze the converge event and demonstrate that the properties of chain growth, common prefix, and chain quality still hold with reasonable parameters in our stronger model.