Mined Block Withholding and Imposed Fork by Using Mining Pool Alliance Strategic—A Case Study in Bitcoin System

In the proof-of-work (PoW) blockchain consensus mechanism, miners perform numerous hash calculations to obtain a value below the difficulty threshold to generate a new block and obtain rewards. As the difficulty of mining increases, pools may develop competition strategies to reduce time and increase the rewards for mining blocks. This study investigates these strategies by examining whether mining pools in an alliance can perform selective broadcasting, hold mined blocks, and impose fork attacks. We developed algorithms to conduct simulation solutions based on the consensus mechanism of the Bitcoin operation, except for the hash function execution. The calculation results are replaced with two types of balls that represent hash values that satisfy the threshold of the mined block. The simulation algorithms were validated by comparing them with the expected average mining times. The results revealed a bias of less than 4%. Twelve simulation cases with various holding thresholds, holding periods, and forks for strategic alliance mining pools were simulated and evaluated. The results show that the mining rates of alliance mining pools increase, which means that the reward increases. The effects of these strategies on the winning rate reached 21.77% when the top three mining pools were constructed as alliances with withholding and imposing fork strategies. The effect of the average mining time is evaluated for mining pools with the same computing power distribution as practical mining pools for the Bitcoin system.