Why Not Wait and See: An Effective BDoS Mitigation Strategy From a Two-Stage Evolutionary Game Perspective

Bitcoin's security is based on the assumption that a sufficient amount of benign computing power participates in “mining” new blocks by generating publicly verifiable proofs. The blockchain denial of service (BDoS) attackers generate a valid proof but withhold the whole block, resulting in honest miners stopping the participation service but waiting for the exposure of the new block, and attackers achieving 21% computing power would significantly threaten the security of blockchain applications. We find that the threshold value 21% is based on the assumption that honest miners are only concerned with current short-term benefits, i.e., they have an immediate tendency to stop mining once a BDoS attack occurs and their short-term gains decline. However, similar to the altruistic behavior observed in biological systems, certain blockchain nodes exhibit a form of rational altruism during attacks. When the blockchain system is under threat, these nodes prioritize the long-term stability of the network and choose to continue mining honestly. This phenomenon has not yet been well studied. Motivated by the above observation, we propose a resumption strategy that enables honest miners to resume mining after pausing ($S_\text{CMP}$) for a while, mitigating BDoS attacks and maintaining blockchain security. Subsequently, we formalize a two-stage evolutionary game model to quantitatively analyze the defensive capacity against BDoS with the$S_\text{CMP}$strategy. Theoretical analysis shows that BDoS attackers can only successfully stop blockchain mining when the attacking power and profit factor satisfy a certain condition$\text{Cd}_{dead}(\gamma,w,\alpha _{A},c)$, where our proposed strategy enables the attack mining power threshold to be raised to 33.1% approaching 1/3, which is the upper bound of the byzantine false tolerance. Real-world experimental results also indicate that the Bitcoin system would be subject to a BDoS attack by 2028.