Numerous methods have been proposed for suppressing intentional forks by attackers in blockchain systems. Among these, last-generated rules, which select the latest chain among chains in a tie, are effective methods that do not require significant changes to the blockchain protocol. However, existing methods either require a trusted third party or rely on timestamps that attackers can manipulate which makes applying a last-generated rule to existing systems such as Bitcoin challenging. To address these issues, we propose a last-generated rule that can be easily applied to existing proof of work blockchain systems. Our method uses partial proof of work, which does not function as a block, as a time standard with finer granularity. Only weak synchronization, which is already met by existing systems, is required for effective functioning. We evaluated the proposed method through a detailed analysis that is lacking in existing works. In networks that adopt our method, the proportion of the attacker hashrate necessary for selfish mining was approximately 0.31479 or higher, regardless of the block propagation capability of the attacker. Furthermore, we demonstrated through extended selfish mining that the impact of Match against pre-generated block, which is a concern in all last-generated rules, can be mitigated with appropriate parameter settings.

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