Proof-of-Work (PoW) blockchains with symmetric consensus face threats such as selfish mining, bribery mining, block withholding, and replay attacks. This paper introduces a hybrid attack, Bribery–Stubborn Mining (BSbM), which integrates stubborn mining’s delayed chain publication with bribery incentives to recruit miners during forks. Simulation experiments confirm that BSbM yields additional revenue. To obtain even higher revenue, we propose Leading Hidden Bribery–Stubborn Mining (LHBSbM) based on BSbM. By concealing and delaying broadcasts, LHBSbM constructs a triple fork, maintaining three chains at the same height. Upon revealing the private chain, two public blocks can be isolated, breaking the single-block limit of double-fork attacks. Theoretical analysis shows that LHBSbM raises the attacker’s maximum effective block rate from α/(1−α) to α/(1−α−β). Experimental results indicate that, under ideal conditions (r=0), BSbM becomes profitable once the attacker’s hash rate (α) exceeds approximately 34% and further confirm that, under certain conditions, LHBSbM nearly doubles isolated blocks compared to BSbM, yielding greater profits. Finally, potential defenses against such hybrid attacks are discussed, offering new insights for blockchain security.
Li et al. (Tue,) studied this question.