Pool Block Withholding Attack with Rational Miners

We revisit pool block withholding (PBW) attack in this work, while taking miners’ rationality into consideration. It has been shown that a malicious mining pool in Bitcoin may attack other pools by sending some dummy miners who do not reveal true solutions but obtain reward portions from attacked pools. This result assumes that the infiltrating miners are always loyal and behave as the malicious pool desires; but why? In this work, we study rational infiltrating miners who behave by maximizing their own utilities. We characterize the infiltrating miners’ optimal strategies for two kinds of betraying behaviors depending on whether they return to the original pool or not. Our characterizations show that the infiltrating miners’ optimal strategy is simple and binary: they either betray or stay loyal all together, which depends on the total amount of them sent out by the malicious pool. Accordingly, we further compute the pool’s optimal attacking strategy given the miners’ strategic behaviors. Our experiments also show that by launching PBW attacks, the benefit to a pool is actually incremental.