Stubborn Mining: Generalizing Selfish Mining and Combining with an Eclipse Attack

Selfish mining, originally discovered by Eyal et al. [9], is a well-known attack where a selfish miner, under certain conditions, can gain a disproportionate share of reward by deviating from the honest behavior. In this paper, we expand the mining strategy space to include novel "stubborn" strategies that, for a large range of parameters, earn the miner more revenue. Consequently, we show that the selfish mining attack is not (in general) optimal. Further, we show how a miner can further amplify its gain by non-trivially composing mining attacks with network-level eclipse attacks. We show, surprisingly, that given the attacker's best strategy, in some cases victims of an eclipse attack can actually benefit from being eclipsed!