Stubborn Mining: Double-Spend at No-Cost

Although, both double-spending and selfish-mining attacks have been extensively studied since the "Bitcoin" whitepaper of Nakamoto and the "majority is not enough" paper of Eyal and Sirer, there has been no rigorous stochastic analysis of an attack that combines the two, except for the complicated MDP models. For the first time in the literature, we provide a rigorous and explicit stochastic analysis of the combination of the two celebrated attacks: double-spending and selfish mining. We provide a simple formula to calculate revenues, double-spend risks and optimal attacks compared to complicated prescriptions of MDPs. As we do not deal with MDPs, the results are extremely easy-to-analyze and provide a great insight at first sight.