Optimal Selfish Mining Strategies in Bitcoin

TL;DR

This paper extends the model of selfish mining in Bitcoin, providing algorithms to find optimal attack strategies, revealing lower profit thresholds, and analyzing the impact of delays and countermeasures on attack profitability.

Contribution

It introduces an algorithm for epsilon-optimal selfish mining policies, tight bounds on attacker revenue, and insights into the effects of delays and countermeasures on mining incentives.

Findings

Optimal policies outperform SM1 scheme in profitability.

Profit threshold for selfish mining is lower than previously thought.

Communication delays eliminate the profit threshold, encouraging attacks.

Abstract

Bitcoin is a decentralized crypto-currency, and an accompanying protocol, created in 2008. Bitcoin nodes continuously generate and propagate blocks---collections of newly approved transactions that are added to Bitcoin's ledger. Block creation requires nodes to invest computational resources, but also carries a reward in the form of bitcoins that are paid to the creator. While the protocol requires nodes to quickly distribute newly created blocks, strong nodes can in fact gain higher payoffs by withholding blocks they create and selectively postponing their publication. The existence of such selfish mining attacks was first reported by Eyal and Sirer, who have demonstrated a specific deviation from the standard protocol (a strategy that we name SM1). In this paper we extend the underlying model for selfish mining attacks, and provide an algorithm to find $\epsilon$-optimal policies for attackers within the model, as well as tight upper bounds on the revenue of optimal policies. As a consequence, we are able to provide lower bounds on the computational power an attacker needs in order to benefit from selfish mining. We find that the profit threshold -- the minimal fraction of resources required for a profitable attack -- is strictly lower than the one induced by the SM1 scheme. Indeed, the policies given by our algorithm dominate SM1, by better regulating attack-withdrawals. Using our algorithm, we show that Eyal and Sirer's suggested countermeasure to selfish mining is slightly less effective than previously conjectured. Next, we gain insight into selfish mining in the presence of communication delays, and show that, under a model that accounts for delays, the profit threshold vanishes, and even small attackers have incentive to occasionally deviate from the protocol. We conclude with observations regarding the combined power of selfish mining and double spending attacks.