Undetectable Selfish Mining
Maryam Bahrani, S. Matthew Weinberg
TL;DR
The paper investigates incentive robustness in proof-of-work longest-chain protocols by constructing a statistically undetectable selfish mining strategy. It extends the canonical Eyal–Sirer model with a latency-augmented Nakamoto Consensus Game ($\ell$-NCG) and formalizes a notion of $\ell'$-statistical undetectability, showing that a miner can profit without changing the observable block-view distribution. The authors present a warmup result (SP-Simple) and two main results: Main Result I proves the existence of a profitable, undetectable strategy when the attacker’s share exceeds a threshold near $0.381966$, even against full honest tiebreaking, and Main Result II extends profitability to general latency models with $\ell>0$, using a Bayesian, world-conditioned analysis. The work highlights that detectability alone cannot suffice to deter profitable deviations and emphasizes the need for incentive-compatible protocol designs that remain robust under undetectable strategies, with implications for centralization risk and ecosystem value.
Abstract
Seminal work of Eyal and Sirer (2014) establishes that a strategic Bitcoin miner may strictly profit by deviating from the intended Bitcoin protocol, using a strategy now termed *selfish mining*. More specifically, any miner with $>1/3$ of the total hashrate can earn bitcoin at a faster rate by selfish mining than by following the intended protocol (depending on network conditions, a lower fraction of hashrate may also suffice). One convincing critique of selfish mining in practice is that the presence of a selfish miner is *statistically detectable*: the pattern of orphaned blocks created by the presence of a selfish miner cannot be explained by natural network delays. Therefore, if an attacker chooses to selfish mine, users can detect this, and this may (significantly) negatively impact the value of BTC. So while the attacker may get slightly more bitcoin by selfish mining, these bitcoin may be worth significantly less USD. We develop a selfish mining variant that is provably *statistically undetectable*: the pattern of orphaned blocks is statistically identical to a world with only honest miners but higher network delay. Specifically, we consider a stylized model where honest miners with network delay produce orphaned blocks at each height independently with probability $β'$. We propose a selfish mining strategy that instead produces orphaned blocks at each height independently with probability $β> β'$. We further show that our strategy is strictly profitable for attackers with $38.2\% \ll 50\%$ of the total hashrate (and this holds for all natural orphan rates $β'$).