Breaking BFT: Quantifying the Cost to Attack Bitcoin and Ethereum

41 Pages Posted: 4 Mar 2024

Date Written: February 15, 2024


Much has been hypothesized and feared about 51% attacks on Bitcoin and 34% attacks on Ethereum. However, the costs and benefits associated with perpetrating these attacks remain a mystery. In this paper, we present a novel model to quantify the costs to breach Byzantine fault tolerance thresholds in Bitcoin and Ethereum. We introduce a new metric called Total Cost to Attack (TCA) which encompasses the operational and capital expenditures associated with these attacks. We explore the motivations and expected utility of both profit-driven and ideologically-motivated actors. Our findings suggest that the current state of security in Bitcoin and Ethereum make attacks economically unfeasible and provide empirical evidence of Nash Equilibrium in these networks. This study also challenges the notion that there is a linear relationship between fee revenue and network security, an assumption frequently made when discussing Bitcoin’s declining subsidies. Instead, our findings suggest that block producers engage in speculative behavior ahead of fee cycles, which ends up increasing network security even when fees are low and trending downwards. Our analysis contributes to the discourse around the long term viability of deflationary monetary policies used by Bitcoin and Ethereum and their impact on miner incentives and network security.

Keywords: 51% attacks, Bitcoin Security, Ethereum Churn Limit, Bitcoin Declining Subsidies, Crypto Network Security

JEL Classification: L86, O33

Suggested Citation

Nuzzi, Lucas and Waters, Kyle and Andrade, Matias, Breaking BFT: Quantifying the Cost to Attack Bitcoin and Ethereum (February 15, 2024). Available at SSRN: or

Lucas Nuzzi (Contact Author)


SUITE 310 A120
Cheyenne, WY 82001
United States

Kyle Waters

Independent ( email )

Matias Andrade

Independent ( email )

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