Differential Privacy in Constant Function Market Makers

Abstract

Constant function market makers (CFMMs) are the most popular mechanism for facilitating decentralized trading. While these mechanisms have facilitated hundreds of billions of dollars of trades, they provide users with little to no privacy. Recent work illustrates that privacy cannot be achieved in CFMMs without forcing worse pricing and/or latency on end users. This paper quantifies the trade-off between pricing and privacy in CFMMs. We analyze a simple privacy-enhancing mechanism called Uniform Random Execution and prove that it provides (ϵ, δ) -differential privacy. The privacy parameter ϵ depends on the curvature of the CFMM trading function and the number of trades executed. This mechanism can be implemented in any blockchain system that allows smart contracts to access a verifiable random function. Our results provide an optimistic outlook on providing partial privacy in CFMMs.