Cryptocurrencies aim to replicate physical cash in the digital realm while removing centralized middlemen. Decentralization is achieved by the blockchain, a permanent public ledger that contains a record of every transaction. The public ledger ensures transparency, which enables public verifiability but harms fungibility and anonymity. Even though cryptocurrencies attracted millions of users in the last decade with their total market cap reaching approximately one trillion USD, their anonymity guarantees are poorly understood. Indeed, previous notions of privacy, anonymity, and fungibility for cryptocurrencies are either non-quantitative or inapplicable, e.g., computationally hard to measure. In this work, we put forward a formal framework to measure the fungibility and anonymity of cryptocurrencies, allowing us to quantitatively reason about the mixing characteristics of cryptocurrencies and the privacy-enhancing technologies built on top of them. Our methods apply absorbing Markov chains combined with Shannon entropy. To the best of our knowledge, our work is the first to assess the fungibility of cryptocurrencies. Among other results, we find that in the studied one-week interval, the Bitcoin network, on average, provided comparable but quantifiably more fungibility than the Ethereum network.

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