Analysis of Input-Output Mappings in Coinjoin Transactions with Arbitrary Values

A coinjoin protocol aims to increase transactional privacy for Bitcoin and Bitcoin-like blockchains via collaborative transactions, by violating assumptions behind common analysis heuristics. Estimating the resulting privacy gain is a crucial yet unsolved problem due to a range of influencing factors and large computational complexity. We adapt the BlockSci on-chain analysis software to coinjoin transactions, demonstrating a significant (10-50%) average post-mix anonymity set size decrease for all three major designs with a central coordinator: Whirlpool, Wasabi 1.x, and Wasabi 2.x. The decrease is highest during the first day and negligible after one year from a coinjoin creation. Moreover, we design a precise, parallelizable privacy estimation method, which takes into account coinjoin fees, implementation-specific limitations and users' post-mix behavior. We evaluate our method in detail on a set of emulated and real-world Wasabi 2.x coinjoins and extrapolate to its largest real-world coinjoins with hundreds of inputs and outputs. We conclude that despite the users' undesirable post-mix behavior, correctly attributing the coins to their owners is still very difficult, even with our improved analysis algorithm.