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

TL;DR

This work tackles the open problem of quantifying privacy in coinjoin transactions with arbitrary input values. It extends BlockSci to detect post-mix consolidations and introduces a fee-aware, mapping-enumeration framework that models $T=(I,O,v)$ and uses entropy-based metrics, including $E(T) = -\sum_{M} p(M) \log p(M)$, to assess anonymity. The authors show that post-mix anonymity loss peaks within the first day and stabilizes over time, with Wasabi 2.x displaying the strongest long-run privacy resilience among the designs studied. A Bayesian form of mapping probability, along with a conservative user-centric metric $p(I,o)$, enables principled estimation of attribution risk, and empirical results on emulated and real Wasabi 2.x coinjoins demonstrate that large real-world coinjoins may still offer substantial privacy under realistic constraints.

Abstract

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.

Figures (5)

• Figure 1: An example of a coinjoin with arbitrary output denominations, without fees and with 4 of 24 possible input-output mappings visualized.
• Figure 2: Anonymity set loss over time for Whirlpool, Wasabi 1.x, and Wasabi 2.x as a result of users' post-mix actions within a specific time interval. The darkest part marks the remaining fraction of the initial anonymity set. For Wasabi 2.x, the last sub-figure also shows the Q1 and Q3 quartiles. The anonymity set loss is averaged over all output denominations of coinjoins created at a given time.
• Figure 3: Number of numeric mappings for different sizes of coinjoins. The size is defined as the sum of the number of inputs and outputs. The trend line shows how the number of numeric mappings grows with size. The y-axis is logarithmic.
• Figure 4: Distribution of the number of possible output selections and the order of the matching output.
• Figure 5: Anonymity set loss for Wasabi 1.x, Whirlpool and Wasabi 2.x for different output denominations. All graphs have a y-axis range from 40% to 100%.

Theorems & Definitions (2)

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