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The Danger of Small Anonymity Sets in Privacy-Preserving Payment Systems

Unlike suggested during their early years of existence, Bitcoin and similar cryptocurrencies in fact offer significantly less privacy as compared to traditional banking. A myriad of privacy-enhancing extensions to those cryptocurrencies as well as several clean-slate privacy-protecting cryptocurrencies have been proposed in turn. To convey a better understanding of the protection of popular design decisions, we investigate expected anonymity set sizes in an initial simulation study. The large variation of expected transaction values yields soberingly small effective anonymity sets for protocols that leak transaction values. We hence examine the effect of preliminary, intuitive strategies for merging groups of payments into larger anonymity sets, for instance by choosing from pre-specified value classes. The results hold promise, as they indeed induce larger anonymity sets at comparatively low cost, depending on the corresponding strategy