## 3 Linkability of Transactions  
Once an adversary has established a list of active entities on the Bitcoin network, he may continuously update this list based on incoming new transactions. Whenever he observes that two (or more) public keys associated with purportedly different entities appear as input in one transaction at the same time, he can merge all these entities into a new entity, as the transaction must have been authorized by the same economically active person or institution. We call such an event a \"merging event\". Every merge operation indicates a successful attack on unlinkability: a passive adversary who looks at the block chain can be certain that all merged transactions were authorized by the same entity. For individuals participating in Bitcoin, it is advisable to maintain several independent entities and avoid merging events. This limits linkability of transactions and increases the anonymity set.  
Despite the availability of all transaction data, one must be very careful when trying to establish links between addresses. Some Bitcoin services are designed to obfuscate the ownership of bitcoins, such as laundries and mixers. Other services, namely online wallets, do not promise enhancing the privacy of Bitcoin, but nevertheless make it more difficult to trace bitcoins. Typically these services work as follows: Some user \(X\) sends bitcoins to the service using address \(A\) and can then use this service to send coins to another address \(B\). While the user \"owns\" address \(A\), he most likely owns none of the addresses \(C_{n}\) that are used to send coins to address \(B\). Associating the addresses \(C_{n}\) with user \(A\) would be a wrong conclusion, as those addresses actually belong to one or more different user(s) or the wallet service itself.  
Figure 9 shows a two-dimensional histogram of the number of such merging events depending on date and the total number of merged public keys. As the most used public keys account for a significant portion of the network activity (_cf._ Figure 8), the number of merging events increased drastically. Also, there is a hot spot around the time of the hype (June/July 2011). This can probably be explained by users transferring a significant fraction of their bitcoins to another address, most likely because they sold  
Figure 8: Total number of transactions (logarithmic scale).  
them in exchange for fiat currency at this time. When considering the public keys assigned to an entity for the first time before and after block 180,000 (13 May 2012), we note that the number of public keys that received a single so-called satoshi (\(1\times 10^{-8}\) bitcoins, currently the smallest unit that can be used) greatly increased. Most of them can be attributed to the SatoshiDice game (receiving a satoshi signals a loss to a player). Before the said block, those public keys only made about 0.08% of all newly assigned public keys, whereas after this time this value increased to 1.12%. This also leads to the conclusion that SatoshiDice has a big influence on the number of merging events: Outputs consisting of tiny (or even, as in this case, smallest possible) amounts can, in almost all cases, only be used as a combined input.