Cryptocurrencies promise to revolutionize the financial industry, forever changing the way we transfer money. Instead of relying on a central authority (for example, a government entity or a bank) to issue and manage money, cryptocurrencies rely on the mathematical design and security proofs of the underlying cryptographic protocols. Using cryptography and distributed algorithms, cryptocurrencies offer a fully decentralized setting where no single entity can monitor or block the transfer of funds. Cryptocurrencies have grown from early prototypes to a global phenomenon with millions of participating individuals and institutions.17 Bitcoin28 was the first such currency launched in 2009 and in the years since has grown to a market capitalization of over $15 billion (as of January 2017). This has led to the emergence of many alternative cryptocurrencies with additional services or different properties as well as to a fruitful line of academic research.
Apart from its other benefits (decentralized architecture, small transaction fees, among others), Bitcoin's design attempts to provide some level of "pseudonymity" by not directly publishing the identities of the participating parities. Every user interacts with the network by establishing a public address that acts as a "pseudonymous identity." In practice, there is no bound on the number of addresses a user can create; therefore there exists no single address a user can be related with. However, this pseudonymity is far from the desired unlinkability property in centralized e-cash protocols,11 where when Alice sends an amount to Bob, the original source of these funds cannot be deduced. The reason for this problem is that in most decentralized cryptocurrencies all transaction information (payer and payee address, amount, among others) is publicly visible, stored in a distributed data structure called blockchain (for example, see www.blockchain.info). Therefore, an attacker can easily observe how money flows. This can lead to quite devastating deanomyization attacks and therefore there is a need for cryptocurrencies with stronger privacy guarantees.
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