Abstract-Bitcoin is the first digital currency to see widespread adoption. While payments are conducted between pseudonyms, Bitcoin cannot offer strong privacy guarantees: payment transactions are recorded in a public decentralized ledger, from which much information can be deduced. Zerocoin (Miers et al., IEEE S&P 2013) tackles some of these privacy issues by unlinking transactions from the payment's origin. Yet, it still reveals payments' destinations and amounts, and is limited in functionality.In this paper, we construct a full-fledged ledger-based digital currency with strong privacy guarantees. Our results leverage recent advances in zero-knowledge Succinct Non-interactive ARguments of Knowledge (zk-SNARKs).First, we formulate and construct decentralized anonymous payment schemes (DAP schemes). A DAP scheme enables users to directly pay each other privately: the corresponding transaction hides the payment's origin, destination, and transferred amount. We provide formal definitions and proofs of the construction's security.Second, we build Zerocash, a practical instantiation of our DAP scheme construction. In Zerocash, transactions are less than 1 kB and take under 6 ms to verify -orders of magnitude more efficient than the less-anonymous Zerocoin and competitive with plain Bitcoin.

Bitcoin is the first e-cash system to see widespread adoption. While Bitcoin offers the potential for new types of financial interaction, it has significant limitations regarding privacy. Specifically, because the Bitcoin transaction log is completely public, users' privacy is protected only through the use of pseudonyms. In this paper we propose Zerocoin, a cryptographic extension to Bitcoin that augments the protocol to allow for fully anonymous currency transactions. Our system uses standard cryptographic assumptions and does not introduce new trusted parties or otherwise change the security model of Bitcoin. We detail Zerocoin's cryptographic construction, its integration into Bitcoin, and examine its performance both in terms of computation and impact on the Bitcoin protocol.

We describe Charm, an extensible framework designed for rapid prototyping of cryptographic systems that utilize the latest advances in cryptography, such as identity and attribute-based encryption, as well as the traditional cryptographic functions. Charm is designed to minimize code complexity, promote code re-use, and to automate interoperability, while not compromising on efficiency.Charm was designed from the ground up to support the implementation of advanced cryptographic schemes. It includes support for multiple cryptographic settings, an extensive library of re-usable code, and a protocol engine to aid in the development of interactive protocols. Our framework also provides a series of specialized tools that enable different cryptosystems to interoperate.We implemented over twenty cryptographic schemes using Charm, including some new ones that to our knowledge have never been built in practice. This paper describes our modular architecture, which includes a built-in benchmarking module that we use to compare the performance of primitives written in Python to comparable C implementations. We show that in many cases our techniques result in a potential order of magnitude decrease in code size, while inducing an acceptable performance impact.

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By design, existing (pre-processing) zk-SNARKs embed a secret trapdoor in a relation-dependent common reference strings (CRS). The trapdoor is exploited by a (hypothetical) simulator to prove the scheme is zero knowledge, and the secret-dependent structure facilitates a linear-size CRS and linear-time prover computation. If known by a real party, however, the trapdoor can be used to subvert the security of the system. The structured CRS that makes zk-SNARKs practical also makes deploying zk-SNARKS problematic, as it is difficult to argue why the trapdoor would not be available to the entity responsible for generating the CRS. Moreover, for pre-processing zk-SNARKs a new trusted CRS needs to be computed every time the relation is changed. In this paper, we address both issues by proposing a model where a number of users can update a universal CRS. The updatable CRS model guarantees security if at least one of the users updating the CRS is honest. We provide both a negative result, by showing that zk-SNARKs with private secret-dependent polynomials in the CRS cannot be updatable, and a positive result by constructing a zk-SNARK based on a CRS consisting only of secret-dependent monomials. The CRS is of quadratic size, is updatable, and is universal in the sense that it can be specialized into one or more relation-dependent CRS of linear size with linear-time prover computation.