No abstract

Ledger-based systems that support rich applications often suffer from two limitations. First, validating a transaction requires re-executing the state transition that it attests to. Second, transactions not only reveal which application had a state transition but also reveal the application's internal state.We design, implement, and evaluate Zexe, a ledger-based system where users can execute offline computations and subsequently produce transactions, attesting to the correctness of these computations, that satisfy two main properties. First, transactions hide all information about the offline computations. Second, transactions can be validated in constant time by anyone, regardless of the offline computation.The core of Zexe is a construction for a new cryptographic primitive that we introduce, decentralized private computation (DPC) schemes. In order to achieve an efficient implementation of our construction, we leverage tools in the area of cryptographic proofs, including succinct zero knowledge proofs and recursive proof composition. Overall, transactions in Zexe are 968 bytes regardless of the offline computation, and generating them takes less than 1 min plus a time that grows with the offline computation.We demonstrate how to use Zexe to realize privacy-preserving analogues of popular applications: private user-defined assets and private decentralized exchanges for these assets.2For example, in Zerocash the single transition function is the one governing cash flow of a single currency.

Ever since their introduction, zero-knowledge proofs have become an important tool for addressing privacy and scalability concerns in a variety of applications. In many systems each client downloads and verifies every new proof, and so proofs must be small and cheap to verify. The most practical schemes require either a trusted setup, as in (pre-processing) zk-SNARKs, or verification complexity that scales linearly with the complexity of the relation, as in Bulletproofs. The structured reference strings required by most zk-SNARK schemes can be constructed with multi-party computation protocols, but the resulting parameters are specific to an individual relation. Groth et al. discovered a zk-SNARK protocol with a universal structured reference string that is also updatable, but the string scales quadratically in the size of the supported relations.Here we describe a zero-knowledge SNARK, Sonic, which supports a universal and continually updatable structured reference string that scales linearly in size. We also describe a generally useful technique in which untrusted "helpers" can compute advice that allows batches of proofs to be verified more efficiently. Sonic proofs are constant size, and in the "helped" batch verification context the marginal cost of verification is comparable with the most efficient SNARKs in the literature.