Zero-Knowledge Proof for Blockchain

Abstract

Privacy preservation is an important topic in the advances of blockchain. Zero-knowledge proof (ZKP) has long been used to achieve zero leakage of private information. Mainly, zk-SNARKs (a variant of ZKP) have been extensively studied and tentatively deployed in building crypto-currencies due to their concise proofs and verification times.} This chapter dives deeply into the study of zero-knowledge proof system. It first reviews the background and knowledge of zero-knowledge. Specifically, it shows sequential instructions to build zk-SNARKs in the generic method. This chapter then reviews three notable works of zero-knowledge proof: GS08, GR16 and CA07 schemes. Concretely, GS08 scheme exploits bilinear maps to build efficient non-interactive zero-knowledge proof. GR16 scheme gives tentative answer to how efficient pairing-based succinct non-interactive arguments of knowledge can be. CA17 scheme investigates two main shortcomings and countermeasure of proposals for ZKCP (a zero-knowledge proof based service). The review of the above schemes helps readers gain empirical knowledge of designing and analyzing ZKP schemes. Finally, this chapter reviews the practical implementation of zk-SNARK in Zcash, its performance and other associated problems. This chapter is summarized as follows: (1) It is not trivial to generate a zk-SNARK. The reader should devote hard works in learning what zk-NARKs is about and how it works. (2) Current ZKP schemes quickly develop and extend to various research fields}. The analysis of ZKP scheme generally does not involve complex or skilled proof techniques. However, to fully figure out the meanings of many notations and terms, the reader} ought to follow specific research line and keep track of relevant works. (3) Due to complex and sophisticated design, it is generally infeasible to derive practical zk-SNARK. Meanwhile, the assumption of an honest setup or entity to initiate system parameter contradicts blockchain&s;s decentralization. Therefore, a true ZKP scheme or variant (like zk-SNARK) designed for blockchain should overcome the above problems.