简洁非交互零知识证明综述

A survey on succinct non-interactive zero-knowledge proofs

零知识证明允许证明者向一个验证者证明一个断言的正确性而不泄漏其它任何知识。在理论层面,这一概念的提出对密码学和计算机科学都产生了深远影响。在应用层面,零知识证明以及它所衍生出来的可验证计算为近年来迅猛发展的以区块链为代表的金融科技提供数据隐私保护和去中心化的技术。近年来高效简洁非交互零知识证明(zero-knowledge Succinct Non-interactive Arguments of Knowledge,zk-SNARKs)方面的研究取得了令人瞩目的进展,其更是凭借简洁高效的特点被广泛应用于电子金融领域之中。文章主要梳理了zk-SNARKs的发展历程,并依据它们依赖的不同模型进行分类与总结。

Zero knowledge proof allows the prover to prove the correctness of a statement to a verifier without revealing any other knowledge.At the theoretical level,this concept has a profound impact on cryptography and computer science.While at the application level,zero knowledge proof and its derived verifiable computation provide data privacy protection and decentralization technology for the rapid development of financial technology represented by blockchain in recent years.In the last decade,the research on zero-knowledge succinct non-interactive arguments of knowledge(zk-SNARKs)has made remarkable progress,and it is widely used in the field of e-finance by virtue of its simplicity and efficiency.This paper surveys the development process of zk-SNARKs,and summarizes them according to the different models they rely on.