基于超奇异同源的零知识证明及群签名方案  

Zero-knowledge proof and group signatures based on supersingular isogeny

作　　者：赵兴波 李梦东 王颖 朱屹霖 Zhao Xingbo;Li Mengdong;Wang Ying;Zhu Yilin(Dept.of Cryptology Science&Technology,Beijing Electronic Science&Technology Institute,Beijing 100070,China)

机构地区：[1]北京电子科技学院密码科学与技术系,北京100070

出　　处：《计算机应用研究》2022年第9期2826-2831,共6页Application Research of Computers

基　　金：教育部信息安全一流专业建设点项目。

摘　　要：Bullens等人在CSI-Fish中留下了一个开放问题,即设计一个识别协议,允许系统挑战空间是Z_(n),而不是小集合{-S,…,S}。提出了一个基于超奇异同源的零知识证明方案。该方案将挑战C作为一个同源,从而解决了这一问题,并实现了更小的稳固性误差以及公钥长度。该方案也可以通过Fiat-Shamir变换为非交互零知识证明,进而可以在量子随机预言下实现基于超奇异同源的签名方案以及群签名方案,最后分析了方案的安全性以及正确性。Bullens et al.left an open problems in CSI-Fish was to devise an identification protocol that allowed for the challenge set to be Z_(N) rather than the small set{-S,…,S}.This paper proposed a zero-knowledge proof scheme based on super-singular isogeny.This scheme addressed the open problem by taking the challenge C as an isogeny,and reduced the soundness error and the size of public key.This scheme could be turned into non-interactive zero-knowledge proof scheme using the Fiat-Shamir transform.Then signature scheme and group signature scheme based on supersingular isogeny could be implemented under the quantum random oracles model.And this paper analyzed the security and correctness of these schemes.

关 键 词：零知识证明 超奇异 同源 群签名 

分 类 号：TP393.04[自动化与计算机技术—计算机应用技术]