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自从2002年Cramer和Shoup首次提出哈希证明系统(Hash Proof System)的概念以来,人们逐渐发现了其所蕴含的巨大密码学价值.作为对某一个NP语言的特殊非交互式零知识证明系统,哈希证明系统在密码学理论的发展过程中有着不可替代的作用.到目前为止,对哈希证明系统的研究依然是密码学界一个热点话题.尤其是随着后量子密码时代的到来,对具有抗量子计算攻击特性的哈希证明系统的研究显得更为重要.本文首先概述了哈希证明系统的概念、密码学用途及在传统困难假设下的一般化构造方法.然后分别给出哈希证明系统、基于身份哈希证明系统和基于属性哈希证明系统的形式化定义以及各个定义中的关键点.最后,着重对基于格困难问题构造哈希证明系统的研究现状进行了总结和梳理,分析了一些具有代表性的已有构造的特点,并指出当前基于格构造哈希证明系统的研究过程中所面临的一些问题.
Since Cramer and Shoup proposed the concept of Hash Proof System for the first time in 2002, people gradually discovered the great cryptographic value they contain.As a special non-interactive zero-knowledge proof system for a certain NP language, Hash shows that system plays an irreplaceable role in the development of cryptography theory. Up to now, the research on Hash proof system remains a hot topic in cryptology. Especially with the advent of post-quantum cryptography, The research of hash proof system against the characteristics of quantum computing attack is more important.Firstly, this paper summarizes the concept of hashing system, the usage of cryptography and the generalized construction method under the traditional assumption of difficulty.And then, System, the formal definition of identity-based hash certification system and attribute-based hash certification system, and the key points of each definition.Finally, the research status quo of constructing hash certification system based on lattice-hard problems is summarized and analyzed, and analyzed Some representative features of the existing structure, and pointed out that the current research on lattice-based hashing proof system Some problems facing the process.