格上基于身份哈希证明系统的新型构造

隐私保护是当前大数据信息时代所亟待解决的重要安全问题。而密码学是实现对内容和身份等隐私信息进行有效保护的关键理论和技术基础之一。基于身份哈希证明系统（Identity-based hash proof system）是一个基本的密码学原型，能够用来构造多种对隐私信息进行保护的密码方案。本文通过分析得知，已有基于格的基于身份哈希证明系统的密文尺寸较大，会对所构造密码方案的效率产生较大的影响。如何降低基于格的基于身份哈希证明系统的密文尺寸，是一个有意义的研究问题。为此，本文首先基于标准带错误学习（Learning with errors，简记为LWE）困难假设，在标准模型下构造了一个新的哈希证明系统，并利用随机格上离散高斯分布与光滑参数的性质，证明其是光滑（Smooth）的；再在随机谕言机（Random oracle）的作用下，利用Gentry等人所提出的原像抽样函数提取身份私钥，从而得到一个光滑并且密文尺寸较小的基于身份哈希证明系统。作为对所构造新型哈希证明系统的扩展，本文也在标准模型下提出一个可更新的哈希证明系统。最后，详细分析本文所提出新型构造的效率，并与已有相关构造进行对比。

Novel Construction of Identity-Based Hash Proof System Based on Lattices

Privacy protection is an important security issue in this big data information times. As one of theoretic and technical bases, cryptography can be utilized to protect several kinds of privacy information, such as content and identity. Identity-based hash proof system is a basic cryptographic primitive, which can be used to construct lots of schemes for privacy protection. Through analyzing all existing identity-based hash proof systems based on lattices, we know one of their common deficiencies is the large bit size of ciphertext, which further result in the low efficiency of the related cryptographic schemes. Thus it should be of great significant for us to reduce the size of their cipheretexts. In this paper, we first present a new hash proof system basd on the learning with errors assumption in the standard model, and prove it to be smooth through employing the properties of discret Gaussian distribution and smooth parameter over lattices. Then, in order to transform this new hash proof system into the identity setting, we use the preimage sampleable function proposed by Gentry et.al. to sample the identity secret key for any identity id with the help of random oracle. As an extension for our new hash proof system based on lattices, we also modify it to be an updatable hash proof system in the standard model. Finally, we analyze the efficiency of these new constructions, and compare with other existing constructions.