摘要: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之一.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.基于身份的哈希证明系统（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.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.如何降低格上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，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，证明其是光滑的（smooth）；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的哈希证明系统.作为对所构造的新型哈希证明系统的扩展，在标准模型下提出一个可更新的哈希证明系统.最后，详细分析所提出的新型构造的效率，并与已有相关构造进行对比.



Abstract:Privacy protection is an important security issue in today's big data information era. As one of theoretical 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, this work reveals that one of their common deficiencies is the large bit size of ciphertext, which further results in the low efficiency of the related cryptographic schemes. Thus it is of great significance to reduce the size of their cipheretexts. In this paper, a new hash proof system is first presented based on the learning with errors assumption in the standard model, and the smoothness of the system is proved through employing the properties of discrete Gaussian distribution and smooth parameter over lattices. Then, in order to transform this new hash proof system into the identity setting, the preimage sampling function proposed by Gentry, et al. is used to sample the identity secret key for any identity id with the help of random oracle. As an extension for this new hash proof system based on lattices, an updatable hash proof system can also be obtained in the standard model. Finally, the efficiency of these new constructions is analyzed, and a comparison with other existing constructions is performed.



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