格上基于身份的分级加密方案研究

发布时间：2018-10-09 21:25

【摘要】：基于格的密码方案主要是建立在格的困难问题上的,不仅能抵御量子攻击,而且还有普通公钥密码体制不具备的优势。普通公钥密码在不同的困难问题下的困难性是不同的。而基于格建立的密码体制,其最难的问题实例的安全性与任意一般的实例的安全性是等价的。在证明安全性的问题上,可以选择任意实例。因此基于格的密码方案层出不穷,其中基于格的签名方案和加密方案尤为丰富。基于身份的加密体制在电子商务、云计算中有着重要的作用,但是随着用户身份数量的增加,证书管理问题愈见突出。格上基于身份的分级加密方案,能够更好的处理用户数量过大带来的证书管理问题,降低了开销,而且运算效率较高。文章介绍了格公钥密码的基本方法,围绕基于身份的密码体制进行讨论。关于格的相关理论进行综述,重点介绍了格的定义及格上的困难问题,盆景树原理,原像抽样函数,格基的委派算法,格基的生成算法。算法主要包括Micciancio和Peikert提出的DTrapGen陷门生成算法,以及Agrawal和Boneh提出的两个不同的SampleLeft和SampleRight算法。最后文章还研究了格上基于身份的分级加密方案,在该方案的基础上提出了新的方案。新方案利用MP12陷门生成算法和左右抽样算法,原像抽样算法,基于盆景树的原理,构建了标准模型下格上基于身份的分级加密方案。构建的新方案更加快速、高效,并且在并行计算下更容易执行。方案基于格上带误差问题学习的困难性,并给出了安全性证明。同时利用Waters的方法将方案改为自适应身份安全的基于属性的分级加密方案。本文还利用了Micciancio和Peikert的陷门委派技术,对生成的新陷门进行陷门委派,用来对2010年Agrawal和Boneh提出的固定维数和短密文的基于身份(分级)加密方案进行了优化改进,并给出了安全行证明。
[Abstract]:The lattice-based cryptosystem is mainly based on the difficult problem of lattice, which not only can resist quantum attack, but also has the advantage that the common public key cryptosystem does not have. Common public key cryptography has different difficulties under different difficult problems. The security of the most difficult instance is equivalent to that of any general instance. In the problem of proving security, we can choose any instance. Therefore, the lattice-based cryptography schemes emerge one after another, among which the lattice-based signature schemes and encryption schemes are particularly rich. ID-based encryption plays an important role in electronic commerce and cloud computing, but with the increase of the number of user identity, the issue of certificate management becomes more and more prominent. The hierarchical encryption scheme based on identity can better deal with the problem of certificate management brought by the excessive number of users, reduce the cost, and have high computational efficiency. This paper introduces the basic methods of lattice public key cryptography and discusses the identity-based cryptosystem. The related theories of lattice are summarized, and the difficult problems in defining lattice, the principle of bonsai tree, the sampling function of original image, the assignment algorithm of lattice base and the algorithm of generating lattice base are introduced emphatically. The algorithm mainly includes DTrapGen trapdoor generation algorithm proposed by Micciancio and Peikert, and two different SampleLeft and SampleRight algorithms proposed by Agrawal and Boneh. Finally, the paper studies the hierarchical encryption scheme based on identity on the lattice, and puts forward a new scheme based on the scheme. The new scheme uses MP12 trapdoor generation algorithm, left and right sampling algorithm, original image sampling algorithm, and based on the principle of bonsai tree, constructs an identity-based hierarchical encryption scheme on the grid under the standard model. The new scheme is faster, more efficient and easier to execute under parallel computing. The scheme is based on the learning difficulty of the problem with errors on the lattice, and the security proof is given. At the same time, the method of Waters is used to change the scheme to an adaptive identity secure hierarchical encryption scheme based on attributes. This paper also makes use of the trapdoor delegation technology of Micciancio and Peikert to delegate the new trapdoor, which is used to optimize and improve the ID-based (hierarchical) encryption scheme of fixed dimension and short ciphertext proposed by Agrawal and Boneh in 2010. The security proof is given.
【学位授予单位】：西安电子科技大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN918.4

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