同态密码理论的研究与应用

发布时间：2018-05-19 23:41

本文选题：全同态密码体制 + 单同态密码体制　；参考：《西安电子科技大学》2014年硕士论文

【摘要】：随着云计算和大数据的飞速发展，数据存储与分析的安全性得到了普遍重视。同态密码以其能够对经过该体制加密的数据进行分析和处理的特性，成为保护数据安全，提高密文分析能力的关键技术。本文对常见公钥码体制的同态性进行了分析和改进，研究其应用价值。通过对基于整数环的全同态加密体制实现过程的分析，设计了改进版的基于整数的全同态密码体制。主要做了以下工作： 1.提出了常见密码体制的同态性分析方法和同态密码体制的分类方法，进而给出了公钥密码体制（RSA，Paillier，ElGamal，Bresson，NTRU）同态性的详细分析和分类。然后，基于单一同态密码体制设计了无线自组网组密钥管理方案和具有双同态性质的云计算方案。组密钥管理方案适用于面向群组和拓扑易变的网络，同态加密特性使其具备较高的效率和安全性。双同态云计算方案支持加法和乘法计算，实现了公有云服务器的密文处理，满足了云计算环境下多种计算形式的需求。 2.在对ElGamal密码体制同态特性分析的基础上，设计了一种ElGamal变体，该变体满足加法同态和常数乘法同态，且在随机预言机模型下证明了其安全性。然后，基于该变体设计了过私有点直线方程的安全两方计算协议，在半诚实模型下，该协议的安全性得到了证明。同时，将该协议扩展到了其他安全多方计算问题中。与传统协议相比，同态密码体制的引入使其具有更高的执行效率，降低了通信负担。 3.对Gentry等提出的基于整数的全同态加密体制实现技术进行了分析，研究了其提到的电路压缩算法， Somewhat同态加密算法以及如何通过自举技术实现全同态的过程。然后，结合Gentry全同态密码算法的构造思想和技术，提出了改进的基于整数的全同态密码体制，并对其正确性和安全性进行了证明。最后，对本文所做的工作进行了系统的总结，指出了同态加密领域需要进一步研究的问题。
[Abstract]:With the rapid development of cloud computing and big data, the security of data storage and analysis has been paid more and more attention. Homomorphic cryptography has become a key technology to protect data security and improve the ability of ciphertext analysis because of its ability to analyze and process encrypted data. In this paper, the homomorphism of common public key code systems is analyzed and improved, and its application value is studied. Based on the analysis of the implementation process of full homomorphic encryption based on integer ring, an improved integer based full homomorphic cryptosystem is designed. The main tasks are as follows: 1. The homomorphism analysis method of common cryptographic systems and the classification method of homomorphic cryptosystems are presented. Furthermore, the detailed analysis and classification of homomorphism of public key cryptosystems are given. Then, based on a single homomorphic cryptosystem, a group key management scheme for wireless ad hoc networks and a cloud computing scheme with double homomorphism are designed. The group key management scheme is suitable for group-oriented and topological networks with high efficiency and security due to homomorphic encryption. The dual-homomorphic cloud computing scheme supports addition and multiplication computing and implements ciphertext processing of public cloud servers which meets the needs of various computing forms in cloud computing environment. 2. Based on the analysis of the homomorphism of ElGamal cryptosystem, a ElGamal variant is designed, which satisfies the additive homomorphism and the constant multiplicative homomorphism, and proves its safety under the stochastic prophecy model. Then, based on this variant, a secure two-party computing protocol is designed, and the security of the protocol is proved under the semi-honest model. At the same time, the protocol is extended to other secure multi-party computing problems. Compared with the traditional protocol, homomorphic cryptosystem has higher execution efficiency and lower communication burden. 3. This paper analyzes the implementation technology of full homomorphism encryption based on integer proposed by Gentry et al, and studies the circuit compression algorithm, Somewhat homomorphic encryption algorithm and how to realize full homomorphism by bootstrap technology. Then, combining with the construction idea and technology of Gentry homomorphic cipher algorithm, an improved integer based full homomorphic cryptosystem is proposed, and its correctness and security are proved. Finally, the work done in this paper is summarized systematically, and some problems need further study in the field of homomorphic encryption are pointed out.
【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】：TN918.1

【共引文献】