基于ECC的同态加密算法研究与改进

发布时间：2018-06-27 06:32

本文选题：云计算 + 数据安全　；参考：《中北大学》2017年硕士论文

【摘要】：随着一个大规模的生成、共享、利用数据的时代正在接近,数据安全中包括的隐私保护问题,已经成为当前云计算所遇到的重大安全挑战。通过合理有效的方法保护个人隐私与数据安全成为当今信息安全领域研究的重点,这涉及到数据的保密计算,是云环境中最关键的问题。在数据安全问题方面,近些年来,许多研究者均做了大量分析与探索。与以往普通的加密技术不同,在安全的云存储和云计算中使用同态加密技术,是解决其数据安全问题的一项重要技术。但是,目前基于公钥密码体制的同态加密方法计算效率低,普遍存在公钥尺寸过大和计算复杂度较高的缺点,为解决这一问题,提出一种改进的同态加密方法。本文的主要工作如下:(1)基于椭圆曲线的相关理论研究。给出椭圆曲线加密相应理论基础,包括有限域、点加、倍点等相关知识。并对其安全性能进行分析。最后介绍的是其加密步骤,为基于ECC的同态加密算法实现提供依据。(2)标量乘运算基本算法。重点描述二进制法、NAF法、Comb法、窗口法等。对其各自的特点进行分析。通过传统标量乘算法在存储空间与计算性能方面的分析和比较,为基于ECC的同态加密算法实现提供依据。(3)提出一种基于ECC的同态加密改进算法。在本文中规定了k的生成方法。这样可以有效提高其运算效率。同时结合二进制法与窗口法的优势,使得运算中平均点加数仅为传统法14.69%。提出一种基于ECC的同态加密改进算法。在其算法基础上,构造出加法、乘法两种同态加密方法。通过实验结果分析可知本文算法在加法同态运算与乘法同态运算中的耗时明显低于传统二进制法,使得运算效率有显著提高且降低存储空间。(4)通过对基于ECC的同态加密算法进行实验分析。通过对比试验效果、从点加及点乘次数、分析实验所用时间、数据结果图表等。在保证安全性的同时,显著提高了同态加密方法的计算效率,同时分析了方法中各项参数对加解密效率的影响。理论分析与实验结果均证明,该方法具有较高的安全性,在计算性能上是一种高效的方法。
[Abstract]:With a large-scale generation, sharing, the use of data is approaching the era, data security, including privacy protection, has become a major security challenge to cloud computing. To protect personal privacy and data security through reasonable and effective methods has become the focus of research in the field of information security, which involves the confidential calculation of data, and is the most critical problem in the cloud environment. In data security, in recent years, many researchers have done a lot of analysis and exploration. Different from the common encryption technology in the past, the application of homomorphic encryption in secure cloud storage and cloud computing is an important technology to solve the problem of data security. However, the computation efficiency of homomorphic encryption based on public key cryptosystem is low, and the shortcomings of large size of public key and high computational complexity are common. In order to solve this problem, an improved homomorphic encryption method is proposed. The main work of this paper is as follows: (1) theoretical research based on elliptic curve. The theoretical basis of elliptic curve encryption is given, including the knowledge of finite field, point addition, point doubling and so on. And its security performance is analyzed. Finally, the encryption steps are introduced, which provide the basis for the realization of the homomorphic encryption algorithm based on ECC. (2) the basic algorithm of scalar multiplication. The binary method NAF method Comb method, window method and so on are described in detail. Their respective characteristics are analyzed. By analyzing and comparing the storage space and computing performance of the traditional scalar multiplication algorithm, this paper provides the basis for the implementation of the homomorphic encryption algorithm based on ECC. (3) an improved algorithm of homomorphic encryption based on ECC is proposed. The generation method of k is defined in this paper. In this way, the computational efficiency can be improved effectively. At the same time, combining the advantages of binary method and window method, the addition of average point in operation is only 14.69. An improved homomorphic encryption algorithm based on ECC is proposed. On the basis of its algorithm, two homomorphic encryption methods, addition and multiplication, are constructed. The experimental results show that the time consuming of this algorithm in addition homomorphism operation and multiplication homomorphism operation is obviously lower than that in traditional binary method. The computational efficiency is improved significantly and the storage space is reduced. (4) the experimental analysis of the homomorphic encryption algorithm based on ECC is carried out. By comparing the results of the experiment, the time used in the experiment and the chart of the data are analyzed from the point addition and the times of point multiplication. At the same time, the computation efficiency of homomorphic encryption method is improved significantly, and the influence of the parameters on the efficiency of encryption and decryption is analyzed. The theoretical analysis and experimental results show that this method has high security and is an efficient method in computing performance.
【学位授予单位】：中北大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP309.7

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