基于安全多方计算的若干问题研究

发布时间：2019-05-20 08:43

【摘要】：在网络信息技术快速发展的今天,海量的数据资源被共享,信息安全问题逐渐成为人们关注的热点话题。一方面,企业和组织机构在发展的过程中需要保密自己的有价值数据,另一方面又要通过合作完成一些计算,获得利益。在此背景下安全多方计算(Secure Multi-party Computation, SMC)应运而生,最早由A.C YAO在1982年提出。安全多方计算一经提出就在密码学研究领域中占据重要的位置,有着广泛的研究和应用领域。在本文中,主要研究的是安全多方计算众多领域的一种——基于隐私保护的计算几何。隐私保护的计算几何的研究问题也比较多,之前的众多学者对该研究取得了骄傲的成果。所以在本文中,我们总结了前人的成果,同时在前辈的基础上,提出一些新的研究成果。主要工作如下： 1.主要介绍了安全多方计算的一些基本知识,包括问题的提出、研究的背景意义和在工程中的应用领域。我们对安全多方计算的研究做了分析和总结,介绍了安全多方计算的一些基本密码学基础以及部分基础协议。主要包括安全多方计算的安全定义、参与方模型、安全性定义、同态加密、秘密分享、零知识证明、安全比较协议、点积协议以及不经意传输等。 2.我们的重点目标是要得出线段与圆的保密关系判定,但是在提出此协议之前我们需要一些基本的协议和定理。接着我们提出了新的安全的点线、点圆位置关系的判定协议,并证明了其正确性和安全性。再然后利用之前介绍及提出的协议,提出了线段与圆的安全协议,对协议做分析,并证明了该协议的正确性和安全性。 3.提出基于隐私保护的n-凸多边形面积计算的保密协议,由三角形坐标面积公式推出了n-凸多边形的面积公式。基于茫然第三方和同态加密方案提出了凸多边形面积安全计算协议以及容忍恶意模型下的安全n-凸多边形的面积计算协议并对协议从正确性、安全性以及复杂性三个方面做了分析。
[Abstract]:With the rapid development of network information technology, massive data resources are shared, and information security has gradually become a hot topic. On the one hand, enterprises and organizations need to keep their own valuable data confidential in the process of development, on the other hand, they should complete some calculations through cooperation to obtain benefits. In this context, secure multi-party computing (Secure Multi-party Computation, SMC) emerges as the times require, which was first proposed by A.C YAO in 1982. As soon as secure multi-party computing is proposed, it occupies an important position in the field of cryptography research, and has a wide range of research and application fields. In this paper, we mainly study the computational geometry based on privacy protection, which is a kind of secure multi-party computing. There are many problems in computational geometry of privacy protection, and many scholars have made proud achievements in this research. Therefore, in this paper, we summarize the previous results, and at the same time, on the basis of the previous generation, put forward some new research results. The main work is as follows: 1. This paper mainly introduces some basic knowledge of secure multi-party computing, including the putting forward of the problem, the background significance of the research and the application field in engineering. We analyze and summarize the research of secure multi-party computing, and introduce some basic cryptography basis and some basic protocols of secure multi-party computing. It mainly includes the security definition of secure multi-party computing, participant model, security definition, homomorphism encryption, secret sharing, zero knowledge proof, security comparison protocol, dot product protocol and inadvertent transmission. 2. Our key goal is to determine the confidentiality relationship between line segments and circles, but before we propose this protocol, we need some basic protocols and theorem. Then we propose a new secure protocol for determining the relationship between point line and point circle position, and prove its correctness and security. Then, by using the protocol introduced and proposed earlier, the security protocol of line segment and circle is proposed, the protocol is analyzed, and the correctness and security of the protocol are proved. 3. A confidentiality protocol for calculating the area of n-convex polygons based on privacy protection is proposed. The area formula of n-convex polygons is derived from the triangular coordinate area formula. Based on the blank third party and homomorphism encryption scheme, the area security calculation protocol of convex polygons and the area calculation protocol of secure n-convex polygons under malicious model are proposed and correct. The security and complexity are analyzed.
【学位授予单位】：云南大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TP393.08

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