【摘要】：在網(wǎng)絡(luò)信息技術(shù)快速發(fā)展的今天,海量的數(shù)據(jù)資源被共享,信息安全問題逐漸成為人們關(guān)注的熱點(diǎn)話題。一方面,企業(yè)和組織機(jī)構(gòu)在發(fā)展的過程中需要保密自己的有價(jià)值數(shù)據(jù),另一方面又要通過合作完成一些計(jì)算,獲得利益。在此背景下安全多方計(jì)算(Secure Multi-party Computation, SMC)應(yīng)運(yùn)而生,最早由A.C YAO在1982年提出。安全多方計(jì)算一經(jīng)提出就在密碼學(xué)研究領(lǐng)域中占據(jù)重要的位置,有著廣泛的研究和應(yīng)用領(lǐng)域。 在本文中,主要研究的是安全多方計(jì)算眾多領(lǐng)域的一種——基于隱私保護(hù)的計(jì)算幾何。隱私保護(hù)的計(jì)算幾何的研究問題也比較多,之前的眾多學(xué)者對(duì)該研究取得了驕傲的成果。所以在本文中,我們總結(jié)了前人的成果,同時(shí)在前輩的基礎(chǔ)上,提出一些新的研究成果。主要工作如下： 1.主要介紹了安全多方計(jì)算的一些基本知識(shí),包括問題的提出、研究的背景意義和在工程中的應(yīng)用領(lǐng)域。我們對(duì)安全多方計(jì)算的研究做了分析和總結(jié),介紹了安全多方計(jì)算的一些基本密碼學(xué)基礎(chǔ)以及部分基礎(chǔ)協(xié)議。主要包括安全多方計(jì)算的安全定義、參與方模型、安全性定義、同態(tài)加密、秘密分享、零知識(shí)證明、安全比較協(xié)議、點(diǎn)積協(xié)議以及不經(jīng)意傳輸?shù)取?2.我們的重點(diǎn)目標(biāo)是要得出線段與圓的保密關(guān)系判定,但是在提出此協(xié)議之前我們需要一些基本的協(xié)議和定理。接著我們提出了新的安全的點(diǎn)線、點(diǎn)圓位置關(guān)系的判定協(xié)議,并證明了其正確性和安全性。再然后利用之前介紹及提出的協(xié)議,提出了線段與圓的安全協(xié)議,對(duì)協(xié)議做分析,并證明了該協(xié)議的正確性和安全性。 3.提出基于隱私保護(hù)的n-凸多邊形面積計(jì)算的保密協(xié)議,由三角形坐標(biāo)面積公式推出了n-凸多邊形的面積公式。基于茫然第三方和同態(tài)加密方案提出了凸多邊形面積安全計(jì)算協(xié)議以及容忍惡意模型下的安全n-凸多邊形的面積計(jì)算協(xié)議并對(duì)協(xié)議從正確性、安全性以及復(fù)雜性三個(gè)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.
【學(xué)位授予單位】：云南大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：TP393.08

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