【摘要】：信息安全問(wèn)題是信息社會(huì)最大的威脅之一,作為解決信息安全問(wèn)題的重要工具,多方保密計(jì)算引起了人們的高度關(guān)注。多方保密計(jì)算是指擁有秘密輸入的兩個(gè)或多個(gè)用戶(hù),希望在不泄露各自私有信息的前提下合作執(zhí)行某項(xiàng)計(jì)算任務(wù),其在科學(xué)計(jì)算、幾何計(jì)算等方面有廣泛應(yīng)用。本文主要對(duì)科學(xué)計(jì)算、幾何計(jì)算中的兩個(gè)基礎(chǔ)問(wèn)題進(jìn)行深入研究,并設(shè)計(jì)了若干應(yīng)用于特定領(lǐng)域的協(xié)議。首先研究了向量差的范數(shù)問(wèn)題,基于同態(tài)加密技術(shù)和安全兩方置換技術(shù)設(shè)計(jì)了保密計(jì)算向量差的范數(shù)協(xié)議,由于此協(xié)議不適用于二維向量,因此基于Clifton所構(gòu)造的內(nèi)積協(xié)議的思想設(shè)計(jì)了另一種保密計(jì)算向量差的范數(shù)協(xié)議。其次研究了百萬(wàn)富翁問(wèn)題,總結(jié)和分析了該問(wèn)題的現(xiàn)有解決方案,針對(duì)存在的效率較低的問(wèn)題,提出了改進(jìn)方案。隨后,基于數(shù)據(jù)偽裝技術(shù)和同態(tài)加密算法提出了新的百萬(wàn)富翁協(xié)議。與以往方案相比,本文的兩種方案都減少了加解密次數(shù)和模乘模冪運(yùn)算總次數(shù),提高了方案的效率。最后基于向量差的范數(shù)協(xié)議,解決了兩個(gè)應(yīng)用問(wèn)題——保密計(jì)算高維空間平行四邊形面積問(wèn)題和數(shù)據(jù)對(duì)應(yīng)成比例問(wèn)題;基于百萬(wàn)富翁協(xié)議,解決了三個(gè)應(yīng)用問(wèn)題——向量?jī)?yōu)勢(shì)統(tǒng)計(jì)問(wèn)題、兩矩形位置關(guān)系判定問(wèn)題和整除問(wèn)題。設(shè)計(jì)了相應(yīng)的協(xié)議,并對(duì)協(xié)議進(jìn)行了正確性分析、安全性證明和效率分析。通過(guò)對(duì)比分析表明本文協(xié)議的安全性更強(qiáng),效率更高。
[Abstract]:The problem of information security is one of the greatest threats in the information society. As an important tool to solve the problem of information security, multi-party confidential computing has attracted great attention. Multi-party secure computing refers to two or more users who have secret input and hope to cooperate in carrying out a certain computing task without revealing their private information. It is widely used in scientific calculation geometric calculation and so on. In this paper, two basic problems in scientific computation and geometric computation are studied in depth, and some protocols applied in specific fields are designed. Firstly, the norm problem of vector difference is studied. Based on homomorphic encryption technique and secure two-party permutation technique, the norm protocol for secret computation of vector difference is designed, because this protocol is not suitable for two-dimensional vector. Therefore, based on the idea of inner product protocol constructed by Clifton, another norm protocol for secret computation of vector difference is designed. Secondly, the millionaire problem is studied, and the existing solutions to the problem are summarized and analyzed. Then, a new millionaire protocol based on data camouflage and homomorphic encryption algorithm is proposed. Compared with the previous schemes, the two schemes in this paper reduce the number of encryption and decryption and the total number of modular multiplication and modular power operations, and improve the efficiency of the scheme. Finally, based on the norm protocol of vector difference, two application problems are solved, namely, the problem of secure computation of parallelogram area in high-dimensional space and the problem of corresponding proportion of data, and the problem based on millionaire protocol. Three application problems are solved, namely, vector dominant statistics problem, two rectangular position relation decision problem and integral division problem. The corresponding protocol is designed, and the correctness analysis, security proof and efficiency analysis of the protocol are carried out. The comparison and analysis show that the protocol is more secure and efficient.
【學(xué)位授予單位】：西安科技大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：TP309

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本文編號(hào)：2289239