多方保密计算中基础协议及其应用研究

发布时间：2018-10-23 12:29

【摘要】：信息安全问题是信息社会最大的威胁之一,作为解决信息安全问题的重要工具,多方保密计算引起了人们的高度关注。多方保密计算是指拥有秘密输入的两个或多个用户,希望在不泄露各自私有信息的前提下合作执行某项计算任务,其在科学计算、几何计算等方面有广泛应用。本文主要对科学计算、几何计算中的两个基础问题进行深入研究,并设计了若干应用于特定领域的协议。首先研究了向量差的范数问题,基于同态加密技术和安全两方置换技术设计了保密计算向量差的范数协议,由于此协议不适用于二维向量,因此基于Clifton所构造的内积协议的思想设计了另一种保密计算向量差的范数协议。其次研究了百万富翁问题,总结和分析了该问题的现有解决方案,针对存在的效率较低的问题,提出了改进方案。随后,基于数据伪装技术和同态加密算法提出了新的百万富翁协议。与以往方案相比,本文的两种方案都减少了加解密次数和模乘模幂运算总次数,提高了方案的效率。最后基于向量差的范数协议,解决了两个应用问题——保密计算高维空间平行四边形面积问题和数据对应成比例问题;基于百万富翁协议,解决了三个应用问题——向量优势统计问题、两矩形位置关系判定问题和整除问题。设计了相应的协议,并对协议进行了正确性分析、安全性证明和效率分析。通过对比分析表明本文协议的安全性更强,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.
【学位授予单位】：西安科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP309

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