向量等分量数的保密计算及应用  

Securely Computing Equal Components of Private Vectors and Its Applications

作　　者：窦家维[1] 陈明艳 成雯 DOU Jia-Wei;CHEN Ming-Yan;CHENG Wen(School of Mathematics and Information Science,Shaanxi Normal University,Xi’an 710119,China;School of Computer Science,Shaanxi Normal University,Xi’an 710119,China)

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710119 [2]陕西师范大学计算机科学学院,陕西西安710119

出　　处：《软件学报》2022年第5期1907-1921,共15页Journal of Software

基　　金：国家自然科学基金(61272435)。

摘　　要：随着信息技术的快速发展,在保护数据隐私的条件下进行多方合作计算变得越来越普及,安全多方计算已经成为解决这类保密计算问题的核心技术.向量的保密计算是安全多方计算的重要研究方向,目前有很多研究成果,包括保密计算向量的点积,保密的向量求和等.但关于保密计算向量等分量数的研究成果还很少,且主要研究向量分量在有全集限制下的两方保密计算问题.主要研究多方参与者隐私向量的等分量数以及相关阈值的安全计算问题.首先针对向量设计了分量-矩阵编码方法,结合ElGamal门限加密系统,构造了多方向量等分量数保密计算协议.进一步以向量等分量数保密计算协议为基础,研究设计了多方向量等分量数阈值问题保密计算协议.所有向量分量没有全集的限制.应用模拟范例方法对文中所有协议的安全性进行了严格证明.效率分析和实验验证表明设计的协议是简单高效的.最后,将所设计的协议应用于解决一些实际安全计算问题.With the rapid development of the information technology,it becomes more and more popular that multiparty performs cooperative computation on their private data while preserving their privacy.Secure multiparty computation is a key privacy-preserving technology to address such security issues.The secure vector computation is an active area of secure multiparty computation.At present,there are many researches into secure vector computation such as private scalar product and private vector summation.There are few researches on securely computing the number of equal components of private vectors.These researches focus on secure two-party computation that all the components of vectors are drawn from a restricted range.This study focuses on privately computing the number of equal component of vectors and determining the relationship between the number and a threshold value.To this end,a componentmatrix encoding is firstly proposed to encode a component of a vector.Then based on the ElGamal cryptosystem,a simple and efficient secure multiparty protocol is designed to compute number of equal components of vectors.Based on this protocol,an efficient secure multiparty protocol is designed to determine whether the number of equal components of vectors is larger than a threshold.The protocols do not restrict the data range of components.The correctness of the protocols is analyzed and it is proved that they are secure in the semihonest model.Theoretical efficiency analysis and experimental result show that these protocols are simple and efficient.Finally,these protocols are used as building block to solve some practical secure multiparty computation problems.

关 键 词：密码学 安全多方计算 向量等分量数 同态加密 编码方法 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]