安全多方向量计算  

Secure Multiparty Vector Computation

作　　者：周素芳[1] 窦家维[2] 郭奕旻[1,3] 毛庆[1] 李顺东[1] 

机构地区：[1]陕西师范大学计算机科学学院,西安710062 [2]陕西师范大学数学与信息科学学院,西安710062 [3]中国科学院软件研究所可信计算与信息保障实验室,北京100190

出　　处：《计算机学报》2017年第5期1134-1150,共17页Chinese Journal of Computers

基　　金：国家自然科学基金面上项目(61272435);中央高校基本科研业务费专项资金(2016TS061)资助~~

摘　　要：安全多方计算是密码学一个重要研究方向,是国际密码学界的热点.文中研究向量问题的安全多方计算.一个向量通常由多个分量组成,每个分量可以表示不同的物理意义,因此对向量的计算,相当于同时对具有不同物理意义的分量分别计算.对向量进行高效保密计算,具有重要的理论与实际意义,因此安全多方向量计算成为安全多方计算的一个重要问题.但是该问题现在还没有直接的解决方案,现有的相关方案都是一些朴素的解决方案,即利用加法同态加密算法对向量的每个分量分别加密,然后计算所有向量分量的和,进而实现向量的计算,其效率比较低.文中利用哥德尔编码将向量和自然数一一对应,并借助语义安全乘法同态加密算法设计了一个可以直接对向量进行计算的高效保密计算方案.文中进一步将向量与多项式对应,利用NTRU加密算法设计了一种可能抵抗量子攻击的高效向量计算方案.使用安全多方计算普遍采用的模拟范例证明方法证明了这些方案在半诚实模型下是安全的.作为方案的应用,文中提出了高效的安全统计方案和高效的安全电子选举方案.Secure multiparty computation is an important field of cryptography a focus of international cryptographic community.This paper studies secure multiparty vector computation.A vector is often composed of multiple components,and each component may has different practical meaning.Therefore vector computation is equivalent to compute the components with different physical meanings at the same time.Privately and efficiently performing vector computation is of theoretical and practical significance.Therefore,secure multiparty vector computation is an important problem of secure multiparty computation.However,to the best of our knowledge,there is no direct and efficient solution to this problem.Existing protocols are trivial.These protocols implement the vectors computation using additively homomorphic encryption scheme to encrypt each component of vectors,and then to privately add the corresponding components of vectors.Such protocols are inefficient.In this study,we use G9 del number to encode a vector into a natural number,and a semantically secure and multiplicatively homomorphic encryption scheme,and then design an efficient scheme enabling direct computation of linear combinations ofvectors privately.In order to make secure multiparty vector computation scheme secure against quantum attack,we further devise an efficient protocol based on the NTRU cryptosystem,and mapping a vector to a polynomial.These schemes are proven to be secure in the semi-honest model using the simulation paradigm which is widely used in secure multiparty computation.As the applications of these protocols,we demonstrate how to use them to perform secure statistics and secure electronic elections.

关 键 词：密码学 安全多方计算 向量计算 安全统计 安全电子选举 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]