云环境下多方保密计算最大值、最小值及其统计学应用  

Secure Multiparty Computation of the Maximum and the Minimum in Cloud Environment and Its Statistics Application

作　　者：李占利[1] 陈立朝 陈振华[1] 刘娅茹 LI Zhan-Li;CHEN Li-Chao;CHEN Zhen-Hua;LIU Ya-Ru(College of Computer Science and Technology,Xi’an University of Science and Technology,Xi’an 710054,China)

机构地区：[1]西安科技大学计算机科学与技术学院,西安710054

出　　处：《密码学报》2019年第2期219-233,共15页Journal of Cryptologic Research

基　　金：国家自然科学基金(U1261114)

摘　　要：安全多方计算是近年来密码学的研究热点,本文主要研究保密科学计算中最值(最大值、最小值)问题的安全多方计算,关于该问题现有的解决方案不多,而且目前尚未出现架构在云计算环境下的解决方案.针对此问题,本文首先对保密数据进行0-1编码,使得保密数据隐藏于所编码的0-1数组中,然后利用多密钥NTRU全同态加密算法,分别设计了在云计算环境下解决最大值、最小值问题的协议,并且,在半诚实模型下,利用模拟范例的方法,对本文提出协议的安全性进行了证明.本文分析表明:在性能方面,和以往协议相比,本文提出的的最大值、最小值解决方案,不仅是首次架构在云计算环境下的解决方案,而且该方案还可以抗量子攻击;在效率方面,由于本文构造的协议都架构在云计算平台上,这能为用户节省大量的计算成本,所以本文给出的协议取得了更高的效率.最后,本文将设计的两个新协议应用在统计学领域,解决了一个新问题—多方保密计算极差问题,该方案简洁安全.Secure multiparty computation becomes a cryptography research hotspot in recent years.This work mainly studies how to compute the maximum and minimum values securely for some privately input numbers.This is a problem of private-preserving scientific computation.However,so far,very few results are known,and there are no solutions designed for the cloud computing environment.Aiming at these issues,we first adopt 0-1 encoding to encode a private number into an array.This coding technique can hide the confidential data in the array encoded with 0-1.The protocols to compute the maximum and the minimum values are designed by using the multikey NTRU fully homomorphic encryption algorithm in cloud environment.The security of the proposed protocols in this study is analyzed in the semi-honest model,the security proof utilizes the method of simulation paradigm.It is the first time to construct secure computation protocols for the maximum and the minimum values in cloud computing environment,and the solutions can also resist quantum attack.The schemes designed in this study have been adapted to the cloud environment,which can save a large amount of computation cost for users.Finally,the proposed protocols are applied to statistics,and a new problem about the secure multiparty computation of range problem is solved.The solution is simple and secure.

关 键 词：安全多方计算 同态加密 云环境 最大值、最小值 极差 

分 类 号：TN918[电子电信—通信与信息系统]