隐私保护整数区间位置关系判定问题  

Private-preserving determination problem of integer-interval positional relationship

作　　者：马敏耀 刘卓[1,2] 徐艺 吴恋[1,2] MA Minyao;LIU Zhuo;XU Yi;WU Lian(School of Mathematics and Big Data,Guizhou Education University,Guiyang Guizhou 550018,China;Key Laboratory of Cyberspace Security,Guizhou Education University,Guiyang Guizhou 550018,China)

机构地区：[1]贵州师范学院数学与大数据学院,贵阳550018 [2]贵州师范学院网络空间安全重点实验室,贵阳550018

出　　处：《计算机应用》2020年第9期2657-2664,共8页journal of Computer Applications

基　　金：贵州省科学技术基金计划项目(黔科合基础[2016]1115,黔科合基础[2019]1249);国家科技部和国家自然科学基金奖励补助项目(黔科合平台人才[2017]5790-09);贵州省教育厅青年科技人才成长项目(黔教合KY字[2017]210,黔教合KY字[2018]260);贵州省省级重点学科“计算机科学与技术”(ZDXK[2018]007);贵州省省级重点支持学科“计算机应用技术”(黔学位合字ZDXK[2016]20);贵州师范学院专业建设项目“计算机科学与技术”(贵师院发[2018]99)。

摘　　要：整数区间是指区间的左右端点都是整数,由左右端点及它们之间的所有整数构成的集合。整数区间的位置关系是指两个整数区间在数轴上的位置的相对关系。针对整数区间位置关系提出一种安全两方计算问题,即隐私保护整数区间位置关系判定问题,该问题旨在帮助拥有隐私整数区间的两个用户,在保护输入隐私的前提下,正确地判断出他们的整数区间的位置关系。定义了整数区间的6种位置关系,给出了整数区间的0-1编码方案,并证明了整数区间位置关系的一种判定准则。基于Goldwasser-Micali加密体制在半诚实攻击者模型下设计了解决整数区间位置关系判定问题的一个两方计算协议,证明了协议的正确性和安全性,并对协议的性能进行了分析和说明。Integer-interval means the set of the left and right endpoints of the interval(which are integers)and all integers between them.The positional relationship between integer-intervals is the relation between the positions of two integer-intervals.Aiming at the positional relationship between integer-intervals,a secure two-party computation problem was proposed,in other words,a private-preserving determination problem of integer-interval positional relationship was proposed.In this problem,two users with private-preserving integer-intervals were helped to correctly determine the positional relationship between the two integer-intervals of them with the private preserved.Six positional relationships between two integer-intervals were defined,the 0-1 coding scheme of integer-intervals was given,and a determination rule for integer-interval positional relationship was proved.Then,based on the Goldwasser-Micali cryptosystem and semi-honest attacker model,a secure two-party computation protocol for solving the private-preserving determination problem of integerinterval positional relationship was designed.The protocol was proved to be both correct and secure,and the performance of the protocol was analyzed and explained.

关 键 词：区间位置 整数 隐私保护 安全多方计算 同态加密 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]