点包含问题的安全多方计算

摘要

安全多方计算是近年来国际密码学界研究的热点问题,计算几何的多方保密计算越来越受到重视,点包含问题的多方保密计算作为保密计算几何中的一个重要问题也越来越受到关注.考虑到要保密地解决点包含的问题,基于安全多方计算的几个基础协议,即向量点积协议和姚式百万富翁协议,设计了一个可以保密判断线段是否相交的协议,基于此协议的核心思想同时联系相关几何知识,设计了可以保密判断点包含问题的协议,理论分析结果表明所设计的协议在半诚实模型下是正确的和安全的.它们作为重要的安全多方计算基础协议对解决保密计算几何其他相关问题有着重要的实用价值,可以用来进一步解决两个或多个图形是否相交的问题、多个点是否包含在一个图形中的问题等.%Secure multi-party computation is one of the hot spots in international cryptography research community in recent years,and more and more attention has been paid to the secure computational geometry.As an important problem of secure computational geometry,more interests have been paid on point-inclusion problem.A secure protocol for determining whether two segments are intersecting with several basic protocols,Scalar Product Protocol and Yao's Millionaire's Protocol,has been developed.Thus based on core of the protocol designed and related geometric knowledge,a secure protocol to solve the point-inclusion problem has been developed.Theoretical analysis results show that these two protocols are correct and secure under semi honest model.As a part of important secure multi-party computational protocols,they both imply important practical value in solving the problem of secure multi-party computational geometry and can be used to solve the problems,whether two or more graphics are intersected and whether multiple points are contained in a graphic etc..