空间几何对象相对位置判定中的私有信息保护

保护私有信息的计算几何是一类特殊的安全多方计算问题，它是指在一个互不信任的多用户网络中，几个用户基于各自输入的几何信息共同协作来完成某项可靠的计算任务，但任何一个用户都不愿意向其他用户暴露自己的输入，该问题在协作进行太空开发等领域有着重要的应用前案．秘密判定两组数据是否对应成比例是安全多方计算的一个基本问题，在判定空间几何对象相对位置关系中起着重要作用．设计了判断两组数据是否对应成比例的秘密判定协议；分析了该协议的正确性、安全性及复杂性；在保护用户私有输入信息的条件下，解决了空间中点、直线、平面等几何对象之间的相对位置判定问题．

Privacy Protection in the Relative Position Determination for Two Spatial Geometric Objects

Privacy-preserving computational geometry is a special secure multi-party computation problem. It can be defined as the problem of several users computing a cooperative task of their geometric input in a distributed network, where no user is willing to disclose his secret inputs to anyone else. This problem may be applied in the field of research and exploitation of the outer space. Private determination of whether two sets of data are proportional correspondingly is a basic problem of secure multi party computation, and it also plays an important role in the relative position determination for two spatial geometric objects. In this paper, a protocol for determining whether two sets of data are proportional correspondingly is developed, its correctness, security and efficiency are analyzed, and the corresponding algorithms for determining the relative position of spot, line and plane in space are also presented.