中文摘要：

基于隐私保护的不同坐标系下的点球关系判定是计算几何中的一类基本问题,针对该问题进行了研究并提出一种新的解决方案。在点积协议基础上设计了一种点球关系判定协议,使得双方均在不透露自己任何信息的情况下,能够完成坐标系的转换,并判定点是否包含在球体内,分析了该判定协议的正确性、安全性和复杂性。最后提出可以使用该协议来解决一类与此相似的几何对象关系的判定问题。

英文摘要：

A secure determination problem of point-sphere relationship based on different coordinate systems is a basic problem in privacy-preserving computational geometry. This paper presented a new solution for this problem,and designed a new secure determination protocol of point-sphere based on the scalar product protocol. The two sides completed the coordinate system conversion, and determined whether the sphere contained the point, but didn＇ t disclose any information about their own. In the end, this paper analyzed it＇ s correctness, security and efficiency, and proposed to use this protocol toresolve the similar problems that are geometric objects relations problem determination based on the different coordinate systems.