Abstract: Specific secure multi-party computation problems are a research focus in international cryptographic community in recent years.Privacy-preserving computational geometry problem is one of them.In this problem，two or more mutually untrusted parties wish to jointly solve some computational geometric problem with their private geometric information as input，while the parties wish to ensure that any private input information of them is not revealed to other parties beyond the specified output.In this paper，private-preserving determination protocol of distance relation between two-point based on threshold，private-preserving determination protocol of point-line distance relation based on threshold，and private-preserving determination protocol of position relation between point and two parallel lines are presented.These protocols are used to construct a private-preserving determination protocol of distance relation between point and line segment based on threshold.These protocols have potential applications in engineering，commerce and military field.

Key words: secure multi-party computation, computational geometry, millionaires’ protocol, dot product protocol

摘要： 特殊安全多方计算问题是近几年国际密码学界一个研究热点。保密计算几何问题就是其中之一，它是指两个或多个互不信任的参与方希望利用他们私有的几何信息作为输入协作解决某一计算几何问题，同时他们想要确保没有把自己的任何私有输入信息泄露给其他参与方，除了规定的输出。设计了基于阈值的两点之间、点线之间距离关系的保密判定协议，点与两平行直线位置关系的保密判定协议，使用这几个协议构造了基于阈值的点与线段之间距离关系的保密判定协议。这些协议在工程、商业和军事等领域中有着潜在的应用前景。

关键词: 安全多方计算, 计算几何, 百万富翁协议, 点积协议