A Secure Protocol for Point-Segment Position Problem

Privacy Preserving Computation Geometry is an important direction in the application of Secure Multi-party Computation and contains many research subjects, such as intersection problem, point-inclusion problem, convex hull, rang searching and so on. Particularly, point-inclusion problem is of great practical significance in our daily life. In this paper, we will devote our attention to the point-segment position problem in point-inclusion and aim to determine the relationship of a point and a segment. In our solution, we present a concise secure protocol based on two basic protocols, secure scalar product protocol and secure comparison protocol. Compared with precious solutions, which may disclose at least one inside point, our protocol performs better in terms of preserving privacy. It will not reveal any inside point, which is crucially significant in some special occasion.

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