Privacy-Preserving Point-Inclusion Two-Party Computation Protocol

Privacy Preserving Computational Geometry (PPCG) is a new study field of Secure Multi-party Computation(SMC), its main contents include: Point Inclusion problem, Polygon Intersection problem, Closest Pair problem, Convex Hulls problem and so on. In this paper, we focus on the point inclusion problem. This problem is defined in two parties setting, while Alice has a secret point z, and Bob has a secret domain P. Both of them want to know whether the point is included in the domain. Researchers have proposed many protocols to deal with point inclusion problems, however most of them mainly solved the problem of the relation between point and the regular graphics, like circle, ellipse, convex polygon etc. In this paper, we propose a two-party protocol for point-arbitrary polygons inclusion problem based on the angle-rotation method, without revealing any private information, and then we give the correctness and security analysis.