Relationship between Secure Decision Points and Arbitrary Polygon Positions in Malicious Models

The problem of determining the position relationship between points and polygons is very extensive in practical applications. However, the existing solutions are only applicable to the case of convex polygons, and no solutions are given for arbitrary polygons. In addition, most of the existing schemes are carried out under the semi-honest model, and cannot resist the active attack of malicious adversaries. In order to solve these problems, this paper uses Paillier's encryption scheme, the idea of zero-knowledge proof to design a decision protocol to protect the position relationship between points and arbitrary polygons, which can not only prevent the deceptive behavior of malicious adversaries, but also extend the application from convex polygons to arbitrary polygons. A simulation example is used to prove that this paper is safe and efficient under the malicious model.