Secure Judgment of Line Segments Intersection Under the Malicious Model

Confidential computational geometry problems are one of the more popular classes of topics in secure multi-party computation. In the secure computation of geometric problems, the cross product can be used to judge the intersection of line segments. In this paper, we transform the problem of judging line segment intersection into the problem of computing cross product, propose a cross product computation protocol for protecting private information under the semi-honest model, and analyze the security and correctness. And further, this paper design a confidential protocol for computing cross product under malicious model and then judge line segment intersection, which utilizes segmentation-selection method and zero-knowledge proof to prevent or detect malicious behavior, and prove the security of the protocol with ideal-practical examples.