Privacy-Preserving Computational Geometry Problems on Conic Sections

Privacy-preserving computational geometry is a special secure multi-party computation and has many applications. In recent years, many scholars have focused on privacy-preserving computational geometry problems which are based on circle and polygon. However, as a branch of computational geometry problems, the private-computing on conic sections must be considered. Consequently, we study secure computational protocols on conic sections in our paper. Using secure scalar product protocol, Millionaire protocol and homomorphic encryption scheme as building blocks, we present secure efficient constant-round protocols for solving point-included and line-intersected problems on conic sections in the semi-honest model. Meanwhile, we prove their security under the simulation paradigm and analyze the complexity. By comparing with others, we conclude that our protocols have better efficiency.