A practical three-dimensional Privacy-preserving approximate convex hulls protocol

Convex Hulls Problem is a special case of Privacy-preserving Geometry Problem in the inquiry of Secure Multi-Party Computation. In the past, only in two-dimensional space privacy-preserving convex hulls have been investigated, and there is little focus in the three-dimensional space. However, three-dimensional privacy-preserving convex hulls can be applied in many fields, such as researching and exploration of the space, military, corporately finding the union range based on sensitive data from two parties. Approximate convex hulls have more advantages than conventional convex hulls in the theme of Secure Multi-Party Computation because it can hide the private points on the vertices. In this paper, we first present a practical privacy-preserving protocol to solve the three dimensional approximate convex hulls problem; we also discuss the correctness, security, and performance of our protocol.