Privacy-preserving practical Convex Hulls protocol

Secure Multi-party Computation has been a hot research topic of cryptograhy for about two decades, and the Convex Hulls problem is a special case of it. However, the precise convex hulls will certainly expose all vertexes and even bring about unfairness. Therefore the practical approximate convex hulls are in need. In this paper, we summarize and discuss the Convex Hulls problem, and then we present a more effective new protocol to compute the approximate convex hulls. Furthermore, we analyze the security, communication complexity and efficiency of the protocol, and compare the new scheme with other privacy-preserving convex hulls protocols through simulated experiments. It shows that our privacy-preserving approximate convex hulls protocol is more effective than the previous privacy-preserving ones, and the new protocol is practical enough in many situations. Perfectly keeping privacy preserving and eliminating unfairness are the great advantages of our scheme.