Efficient Secure Protocols to Determine Whether a Point is inside a Convex Hull

Secure multi-party computation (SMC) is dedicated to solve trust problems in cooperative computing with each participantpsilas private data. Privacy preserving computational geometry (PPCG) is a special area in SMC and is being widely used. This paper investigates the problem of judging whether a point is in a convex hull or not. We firstly present a secure protocol to determine the position of a private point and a private line, based on which two efficient point-inclusion schemes are proposed. Compared with previous solutions, our protocols perform better in efficiency, especially when the number of the convex hullpsilas points is large.