Secure Two-Party Point-Circle Inclusion Problem

Privacy-preserving computational geometry is a specialsecure multi-party computation and has many applications. Previousprotocols for determining whether a point is inside a circle are notsecure enough. We present a two-round protocol for computing thedistance between two private points and develop a more efficientprotocol for the point-circle inclusion problem based on the distanceprotocol. In comparison with previous solutions, our protocol not onlyis more secure but also reduces the number of communication rounds andthe number of modular multiplications significantly.