Secure Two-Party Point-Circle Inclusion Problem

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