Privacy-preserving cross product protocol and its applications

In computational geometry, computing cross products is at the heart of line-segment methods. If the points and the line segments of the cross product algorithms are of several users and the privacy of any user is not considered, the problem can be solved through traditional methods, because we can assume the existence of a user who knows inputs from all the users. However, the traditional methods or simply improved methods aren't fit for the situation where no user is willing to disclose his private data to other users and some new methods should be developed to solve the new problem. In this paper, privacy-preserving point-segment cross product protocol is firstly presented under the semi-honest model and its security and correctness are also discussed. Privacy-preserving cross product protocol can be used to solve many privacy-preserving computational geometry problems. As an example, a secure protocol for determining whether two line-segments intersect is developed based on the privacy-preserving point-segment cross product protocol.