Numerous privacy-preserving issues have emerged along with the fast development of Internet, both in theory and in real-life applications. To settle the privacy-preserving problems, secure multi-party computation is essential and critical. In this paper, we have solved two problems regarding to how to determine the position relation between points and curves without revealing any private information. Two protocols have been proposed in order to solve the problems in different conditions. In addition, some building blocks have been developed, such as scalar product protocol, so that we can take advantage of them to settle the privacy-preserving computational geometry problems which are a kind of special secure multi-party computation problems. Moreover, oblivious transfer and power series expansion serve as significant parts in our protocols. Analyses and proofs have also been given to argue our conclusion.
