A Secure Scalar Product Protocol and Its Applications to Computational Geometry

A secure scalar product protocol is a type of specific SMC problem, and has found various applications in many areas such as privacy-preserving data mining, privacy-preserving cooperative statistical analysis, and privacy-preserving geometry computation. In this paper, we firstly extend to a solution of homomorphic-encryption based secure scalar product protocol such that it enables the scheme to be used in distributed decryption, and to deal with negative vectors. Secondly, we propose two-party secure computation of a public Boolean function on private inputs of each party. Thirdly, we describe two applications of our secure scalar product protocol to computational geometry: determining securely location of a point to a directed line segment, and conditional oblivious transfer based on the relation between a private point and a private directed line.