¹ School of Computer Science, Shaanxi Normal University, Xi’an, 710062, PR China
² Graduate Institute of Information and Computer Education, National Kaohsiung Normal University, Tai-wan
³ School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, 610054, PR China

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Abstract—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.

Index Terms—Secure multi-party computation, computational geometry, secure scalar product protocol, conditional oblivious transfer

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Cite: Bo Yang, Chung-huang Yang, Yong Yu, and Dan Xie, " A Secure Scalar Product Protocol and Its Applications to Computational Geometry," Journal of Computers vol. 8, no. 8, pp. 2018-2026, 2013.