Materials and Energy Research CenterInternational Journal of Engineering1025-249534420210401Private Trajectory Intersection Testing: Is Garbled Circuit Better than Custom Protocols?86387212626610.5829/ije.2021.34.04a.12ENM.DehghanDepartment of Computer Engineering, Amirkabir University of Technology, Tehran, IranB.SadeghiyanDepartment of Computer Engineering, Amirkabir University of Technology, Tehran, IranE.KhosravianDepartment of Mechanical Engineering, Payame Noor University, Tehran, IranJournal Article20200714In this paper, two protocols are presented for private intersection detection of two moving objects’ trajectories. Assuming that the movement trajectory of an object can be described by a time-dependent polynomial function, the problem of finding the intersection points is simplified to the problem of finding the common roots of the corresponding polynomials. Thereafter, GrÖbner Basis is used to design a novel secure protocol of finding the common roots of the polynomials. Another protocol is also designed based on the distance computation of two trajectories’ curves. <br /> Moreover, we present the complexity analysis of the protocol for private trajectory intersection testing of two moving objects, which is based on GrÖbner Basis. Then, we compare its complexity by the garbled circuit-based protocol for Euclidean Distance Computation of l points. We also prove the security of our proposed protocol, which is based on the distance computation of two curves. <br /> Keywords: Private Trajectory Intersection Testing, GrÖbner Basis, Distance Computation, Complexity , Garbled Circuit, Euclidean Distancehttps://www.ije.ir/article_126266_2d65afd1c0b5b9c97ee719121634aee1.pdf