“…Compared with the classical related protocols, our solution has the advantage of higher security and lower communication complexity. In addition, our proposed protocol can also be extended to some other complicated privacy-preserving computation problems, such as privacy-preserving database queries over cloud data [Cao, Wang, Li et al (2014); Shen, Li, Li et al (2017)], privacy-preserving set operations in cloud computing [Cao, Li, Dang et al (2017); Zhuo, Jia, Guo et al 2017], and privacy-preserving reversible data hiding over encrypted image [Cao, Du, Wei et al (2016)]. Furthermore, the method of the oracle operation applied in the presented protocols is general and can be employed to solve other similar privacy-preserving computation geometry problems, such as convex hull, polygon inclusion, etc.…”