Privacy-preserving computational geometry

Privacy-preserving computational geometry is the research area on the intersection of the domains of secure multi-party computation (SMC) and computational geometry. Classical problems of computational geometry reconsidered from the point of view of SMC include shape intersection, private point inclusion problem, range searching, convex hull,{{Cite web |url=http://www.joics.com/publishedpapers/2012_9_4_915_929.pdf |title=Archived copy |access-date=2013-11-12 |archive-date=2013-11-12 |archive-url=https://web.archive.org/web/20131112073625/http://www.joics.com/publishedpapers/2012_9_4_915_929.pdf |url-status=dead }} and more.Kaitai LIANG, Bo YANG, Dake HE, Min ZHOU, [http://www.jofcis.com/publishedpapers/2011_7_6_1910_1923.pdf Privacy-Preserving Computational Geometry Problems on Conic Sections], Journal of Computational Information Systems 7: 6 (2011) 1910–1923

A pioneering work in this area was a 2001 paper by Atallah and Du,Atallah M J, Du W. [https://www.cerias.purdue.edu/assets/pdf/bibtex_archive/mja1.pdf Secure Multiparty Computational Geometry]. In Proc. Algorithms and Data Structures: 7th International Workshop, WADS 2001, Lecture Notes in Computer Science, LNCS 2125, Providence, RI, USA, pages 165–179, August 8–10, 2001. (As cited by Liang et al. 2011) in which the secure point in polygon inclusion and polygonal intersection problems were considered.

Other problems are computation of the distance between two private pointsLi S D, Dai Y Q. Secure two-party computational geometry. Journal of Computer Science and Technology, 20(2): pages 258–263, 2005. and secure two-party point-circle inclusion problem.Luo Y L, Huang L S, Zhong H. Secure two-party point-circle inclusion problem. Journal of Computer Science and Technology, 22(1): pages 88–91, 2007