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,[1] and more.[2]
A pioneering work in this area was a 2001 paper by Atallah and Du,[3] in which the secure point in polygon inclusion and polygonal intersection problems were considered.
Other problems are computation of the distance between two private points[4] and secure two-party point-circle inclusion problem.[5]
The problems use the conventional "Alice and Bob" terminology. In all problems the required solution is a protocol of information exchange during which no additional information is revealed beyond what may be inferred from the answer to the required question.
- Point-in-polygon: Alice has a point a, and Bob has a polygon B. They need to determine whether a is inside B.[3]
- Polygon pair intersection: Alice has a polygon A, and Bob has a polygon B. They need to determine whether A intersects B.[3]
- ^ "Archived copy" (PDF). Archived from the original (PDF) on 2013-11-12. Retrieved 2013-11-12.
{{cite web}}: CS1 maint: archived copy as title (link)
- ^ Kaitai LIANG, Bo YANG, Dake HE, Min ZHOU, Privacy-Preserving Computational Geometry Problems on Conic Sections, Journal of Computational Information Systems 7: 6 (2011) 1910–1923
- ^ a b c Atallah M J, Du W. 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)
- ^ Li S D, Dai Y Q. Secure two-party computational geometry. Journal of Computer Science and Technology, 20(2): pages 258–263, 2005.
- ^ 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
