# 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,[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]

## Problem statements

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]

## References

1. ^ [1]
2. ^ 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
3. ^ 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)
4. ^ Li S D, Dai Y Q. Secure two-party computational geometry. Journal of Computer Science and Technology, 20(2): pages 258–263, 2005.
5. ^ 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