Relationship between Secure Decision Points and Arbitrary Polygon Positions in Malicious Models


Published: 2023-04-08

DOI: 10.56557/ajomcor/2023/v30i18191

Page: 48-57

Xueli Yan *

College of Science, North China University of Technology, Beijing-100144, P. R. China.

*Author to whom correspondence should be addressed.


The problem of determining the position relationship between points and polygons is very extensive in practical applications. However, the existing solutions are only applicable to the case of convex polygons, and no solutions are given for arbitrary polygons. In addition, most of the existing schemes are carried out under the semi-honest model, and cannot resist the active attack of malicious adversaries. In order to solve these problems, this paper uses Paillier's encryption scheme, the idea of zero-knowledge proof to design a decision protocol to protect the position relationship between points and arbitrary polygons, which can not only prevent the deceptive behavior of malicious adversaries, but also extend the application from convex polygons to arbitrary polygons. A simulation example is used to prove that this paper is safe and efficient under the malicious model.

Keywords: Secure multi-party computing, points and arbitrary polygons, malicious model, zero knowledge proof

How to Cite

Yan, X. (2023). Relationship between Secure Decision Points and Arbitrary Polygon Positions in Malicious Models. Asian Journal of Mathematics and Computer Research, 30(1), 48–57.


Download data is not yet available.


Li Shundong, Wang Wenli, Du Runmeng. Solutions to the problem of millionaires against malicious adversaries [J]. China Science: Information Science. 2021;51 (01):75-88

Yao AC. Protocols for secure computations[C]// Proc. of the 23rd Annual IEEE Symposium on Foundations of Computer Science. 1982;160-164.

Daoshun Wang, Yiqi, et al. Secure multiparty computation of solid geometric problems and their applications[J]. Information Sciences: An International Journal. 2014;282:401-413

Zhu Rujin, Yang Bo Protocol for determining the location relationship between points and polygons for privacy protection [J] Computer Science. 2012;39(B06):4.

Chen Zhenhua, Li Shundong, Huang Qiong, etc A new solution to the problem of determining two secret positions [J] Journal of Computer Science. 2018;41(2):13.

Gong Linming, GONG Linming, Li Shundong, et al Secret social willingness detection [J] Journal of Software. 2019;30(11):14.

Zhang Mingwu, Leng Wentao, Shen Hua Determination of the position relationship between points and arbitrary polygons for privacy protection [J] Journal of Cryptography. 2019;6(4):12.

Liu Xin, Zhang Ruiling, Xu Gang, etc Inclusion relationship between secret decision point and convex polygon under malicious model [J] Journal of Cryptography. 2022(009-003).

Paillier P. Public-key cryptosystems based on composite degree residuosity classes[J]. Proc. EUROCRYPT'99, Czech Republic. 1999;223-228.

Dou Jiawei, Ge Xue, Wang Yingnan. Manhattan distance calculation for privacy protection and its promotion and application [J]. Journal of Computer Science, 2020,43 (02): 352-365

Li Shundong, Xu Wenting, Wang Wenli, et al. Maximum (minimum) value secret calculation under malicious model [J]. Journal of Computer Science. 2021;44(10):2076-2089.

Du W, Zhan Z. A practical approach to solve secure multi-party computation problems [J]. Center for Systems Assurance Department of Electrical Engineering and Computer Science Syracuse University, Syracuse, NY 13244; 2002.

Chen Zhenhua, Huang Luqi, Shi Xiaonan, Nie Jingjing. Three basic outsourcing computing protocols for information theory security and spatial location relationship confidentiality judgment [J]. Journal of Xi'an University of Science and Technology. 2019;39(06):1049-1056.

Wu Hongfeng, Song Zhenzhen. Efficient Manhattan distance security calculation [J]. Cyberspace Security. 2021;12(Z3):49-55.