Secure Judgment of Point and Line Relationship Against Malicious Adversaries and Its Applications

Xin Liu,
Yang Xu,
Gang Xu,
Xiu-Bo Chen,
Yu-Ling Chen,

Abstract


With the rapid development of the Internet and information technology, the problem of zero-trust networks has become increasingly prominent, and secure multi-party computation has become a research hotspot to solve the problem of zero-trust networks. The secure judgment of point and line relationship is an important research branch of secure computing set geometry. However, most of resent secure computing protocols of point and line relationship are designed in the semi-honest model and cannot resist malicious attacks. Therefore, this paper analyzes the possible malicious adversary behaviors and designs a secure protocol in the malicious model. In this paper, the Paillier cryptosystem, zero- knowledge proof, and cut-choose method are used to resist malicious behavior, and the real/ideal model paradigm method is used to prove the security of the protocol. Compared with the existing solutions, the malicious model protocol is still efficient and widely used in real applications.

Keywords


Secure multi-party computation, Point and line relationship, Malicious model, Real/ideal model paradigm

Citation Format:
Xin Liu, Yang Xu, Gang Xu, Xiu-Bo Chen, Yu-Ling Chen, "Secure Judgment of Point and Line Relationship Against Malicious Adversaries and Its Applications," Journal of Internet Technology, vol. 23, no. 5 , pp. 1019-1027, Sep. 2022.

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