Open Access Open Access  Restricted Access Subscription Access

Confidentially Compare Rational Numbers under the Malicious Model

Xin Liu,
Xiaomeng Liu,
Dan Luo,
Gang Xu,
Xiu-Bo Chen,


Secure multi-party computation is a hotspot in the cryptography field, and it is also a significant means to realize privacy computation. The Millionaires’ problem is the most fundamental problem among them, which is the basic module of secure multi-party computation protocols. Although there are many solutions to this problem, there are few anti-malicious adversarial protocols besides protocols based on Yao’s garbled circuit. Only a few solutions have low efficiency, and there is no protocol for rational numbers comparison under the malicious model, which restricts the solution of many secure multi-party computation problems. In this paper, the possible malicious behaviors are analyzed in the existing Millionaires’ problem protocols. These behaviors are discovered and taken precautions against through the triangle area formula, zero-knowledge proof, and cut-and-choose method, so the protocol of comparing confidentially rational numbers is proposed under the malicious model. And this paper adopts the real/ideal model paradigm to prove the security of the malicious model protocol. Efficiency analysis indicates that the proposed protocol is more effective than existing protocols. The protocol of rational numbers comparison under the malicious model is more suitable for the practical applications of secure multi-party computation, which has important theoretical and practical significance.


Secure multi-party computation, Malicious model, Rational numbers comparison, Real/ideal model paradigm

Citation Format:
Xin Liu, Xiaomeng Liu, Dan Luo, Gang Xu, Xiu-Bo Chen, "Confidentially Compare Rational Numbers under the Malicious Model," Journal of Internet Technology, vol. 25, no. 3 , pp. 355-363, May. 2024.

Full Text:



  • There are currently no refbacks.

Published by Executive Committee, Taiwan Academic Network, Ministry of Education, Taipei, Taiwan, R.O.C
JIT Editorial Office, Office of Library and Information Services, National Dong Hwa University
No. 1, Sec. 2, Da Hsueh Rd., Shoufeng, Hualien 974301, Taiwan, R.O.C.
Tel: +886-3-931-7314  E-mail: