Multi-Party Quantum Private Comparison with Qudit Shifting Operation
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Multi-Party Quantum Private Comparison with Qudit Shifting Operation Duan Ming-Yi 1 Received: 23 April 2020 / Accepted: 21 July 2020/ # Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract
In this paper, a multi-party quantum private comparison (MQPC) protocol is proposed based on the qudit shifting operation. The semi-honest third party (TP) prepares the initial particles and sends them to the first user. Then, each of n users encodes his private integers on the travelling particles with the qudit shifting operations and transmits them to the next user. Finally, the travelling particles are transmitted back to TP. The equality of the private integers from n users can be determined within one time execution of the protocol. It is verified that the proposed protocol is secure against both the outside attack and the participant attack. One user cannot obtain other users’ private integers except for the case that their private integers are same. TP cannot know the private integers from n users except their comparison result. Keywords Multi-party quantum private comparison (MQPC) . Circular transmission . Qudit shifting operation
1 Introduction In 1982, Yao [1] introduced the millionaire problem, i.e., two millionaires want to know who is richer while keeping their genuine assets secret to each other. Since then, secure multi-party computation (SMPC) in classical cryptography began to arouse the interests of researchers, as it has important applications in many circumstances such as private bidding and auctions, secret ballot elections, e-commerce, data mining et al.. In 2009, Yang and Wen [2] put forward quantum private comparison (QPC) for the first time, in order to judge whether two inputs from two users are equal or not while keeping them secret through the quantum means. Since then, a lot of attentions from researchers have been focused on it. In the early development, numerous two-party QPC protocols [2–9] were
* Duan Ming-Yi [email protected]
1
College of Information and Engineering, Zhengzhou Institute of Technology, Zhengzhou 450044, People’s Republic of China
International Journal of Theoretical Physics
designed through different quantum technologies. Later, researchers became more interested in constructing multi-party quantum private comparison (MQPC) protocols, as it can accomplish the comparison of equality among many users within one execution of protocol. Until now, numerous MQPC protocols [10–19] have been proposed through different quantum technologies. In 2013, Chang et al. [10] proposed the first MQPC protocol using GHZ class states. In 2014, Wang et al. [11] proposed a MQPC protocol withn-level entangled states. In 2015, Huang et al. [12] put forward a MQPC protocol with an almost-dishonest third party. In 2016, Ye [13] put forward a MQPC protocol based on entanglement swapping of Bell entangled states; Liu and Wang [14] suggested a dynamic MQPC protocol with single photons in both polarization and spatial-mode degrees of freedom; Huang et al. [15] designed a M
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