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arXiv:1911.12947 · Communications in Theoretical Physics

Cryptanalysis and improvement of several quantum private comparison protocols

Zhaoxu Ji, Peiru Fan, Huanguo Zhang, Hou-Zhen Wang

Published Jul 15, 2020• 3 citations
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Abstract

Abstract Recently, Wu et al (2019 Int. J. Theor. Phys. 58 1854) found a serious information leakage problem in Ye and Ji’s quantum private comparison protocol (2017 Int. J. Theor. Phys. 56 1517), that is, a malicious participant can steal another’s secret data without being detected through an active attack means. In this paper, we show that Wu et al ’s active attack is also effective for several other existing protocols, including the ones proposed by Ji et al and Zha et al (2016 Commun. Theor. Phys. 65 711; 2018 Int. J. Theor. Phys. 57 3874). In addition, we propose what a passive attack means, which is different from Wu et al ’s active attack in that the malicious participant can easily steal another’s secret data only by using his own secret data after finishing the protocol, instead of stealing the data by forging identities when executing the protocol. Furthermore, we find that several other existing quantum private comparison protocols also have such an information leakage problem. In response to the problem, we propose a simple solution, which is more efficient than the ones proposed by Wu et al , because it does not consume additional classical and quantum resources.

DOI
10.1088/1572-9494/ab8a0c

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Abstract Recently, Wu et al (2019 Int. J. Theor. Phys. 58 1854) found a serious information leakage problem in Ye and Ji’s quantum private comparison protocol (2017 Int. J. Theor. Phys. 56 1517), that is, a malicious participant can steal another’s secret data without being detected through an active attack means. In this paper, we show that Wu et al ’s active attack is also effective for several other existing protocols, including the ones proposed by Ji et al and Zha et al (2016 Commun. Theor. Phys. 65 711; 2018 Int. J. Theor. Phys. 57 3874). In addition, we propose what a passive attack means, which is different from Wu et al ’s active attack in that the malicious participant can easily steal another’s secret data only by using his own secret data after finishing the protocol, instead of stealing the data by forging identities when executing the protocol. Furthermore, we find that several other existing quantum private comparison protocols also have such an information leakage problem. In response to the problem, we propose a simple solution, which is more efficient than the ones proposed by Wu et al , because it does not consume additional classical and quantum resources.
Recently, Liu et al. [ Commun. Theor. Phys. 57 (2012) 583 ] proposed a quantum private comparison protocol based on entanglement swapping of Bell states, which aims to securely compare the equality of two participants' information with the help of a semi-honest third party (TP). However, the present study points out there is a fatal loophole in Liu et al.'s protocol, and TP can make Bell-basis measurement to know all the participants' secret inputs without being detected. To fix the problem, a simple solution, which uses one-time eavesdropper checking with decoy photons instead of twice eavesdropper checking with Bell states, is demonstrated. Compared with the original protocol, it not only reduces the Bell states consumption but also simplifies the protocol steps.
Ji et al. [Mod. Phys. Lett. A 34, 1950229 (2019)] and Fan et al. [Mod. Phys. Lett. A 37, 2250026 (2022)] proposed two-party quantum private comparison (QPC) protocols based on 7-qubit and 8-qubit states, respectively. However, these two QPC protocols did not consider third-party (TP) attacks. Therefore, this study focuses on TP attacks and demonstrates that the property of a 7-qubit or 8-qubit entanglement state is useless in this attack situation; that is, the participant wastes resources to maintain the qubits. For the same assumption environment proposed by Ji et al. and Fan et al., this study proposes an improvement and simplification protocol that allows participants to reach the goal of private comparison by using only classical computation and the classical communication channel without any entanglement state.
In a recent paper [Int. J. Quantum Inf. 17 (2019) 1950026], the authors discussed the shortcomings in the security of a quantum private comparison protocol that we previously proposed [Int. J. Quantum Inf. 15 (2017) 1750014]. They also proposed a new protocol aimed to avoid these problems. Here, we analyze the information leaked in their protocol, and find that it is even less secure than our protocol in certain cases. We further propose an improved version which has the following advantages: (1) no entanglement needed, (2) quantum memory is no longer required, and (3) less information leaked. Therefore, better security and great feasibility are both achieved.
Abstract Based on Bell states, a new semi-quantum private comparison protocol is proposed that enables two classical users to securely compare the equality of their private information with the aid of a semi-honest third party. Different from the existing semi-quantum private comparison protocols, the two classical participants in the presented protocol do not need to measure and prepare any quantum state, which not only reduces the consumption of quantum devices, but also greatly improves the feasibility of the protocol. Performing different unitary operations on the received particles, classical users can securely compare their secret information. Besides, the devised protocol has higher qubit efficiency than the other similar counterparts, since participants can compare a two-bit privacy each time with one qubit. Meanwhile, after completing the comparison process, all Bell states could be reused since they still retain the corresponding entanglement property, which greatly facilitates the recycle of quantum resources. Security analyses indicate that the designed scheme is secure against external attack and internal attack. Moreover, the operations involved in our scheme are simulated on the IBM Quantum Experience to demonstrate the effectiveness and security of our scheme.
Abstract Recently, Liu et al. proposed a two-party quantum private comparison (QPC) protocol using entanglement swapping of Bell entangled state (Commun. Theor. Phys. 57 (2012) 583). Subsequently Liu et al. pointed out that in Liu et al.'s protocol, the TP can extract the two users' secret inputs without being detected by launching the Bell-basis measurement attack, and suggested the corresponding improvement to mend this loophole (Commun. Theor. Phys. 62 (2014) 210). In this paper, we first point out the information leakage problem toward TP existing in both of the above two protocols, and then suggest the corresponding improvement by using the one-way hash function to encrypt the two users' secret inputs. We further put forward the three-party QPC protocol also based on entanglement swapping of Bell entangled state, and then validate its output correctness and its security in detail. Finally, we generalize the three-party QPC protocol into the multi-party case, which can accomplish arbitrary pair's comparison of equality among K users within one execution.
In this paper, we carry out an in-depth analysis of the quantum private comparison (QPC) protocol with the semi-honest third party (TP). The security of QPC protocol using the EPR pairs is re-examined. Unfortunately, we find that TP can use the fake EPR pairs to steal all the secret information. Furthermore, we give two simple and feasible solutions to improve the original QPC protocol. It is shown that the improved protocol is secure, which can resist various kinds of attacks from both the outside eavesdroppers and the inside participants, even the semi-honest TP.