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arXiv:1405.6765

Comment on "Fault-Tolerate Quantum Private Comparison Based on GHZ States and ECC"

Sai Ji, Wang Sheng Fang, Wenjie Liu, Chao Liu, Haibin Wang

Published May 27, 2014• 0 citations
arXivHTMLPDF

Abstract

A two-party quantum private comparison scheme using GHZ states and error-correcting code (ECC) was introduced in Li et al.'s paper [Int. J. Theor. Phys. 52: 2818-2815, 2013], which holds the capability of fault-tolerate and could be performed in a none-ideal scenario. However, this study points out there exists a fatal loophole under a special attack, namely the twice-Hadamard-CNOT attack. A malicious party may intercept the other's particles, firstly executes the Hadamard operations on these intercepted particles and his (her) own ones respectively, and then sequentially performs twice CNOT operations on them and the auxiliary particles prepared in advance. As a result, the secret input will be revealed without being detected through measuring the auxiliary particles. For resisting this special attack, an improvement is proposed by applying a permutation operator before TP sends the particle sequences to all the participants.

DOI
10.48550/arxiv.1405.6765

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A two-party quantum private comparison scheme using GHZ states and error-correcting code (ECC) was introduced in Li et al.'s paper [Int. J. Theor. Phys. 52: 2818-2815, 2013], which holds the capability of fault-tolerate and could be performed in a none-ideal scenario. However, this study points out there exists a fatal loophole under a special attack, namely the twice-Hadamard-CNOT attack. A malicious party may intercept the other's particles, firstly executes the Hadamard operations on these intercepted particles and his (her) own ones respectively, and then sequentially performs twice CNOT operations on them and the auxiliary particles prepared in advance. As a result, the secret input will be revealed without being detected through measuring the auxiliary particles. For resisting this special attack, an improvement is proposed by applying a permutation operator before TP sends the particle sequences to all the participants.
Recently, Li et al. presented a two-party quantum private comparison scheme using Greenberger-Horne-Zeilinger (GHZ) states and error-correcting code (ECC) [ Int. J. Theor. Phys. 52, 2818 (2013)], claiming it is fault-tolerant and could be performed in a non-ideal scenario. However, there exists a fatal loophole in their private comparison scheme under a special attack, namely the twice-Hadamard-CNOT attack. Specifically, a malicious party may intercept the other party’s particles and execute Hadamard operations on the intercepted particles as well as on his or her own particles. Then, the malicious party could sequentially perform a controlled-NOT (CNOT) operation between intercepted particles and the auxiliary particles, as well as between his or her own particles and the auxiliary particles prepared in advance. By measuring the auxiliary particles, the secret input will be revealed to the malicious party without being detected. For resisting this special attack, a feasible improved scheme is proposed by introducing a permutation operator before the third party (TP) sends the particle sequences to each participant.
Abstract In this paper, we propose two multi-party quantum private comparison protocols based on the properties of the d-dimensional GHZ state. Protocol 1 is designed to compare the equality of multiple participants’ secrets with the help of a semi-honest third party TP. The semi-honest TP will follow the protocol honestly, but he may attempt to learn additional information from the protocol execution. In this protocol, multiple participants encode their secret information into the corresponding particles in turn through unitary operations, thereby achieving the comparison of the equality of their multiple secrets in a single execution. This protocol has a wide range of applications. For example, by combining the basic model framework of this protocol with the Chinese Remainder Theorem, we propose Protocol 2. In this protocol, multiple participants compare the size relationships of their multiple secrets with the help of a semi-honest third party TP. Therefore, based on the same basic model framework, the two protocols proposed in this paper can be applied respectively to the comparison of the equality and the size relationships of multiple participants’ secrets. Importantly, the two protocols do not require pre-shared keys. Security analysis shows that the proposed protocols can resist various attacks, including entangle-measure attack, intercept-resend attack, third party attacks, and participant attacks.
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, an efficient quantum private comparison (QPC) protocol based on GHZ-type states is proposed. Two participants can compare the equality of two classical bits in each comparison, which could greatly reduce comparison times and increase efficiency. A semi-honest third-party (TP) is involved in assisting the participants to compare their secrets. TP may misbehave on her own, but she is not allowed to conspire with any participants. Besides, the proposed protocol needs Hadamard operation as well as single-particle measurements and Bell measurements, which are easy to implement with current technologies. Finally, the analysis shows the proposed protocol is correct and it can resist various attacks including outside attacks and dishonest participant attacks.
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.