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Laser Physics Letters

Circular semiquantum private comparison protocol of size relation based on d-dimensional Bell states

Shen Rao, Zhi-Gang Gan

Published Aug 1, 2025• 1 citation
Publisher

Abstract

Abstract In this paper, a circular semiquantum private comparison protocol of size relation without a pre-shared key is designed by utilizing d-dimensional Bell states, where the traveling particles undergo a round trip among three participants. This protocol does not employ unitary operations, quantum entanglement swapping or any pre-shared key. It is proven to have security against both outside and inside attacks.

DOI
10.1088/1612-202x/adfad7

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Abstract In this paper, a circular semiquantum private comparison protocol of size relation without a pre-shared key is designed by utilizing d-dimensional Bell states, where the traveling particles undergo a round trip among three participants. This protocol does not employ unitary operations, quantum entanglement swapping or any pre-shared key. It is proven to have security against both outside and inside attacks.
In this paper, we adopt \c{hi}-type states to design a novel circular semiquantum private comparison (SQPC) protocol which can determine the equality of private inputs from two semiquantum users within one round implementation under the help of a semi-honest third party (TP) who possesses complete quantum capabilities. Here, it is assumed that the semi-honest TP has the abilities to launch all possible attacks to steal useful information about two semiquantum users' private inputs but cannot conspire with anyone else. The travelling particles go from TP to Alice, Alice to Bob and back from Bob to TP. The security analysis turns out the proposed SQPC protocol can resist both the outside attacks and the inside attacks. The proposed SQPC protocol has no demand for unitary operations. Compared with some existing SQPC protocols of equality with quantum entangled states, the proposed SQPC protocol has some advantages more or less:(1)it requires no pre-shared key among different participants; (2)it doesn't need quantum entanglement swapping; and(3)it employs no delay lines.
Abstract In order to cut down the resource expended by the preshared key, this paper uses d -level single-particle states to design a novel circular two-party semiquantum private comparison scheme with a quantum semi-honest third party who does not need any preshared key. This scheme is capable of determining the size relationship of two integer sequences from two semiquantum communicants. The traveling particles are transmitted in a circular way. This protocol does not use quantum entangled states, quantum entanglement swapping, unitary operations or delay lines. This protocol does not require the semiquantum communicants to use any quantum memory either. Its security toward external attacks and internal attacks is fairly good.
In this paper, we adopt $\ensuremath{\chi}$-type states to design an alternative circular semiquantum private comparison (SQPC) protocol, which can determine the equality of private inputs from two semiquantum users within one round implementation under the help of a semihonest third party (TP) who possesses complete quantum capabilities. Here, it is assumed that the semihonest TP has the abilities to launch all possible attacks to steal useful information about two semiquantum users' private inputs but cannot conspire with anyone else. The traveling particles go from TP to Alice, then from Alice to Bob, and back from Bob to TP. The security analysis turns out the proposed SQPC protocol can resist both the outside attacks and the inside attacks. Furthermore, it has been proven to be information-theoretically secure in the asymptotic scenario. Compared with some existing SQPC protocols of equality with quantum entangled states, the proposed SQPC protocol has some advantages: ◯1◯\phantom{\rule{-9pt}{0ex}}1◯1 it requires no preshared key among different participants; ◯2◯\phantom{\rule{-9pt}{0ex}}2◯2 it does not need quantum entanglement swapping; ◯3◯\phantom{\rule{-9pt}{0ex}}3◯3 it employs no delay lines; ◯4◯\phantom{\rule{-9pt}{0ex}}4◯4 it adopts no unitary operations; and ◯5◯\phantom{\rule{-9pt}{0ex}}5◯5 it has fewer qubits transmitted and fewer classical modulo 2 addition computations.
Many semi-quantum private comparison (SQPC) protocols have been proposed to compare the equality of participants, but they suffer from low qubit efficiency and require classical participants to perform quantum state measurement and preparation operations. We here propose a novel SQPC protocol based on d-dimensional Bell states. With the assistance of a semi-honest third party, classical participants can compare the sizes of their privacies merely through particle reflection and simple unitary operations, but they do not need to prepare and measure quantum states. Furthermore, participants can compare two bits of privacy just once with one qubit. By combining decoy state eavesdropping detection with pre-shared key encryption as dual security strategies, analysis shows that the proposed protocol is secure against internal and external attack in theory. The qubit efficiency of the protocol reaches 66.7 % , which is significantly superior to existing schemes.
Abstract Semi-quantum private comparison allows multiple ‘classical’ users who have restricted quantum capabilities to compare their private data with the assistance of a quantum third party. In this work, we propose a novel dynamic semi-quantum private comparison protocol using a circular transmission mode along with d-dimensional single-particle states. The protocol enables the comparison of data size relations among several ‘classical’ users, while the third party can only determine the relative sizes without accessing the users’ secret information. Security evaluations demonstrate that the designed protocol withstands typical external and internal attacks. Compared to previous works, this protocol offers several improvements: first, it supports dynamic addition or removal of users, enhancing applicability in practical scenarios; second, it eliminates the need for pre-shared keys, reducing quantum resource consumption; third, it avoids the use of high-dimensional multi-particle entangled states, thereby enhancing the feasibility of implementation. Therefore, the proposed protocol may have more practical potential compared to previous protocols.
Abstract In this paper, we put forward a multi-party quantum private comparison (MQPC) protocol with two semi-honest third parties (TPs) by adopting d -dimensional Bell states, which can judge the size relationship of private integers from more than two users within one execution of protocol. Each TP is permitted to misbehave on her own but cannot collude with others. In the proposed MQPC protocol, TPs are only required to apply d -dimensional single-particle measurements rather than d -dimensional Bell state measurements. There are no quantum entanglement swapping and unitary operations required in the proposed MQPC protocol. The security analysis validates that the proposed MQPC protocol can resist both the outside attacks and the participant attacks. The proposed MQPC protocol is adaptive for the case that n users want to compare the size relationship of their private integers under the control of two supervisors. Furthermore, the proposed MQPC protocol can be used in the strange user environment, because there are not any communication and pre-shared key between each pair of users.