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IEEE Transactions on Computers

A Novel Two-Round Two-Party Quantum Private Comparison Protocol Based on Quantum Walks

Jin-Tao Wang, Tian-Yu Ye

Published May 5, 2025• 3 citations
Publisher

Abstract

In order to compare the size relationship and the equality of private integers from two users without any risk of leaking their secrets, we put forward a novel two-round two-party quantum private comparison (QPC) protocol with a third party (TP) based on one-direction quantum walks on a circle (ODQWC). Here, TP is allowed to launch all kinds of possible attacks except the collusion attack. This protocol adopts quantum walk (QW) states as the initial quantum resource, which are actually a kind of two-particle product states. This protocol doesn’t need any pre-shared secret key or quantum entanglement swapping operation, and only adopts unitary operations andd-dimensional single particle measurements. Security analysis validates the security of the proposed protocol against both the outside attacks and the participant attacks. Compared with previous QPC protocols based on QW, this protocol is more efficient under certain conditions. Moreover, we construct quantum circuits for this protocol and reveal its correctness and feasibility by IBM Qiskit simulator.

DOI
10.1109/tc.2025.3566897

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In order to compare the size relationship and the equality of private integers from two users without any risk of leaking their secrets, we put forward a novel two-round two-party quantum private comparison (QPC) protocol with a third party (TP) based on one-direction quantum walks on a circle (ODQWC). Here, TP is allowed to launch all kinds of possible attacks except the collusion attack. This protocol adopts quantum walk (QW) states as the initial quantum resource, which are actually a kind of two-particle product states. This protocol doesn’t need any pre-shared secret key or quantum entanglement swapping operation, and only adopts unitary operations andd-dimensional single particle measurements. Security analysis validates the security of the proposed protocol against both the outside attacks and the participant attacks. Compared with previous QPC protocols based on QW, this protocol is more efficient under certain conditions. Moreover, we construct quantum circuits for this protocol and reveal its correctness and feasibility by IBM Qiskit simulator.
Using the highly entangled six-qubit genuine state we present a quantum private comparison(QPC)protocol, which enables two users to compare the equality of two bits of their secrets in every round comparison with the assistance of a semi-honest third party(TP). The proposed protocol needs neither unitary operations nor quantum entanglement swapping technology, both of which may consume expensive quantum devices. Single particle measurements and Bell-basis measurements, which are easy to implement with current technologies, are employed by two users and TP in the proposed protocol, respectively. The proposed protocol can withstand all kinds of outside attacks and participant attacks. Moreover, none of information about the two users’ private secrets and the comparison result is leaked out to TP.
Abstract Using the highly entangled six-qubit genuine state we present a quantum private comparison (QPC) protocol, which enables two users to compare the equality of two bits of their secrets in every round comparison with the assistance of a semi-honest third party (TP). The proposed protocol needs neither unitary operations nor quantum entanglement swapping technology, both of which may consume expensive quantum devices. Single particle measurements and Bell-basis measurements, which are easy to implement with current technologies, are employed by two users and TP in the proposed protocol, respectively. The proposed protocol can withstand all kinds of outside attacks and participant attacks. Moreover, none of information about the two users' private secrets and the comparison result is leaked out to TP.
Abstract The first quantum private comparison (QPC) protocol via cavity quantum electrodynamics (QED) is proposed in this paper by making full use of the evolution law of atom via cavity QED, where the third party (TP) is allowed to misbehave on his own but cannot conspire with either of the two users. The proposed protocol adopts two-atom product states rather than entangled states as the initial quantum resource, and only needs single-atom measurements for two users. Both the unitary operations and the quantum entanglement swapping operation are not necessary for the proposed protocol. The proposed protocol can compare the equality of one bit from each user in each round comparison with one two-atom product state. The proposed protocol can resist both the outside attack and the participant attack. Particularly, it can prevent TP from knowing two users’ secrets. Furthermore, the qubit efficiency of the proposed protocol is as high as 50%.
In this paper, we leverage the properties of the swap test to evaluate the similarity of two qubits and propose a two-party quantum private comparison (QPC) protocol involving a semi-trusted third party (TP). The TP facilitates the comparison between participants without accessing their private information, other than the final comparison results. Our protocol encodes participants’ secret integers directly into the amplitudes of single-photon states and introduces a novel method for secret-to-secret comparison rather than the traditional bit-to-bit comparison, resulting in improved scalability. To ensure security, the encoded single-photon states are concealed using rotation operations. The comparison results are derived through the implementation of the swap test. A simulation on the IBM Quantum Platform demonstrates the protocol’s feasibility, and a security analysis confirms its robustness against potential eavesdropping and participant attacks. Compared with existing QPC protocols that employ bit-to-bit comparison methods, our approach offers improved practicality and scalability. Specifically, it integrates single-photon states, rotation operations, and the swap test as key components for direct secret comparison, facilitating easier implementation with quantum technology.
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.
By using swap test, a quantum private comparison (QPC) protocol of arbitrary single qubit states with a semi-honest third party is proposed. The semi-honest third party (TP) is required to help two participants perform the comparison. She can record intermediate results and do some calculations in the whole process of the protocol execution, but she cannot conspire with any of participants. In the process of comparison, the TP cannot get two participants’ private information except the comparison results. According to the security analysis, the proposed protocol can resist both outsider attacks and participants’ attacks. Compared with the existing QPC protocols, the proposed one does not require any entanglement swapping technology, but it can compare two participants’ qubits by performing swap test, which is easier to implement with current technology. Meanwhile, the proposed protocol can compare secret integers. It encodes secret integers into the amplitude of quantum state rather than transfer them as binary representations, and the encoded quantum state is compared by performing the swap test. Additionally, the proposed QPC protocol is extended to the QPC of arbitrary single qubit states by using multi-qubit swap test.