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Quantum Information Processing

Secure two-party integer comparison protocol without any third party

Runhua Shi, Bai Liu, Mingwu Zhang

Published Nov 24, 2021• 5 citations
Publisher
DOI
10.1007/s11128-021-03344-1

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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.
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.