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An Improved Quantum Private Set Intersection Protocol Based on Hadamard Gates

Wenjie Liu, Wenbo Li, Haibin Wang

TL;DR

This work identifies a privacy leakage issue in a quantum private set intersection (QPSI) protocol based on the quantum Fourier transform and proposes an improved Hadamard-gate–based QPSI that enhances privacy. By replacing the QFT with Hadamard gates and encoding private information on an auxiliary register via exclusive OR, the protocol prevents leakage of the difference set ${S_{ ext{diff}}}$ and protects private inputs outside the intersection. The authors provide a correctness proof and security analysis, showing resilience to both external eavesdroppers and participant-side attacks, and they emphasize practical advantages from implementation simplicity and privacy guarantees. The approach strengthens privacy-preserving quantum data collaboration and motivates further work on verifiable PSC in quantum settings.

Abstract

Recently, Liu and Yin (Int. J. Theor. Phys. 60, 2074-2083 (2021)) proposed a two-party private set intersection protocol based on quantum Fourier transform. We find the participant can deduce the other party's private information, which violates the security requirement of private set computation. In order to solve this problem, an improved private set intersection protocol based on Hadamard gate is proposed. Firstly, the more feasible Hadamard gates are used to perform on the original n qubits instead of the quantum Fourier transform, which may reduce the difficulty of implementation. In addition, through the exclusive OR calculation, the participant's private information is randomly chosen and encoded on the additional n qubits, which prevents participants from obtaining the result of the difference set S-diff , and then avoids the internal leakage of private information. Finally, the correctness and security analysis are conducted to show the proposed protocol can guarantee the correctness of computation result as well as resist outside attacks and participant internal attacks.

An Improved Quantum Private Set Intersection Protocol Based on Hadamard Gates

TL;DR

This work identifies a privacy leakage issue in a quantum private set intersection (QPSI) protocol based on the quantum Fourier transform and proposes an improved Hadamard-gate–based QPSI that enhances privacy. By replacing the QFT with Hadamard gates and encoding private information on an auxiliary register via exclusive OR, the protocol prevents leakage of the difference set and protects private inputs outside the intersection. The authors provide a correctness proof and security analysis, showing resilience to both external eavesdroppers and participant-side attacks, and they emphasize practical advantages from implementation simplicity and privacy guarantees. The approach strengthens privacy-preserving quantum data collaboration and motivates further work on verifiable PSC in quantum settings.

Abstract

Recently, Liu and Yin (Int. J. Theor. Phys. 60, 2074-2083 (2021)) proposed a two-party private set intersection protocol based on quantum Fourier transform. We find the participant can deduce the other party's private information, which violates the security requirement of private set computation. In order to solve this problem, an improved private set intersection protocol based on Hadamard gate is proposed. Firstly, the more feasible Hadamard gates are used to perform on the original n qubits instead of the quantum Fourier transform, which may reduce the difficulty of implementation. In addition, through the exclusive OR calculation, the participant's private information is randomly chosen and encoded on the additional n qubits, which prevents participants from obtaining the result of the difference set S-diff , and then avoids the internal leakage of private information. Finally, the correctness and security analysis are conducted to show the proposed protocol can guarantee the correctness of computation result as well as resist outside attacks and participant internal attacks.
Paper Structure (14 sections, 10 equations, 1 figure, 2 tables)

This paper contains 14 sections, 10 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. Review and analysis of NQPSI protocol
  3. Review on the NQPSI protocol
  4. Vulnerability analysis
  5. QPSI protocol based on $\rm H$ gates
  6. Correctness and security analysis
  7. Correctness analysis
  8. Security analysis
  9. Participant attack
  10. Case 1:
  11. Case 2:
  12. Case 3:
  13. Outside attack
  14. Conclusion

Figures (1)

  • Figure 1: Schematic diagram of QPSI protocol based on $\rm H$ gates. The line is the process from Step 1 to Step 6 in the protocol. Insertion of decoy photons and the eavesdropper detection are omitted here.