Quantum Scheme for Private Set Intersection and Union Cardinality based on Quantum Homomorphic Encryption

TL;DR

This paper introduces a quantum protocol leveraging quantum homomorphic encryption to securely compute the intersection and union cardinalities of private sets, enhancing privacy and feasibility with simple quantum operations.

Contribution

It presents the first quantum PSI and PSU cardinality protocol based on QHE that uses only basic quantum gates, improving practicality and privacy.

Findings

Protocol operates on encrypted quantum states to prevent data leakage.

Uses only simple Pauli and CNOT gates, avoiding complex quantum operations.

Offers improved feasibility and privacy protection over existing methods.

Abstract

Private set intersection (PSI) and private set union (PSU) are the crucial primitives in secure multiparty computation protocols, which enable several participants to jointly compute the intersection and union of their private sets without revealing any additional information. Quantum homomorphic encryption (QHE) offers significant advantages in handling privacy-preserving computations. However, given the current limitations of quantum resources, developing efficient and feasible QHE-based protocols for PSI and PSU computations remains a critical challenge. In this work, a novel quantum private set intersection and union cardinality protocol is proposed, accompanied by the corresponding quantum circuits. Based on quantum homomorphic encryption, the protocol allows the intersection and union cardinality of users' private sets to be computed on quantum-encrypted data with the assistance of a semi-honest third party. By operating on encrypted quantum states, it effectively mitigates the risk of original information leakage. Furthermore, the protocol requires only simple Pauli and CNOT operations, avoiding the use of complex quantum manipulations (e.g., $T$ gate and phase rotation gate). Compared to related protocols, this approach offers advantages in feasibility and privacy protection.