Quantum Secure Hamming Distance Computation Based on Single-Particle States

Secure Hamming distance computation is a critical problem in secure multiparty computation, enabling two parties to compute the Hamming distance between their private data while ensuring confidentiality. The Hamming distance measures the difference between two binary strings of equal length, making it an effective metric for data similarity. It has wide applications in fields such as data error correction (Hamming code), privacy-preserving computation, machine learning, pattern recognition, and so on. In this paper, we propose a quantum protocol for Hamming distance computation. With the assistance of a semi-honest third party (TP), two participants can securely compute the Hamming distance using single-particle states. The protocol requires only the application of the quantum operators \(X\) and \(I\) by the participants, with no need to prepare or measure the quantum state, ensuring its practical feasibility. The correctness and fairness analysis demonstrates the viability of the protocol, while the security analysis confirms its resilience to both internal and external attacks.