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IEEE Access

A Quantum Protocol for Secure Manhattan Distance Computation

Wen Liu, Wei Zhang

Published Jan 1, 2020• 6 citations
Publisher

Abstract

Secure Manhattan distance computation allows two parties to privately compute the Manhattan distance of their points, which is important and has broad applications. In this paper, we present a protocol for secure Manhattan distance computation based on phase shift operation. Because of quantum mechanics' physical principle, our protocol can also resist outside attacks and don't leak any private information of participants.

DOI
10.1109/access.2020.2966800

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Secure Manhattan distance computation allows two parties to privately compute the Manhattan distance of their points, which is important and has broad applications. In this paper, we present a protocol for secure Manhattan distance computation based on phase shift operation. Because of quantum mechanics' physical principle, our protocol can also resist outside attacks and don't leak any private information of participants.
Manhattan distance is mainly used to calculate the total absolute wheelbase of two points in the standard coordinate system. The secure computation of Manhattan distance is a new geometric problem of secure multi-party computation. At present, the existing research secure computing protocols for Manhattan distance cannot resist the attack of malicious participants. In the real scene, the existence of malicious participants makes it necessary to study a solution that can resist malicious attacks. This paper first analyzes malicious attacks of the semi-honest model protocol of computing Manhattan distance and then designs an advanced protocol under the malicious model by using the Goldwasser–Micali encryption system and Paillier encryption algorithm, and utilizing some cryptographic tools such as the cut-choose method and zero-knowledge proof. Finally, the real/ideal model paradigm method is used to prove the security of the malicious model protocol. Compared with existing protocols, the experimental simulation shows that the proposed protocol can resist malicious participant attacks while maintaining high efficiency. It has practical value.
With the advent of the big data era, crossorganizational collaborative data computing faces challenges in privacy protection. Traditional secure multi-party computation (MPC) protocols suffer from security insufficiency under the threat of quantum computing against classical encryption algorithms. To address this issue, this paper proposes a secure quantum protocol based on mutually unbiased bases (MUBs) in dlevel quantum systems. By leveraging quantum entanglement and quantum measurement techniques, the protocol accurately calculates the Euclidean distance between participants while ensuring privacy protection during the computation. Experimental results demonstrate that the protocol not only enhances computational efficiency but also effectively resists external attacks, participant attacks, and semi-honest third-party attacks, providing a new approach for the application of quantumsafe computing in privacy protection.
Semi-Quantum Private Comparison and Hamming Distance Calculation Based on ddd–Dimensional Bell States
This paper presents a semi-quantum private comparison and Hamming distance computation protocol based onddd-dimensional Bell states. The proposed protocol enables two parties, with the assistance of a trusted third party (TP), to determine whether their private information is identical and compute the Hamming distance without disclosing their secrets. In this protocol, the TP preparesddd-dimensional Bell states and distributes the entangled particles to Alice and Bob. Alice and Bob predetermine specific positions where they will perform REFLECT or MEASURE operations. Based on their measurement results, both parties encode their secret information and transmit the results to the TP via a classical channel. The TP then compares the data by incorporating pre-recorded offsets to determine whether the secrets are equal and to compute the Hamming distance, while ensuring that no private information is directly exposed. Compared to existing protocols, the proposed method demonstrates broader applicability in scenarios with limited quantum resources. To validate the protocol, we provide concrete examples demonstrating its theoretical and practical feasibility. Furthermore, security and efficiency analyses confirm its robustness against various external attacks and potential internal threats, including dishonest TP behavior.
Private Comparison (PC) is an extension of Yao's millionaire problem: two millionaires want to know if their wealth is equal, but they don't want to reveal their specific wealth. In classical cryptography, this problem has been well studied. However, the security issues of these protocols are based on computational complexity assumptions, which means they cannot resist powerful quantum computing. In this paper, a quantum private comparison of equality with better performance in resisting outside attack is proposed based on two parties. Compared with the previous protocol, our protocol greatly reduce the total probability of obtaining the wrong result. And it also can compare successfully even if the two hash value string are short and close. Meanwhile, our protocol can be implemented easily without using entanglement, joint measurements and quantum memory and so on. Finally, we show that our protocol can be secure against the attacks from both the outside eavesdroppers and the inside participants.
Secure multi-party computation (SMC) is an important privacy-preserving technology with broad applications in fields such as data mining and cloud computing. As a significant branch of SMC, private set computation (PSC) allows the computation of the intersection or union of private datasets from two or more participants while protecting their data privacy. Quantum private set computation (QPSC) is a new direction that combines PSC with quantum mechanics and has recently garnered widespread attention. Most existing QPSC protocols rely on quantum measurements performed by participants or third parties, but the measurement devices used in practice may be vulnerable to side-channel attacks. To address this issue, this paper proposes a measurement-device-independent QPSC protocol. In this protocol, participants can utilize post-selected Greenberger-Horne-Zeilinger (GHZ) state entanglement to compute the private intersection and union of their datasets securely. Analysis shows that this protocol is correct and can resist potential external and internal attacks. Finally, the protocol's feasibility is verified through simulation on the HIQ quantum computing cloud platform using the MindSpore Quantum framework.