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Modern Physics Letters A

Quantum private set intersection with correlated sum using single photons

Yaohua Lu, Gangyi Ding

Published Dec 14, 2024• 0 citations

Abstract

Secure multi-party computation (SMC) enables multiple parties to collaboratively perform computational tasks without revealing their private data. A specific application scenario within SMC is Private Set Intersection with Correlated Sum (PSI-CS), where two participating parties compute the sum of associated elements in their intersection while preserving the privacy of their individual sets. This problem arises in various contexts, including calculating conversion amounts between suppliers and platforms, such as advertising conversion amounts and agency business conversion amounts. The paper proposes a protocol that employs quantum single-photon technology to compute the PSI-CS, provides four technical solutions suitable for various scenarios ranging from small to large data volumes, sparse to dense datasets, and without revealing the cardinality of the intersection. Additionally, the method extends to computing the union set with correlated sums. We experimentally validate the proposed protocol, conduct correctness and security analyses, and demonstrate its practical significance and application value. By utilizing single-photon technology, quantum gate operations, and measurements become more accessible, simplifying the protocol’s implementation. Notably, our approach provides unconditional security against quantum computational attacks, representing a substantial improvement in both efficiency and practical applicability compared to classical domain protocols.

DOI: 10.1142/s0217732324501839

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Secure multi-party computation (SMC) enables multiple parties to collaboratively perform computational tasks without revealing their private data. A specific application scenario within SMC is Private Set Intersection with Correlated Sum (PSI-CS), where two participating parties compute the sum of associated elements in their intersection while preserving the privacy of their individual sets. This problem arises in various contexts, including calculating conversion amounts between suppliers and platforms, such as advertising conversion amounts and agency business conversion amounts. The paper proposes a protocol that employs quantum single-photon technology to compute the PSI-CS, provides four technical solutions suitable for various scenarios ranging from small to large data volumes, sparse to dense datasets, and without revealing the cardinality of the intersection. Additionally, the method extends to computing the union set with correlated sums. We experimentally validate the proposed protocol, conduct correctness and security analyses, and demonstrate its practical significance and application value. By utilizing single-photon technology, quantum gate operations, and measurements become more accessible, simplifying the protocol’s implementation. Notably, our approach provides unconditional security against quantum computational attacks, representing a substantial improvement in both efficiency and practical applicability compared to classical domain protocols.

Abstract Private Set Intersection (PSI) is a crucial Secure Multi-Party Computation (SMPC) primitive which enables participants to securely obtain the intersection of their private sets without revealing their individual set information. The advent of quantum computing threatens classical PSI protocols, driving the development of Quantum PSI (QPSI) alternatives. We propose a two-party QPSI protocol based on a semi-honest third party. This protocol achieves set intersection using only single-qubit unitary operations and single-qubit states. Security analysis shows that our protocol can resist common attacks. Validation experiments conducted on the IBM Qiskit simulator confirm the protocol's correctness and feasibility. Furthermore, we compare the proposed protocol with existing QPSI protocols in terms of quantum states, unitary operations, measurements, and fairness, demonstrating gains in quantum resource efficiency, fairness, and practical feasibility.

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.

Abstract Quantum private set computation plays a crucial role in secure multi-party computation and privacy-preserving data mining. However, in quantum resource-constrained scenarios, most existing semi-quantum private set computation protocols rely on entangled states, making them difficult to scale effectively to multi-party settings. To address these limitations, this paper proposes a semi-quantum protocol for private set intersection and union cardinality computation. The proposed protocol uses single-particle states as information carriers and establishes the required keys by exploiting the correlations between prepared quantum states and selected measurement bases, thus avoiding the need for entangled states and pre-shared keys. By adopting a star topology, the protocol is further extended to general multiparty scenarios, with resource costs increasing linearly rather than exponentially. Security and performance analyses show that the proposed protocol can resist typical external and internal attacks. Compared with existing protocols, it reduces quantum resource requirements while achieving advantages in qubit efficiency and scalability.

Private Set Intersection Cardinality (PSI-CA) is to compute privately the cardinality of the intersection of two sets, and there are many practical applications of PSI-CA, e.g., data mining and data analysis with the privacy protection. The current classical protocols for PSI-CA could not resist the attacks of quantum computers. In this paper, we present a novel quantum protocol for PSI-CA based on the basic laws of quantum mechanics, which can resist well-known quantum attacks. This protocol utilizes single photons as quantum resources and only needs to apply simple single-photon operators and measurements. Therefore, it is more feasible to implement this protocol, compared with the related quantum protocols, which require entangled states and other complicated operators.

Recently, we proposed a quantum solution to the problem of private set intersection cardinality (PSI-CA) (Information Sciences 370–371 (2016) 147–158). Compared to classical solutions, the proposed quantum PSI-CA protocol achieves an exponential reduction in communication complexity, since it only needs

O(1)

communication cost. However, this protocol requires two additional assumptions about the cardinalities of the sets, which may limit its wider applications. In this paper, we successfully discard these assumptions and present a stronger quantum PSI-CA protocol without any limitation. The new protocol ensures the parties’ private security, i.e., unconditionally secure server privacy and statistically secure client privacy, and it achieves the constant computation and communication complexities, which are independent of the size of the sets. Therefore, it is more suitable for practical applications with big data sets.

Abstract As we know that data sharing, a critical element in social networks, has the benefits of exploring important information, while also has the disadvantage of information leakage. Therefore, without the reliable third party arbitration agency, it is impossible to share information privately by distrustful multi-party. In this paper, we proposed a protocol called Quantum Secure Multi-party Private Set Intersection Cardinality (QSMS-IC), which has the capability of resisting quantum attacks. QSMS-IC, the extension of two-parity private set intersection cardinality which was proposed in Information Sciences(2016,147-158), utilizes quantum transformation, quantum measurements and quantum parallelism to solve multi-party private set intersection cardinality problems. Compared with two-party PSI-CA protocols, our proposed protocol can solve the data sharing among multi-party without the reliable third party arbitration agency. It also can be used in numerous applications and more suitable to the actual cases. For instance, large-scale social networks and privacy-preserving data ming.