Private set intersection (PSI) is a cryptographic protocol that enables two parties to securely determine the intersection of their private datasets without revealing anything except the intersection. Most of the existing PSI protocols are based on traditional number theoretic problems, such as discrete logarithm problem and factorisation problem. Unfortunately, these protocols would be broken if efficient quantum computer emerges. The post-quantum PSI is an important alternative to traditional PSI protocols for its potential to resist future attacks of quantum computers. In this work, we present first post-quantum PSI protocol that achieves size-hiding property. Space-efficient probabilistic data structure Bloom filter along with lattice-based public key encryption are used as building blocks of our construction. It attains linear complexity and security in standard model under the decisional learning with errors (DLWE) assumption. Moreover, we extend our post-quantum PSI to its authorised variant APSI retaining all the properties.
Private set intersection (PSI) is a cryptographic protocol that enables two parties to securely determine the intersection of their private datasets without revealing anything except the intersection. Most of the existing PSI protocols are based on traditional number theoretic problems, such as discrete logarithm problem and factorisation problem. Unfortunately, these protocols would be broken if efficient quantum computer emerges. The post-quantum PSI is an important alternative to traditional PSI protocols for its potential to resist future attacks of quantum computers. In this work, we present first post-quantum PSI protocol that achieves size-hiding property. Space-efficient probabilistic data structure Bloom filter along with lattice-based public key encryption are used as building blocks of our construction. It attains linear complexity and security in standard model under the decisional learning with errors (DLWE) assumption. Moreover, we extend our post-quantum PSI to its authorised variant APSI retaining all the properties.
Nowadays, the necessity of electronic information increases rapidly. As a consequence, often, that information needs to be shared among mutually distrustful parties. In this area, private set intersection (PSI) and its variants play an important role when the participants wish to do secret operations on their input sets. Unlike the most modern public key cryptosystems relying on number theoretic problems, lattice‐based cryptographic constructions provide security in the presence of a quantum computer. Consequently, developing PSI and its variants using lattice based cryptosystem becomes an interesting direction for research. This study presents the first size‐hiding post quantum PSI cardinality (PSI‐CA) protocol whose complexity is linear in the size of the sets of the participants. The authors use space‐efficient probabilistic data structure (Bloom filter) as its building block. Further, they extend the authors’ PSI‐CA to its authorised version, i.e. authorised PSI‐CA. Security for both of them is achieved in the standard model based on the hardness of the decisional learning with errors problem.
The healthcare pandemic (for instance, the recently ongoing Coronavirus disease (COVID-19) pandemic) presented a challenge for researchers to find novel techniques to limit the transmission of the virus. In this context, contact tracing has emerged as an important method to curb the spread of disease. Although it can help combat disease outbreaks, if the contact tracing is executed without careful consideration then it could jeopardize the users’ privacy. The cryptographic technique, private set intersection (PSI) appears to be a logical solution. However, many existing PSI protocols rely on the security of number theory based problems, which are vulnerable in the quantum domain. Therefore, to address this issue we present a PSI protocol (namely qPSI) based on quantum cryptography. The communication and computational costs of existing schemes depend on the universal set size N. In comparison, qPSI requires computational and communication costs, which are independent of the universal set size N. Moreover, the existing Bloom filter based quantum PSI does not provide the exact intersection due to high false positive rate of the Bloom filter of server’s private set, whereas qPSI is not affected by the false positive rate and provides the exact set intersection. In addition, quantum PSI protocols use multi-particle entangled state or N single photons, and complicated oracle operators in N-dimensional Hilbert space. On the other hand, qPSI only utilizes single-photon quantum resources and projective measurements operations over a 2-dimensional Hilbert space. Therefore, qPSI is simple and efficient when compared to other existing PSI protocols in the state-of-the-art.
While tremendous progress has been made towards achieving highly efficient and practical Private Set Intersection (PSI) protocols during the last decade, the development of post-quantum PSI is still far from satisfactory. Existing post-quantum PSI protocols encounter a dilemma: while those based on fully homomorphic encryption (FHE) achieve low online communication, they suffer from significant online computation; conversely, protocols based on post-quantum Oblivious Pseudorandom Functions (OPRFs) exhibit excellent online computational performance but incur substantially high online communication. To overcome this dilemma, we present a lattice-based PSI protocol that achieves optimal online performance in both communication and computation. Our solution introduces two core innovations: a robust signal comparison algorithm based on RLWE key exchange, which determines the intersection through signal consistency rather than direct shared key comparison, and an optimized Oblivious Key–Value Stores (OKVS) implementation featuring a composite key–value mapping for efficient handling of high-dimensional RLWE polynomials. We implement the protocol and conduct extensive benchmarks in both symmetric and asymmetric set-size settings. The results show that our construction achieves the lowest online overhead in both computation and communication among all tests. For example, with asymmetric set sizes (212,11041), the online phase requires only 0.132 s, yielding 19× and 282× improvements over FHE-based (CCS’21) and OPRF-based (EUROCRYPT’25) protocols, respectively. Even at (224,11041), our online communication time is only 0.201 s, which is 226× and 184× that of FHE-based and OPRF-based PSI, respectively. Additionally, our online communication overhead is the lowest in all tests; however, this comes at the cost of heavy offline communication overhead for very large set sizes, revealing a clear trade-off between pre-computation and online efficiency. This work addresses a critical gap in post-quantum PSI by delivering a protocol that achieves balanced online communication and computational overhead, thereby enabling broader practical deployment.
Private set intersection (PSI) is a cryptographic primitive that allows two or more parties to learn the intersection of their input sets and nothing else. In this paper, we introduce a new secure multi-party quantum computation for the greatest common divisor (GCD) and a PSI protocol based on it. The protocol extends the recent least common multiple (LCM)-based quantum private set union protocol by Liu et al. Performance analysis verifies the correctness and demonstrates the entire security of the suggested protocols in the semi-honest model. Additionally, it has been demonstrated that the complexity is efficient in terms of the input set size.
In this study, we propose a novel post‐quantum private set intersection (PSI) protocol based on the ring learning with errors (RLWE) assumption. Different from existing PSI protocols based on post‐quantum oblivious pseudorandom functions (EUROCRYPT’25) and fully homomorphic encryption (FHE) (CCS’21), our construction follows the Diffie–Hellman (DH)‐based PSI paradigm and uses post‐quantum key exchange to achieve PSI functionality. Our key technique is a signal matching (SigMa) mechanism, which determines whether two items match by checking the consistency of the reconciliation signals derived from their corresponding shared keys. The resulting PSI protocol completes in three rounds. In the first two rounds, the parties exchange RLWE‐based public keys associated with their items; in the third round, the sender transmits the corresponding signals. The receiver then applies SigMa to compare the received signals with its locally computed signals and thereby identify the intersection. We implement our protocol and compare it with Cong et al. (CCS’21) and Heimberger et al. (EUROCRYPT’25). Our protocol achieves the lowest online communication across all evaluated symmetric and asymmetric set‐size configurations, at the cost of additional offline communication. It also achieves the lowest online and total times among the evaluated protocols for all symmetric settings with | X | = | Y | ∈ {2 12 , 2 16 , 2 20 } and all asymmetric settings with | X | ∈ {2 12 , 2 16 , 2 20 } and | Y | ∈ {5535, 11041}. We believe that our work not only supplements existing post‐quantum PSI frameworks but also opens the opportunity for broader applications of post‐quantum PSI.
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.