Private set intersection (PSI) is a fundamental cryptographic task that allows two mutually distrusting parties, each holding a private set of elements, to jointly compute the intersection of their sets. It ensures a symmetric information structure where neither party gains any knowledge about the other’s elements beyond those in the shared intersection. Traditional PSI protocols are primarily designed for static settings, which limits their applicability and efficiency in dynamic scenarios where input sets continuously evolve. To address this challenge, the notion of updatable PSI (UPSI) was introduced, enabling repeated PSI computations over changing inputs while preserving the symmetric privacy guarantees between participants. Despite the numerous recent advancements in UPSI research, it still suffers from significant communication overhead. In this paper, we address this challenge by introducing LcUPSI (low-communication UPSI), a new updatable PSI protocol that achieves remarkably low communication overhead. We formally prove that LcUPSI is secure in the semi-honest model. Furthermore, we compare the LcUPSI protocol with the state-of-the-art UPSI protocol BMSTZ24 (ASIACRYPT). The results demonstrate that LcUPSI significantly reduces communication overhead, highlighting its advantages in low-bandwidth conditions.
Private set intersection (PSI) is a fundamental cryptographic task that allows two mutually distrusting parties, each holding a private set of elements, to jointly compute the intersection of their sets. It ensures a symmetric information structure where neither party gains any knowledge about the other’s elements beyond those in the shared intersection. Traditional PSI protocols are primarily designed for static settings, which limits their applicability and efficiency in dynamic scenarios where input sets continuously evolve. To address this challenge, the notion of updatable PSI (UPSI) was introduced, enabling repeated PSI computations over changing inputs while preserving the symmetric privacy guarantees between participants. Despite the numerous recent advancements in UPSI research, it still suffers from significant communication overhead. In this paper, we address this challenge by introducing LcUPSI (low-communication UPSI), a new updatable PSI protocol that achieves remarkably low communication overhead. We formally prove that LcUPSI is secure in the semi-honest model. Furthermore, we compare the LcUPSI protocol with the state-of-the-art UPSI protocol BMSTZ24 (ASIACRYPT). The results demonstrate that LcUPSI significantly reduces communication overhead, highlighting its advantages in low-bandwidth conditions.
Private set intersection (PSI) is a cryptographic functionality for two parties to learn the intersection of their input sets, without leaking any other information. Circuit-PSI is a stronger PSI functionality where the parties learn only a secret-shared form of the desired intersection, thus without revealing the intersection directly. These secret shares can subsequently serve as input to a secure multiparty computation of any function on this intersection. In this paper we consider several settings in which parties take part in multiple Circuit-PSI executions with the same input set, and aim to amortize communications and computations. To that end, we build up a new framework for Circuit-PSI around generalizations of oblivious (programmable) PRFs that are extended with offline setup phases. We present several efficient instantiations of this framework with new security proofs for this setting. As a side result, we obtain a slight improvement in communication and computation complexity over the state-of-the-art semi-honest Circuit-PSI protocol by Bienstock et al. (USENIX '23). Additionally, we present a novel Circuit-PSI protocol from a PRF with secret-shared outputs, which has linear communication and computation complexity in the parties' input set sizes, and is able to realize a stronger security notion. Lastly, we derive the potential amortizations over multiple protocol executions, and observe that each of the presented instantiations is favorable in at least one of the multiple-execution settings.
Private set intersection (PSI) is a valuable technique with various practical applications, including secure matching of communication packets in the Internet of Things. However, most of the currently available two-party PSI protocols are based on the oblivious transfer (OT) protocol, which is computationally expensive and results in significant communication overhead. In this paper, we propose a new coding method to design a two-party PSI protocol under the semi-honest model. We analyze possible malicious attacks and then develop a PSI protocol under the malicious model using the Paillier cryptosystem, cut-and-choose, zero-knowledge proof, and other cryptographic tools. By adopting the real/ideal model paradigm, we prove the protocol’s security under the malicious model, which is more efficient compared to the existing related schemes.
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.
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.
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 needsO(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.
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.