We describe a protocol for two-party private set intersection (PSI) based on Diffie-Hellman key agreement. The protocol is proven secure against malicious parties, in the ideal permutation + random oracle model.
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.
Abstract Card-based cryptography aims to realize secure multiparty computation with physical cards. This paper is the first to address Private Set Intersection (PSI) and Private Set Union (PSU) in card-based cryptography. PSI and PSU are well-studied secure computation protocols to compute the set intersection and the set union, respectively. We show two-party PSI and PSU protocols in each of the two operation models: one is the shuffle-based model in which parties perform all operations publicly, and the other is the private-permutation-based model that allows parties to perform some operations privately. In the shuffle-based model, we show PSI and PSU protocols can be realized with existing secure AND and OR protocols, respectively. However, these protocols have an issue of increasing the number of shuffles depending on the size of the universal set. To resolve the issue, we further propose PSI and PSU protocols with only one shuffle at the cost of increasing the number of cards. In the private-permutation-based model, we show PSI and PSU protocols can be achieved with existing secure AND and OR protocols, respectively, as in the shuffle-based protocols. These protocols have an advantage of requiring only one private permutation and one communication. We further show that the number of cards of these protocols can be reduced at the cost of increasing the number of private permutations and communications.
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 paper we focus on protocols for private set intersection (PSI), through which two parties, each holding a set of inputs drawn from a ground set, jointly compute the intersection of their sets. Ideally, no further information than which elements are actually shared is compromised to the other party, yet the input set sizes are often considered as admissible leakage.In the unconditional setting we evidence that PSI is impossible to realize and that unconditionally secure size-hiding PSI is possible assuming a set-up authority is present in an set up phase. In the computational setting we give a generic construction using smooth projective hash functions for languages derived from perfectly-binding commitments. Further, we give two size-hiding constructions: the first one is theoretical and evidences the equivalence between PSI, oblivious transfer and the secure computation of the AND function. The second one is a twist on the oblivious polynomial evaluation construction of Freedman et al. from EUROCRYPT 2004. We further sketch a generalization of the latter using algebraic-geometric techniques. Finally, assuming again there is a set-up authority (yet not necessarily trusted) we present very simple and efficient constructions that only hide the size of the client's set.
Private set intersection (PSI) has important application value, however, current quantum PSI protocols are either unsuitable for multi-party scenarios or inefficient. Recently, Imran (arXiv: 2303.17196v3 , 2023) proposed two quantum secure multi-party greatest common divisor (GCD) protocols that can be used for PSI, but with the downside of information leakage and resource consumption. In this paper, we propose a novel quantum secure multi-party GCD protocol that has higher security and lower complexity. To hide privacy, each party randomly selects a coefficient within a range determined by his input integer, and with the assistance of a semi-honest third party TP, all parties secretly calculate the linear combination of their inputs under these coefficients. Once enough linear combinations are collected, TP calculates the GCD of these combinations, which is equal to the GCD of all input integers. To verify the honesty of participants, a quantum zero-knowledge proof sub-protocol is designed. Analysis shows that our GCD protocol is correct and has security against malicious attacks. Moreover, its complexity is polynomial level and lower than Imran’s. Furthermore, we demonstrate the scalability of our GCD protocol in private set operations, such as private set intersection, private set intersection cardinality, private multi-set intersection, etc.