Minglang Dong | Searcharxiv

arXiv2025

Multi-Party Private Set Operations from Predicative Zero-Sharing

Typical protocols in the multi-party private set operations (MPSO) setting enable m > 2 parties to perform certain secure computation on the intersection or union of their private sets, realizing a very limited range of MPSO functionalities. Most works in this field focus on just one or two specific functionalities, resulting in a large variety of isolated schemes and a lack of a unified framework in MPSO research. In this work, we present an MPSO framework, which allows m parties, each holding a set, to securely compute any set formulas (arbitrary compositions of a finite number of binary set operations, including intersection, union and difference) on their private sets. Our framework is highly versatile and can be instantiated to accommodate a broad spectrum of MPSO functionalities. To the best of our knowledge, this is the first framework to achieve such a level of flexibility and generality in MPSO, without relying on generic secure multi-party computation (MPC) techniques. Our framework exhibits favorable theoretical and practical performance. The computation and communication complexity scale linearly with the set size n, and it achieves optimal complexity that is on par with the naive solution for widely used functionalities, such as multi-party private set intersection (MPSI), MPSI with cardinality output (MPSI-card), and MPSI with cardinality and sum (MPSI-card-sum), in the standard semi-honest model. Furthermore, the instantiations of our framework mainly from symmetric-key techniques yield efficient protocols for MPSI, MPSI-card, MPSI-card-sum, and multi-party private set union (MPSU), with online performance surpassing or matching the state of the art.

cs.CR↗

arXiv2024

Breaking Free: Efficient Multi-Party Private Set Union Without Non-Collusion Assumptions

Multi-party private set union (MPSU) protocol enables $m$ $(m > 2)$ parties, each holding a set, to collectively compute the union of their sets without revealing any additional information to other parties. There are two main categories of multi-party private set union (MPSU) protocols: The first category builds on public-key techniques, where existing works require a super-linear number of public-key operations, resulting in their poor practical efficiency. The second category builds on oblivious transfer and symmetric-key techniques. The only work in this category, proposed by Liu and Gao (ASIACRYPT 2023), features the best concrete performance among all existing protocols, but still has super-linear computation and communication. Moreover, it does not achieve the standard semi-honest security, as it inherently relies on a non-collusion assumption, which is unlikely to hold in practice. There remains two significant open problems so far: no MPSU protocol achieves semi-honest security based on oblivious transfer and symmetric-key techniques, and no MPSU protocol achieves both linear computation and linear communication complexity. In this work, we resolve both of them. - We propose the first MPSU protocol based on oblivious transfer and symmetric-key techniques in the standard semi-honest model. This protocol is $3.9-10.0 \times$ faster than Liu and Gao in the LAN setting. Concretely, our protocol requires only $4.4$ seconds in online phase for 3 parties with sets of $2^{20}$ items each. - We propose the first MPSU protocol achieving both linear computation and linear communication complexity, based on public-key operations. This protocol has the lowest overall communication costs and shows a factor of $3.0-36.5\times$ improvement in terms of overall communication compared to Liu and Gao.

cs.CR↗