International Association
for Cryptologic Research

Private set intersection (PSI) allows Sender holding a set \(X\) and Receiver holding a set \(Y\) to compute only the intersection \(X\cap Y\) for Receiver. We focus on a variant of PSI, called fuzzy PSI (FPSI), where Receiver only gets points in \(X\) that are at a distance not greater than a threshold from some points in \(Y\). Most current FPSI approaches first pick out pairs of points that are potentially close and then determine whether the distance of each selected pair is indeed small enough to yield FPSI result. Their complexity bottlenecks stem from the excessive number of point pairs selected by the first picking process. Regarding this process, we consider a more general notion, called fuzzy mapping (Fmap), which can map each point of two parties to a set of identifiers, with closely located points having a same identifier, which forms the selected point pairs. We initiate the formal study on Fmap and show novel Fmap instances for Hamming and \(L_\infty\) distances to reduce the number of selecte

Multi-party private set union (MPSU) allows \(k(k\geq 3)\) parties, each holding a dataset of known size, to compute the union of their sets without revealing any additional information. Although two-party PSU has made rapid progress in recent years, applying its effective techniques to the multi-party setting would render information leakage and thus cannot be directly extended. Existing MPSU protocols heavily rely on computationally expensive public-key operations or generic secure multi-party computation techniques, which are not scalable. In this work, we present a new efficient framework of MPSU from multi-party secret-shared shuffle and a newly introduced protocol called multi-query secret-shared private membership test (mq-ssPMT). Our MPSU is mainly based on symmetric-key operations and is secure against any semi-honest adversary that does not corrupt the leader and clients simultaneously. We also propose new frameworks for computing other multi-party private set operations (MPSO), such as the intersection, and the cardinality of the union and the intersection, meeting the same security requirements. We demonstrate the scalability of our MPSU protocol with an implementation and a comparison with the state-of-the-art MPSU. Experiments show that when computing on datasets of \(2^{10}\) elements, our protocol is \(109\times\) faster than the state-of-the-art MPSU, and the improvement becomes more significant as the set size increases. To the best of our knowledge, ours is the first protocol that reports on large-size experiments. For 7 parties with datasets of \(2^{20}\) elements each, our protocol requires only 46 seconds.

We improve the first and the only existing prime-order fully adaptively secure decentralized Multi-Authority Attribute-Based Encryption (MA-ABE) scheme for NC1 in Datta-Komargodski-Waters [Eurocrypt '23]. Compared with Datta-Komargodski-Waters, our decentralized MA-ABE scheme extra enjoys shorter parameters and meanwhile supports many-use of attribute. Shorter parameters is always the goal for Attribute-Based Encryption (ABE), and many-use of attribute is a native property of decentralized MA-ABE for NC1. Our scheme relies on the Matrix Decision Diffie-Hellman (MDDH) assumption and is in the random oracle model, as Datta-Komargodski-Waters.