Multi-party private set intersection (MPSI) allows 𝑛(𝑛 ≥ 3) participants, each holding a dataset of size 𝑚, to compute the intersection of their sets without revealing any additional information.We extract a primitive called bicentric zero-sharing, which can reduce MPSI to two-party PSI between two central participants named Pivot and Leader.We introduce an efficient instantiation of bicentric zero-sharing, which involves a round of sharing and reconstruction of an oblivious key-value store (OKVS) object.We then combine this construction with two-party PSI to propose a new efficient scalable MPSI protocol.We also propose protocols for computing MPSI variants based on bicentric zero-sharing, such as multi-party private set intersection cardinality (MPSI-CA) and multi-party threshold private set intersection (MTPSI).Our protocols are mainly based on symmetric-key operations, and the communication complexity of each participant is at most O (𝑛 + 𝑚).The security of our protocols relies on the assumption * The first two authors contribute equally.

Vector databases have emerged as crucial tools for managing and retrieving representation embeddings of unstructured data. Given the explosive growth of data, vector data is often distributed and stored across multiple organizations. However, privacy concerns and regulations like GDPR present new challenges in collaborative and secure queries, also known as federated queries, over those vector data distributed across various data owners. Although existing research has attempted to enable such query services for low-dimensional data, such as relational and spatial data, these solutions can be inefficient in answering vector similarity queries involving high-dimensional data. Therefore, we are motivated to develop a new prototype system called FedSQ that (1) ensures privacy protection across data owners and (2) balances query efficiency and result accuracy when processing federated vector similarity queries. To achieve these goals, FedSQ utilizes advanced secure multi-party computation techniques to prevent information leakage during query processing and incorporates indexing and sampling based optimizations to strike a proper performance balance.