Paper 2024/1494 Original: eprint.iacr.org/2024/1494 ↗

Concretely Efficient Private Set Union via Circuit-based PSI

Abstract

Private set intersection (PSI) is a type of private set operation (PSO) for which concretely efficient linear-complexity protocols do exist. However, the situation is currently less satisfactory for other relevant PSO problems such as private set union (PSU): For PSU, the most promising protocols either rely entirely on computationally expensive public-key operations or suffer from substantial communication overhead. In this work, we present the first PSU protocol that is mainly based on efficient symmetric-key primitives yet enjoys comparable communication as public-key-based alternatives. Our core idea is to re-purpose state-of-the-art circuit-based PSI to realize a multi-query reverse private membership test (mq-RPMT), which is instrumental for building PSU. We carefully analyze a privacy leakage issue resulting from the hashing paradigm commonly utilized in circuit-based PSI and show how to mitigate this via oblivious pseudorandom function (OPRF) and new shuffle sub-protocols. Our protocol is modularly designed as a sequential execution of different building blocks that can be easily replaced by more efficient variants in the future, which will directly benefit the overall performance. We implement our resulting PSU protocol, showing a run-time improvement of 10% over the state-of-the-art public-key-based protocol of Chen et al. (PKC'24) for input sets of size $2^{20}$. Furthermore, we improve communication by $1.6\times$ over the state-of-the-art symmetric-key-based protocol of Zhang et al. (USENIX Sec'23).