Laconic updatable private set intersection

Abstract

A laconic private set intersection (PSI) protocol features a two-round communication process with an initial message that remains independent of the set sizes. It is useful for efficiently matching large server sets with smaller client sets without multiple rounds of interaction. The previous work by Aranha et al. (CCS’22) demonstrated superior efficiency but relied on a trusted third party to generate a secret value $s$ and all its powers, denoted as $(g,g^s,\dots ,g^{s^2},\dots ,g^{s^{\left|X\right|}})$, where $\left|X\right|$ represents the size of the receiver’s set $X$. However, these protocols did not address the practical need for updatable sets for both the receiver and sender, which implies the ability to add new elements, delete existing ones, or update an element by deleting it and subsequently adding a new one. In our work, we present an updatable private set intersection protocol that eliminates the need for a trusted third party. Our approach achieves constant communication complexity from the receiver to the sender and linear complexity from the sender to the receiver while partially hiding the size of the receiver’s set. We first establish an efficient PSI protocol and then propose two variants that allow both parties to modify their sets. Additionally, we prove the security of our proposed protocol against semi-honest participants within our security model.