Card-based Cryptographic Protocols for Private Set Intersection

Card-based cryptography is a cryptographic technique that realizes Multi-Party Computation (MPC) using physical cards. Although various protocols have been studied in card-based cryptography, there is no research on card-based Private Set Intersection (PSI). PSI is one of the well-studied MPC protocols which enables parties to compute the set intersection while keeping their data sets secret. This paper focuses on PSI in card-based cryptography for the first time, and shows several card-based PSI protocols. In card-based cryptography, there are two operation models: one assumes that all operations are performed publicly, and the other allows private operations. We propose PSI protocols under each model. We first show that PSI can be realized under each model by utilizing the existing card-based AND protocols. Furthermore, we propose more efficient PSI protocols than the PSI protocols based on AND protocols under each model.