AnonPSI: An Anonymity Assessment Framework for PSI

Private Set Intersection (PSI) is a widely used protocol that enables two parties to securely compute a function over the intersected part of their shared datasets and has been a significant research focus over the years. However, recent studies have highlighted its vulnerability to Set Membership Inference Attacks (SMIA), where an adversary might deduce an individual's membership by invoking multiple PSI protocols. This presents a considerable risk, even in the most stringent versions of PSI, which only return the cardinality of the intersection. This paper explores the evaluation of anonymity within the PSI context. Initially, we highlight the reasons why existing works fall short in measuring privacy leakage, and subsequently propose two attack strategies that address these deficiencies. Furthermore, we provide theoretical guarantees on the performance of our proposed methods. In addition to these, we illustrate how the integration of auxiliary information, such as the sum of payloads associated with members of the intersection (PSI-SUM), can enhance attack efficiency. We conducted a comprehensive performance evaluation of various attack strategies proposed utilizing two real datasets. Our findings indicate that the methods we propose markedly enhance attack efficiency when contrasted with previous research endeavors. {The effective attacking implies that depending solely on existing PSI protocols may not provide an adequate level of privacy assurance. It is recommended to combine privacy-enhancing technologies synergistically to enhance privacy protection even further.