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Private set intersection (PSI) is a fundamental cryptographic protocol which has a wide range of applications. It enables two clients to compute the intersection of their private datasets without revealing non-matching elements. The advent of cloud computing drives the ambition to reduce computation and data management overhead by outsourcing such computations. However, since the cloud is not trustworthy, some cryptographic methods should be applied to maintain the confidentiality of datasets. But, in doing so, data owners may be excluded from access control on their outsourced datasets. Therefore, to control access rights and to interact with authorized users, they have to be online during the protocol. On the other hand, none of the existing cloud-based PSI schemes support fine-grained access control over outsourced datasets. This paper, for the first time, proposes an attribute-based private set intersection …