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In this paper, we propose a two‐way oblivious pseudorandom function (mOPRF) secure in standard model against malicious parties under the decisional composite residuosity and decisional Diffie–Hellman assumptions. Using this two‐way OPRF, we construct an optimistic mutual private set intersection (PSI) protocol conserving fairness. In our PSI protocol, fairness is obtained by a semi‐trusted arbiter in the sense that it cannot get access to the private information of the two parties, but we believe that it will follow the protocol. To the best of our knowledge, our PSI protocol is the first fair PSI with linear communication and computation complexities and is proven to be secure in standard model against malicious adversaries under decisional q‐Diffie–Hellman inversion, decisional composite residuosity, and decisional Diffie–Hellman assumptions. Apart from that, we present a modified version of the OPRF that requires less number of communication rounds. Copyright © 2016 John Wiley & Sons, Ltd.

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In the field of privacy preserving protocols, Private Set Intersection (PSI) plays an important role. In most of the cases, PSI allows two parties to securely determine the intersection of their private input sets, and no other information. In this paper, employing a Bloom filter, we propose a Multiparty Private Set Intersection Cardinality (MPSI-CA), where the number of participants in PSI is not limited to two. The security of our scheme is achieved in the standard model under the Decisional Diffie-Hellman (DDH) assumption against semi-honest adversaries. Our scheme is flexible in the sense that set size of one participant is independent from that of the others. We consider the number of modular exponentiations in order to determine computational complexity. In our construction, communication and computation overheads of each participant is O(vmaxk) except that the complexity of the designated party is O(v 1), where vmax is the maximum set size, v 1 denotes the set size of the designated party and k is a security parameter. Particularly, our MSPI-CA is the first that incurs linear complexity in terms of set size, namely O(nvmaxk), where n is the number of participants. Further, we extend our MPSI-CA to MPSI retaining all the security attributes and other properties. As far as we are aware of, there is no other MPSI so far where individual computational cost of each participant is independent of the number of participants. Unlike MPSI-CA, our MPSI does not require any kind of broadcast channel as it uses star network topology in the sense that a designated party communicates with everyone else.