Efficient protocols for set intersection and pattern matching with security against malicious and covert adversaries

In this paper, we construct efficient secure protocols for set intersection and pattern matching. Our protocols for secure computing the set intersection functionality are based on secure pseudorandom function evaluations, in contrast to previous protocols that are based on polynomials. In addition to the above, we also use secure pseudorandom function evaluation in order to achieve secure pattern matching. In this case, we utilize specific properties of the Naor-Reingold pseudorandom function in order to achieve high efficiency. Our results are presented in two adversary models. Our protocol for secure pattern matching and one of our protocols for set intersection achieve security against malicious adversaries under a relaxed definition where one corruption case is simulatable and, for the other, only privacy (formalized through indistinguishability) is guaranteed. We also present a protocol for set intersection that is fully simulatable in the model of covert adversaries. Loosely speaking, this means that a malicious adversary can cheat but will then be caught with good probability.