Collusion-resistant outsourcing of private set intersection

Set intersection is a building block for many data analysis techniques, e.g. in data mining. Private set intersection enables to compute the set intersection without revealing the non-matching items. The advent of cloud computing drives the desire to outsource such computations, but without the need to trust the service provider. Homomorphic encryption enables secure, outsourced computations, but in case of multiple clients cannot prevent collusion. In this paper we present non-interactive, encrypted computation of the set intersection using an untrusted service provider. Two or more clients submit their encrypted sets to the service provider which facilitates the computation of their intersection. The service provider either learns the intersection or remains completely obvious to both input and output - including the intersection's size. We prove our protocols secure in the random oracle model and under the RSA assumption. Our prototypical implementation shows the difference between the protocols using different cryptographic techniques and that even a fully untrusted service provider can be practically feasible.

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