Relation intersection is a fundamental problem, which becomes non-trivial when the relations to be intersected are too large to fit on a single machine. Hence, a natural approach is to design parallel algorithms that are executed on a cluster of machines rented from a public cloud provider. Intersection of relations becomes even more difficult when each relation belongs to a different data owner that wants to protect her data privacy. We consider the popular MapReduce paradigm for outsourcing data and computations to a semi-honest public cloud. Our main contribution is the SI protocol (for Secure Intersection) that allows to securely compute the intersection of an arbitrary number of relations, each of them being encrypted by its owner. The user allowed to query the intersection result has only to decrypt the result sent by the public cloud. SI does not leak (to the public cloud or to the user) any information on tuples that are not in the final relation intersection result, even if t he public cloud and the user collude i.e., they share all their private information. We prove the security of SI and provide an empirical evaluation showing its efficiency.