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In this paper, a private searching protocol on MapReduce is introduced and formalized within the Mapping-Filtering-Reducing framework. The idea behind of our construction is that a map function Map is activated to generate (key, value) pairs; an intermedial filtering protocol is invoked to filter (key, value) pairs according to a query criteria; a reduce function Reduce is then applied to aggregate the resulting (key, value) pairs generated by the filter. The map function Map and the reduce function Reduction are inherently derived from the MapReduce program while the intermedial filtering algorithm is constructed from the state-of-the-art filtering protocol which in turn can be constructed from a Bloom-Filter with Storage and an additively homomorphic public-key encryption scheme. We show that if the underlying additively homomorphic public-key encryption is semantically secure, then the proposed private searching protocol on MapReduce is semantically secure.