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Besides their security, the efficiency of searchable encryption schemes is a major criteria when it comes to their adoption: in order to replace an unencrypted database by a more secure construction, it must scale to the systems which rely on it. Unfortunately, the relationship between the efficiency and the security of searchable encryption has not been widely studied, and the minimum cost of some crucial security properties is still unclear. In this paper, we present new lower bounds on thedoi:10.2478/popets-2019-0062 dblp:journals/popets/BostF19 fatcat:75qkqxl4mffkdgj3qp5udrkjki