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Abstract: We study a security model for searching documents containing each of several keywords (conjunctive keyword search) over encrypted documents. A conjunctive keyword search protocol consists of three entities: a data supplier, a storage system such as database, and a user of storage system. A data supplier uploads encrypted documents on a storage system, and then a user of the storage system searches documents containing each of several keywords with a private trapdoor. That is, a valid user is able to use boolean combinations of queries. Up to now only few conjunctive keyword search schemes have been proposed in the literature. However, the relying security model has not been based on relational databases such as Oracle and MS-Access, hence it is not easy to apply them in practice. Moreover, they have not considered an important security notion for user's trapdoor queries. In this paper, we first formally define a security model for conjunctive keyword search schemes including trapdoor security based on a practical relational database. We apply our security model to the existing conjunctive keyword scheme and discuss its vulnerability and countermeasure.