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Data outsourcing on to the public cloud faces several security challenges. Ensuring the confidentiality of the outsourced sensitive data is of paramount importance for the adoption of public cloud for data outsourcing. Often the cloud storage servers are untrusted. Encryption method is used for maintaining the confidentiality of the outsourced data. Performing the queries on the encrypted data is a challenging task. Adversary should not gain any significant information other than the minimal information by observing the queries and the query responses. In this work, we provide two solutions which are efficient in processing the queries on the encrypted data. We focus on improving the performance of the query processing without compromising the privacy of the data and the queries. We show that adversary can gain no significant information about the data other than the minimal information which cannot be avoided. We conduct the empirical performance evaluations and compare with the scheme available in the literature. Our experiments show that the proposed schemes are efficient in comparison with the existing scheme.