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In this article, we propose a novel model, Priv-GenDB, for securely storing and efficiently conducting different queries on genomic data outsourced to an honest-but-curious cloud server. To instantiate PrivGenDB, we use searchable symmetric encryption (SSE) to ensure confidentiality while providing the required functionality. To the best of our knowledge, Priv-GenDB construction is the first SSE-based approach ensuring the confidentiality of shared single nucleotide polymorphism (SNP)-phenotype data through encryption while making the computation/query process efficient and scalable for biomedical research and care. It supports a variety of query types on genomic data, including count queries, Boolean queries, and k -out-of-k match queries. Finally, the PrivGenDB model not only can handle the dataset containing both genotype and phenotype, but it also supports storing and managing other metadata like gender and ethnicity privately. Computer evaluations on a dataset with 5, 000 records and 1, 000 SNPs demonstrate that a count/Boolean query and a k -out-of-k match query over 40 SNPs take approximately 4.3s and 86.4µs, respectively, that outperforms the existing schemes.