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Background While genomic variations can provide valuable information for health care and ancestry, the privacy of individual genomic data must be protected. Thus, a secure environment is desirable for a human DNA database such that the total data are queryable but not directly accessible to involved parties (eg, data hosts and hospitals) and that the query results are learned only by the user or authorized party. Objective In this study, we provide efficient and secure computations on panels of single nucleotide polymorphisms (SNPs) from genomic sequences as computed under the following set operations: union, intersection, set difference, and symmetric difference. Methods Using these operations, we can compute similarity metrics, such as the Jaccard similarity, which could allow querying a DNA database to find the same person and genetic relatives securely. We analyzed various security paradigms and show metrics for the protocols under several security assumptions, such as semihonest, malicious with honest majority, and malicious with a malicious majority. Results We show that our methods can be used practically on realistically sized data. Specifically, we can compute the Jaccard similarity of two genomes when considering sets of SNPs, each with 400,000 SNPs, in 2.16 seconds with the assumption of a malicious adversary in an honest majority and 0.36 seconds under a semihonest model. Conclusions Our methods may help adopt trusted environments for hosting individual genomic data with end-to-end data security.