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Objective  Developed sequencing techniques are yielding large-scale genomic data at low cost. A genome-wide association study (GWAS) targeting genetic variations that are significantly associated with a particular disease offers great potential for medical improvement. However, subjects who volunteer their genomic data expose themselves to the risk of privacy invasion; these privacy concerns prevent efficient genomic data sharing. Our goal is to presents a cryptographic solution to this problem.    Methods  To maintain the privacy of subjects, we propose encryption of all genotype and phenotype data. To allow the cloud to perform meaningful computation in relation to the encrypted data, we use a fully homomorphic encryption scheme. Noting that we can evaluate typical statistics for GWAS from a frequency table, our solution evaluates frequency tables with encrypted genomic and clinical data as input. We propose to use a packing technique for efficient evaluation of these frequency tables.    Results  Our solution supports evaluation of the  D′  measure of linkage disequilibrium, the Hardy-Weinberg Equilibrium, the  χ  2  test, etc. In this paper, we take  χ  2  test and linkage disequilibrium as examples and demonstrate how we can conduct these algorithms securely and efficiently in an outsourcing setting. We demonstrate with experimentation that secure outsourcing computation of one  χ  2  test with 10, 000 subjects requires about 35 ms and evaluation of one linkage disequilibrium with 10, 000 subjects requires about 80 ms.    Conclusions  With appropriate encoding and packing technique, cryptographic solutions based on fully homomorphic encryption for secure computations of GWAS can be practical.

Privacy-preserving genome-wide association studies on cloud environment using fully homomorphic encryption