Achieving GWAS with Homomorphic Encryption

One way of investigating how genes affect human traits would be with a genome-wide association study (GWAS). Genetic markers, known as single-nucleotide polymorphism (SNP), are used in GWAS. This raises privacy and security concerns as these genetic markers can be used to identify individuals uniquely. This problem is further exacerbated by a large number of SNPs needed, which produce reliable results at a higher risk of compromising the privacy of participants. We describe a method using homomorphic encryption (HE) to perform GWAS in a secure and private setting. This work is based on a semi-parallel logistic regression algorithm proposed to accelerate GWAS computations. Our solution involves homomorphically encrypted matrices and suitable approximations that adapts the original algorithm to be HE-friendly. Our best implementation took $24.70$ minutes for a dataset with $245$ samples, $4$ covariates and $10643$ SNPs. We demonstrate that it is possible to achieve GWAS with homomorphic encryption with suitable approximations.