Achieving GWAS with Homomorphic Encryption

Jun Jie Sim, Fook Mun Chan, Shibin Chen, Benjamin Hong Meng Tan, Khin Mi Mi Aung

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 proposed algorithm. Our solution mainly involves homomorphically encrypted matrix operations and suitable approximations that adapts the semi-parallel GWAS algorithm for HE. We leverage the complex space of the CKKS encryption scheme to increase the number of SNPs that can be packed within a ciphertext. We have also developed a cache module that manages ciphertexts, reducing the memory footprint. We have implemented our solution over two HE open source libraries, HEAAN and SEAL. Our best implementation took $24.70$ minutes for a dataset with $245$ samples, over $4$ covariates and $10643$ SNPs. We demonstrate that it is possible to achieve GWAS with homomorphic encryption with suitable approximations.

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