Private Genomes and Public SNPs: Homomorphic encryption of genotypes and phenotypes for shared quantitative genetics

Abstract

Sharing human genotype and phenotype data presents a challenge because of privacy concerns, but is essential in order to discover otherwise inaccessible genetic associations. Here we present a method of homomorphic encryption that obscures individuals genotypes and phenotypes and is suited to quantitative genetic association analysis. Encrypted ciphertext and unencrypted plaintext are interchangeable from an analytical perspective. This allows one to store ciphertext on public web services and share data across multiple studies, while maintaining privacy. The encryption method uses as its key a high-dimensional random linear orthogonal transformation that leaves the likelihood of quantitative trait data unchanged under a linear model with normally distributed errors. It also preserves linkage disequilibrium between genetic variants and associations between variants and phenotypes. It scrambles relationships between individuals: encrypted genotype dosages closely resemble Gaussian deviates, and in fact can be replaced by quantiles from a Gaussian with only negligible effects on accuracy. Standard likelihood-based inferences are unaffected by orthogonal encryption. These include the use of mixed linear models to control for unequal relatedness between individuals, the estimation of heritability, and the inclusion of covariates when testing for association. Orthogonal transformations can also be applied in a modular fashion that permits multi-party federated mega-analyses. Under this scheme any number of parties first agree to share a common set of genotype sites and covariates prior to encryption. Each party then privately encrypts and shares their own ciphertext, and analyses the other parties ciphertexts. In the absence of private variants, or knowledge of the key, we show that it is infeasible to decrypt ciphertext using existing brute-force or noise reduction attacks. Therefore, we present the method as a challenge to the community to determine its security.