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Sharing human genotype and phenotype data is essential to discover otherwise inaccessible genetic associations, but is a challenge because of privacy concerns. 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 analytically interchangeable. The encryption uses a high-dimensional random linear orthogonal transformation key 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 can be replaced by quantiles from a Gaussian with negligible effects on accuracy. Likelihood-based inferences are unaffected by orthogonal encryption. These include linear mixed models to control for unequal relatedness between individuals, heritability estimation, and including covariates when testing association. Orthogonal transformations can be applied in a modular fashion for multiparty federated mega-analyses where the parties first agree to share a common set of genotype sites and covariates prior to encryption. Each then privately encrypts and shares their own ciphertext, and analyses all 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. We present the method as a challenge to the community to determine its security.

Private Genomes and Public SNPs: Homomorphic Encryption of Genotypes and Phenotypes for Shared Quantitative Genetics