Homomorphic Training of 30, 000 Logistic Regression Models.

In this work, we demonstrate the use the CKKS homomorphic encryption scheme to train a large number of logistic regression models simultaneously, as needed to run a genome-wide association study (GWAS) on encrypted data. Our implementation can train more than 30,000 models (each with four features) in about 20min. To that end, we rely on a similar iterative Nesterov procedure to what was used by Kim, Song, Kim, Lee, and Cheon to train a single model [14]. We adapt this method to train many models simultaneously using the SIMD capabilities of the CKKS scheme. We also performed a thorough validation of this iterative method and evaluated its suitability both as a generic method for computing logistic regression models, and specifically for GWAS.