Doing real work with FHE: The case of logistic regression

We describe our recent experience, building a system that uses fully-homomorphic encryption (FHE) to approximate the coefficients of a logistic-regression model, built from genomic data. The aim of this project was to examine the feasibility of a solution that operates "deep within the bootstrapping regime," solving a problem that appears too hard to be addressed just with somewhat-homomorphic encryption. As part of this project, we implemented optimized versions of many bread and butter FHE tools. These tools include binary arithmetic, comparisons, partial sorting, and low-precision approximation of arbitrary functions (used for reciprocals, logarithms, etc.). Our solution can handle thousands of records and hundreds of fields, and it takes a few hours to run. To achieve this performance we had to be extremely frugal with expensive bootstrapping and data-movement operations. We believe that our experience in this project could serve as a guide for what is or is not currently feasible to do with fully-homomorphic encryption.