Paper 2018/202

Doing Real Work with FHE: The Case of Logistic Regression

Jack L.H. Crawford and Craig Gentry and Shai Halevi and Daniel Platt and Victor Shoup

Abstract

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 "complicated functions" such as reciprocals and logarithms. Our eventual 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 server as a guide for what is or is not currently feasible to do with fully-homomorphic encryption.