Fully Homomorphic Encryption with Applications to Privacy-Preserving Machine Learning

Abstract

There are two dominant trends today that appear to be mutually exclusive: on the one hand, machine learning services that provide accurate predictions based on personal data have become widespread, but on the other hand, data privacy has become a paramount concern for many people. Furthermore, the use of machine learning is heavily restricted in situations like healthcare where it would be most impactful due to regulations preventing the sharing of private data. Fully Homomorphic Encryption (FHE) is the magic bullet that lets us “have our cake and eat it too,” allowing users to send their data to a remote machine learning provider and receive accurate predictions while mathematically guaranteeing complete data security. In this thesis, I give an exposition of Fully Homomorphic Encryption from first principles. I present the mathematical foundations of FHE, notably the Learning With Errors problem (and its Ring variant) used to prove FHE schemes secure, and then I describe two popular FHE schemes. Finally, I survey how FHE is currently used for machine learning, with a particular focus on settings where FHE unlocks opportunities that are otherwise infeasible due to privacy concerns. The primary contribution of this work is the completeness of its exposition, which takes a reader with no cryptography background to the forefront of current research in this revolutionary technology.