HOMOMORPHIC ENCRYPTION AND ALGEBRAIC GEOMETRY FOR PRIVACY-PRESERVING MACHINE LEARNING

Abstract

The increasing acceptance of machine learning (ML) in sensitive applications such as health care, finance, and enforcement brings many serious privacy concerns requiring privacy-preserving techniques to be developed. Homomorphic encryption (HE) seems to be a good approach permitting various computations to be carried out on encrypted data without decryption thereby preserving data privacy. The disadvantages of HE are essentially the time required to do the computation and also its scalability. The results obtained have great consequences since the security obtained through this scheme seems to make it possible to apply encryption to large scale ML models. These disadvantages can be solved to a great extent through the introduction of the mathematics of algebraic geometry where polynomial equations are considered. Algebraic geometry will now play an important part in rendering schemes of HE economical and practicable through research within this field. This article reveals the close inter-relation existing between homomorphic encryption and algebraic geometry and attempts to outline briefly some of the developments, problems and possibilities of this forthcoming research. However, in spite of the great advantages to be gained or the possibilities of privacy preserving schemes of HE and algebraic geometry in ML, ML is as yet under threat of moral, scalability and computational disadvantages which threaten its complete acceptance.