  Fully Homomorphic Encryption (FHE) is a relatively recent advancement in the
field of privacy-preserving technologies. FHE allows for the arbitrary depth
computation of both addition and multiplication, and thus the application of
abelian/polynomial equations, like those found in deep learning algorithms.
This project investigates, derives, and proves how FHE with deep learning can
be used at scale, with relatively low time complexity, the problems that such a
system incurs, and mitigations/solutions for such problems. In addition, we
discuss how this could have an impact on the future of data privacy and how it
can enable data sharing across various actors in the agri-food supply chain,
hence allowing the development of machine learning-based systems. Finally, we
find that although FHE incurs a high spatial complexity cost, the time
complexity is within expected reasonable bounds, while allowing for absolutely
private predictions to be made, in our case for milk yield prediction.
