  Applying machine learning algorithms to private data, such as financial or
medical data, while preserving their confidentiality, is a difficult task.
Homomorphic Encryption (HE) is acknowledged for its ability to allow
computation on encrypted data, where both the input and output are encrypted,
which therefore enables secure inference on private data. Nonetheless, because
of the constraints of HE, such as its inability to evaluate non-polynomial
functions or to perform arbitrary matrix multiplication efficiently, only
inference of linear models seem usable in practice in the HE paradigm so far.
  In this paper, we propose Cryptotree, a framework that enables the use of
Random Forests (RF), a very powerful learning procedure compared to linear
regression, in the context of HE. To this aim, we first convert a regular RF to
a Neural RF, then adapt this to fit the HE scheme CKKS, which allows HE
operations on real values. Through SIMD operations, we are able to have quick
inference and prediction results better than the original RF on encrypted data.
