IEEE Computational Intelligence Magazine - August 2022 - 25

models. The next challenge to address is the training of
machine and deep learning models directly on encrypted
data. The main issue to be addressed here is to manage the
NB consumption not only during the inference, but also
during the training of the privacy-preserving model.
Having outlined the main challenges to be addressed in this
research area, the next section presents a collection of useful
resources for privacy-preserving deep learning with HE.
VI. Available Resources for Privacy-Preserving Deep
Learning With Homomorphic Encryption
Two main frameworks for HE, which can be used to facilitate
the design of privacy-preserving deep learning solutions, are
available in the literature: SEAL and HElib. SEAL [19] is a
Microsoft C++ library that implements the BFV and CKKS
schemes. It offers helper functions for selecting the encryption
parameters as well as provides support for basic HE operations
(e.g., encrypting and decrypting values). Python users may refer
to Pyfhel [27] and TenSEAL [28], which are Python wrappers
for SEAL. The code used in the present study relies on SEAL
and Pyfhel, while Torch [29] was used for the training of the
plain-version of the CNNs. HElib [30] is a C++ library that
implements the CKKS scheme, among others. HElib also
includes optimization mechanisms for efficient homomorphic
evaluation, focusing on the effective use of ciphertext packing
techniques and Gentry-Halevi-Smart optimizations.
Concrete [31] is a Rust implementation of the TFHE
scheme, while a few examples of software libraries specifically
intended for HE-based machine and deep learning are available,
such as PyCrCNN [32], nGraph-HE [9], and CHET [33].
VII. Conclusions
The aim of this study was to explore the promising but highly
challenging research area of privacy-preserving deep learning
based on HE. Specifically, the BFV scheme and its privacy-preserving
operations were introduced both theoretically and algorithmically
through Python code examples. A methodology for
designing privacy-preserving CNNs was also proposed, which
was applied to the design of a privacy-preserving version of the
well-known LeNet-1. Experimental results on two datasets highlighted
that it is possible to design privacy-preserving CNNs
with HE, which are characterized by a negligible loss in accuracy
(w.r.t. the original version) and relevant increases in memory and
computational demand. Finally, this paper described the research
challenges to be addressed in this field as well as the available
software resources for privacy-preserving deep learning.
The path toward privacy-preserving deep learning with HE
has now been traced. Over the next few years, great advances
will be made in this direction.
Acknowledgment
This work was partially funded by the CATCH 4.0 project
within the Italian Programma Operativo Nazionale (PON)
" Imprese e competitività " FESR 2014/2020, and by Dhiria
S.r.l., a spin-off of Politecnico di Milano.
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