  Homomorphic Encryption (HE) is a set of powerful properties of certain
cryptosystems that allow for privacy-preserving operation over the encrypted
text. Still, HE is not widespread due to limitations in terms of efficiency and
usability. Among the challenges of HE, scheme parametrization (i.e., the
selection of appropriate parameters within the algorithms) is a relevant
multi-faced problem. First, the parametrization needs to comply with a set of
properties to guarantee the security of the underlying scheme. Second,
parametrization requires a deep understanding of the low-level primitives since
the parameters have a confronting impact on the precision, performance, and
security of the scheme. Finally, the circuit to be executed influences, and it
is influenced by, the parametrization. Thus, there is no general optimal
selection of parameters, and this selection depends on the circuit and the
scenario of the application. Currently, most of the existing HE frameworks
require cryptographers to address these considerations manually. It requires a
minimum of expertise acquired through a steep learning curve. In this paper, we
propose a unified solution for the aforementioned challenges. Concretely, we
present an expert system combining Fuzzy Logic and Linear Programming. The
Fuzzy Logic Modules receive a user selection of high-level priorities for the
security, efficiency, and performance of the cryptosystem. Based on these
preferences, the expert system generates a Linear Programming Model that
obtains optimal combinations of parameters by considering those priorities
while preserving a minimum level of security for the cryptosystem. We conduct
an extended evaluation where we show that an expert system generates optimal
parameter selections that maintain user preferences without undergoing the
inherent complexity of analyzing the circuit.
