Optimizing Parameter Selection for Fully Homomorphic Encryption

Description

Fully Homomorphic Encryption (FHE) is a key technology for implementing privacypreserving
applications. While many FHE schemes are becoming more usable with
regard to performance overhead, a main challenge remains: selecting good parameters
for a specific application. The problem with parameter selection in FHE is that
parameters must not only be selected with respect to security, but with consideration
of performance and correctness of the homomorphic evaluation. Therefore, in this
work, we comprehensively describe the most important parameters and their impact
on security and their functionality for the BGV encryption scheme. We extend the
existing OpenFHE approach for parameter selection with newer noise estimations.
Furthermore, we introduce two optimization approaches that iteratively reduce moduli
sizes, thereby minimizing overall parameter sizes based on a level-wise circuit model
to allow for fast iterations.