Optimizing parameters for efficient computation with fully homomorphic encryption schemes

In this study, we aim to provide a parameter selection approach for the BFVrns scheme, one of the prominent fully homomorphic encryption (FHE) schemes. Selecting parameters for lattice-based FHE schemes poses a practical challenge for both experts and nonexperts. To solve this problem, we introduce a hybrid approach that combines theoretical approach with experimental analysis. First, we employ regression analysis to examine the impact of parameters on both performance and security. The varying behavior of FHE parameters in terms of performance, security, and ciphertext expansion factor (CEF) makes parameter selection more challenging. To address this issue, we employ a multi-objective optimization algorithm to determine the optimal parameter set for performance, CEF, and security simultaneously. As a result of this optimization, we obtain an improved parameter set that enhances performance at a given security level while ensuring correctness and resistance to lattice-based attacks, maintaining at least 128-bit security. Our results achieve an average ∼ 5× reduction in CEF and generally better performance compared to the parameter sets in a previous BFVrns study. Our approach serves as a semi-automated parameter selection method for the PALISADE homomorphic encryption library, a widely recognized FHE library. This study sets a precedent for other FHE libraries.