  Fully homomorphic encryption (FHE) has experienced significant development
and continuous breakthroughs in theory, enabling its widespread application in
various fields, like outsourcing computation and secure multi-party computing,
in order to preserve privacy. Nonetheless, the application of FHE is
constrained by its substantial computing overhead and storage cost. Researchers
have proposed practical acceleration solutions to address these issues. This
paper aims to provide a comprehensive survey for systematically comparing and
analyzing the strengths and weaknesses of FHE acceleration schemes, which is
currently lacking in the literature. The relevant researches conducted between
2019 and 2022 are investigated. We first provide a comprehensive summary of the
latest research findings on accelerating FHE, aiming to offer valuable insights
for researchers interested in FHE acceleration. Secondly, we classify existing
acceleration schemes from algorithmic and hardware perspectives. We also
propose evaluation metrics and conduct a detailed comparison of various
methods. Finally, our study presents the future research directions of FHE
acceleration, and also offers both guidance and support for practical
application and theoretical research in this field.
