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.
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