From accuracy to approximation: A survey on approximate homomorphic encryption and its applications

Due to the increasing popularity of application scenarios such as cloud computing, and the growing concern of users about the security and privacy of their data, information security and privacy protection technologies are facing new challenges. Consequently, Homomorphic Encryption (HE) technology has been developed. HE technology has evolved from Partially Homomorphic Encryption (PHE) to fully homomorphic encryption, from theory to practice Recently, the surge in machine learning applications has brought new challenges to HE technology. These applications require floating-point arithmetic numbers while adapting to a certain degree of precision loss, which has brought approximate homomorphic encryption (AHE) technology into the forefront of information security research. This work examines the development trajectory from PHE to AHE, and summarizes and analyzes the research works related to AHE from the three aspects: bootstrapping, improved precision, and variants. In addition, this work shows three different application scenarios of AHE from low level to high level, and combs the related works to present the readers with the latest application trend of AHE schemes.