全同态加密应用的编码技术综述OA北大核心CSTPCD

Fully homomorphic encryption(FHE)allows arbitrary computations to be performed on ciphertexts without decrypting them,providing an excellent solution to the need for data to be"avail-able but not visible".Due to efficiency and security reasons,the plaintext space of FHE is mainly defined on polynomial ring or finite field algebraic structures.Currently,practical FHE schemes are second-generation schemes represented by BGV,BFV,and CKKS,and third-generation schemes represented by FHEW and TFHE,among which the basic computation types of second-generation schemes include algebraic addition and multiplication while the core computation of third-generation schemes is gate bootstrapping.However,the data types involved in real-life applications include inte-ger,floating-point number,complex number,matrix,vector,etc.The types of function computation include polynomial function and various non-polynomial functions such as trigonometric,inverse,and comparison functions.Therefore,efficient message encoding and function computing encoding must be designed to adapt to actual computing tasks and improve overall performance efficiency when using FHE.This paper systematically summarizes the message encoding involved in the second-generation FHE and analyzes the homomorphic computation encoding strategies for some common functions in different FHE schemes.Finally,this paper gives a specific analysis and testing on two examples:convolutional neural network inference and symmetric encryption algorithm(AES).