An Optimized Computation Method for Cipher Symbol Functions Based on Homomorphic Encryption
Fully homomorphic encryption extends encryption to computations,allowing ciphertext processing without decryption.Comparative operations,crucial in applications like deep learning,pose a challenge in homomorphic encryption environments restricted to addition and multiplication.Feng et al.(CNS 2023)proposed a comparison method using dynamic polynomial combinations.This paper enhances dynamic polynomial,allowing polynomial fluctuations within(-2,2).It introduces a novel equation system for solving dynamic polynomials and utilizes finite third and fifth-degree polynomials to construct more precise composite polynomials for approximating the sign function.It analyzes the method's optimality in depth consumption and computational complexity,achieving a 32％reduction in runtime compared to the optimal method in a previous study(CNS 2023).The homomorphic comparison algorithm in this paper,for ε=2-20,α=20 requires only 0.69 ms in amortized runtime.
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