Research on Noise Management Technology for Fully Homomorphic Encryption

Abstract

Fully homomorphic encryption (FHE) has gradually become an important tool for solving data security and privacy protection issues, because it supports arbitrary computation of encrypted data without the need for prior decryption. The key to constructing a fully homomorphic encryption scheme is to effectively manage the noise in the ciphertext to achieve more or even any number of homomorphic operations. This paper classifies FHE noise management methods and proposes the strengths and weaknesses of each method on the basis of introducing their technical principles, proposes and proves the application advantages of the gadget matrix in FHE noise management, and proposes optimization suggestions for noise management on the basis of analyzing and comparing the noise dependence, noise growth forms, and parameter size of current representative FHE schemes. Finally, we optimize the noise management of the GSW scheme using a gadget matrix and reduce the size of the private key and ciphertext by $\left \lceil {{\log q}}\right \rceil $ times, and we show that the optimized GSW performs better in complexity than the original GSW.

Keywords

• Fully homomorphic encryption
• noise management
• bootstrapping
• bit expansion
• gadget matrix
• modulus switching