A Regev-Type Fully Homomorphic Encryption Scheme Using Modulus Switching

A critical challenge in a fully homomorphic encryption (FHE) scheme is to manage noise. Modulus switching technique is currently the most efficient noise management technique. When using the modulus switching technique to design and implement a FHE scheme, how to choose concrete parameters is an important step, but to our best knowledge, this step has drawn very little attention to the existing FHE researches in the literature. The contributions of this paper are twofold. On one hand, we propose a function of the lower bound of dimension value in the switching techniques depending on the LWE specific security levels. On the other hand, as a case study, we modify the Brakerski FHE scheme (in Crypto 2012) by using the modulus switching technique. We recommend concrete parameter values of our proposed scheme and provide security analysis. Our result shows that the modified FHE scheme is more efficient than the original Brakerski scheme in the same security level.