An Encryption Depth Optimization Scheme for Fully Homomorphic Encryption

Fully homomorphic encryption scheme over the integers uses integer modular arithmetic and is conceptually simple. However, its efficiency is low and the re-encryption process is complex. According to the depth analysis of the somewhat homomorphic encryption scheme, we propose a re-encryption optimization scheme over the given arbitrary function, which designs a depth threshold value and do function decomposition while the depth value of given function is deeper than the designed depth threshold value. Then, an encryption-depth optimization fully homomorphic encryption (EDO-FHE) scheme is constructed. Based on analysis results, the complexity of the proposed EDO-FHE scheme is far less than the DGHV scheme. It greatly improved the efficiency of the fully homomorphic encryption scheme, while the security is also proved based on the approximate GCD problem.