On DGHV and BGV fully homomorphic encryption schemes

Homomorphic Encryption (HE) is a new cryptographic topic that allows untrusted parties to compute over encrypted data. This new encryption scheme is very famous in a cloud scenario, because it leverages cryptographic techniques in the cloud by allowing it to store encrypted data, and to process encrypted query over it. In this paper, we consider two important HE schemes: Dijk-Gentry-Halevi-Vaikutanathan (DGHV) and, Brakerski-Gentry-Vaikunathan (BV-BGV). The first one is based on computing over real integers while the other one is based on LWE (Lattice based Encryption). We present a detailed explanation of both schemes showing their efficient techniques including Bootstrapping and Modulus switching and we finally draw several conclusions.