Review of how to construct a fully homomorphic encryption scheme

Abstract

Fully homomorphic encryption (FHE) allows one to perform arbitrary computation on encrypted data. From the cloud computing perspective, a FHE scheme can be used to outsource a computation to a remote cloud server without revealing the computed data to the server. This is a very attractive cryptographic primitive. Existing methods used to construct FHE schemes are complicated, and often these methods are difficult to understand except by experts in the field. This paper aims to explain how to construct a FHE scheme in an easily understandable way. We first present a general overview of FHE scheme construction. We then take the van Dijk et al FHE scheme as an example and explain how a FHE scheme is obtained from a simple integer-based encryption scheme. Our explanation gives details of the noise bound, how noise growth can be controlled and how the vanDijk scheme is implemented. © 2014 SERSC International Journal of Security and Its Applications.