Efficient public key generation for homomorphic encryption over the integers

Abstract

The 'Holy Grail' of cryptography called Fully Homomorphic Encryption (FHE), which allows encrypted data processing and delegation of computational tasks to the remote untrusted server, has become a hot research topic in light of the privacy concerns related to cloud computing. Several FHE schemes were found after the first construction of such scheme by Craig Gentry in 2009. One of the several reasons making these theoretically feasible schemes unpractical is their high computational costs. In this paper, a simplest possible key generation method is proposed for the somewhat homomorphic scheme of Van Dijk et al., which leads to an efficient integer based FHE scheme. Also, the security and practicality of the proposed scheme is thoroughly analyzed with respect to the new key generation method suggested. © 2012 ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering.