A faster fully homomorphic encryption scheme in big data

Abstract

Nowadays privacy leakage related with big data spells big trouble for individuals. Generally, we provide data security and privacy protection through encrypted data but at the expense of usability. Fully homomorphic encryption allows to perform unlimited chaining of mathematical operations on encrypted data making it possible for some legal companies and institutions to use it. Compared to Gentry's scheme, fully homomorphic scheme over the integers can make complicated matters simplified but have not been widely applied due to the low efficiency. In this paper, a new improved FHE scheme based on DGHV scheme is proposed. We reduce the public key size significantly by introducing a pseudo-random number generator and encrypting with a cubic form rather than a linear form in the public key elements, which makes our scheme more efficient. Another part of our work is proving the scheme is semantically secure under the error-free approximate GCD problem. Finally, we propose a system model in purpose of illustrating the practical application of FHE scheme in big data.