Towards Fully Homomorphic Encryption From Gentry-Peikert-Vaikuntanathan Scheme

Abstract

Despite the convenience brought by cloud computing, internet users, meanwhile, are faced with risks of data theft, tampering, forgery, etc. Fully homomorphic encryption (FHE) has the ability to deal with the ciphertext directly, which can solve the problem of data security in cloud computing. Therefore, fully homomorphic encryption (FHE) has been widely used in cloud computing as well as multiparty computing, functional encryption and private information retrieval, etc. However, previous FHE schemes are based on standard (ring) learning with errors (LWE) assumption and the most typical schemes were created by Brakerski (CRYPTO2012) and Gentry-Sahai-Waters (GSW) (CRYPTO2013). Moreover, inspired by the work of Li et al. at ICPADS2016, they made use of Brakerski’s scale-invariant technology and constructed a new FHE scheme with errorless key switching under Dual-First-is-errorless LWE (Dual-Ferr.LWE) problem. Hence, armed with Li et al.’s work, in this paper, we use Gentry-Peikert-Vaikuntanathan’s scheme (i.e., under dual LWE assumption) as building block to construct a FHE scheme. Lastly, under the assumption of decisional learning with errors (LWE), we prove that our scheme is CPA (chosen-plaintext-attack) secure.