Multi-bit leveled homomorphic encryption via Dual.LWE-based

Abstract

Fully Homomorphic Encryption (FHE) is a cryptographic primitive that allows computing over encrypted data without decrypting the corresponding ciphertexts. In general, existing FHE schemes can be achieved using standard Learning with Errors (LWE) assumption and most of the schemes are single-bit encryption. Hence, the construction of multi-bit FHE with high efficiency remains an open problem in cryptography. In this paper, we propose multi-bit versions of Public Key Encryption (PKE) via the dual LWE-based firstly proposed by Gentry, Peikert, and Vaikuntanathan at STOC 2008. We initially develop an universal construction derived from a general structure of the underlying combined public matrix for constructing the multi-bit version which increases the size of ciphertexts linearly. Then, utilizing multi-bit PKE scheme as building block, we propose a new multi-bit FHE scheme under the assumption of decisional LWE is hard and prove the scheme is IND-CPA-secure.