Paper 2015/641

Noise-Free Symmetric Fully Homomorphic Encryption Based on Non-Commutative Rings

Jing Li, Licheng Wang

Abstract

A framework of noise-free symmetric fully homomorphic encryption (FHE) is proposed in this work. Dierent from the frameworks that are dened over non-commutative groups, our framework is constructed from matrices over noncommutative rings. The scheme is one-way secure against chosen plaintext attacks (OW-CPA) based on the factorization problem of matrices over noncommutative rings as well as the hardness of an overdened system of multivariate polynomial equations over the given non-commutative algebraic structure. On the basis of this framework, a verifiable FHE is proposed, where the receiver can check the validity of ciphertexts.