Noise-free Symmetric Fully Homomorphic Encryption based on noncommutative rings.
Jing Li, Licheng Wang · 2015
A framework of noise-free symmetric fully homomorphic en-cryption (FHE) is proposed in this work. Different from the frameworks that are defined over non-commutative group-s, our framework is constructed from matrices over non-commutative rings. The scheme is one-way secure against chosen plaintext attacks (OW-CPA) based on the factor-ization problem of matrices over noncommutative rings as well as the hardness of an overdefined system of multivari-ate polynomial equations over the given non-commutative algebraic structure. On the basis of this framework, a ver-ifiable FHE is proposed, where the receiver can check the validity of ciphertexts.