Lattice-based cryptosystems

Abstract

We describe a generalization of the NTRU cryptosystem over rings other than Z after giving a survey of some of the most famous lattice-based cryptosystems, namely, Ajtai-Dwork, GGH and NTRU. Our generalization, which follows the idea of CTRU and NTRU over Gaussian integers, implies one may extend the NTRU encryption scheme over integral domains up to some constraints. We give details for realizing such extensions over Euclidean domains and denote by ETRU the corresponding class of cryptosystems.