GR-NTRU: Dihedral group over ring of Eisenstein integers

Abstract

NTRU is a lattice-based cryptosystem built on a convolutional ring of polynomials. There are many generalizations of NTRU in the literature; however, group ring NTRU, or GR-NTRU, is the most reasonable description of NTRU as a general framework to design its variants. Most versions are commutative and are obtained by changing the ring of coefficients while keeping the cyclic structure intact. In this work, we analyze the noncommutative version of GR-NTRU designed with the group ring of dihedral group over the ring of Eisenstein integers. We experimentally test the size of the keyspace of this new variant and find that it is comparable and even larger for certain parameters compared to the existing commutative counterpart. We observe that although it is slightly slow in terms of speed of encryption and decryption, it has higher lattice security.