Matrix NTRU Cryptosystem over Integral Domain

NTRU is one of the cryptosystems which has efficient public keys. Lattice L is a set of vectors in $\mathbb{R}^{n}$ which is generated by linearly independent vectors with a linear combination of integer coefficients. Nayak et al. introduced an NTRU based on matrices and Nanda et al. observed an NTRU based on matrices over Gaussian integer $\mathbb{Z}[i]$ as the continuation. In this paper, we observe an NTRU based on matrices over an integral domain $\mathbb{Z}[\sqrt{-3}]$. Moreover, we propose the algorithm of key choice, computational aspects, and the restriction of parameters and show that the number of decryption failures of the proposed algorithm is very low for the proposed parameters.