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NTRU is one of cryptosystems which has efficient public keys. Lattice L is a set of vectors in R^n which is generated by linearly independence vectors with linear combination of integer coefficients. Nayak et al. (2011)  introduce an NTRU based on matrices and Nanda et al. (2015) observe an NTRU based on matrices over Gaussian integer as continuation. In this paper we observe an NTRU based on matrices over an integral domain Z[\sqrt{-3}]. Moreover, we propose the algorithm of keys choice, computational aspects and the restriction of parameters.