The NTRU public key cryptosystem was first presented by J. Hoffstein,J. H. Silverman and J. Pipher in 1996. This system is based on shortest and closest vector problem in a lattice and its operations are based on objects of a truncated polynomial ring. In this paper, we have show that applying Pauli Matrix for the matrix formulation algorithm in NTRU public key cryptosystem substantially increases its efficiency as compared to other matrix formulation for NTRU cryptosystem with invertible matrix, such as Nayak et al. [8]. The Pauli Matrix facilitates the development and understanding of numerical algorithms.