NTRU is the first public key Cryptosystem based on the polynomial ring Z[X] X N −1. The hard problem underlying this cryptosystem is related to finding short vectors in a lattice. Several generalizations of NTRU was designed over various integral ring such as Z, Z[i], Z[w] and H. In this paper, we use the ring with zeros divisors D = Z + Z, 2 = 0 (called the ring of Dual Integers) in order to design a new version of NTRU. To achieve this objective, we have studied the elementary arithmetic properties of the ring of Dual integers in a previous paper. The main difficulty is to be able to perform a division algorithm with a unique remainder and to invert polynomials with coefficients in quotient ring of the ring of Dual integers. Nevertheless, we have successfully design NTRU over Dual integers (called DTRU) in a particular quotient ring of the ring of Dual integers. Our scheme has the same level security than NTRU, but is not more efficient. This work shows also that NTRU can be designed even if the ring has zeros divisors! We have also design over the ring of Dual Integer the cryptosystem NTRU with Non-inverible polynomial proposed by Banks and Shparlinski. This this version is more secure than NTRU but is less efficient too.