In this study, the NTRU cryptosystem is examined on companion matrices. These matrix types have been studied due to the rapid selection of matrices that will serve as private keys. Again, using some interesting and important linear algebra properties of companion matrices, the NTRU cryptosystem has been studied in a different and specific ring. Some results obtained place the NTRU crypto system on solid foundations in algebraically. NTRU cryptosystem was found to be stronger than Knapsack method. And a new type of digital signature has been obtained over companion matrices.