After a detail demonstration of AES (Advanced Encryption Standard) , we explainedrnthe procedure of changing the key-recovery problem of AES-128 to a zero dimensionalrnideal from a single plain text /cipher text pair. Followed by explaining a method,rnBuchberger's Algorithm for computing a Groebner basis for this ideal. Then, fnallyrnwe will discuss on the implication of the result from the cryptanalytic point of view.rn(i.e. What security implication the existence of the Groebner basis has?)