The faults that occur in the hardware implementations of the Advanced Encryption Standard (AES) may cause incorrect encrypted/decrypted output. The use of appropriate fault detection schemes for the AES makes it vigorous to inner defects as well as fault attacks. In this paper, the authors present a lightweight concurrent fault detection scheme for the AES. In this paper, the composite field S-box and inverse S-box are divided into blocks and the projected parities of these blocks are obtained. Through exhaustive searches, they have found the optimum solutions for the least overhead parity-based fault detection structures.