Application of the Composite Field in the Design of an Improved AES S-box Based on Inversion

The hardware implementation of the Substitution-Box (S-box) of the Advanced Encryption Standard (AES) always employs composite field GF ((2)) to obtain better efficiency. In this paper, an improved class of S-boxes by direct inversion in composite field is presented, and the choice of the subfield leading to the most efficient implementation is discussed. Eliminating the field isomorphic transformations, such a composite field is easier to fix and the resulting hardware implementation is more efficient than that of AES S-box. Some common cryptographic characteristics for the composite field based S-boxes are examined, and it turns out that direct inversion in composite field does not weaken the cryptographic characteristics. In addition, a demonstration for the immunity against the potential algebraic attack on AES with the replacement of our S-box is given, and it is proven that the revised AES is even more secure than the original AES against the algebraic attack. As a result of this work, it could be predicted that the isomorphism implies equal immunity from certain cryptanalysis. Our S-box is suitable for the area-limited hardware production. Keywords–AES; Composite field; S-box; Hardware implementation.