Reply to Arshad, R.; Jalil, M. Comment on “Nizam Chew, L.C.; Ismail, E.S. S-box Construction Based on Linear Fractional Transformation and Permutation Function. Symmetry 2020, 12, 826”

In this reply paper, we provide a response to the comment paper of a comment on “S-box Construction Based on Linear Fractional Transformation and Permutation Function” written by Razi Arshad and Mudassar Jalil [1]. They pointed out that the polynomial $P\left(t\right)=t^8+t^4+t^3+t^2+t+1$ written in Chew et al. [2] is not irreducible. We thank the authors [1] for this observation.

However, we can confirm that there was a typing error in the polynomial. The actual polynomial used in our S-box design was $P\left(t\right)=t^8+t^4+t^3+t^2+1$, which is also stated clearly in Table 1 in [2] (refer to the 16th polynomial). We also confirmed and verified that all results obtained in [2] were from the irreducible polynomial $P\left(t\right)=t^8+t^4+t^3+t^2+1$.