This article presents an in-depth investigation into the impact of irreducible polynomials (IP) on the cryptographic properties of the nonlinear component in a block cipher. Specifically, we focus on the set of 30 monic irreducible polynomials of degree 8 over the finite field \({\mathbb{F}}_{2}\) , with 16 of them being primitive irreducible polynomials (PIP) and the remaining 14 being regular IP. To analyze their impact, we construct isomorphic Galois fields of order 256 corresponding to each IP. Subsequently, we construct 30 substitution boxes (S-boxes) using a linear fractional transformation (LFT) of the form \(\mapsto \frac{ax+b}{cx+d}\) , where \(a, b, c,\) and \(d\) are elements of \(GF\left({2}^{8}\right)\) excluding zero, and x represents an arbitrary element from \(GF\left({2}^{8}\right)\) . These constructed S-boxes undergo a comprehensive analysis, including vulnerability assessment against various attacks. The results demonstrate that the S-boxes constructed over the isomorphic fields effectively preserve the algebraic properties expected of S-boxes. However, these S-boxes do not provide protection against side-channel analysis. The findings highlight the need for additional security measures when utilizing S-boxes based on IP to mitigate the vulnerabilities associated with side-channel attacks.
