An AES-inspired Construction of a Cryptographically Strong 8×8 S-box Using Modified Algebraic and Affine Parameters
TL;DR
The proposed 8×8 S-box is proposed based on an AES-inspired inverse-affine construction that simultaneously modifies the irreducible polynomial, the nonsingular affine matrix, and the constant vector to generate a different substitution table over GF.
Abstract
Substitution boxes (S-boxes) are essential nonlinear components in symmetric-key block ciphers and play a central role in providing resistance against linear and differential cryptanalytic attacks. In this paper, a new 8×8 S-box is proposed based on an AES-inspired inverse-affine construction. Unlike the standard AES S-box, the proposed design simultaneously modifies the irreducible polynomial, the nonsingular affine matrix, and the constant vector to generate a different substitution table over GF (2 8 ). The novelty of the proposed approach lies in the joint modification of these three structural parameters while preserving the mathematical clarity and reproducibility of the AES inverse-affine construction. The main objective of this approach is to preserve the strong algebraic structure of AES-like S-box construction while maintaining important cryptographic properties. The proposed S-box was implemented in Python and evaluated using several standard cryptographic criteria, including nonlinearity, algebraic degree, Strict Avalanche Criterion (SAC), Linear Approximation Probability (LAP), and Differential Probability (DP). The experimental results show that the proposed S-box achieves minimum, maximum, and mean nonlinearity values of 112, while its algebraic degree is equal to 7. Moreover, the SAC values range from 0.4375 to 0.5469, with an average value of 0.5, indicating balanced avalanche behavior. The proposed S-box also obtains an LAP value of 0.0625 and a DP value of 4/256, demonstrating competitive resistance against linear and differential attacks. The obtained results were compared with AES, SM4, O‘zDSt 1105: 2009, and several recently reported 8×8 S-box constructions. The comparative analysis confirms that the proposed S-box provides a strong balance between nonlinearity, avalanche behavior, linear approximation resistance, and differential uniformity. Therefore, the proposed AES-inspired parameter modification approach can be considered a promising and reproducible method for designing secure substitution boxes for symmetric-key block cipher algorithms.