@article{Hazzazi2025, 
author = {Mohammad Mazyad Hazzazi and Farooq E Azam and Rashad Ali and Muhammad Kamran Jamil and Sameer Abdullah Nooh and Fahad Alblehai},
title = {Batch generated strongly nonlinear S-Boxes using enhanced quadratic maps},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {3},
pages = {5671-5695},
keywords = {2D Enhanced Quadratic Map (2D-EQM), affine transformation, cryptographic algorithms, nonlinearity, S-Box design},
url = {https://www.sciopen.com/article/10.3934/math.2025262},
doi = {10.3934/math.2025262},
abstract = {One of the most crucial elements in the design of a block cipher is the substitution box or S-box. Its cipher strength directly impacts the cipher algorithm's security, and the block cipher algorithm requires a good S-box. According to the cryptanalysis result of the S-box construction in AES: (1) the number of irreducible polynomials can be increased to 30; (2) the affinity transformation constant c can be chosen from all elements if the existence of fixed points and reverse fixed points in an S-box is ignored; and (3) the S-box in AES is fixed, which poses possible security risks to the AES algorithm. The study above led us to build a non-degenerate 2D enhanced quadratic map (2D-EQM) with unpredictability and ergodicity. From there, we generated affine transformation constants and affine transformation matrices, which were then applied to seed S-boxes to create a batch of strongly nonlinear S-boxes. Finally, we assessed the performance of suggested S-boxes using six criteria. Security and statistical research showed that the suggested S-box batch generation procedure was practical and effective.}
}