Hybrid S-box Construction over GF(2⁸) Using Irreducible Polynomial and Affine Transformation

Alamsyah; Yusuf Muhammad; Budi Prasetiyo; Yahya Nur Ifriza; Much Aziz Muslim; Shahrul Nizam Salahudin; Nur Atiqah Sia Abdullah; Yusuf Wisnu Mandaya

doi:10.15575/join.v11i2.1841

Authors

Alamsyah Department of Computer Science, Universitas Negeri Semarang, Semarang, Indonesia
Yusuf Muhammad Department of Computer Science, Universitas Negeri Semarang, Semarang, Indonesia
Budi Prasetiyo Department of Computer Science, Universitas Negeri Semarang, Semarang, Indonesia
Yahya Nur Ifriza Department of Computer Science, Universitas Negeri Semarang, Semarang, Indonesia
Much Aziz Muslim Department of Computer Science, Universitas Negeri Semarang, Semarang, Indonesia
Shahrul Nizam Salahudin Faculty of Technology Management and Business, Universiti Tun Hussein Onn Malaysia, Malaysia
Nur Atiqah Sia Abdullah College of Computing, Informatics and Mathematics, Universiti Teknologi MARA, Malaysia
Yusuf Wisnu Mandaya Universitas Islam Negeri Sunan Kudus, Indonesia

DOI:

https://doi.org/10.15575/join.v11i2.1841

Keywords:

AES, Affine Transformation, Irreducible Polynomial, S-box, SDGs

Abstract

The S-box, also known as the substitution box, is an essential component in symmetric encryption because it provides the nonlinear mapping required to transform input bits into output bits. The most widely used S-box is the AES S-box, which is constructed using the irreducible polynomial, an 8×8 affine matrix with the first row (10001111), and an 8-bit constant (01100011). This study presents a Hybrid S-box construction over GF(2⁸) that combines irreducible-polynomial arithmetic and affine transformation to obtain a secure and lightweight substitution mapping. The proposed method uses the irreducible polynomial, an 8×8 affine matrix with the first row (01010111), and an 8-bit constant (00000000). The originality of this research lies in combining polynomial-based finite-field inversion and affine bit mixing to produce a reproducible Hybrid S-box design that balances cryptographic strength and implementation efficiency. The resulting Hybrid S-box is evaluated using six standard cryptographic indicators: Nonlinearity (NL), Strict Avalanche Criterion (SAC), Bit Independence Criterion in terms of nonlinearity (BIC-NL) and avalanche (BIC-SAC), Differential Uniformity (DU), and Algebraic Degree (AD). The experimental results show that the proposed Hybrid S-box achieves NL = 112, SAC = 0.49756, BIC-NL = 112, BIC-SAC = 0.50119, DU = 4, and AD = 7. Compared with the AES S-box and recent S-box designs, the proposed Hybrid S-box attains AES-level nonlinearity and differential uniformity while producing SAC and BIC-SAC values closer to the ideal value of 0.5. These findings indicate that the proposed Hybrid S-box can enhance data security in Internet of Things devices, embedded controllers, and smart-card platforms. This work also supports Sustainable Development Goal 9 by contributing to secure, resilient, and resource-efficient digital infrastructure.

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