Nonlinear Dynamics

, Volume 93, Issue 4, pp 2105–2118 | Cite as

The replacement of irreducible polynomial and affine mapping for the construction of a strong S-box

  • Alamsyah
  • Agus Bejo
  • Teguh Bharata AdjiEmail author
Original Paper


Substitution box (S-box) is a critical part of the data encryption and decryption procedures. The primary function of the S-box in advanced encryption standard algorithm is to randomize the 8-bit input into 8-bit output. This paper presents a novel approach to S-box construction based on the replacement of irreducible polynomial and affine mapping. The strength of the created S-box is assessed by applying several standard tests, e.g., balance, bijective, nonlinearity, strict avalanche criterion, and bit independence criterion-nonlinearity. The strength of the S-box outperforms those of available S-boxes.


AES S-box Irreducible polynomial Affine mapping Affine matrix 



We are grateful to the anonymous reviewers for helpful comments leading to the improvement of the exposition. Special thanks are also given to Overseas Seminar Assistance Program, Directorate General of Research and Development Strengthening, Ministry of Research, Technology, and Higher Education, Indonesia. We would also like to show our gratitude to the Directorate of Research and Community Service (Grants No 084/SP2H/LT/DRPM/IV/2017 and No. 075/SP2H/LT/DRPM/I/2018), Directorate General of Research and Development, Ministry of Research, Technology and Higher Education, Indonesia.


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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Electrical Engineering and Information TechnologyUniversitas Gadjah MadaYogyakartaIndonesia
  2. 2.Department of Computer ScienceUniversitas Negeri SemarangKota SemarangIndonesia

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