Design of S-Boxes Based on Alternative Irreducible Polynomials

Zhanat Saukhanova; Gulmira Shakhmetova; Altynbek Sharipbay; Alibek Barlybayev; Sayat Raykul; Altay Khassenov

Design of S-Boxes Based on Alternative Irreducible Polynomials

Abstract

In the era of rapid digital technology development, the volume of information transmitted in cyberspace is significantly increasing, thereby intensifying the need to ensure confidentiality and the protection of personal data. Modern cryptographic methods are used for such purposes. One of the most widely used encryption algorithms is Advanced Encryption Standard (AES), which employs substitution box (S-box) to enhance the security of the encryption process. S-box is one of the important components of the block algorithm. The robustness of an S-box is largely determined by its architecture and algebraic basis. In this paper, a method for constructing S-boxes is proposed based on various alternative irreducible polynomials with the addition of a constant 8-bit vector, different from that used in the AES standard. A total of 16 S-boxes were constructed and their performance was evaluated using standard cryptographic criteria, including nonlinearity, strict avalanche effect, etc. The results demonstrated that the proposed S-boxes exhibit performance comparable to that of the standard AES S-box. This study is conducted within the framework of grant funding from the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan (grant No. AP19677422).

Keywords

References

Saukhanova, Z., Shakhmetova G., Sharipbay A., Barlybayev A., Raykul S., & Khassenov A. (2025). Design of S-boxes based on alternative irreducible polynomials. The Eurasia Proceedings of Science, Technology, Engineering and Mathematics (EPSTEM), 36, 102-109.

Details

Primary Language

English

Subjects

Statistics (Other)

Journal Section

Research Article

Authors

Zhanat Saukhanova This is me
Kazakhstan

Gulmira Shakhmetova This is me
Kazakhstan

Altynbek Sharipbay This is me
Kazakhstan

Alibek Barlybayev This is me
Kazakhstan

Sayat Raykul This is me
Kazakhstan

Altay Khassenov This is me
Kazakhstan

Early Pub Date

November 4, 2025

Publication Date

-

Submission Date

July 7, 2025

Acceptance Date

August 13, 2025

Published in Issue

Year 2025 Volume: 36

IZ

https://izlik.org/JA82LT32NU

Cite

RIS / Bibtex

APA

Saukhanova, Z., Shakhmetova, G., Sharipbay, A., Barlybayev, A., Raykul, S., & Khassenov, A. (2025). Design of S-Boxes Based on Alternative Irreducible Polynomials. The Eurasia Proceedings of Science Technology Engineering and Mathematics, 36, 102-109. https://izlik.org/JA82LT32NU

AMA

1.Saukhanova Z, Shakhmetova G, Sharipbay A, Barlybayev A, Raykul S, Khassenov A. Design of S-Boxes Based on Alternative Irreducible Polynomials. EPSTEM. 2025;36:102-109. https://izlik.org/JA82LT32NU

Chicago

Saukhanova, Zhanat, Gulmira Shakhmetova, Altynbek Sharipbay, Alibek Barlybayev, Sayat Raykul, and Altay Khassenov. 2025. “Design of S-Boxes Based on Alternative Irreducible Polynomials”. The Eurasia Proceedings of Science Technology Engineering and Mathematics 36 (November): 102-9. https://izlik.org/JA82LT32NU.

EndNote

Saukhanova Z, Shakhmetova G, Sharipbay A, Barlybayev A, Raykul S, Khassenov A (November 1, 2025) Design of S-Boxes Based on Alternative Irreducible Polynomials. The Eurasia Proceedings of Science Technology Engineering and Mathematics 36 102–109.

IEEE

[1]Z. Saukhanova, G. Shakhmetova, A. Sharipbay, A. Barlybayev, S. Raykul, and A. Khassenov, “Design of S-Boxes Based on Alternative Irreducible Polynomials”, EPSTEM, vol. 36, pp. 102–109, Nov. 2025, [Online]. Available: https://izlik.org/JA82LT32NU

ISNAD

Saukhanova, Zhanat - Shakhmetova, Gulmira - Sharipbay, Altynbek - Barlybayev, Alibek - Raykul, Sayat - Khassenov, Altay. “Design of S-Boxes Based on Alternative Irreducible Polynomials”. The Eurasia Proceedings of Science Technology Engineering and Mathematics 36 (November 1, 2025): 102-109. https://izlik.org/JA82LT32NU.

JAMA

1.Saukhanova Z, Shakhmetova G, Sharipbay A, Barlybayev A, Raykul S, Khassenov A. Design of S-Boxes Based on Alternative Irreducible Polynomials. EPSTEM. 2025;36:102–109.

MLA

Saukhanova, Zhanat, et al. “Design of S-Boxes Based on Alternative Irreducible Polynomials”. The Eurasia Proceedings of Science Technology Engineering and Mathematics, vol. 36, Nov. 2025, pp. 102-9, https://izlik.org/JA82LT32NU.

Vancouver

1.Zhanat Saukhanova, Gulmira Shakhmetova, Altynbek Sharipbay, Alibek Barlybayev, Sayat Raykul, Altay Khassenov. Design of S-Boxes Based on Alternative Irreducible Polynomials. EPSTEM [Internet]. 2025 Nov. 1;36:102-9. Available from: https://izlik.org/JA82LT32NU