Design of S-Boxes Based on Alternative Irreducible Polynomials

Year 2025, Volume: 36, 102 - 109

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

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

Cryptography , Advanced encryption standard (AES) , Substitution box (S-box) , Irreducible polynomial

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.