A Novel Scheme for Construction of S-Box Using Action of Power Associative Loop and Its Applications in Text Encryption

Substitution boxes (S-boxes) play an important role in symmetric key cryptography because they add complexity and resist cryptanalysis, improving the overall security of encrypted data. The conventional construction of substitution boxes (S-boxes) has long relied on associative algebras such as Galois fields and cyclic groups. However, recent developments have motivated researchers to investigate non-associative algebras. This study contributes to this evolving narrative by using the Möbius transformation over power associative loop for S-box construction. The S256 symmetric group’s permutations are applied to further enhance the design of the S-box. This deliberate variation contributes to greater non-linearity and confusion, both of which are necessary elements for cryptographic strength. The practical importance of the S-box was further assessed by using a variety of criteria, including nonlinearity, strict avalanche criteria, bit independence criteria, differential probability, and linear approximation probability. To evaluate the reliability of the S-box, its performance results are compared to the results of previously created S-boxes. Furthermore, we employed the proposed S-Box to encrypt text using the AES algorithm. The Avalanche Effect test is used to examine the effectiveness of our technique, and it confirmed the robustness and security of our encryption scheme.