Abstract
The contemporary cryptographic field is marked by efforts to enhance traditional methods through the integration of novel mathematical concepts. This fusion seeks to address the shortcomings of classical cryptography, tackle emerging security challenges, and devise more sophisticated data protection systems. Among these innovations is the application of finite automata, or CryptoAutomata, used as encoders and decoders. The object of this research is the use of finite automata, specifically CryptoAutomata, in cryptographic systems. The study addresses the problem of vulnerabilities in classical cryptographic methods, which include susceptibility to emerging cryptanalytic attacks and inefficiencies in computational overhead. The essence of the obtained results lies in demonstrating the practical implementation and cryptographic advantages of reversible finite automata, including surjective and Mealy automata, integrated into encryption systems. Due to the inherent properties of these automata, such as reversibility, composability, and computational efficiency, the authors were able to increase the security of encryption, significantly complicating cryptanalysis attempts. These results are primarily explained by the compositional approach, which involves combining multiple finite automata to form complex encryption structures. Rigorous statistical evaluations were carried out, including NPCR and UACI, which yielded NPCR values ranging between 99.56% to 99.61% and UACI values around 33%, affirming strong resistance to differential attacks. Additionally, noise resilience was confirmed through PSNR evaluations, achieving values above 35 dB even under significant noise conditions, thereby validating robustness in practical scenarios. Furthermore, the cryptographic strength was substantiated by NIST statistical randomness tests