Logistic and Circle Maps for Robust S-Box Construction in Cryptography

Abstract

Cryptology, a pivotal discipline in ensuring information security and communication confidentiality, relies on symmetric cryptology, where the same key is employed for both encryption and decryption processes. Prominent algorithms like DES and AES fall within the domain of symmetric cryptography, addressing challenges related to secure key sharing. This approach is extensively utilized in various applications, including data encryption, confidential information transfer, and secure file storage. Within the realm of symmetric encryption, S-Boxes (Substitution Boxes) play a crucial role in enhancing algorithm security. These S-Boxes introduce non-linearity, diffusion, avalanche effects, differential cryptanalysis resistance, and key independence. By doing so, they contribute to the robustness of the encryption process. In an ongoing program, chaotic systems are utilized to generate S-Boxes for AES. Optimized versions of chaotic maps, such as the logistic map and circle map, are employed in this process. This study aims to generate resilient S-Box structures for symmetric encryption. The successful outcomes, with non-linearity values surpassing 106, highlight the significance of well-designed S-Boxes in fortifying algorithm resistance levels. The generated S-Box structures are also compared with existing literature, emphasizing their role in advancing cryptographic techniques. In conclusion, this research successfully achieves its goal of producing robust S-Box structures for symmetric encryption, contributing to the ongoing evolution and enhancement of cryptographic methodologies.