Degree, closeness and eigenvector for the construction of cryptographically secure S-boxes
Amal S. Alali, Muhammad Kamran Jamil, Rashad Ali, Refah Mohammed Alotaibi, Wedad Albalawi · Ain Shams Engineering Journal · 2025
Facial identification systems are crucial in biometric security, making their protection against adversarial attacks essential. Ensuring the robustness of encryption methods in these systems is vital to prevent identity fraud and unauthorized access. This research examines the intersection of cryptography, substitution boxes (S-box) and graph theory, which focus on creating very secure cryptographic systems. In particular, we check the use of random graphs with 16 vertices in the construction of S-box, which are important components of many cryptographic algorithms, including block cipher. This research paper delves into the relationship between the graph properties, such as degrees, closeness, eigenvector and their impact on the design of strong S-box. By using a random graph structure, we analyze how these graphs can be utilized to increase nonlinearity and analyze the properties of S-boxes, which are necessary to oppose cryptanalysis attacks. The study highlights the ability to use graph-theoretic concepts to generate S-box with better cryptographic protection contributes to a broad understanding of rareness and graphic properties that can be effectively used in cryptography. The results show the importance of integrating graph theory into cryptographic design, which provides a new approach to improve the flexibility and performance of the cryptographic system.