Bit-Independent Criteria Evaluation of Custom S-Boxes: Enhanced AES Encryption Security
Abstract Cryptography plays a pivotal role in safeguarding data from unauthorized access. Various encryption techniques have been developed and implemented to secure data during transmission through robust encoding measures across diverse systems, contributing to standardizing cryptographic practices. Previous studies have introduced several algorithms that focused on augmenting encryption security, such as the Key Scheduling Algorithm (KSA), S-Boxes customized to incorporate key, and PT dependencies within the RC4 algorithm. These S-Boxes were later expanded by integrating Henon Chaotic Maps and Logistic Chaotic Maps. The main objective was to create distinct S-Boxes with high-strengthening security features of the Advanced Encryption Standard (AES) algorithm. Different evaluations, such as tests for nonlinearity, Avalanche Effect (AE), the Strict Avalanche Effect (SAE), and Execution Time Performance Efficiency in percentage (ETPE %) were employed to assess the robustness of these S-Boxes.This paper is dedicated to evaluating the robustness of different S-Boxes using Bit-Independent Criteria. We incorporated five distinct S-Boxes into the AES algorithm, presenting an innovative approach. The novelty of our work lies in applying Bit-Independent Criteria tests, quantitatively measuring the strength of each S-Box individually. Tests show that the S-Boxes produced through chaotic maps noticeably strengthen encryption. The Henon based S-Box, using secret key “0123456789ABCDEF”, achieved an average BIC value of -0.009, while the standard AES S-Box recorded -0.04, indicting a relative improvement of approximately 77.5 % in the output bit independence. Similar gains appeared with Logistic map-based S-Boxes under various key settings. By utilizing the Bit-Independent Criteria, our research aims to offer a comprehensive assessment of the S-Boxes’ effectiveness in enhancing AES encryption security. This endeavor ultimately contributes to advancements in secure data transmission practices. Overall, our results demonstrate that chaotic S-Box design boosts AES security and guides future work on tougher cryptographic schemes.
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Felicisimo, V., & Wenceslao, Jr. (2015). Performance efficiency of modified AES algorithm using multiple S-boxes. International Journal of New Computer Architectures and their Applications, 5(1) 1-9. https://doi.org/10.17781/P001620
Hamdi, M., Rhouma, R., & Belghith, S. (2015). A very efficient pseudo-random number generator based on chaotic maps and S-box tables. International Journal of Electronics and Communication Engineering, 9(2) 481-485. https://doi.org/10.5281/zenodo.1100418
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Shannon, C. (1998). Communication theory of secrecy systems. Bell Systems Technical Journal, MD Computing, 15, 57-64. https://doi.org/10.1002/j.1538-7305.1949.tb00928.x
Sosa, P. M. (2016). Calculating nonlinearity of Boolean functions with Walsh Hadamard transform. UCSB, Santa Barbara, CA-USA, pp. 1-4. http://konukoii.com/blog/wp-content/uploads/2016/06/FinalPaper.pdf
Stallings, W. (2006). Cryptography and Network Security, Principles and Practices. 4th Ed. Pearson Education, Prentice-Hall of India Pvt. Limited, India. https://dl.acm.org/doi/book/10.5555/280574
Webster, A. F., & Travares, S. E. (1998). On the design of S-boxes. Queen’s University Kingston, Springer-Verlag, Canada. https://doi.org/10.1007/3-540-39799-X_41
Wen, H. (2014). A review of the Henon map and its physical interpretations. School of Physics Georgia Institute of Technology, Atlanta, GA 30332-0430, USA. http://chaosbook.org/projects/Wen14.pdf
Ahmad, J., & Hwang, S. O. (2015). Chaos-based diffusion for highly autocorrelated data in encryption algorithms. Signal Image Video Process, 13(82) 1839–1850. https://doi.org/10.1007/s11071-015-2281-0
Alharbi, A. R., Jamal, S. S., Khan, M. F., Gondal, M. A., & Abbasi, A. A. (2023). Construction and optimization of dynamic s-boxes based on Gaussian distribution. IEEE Access, 11, 35818-35829. https://doi.org/10.1109/ACCESS.2023.3262313
Chari, S., Jutla, C., Rao, J. R., & Rohatgi, P. (1999). A cautionary note regarding evaluation of AES candidates on smart-cards. Proceeding of Second Advanced Encryption Standard (AES) Candidate Conference, Rome, Italy, pp. 1-15. https://doi.org/10.1.1.38.9312
Ejaz, A., Shoukat, I. A., Iqbal, U., Abdul, R., & Kanwal A. (2021). A secure key dependent dynamic substitution method for symmetric cryptosystems. PeerJ Computer Science, 7, Article e587. https://doi.org/10.7717/peerj-cs.587
El Batouty, A. S., Farag, H. H., Mokhtar, A. A., El-Badawy, E. A., & Aly, M. H. (2020). Improvement of radio frequency identification security using new hybrid advanced encryption standard substitution box by chaotic maps. Electronics, 9(7), Article 1168. https://doi.org/10.3390/electronics9071168
El Batouty, A. S., Farag, H. H., Mokhtar, A. A., & El-Badawy, E. A. (2019). New hybrid AES static s-box algorithm using chaotic maps. Proceedings of the 2019 IEEE International Conference on Information Technologies (InfoTech-2019), Constantine and Elena, Bulgaria, pp. 1-5. https://doi.org/10.1109/InfoTech.2019.8860892
Eshmawi, A. A., & Mahmoud, E. E. (2020). Secure communications via complex phase synchronization of pair complex chaotic structures with a similar structure of linear terms with modifying in nonlinear terms. Alexandria Engineering Journal, 59. https://doi.org/10.1016/j.aej.2020.01.003
Fahmy, F., & Salama, G. (2005). A proposal for key-dependent AES. Proceeding of 3rd International Conference: Sciences of Electronic, Technologies of Information and Telecommunications (SETIT2005), Tunisia, pp. 1-7. http://www.setit.rnu.tn/last_edition/setit2005/image-video/53.pdf
Felicisimo, V., & Wenceslao, Jr. (2015). Performance efficiency of modified AES algorithm using multiple S-boxes. International Journal of New Computer Architectures and their Applications, 5(1) 1-9. https://doi.org/10.17781/P001620
Hamdi, M., Rhouma, R., & Belghith, S. (2015). A very efficient pseudo-random number generator based on chaotic maps and S-box tables. International Journal of Electronics and Communication Engineering, 9(2) 481-485. https://doi.org/10.5281/zenodo.1100418
Hosseinkhani, R., & Javadi, H. H. S. (2012). Using cipher key to generate dynamic S-Box in AES cipher system. International Journal of Computer Science and Security, 6(1) 19-28. https://www.cscjournals.org/manuscript/Journals/IJCSS/Volume6/Issue1/IJCSS630.pdf
Hussain, I., Anees, A., & Al-Maadeed, T. A. (2023). A novel encryption algorithm using multiple semifield S-boxes based on permutation of symmetric group. Computational and Applied Mathematics, 42, Article 80. https://doi.org/10.1007/s40314-023-02208-x
José, E., Capó, M., Miguel, C., Pérez, L., Rojas, O., Gómez, G. S., & Llanes, R. S. (2020). Bit independence criterion extended to stream ciphers. Appl. Sci., 10(21). Article 7668. https://doi.org/10.3390/app10217668
Shannon, C. (1998). Communication theory of secrecy systems. Bell Systems Technical Journal, MD Computing, 15, 57-64. https://doi.org/10.1002/j.1538-7305.1949.tb00928.x
Sosa, P. M. (2016). Calculating nonlinearity of Boolean functions with Walsh Hadamard transform. UCSB, Santa Barbara, CA-USA, pp. 1-4. http://konukoii.com/blog/wp-content/uploads/2016/06/FinalPaper.pdf
Stallings, W. (2006). Cryptography and Network Security, Principles and Practices. 4th Ed. Pearson Education, Prentice-Hall of India Pvt. Limited, India. https://dl.acm.org/doi/book/10.5555/280574
Webster, A. F., & Travares, S. E. (1998). On the design of S-boxes. Queen’s University Kingston, Springer-Verlag, Canada. https://doi.org/10.1007/3-540-39799-X_41
Wen, H. (2014). A review of the Henon map and its physical interpretations. School of Physics Georgia Institute of Technology, Atlanta, GA 30332-0430, USA. http://chaosbook.org/projects/Wen14.pdf
El Batouty, A. S., Hamdalla, T. A., Fayed, H. A., & Aly, M. H. (2025). Bit-Independent Criteria Evaluation of Custom S-Boxes: Enhanced AES Encryption Security. ADCAIJ: Advances in Distributed Computing and Artificial Intelligence Journal, 14, e32318. https://doi.org/10.14201/adcaij.32318
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