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Classification of Nonlinear Confusion Component Using Hybrid Multi-Criteria Decision Making

Nabilah Abughazalah1, Iqra Ishaque2, Majid Khan2,*, Ammar S. Alanazi3, Iqtadar Hussain4,5

1 Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O.Box 84428, Riyadh 11671, Saudi Arabia
2 Department of Applied Mathematics and Statistics, Institute of Space Technology, Islamabad, Pakistan
3 Department of Mathematics, King Abdulaziz University, Faculty of Science, Jeddah, Saudi Arabia
4 Mathematics Program, Department of Mathematics, Statistics and Physics, College of Arts and Sciences, Qatar University, 2713, Doha, Qatar
5 Statistical Consulting Unit, College of Arts and Science, Qatar University, Doha, Qatar

* Corresponding Author: Majid Khan. Email:

Intelligent Automation & Soft Computing 2023, 36(2), 1451-1463.


In today’s digital world, the most inevitable challenge is the protection of digital information. Due to the weak confidentiality preserving techniques, the existing world is facing several digital information breaches. To make our digital data indecipherable to the unauthorized person, a technique for finding a cryptographically strong Substitution box (S-box) have presented. An S-box with sound cryptographic assets such as nonlinearity (NL), strict avalanche criterion (SAC), bit independence criteria (BIC), bit independence criteria of nonlinearity (BIC-NL), Bit independence criteria of Strict avalanche criteria (BIC-SAC), and Input/output XOR is considered as the robust S-box. The Decision-Making Trial and Evaluation Laboratory (DEMATEL) approach of multi-criteria decision making (MCDM) is proposed for finding the interrelation among cryptographic properties. A combination of two MCDM methods namely Entropy and multi-objective optimization based on ratio analysis (MOORA) is applied for the best S-box selection. A robust substitution box is selected for secure communications in cryptography by using the combination of DEMETAL selection criteria, entropy weight assigning, and MOORA ranking scheme. The combination of these three methods provides a fast selection procedure for the secure confusion component. The offered selection method can also be utilized for the choice of the best cryptosystem with highly secure properties and resistive against all possible linear and differential attacks in the cryptanalysis.


Cite This Article

N. Abughazalah, I. Ishaque, M. Khan, A. S. Alanazi and I. Hussain, "Classification of nonlinear confusion component using hybrid multi-criteria decision making," Intelligent Automation & Soft Computing, vol. 36, no.2, pp. 1451–1463, 2023.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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