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Novel Scheme for Robust Confusion Component Selection Based on Pythagorean Fuzzy Set

Nabilah Abughazalah1, Mohsin Iqbal2, Majid Khan3,*, 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 Mathematics & Statistics, Riphah International University, Islamabad, Pakistan
3 Department of Applied Mathematics & Statistics, Institute of Space Technology, Islamabad, Pakistan
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:

Computers, Materials & Continua 2023, 74(3), 6523-6534.


The substitution box, often known as an S-box, is a nonlinear component that is a part of several block ciphers. Its purpose is to protect cryptographic algorithms from a variety of cryptanalytic assaults. A MultiCriteria Decision Making (MCDM) problem has a complex selection procedure because of having many options and criteria to choose from. Because of this, statistical methods are necessary to assess the performance score of each S-box and decide which option is the best one available based on this score. Using the Pythagorean Fuzzy-based Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method, the major objective of this investigation is to select the optimal S-box to be implemented from a pool of twelve key choices. With the help of the Pythagorean fuzzy set (PFS), the purpose of this article is to evaluate whether this nonlinear component is suitable for use in a variety of encryption applications. In this article, we have considered various characteristics of S-boxes, including nonlinearity, algebraic degree, strict avalanche criterion (SAC), absolute indicator, bit independent criterion (BIC), sum of square indicator, algebraic immunity, transparency order, robustness to differential cryptanalysis, composite algebraic immunity, signal to noise ratio-differential power attack (SNR-DPA), and confusion coefficient variance on some standard S-boxes that are Advanced Encryption Following this, the findings of the investigation are changed into Pythagorean fuzzy numbers in the shape of a matrix. This matrix is then subjected to an analysis using the TOPSIS method, which is dependent on the Pythagorean fuzzy set, to rank the most suitable S-box for use in encryption applications.


Cite This Article

N. Abughazalah, . M. Iqbal, . M. Khan and . I. Hussain, "Novel scheme for robust confusion component selection based on pythagorean fuzzy set," Computers, Materials & Continua, vol. 74, no.3, pp. 6523–6534, 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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