Open Access
ARTICLE
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. https://doi.org/10.32604/cmc.2022.031859
Received 28 April 2022; Accepted 01 September 2022; Issue published 28 December 2022
Abstract
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.
Keywords
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. https://doi.org/10.32604/cmc.2022.031859