Enhancement of Non-Permutation Binomial Power Functions to Construct Cryptographically Strong S-Boxes

Herman Isa (), Syed Alwee Aljunid Syed Junid (), Muhammad Reza Z’aba, Rosdisham Endut, Syed Mohammad Ammar and Norshamsuri Ali
Additional contact information
Herman Isa: Faculty of Electronic Engineering & Technology, Universiti Malaysia Perlis, Arau 02600, Perlis, Malaysia
Syed Alwee Aljunid Syed Junid: Faculty of Electronic Engineering & Technology, Universiti Malaysia Perlis, Arau 02600, Perlis, Malaysia
Muhammad Reza Z’aba: MIMOS Berhad, Kuala Lumpur 57000, Malaysia
Rosdisham Endut: Faculty of Electronic Engineering & Technology, Universiti Malaysia Perlis, Arau 02600, Perlis, Malaysia
Syed Mohammad Ammar: Faculty of Electronic Engineering & Technology, Universiti Malaysia Perlis, Arau 02600, Perlis, Malaysia
Norshamsuri Ali: Faculty of Electronic Engineering & Technology, Universiti Malaysia Perlis, Arau 02600, Perlis, Malaysia

Mathematics, 2023, vol. 11, issue 2, 1-22

Abstract: A Substitution box (S-box) is an important component used in symmetric key cryptosystems to satisfy Shannon’s property on confusion. As the only nonlinear operation, the S-box must be cryptographically strong to thwart any cryptanalysis tools on cryptosystems. Generally, the S-boxes can be constructed using any of the following approaches: the random search approach, heuristic/evolutionary approach or mathematical approach. However, the current S-box construction has some drawbacks, such as low cryptographic properties for the random search approach and the fact that it is hard to develop mathematical functions that can be used to construct a cryptographically strong S-box. In this paper, we explore the non-permutation function that was generated from the binomial operation of the power function to construct a cryptographically strong S-box. By adopting the method called the Redundancy Removal Algorithm , we propose some enhancement in the algorithm such that the desired result can be obtained. The analytical results of our experiment indicate that all criteria such as bijective, nonlinearity, differential uniformity, algebraic degree and linear approximation are found to hold in the obtained S-boxes. Our proposed S-box also surpassed several bijective S-boxes available in the literature in terms of cryptographic properties.

Keywords: s-box; cryptographically strong s-box; binomial power function; non-permutation function; redundancy removal algorithm (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/2/446/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/2/446/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:2:p:446-:d:1035693

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().