Enhancement of Non-Permutation Binomial Power Functions to Construct Cryptographically Strong S-Boxes
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 construct...
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-01-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/11/2/446 |
| _version_ | 1797439028848492544 |
|---|---|
| author | Herman Isa Syed Alwee Aljunid Syed Junid Muhammad Reza Z’aba Rosdisham Endut Syed Mohammad Ammar Norshamsuri Ali |
| author_facet | Herman Isa Syed Alwee Aljunid Syed Junid Muhammad Reza Z’aba Rosdisham Endut Syed Mohammad Ammar Norshamsuri Ali |
| author_sort | Herman Isa |
| collection | DOAJ |
| description | 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 <i>Redundancy Removal Algorithm</i>, 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. |
| first_indexed | 2024-03-09T11:45:56Z |
| format | Article |
| id | doaj.art-da0d3a41147646d6b66f85c21294e032 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T11:45:56Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-da0d3a41147646d6b66f85c21294e0322023-11-30T23:22:20ZengMDPI AGMathematics2227-73902023-01-0111244610.3390/math11020446Enhancement of Non-Permutation Binomial Power Functions to Construct Cryptographically Strong S-BoxesHerman Isa0Syed Alwee Aljunid Syed Junid1Muhammad Reza Z’aba2Rosdisham Endut3Syed Mohammad Ammar4Norshamsuri Ali5Faculty of Electronic Engineering & Technology, Universiti Malaysia Perlis, Arau 02600, Perlis, MalaysiaFaculty of Electronic Engineering & Technology, Universiti Malaysia Perlis, Arau 02600, Perlis, MalaysiaMIMOS Berhad, Kuala Lumpur 57000, MalaysiaFaculty of Electronic Engineering & Technology, Universiti Malaysia Perlis, Arau 02600, Perlis, MalaysiaFaculty of Electronic Engineering & Technology, Universiti Malaysia Perlis, Arau 02600, Perlis, MalaysiaFaculty of Electronic Engineering & Technology, Universiti Malaysia Perlis, Arau 02600, Perlis, MalaysiaA 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 <i>Redundancy Removal Algorithm</i>, 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.https://www.mdpi.com/2227-7390/11/2/446s-boxcryptographically strong s-boxbinomial power functionnon-permutation functionredundancy removal algorithm |
| spellingShingle | Herman Isa Syed Alwee Aljunid Syed Junid Muhammad Reza Z’aba Rosdisham Endut Syed Mohammad Ammar Norshamsuri Ali Enhancement of Non-Permutation Binomial Power Functions to Construct Cryptographically Strong S-Boxes Mathematics s-box cryptographically strong s-box binomial power function non-permutation function redundancy removal algorithm |
| title | Enhancement of Non-Permutation Binomial Power Functions to Construct Cryptographically Strong S-Boxes |
| title_full | Enhancement of Non-Permutation Binomial Power Functions to Construct Cryptographically Strong S-Boxes |
| title_fullStr | Enhancement of Non-Permutation Binomial Power Functions to Construct Cryptographically Strong S-Boxes |
| title_full_unstemmed | Enhancement of Non-Permutation Binomial Power Functions to Construct Cryptographically Strong S-Boxes |
| title_short | Enhancement of Non-Permutation Binomial Power Functions to Construct Cryptographically Strong S-Boxes |
| title_sort | enhancement of non permutation binomial power functions to construct cryptographically strong s boxes |
| topic | s-box cryptographically strong s-box binomial power function non-permutation function redundancy removal algorithm |
| url | https://www.mdpi.com/2227-7390/11/2/446 |
| work_keys_str_mv | AT hermanisa enhancementofnonpermutationbinomialpowerfunctionstoconstructcryptographicallystrongsboxes AT syedalweealjunidsyedjunid enhancementofnonpermutationbinomialpowerfunctionstoconstructcryptographicallystrongsboxes AT muhammadrezazaba enhancementofnonpermutationbinomialpowerfunctionstoconstructcryptographicallystrongsboxes AT rosdishamendut enhancementofnonpermutationbinomialpowerfunctionstoconstructcryptographicallystrongsboxes AT syedmohammadammar enhancementofnonpermutationbinomialpowerfunctionstoconstructcryptographicallystrongsboxes AT norshamsuriali enhancementofnonpermutationbinomialpowerfunctionstoconstructcryptographicallystrongsboxes |