Chaos and Cellular Automata-Based Substitution Box and Its Application in Cryptography
Substitution boxes are the key factor in symmetric-key cryptosystems that determines their ability to resist various cryptanalytic attacks. Creating strong substitution boxes that have multiple strong cryptographic properties at the same time is a challenging task for cryptographers. A significant a...
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MDPI AG
2023-05-01
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| Series: | Mathematics |
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| author | Arslan Shafique Kashif Hesham Khan Mohammad Mazyad Hazzazi Ismail Bahkali Zaid Bassfar Mujeeb Ur Rehman |
| author_facet | Arslan Shafique Kashif Hesham Khan Mohammad Mazyad Hazzazi Ismail Bahkali Zaid Bassfar Mujeeb Ur Rehman |
| author_sort | Arslan Shafique |
| collection | DOAJ |
| description | Substitution boxes are the key factor in symmetric-key cryptosystems that determines their ability to resist various cryptanalytic attacks. Creating strong substitution boxes that have multiple strong cryptographic properties at the same time is a challenging task for cryptographers. A significant amount of research has been conducted on S-boxes in the past few decades, but the resulting S-boxes have been found to be vulnerable to various cyberattacks. This paper proposes a new method for creating robust S-boxes that exhibit superior performance and possess high scores in multiple cryptographic properties. The hybrid S-box method presented in this paper is based on Chua’s circuit chaotic map, two-dimensional cellular automata, and an algebraic permutation group structure. The proposed <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>16</mn><mo>×</mo><mn>16</mn></mrow></semantics></math></inline-formula> S-box has an excellent performance in terms of security parameters, including a minimum nonlinearity of 102, the absence of fixed points, the satisfaction of bit independence and strict avalanche criteria, a low differential uniformity of 5, a low linear approximation probability of 0.0603, and an auto-correlation function of 28. The analysis of the performance comparison indicates that the proposed S-box outperforms other state-of-the-art S-box techniques in several aspects. It possesses better attributes, such as a higher degree of inherent security and resilience, which make it more secure and less vulnerable to potential attacks. |
| first_indexed | 2024-03-11T03:31:51Z |
| format | Article |
| id | doaj.art-f68f196c69784cb8ae115adc1dc25a86 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T03:31:51Z |
| publishDate | 2023-05-01 |
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| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-f68f196c69784cb8ae115adc1dc25a862023-11-18T02:19:21ZengMDPI AGMathematics2227-73902023-05-011110232210.3390/math11102322Chaos and Cellular Automata-Based Substitution Box and Its Application in CryptographyArslan Shafique0Kashif Hesham Khan1Mohammad Mazyad Hazzazi2Ismail Bahkali3Zaid Bassfar4Mujeeb Ur Rehman5Department of Electrical Engineering, Riphah International University, Islamabad 46000, PakistanDepartment of Computer Science, RMIT University, Melbourne 3001, AustraliaDepartment of Mathematics, College of Science, King Khalid University, Abha 61421, Saudi ArabiaDepartment of Information Science, King Abdulaziz University, Jeddah 21589, Saudi ArabiaDepartment of Information Technology, University of Tabuk, Tabuk 71491, Saudi ArabiaSchool of Science, Technology and Health, York St. John University, York YO31 7EX, UKSubstitution boxes are the key factor in symmetric-key cryptosystems that determines their ability to resist various cryptanalytic attacks. Creating strong substitution boxes that have multiple strong cryptographic properties at the same time is a challenging task for cryptographers. A significant amount of research has been conducted on S-boxes in the past few decades, but the resulting S-boxes have been found to be vulnerable to various cyberattacks. This paper proposes a new method for creating robust S-boxes that exhibit superior performance and possess high scores in multiple cryptographic properties. The hybrid S-box method presented in this paper is based on Chua’s circuit chaotic map, two-dimensional cellular automata, and an algebraic permutation group structure. The proposed <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>16</mn><mo>×</mo><mn>16</mn></mrow></semantics></math></inline-formula> S-box has an excellent performance in terms of security parameters, including a minimum nonlinearity of 102, the absence of fixed points, the satisfaction of bit independence and strict avalanche criteria, a low differential uniformity of 5, a low linear approximation probability of 0.0603, and an auto-correlation function of 28. The analysis of the performance comparison indicates that the proposed S-box outperforms other state-of-the-art S-box techniques in several aspects. It possesses better attributes, such as a higher degree of inherent security and resilience, which make it more secure and less vulnerable to potential attacks.https://www.mdpi.com/2227-7390/11/10/2322chaos theorycyberattackssubstitution boxesdata security |
| spellingShingle | Arslan Shafique Kashif Hesham Khan Mohammad Mazyad Hazzazi Ismail Bahkali Zaid Bassfar Mujeeb Ur Rehman Chaos and Cellular Automata-Based Substitution Box and Its Application in Cryptography Mathematics chaos theory cyberattacks substitution boxes data security |
| title | Chaos and Cellular Automata-Based Substitution Box and Its Application in Cryptography |
| title_full | Chaos and Cellular Automata-Based Substitution Box and Its Application in Cryptography |
| title_fullStr | Chaos and Cellular Automata-Based Substitution Box and Its Application in Cryptography |
| title_full_unstemmed | Chaos and Cellular Automata-Based Substitution Box and Its Application in Cryptography |
| title_short | Chaos and Cellular Automata-Based Substitution Box and Its Application in Cryptography |
| title_sort | chaos and cellular automata based substitution box and its application in cryptography |
| topic | chaos theory cyberattacks substitution boxes data security |
| url | https://www.mdpi.com/2227-7390/11/10/2322 |
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