Cryptanalysis of hyperchaotic S-box generation and image encryption

Mohammad Mazyad Hazzazi; Gulraiz; Rashad Ali; Muhammad Kamran Jamil; Sameer Abdullah Nooh; Fahad Alblehai; Mohammad Mazyad Hazzazi; Gulraiz; Rashad Ali; Muhammad Kamran Jamil; Sameer Abdullah Nooh; Fahad Alblehai

doi:10.3934/math.20241714

AIMS Mathematics

2024, Volume 9, Issue 12: 36116-36139. doi: 10.3934/math.20241714

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Cryptanalysis of hyperchaotic S-box generation and image encryption

1.
Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia
2.
Govt. High School Gulistan Colony Mustafa Abad (EX-MCL), Dharampura, 05478, Lahore, Pakistan
3.
Department of Mathematics, University of Trento, 38122 Trento, Italy
4.
Department of Mathematics, Riphah International University, 54660 Lahore, Pakistan
5.
Department of Information Systems, Faculty of Computing and Information Technology, King Abdulaziz University Jeddah 21589, Saudi Arabia
6.
Computer Science Department, Community College, King Saud University, Riyadh 11437, Saudia Arabia

Received: 20 November 2024 Revised: 09 December 2024 Accepted: 13 December 2024 Published: 26 December 2024
MSC : 94A60, 68P25

Cryptography serves as the cornerstone for safe communication and data security in today's digital environment. Because they feature substitution boxes, substitution-permutation networks (SPNs) are crucial for cryptographic algorithms such as the popular Advanced Encryption Standard (AES). The structure and properties of S-boxes have a significant impact on the overall security of cryptographic systems. This article aims to improve cryptographic security through unique S-box construction methodologies. The proposed S-boxes improve the security features by employing chaotic maps and Galois fields, which go beyond traditional design approaches. The S-boxes were analyzed and the weaknesses were removed to design strong candidate S-boxes. The efficiency of the proposed S-boxes in increasing cryptographic resilience is thoroughly explored thereby taking nonlinearity, strict avalanche requirements, bit independence constraints, linear approximation, and differential approximation into account. The dynamic S-boxes have average scores of nonlinearity, strict avalanche criteria(SAC), nonlinearity of Bit Independence Criteria (BIC Nonlinearity), SAC of Bit Independence Criteria (BIC SAC), Linear Approximation Probability (LAP) and Differential Approximation Probability (DAP) is 111.1025, 111.1022, 0.5014, 0.5024, 111.1082, 111.0964, 0.5024, 0.5022, 0.0726, 0.0729 and 0.0214, 0.0219, respectively. Furthermore, given the prevalence of images in modern communication and data storage, this work studies the seamless incorporation of advanced S-boxes into image encryption systems. With its thorough research, the paper contributes to the current discussion on cryptographic security by providing theoretical understandings and practical solutions to improve digital communication and data security in an era of rising cyber dangers and ubiquitous connectivity.
- affine matrices,
- cryptanalysis,
- encryption,
- hyperchaos,
- S-box
Citation: Mohammad Mazyad Hazzazi, Gulraiz, Rashad Ali, Muhammad Kamran Jamil, Sameer Abdullah Nooh, Fahad Alblehai. Cryptanalysis of hyperchaotic S-box generation and image encryption[J]. AIMS Mathematics, 2024, 9(12): 36116-36139. doi: 10.3934/math.20241714

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Abstract

Cryptography serves as the cornerstone for safe communication and data security in today's digital environment. Because they feature substitution boxes, substitution-permutation networks (SPNs) are crucial for cryptographic algorithms such as the popular Advanced Encryption Standard (AES). The structure and properties of S-boxes have a significant impact on the overall security of cryptographic systems. This article aims to improve cryptographic security through unique S-box construction methodologies. The proposed S-boxes improve the security features by employing chaotic maps and Galois fields, which go beyond traditional design approaches. The S-boxes were analyzed and the weaknesses were removed to design strong candidate S-boxes. The efficiency of the proposed S-boxes in increasing cryptographic resilience is thoroughly explored thereby taking nonlinearity, strict avalanche requirements, bit independence constraints, linear approximation, and differential approximation into account. The dynamic S-boxes have average scores of nonlinearity, strict avalanche criteria(SAC), nonlinearity of Bit Independence Criteria (BIC Nonlinearity), SAC of Bit Independence Criteria (BIC SAC), Linear Approximation Probability (LAP) and Differential Approximation Probability (DAP) is 111.1025, 111.1022, 0.5014, 0.5024, 111.1082, 111.0964, 0.5024, 0.5022, 0.0726, 0.0729 and 0.0214, 0.0219, respectively. Furthermore, given the prevalence of images in modern communication and data storage, this work studies the seamless incorporation of advanced S-boxes into image encryption systems. With its thorough research, the paper contributes to the current discussion on cryptographic security by providing theoretical understandings and practical solutions to improve digital communication and data security in an era of rising cyber dangers and ubiquitous connectivity.

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