Batch generated strongly nonlinear S-Boxes using enhanced quadratic maps
One of the most crucial elements in the design of a block cipher is the substitution box or S-box. Its cipher strength directly impacts the cipher algorithm's security, and the block cipher algorithm requires a good S-box. According to the cryptanalysis result of the S-box construction in AES:...
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| Format: | Article |
| Language: | English |
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AIMS Press
2025-03-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025262 |
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| author | Mohammad Mazyad Hazzazi Farooq E Azam Rashad Ali Muhammad Kamran Jamil Sameer Abdullah Nooh Fahad Alblehai |
| author_facet | Mohammad Mazyad Hazzazi Farooq E Azam Rashad Ali Muhammad Kamran Jamil Sameer Abdullah Nooh Fahad Alblehai |
| author_sort | Mohammad Mazyad Hazzazi |
| collection | DOAJ |
| description | One of the most crucial elements in the design of a block cipher is the substitution box or S-box. Its cipher strength directly impacts the cipher algorithm's security, and the block cipher algorithm requires a good S-box. According to the cryptanalysis result of the S-box construction in AES: (1) the number of irreducible polynomials can be increased to 30; (2) the affinity transformation constant c can be chosen from all elements if the existence of fixed points and reverse fixed points in an S-box is ignored; and (3) the S-box in AES is fixed, which poses possible security risks to the AES algorithm. The study above led us to build a non-degenerate 2D enhanced quadratic map (2D-EQM) with unpredictability and ergodicity. From there, we generated affine transformation constants and affine transformation matrices, which were then applied to seed S-boxes to create a batch of strongly nonlinear S-boxes. Finally, we assessed the performance of suggested S-boxes using six criteria. Security and statistical research showed that the suggested S-box batch generation procedure was practical and effective. |
| format | Article |
| id | doaj-art-11da8c7a2fed4f07a4b1623649ea50d8 |
| institution | DOAJ |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-11da8c7a2fed4f07a4b1623649ea50d82025-08-20T03:16:57ZengAIMS PressAIMS Mathematics2473-69882025-03-011035671569510.3934/math.2025262Batch generated strongly nonlinear S-Boxes using enhanced quadratic mapsMohammad Mazyad Hazzazi0Farooq E Azam1Rashad Ali2Muhammad Kamran Jamil3Sameer Abdullah Nooh4Fahad Alblehai5Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi ArabiaDepartment of Mathematics, Riphah International University, 50390 Lahore, PakistanDepartment of Mathematics, University of Trento, 38122 Trento, ItalyDepartment of Mathematics, Riphah International University, 54660 Lahore, PakistanFaculty of Computing and Information Technology King AbdulAziz University Jeddah 80200, Saudi ArabiaComputer Science Department, Community College, King Saud University, Riyadh 11437, Saudia ArabiaOne of the most crucial elements in the design of a block cipher is the substitution box or S-box. Its cipher strength directly impacts the cipher algorithm's security, and the block cipher algorithm requires a good S-box. According to the cryptanalysis result of the S-box construction in AES: (1) the number of irreducible polynomials can be increased to 30; (2) the affinity transformation constant c can be chosen from all elements if the existence of fixed points and reverse fixed points in an S-box is ignored; and (3) the S-box in AES is fixed, which poses possible security risks to the AES algorithm. The study above led us to build a non-degenerate 2D enhanced quadratic map (2D-EQM) with unpredictability and ergodicity. From there, we generated affine transformation constants and affine transformation matrices, which were then applied to seed S-boxes to create a batch of strongly nonlinear S-boxes. Finally, we assessed the performance of suggested S-boxes using six criteria. Security and statistical research showed that the suggested S-box batch generation procedure was practical and effective.https://www.aimspress.com/article/doi/10.3934/math.20252622d enhanced quadratic map (2d-eqm)affine transformationcryptographic algorithmsnonlinearitys-box design |
| spellingShingle | Mohammad Mazyad Hazzazi Farooq E Azam Rashad Ali Muhammad Kamran Jamil Sameer Abdullah Nooh Fahad Alblehai Batch generated strongly nonlinear S-Boxes using enhanced quadratic maps AIMS Mathematics 2d enhanced quadratic map (2d-eqm) affine transformation cryptographic algorithms nonlinearity s-box design |
| title | Batch generated strongly nonlinear S-Boxes using enhanced quadratic maps |
| title_full | Batch generated strongly nonlinear S-Boxes using enhanced quadratic maps |
| title_fullStr | Batch generated strongly nonlinear S-Boxes using enhanced quadratic maps |
| title_full_unstemmed | Batch generated strongly nonlinear S-Boxes using enhanced quadratic maps |
| title_short | Batch generated strongly nonlinear S-Boxes using enhanced quadratic maps |
| title_sort | batch generated strongly nonlinear s boxes using enhanced quadratic maps |
| topic | 2d enhanced quadratic map (2d-eqm) affine transformation cryptographic algorithms nonlinearity s-box design |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025262 |
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