On the construction of even-variable rotation symmetric Boolean functions with optimal algebraic immunity and high nonlinearity.
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| Title: | On the construction of even-variable rotation symmetric Boolean functions with optimal algebraic immunity and high nonlinearity. |
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| Authors: | Wei, Huanhuan1 (AUTHOR), Guo, Fei1 (AUTHOR), Li, Zongying1 (AUTHOR), Duan, Ming1 (AUTHOR) mdscience@sina.com |
| Source: | Discrete Applied Mathematics. Sep2026, Vol. 390, p186-197. 12p. |
| Subjects: | Boolean functions, Cryptography, Nonlinear theories, Block ciphers |
| Abstract: | Rotation symmetric Boolean functions (RSBFs) are highly valued in the construction of S-boxes for block ciphers and hash functions, owing to their efficient implementation and strong cryptographic performance. This paper introduces a novel construction of RSBFs on even numbers of variables that achieve optimal algebraic immunity. A key breakthrough is that for n ≥ 16 , the nonlinearity of our newly constructed functions significantly surpasses that of all previously known RSBFs with optimal algebraic immunity. Furthermore, we prove that the algebraic degree of these functions is optimal or suboptimal for special variable sizes. The fast algebraic immunity is also evaluated for some small numbers of variables. [ABSTRACT FROM AUTHOR] |
| Copyright of Discrete Applied Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 193680382 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: On the construction of even-variable rotation symmetric Boolean functions with optimal algebraic immunity and high nonlinearity. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Wei%2C+Huanhuan%22">Wei, Huanhuan</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Guo%2C+Fei%22">Guo, Fei</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Li%2C+Zongying%22">Li, Zongying</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Duan%2C+Ming%22">Duan, Ming</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> mdscience@sina.com</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Discrete+Applied+Mathematics%22">Discrete Applied Mathematics</searchLink>. Sep2026, Vol. 390, p186-197. 12p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Boolean+functions%22">Boolean functions</searchLink><br /><searchLink fieldCode="DE" term="%22Cryptography%22">Cryptography</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+theories%22">Nonlinear theories</searchLink><br /><searchLink fieldCode="DE" term="%22Block+ciphers%22">Block ciphers</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Rotation symmetric Boolean functions (RSBFs) are highly valued in the construction of S-boxes for block ciphers and hash functions, owing to their efficient implementation and strong cryptographic performance. This paper introduces a novel construction of RSBFs on even numbers of variables that achieve optimal algebraic immunity. A key breakthrough is that for n ≥ 16 , the nonlinearity of our newly constructed functions significantly surpasses that of all previously known RSBFs with optimal algebraic immunity. Furthermore, we prove that the algebraic degree of these functions is optimal or suboptimal for special variable sizes. The fast algebraic immunity is also evaluated for some small numbers of variables. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Discrete Applied Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.dam.2026.04.029 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 12 StartPage: 186 Subjects: – SubjectFull: Boolean functions Type: general – SubjectFull: Cryptography Type: general – SubjectFull: Nonlinear theories Type: general – SubjectFull: Block ciphers Type: general Titles: – TitleFull: On the construction of even-variable rotation symmetric Boolean functions with optimal algebraic immunity and high nonlinearity. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Wei, Huanhuan – PersonEntity: Name: NameFull: Guo, Fei – PersonEntity: Name: NameFull: Li, Zongying – PersonEntity: Name: NameFull: Duan, Ming IsPartOfRelationships: – BibEntity: Dates: – D: 15 M: 09 Text: Sep2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 0166218X Numbering: – Type: volume Value: 390 Titles: – TitleFull: Discrete Applied Mathematics Type: main |
| ResultId | 1 |
