| Title: | Rotation-symmetric bent functions outside the completed Maiorana-McFarland class |
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| Authors: | ID Polujan, Alexandr (Author)
ID Kudin, Sadmir (Author)
ID Pašalić, Enes (Author) |
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| Files: |  RAZ_Polujan_Alexandr_2026.pdf (342,17 KB)
MD5: D7943AD489B9ADA5253FC4152CB98CA2
 https://ieeexplore.ieee.org/document/11483153
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | FAMNIT - Faculty of Mathematics, Science and Information Technologies
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| Abstract: | Rotation-symmetric (RS) bent functions, which are invariant under the action of the cyclic group, have attracted significant attention over the past three decades due to their importance in cryptographic applications. For the last three decades of research on these objects, most known RS bent func- tions have been obtained by applying extended-affine equivalence to specific Maiorana-McFarland bent functions, in a way that ensures the resulting function retains invariance under the cyclic group action. Due to the intrinsic difficulty of characterizing RS bent functions that do not belong to the completed Maiorana- McFarland class M#, there has been no evidence for the existence of such functions until now. In this paper, we provide, for the first time, a solution to this problem. First, we perform a computational classification of RS cubic bent functions in ten variables under extended-affine equivalence and demonstrate that one of the resulting classes is outside the M# class. Next, we prove that an infinite family of RS bent functions on Fn 2 of maximum algebraic degree n/2 (Su, Adv. Math. Commun. 13(2): 253–265, 2019) does not belong to M#, for all n ≥ 8. Finally, we show that a family of quartic RS bent functions on Fn 2 (Carlet, Gao, and Liu, J. Comb. Theory Ser. A 127: 161–175, 2014), does not belong to the M# class for infinitely many n. |
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| Keywords: | bent function, rotation-symmetry, Maiorana-McFarland class |
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| Publication version: | Author Accepted Manuscript |
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| Publication date: | 17.04.2026 |
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| Year of publishing: | 2026 |
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| Number of pages: | str. 4341-4351 |
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| Numbering: | Vol. 72, no. 6 |
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| PID: | 20.500.12556/RUP-23519  |
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| UDC: | 51 |
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| ISSN on article: | 0018-9448 |
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| DOI: | 10.1109/TIT.2026.3685133 |
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| COBISS.SI-ID: | 283209475 |
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| Publication date in RUP: | 19.08.2026 |
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| Views: | 35 |
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| Downloads: | 2 |
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