Further study on constructing bent functions outside the completed Maiorana–McFarland class
| Autor: | Enes Pasalic, Shishi Liu, Shixiong Xia, Fengrong Zhang, Zepeng Zhuo |
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| Rok vydání: | 2020 |
| Předmět: |
Discrete mathematics
Class (set theory) Bent function Degree (graph theory) Computer Networks and Communications Bent molecular geometry 020206 networking & telecommunications 0102 computer and information sciences 02 engineering and technology 01 natural sciences Permutation 010201 computation theory & mathematics Simple (abstract algebra) 0202 electrical engineering electronic engineering information engineering Physics::Accelerator Physics Algebraic number Boolean function Software Information Systems Mathematics |
| Zdroj: | IET Information Security. 14:654-660 |
| ISSN: | 1751-8717 1751-8709 |
| DOI: | 10.1049/iet-ifs.2018.5425 |
| Popis: | In the mid-sixties, Rothaus introduced the notion of bent function and later presented a secondary construction of bent functions (building new bent functions from already defined ones), called Rothaus’ construction. In Zhang et al. 2017 (‘Constructing bent functions outside the Maiorana–Mcfarland class using a general form of Rothaus,’ IEEE Transactions on Information Theory, 2017, vol. 63, no. 8, pp. 5336–5349.’) provided two constructions of bent functions using a general form of Rothaus and showed that the obtained classes lie outside the completed Maiorana–McFarland ( M M ) class. In this study, the authors propose two similar methods for constructing bent functions outside the completed M M class but with significantly simplified sufficient conditions compared to those in Zhang et al. 2017. These simplified conditions do not induce any serious restrictions on the choice of permutations used in the construction apart from a simple requirement on their algebraic degree and the request that the component functions of one permutation do not admit linear structures. This enables us to generate a huge class of bent functions lying outside the completed M M class. Even more importantly, they prove that the new classes of bent functions are affine inequivalent to the bent functions in Zhang et al. 2017. |
| Databáze: | OpenAIRE |
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