Academic Journal
Asymptotic bounds on the numbers of certain bent functions
| Title: | Asymptotic bounds on the numbers of certain bent functions |
|---|---|
| Authors: | Potapov, Vladimir N., Özbudak, Ferruh |
| Source: | Cryptography and Communications. 16:1289-1307 |
| Publisher Information: | Springer Science and Business Media LLC, 2024. |
| Publication Year: | 2024 |
| Subject Terms: | bent function, Algebraic coding theory, cryptography (number-theoretic aspects), 0102 computer and information sciences, 02 engineering and technology, 01 natural sciences, Combinatorial aspects of block designs, generalized Maiorana-McFarland bent function, transversal, Cryptography, 0202 electrical engineering, electronic engineering, information engineering, Orthogonal arrays, Latin squares, Room squares, Boolean functions, subspace design |
| Description: | Using recent results of Keevash et al. [10] and Eberhard et al. [8] together with further new detailed techniques in combinatorics, we present constructions of two concrete families of generalized Maiorana-McFarland bent functions. Our constructions improve the lower bounds on the number of bent functions in n variables over a finite field $${\mathbb F}_p$$ F p if p is odd and n is odd in the limit as n tends to infinity. Moreover we obtain the asymptotically exact number of two dimensional vectorial Maiorana-McFarland bent functions in n variables over $${\mathbb F}_2$$ F 2 as n tends to infinity. |
| Document Type: | Article |
| File Description: | application/xml |
| Language: | English |
| ISSN: | 1936-2455 1936-2447 |
| DOI: | 10.1007/s12095-024-00726-x |
| Access URL: | https://zbmath.org/7985183 https://doi.org/10.1007/s12095-024-00726-x |
| Rights: | CC BY |
| Accession Number: | edsair.doi.dedup.....2ecf55dce1bc7bb2931275ed3b7b5413 |
| Database: | OpenAIRE |
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