Anbar Meidl, Nurdagül and Kalaycı, Tekgül and Meidl, Wilfried and Merai, Laszlo (2022) On a class of functions with the maximal number of bent components. IEEE Transactions on Information Theory . ISSN 0018-9448 (Print) 1557-9654 (Online) Published Online First http://dx.doi.org/10.1109/TIT.2022.3174672
There is a more recent version of this item available.
PDF
akmm_maximum_bent_components.pdf
Restricted to Registered users only
Download (869kB) | Request a copy
akmm_maximum_bent_components.pdf
Restricted to Registered users only
Download (869kB) | Request a copy
Official URL: http://dx.doi.org/10.1109/TIT.2022.3174672
Abstract
A function F : Fn2 → Fn2, n = 2m, can have at most 2n - 2m bent component functions. Trivial examples are vectorial bent functions from Fn2 to Fm2, seen as functions on Fn2. The first nontrivial example is given in univariate form as x2r Trn m(x), 1 ≤ r < m (Pott et al. 2018), a few more examples of similar shape are given by Mesnager et al. 2019, and finally it has been shown that the quadratic function F(x) = x2r Trn m(Λ(x)), has 2n - 2m bent components if and only if Λ is a linearized permutation polynomial of F2m[x] (Anbar et al. 2021). In the first part of this article, an upper bound for the nonlinearity of plateaued functions with 2n-2m bent components is shown, which is attained by the example x2r Trn m(x). We then analyse in detail nonlinearity and differential spectrum of the class of functions F(x) = x2r Trn m(Λ(x)), which, as will be seen, requires the study of the functions x2r Λ(x). In the last part we demonstrate that this class belongs to a larger class of functions with 2n - 2m Maiorana-McFarland bent components, which also contains nonquadratic and non-plateaued functions.
Item Type: | Article |
---|---|
Subjects: | Q Science > QA Mathematics > QA150-272.5 Algebra |
Divisions: | Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics Faculty of Engineering and Natural Sciences |
Depositing User: | Nurdagül Anbar Meidl |
Date Deposited: | 29 Jun 2022 10:56 |
Last Modified: | 21 Aug 2022 16:19 |
URI: | https://research.sabanciuniv.edu/id/eprint/42846 |
Available Versions of this Item
- On a class of functions with the maximal number of bent components. (deposited 29 Jun 2022 10:56) [Currently Displayed]