Research Article
On upper bounds on algebraic immunity of some $\mathcal{PS}_{ap}$ and Niho bent functions
@INPROCEEDINGS{10.1109/ChinaCom.2013.6694625, author={Enes Pasalic and Sugata Gangopadhyay and Brajesh Singh}, title={On upper bounds on algebraic immunity of some \textdollar{}\textbackslashmathcal\{PS\}_\{ap\}\textdollar{} and Niho bent functions}, proceedings={8th International Conference on Communications and Networking in China}, publisher={IEEE}, proceedings_a={CHINACOM}, year={2013}, month={11}, keywords={boolean function bent function algebraic immunity partial spreads niho bent}, doi={10.1109/ChinaCom.2013.6694625} }- Enes Pasalic
Sugata Gangopadhyay
Brajesh Singh
Year: 2013
On upper bounds on algebraic immunity of some $\mathcal{PS}_{ap}$ and Niho bent functions
CHINACOM
IEEE
DOI: 10.1109/ChinaCom.2013.6694625
Abstract
In this paper we obtain nontrivial upper bounds on algebraic immunity of Boolean bent functions belonging to a subclass of ${\mathcal PS}{ap}$ and another of Niho bent functions. Some recent results indicate the existence of bent functions in ${\mathcal PS}{ap}$ having maximum algebraic immunity. On contrary, we identify a class of bent functions in ${\mathcal PS}_{ap}$, having monomial trace representation, which cannot have maximum algebraic immunity when the number of input variables $n \ge 16$. We also consider a class of Niho bent functions having two terms in their trace representation and obtain an upper bound on their algebraic immunity which is again not optimal.
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