Characterizations of Partially Bent and Plateaued Functions over Finite Fields

Mesnager, Sihem; Özbudak, Ferruh; Sınak, Ahmet

doi:10.1007/978-3-030-05153-2_12

Arithmetic of Finite Fields

2018

DOI: 10.1007/978-3-030-05153-2_12

|View full text |Cite

Characterizations of Partially Bent and Plateaued Functions over Finite Fields

Sihem Mesnager¹,

Ferruh Özbudak²,

Ahmet Sınak³

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2021

2023

Publication Types

Select...

Article3

Relationship

Self Cite0

Independent3

Authors

Journals

Cited by 3 publications

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Generalized partially bent functions, generalized perfect arrays, and cocyclic Butson matrices

Armario,

Egan,

Flannery

2023

Cryptogr. Commun.

View full text Add to dashboard Cite

In a recent survey, Schmidt compiled equivalences between generalized bent functions, group invariant Butson Hadamard matrices, and abelian splitting relative difference sets. We establish a broader network of equivalences by considering Butson matrices that are cocyclic rather than strictly group invariant. This result has several applications; for example, to the construction of Boolean functions whose expansions are generalized partially bent functions, including cases where no bent function can exist.

show abstract

Generalized partially bent functions, generalized perfect arrays, and cocyclic Butson matrices

Armario,

Egan,

Flannery

2023

Cryptogr. Commun.

View full text Add to dashboard Cite

show abstract

Nonlinearity of functions over finite fields

Ryabov

2023

Discrete Mathematics and Applications

View full text Add to dashboard Cite

The nonlinearity and additive nonlinearity of a function are defined as the Hamming distances, respectively, to the set of all affine mappings and to the set of all mappings having nontrivial additive translators. On the basis of the revealed relation between the nonlinearities and the Fourier coefficients of the characters of a function, convenient formulas for nonlinearity evaluation for practically important classes of functions over an arbitrary finite field are found. In the case of a field of even characteristic, similar results were obtained for the additive nonlinearity in terms of the autocorrelation coefficients. The formulas obtained made it possible to present specific classes of functions with maximal possible and high nonlinearity and additive nonlinearity.

show abstract

Nonlinearity of functions over finite fields

Рябов¹

2021

Дискрет. матем.

View full text Add to dashboard Cite

Нелинейность и аддитивная нелинейность функции определяются как расстояния Хэмминга до множества всех аффинных отображений и множества всех отображений, имеющих нетривиальные аддитивные трансляторы, соответственно. На основе выявленной связи параметров нелинейности с коэффициентами Фурье характеров функции найдены удобные формулы для вычисления нелинейности для практически значимых классов функций над произвольным конечным полем. В случае поля четной характеристики в терминах коэффициентов автокорреляции получены аналогичные результаты для аддитивной нелинейности. Полученные формулы позволили определить конкретные классы функций с максимально возможной и высокой нелинейностью и аддитивной нелинейностью.

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Characterizations of Partially Bent and Plateaued Functions over Finite Fields

Cited by 3 publications

References 29 publications

Generalized partially bent functions, generalized perfect arrays, and cocyclic Butson matrices

Generalized partially bent functions, generalized perfect arrays, and cocyclic Butson matrices

Nonlinearity of functions over finite fields

Nonlinearity of functions over finite fields

Contact Info

Product

Resources

About