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Constructing differentially 4-uniform involutions over F22k by using Carlitz form
Title
Constructing differentially 4-uniform involutions over F22k by using Carlitz form
Authors
Jeong J.
;
Koo N.
;
Kwon S.
Ewha Authors
구남훈
SCOPUS Author ID
구남훈
Issue Date
2022
Journal Title
Finite Fields and their Applications
ISSN
1071-5797
Citation
Finite Fields and their Applications vol. 78
Keywords
Algebraic degree
;
Carlitz rank
;
Differential uniformity
;
Differentially 4-uniform permutation
;
Involution
;
Nonlinearity
;
Substitution box (S-box)
Publisher
Academic Press Inc.
Indexed
SCIE; SCOPUS
Document Type
Article
Abstract
Differentially 4-uniform involutions on F22k play important roles in the design of substitution boxes (S-boxes). Despite the active researches on differentially 4-uniform permutation, there is not so much research on differentially 4-uniform involutions, especially over the field F2n with 4|n. In this paper, we introduce a new approach to construct differentially 4-uniform involutions by using Carlitz form. With this approach, we explicitly construct two new classes of differentially 4-uniform involutions over F2n with 4|n. We also show that our constructions have high nonlinearity and optimal algebraic degree. With the help of computer, we show that our constructions are CCZ-inequivalent to the known differentially 4-uniform involutions over F28. © 2021 Elsevier Inc.
DOI
10.1016/j.ffa.2021.101957
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