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On the boomerang uniformity of permutations of low Carlitz rank
Title
On the boomerang uniformity of permutations of low Carlitz rank
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. 81
Keywords
APN
;
Boolean function
;
Boomerang uniformity
;
Differential uniformity
;
Permutation
Publisher
Academic Press Inc.
Indexed
SCIE; SCOPUS
Document Type
Article
Abstract
Finding permutation polynomials with low differential and boomerang uniformity is an important topic in S-box designs of many block ciphers. For example, AES chooses the inverse function as its S-box, which is differentially 4-uniform and boomerang 6-uniform. Also there has been considerable research on many non-quadratic permutations which are modifications of the inverse function. In this paper, we give a novel approach which shows that plenty of existing modifications of the inverse function are in fact affine equivalent to permutations of low Carlitz rank, and those modifications cannot be APN. We also present the complete list of permutations of Carlitz rank 3 having the boomerang uniformity six, and give the complete classification of the differential uniformities of permutations of Carlitz rank 3. As an application, we provide all the involutions of Carlitz rank 3 having the boomerang uniformity six. © 2022 The Author(s)
DOI
10.1016/j.ffa.2022.102033
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