Almost perfect nonlinear families which are not equivalent to permutations
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10420794" target="_blank" >RIV/00216208:11320/20:10420794 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=7ZnoZk.tkt" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=7ZnoZk.tkt</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.ffa.2020.101707" target="_blank" >10.1016/j.ffa.2020.101707</a>
Alternative languages
Result language
angličtina
Original language name
Almost perfect nonlinear families which are not equivalent to permutations
Original language description
An important problem on almost perfect nonlinear (APN) functions is the existence of APN permutations on even-degree extensions of F-2 larger than 6. Browning et al. (2010) gave the first known example of an APN permutation on the degree-6 extension of F-2. The APN permutation is CCZ-equivalent to the previously known quadratic Kim kappa-function (Browning et al. (2009)). Aside from the computer based CCZ-inequivalence results on known APN functions on even-degree extensions of F-2 with extension degrees less than 12, no theoretical CCZ-inequivalence result on infinite families is known. In this paper, we show that Gold and Kasami APN functions are not CCZ-equivalent to permutations on infinitely many even-degree extensions of F-2. In the Gold case, we show that Gold APN functions are not equivalent to permutations on any even-degree extension of F-2, whereas in the Kasami case we are able to prove inequivalence results for every doubly-even-degree extension of F-2. (C) 2020 Elsevier Inc. All rights reserved.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA18-19087S" target="_blank" >GA18-19087S: Cryptography based on Finite Fields</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Finite Fields and their Applications
ISSN
1071-5797
e-ISSN
—
Volume of the periodical
2020
Issue of the periodical within the volume
67
Country of publishing house
US - UNITED STATES
Number of pages
21
Pages from-to
101707
UT code for WoS article
000570237000015
EID of the result in the Scopus database
2-s2.0-85087669793