Inverse function is not component-wise uniform
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10420793" target="_blank" >RIV/00216208:11320/20:10420793 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=I3iN_SG-.C" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=I3iN_SG-.C</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s12095-020-00441-3" target="_blank" >10.1007/s12095-020-00441-3</a>
Alternative languages
Result language
angličtina
Original language name
Inverse function is not component-wise uniform
Original language description
Recently, Carlet introduced (Carlet Finite. Fields Appl. 53, 226-253 (2018)) the concept of component-wise uniform (CWU) functions which is a stronger notion than being almost perfect nonlinear (APN). Carlet showed that crooked functions (in particular quadratic functions, including Gold functions) and the compositional inverse of a specific Gold function are CWU. Carlet also compiled a table on the component-wise uniformity of APN power functions, where for the extension degrees less than 12, the APN power functions which are always CWU are Gold, the compositional inverse of the specific Gold function and Kasami. In this paper, we show that the Inverse function is not CWU if n > 5. We also show that any additive shift of a derivative of the Inverse function is not a cyclic difference set.
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
Cryptography and Communications
ISSN
1936-2447
e-ISSN
—
Volume of the periodical
2020
Issue of the periodical within the volume
12
Country of publishing house
US - UNITED STATES
Number of pages
16
Pages from-to
1179-1194
UT code for WoS article
000543015700001
EID of the result in the Scopus database
2-s2.0-85087636008