On CCZ-inequivalence of some families of almost perfect

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10436281" target="_blank" >RIV/00216208:11320/21:10436281 - isvavai.cz</a>

Result on the web

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=qQcKLXZywh" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=qQcKLXZywh</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s12095-021-00476-0" target="_blank" >10.1007/s12095-021-00476-0</a>

Result language

angličtina

Original language name

On CCZ-inequivalence of some families of almost perfect

Original language description

Browning et al. (2010) exhibited almost perfect nonlinear (APN) permutations on F26. This was the first example of an APN permutation on an even degree extension of F2. In their approach of finding an APN permutation, Browning et al. made use of a necessary and sufficient condition based on the Walsh transform. In this paper, we give an algorithm based on a related necessary condition which checks whether a vectorial Boolean function is CCZ-inequivalent to a permutation. Using this algorithm, we are able to show that no function belonging to a known family of APN functions is equivalent to a permutation on F22m, where m &lt;= 6 (except for the known case on F26). We also give an EA-invariant based on the condition. Finally, we give a theoretical proof of the fact that no member of a specific family of APN functions is equivalent to a permutation on doubly-even degree extensions of F2. Access provided by Charles University

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10101 - Pure mathematics

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)

Publication year

2021

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Cryptography and Communications

ISSN

1936-2447

e-ISSN

—

Volume of the periodical

2021

Issue of the periodical within the volume

13

Country of publishing house

US - UNITED STATES

Number of pages

15

Pages from-to

377-391

UT code for WoS article

000629437800001

EID of the result in the Scopus database

2-s2.0-85102902097