On CCZ-inequivalence of some families of almost perfect

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

On CCZ-inequivalence of some families of almost perfect

Popis výsledku v původním jazyce

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

Název v anglickém jazyce

On CCZ-inequivalence of some families of almost perfect

Popis výsledku anglicky

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

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA18-19087S" target="_blank" >GA18-19087S: Kryptografie založená na konečných tělesech</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název periodika

Cryptography and Communications

ISSN

1936-2447

e-ISSN

—

Svazek periodika

2021

Číslo periodika v rámci svazku

13

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

15

Strana od-do

377-391

Kód UT WoS článku

000629437800001

EID výsledku v databázi Scopus

2-s2.0-85102902097