Almost perfect nonlinear families which are not equivalent to permutations

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Almost perfect nonlinear families which are not equivalent to permutations

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Almost perfect nonlinear families which are not equivalent to permutations

Popis výsledku anglicky

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.

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

2020

Kód důvěrnosti údajů

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

Název periodika

Finite Fields and their Applications

ISSN

1071-5797

e-ISSN

—

Svazek periodika

2020

Číslo periodika v rámci svazku

67

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

21

Strana od-do

101707

Kód UT WoS článku

000570237000015

EID výsledku v databázi Scopus

2-s2.0-85087669793