EQUIVALENCES OF BIPROJECTIVE ALMOST PERFECT NONLINEAR FUNCTIONS

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10509207" target="_blank" >RIV/00216208:11320/25:10509207 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=LxoOLj1-S-" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=LxoOLj1-S-</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.5070/C65365555" target="_blank" >10.5070/C65365555</a>

Jazyk výsledku

angličtina

Název v původním jazyce

EQUIVALENCES OF BIPROJECTIVE ALMOST PERFECT NONLINEAR FUNCTIONS

Popis výsledku v původním jazyce

Two important problems on almost perfect nonlinear (APN) functions are the enumeration and equivalence problems. In this paper, we solve these two problems for any biprojective APN function family by introducing a group theoretic method for those functions. Roughly half of the known APN families of functions on even dimensions are biprojective. By our method, we settle the equivalence problem for all known biprojective APN functions. Furthermore, we give a new family of such functions. Using our method, we count the number of inequivalent APN functions in all known biprojective APN families and show that the new family found in this paper gives exponentially many new inequivalent APN functions. Quite recently, the Taniguchi family of APN functions was shown to contain an exponential number of inequivalent APN functions by Kaspers and Zhou (J. Cryptol. 34(1), 2021) which improved their previous count (J. Comb. Th. A 186, 2022) for the Zhou-Pott family. Our group theoretic method substantially simplifies the work required for proving those results and provides a generic natural method for every family in the large super-class of biprojective APN functions that contains these two family along with many others.

Název v anglickém jazyce

EQUIVALENCES OF BIPROJECTIVE ALMOST PERFECT NONLINEAR FUNCTIONS

Popis výsledku anglicky

Two important problems on almost perfect nonlinear (APN) functions are the enumeration and equivalence problems. In this paper, we solve these two problems for any biprojective APN function family by introducing a group theoretic method for those functions. Roughly half of the known APN families of functions on even dimensions are biprojective. By our method, we settle the equivalence problem for all known biprojective APN functions. Furthermore, we give a new family of such functions. Using our method, we count the number of inequivalent APN functions in all known biprojective APN families and show that the new family found in this paper gives exponentially many new inequivalent APN functions. Quite recently, the Taniguchi family of APN functions was shown to contain an exponential number of inequivalent APN functions by Kaspers and Zhou (J. Cryptol. 34(1), 2021) which improved their previous count (J. Comb. Th. A 186, 2022) for the Zhou-Pott family. Our group theoretic method substantially simplifies the work required for proving those results and provides a generic natural method for every family in the large super-class of biprojective APN functions that contains these two family along with many others.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název periodika

Combinatorial Theory

ISSN

2766-1334

e-ISSN

2766-1334

Svazek periodika

5

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

29

Strana od-do

7

Kód UT WoS článku

001605560500003

EID výsledku v databázi Scopus

2-s2.0-105017571257