EQUIVALENCES OF BIPROJECTIVE ALMOST PERFECT NONLINEAR FUNCTIONS
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
EQUIVALENCES OF BIPROJECTIVE ALMOST PERFECT NONLINEAR FUNCTIONS
Original language description
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.
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
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Combinatorial Theory
ISSN
2766-1334
e-ISSN
2766-1334
Volume of the periodical
5
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
29
Pages from-to
7
UT code for WoS article
001605560500003
EID of the result in the Scopus database
2-s2.0-105017571257