Classification of (q, q)-biprojective APN functions
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10453382" target="_blank" >RIV/00216208:11320/22:10453382 - isvavai.cz</a>
Alternative codes found
RIV/00216208:11320/23:10472169
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=vWLIkVRWrC" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=vWLIkVRWrC</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1109/TIT.2022.3220724" target="_blank" >10.1109/TIT.2022.3220724</a>
Alternative languages
Result language
angličtina
Original language name
Classification of (q, q)-biprojective APN functions
Original language description
-In this paper, we classify (q, q)-biprojective almostperfect nonlinear (APN) functions over L x L under the naturalleft and right action of GL(2, L) where L is a finite field ofcharacteristic 2. This shows in particular that the only quadraticAPN functions (up to CCZ-equivalence) over L x L that satisfythe so-called subfield property are the Gold functions and thefunction κ : F64 RIGHTWARDS ARROW F64 which is the only known APN functionthat is equivalent to a permutation over L x L up to CCZequivalence as shown in (Browning, Dillon, McQuistan, andWolfe, 2010). Deciding whether there exist other quadratic APNfunctions CCZ-equivalent to permutations that satisfy subfieldproperty or equivalently, generalizing κ to higher dimensionswas an open problem listed for instance in (Carlet, 2015) as oneof the interesting open problems on cryptographic functions.
Czech name
—
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
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
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)
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
IEEE Transactions on Information Theory
ISSN
0018-9448
e-ISSN
1557-9654
Volume of the periodical
2022
Issue of the periodical within the volume
02
Country of publishing house
US - UNITED STATES
Number of pages
12
Pages from-to
1988-1999
UT code for WoS article
000966885700001
EID of the result in the Scopus database
2-s2.0-85141600112