On APN and AB power functions | Vidéo | Carmin.tv

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On APN and AB power functions

De Lilya Budaghyan

Apparaît dans la collection : ALCOCRYPT - ALgebraic and combinatorial methods for COding and CRYPTography

APN and AB functions are S-boxes with optimal resistance to the linear and differential cryptanalysis. In this talk we survey known constructions and classifications of these functions and discuss big open problems for the monomial case. Among these problems are the Dobbertin's conjecture on nonexistence of new APN monomials (open since 2000), the Walsh spectrum of Dobbertin's APN monomials (open since 2000), the existence of APN permutations of the form $x^d+L(x)$ where $x^d$ is some of the known APN monomials and $L$ is a nonzero linear map.

Remark : On page 18 the speaker refers the classification result by Brinkmann [3] for functions from the field $F_{2^4}$ of order 16 to itself.

Informations sur la vidéo

Date de captation 23/02/2023
Date de publication 08/03/2023
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs, Doctorants
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.20005903
Citer cette vidéo Budaghyan, Lilya (23/02/2023). On APN and AB power functions. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20005903
URL https://dx.doi.org/10.24350/CIRM.V.20005903

Domaine(s)

Bibliographie

Lilya Budaghyan, Marco Calderini, Claude Carlet, Diana Davidova, Nikolay S. Kaleyski: On Two Fundamental Problems on APN Power Functions. IEEE Trans. Inf. Theory 68(5): 3389-3403 (2022) - https://doi.org/10.1109/TIT.2022.3147060
Claude Carlet, Stjepan Picek: On the exponents of APN power functions and Sidon sets, sum-free sets, and Dickson polynomials. IACR Cryptol. ePrint Arch. 2017: 1179 (2017) - https://ia.cr/2017/1179
Marcus Brinkmann: Extended Affine and CCZ Equivalence up to Dimension 4. IACR Cryptol. ePrint Arch. 2019: 316 (2019) - https://ia.cr/2019/316

Codes MSC

Document(s)

https://www.cirm-math.fr/RepOrga/2804/Slides/Alcocrypt-2023-Budaghyan-1.pdf

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