English
On APN and AB power functions
Multi angle
Auteurs : Budaghyan, Lilya (Auteur de la Conférence)
CIRM (Editeur )
06B30 - Topological lattices, order topologies, See also {06F30, 22A26, 54F05, 54H12}
94A60 - Cryptography
94C10 - Switching theory, application of Boolean algebra; Boolean functions, See also {06E30}
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2804/Slides/Alcocrypt-2023-Budaghyan-1.pdf
CIRM (Editeur )
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Résumé :
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.
Codes MSC : 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.
06B30 - Topological lattices, order topologies, See also {06F30, 22A26, 54F05, 54H12}
94A60 - Cryptography
94C10 - Switching theory, application of Boolean algebra; Boolean functions, See also {06E30}
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2804/Slides/Alcocrypt-2023-Budaghyan-1.pdf
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 08/03/2023 Date de captation : 23/02/2023 Sous collection : Research talks arXiv category : Combinatorics ; Information Theory Domaine : Combinatorics ; Computer Science Format : MP4 (.mp4) - HD Durée : 00:47:15 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-02-23_Budaghyan.mp4 
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Informations sur la Rencontre
Nom de la rencontre : ALCOCRYPTOrganisateurs de la rencontre : Bonnecaze, Alexis ; Mesnager, Sihem ; Solé, Patrick Dates : 20/02/2023 - 24/02/2023 Année de la rencontre : 2023 URL Congrès : https://conferences.cirm-math.fr/2804.html
Données de citation
DOI : 10.24350/CIRM.V.20005903Citer cette vidéo: Budaghyan, Lilya (2023). On APN and AB power functions. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20005903 URI : http://dx.doi.org/10.24350/CIRM.V.20005903 |
Voir aussi
- [Multi angle] Divisible codes / Auteur de la Conférence Kurz, Sascha.
- [Multi angle] Almost there: capacity of private information retrieval from coded and colluding servers / Auteur de la Conférence Hollanti, Camilla.
- [Multi angle] Projective Reed Muller codes revisited / Auteur de la Conférence Ghorpade, Sudhir.
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
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