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On APN and AB power functions
Multi angle
Authors : Budaghyan, Lilya (Author of the conference)
CIRM (Publisher )
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}
Additional resources :
https://www.cirm-math.fr/RepOrga/2804/Slides/Alcocrypt-2023-Budaghyan-1.pdf
CIRM (Publisher )
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Abstract :
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.
MSC Codes : 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}
Additional resources :
https://www.cirm-math.fr/RepOrga/2804/Slides/Alcocrypt-2023-Budaghyan-1.pdf
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 08/03/2023 Conference Date : 23/02/2023 Subseries : Research talks arXiv category : Combinatorics ; Information Theory Mathematical Area(s) : Combinatorics ; Computer Science Format : MP4 (.mp4) - HD Video Time : 00:47:15 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-02-23_Budaghyan.mp4 
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Information on the Event
Event Title : ALCOCRYPTEvent Organizers : Bonnecaze, Alexis ; Mesnager, Sihem ; Solé, Patrick Dates : 20/02/2023 - 24/02/2023 Event Year : 2023 Event URL : https://conferences.cirm-math.fr/2804.html
Citation Data
DOI : 10.24350/CIRM.V.20005903Cite this video as: 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 |
See Also
- [Multi angle] Divisible codes / Author of the conference Kurz, Sascha.
- [Multi angle] Almost there: capacity of private information retrieval from coded and colluding servers / Author of the conference Hollanti, Camilla.
- [Multi angle] Projective Reed Muller codes revisited / Author of the conference Ghorpade, Sudhir.
Bibliography
- 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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