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Regular subgroups with large intersection

  • Riccardo AragonaEmail author
  • Roberto Civino
  • Norberto Gavioli
  • Carlo Maria Scoppola
Article
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Abstract

In this paper, we study the relationships between the elementary abelian regular subgroups and the Sylow 2-subgroups of their normalisers in the symmetric group \({{\,\mathrm{Sym}\,}}({{\,\mathrm{\mathbb {F}}\,}}_2^n)\), in view of the interest that they have recently raised for their applications in symmetric cryptography.

Keywords

Elementary abelian regular subgroups Sylow 2-subgroups Affine groups Block ciphers Cryptanalysis 

Mathematics Subject Classification

20B35 20D20 94A60 

Notes

Acknowledgements

Funding was provided by Ministero dell’Istruzione, dell’Università e della Ricerca (IT) (Grant No. PRIN 2015TW9LSR).

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Dipartimento di Ingegneria e Scienze dell’Informazione e MatematicaUniversità degli Studi dell’AquilaL’AquilaItaly

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