HomeIssuesCharacterization of APN-permutations in terms of Hamming distance between subgroups of symmetric group

Characterization of APN-permutations in terms of Hamming distance between subgroups of symmetric group | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2023. № 60. DOI: 10.17223/20710410/60/1

We study bijective APN mappings defined on a finite field of even characteristic. The property of a bijective mapping to be an APN mapping is expressed in terms of the Hamming distance between subgroups of the symmetric group. A new approach to the construction of bijective APN-mappings is proposed: the problem of constructing an APN-permutation is reduced to finding a subgroup of a symmetric group that is far (in the sense of the Hamming distance) from the shift group of a finite field F2n, and solving a system of conjugation equations.
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  • Title Characterization of APN-permutations in terms of Hamming distance between subgroups of symmetric group
  • Headline Characterization of APN-permutations in terms of Hamming distance between subgroups of symmetric group
  • Publesher Tomask State UniversityTomsk State University
  • Issue Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics 60
  • Date:
  • DOI 10.17223/20710410/60/1
Keywords
APN mapping, permutation, symmetric group, Hamming distance, simultaneous conjugacy
Authors
References
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Characterization of APN-permutations in terms of Hamming distance between subgroups of symmetric group | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2023. № 60. DOI: 10.17223/20710410/60/1
Characterization of APN-permutations in terms of Hamming distance between subgroups of symmetric group | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2023. № 60. DOI: 10.17223/20710410/60/1
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