Characterization of APN-permutations in terms of Hamming distance between subgroups of symmetric group
Aleksandr Belov · PRIKLADNAYa DISKRETNAYa MATEMATIKA · 2023
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.