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Decomposition of permutations in a finite field

Journal Contribution - Journal Article

© 2018, Springer Science+Business Media, LLC, part of Springer Nature. We describe a method to decompose any power permutation, as a sequence of power permutations of lower algebraic degree. As a result we obtain decompositions of the inversion in GF(2 n ) for small n from 3 up to 16, as well as for the APN functions, when n = 5. More precisely, we find decompositions into quadratic power permutations for any n not multiple of 4 and decompositions into cubic power permutations for n multiple of 4. Finally, we use the Theorem of Carlitz to prove that for 3 ≤ n ≤ 16 any n-bit permutation can be decomposed in quadratic and cubic permutations.
Journal: Cryptography and Communications-Discrete-Structures Boolean Functions and Sequences
ISSN: 1936-2447
Issue: 3
Volume: 11
Pages: 379 - 384
Publication year:2019
BOF-keylabel:yes
IOF-keylabel:yes
BOF-publication weight:1
CSS-citation score:1
Authors from:Private, Higher Education
Accessibility:Open