Decomposition of permutations in a finite field

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...

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Bibliographic Details
Published inCryptography and communications Vol. 11; no. 3; pp. 379 - 384
Main Authors Nikova, Svetla, Nikov, Ventzislav, Rijmen, Vincent
Format Journal Article
LanguageEnglish
Published New York Springer US 15.05.2019
Springer Nature B.V
Subjects
Circuits
Coding and Information Theory
Communications Engineering
Computer Science
Data Structures and Information Theory
Decomposition
Fields (mathematics)
Information and Communication
Mathematics of Computing
Networks
Permutations
Special Issue: Mathematical Methods for Cryptography
Boolean functions
Power permutations
94A60
94C10
Threshold implementation
S-Box
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Summary: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.
ISSN:1936-2447
1936-2455
DOI:10.1007/s12095-018-0317-2