Author:

Keywords:

Science & Technology, Technology, Physical Sciences, Computer Science, Theory & Methods, Mathematics, Applied, Computer Science, Mathematics, Boolean functions, S-Box, Power permutations, Threshold implementation, 0101 Pure Mathematics, 0102 Applied Mathematics, 0103 Numerical and Computational Mathematics, 4901 Applied mathematics, 4904 Pure mathematics

Abstract:

© 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.