Decomposition of permutations in a finite field

  • Svetla NikovaEmail author
  • Ventzislav Nikov
  • Vincent Rijmen
Part of the following topical collections:
  1. Special Issue: Mathematical Methods for Cryptography


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(2n) 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.


Boolean functions S-Box Power permutations Threshold implementation 

Mathematics Subject Classification (2010)

94A60 94C10 



This work was supported in part by the Research Council KU Leuven: C16/15/058 and OT/13/071, and by the NIST Research Grant 60NANB15D346.


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Authors and Affiliations

  • Svetla Nikova
    • 1
    Email author
  • Ventzislav Nikov
    • 2
  • Vincent Rijmen
    • 1
  1. 1.KU Leuven, imec-COSICLeuvenBelgium
  2. 2.NXP SemiconductorsLeuvenBelgium

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