Rotation symmetry in algebraically generated cryptographic substitution tables

Authors:
Vincent Rijmen;Paulo S. L. M. Barreto;Décio L. Gazzoni Filho
Affiliations:
IAIK, Graz University of Technology, Inffeldgasse 16a, A-8010 Graz, Austria;Dep. Eng. Computação e Sist. Digitais (PCS), EP-USP, Av. Prof. Luciano Gualberto, 158 trav. 3, São Paulo, Brazil;Dep. Eng. Computação e Sist. Digitais (PCS), EP-USP, Av. Prof. Luciano Gualberto, 158 trav. 3, São Paulo, Brazil
Venue:
Information Processing Letters
Year:
2008

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Abstract

Using some elementary properties of normal bases, we are able to show that bijective substitution tables generated from power maps or exponentiations over finite fields are linear equivalent to rotation-symmetric S-boxes. In the other direction, we show that rotation-symmetric S-boxes can always be described as a sum of power maps over finite fields.