Rotation symmetry in algebraically generated cryptographic substitution tables

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...

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Bibliographic Details
Published inInformation processing letters Vol. 106; no. 6; pp. 246 - 250
Main Authors Rijmen, Vincent, Barreto, Paulo S.L.M., Gazzoni Filho, Décio L.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 15.06.2008
Elsevier Science
Elsevier Sequoia S.A
Subjects
Algebra
Algebraic group theory
Algorithmics. Computability. Computer arithmetics
Applied sciences
Computer science; control theory; systems
Cryptography
Exact sciences and technology
Finite field
Mathematics
Miscellaneous
Number theory
S-box
Sciences and techniques of general use
Studies
Theoretical computing
Cryptography
Finite field
S-box
Computer theory
Substitution
Information processing
Box
Rotation
Algorithm analysis
Power
Symmetry
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Summary: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.
ISSN:0020-0190
1872-6119
DOI:10.1016/j.ipl.2007.09.012