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Designs, Codes and Cryptography

Erschienen in:

01.06.2018

Two notions of differential equivalence on Sboxes

verfasst von: Christina Boura, Anne Canteaut, Jérémy Jean, Valentin Suder

Erschienen in: Designs, Codes and Cryptography | Ausgabe 2-3/2019

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Abstract

In this work, we discuss two notions of differential equivalence on Sboxes. First, we introduce the notion of DDT-equivalence which applies to vectorial Boolean functions that share the same difference distribution table (DDT). Next, we compare this notion to what we call the \(\gamma \)-equivalence, applying to vectorial Boolean functions whose DDTs have the same support. We discuss the relation between these two equivalence notions, demonstrate that the number of DDT- or \(\gamma \)-equivalent functions is invariant under EA- and CCZ-equivalence and provide an algorithm for computing the DDT-equivalence and the \(\gamma \)-equivalence classes of a given function. We study the sizes of these classes for some families of Sboxes. Finally, we prove a result that shows that the rows of the DDT of an APN permutation are pairwise distinct.

Vorheriger Artikel Editorial: Special issue on coding and cryptography

Nächster Artikel On APN exponents, characterizations of differentially uniform functions by the Walsh transform, and related cyclic-difference-set-like structures

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Titel: Two notions of differential equivalence on Sboxes
verfasst von: Christina Boura
Anne Canteaut
Jérémy Jean
Valentin Suder
Publikationsdatum: 01.06.2018
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 2-3/2019
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-018-0496-z

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Two notions of differential equivalence on Sboxes

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