Two Notions of Differential Equivalence on Sboxes

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 γ-equivalence, applying to vectorial Boolean functions whose DDTs have the same support. We discuss the relation between these two equivalence notions and provide an algorithm for computing the DDT-equivalence and the γ-equivalence classes for 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.
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Christina Boura, Anne Canteaut, Jérémy Jean, Valentin Suder. Two Notions of Differential Equivalence on Sboxes. WCC 2017 - Workshop on Coding and Cryptography, Sep 2017, Saint Petersburg, Russia. ⟨hal-01650010⟩

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