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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, demonstrate that the number of DDT- or $γ$--equivalent functions is invariant under EA- and CCZ-equivalence and provide an algorithm for computing the DDT-equivalence and the $γ$-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.
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https://hal.inria.fr/hal-01944565
Contributor : Anne Canteaut <>
Submitted on : Tuesday, December 4, 2018 - 5:14:04 PM
Last modification on : Monday, February 10, 2020 - 6:13:49 PM

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Christina Boura, Anne Canteaut, Jérémy Jean, Valentin Suder. Two Notions of Differential Equivalence on Sboxes. Designs, Codes and Cryptography, Springer Verlag, In press, 87 (2-3), pp.185-202. ⟨10.1007/s10623-018-0496-z⟩. ⟨hal-01944565⟩

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