Cryptology ePrint Archive: Report 2018/617

Two Notions of Differential Equivalence on Sboxes

Christina Boura and Anne Canteaut and Jérémy Jean and Valentin Suder

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.

Category / Keywords: secret-key cryptography / Boolean function, Sbox, APN, difference distribution table, equivalence

Original Publication (in the same form): Designs, Codes and Cryptography

Date: received 19 Jun 2018

Contact author: xristina mpoura at gmail com

Available format(s): PDF | BibTeX Citation

Version: 20180622:145506 (All versions of this report)

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