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Paper 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.

Metadata
Available format(s)
PDF
Category
Secret-key cryptography
Publication info
Published elsewhere. Designs, Codes and Cryptography
DOI
10.1007/s10623-018-0496-z
Keywords
Boolean functionSboxAPNdifference distribution tableequivalence
Contact author(s)
xristina mpoura @ gmail com
History
2018-06-22: received
Short URL
https://ia.cr/2018/617
License
Creative Commons Attribution
CC BY
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