Paper 2018/617
Two Notions of Differential Equivalence on Sboxes
Christina Boura, Anne Canteaut, 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
-
CC BY
BibTeX
@misc{cryptoeprint:2018/617,
author = {Christina Boura and Anne Canteaut and Jérémy Jean and Valentin Suder},
title = {Two Notions of Differential Equivalence on Sboxes},
howpublished = {Cryptology {ePrint} Archive, Paper 2018/617},
year = {2018},
doi = {10.1007/s10623-018-0496-z},
url = {https://eprint.iacr.org/2018/617}
}
