Paper 2018/617 Original: eprint.iacr.org/2018/617 ↗
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 $\gamma$-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
- Preprint.
- History
- 2018-06-22: last updated
- 2018-06-22: published
- Short URL
- https://ia.cr/2018/617
- License
- https://creativecommons.org/licenses/by/4.0/
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},
url = {https://eprint.iacr.org/2018/617}
}